Case 1 x y 1.0 29.750 1.5 19.125 2.0 14.375 3.0 9.500 4.0 7.125 5.0 5.625 6.0 4.875 7.0 4.250 8.0 3.750 9.0 3.375 10.0 3.000 12.0 2.625 14.0 2.250 16.0 2.000 18.0 1.875 20.0 1.750 24.0 1.500 28.0 1.375 32.0 1.250 Source: William Francis Magie, {\em A Source Book in Physics}, Harvard University Press, 1965, p. 87. Description: Pressure of a quantity of enclosed air vs. volume of the air, as published by Boyle in 1662 in partial support of his law $PV=k$. Reference Relation: $y=k/x$ Comments: The reference relation leaves clearly patterned residuals. It is possible to get a better fit of the form $y=k_{1}/x^{2}+k_{2}/x+k_{3}$ or one the form $y+k_{1}=k_{2}/(x+k_{3})$. The former is closer to what scientists now use (see Case 45); the latter is a simple inverse relationship, assuming that Boyle had the origin of his measurement scales slightly off. Note that Boyle's original article (as reproduced by Magie) includes two data sets, of which this is the second. The first fits the reference relation very nicely. --------------------------------------------- Case 2 x y 36.00 88.0 67.25 224.7 93.00 365.3 141.75 687.0 483.80 4332.1 Source: Herbert Simon and Yulin Qin, Laboratory Replication of Scientific Discovery Processes,'' Psychology Department, Carnegie Mellon University, p. 3. Description: Data for five planets---period of revolution vs. distance to the sun---similar to that used by Kepler to discover his third law. See Case 21 for a second data set supporting this law. Reference Relation: $y=kx^{1.5}$ --------------------------------------------- Case 4 x y 0.0288 13.300 0.0293 12.950 0.0298 12.430 0.0314 11.160 0.0514 7.350 0.0557 6.750 0.0927 4.030 0.0912 4.030 0.0949 3.957 0.1035 3.690 0.1100 3.392 0.1498 2.460 0.1880 2.011 Source: William Francis Magie, {\em A Source Book in Physics}, Harvard University Press, 1965, p. 179. Description: Dulong and Petit's data: relative atomic weights vs. specific heat in various materials. Reference Relation: $y=k/x$ --------------------------------------------- Case 5 x y 326.75 2 300.75 4 277.75 6 238.25 10 190.75 18 134.50 34 83.25 66 48.50 130 Source: William Francis Magie, {\em A Source Book in Physics}, Harvard University Press, 1965, p. 469. Description: Ohm's 1826 data in support of Ohm's law: length of a strip of copper vs. current flowing through it. Reference Relation: $y=k_{1}/x+k_{2}$ Comments: The reference relation leaves two strong outliers. --------------------------------------------- Case 6 x y -21 12.9 0 14.0 100 18.6 182 22.2 302 26.8 Source: Francis W. Sears and Gerhard L. Salinger, {\em Thermodynamics, Kinetic Theory and Statistical Thermodynamics}, Addison-Wesley, 1975, p. 298. Description: Viscosity of carbon dioxide vs. Centigrade temperature. Reference Relation: $y=k_{1}(x+273.1)^{.5}+k_{2}$ Comments: Reference relation shows some lack of fit. --------------------------------------------- Case 7 x y 4.0 126 5.0 125 7.0 123 12.0 120 14.0 119 16.0 118 20.0 116 24.0 115 28.0 114 31.0 113 34.0 112 37.5 111 41.0 110 Source: Douglas M. Bates and Donald G. Watts, {\em Nonlinear Regression Analysis and its Applications}, Wiley, 1988, p. 268. Description: Data from a cooling experiment conducted by Count Rumford in 1798: temperature in Fahrenheit vs. time. Reference Relation: $y=k_{1}k_{2}^{x}+k_{3}$ Comments: The law is suggested by Bates and Watts based on work by Newton rather than what Rumford---who was not looking for a time dependency relationship---saw in his data. Reference relation shows strong lack of fit. --------------------------------------------- Case 8 x y 10.5 4570 22.0 2398 33.5 1365 42.6 908 51.0 631 60.7 437 71.0 302 79.0 228 91.8 149 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 78. Description: Resistance vs. Centigrade temperature; for a germanium semiconductor. Reference Relation: $y=k_{1}k_{2}^{(1/(x+273.1))}$ Comments: The source notes that the reference relation is the result of a simplified theory.'' --------------------------------------------- Case 9 x y 468 347.0 413 351.3 330 356.0 290 359.0 267 360.5 240 362.0 202 364.2 173 365.7 146 366.8 110 368.0 88 369.5 65 370.4 30 372.5 0 373.3 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 80. Description: Saturation vapor pressure of water vs. Kelvin temperature. Actually, $y$ is the height of a mercury column and pressure is $762-y$. Reference Relation: $y=k_{1}k_{2}^{1/x}+k_{3}$ --------------------------------------------- Case 10 x y 577.0 1.621 546.1 1.625 496.0 1.631 491.4 1.632 434.9 1.642 407.8 1.650 404.7 1.652 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 82. Description: Refractive index vs. wavelength. Reference Relation: $y=k_{1}/x^{2}+k_{2}$ --------------------------------------------- Case 11 x y 256.0 467.5 288.0 369.7 320.0 299.5 341.3 263.1 384.0 208.0 426.6 168.5 480.0 133.0 512.0 117.0 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 84. Description: Volume of an enclosed quantity of air vs. frequency at which it resonates. Reference Relation: $y=k/x^{2}$ Comments: The fit here is so perfect that I question whether this is really measured data, as the source suggests. --------------------------------------------- Case 12 x y 1 1.16 2 1.61 3 1.97 4 2.27 5 2.53 6 2.74 7 2.96 8 3.17 9 3.37 10 3.55 11 3.69 12 3.86 13 4.04 14 4.18 15 4.30 16 4.45 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 88. Description: Diameter of Newton's rings vs. ordinals. Reference Relation: $y^{2}=k_{1}x+k_{2}$ Comments: The relation $y=k_{1}x^{.5}+k_{2}$ seems to fit just as well. --------------------------------------------- Case 13 x y 1.0 217 6.2 167 12.3 123 19.3 105 27.2 77 37.2 52 49.2 36 63.3 20 79.3 11 97.3 5 115.2 3 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 94. Description: Temperature of a metal bar in nonstandard units vs. distance from a heat source. Reference Relation: $y=k_{1}k_{2}^{x}$ --------------------------------------------- Case 14 x y 0 22.9 36 20.8 72 18.3 107 13.7 143 11.6 179 10.6 215 8.0 250 6.8 286 5.5 322 5.1 357 4.2 Source: D. J. Hustings, {\em Comprehension and Data Analysis Questions in Advanced Physics}, John Murray Press, 1975, p. 97. Description: Count of gamma radiation in particles per second vs. thickness of an absorbing lead shield. Reference Relation: $y=k_{1}k_{2}^{x}$ --------------------------------------------- Case 15 x y 0.02 76 0.02 47 0.06 97 0.06 107 0.11 123 0.11 139 0.22 159 0.22 152 0.56 191 0.56 201 1.10 207 1.10 200 Source: Douglas M. Bates and Donald G. Watts, {\em Nonlinear Regression Analysis and its Applications}, Wiley, 1988, p. 269. Description: Velocity of an enzymatic reaction vs. substrate concentration. Reference Relation: $y=k_{1}x/(k_{2}+x)$ Comments: The reference relation is the Michaelis-Menten equation. --------------------------------------------- Case 16 x y 0.02499 0.3841 0.02500 0.3843 0.02500 0.3845 0.04770 0.3827 0.04974 0.3823 0.04999 0.3822 0.07490 0.3811 0.07500 0.3809 0.09979 0.3798 Source: {\em Journal of Chemical and Engineering Data}, Vol. 31, No. 2, 1986, Transference Number Measurements in Aqueous Solutions at 25$^{\circ}$ C. 2. Sodium Bromide,'' Miguel A. Esteso, Domingo M. Grandoso and M. Mercedes Lemus, pp. 215--218. Description: Best transference number vs. concentration. Reference Relation: $y=k_{1}+k_{2}x^{.5}$ --------------------------------------------- Case 17 x y 27.0 26.76 30.0 26.79 40.0 27.28 40.0 27.86 50.0 26.89 50.5 27.78 59.6 28.11 70.0 28.08 72.0 28.17 Source: {\em Journal of Chemical and Engineering Data}, Vol. 31, No. 3, 1986, Solubility and Metastable Zone Width of Sodium Chloride in Water-Diethylene Glycol Mixtures,'' Angelo Chianese, Sergio Di Cave and Barbara Mazzarotta, pp. 329--332. Description: Solubility vs. temperature. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 18 x y 100 20.0 100 18.5 90 16.1 90 15.1 80 10.1 80 11.5 50 8.9 50 7.4 40 7.2 20 6.0 0 3.5 Source: {\em Journal of Chemical and Engineering Data}, Vol. 31, No. 3, 1986, Solubility and Metastable Zone Width of Sodium Chloride in Water-Diethylene Glycol Mixtures,'' Angelo Chianese, Sergio Di Cave, and Barbara Mazzarotta, pp. 329--332. Description: Range of Centigrade degrees vs. a percentage. See source for details. Reference Relation: $y=k_{1}k_{2}^{x}$ Comments: Possible lack of fit or outlier. --------------------------------------------- Case 19 x y 73.8 100.2 85.6 116.3 94.4 128.6 95.3 131.1 94.9 131.1 62.3 90.0 56.7 81.9 99.3 142.3 118.6 163.7 136.7 189.2 150.1 205.4 158.4 219.0 115.0 167.8 117.7 161.4 121.7 162.6 112.0 156.9 113.5 155.4 111.1 151.7 Source: {\em Journal of Chemical and Engineering Data}, Vol. 32, No. 2, 1987, Thermochemistry of Inorganic Solids. 5. Empirical Relations among Enthalpies of Formation of Oxides, Carbonates, Sulfates, Hydroxides, and Nitrates,'' Mohamed W. M. Hisham and Sydney W. Benson, pp. 243--247. Description: See source for details. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The intercept $k_{2}$ is not significant. --------------------------------------------- Case 20 x y 273.0 0.96 279.5 1.15 283.0 1.46 288.0 1.60 288.0 1.39 289.0 1.57 291.0 1.71 291.5 1.65 292.5 1.68 293.0 1.64 293.0 1.60 293.0 1.77 298.0 1.98 298.0 1.87 298.0 1.95 298.0 2.05 298.0 1.85 298.0 2.00 298.0 1.94 298.0 1.87 298.0 1.90 298.0 1.74 303.0 2.29 303.0 2.15 307.7 2.41 308.0 2.18 313.0 2.80 318.2 3.03 325.0 3.61 327.9 3.68 338.0 4.40 338.0 4.30 348.1 5.40 Source: {\em Journal of Chemical and Engineering Data}, Vol. 33, No. 1, 1988, Solubility and Diffusivity of Acid Gases (CO$_{2}$, N$_{2}$O) in Aqueous Alkanolamine Solutions,'' Geert F. Versteeg and Wim P. M. van Swaaij, pp. 29--34. Description: Diffusivity vs. absolute temperature. Reference Relation: $y=k_{1}k_{2}^{1/x}$ Comments: For this data, $\log x$ and $\log y$ are just about as well linearly related as $\log y$ and $1/x$. --------------------------------------------- Case 21 x y 5.67 1.769 8.67 3.571 14.00 7.155 24.67 16.689 Source: Pat Langley, Herbert Simon, Gary Bradshaw and Jan \.{Z}ytkow, {\em Scientific Discovery: Computational Explorations of the Creative Process}, MIT Press, 1987, p. 85. Description: Borelli's data: period of orbit vs. radius of orbit for Jupiter's satellites. Reference Relation: $y=kx^{1.5}$ Comments: This is an example of data supporting Kepler's third law. See also Case 2. --------------------------------------------- Case 22 x y 8 0.49 8 0.49 10 0.47 10 0.47 10 0.48 10 0.48 12 0.46 12 0.46 12 0.45 12 0.43 14 0.45 14 0.43 14 0.43 16 0.44 16 0.43 16 0.43 18 0.46 18 0.45 20 0.42 20 0.42 20 0.43 22 0.41 22 0.41 22 0.40 24 0.42 24 0.40 24 0.40 26 0.41 26 0.40 26 0.41 28 0.41 28 0.40 30 0.40 30 0.40 30 0.38 32 0.41 32 0.40 34 0.40 36 0.41 36 0.38 38 0.40 38 0.40 40 0.39 42 0.39 Source: N. R. Draper and H. Smith, {\em Applied Regression Analysis}, Wiley, 1981, p. 476. Description: Amount of chlorine in a Proctor and Gamble product vs. number of weeks since manufacture. Reference Relation: $y=k_{1}k_{2}^{x}+k_{3}$ Comments: A residual plot shows clear lack of fit. The relation $y=k_{1}\log x +k_{2}$ fits much better. --------------------------------------------- Case 23 x y 40 490.2 80 585.3 160 673.7 320 759.2 640 837.5 Source: N. R. Draper and H. Smith, {\em Applied Regression Analysis}, Wiley, 1981, p. 519. Description: Wind speed vs. nominal anemometer heights. Reference Relation: $y=k_{1}\log (x+k_{2})+k_{3}$ --------------------------------------------- Case 24 x y 305.15 0.8635 313.15 0.7502 321.15 0.7214 323.15 0.7770 328.15 0.7057 372.70 0.4610 397.70 0.4456 422.60 0.3421 Source: {\em Journal of Chemical and Engineering Data}, Vol. 32, No. 3, 1987, Vapor-Liquid Equilibrium Measurements for the Ethanal-Acetone System at 372.7, 397.7, and 422.6 K,'' Scott W. Campbell, Richard A. Wilsak and George Thodos, pp. 357--362. Description: $\beta$ coefficient of a four-suffix Margules equation vs. absolute temperature. Reference Relation: $y=k_{1}/x+k_{2}$ Comments: The authors express some reservation about the reference relation. The relation $y=kx^{-2.71}$ fits better. --------------------------------------------- Case 25 x y 36.0 36 18.0 144 8.5 576 Source: Duane Roller and Duane H. D. Roller, {\em The Development of the Concept of Electric Charge: Electricity from the Greeks to Coulomb}, Harvard University Press, 1954, pp. 76--77. Description: Force vs. separation, both in degrees (see comments). Reference Relation: $y=k/x^{2}$ Comments: These are Coulomb's original measurements in support of his inverse square law relating the separation of two charged spheres and the force between them. Both separation and force were measured in degrees on his new torsion balance. --------------------------------------------- Case 27 x y 1.008 0.200 12.000 0.850 16.000 1.050 27.100 1.495 32.070 1.760 55.840 2.290 107.880 3.280 195.200 4.140 197.200 4.220 207.200 4.270 Source: George Hevesy and Fritz Paneth, {\em A Manual of Radioactivity}, Oxford University Press, 1926, p. 24 and p. 145. Description: Stopping power of various elements for $\alpha$ radiation vs. atomic weight. Reference Relation: $y=kx^{.5}$ Comments: The reference relation leaves obvious lack of fit. The relation $\log (x+23.1)=k_{1}y+k_{2}$ fits better. --------------------------------------------- Case 28 x y 2.830 1.825e+12 3.194 3.650e+07 3.389 5.767e+05 3.925 1.360e+02 4.122 3.810e+00 4.722 2.118056e-03 Source: George Hevesy and Fritz Paneth, {\em A Manual of Radioactivity}, Oxford University Press, 1926, p. 22 for $x$, pp. 173ff for $y$ and pp. 105--106 for relation. Description: Half-life of various radioactive substances vs. range of $\alpha$ particles. Reference Relation: $\log y=k_{1}\log x +k_{2}$ Comments: One endpoint appears as an outlier in the residual plot. --------------------------------------------- Case 30a x y 0 166 5 116 10 466 15 850 20 1417 25 2149 30 3118 35 4250 40 5466 45 6800 50 8433 55 10500 60 12134 65 14250 70 17134 75 19901 80 21933 85 24250 90 27299 95 31834 100 34117 Source: Generated. Description: Amount of time $y$ for a Lisp program to calculate 1+2 $x^{2}$ times. The program is implemented as a nest of two loops iterating $x$ times each. Reference Relation: $y=kx^{2}$ Comments: Residual plot shows lack of fit which is even clearer in a plot of $x^{2}/y$ vs. $x$. This is also a good example of pronounced heteroscedasticity. --------------------------------------------- Case 30b x y 50 8701 52 9083 54 9850 56 10666 58 11283 60 12051 62 13033 64 13717 66 14884 68 15634 70 16900 72 17500 74 18450 76 19832 78 20316 80 21651 82 22583 84 24766 86 26466 88 28900 90 27766 92 29001 94 34048 96 31967 98 33617 100 34183 Source: Generated. Description: Amount of time $y$ for a Lisp program to calculate 1+2 $x^{2}$ times. The program is implemented as a nest of two loops iterating $x$ times each. Reference Relation: $y=kx^{2}$ Comments: The $x$ range was chosen here to make the relationship look more or less linear. Residuals from the reference relation show definite curvature along with serious heteroscedasticity. Removing points 19, 20 and 23 eliminates the lack of fit. Note though that the intercept in a regression of $y$ on $x^{2}$ is significant. The relation $y=k_{1}x^{2}+k_{2}$ may be more accurate. --------------------------------------------- Case 31 x y 0 16 5 50 10 101 15 67 20 101 25 133 30 167 35 183 40 200 45 233 50 217 55 232 60 266 65 300 70 317 75 317 80 317 85 400 90 367 95 367 100 450 Source: Generated. Description: Amount of time $y$ taken to compute $x$! using a recursive Lisp function. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 35 x y 10.75 4.00 10.25 2.94 9.75 2.06 9.25 1.88 8.75 1.50 8.25 1.06 7.75 0.81 7.25 0.63 Source: Columbia University student laboratory report, Physics 1007, Experiment 1, Summer 1989. Description: This experiment applies a potential to conducting paper in order to map the two-dimensional section corresponding to the plane of the paper of the resulting electric field'' Reference Relation: $y=k_{1}k_{2}^{x}$ Comments: I was unable to determine the definition of the variables from the written report. --------------------------------------------- Case 36 x y 0.5 9.0 1.0 8.1 2.0 6.7 3.0 5.7 5.0 4.0 7.0 2.8 10.0 1.2 Source: Columbia University student laboratory report, Physics 1007, Experiment 1, Summer 1989. Description: See Case 35. Reference Relation: $y=k_{1}k_{2}^{x}$ --------------------------------------------- Case 37a 25 4.3 20 6.7 15 10.0 10 14.4 5 22.2 Source: Columbia University student laboratory report, Physics 1004, Summer 1989. Description: Time in seconds vs. current in microamps measured while charging a capacitor of 20.6 microfarads. Reference Relation: $y=k_{1}\log x +k_{2}$ --------------------------------------------- Case 37b 25 4.2 20 6.6 15 9.8 10 14.3 5 22.3 Source: Columbia University student laboratory report, Physics 1004, Summer 1989. Description: Time in seconds vs. current in microamps measured while discharging a capacitor of 20.6 microfarads. Reference Relation: $y=k_{1}\log x +k_{2}$ --------------------------------------------- Case 38 x y 15 8.93 30 14.20 45 18.25 60 21.54 75 24.68 90 26.86 Source: Michael Kopcha, {\em Development and In-Vitro Characterization of Sustained-Release Acetaminophen Tablets}, Masters thesis in pharmaceutical sciences, Rutgers University, 1986, pp. 6, 30, 45, 63 and 64. Description: Average percent acetaminophen released in artificial gastric fluid at 37$^{\circ}$ Centrigrade from 5\% castor wax vs. time. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ Comments: The reference relation leaves one very bad endpoint outlier. If this is removed, a second endpoint outlier emerges, leaving only four points which themselves show lack of fit. --------------------------------------------- Case 39 x y 0.280 8.6 0.260 13.4 0.235 19.3 0.140 42.3 0.080 61.1 Source: Kenneth Joseph Martchek, {\em A Continuous Enzymatic Process for the Disruption of Viable Yeast Cells}, Masters thesis in chemical and biochemical engineering, Rutgers University, 1975, pp. 61--63. Description: Residence time vs. cell density for a kinetic model. Reference Relation: $y=k_{1}\log x +k_{2}$ Comments: The reference relation shows very strong lack of fit. The relation $y=k_{1}x^{.62}+k_{2}$ fits much better. --------------------------------------------- Case 40 x y 0.238 127.7 0.317 108.1 0.635 86.3 0.794 85.5 0.952 78.1 1.111 79.4 1.270 77.0 1.587 75.1 1.905 70.7 2.540 62.4 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, p. 306. Description: Maximum voltage gradient at the surface of an electrode in kilovolts/cm vs. radius of the inner of a pair of concentric cylinders in cm (outer is 3.81 cm) in a sparkover measurement experiment. Reference Relation: $y=36+43.2/x^{.5}$ Comments: The relation $y=k_{1}\log (x+k_{2}) +k_{3}$ fits much better. --------------------------------------------- Case 41a x y 0.433 0.4936908 0.459 0.7494510 0.624 0.8937235 0.683 0.9359681 0.720 1.2425988 0.628 1.0951607 0.571 0.3960747 0.778 0.9280616 0.735 0.5461082 0.724 0.7091810 0.632 0.9998828 0.644 0.7111177 0.658 1.0268253 0.633 1.1104652 0.680 1.2465279 0.696 1.0691945 0.674 1.0348193 0.588 0.6633147 0.675 1.1581480 0.610 1.0307151 0.888 0.8383056 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, pp. 8--9. Description: Height in meters of drop causing complete failure vs. air dry density in gm/cm$^{3}$ for woods of the fagaceae family (mostly oaks). Reference Relation: $y=2.4x^{1.75}$ Comments: This is only part of the data given in the source. Also, the source tabulates the difference between $y$ and the reference relationship; I converted back to the presumed original data. --------------------------------------------- Case 41b x y 0.433 0.5503492 0.459 0.4918304 0.624 0.8799896 0.683 0.9262730 0.720 1.0274475 0.628 0.8927326 0.571 1.0440644 0.778 1.6122818 0.735 1.4675963 0.724 1.5132149 0.632 0.9404074 0.644 1.0658436 0.658 0.7373163 0.633 0.8855020 0.680 1.1087858 0.696 1.0096862 0.674 0.9661284 0.588 0.7599890 0.675 1.2520856 0.610 0.8147480 0.888 2.4704836 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, pp. 8--9. Description: Compression perpendicular to grain in kg/mm$^{2}$ vs. air dry density in g/cm$^{3}$ for woods of the fagaceae family (mostly oaks). Reference Relation: $y=3.26x^{2.25}$ Comments: This is only part of the data given in the source. Also, the source tabulates the difference between $y$ and the reference relationship; I converted back to the presumed original data. --------------------------------------------- Case 41c x y 0.433 0.7719658 0.459 0.8135618 0.624 1.3050873 0.683 1.3508432 0.720 1.2515192 0.628 1.2410879 0.571 1.0137618 0.778 1.5409945 0.735 1.0877890 0.724 1.2898685 0.632 1.2384672 0.644 1.1398569 0.658 0.9209443 0.633 1.3537279 0.680 1.4393898 0.696 0.9173348 0.674 1.5455487 0.588 0.7544293 0.675 1.2631812 0.610 1.3164609 0.888 1.7988586 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, pp. 8--9. Description: Radial shear in kg/mm$^{2}$ vs. air dry density in gm/cm$^{3}$ for woods of the fagaceae family (mostly oaks). Reference Relation: $y=2.22x^{1.25}$ Comments: This is only part of the data given in the source. Also, the source tabulates the difference between $y$ and the reference relationship; I converted back to the presumed original data. --------------------------------------------- Case 41d x y 0.433 0.3021010 0.624 0.6478049 0.683 0.3422163 0.720 0.4482086 0.628 0.4753116 0.571 0.4570117 0.778 0.8404974 0.724 0.2884016 0.632 0.4761534 0.644 0.3151164 0.633 0.5668948 0.680 0.5148824 0.674 0.4106201 0.588 0.3034595 0.675 0.3819960 0.610 0.5020745 0.888 0.5991357 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, pp. 8--9. Description: Radial tension perpendicular to grain in kg/mm$^{2}$ vs. air dry density in gm/cm$^{3}$ for woods of the fagaceae family (mostly oaks). Reference Relation: $y=1.31x^{2}$ Comments: This is only part of the data given in the source. Also, the source tabulates the difference between $y$ and the reference relationship; I converted back to the presumed original data. --------------------------------------------- Case 42 x y 0.72 6.673389 0.70 5.595745 0.67 5.184289 0.59 4.504256 0.51 5.312361 0.72 5.039090 0.66 6.502494 0.54 5.062712 0.64 4.256669 0.50 3.165322 0.50 4.176466 0.77 6.273778 0.63 7.367731 0.70 5.529913 0.68 7.502639 0.86 10.113483 0.70 7.044056 0.71 7.365870 0.72 9.056742 0.70 5.859075 0.75 8.867814 0.60 4.814881 0.60 5.416741 0.75 5.363597 0.60 4.431879 0.77 6.642824 0.66 6.625183 0.62 5.861768 0.69 6.858769 0.85 7.645606 1.16 8.931053 0.73 5.192423 0.80 8.345514 0.75 6.364802 0.82 8.118918 0.85 7.978024 0.84 5.735279 0.83 10.176200 0.44 3.921913 0.96 11.059734 0.60 6.182745 0.48 4.604723 0.54 4.821630 0.40 4.238029 0.71 5.156109 0.55 3.499572 0.55 3.450282 0.69 4.788197 0.96 6.443497 0.55 4.238918 0.74 6.685333 0.75 7.652065 0.51 4.411961 0.60 4.705452 0.58 3.204533 0.67 6.246132 0.67 5.996286 0.71 9.977406 0.70 7.241553 0.62 5.235754 0.66 8.404167 0.48 4.395418 0.41 3.326084 0.40 3.363515 0.37 2.971223 0.48 4.981473 0.46 4.972111 0.43 3.448350 0.35 2.922828 0.40 4.338934 0.36 3.882895 0.67 4.996905 0.58 5.095733 0.69 4.788197 0.42 3.673311 0.47 5.755167 0.43 3.888565 0.52 6.220985 0.51 3.151401 0.53 4.714682 0.50 4.528169 0.50 4.176466 0.47 4.285763 0.37 2.909960 0.50 4.791946 0.53 5.657619 0.60 4.596023 0.90 8.455436 0.67 5.683980 0.75 7.222978 0.48 4.353557 0.38 2.783200 0.48 4.646584 0.31 2.947830 0.58 5.043200 0.60 6.237459 0.55 4.781106 0.58 6.724267 0.56 5.389280 0.51 3.871721 0.45 2.905612 0.64 5.616438 0.68 5.913097 0.60 4.213021 0.62 4.609740 0.60 3.556446 0.57 5.402074 0.61 4.855528 0.70 9.348186 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, p. 37. Description: Modulus of rupture for static bending in kg/mm$^{2}$ vs. air dry density in gm/cm$^{3}$ for all tabulated woods of Japan and East Asia. Reference Relation: $y=10.1x^{1.2}$ Comments: The source tabulates the difference between $y$ and the reference relationship; I converted back to the presumed original data. --------------------------------------------- Case 43a x y 0.05 1.4 0.10 2.8 0.20 5.6 0.50 11.7 1.00 20.1 2.00 33.5 5.00 61.0 10.00 88.0 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, p. 315. Description: Thermal conductivity in hectoergs per cm$^{2}$ per sec per (degrees Centigrade per cm) vs. air pressure in mm of mercury for quartz powder of average grain diameter .26 mm. Reference Relation: $y=k_{1}\log (x+k_{2}) +k_{3}$ --------------------------------------------- Case 43b x y 0.05 0.6 0.10 1.1 0.20 2.1 0.50 4.8 1.00 8.8 2.00 15.1 5.00 29.7 10.00 48.1 20.00 71.0 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, p. 315. Description: Thermal conductivity in hectoergs per cm$^{2}$ per sec per (degrees Centigrade per cm) vs. air pressure in mm of mercury for quartz powder of average grain diameter .09 mm. Reference Relation: $y=k_{1}\log (x+k_{2}) +k_{3}$ Comments: The reference relation leaves clear lack of fit in the first five points; residuals for the other four look fine. --------------------------------------------- Case 43c x y 0.2 2.0 0.5 5.0 1.0 8.8 2.0 15.1 5.0 28.5 10.0 43.9 20.0 66.0 50.0 88.0 100.0 105.0 200.0 113.0 400.0 121.0 700.0 128.0 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. II, p. 315. Description: Thermal conductivity in hectoergs per cm$^{2}$ per sec per (degrees Centigrade per cm) vs. air pressure in mm of mercury for emery powder of average grain diameter .11 mm. Reference Relation: $y=k_{1}\log (x+k_{2}) +k_{3}$ Comments: The reference relation leaves clear cubic lack of fit. --------------------------------------------- Case 44 x y 0.0166 0.0799 0.0358 0.1350 0.0764 0.2260 0.1200 0.2880 0.1600 0.3790 0.3420 0.5540 0.5280 0.6880 0.7120 0.8430 Source: {\em Transactions of the Faraday Society}, Vol. XLI, 1945, The Dyeing of Cellulose with Direct Dyes. Part II. The Absorption of Chyrsophenine by Cellulose Sheet,'' Hector F. Willis, John O. Warwicker, H. Alan Standing and Alexander R. Urquhart, pp. 512--514. Description: Absorption of chyrsophenine by cellulose at 97.5$^{\circ}$ Centigrade in the presence of sodium sulphate at 4 gm/l; $x$ is concentration in gm/l; $y$ is dye absorbed in gm/100gm. Reference Relation: $y=k_{1}x^{k_{2}}$ Comments: The reference relation leaves clear lack of fit. --------------------------------------------- Case 45 x y .010389000 100 .007036667 150 .005427500 200 .004504000 250 .003913333 300 .003500000 350 .003208750 400 .002991111 450 .002822000 500 .002680000 550 .002562500 600 .002463846 650 .002381429 700 .002312000 750 .002250000 800 .002194706 850 .002144444 900 .002101053 950 .002060000 1000 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. III, p. 9. Description: Pressure in atmospheres for an enclosed mass of air vs. volume of the air at a constant temperature of 15.7$^{\circ}$ Centigrade. Volume would be 1 at 0$^{\circ}$ and 1 atmosphere. Compare with Case 1. Reference Relation: $xy=k_{1}y^{2}+k_{2}y+k_{3}$ Comments: The source gives pressure and the product of pressure and volume. I converted back to the presumed original data. --------------------------------------------- Case 46a x y -95.0 0.0022 -90.0 0.0052 -85.0 0.0117 -80.0 0.0251 -75.0 0.0513 -70.0 0.1020 -65.0 0.1920 -60.0 0.3570 -55.0 0.6280 -50.0 1.0900 -45.0 1.8300 -40.0 2.9800 -35.0 4.7700 -30.0 7.4500 -25.0 11.4000 -20.0 17.1000 -15.0 25.2000 -10.0 36.6000 -7.3 44.4000 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. III, p. 201. Description: Vapor pressure of bromine in mm of mercury vs. temperature in Centrigrade. Reference Relation: $\log y =k_{1}/(x+273.1)+k_{2}$ --------------------------------------------- Case 46b x y -50.0 3.70e-05 -40.0 1.90e-04 -30.0 8.00e-04 -20.0 3.00e-03 -10.0 9.90e-03 0.0 2.99e-02 10.0 8.08e-02 20.0 2.02e-01 30.0 4.71e-01 40.0 1.03e+00 50.0 2.16e+00 60.0 4.31e+00 70.0 8.22e+00 80.0 1.51e+01 90.0 2.68e+01 100.0 4.55e+01 110.0 7.49e+01 114.5 9.01e+01 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. III, p. 201. Description: Vapor pressure of iodine in mm of mercury vs. Centigrade temperature. Reference Relation: $\log y =k_{1}/(x+273.1)+k_{2}$ --------------------------------------------- Case 47 x y 0.40 11.32 0.60 15.20 1.28 29.42 1.34 38.65 1.94 47.14 2.70 57.00 3.60 74.35 9.70 144.60 22.80 171.20 36.00 190.70 79.00 228.00 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. III, p. 250. Description: Adsorption of argon by wood charcoal at 145$^{\circ}$ Kelvin; $x$ is pressure in cm of mercury; $y$ is amount absorbed in cm$^{3}$ per 2.964 gm at temperature and pressure reduced to 0 degrees and 760 mm. Reference Relation: $y=k_{1}x^{k_{2}}$ Comments: A log-log plot shows clear lack of fit in the reference relation. --------------------------------------------- Case 48 x y 21.43 199.40 -22.80 178.80 -70.00 156.40 -102.60 139.20 -184.35 91.85 -198.00 81.54 -252.93 35.03 -258.10 29.46 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. V, p. 2. Description: Viscosity of helium in micropoises vs. Centigrade temperature. Reference Relation: $y=k_{1}(x+273.1)^{.647}$ --------------------------------------------- Case 49 x y 2440 0.0020 2522 0.0059 2800 0.3900 3136 30.0000 2738 0.1510 2825 0.5200 2825 0.5900 2875 1.0100 2875 1.1400 2925 1.7300 2925 2.3300 2930 1.8400 2930 2.4500 Source: {\em Physical Review}, Vol. II, 1913, The Vapor Pressure of Metallic Tungsten,'' Irving Langmuir, p. 329. Description: Rate of evaporation of heated tungsten in gm/cm$^{2}$/sec vs. absolute temperature. Reference Relation: $14\log x + \log y =k_{1}/x+k_{2}$ Comments: A regression of $\log y$ on $\log x$ and $1/x$ shows that the latter is highly insignificant. --------------------------------------------- Case 50 x y 0.01 1670 0.02 1355 0.03 1155 0.04 1000 0.05 893 0.06 820 0.07 770 0.08 735 0.09 695 0.10 663 0.11 629 0.12 610 0.13 591 0.14 571 0.15 552 0.16 538 0.17 523 0.18 511 0.19 500 0.20 485 Source: {\em Physical Review}, Vol. II, 1913, Thermal Conductivity of Air at Low Pressures,'' A. Trowbridge, p. 61. Description: Slope of a line relating temperature rise and the square of the current in a heating element vs. pressure in mm of mercury. Reference Relation: $1/y^{2}=k_{1}x+k_{2}$ Comments: The relation $1/y^{2.25}=k_{1}x+k_{2}$ fits much better. --------------------------------------------- Case 51 x y 0.01600 0.010636592 0.00920 0.009233867 0.00760 0.008961690 0.00740 0.008786412 0.00520 0.007962630 0.00486 0.007942748 0.00320 0.007056883 0.00250 0.006999271 Source: {\em Physical Review}, Vol. II, 1913, Thermal Conductivity of Air at Low Pressures,'' A. Trowbridge, p. 63. Description: Current in unspecified units required to raise temperature by a set amount vs. pressure in mm of mercury. Reference Relation: $y^{4}=k_{1}x+k_{2}$ Comments: The source tabulates $y^{4}$; I converted back to the presumed original data. --------------------------------------------- Case 52 x y 100.0 3.47 50.0 5.62 25.0 8.72 15.0 11.50 10.0 14.74 6.0 19.72 3.5 25.50 Source: {\em Physical Review}, Vol. XXXII, 1911, Measurements of the Rate of Decay of Gas Phosphorescence,'' C. C. Trowbridge, p. 136. Description: Time in seconds, $y$, for phosphorescent nitrogen to decay to various given intensities, $x$, after excitation. Reference Relation: $y=k_{1}/x^{.5}+k_{2}$ Comments: The source notes possible lack of fit in the reference relation. --------------------------------------------- Case 53 x y 0.323 4567.0 0.257 2200.0 0.192 902.0 0.144 364.0 0.106 173.0 0.080 63.3 Source: {\em Physical Review}, Vol. XXXII, 1911, Measurements of the Rate of Decay of Gas Phosphorescence,'' C. C. Trowbridge, p. 142. Description: Intensity vs. initial gas pressure in mm of mercury. Reference Relation: $y=kx^{3}$ Comments: The reference relation shows strong lack of fit. The relation $y=k_{1}x^{3.2}+k_{2}$ fits much better. --------------------------------------------- Case 54 x y 0 4.579 10 9.210 20 17.539 30 31.834 40 55.341 50 92.540 60 149.350 70 233.610 80 355.100 90 525.800 Source: {\em Physical Review}, Vol. XXXII, 1911, A New Formula for the Vapor Tension of Water between 0$^{\circ}$ and 200$^{\circ}$C,'' K. E. Guthe and A. G. Worthing, p. 227. Description: Pressure in mm of mercury vs. Centigrade temperature. Reference Relation: $\log y =k_{1}/(x+273.1)^{1.2808}+k_{2}$ Comments: The source calls this an empirical formula but also claims it is better and simpler than previous formulas. The data is {\em extremely} precise. --------------------------------------------- Case 55 x y 0.0000313 7.384e-10 0.0000358 6.864e-10 0.0000386 6.142e-10 0.0000755 5.605e-10 0.0000967 5.490e-10 0.0000979 5.496e-10 0.0001004 5.483e-10 0.0001006 5.482e-10 0.0001016 5.458e-10 0.0001084 5.448e-10 0.0001109 5.448e-10 0.0001281 5.349e-10 0.0001521 5.293e-10 0.0001730 5.257e-10 0.0001954 5.208e-10 0.0002205 5.143e-10 0.0002234 5.145e-10 0.0002481 5.143e-10 0.0002562 5.139e-10 0.0002815 5.102e-10 0.0002985 5.107e-10 0.0003166 5.065e-10 0.0003344 5.042e-10 0.0003329 5.096e-10 0.0003393 5.061e-10 0.0003712 5.027e-10 0.0003876 5.050e-10 0.0004297 4.989e-10 0.0004447 5.046e-10 0.0005315 4.980e-10 0.0006047 5.060e-10 0.0006104 5.033e-10 0.0006581 4.911e-10 Source: {\em Physical Review}, Vol. XXXII, 1911, The Isolation of an Ion, A Precision Measurement of its Charge, and the Correction of Stoke's Law,'' R. A. Millikan, p. 384. Description: $e_{1}$, apparently an amount of charge, vs. radius in cm, presumably of an oil drop. Reference Relation: $y^{2/3}=k_{1}/x+k_{2}$ Comments: Millikan comments that the first two points are not particularly reliable. The reference relation shows clear lack of fit which can be alleviated somewhat by using $1/x^{.7}$ in place of $1/x$. --------------------------------------------- Case 56a x y 1000 3.24e-15 1100 4.09e-13 1200 2.33e-11 1300 7.36e-10 1400 1.41e-08 1500 1.91e-07 1600 1.89e-06 1700 1.38e-05 1800 8.32e-05 1900 4.14e-04 2000 1.74e-03 2100 6.61e-03 2200 2.14e-02 2300 6.58e-02 2400 1.81e-01 2500 4.62e-01 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. VI, p. 55. Description: Emission of electrons from heated molybdenum in amps/cm$^{2}$ vs. absolute temperature. Reference Relation: $y=k_{1}x^{2}e^{-k_{2}/x}$ Comments: The reference relation is Richardson's equation. --------------------------------------------- Case 56b x y 1000 1.95e-13 1100 1.71e-11 1200 7.21e-10 1300 1.73e-08 1400 1.23e-07 1500 2.89e-06 1600 2.44e-05 1700 1.51e-04 1800 7.94e-04 1900 3.61e-03 2000 1.38e-02 2100 4.62e-02 2200 1.41e-01 2300 3.92e-01 2400 1.00e+00 2500 2.38e+00 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. VI, p. 55. Description: Emission of electrons from heated tantulum in amps/cm$^{2}$ vs. absolute temperature. Reference Relation: $y=k_{1}x^{2}e^{-k_{2}/x}$ Comments: The reference relation is Richardson's equation. --------------------------------------------- Case 56c x y 1000 1.07e-15 1100 1.52e-13 1200 9.73e-12 1300 3.21e-10 1400 6.62e-09 1500 9.14e-08 1600 9.27e-07 1700 7.08e-06 1800 4.47e-05 1900 2.28e-04 2000 1.00e-03 2100 3.93e-03 2200 1.33e-02 2300 4.07e-02 2400 1.16e-01 2500 2.98e-01 Source: National Research Council of the United States of America, {\em International Critical Tables of Numerical Data: Physics, Chemistry and Technology}, McGraw-Hill, 1926, Vol. VI, p. 55. Description: Emission of electrons from heated tungsten in amps/cm$^{2}$ vs. absolute temperature. Reference Relation: $y=k_{1}x^{2}e^{-k_{2}/x}$ Comments: The reference relation is Richardson's equation. --------------------------------------------- Case 58 x y .002293 0.1929 .002170 0.1995 .001846 0.2404 .001746 0.2970 .001461 0.4190 .001382 0.4370 .001369 0.4810 .001326 0.4740 .001308 0.5180 .001369 0.3790 .001077 0.6000 .000906 0.9340 .000898 0.9340 .000757 1.3650 .000719 1.5240 .000696 1.5660 .000679 1.7180 .000674 1.6530 .000653 1.7480 .000637 1.9160 .000608 2.1690 .000604 2.0880 .000585 2.2700 .000580 2.1890 .000560 2.2960 .000541 2.4500 .000541 2.7000 .000522 2.5600 .000505 2.8600 .000492 3.3600 .000466 3.4700 .000461 3.7500 .000453 3.6500 .000449 3.5900 .000433 4.1000 .000432 3.8600 .000427 4.1800 .000426 3.9600 .000417 4.1800 .000416 4.5600 .000407 4.5100 .000393 4.8600 .000385 4.9700 .000385 5.4000 .000382 4.5200 .000373 5.4500 .000368 5.4900 .000355 5.5200 .000350 5.8800 .000346 6.1000 .000346 6.6700 .000339 6.6300 .000335 6.7200 .000334 6.7900 .000704 1.4920 .000571 2.3350 .000562 2.2050 .000518 2.8540 .000502 2.9840 .000490 3.0810 .000473 3.3100 .000413 4.4400 .000378 5.5200 .000370 6.0300 .000361 6.2600 .000351 6.5200 .000327 8.1700 .000317 8.6900 .000303 9.6300 .000287 11.0300 .000274 10.8600 .000273 13.2600 .000238 15.1800 .000238 15.7900 .000218 18.4900 .000213 17.9600 .000210 20.2400 .000192 23.2200 .000191 27.6400 .000162 34.7600 Source: {\em Physical Review}, Vol. XXXIII, 1911, The Terminal Velocity of Small Spheres in Air at Reduced Pressures,'' L. W. McKeehan, p. 169. Description: Reciprocal velocity in sec/cm vs. radius of spheres in units of $10^{-4}$ cm. Reference Relation: $1/y=k_{1}x+k_{2}x^{2}$ Comments: The reference relation leaves patterned residuals. The simple formula $y=k/x^{2}$ fits well and the relation $1/y=k_{1}x^{2}+k_{2}x^{3}$ is even better. --------------------------------------------- Case 59 x y 101.66 0.0139 101.66 0.0138 83.30 0.0154 59.16 0.0227 39.10 0.0344 26.18 0.0517 14.29 0.0945 7.58 0.1780 5.00 0.2620 Source: {\em Physical Review}, Vol. XXXIV, 1912, On the Mobility of Ions in Air at High Pressure,'' A. J. Dempster, p. 55. Description: Mobility of positive ions in cm/sec/volt/cm (sic) vs. air pressure in atmospheres. Reference Relation: $y=k/x$ Comments: A residual plot shows one serious outlying endpoint. Without this the reference relation fits very nicely. --------------------------------------------- Case 60 x y 5 0.767 10 0.720 15 0.697 20 0.687 25 0.685 30 0.690 35 0.702 40 0.716 45 0.733 54 0.769 57 0.782 60 0.794 65 0.816 Source: {\em Physical Review}, Vol. XXXIV, 1912, A Study of the Reversible Pendulum. Part II. Experimental Verifications,'' John C. Shedd, J. A. and W. N. Birchby, p. 114. Description: See source for details. Reference Relation: $y^{2}=(k_{1}x^{2}+k_{2})/(x+k_{3})$ --------------------------------------------- Case 61a x y 194.5 20.79 194.3 20.79 197.9 22.40 198.4 22.67 199.4 23.15 199.9 23.35 200.9 23.89 201.1 23.99 201.4 24.02 201.3 24.01 203.6 25.14 204.6 26.57 209.5 28.49 208.6 27.76 210.7 29.04 211.9 29.88 212.2 30.06 Source: Sanford Weisberg, {\em Applied Linear Regression}, Wiley, 1985, p. 3. Description: Barometric pressure in inches of mercury vs. boiling point in degrees Fahrenheit at various Alpine locations, as originally reported by James D. Forbes in 1857. Reference Relation: $\log y =k_{1}x+k_{2}$ Comments: A residual plot shows one bad outlier in the middle of the $x$ range. Without it, there is a slight appearance of curvature in the residuals. --------------------------------------------- Case 61b x y 210.8 29.211 210.2 28.559 208.4 27.972 202.5 24.697 200.6 23.726 200.1 23.369 199.5 23.030 197.0 21.892 196.4 21.928 196.3 21.654 195.6 21.605 193.4 20.480 193.6 20.212 191.4 19.758 191.1 19.490 190.6 19.386 189.5 18.869 188.8 18.356 188.5 18.507 185.7 17.267 186.0 17.221 185.6 17.062 184.1 16.959 184.6 16.881 184.1 16.817 183.2 16.385 182.4 16.235 181.9 16.106 181.9 15.928 181.0 15.919 180.6 15.376 Source: Sanford Weisberg, {\em Applied Linear Regression}, Wiley, 1985, p. 28. Description: Barometric pressure in inches of mercury vs. boiling point in degrees Fahrenheit at various Himalayan locations, as originally collected by Joseph Hooker and reported by James D. Forbes in 1857. Reference Relation: $\log y =k_{1}x+k_{2}$ --------------------------------------------- Case 62a x y 0.04 672 0.10 709 0.16 729 0.28 778 0.44 797 Source: Sanford Weisberg, {\em Applied Linear Regression}, Wiley, 1985, p. 263. Description: Average body weight of four-week-old male turkeys vs. dosage of supplemental methionine. Reference Relation: $y=k_{1}-k_{2}k_{3}^{x}$ --------------------------------------------- Case 62b x y 0.04 680 0.10 721 0.16 750 0.28 790 0.44 799 Source: Sanford Weisberg, {\em Applied Linear Regression}, Wiley, 1985, p. 263. Description: Average body weight of four-week-old male turkeys vs. dosage of supplemental methionine. Reference Relation: $y=k_{1}-k_{2}k_{3}^{x}$ Comments: Same as Case 62a, but using a different source for the methionine. The reference relation shows lack of fit. --------------------------------------------- Case 63 x y 1 11.5 2 17.0 4 24.1 Source: {\em Physical Review}, Vol. III, 1914, The Physical Properties of Selenium,'' P. J. Nicholson, p. 12. Description: Intensity of rays vs. galvanometer deflection in an experiment showing the effect of roentgen rays on a Giltay cell. Reference Relation: $y=kx^{.5}$ Comments: The source cites only an approximate square root'' law. I interpreted this as indicated and the data seems to corroborate the interpretation. --------------------------------------------- Case 64 x y 0.0146 471 0.0166 436 0.0178 416 0.0185 414 0.0200 405 0.0229 382 0.0250 353 0.0281 356 0.0340 309 0.0370 294 0.0419 270 0.0451 276 0.0543 241 Source: {\em Physical Review}, Vol. III, 1914, The Electrical Discharge from Liquid Points, and a Hydrostatic Method of Measuring the Electric Intensity at their Surfaces,'' John Zeleny, p. 88. Description: Electric intensity in electrostatic units/cm vs. radius of a point of liquid in cm. Reference Relation: $yx^{.5}=k$ --------------------------------------------- Case 66 x y 50 14.7 139 58.8 270 152.0 393 294.2 455 411.0 500 491.0 530 556.0 Source: {\em Physical Review}, Vol. III, 1914, Thermal Electromotive Force at the Junctions of Metals and Metallic Oxides,'' S. L. Brown, p. 239. Description: Electromotive force in millivolts vs. temperature of the hot junction of a thermocouple (cold junction is at constant temperature) in Centigrade. Reference Relation: $y=.105x+.00175x^{2}$ --------------------------------------------- Case 67 x y 18 1.80 14 1.09 8 0.35 6 0.20 4 0.09 3 0.05 Source: {\em Physical Review}, Vol. III, 1914, The Nature and Velocity of Migration of the Positive Ions in Flames,'' A. H. Saxer, p. 332. Description: Specific ionic velocity vs. horizontal distance in Saxer's apparatus from guard to cathode. Reference Relation: $y=kx^{2}$ --------------------------------------------- Case 68 x y 7700 10.2 4850 6.3 2250 3.0 7700 10.9 4850 7.0 7700 10.7 4850 6.9 2250 3.0 7700 11.0 7700 10.7 4850 7.0 2250 3.1 7700 10.0 4850 6.4 2250 3.3 7700 10.8 4850 6.8 2250 3.4 Source: {\em Physical Review}, Vol. III, 1914, The Hall Effect in Flames,'' Harold A. Wilson, p. 380. Description: Hall effect angle in degrees vs. magnetic field strength. Reference Relation: $\tan y =kx$ Comments: Note that $\tan y$ is extremely linear over this range. --------------------------------------------- Case 69 x y 0.5 0.300 2.0 1.000 4.5 2.025 7.4 3.108 10.0 4.400 13.0 5.460 17.8 7.120 21.6 9.288 28.5 13.110 35.0 17.500 46.5 21.390 55.0 24.750 62.0 26.660 Source: {\em Physical Review}, Vol. IV, 1914, The Crystal Forms of Metallic Selenium and Some of their Physical Properties,'' F. C. Brown, p. 93. Description: Change in conductivity after a light is shown on selenium vs. conductivity of the selenium in the dark. Reference Relation: $x/y=k$ Comments: A residual plot shows that the reference relation holds only for low conductivities. The source tabulates $x$ and $y/x$; I converted to get the presumed original data. --------------------------------------------- Case 70a x y 0.60 65.15 1.56 137.60 2.85 205.05 5.03 278.35 9.95 359.90 Source: {\em Physical Review}, Vol. IV, 1914, Rate of Decay of Phosphoresence at Low Temperatures,'' E. H. Kennard, p. 283. Description: Total emission of light in mm of meter deflection vs. time in seconds. Reference Relation: $(x+k_{1})/y=k_{2}x+k_{3}$ Comments: Source says (p. 284) that the reference relation holds up to $x=10$ and only this data is included here. --------------------------------------------- Case 70b x y 0.105 7.65 0.201 17.50 0.306 27.80 0.402 36.90 0.501 44.80 0.595 57.80 1.560 128.40 2.850 189.10 5.030 255.30 6.800 290.30 9.950 333.50 Source: {\em Physical Review}, Vol. IV, 1914, Rate of Decay of Phosphoresence at Low Temperatures,'' E. H. Kennard, p. 283. Description: Total emission of light in mm of meter deflection vs. time in seconds. Reference Relation: $(x+k_{1})/y=k_{2}x+k_{3}$ Comments: Source says (p. 284) that the reference relation holds up to x=10 and only this data is included here. --------------------------------------------- Case 71a x y 1682 0.00617 1800 0.06950 1890 0.37300 1912 0.50300 1982 1.32000 2000 1.88000 Source: {\em Physical Review}, Vol. IV, 1914, The Vapor Pressure of the Metals Platinum and Molybdenum,'' Irving Langmuir and G. M. J. Mackay, pp. 381--382. Description: Evaporation rate of a platinum wire determined by weight vs. absolute temperature. Reference Relation: $\log y +1.76\log x =k_{1}/x+k_{2}$ Comments: Case 49 is similar. --------------------------------------------- Case 71b x y 1994 0.00766 2040 0.03050 2112 0.12400 2121 0.11100 2220 0.63000 2287 1.74000 2312 3.29000 2326 3.65000 2350 6.49000 2373 8.47000 Source: {\em Physical Review}, Vol. IV, 1914, The Vapor Pressure of the Metals Platinum and Molybdenum,'' Irving Langmuir and G. M. J. Mackay, pp. 381--382. Description: Evaporation rate of a molybdenum wire determined by weight vs. absolute temperature. Reference Relation: $\log y +1.76\log x =k_{1}/x+k_{2}$ --------------------------------------------- Case 72 x y 83 212.0 57 142.0 55 132.5 39 91.2 37 84.9 21 39.6 19 36.5 11 14.6 13 15.7 5 3.6 1 5.0 Source: {\em Physical Review}, Vol. V, 1915, Atomic Numbers and Atomic Charges,'' Fernando Sanford. Description: Atomic charge vs. atomic number for univalent elements, charge of hydrogen set to 5. Reference Relation: $y=k_{1}x+k_{2}$ Comments: A residual plot shows one or two outlying endpoints. --------------------------------------------- Case 73 x y 35 2.00 35 2.00 35 2.00 35 2.00 35 1.90 40 1.70 40 1.60 40 1.65 40 1.60 40 1.50 45 1.30 45 1.30 45 1.30 45 1.35 45 1.20 50 1.10 50 1.10 50 1.10 50 1.10 50 1.00 55 0.90 55 0.90 55 0.90 55 0.90 55 0.85 60 0.75 60 0.75 60 0.75 60 0.80 60 0.70 65 0.60 65 0.60 65 0.60 65 0.65 65 0.65 70 0.50 70 0.50 70 0.50 70 0.55 70 0.55 75 0.40 75 0.40 75 0.42 75 0.45 75 0.45 80 0.35 80 0.40 80 0.37 80 0.40 80 0.30 85 0.30 85 0.30 85 0.30 85 0.35 85 0.27 90 0.23 90 0.23 90 0.24 90 0.28 90 0.20 95 0.20 95 0.20 95 0.18 95 0.22 95 0.17 100 0.15 100 0.15 100 0.18 100 0.15 100 0.20 110 0.14 110 0.10 110 0.10 110 0.15 110 0.10 120 0.10 120 0.08 120 0.10 120 0.10 120 0.05 130 0.05 130 0.00 130 0.05 130 0.05 130 0.00 140 0.00 140 0.00 140 0.00 140 0.00 140 0.05 150 0.00 150 0.00 150 0.00 150 0.00 150 0.00 Source: {\em Physical Review}, Vol. V, 1915, Temperature Changes Accompanying the Adiabatic Compression of Steel,'' K. T. Compton and D. B. Webster, p. 163. Description: Galvanometer deflection vs. time in seconds. Reference Relation: $\log y =k_{1}x+k_{2}$ Comments: The source says the reference relation holds for $x>30$ and only this data has been included here. Note that $\log y$ is impossible for $y=0$; an accompanying graph in the source goes only up to $x=100$ to avoid this. --------------------------------------------- Case 74 x y 1000 8.11 2000 8.68 3000 9.11 4000 9.54 6000 10.33 8000 11.11 10000 11.84 12000 12.50 14000 13.13 16000 13.73 Source: {\em Physical Review}, Vol. V, 1914, Magnetic Resistance Change of Pure Iron,'' R. A. Heising, p. 324. Description: Change in resistance vs. internal magnetic field; transverse effect. Reference Relation: $y=kx^{.85}$ Comments: A regression of $y$ on $x^{.85}$ turns up an intercept which is significant with $t$-value 214.8; hence it is extremely implausible that the reference relation is correct. Perhaps I have understood the text incorrectly. Even with an intercept, however, the reference relation would show strong lack of fit. --------------------------------------------- Case 75 x y 850 18 1200 28 2000 44 Source: {\em Physical Review}, Vol. V, 1915, Theory and Use of the Molecular Gauge,'' Saul Dushman, p. 221. Description: Meter deflection in degrees vs. rate of rotation in RPM. Reference Relation: $y=kx$ --------------------------------------------- Case 76a x y 1.47 0.7020 1.63 0.6470 1.85 0.6180 2.91 0.4870 3.48 0.4455 3.80 0.4275 3.93 0.4210 4.04 0.4180 4.04 0.4415 4.05 0.4130 4.01 0.4140 4.02 0.4130 4.10 0.4115 3.98 0.4185 3.92 0.4155 4.05 0.4170 3.91 0.4195 3.95 0.4160 3.96 0.4165 3.98 0.4185 Source: {\em Physical Review}, Vol. V, 1915, The Mechanical Equivalent of Light,'' Herbert E. Ives, W. W. Coblentz and E. F. Kingsbury, p. 290. Description: Air distance at which a comparison lamp is set when a photometric match is made through a green solution vs. galvanometer deflection for a thermopile exposed to green radiation. Reference Relation: $xy^{2}=k$ Comments: Note the apparent outlier at $x=4.04$ in the graph above. --------------------------------------------- Case 76b x y 3.43 0.4560 5.41 0.3600 5.88 0.3420 6.03 0.3380 6.12 0.3400 5.99 0.3460 6.06 0.3395 5.84 0.3450 5.91 0.3455 5.98 0.3465 Source: {\em Physical Review}, Vol. V, 1915, The Mechanical Equivalent of Light,'' Herbert E. Ives, W. W. Coblentz and E. F. Kingsbury, p. 290. Description: Air distance at which a comparison lamp is set when a photometric match is made through a green solution vs. galvanometer deflection for a thermopile exposed to green radiation. Reference Relation: $xy^{2}=k$ --------------------------------------------- Case 76c x y 3.11 0.4675 4.14 0.4050 4.68 0.3800 4.75 0.3810 4.76 0.3785 4.62 0.3840 4.54 0.3870 4.61 0.3860 4.64 0.3860 4.56 0.3860 Source: {\em Physical Review}, Vol. V, 1915, The Mechanical Equivalent of Light,'' Herbert E. Ives, W. W. Coblentz and E. F. Kingsbury, p. 290. Description: Air distance at which a comparison lamp is set when a photometric match is made through a green solution vs. galvanometer deflection for a thermopile exposed to green radiation. Reference Relation: $xy^{2}=k$ --------------------------------------------- Case 77 x y 90 0.030 175 0.067 265 0.104 300 0.120 362 0.144 404 0.163 468 0.190 517 0.211 565 0.231 588 0.240 602 0.246 640 0.278 670 0.288 693 0.300 Source: {\em Physical Review}, Vol. V, 1915, Thermal Electromotive Forces of Iron Oxide and Copper Oxide,'' S. Leroy Brown and L. O. Shuddemagen, p. 389. Description: Electromotive force in volts for an iron-magnetite couple vs. temperature of hot junction in Centigrade; cold junction at 20 degrees. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 78 x y 6.29e-06 1.60e-07 1.35e-05 1.10e-06 1.61e-05 1.80e-06 3.54e-05 1.05e-05 5.08e-05 2.04e-05 6.02e-05 2.79e-05 Source: {\em Physical Review}, Vol. V, 1915, The Nature of Electric Conduction as Required to Explain the Resistance of Metallic Selenium Following Illumination,'' F. C. Brown, p. 398. Description: Change of conductivity vs. conductivity of selenium in light, both in inverse ohms. Reference Relation: $y/x^{2}=k$ Comments: The data have been rearranged in order of increasing $x$ values. The reference relation shows lack of fit. --------------------------------------------- Case 79 x y 2.00e-06 1.41e-06 2.04e-06 1.44e-06 2.33e-06 1.65e-06 2.40e-06 1.65e-06 Source: {\em Physical Review}, Vol. V, 1915, The Nature of Electric Conduction as Required to Explain the Resistance of Metallic Selenium Following Illumination,'' F. C. Brown, p. 398. Description: Equilibrium light sensitiveness vs. conductivity in light. Reference Relation: $y=kx$ Comments: A residual plot shows one outlying endpoint. --------------------------------------------- Case 80a x y 0.10 0.640 0.19 0.440 0.42 0.315 0.43 0.315 0.43 0.300 0.67 0.235 0.90 0.200 1.40 0.170 Source: {\em Physical Review}, Vol. V, 1915, The Cathode Fall in Gases,'' C. A. Skinner, p. 495. Description: Mean free path in mm vs. normal current density in milliamps; for an aluminum cathode in hydrogen. Reference Relation: $xy^{2}=k$ --------------------------------------------- Case 80b x y 0.087 0.550 0.100 0.490 0.167 0.420 0.207 0.370 0.250 0.340 0.300 0.300 0.367 0.265 0.467 0.245 0.567 0.215 0.767 0.195 0.850 0.180 1.200 0.150 1.330 0.145 Source: {\em Physical Review}, Vol. V, 1915, The Cathode Fall in Gases,'' C. A. Skinner, p. 495. Description: Mean free path in mm vs. normal current density in milliamps; for a steel cathode in hydrogen. Reference Relation: $xy^{2}=k$ --------------------------------------------- Case 81a x y 9.60 0.640 6.80 0.440 4.60 0.315 4.50 0.315 4.70 0.300 3.60 0.235 2.70 0.170 2.15 0.135 Source: {\em Physical Review}, Vol. V, 1915, The Cathode Fall in Gases,'' C. A. Skinner, p. 495. Description: Mean free path vs. distance to negative glow, both in mm; for an aluminum cathode in hydrogen. Reference Relation: $x/y=k$ --------------------------------------------- Case 81b x y 11.7 0.550 10.2 0.490 8.4 0.420 7.6 0.370 7.1 0.340 5.7 0.300 5.5 0.265 5.1 0.245 4.6 0.215 4.1 0.195 3.7 0.180 2.9 0.150 3.0 0.145 Source: {\em Physical Review}, Vol. V, 1915, The Cathode Fall in Gases,'' C. A. Skinner, p. 495. Description: Mean free path vs. distance to negative glow, both in mm; for a steel cathode in hydrogen. Reference Relation: $x/y=k$ --------------------------------------------- Case 82a 438.2 235.4 369.8 199.0 288.8 156.7 249.8 135.7 205.7 112.5 175.8 96.6 123.9 68.9 Source: {\em Physical Review}, Vol. VI, 1915,  A Null Method with Photo-Electric Cells,'' F. K. Richtinger, p. 68. Description: See source for details. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 82b x y 404.6 228.4 375.6 212.5 330.0 187.2 260.0 148.1 220.0 125.8 190.0 109.0 170.0 97.6 155.0 89.3 Source: {\em Physical Review}, Vol. VI, 1915,  A Null Method with Photo-Electric Cells,'' F. K. Richtinger, p. 68. Description: See source for details. Reference Relation: $y=k_{1}x+k_{2}$ Comments: Reference relation shows lack of fit. --------------------------------------------- Case 83 x y 8.70e-06 1.67e-05 9.50e-06 1.73e-05 1.03e-05 2.04e-05 1.16e-05 2.18e-05 8.90e-06 1.67e-05 8.80e-06 1.66e-05 9.40e-06 1.81e-05 1.01e-05 1.94e-05 1.15e-05 2.24e-05 8.80e-06 1.65e-05 Source: {\em Physical Review}, Vol. VI, 1915, Electric Double Refraction in Liquids,'' Harold E. McComb, p. 183. Description: B-parallel vs. B-perpendicular, two components of vibration. Reference Relation: $y=kx$ --------------------------------------------- Case 84a x y 30 0.00 42 0.00 88 0.03 92 0.03 205 0.62 209 0.66 220 0.72 222 0.76 232 0.86 243 0.95 262 1.14 284 1.35 306 1.58 331 1.83 358 2.11 413 2.64 1169 5.24 Source: {\em Physical Review}, Vol. VI, 1915, The Variation of the Specific Heat of Solids with Temperature,'' Arthur H. Compton, p. 382. Description: Specific heat of diamond vs. temperature. Reference Relation: $y=k_{1}e^{-k_{2}/x}(k_{2}/x+1)$ --------------------------------------------- Case 84b x y 23.5 0.22 27.7 0.32 33.4 0.54 87.0 3.32 88.0 3.37 137.0 4.53 234.0 5.50 290.0 5.66 323.0 5.75 450.0 5.87 Source: {\em Physical Review}, Vol. VI, 1915, The Variation of the Specific Heat of Solids with Temperature,'' Arthur H. Compton, p. 382. Description: Specific heat of copper vs. temperature. Reference Relation: $y=k_{1}e^{-k_{2}/x}(k_{2}/x+1)$ --------------------------------------------- Case 84c x y 23.0 2.95 28.3 3.91 36.8 4.38 38.1 4.43 85.5 5.57 90.2 5.63 200.0 5.91 273.0 5.99 290.0 5.99 332.0 6.03 409.0 6.15 Source: {\em Physical Review}, Vol. VI, 1915, The Variation of the Specific Heat of Solids with Temperature,'' Arthur H. Compton, p. 382. Description: Specific heat of lead vs. temperature. Reference Relation: $y=k_{1}e^{-k_{2}/x}(k_{2}/x+1)$ --------------------------------------------- Case 84d x y 35.0 1.58 39.1 1.90 42.9 2.26 45.5 2.46 51.4 2.80 53.8 2.89 77.0 4.04 100.0 4.80 200.0 5.61 273.0 5.75 331.0 5.71 535.0 5.90 589.0 5.99 Source: {\em Physical Review}, Vol. VI, 1915, The Variation of the Specific Heat of Solids with Temperature,'' Arthur H. Compton, p. 382. Description: Specific heat of silver vs. temperature. Reference Relation: $y=k_{1}e^{-k_{2}/x}(k_{2}/x+1)$ --------------------------------------------- Case 85 x y 0.00577 0.0139 0.00829 0.0281 0.00863 0.0305 0.00974 0.0398 0.01198 0.0589 0.01599 0.1045 0.01696 0.1217 0.01928 0.1511 0.02090 0.1800 0.02118 0.1842 0.02149 0.1903 0.02194 0.2014 0.02251 0.2113 0.02506 0.2572 0.02659 0.2893 0.02789 0.3226 0.02997 0.3775 0.03779 0.5982 Source: {\em Physical Review}, Vol. VII, 1916, The Fall of Mercury Droplets in a Viscous Medium'' O. W. Silvey, p. 110. Description: Velocity of a falling sphere in cm/sec vs. radius of the sphere in cm. Reference Relation: $y=k_{1}x^{2}/(k_{2}x+k_{3})(k_{4}x+k_{5})$ Comments: I doubt that anything more complex than $y=kx^{2}$ is justified by the data. The residuals for this fit are heteroscedastic, but otherwise unpatterned. A log-log transformation takes care of the heteroscedasticity leaving only a kind of peculiar blank region in the associated residual plot. --------------------------------------------- Case 86 x y 24.0 5.780e+18 34.1 8.270e+18 48.8 1.214e+19 82.0 1.950e+19 89.0 2.240e+19 95.0 2.280e+19 Source: {\em Physical Review}, Vol. VII, 1916, The Maximum Frequency of X-Rays at Constant Voltage between 30,000 and 100,000,'' Albert W. Hull, p. 157. Description: Maximum frequency vs. kilovolts. Reference Relation: $y=kx$ --------------------------------------------- Case 87 x y 5 0.242 10 0.377 13 0.441 16 0.503 20 0.580 23 0.637 26 0.683 30 0.755 33 0.800 36 0.847 40 0.908 42 0.938 Source: {\em Physical Review}, Vol. VII, 1916, Selective Radiation from Osmium Filaments,'' Ernest F. Barker, p. 453. Description: See source for details: $x$ is measured in volts and $y$ in amps. Reference Relation: $\log (y/.91) = k_{1}(\log (x/40.25) )^{2}+k_{2}\log (x/40.25)$ --------------------------------------------- Case 88 x y 5 1.21 10 3.77 13 5.74 16 8.05 20 11.60 23 14.65 26 17.76 30 22.65 33 26.40 36 30.52 40 36.32 42 39.40 Source: {\em Physical Review}, Vol. VII, 1916, Selective Radiation from Osmium Filaments,'' Ernest F. Barker, p. 453. Description: See source for details: $x$ is measured in volts and $y$ in watts. Reference Relation: $\log y =k_{1}\log x +k_{2}$ Comments: A residual plot turns up two potential outliers. --------------------------------------------- Case 89 x y 6.04 18.36 6.54 17.99 1.36 87.18 6.37 12.50 1.52 52.50 6.23 12.71 1.53 52.48 7.27 19.40 1.69 60.50 1.37 61.70 5.55 10.71 1.77 36.28 7.41 15.03 1.64 51.50 6.35 17.70 1.42 59.36 Source: {\em Physical Review}, Vol. VII, 1916, Retrograde Rays from the Cold Cathode,'' Orrin H. Smith, p. 629. Description: Momentum vs. velocity. Reference Relation: $xy=k$ Comments: Reference relation shows lack of fit. --------------------------------------------- Case 90 x y 13.08333 100.0 26.91667 18.9 42.98333 3.9 Source: {\em Physical Review}, Vol. VII, 1916 A Recording X-Ray Spectrometer, and the High Frequency Spectrum of Tungsten,'' Arthur H. Compton, p. 658. Description: Intensity vs. mean angle, in degrees. Reference Relation: $y=k_{1}(1+\cos^{2}2x)e^{k_{2}\sin^{2}x}/\sin^{2}x$ Comments: I have converted the angular measurements from degrees and minutes to decimal degrees. --------------------------------------------- Case 91a x y 0.00386 166000 0.00678 131000 0.00825 125000 0.01200 107000 0.01300 107000 0.02050 93000 0.03250 80000 0.03850 77000 0.05120 71000 0.06420 65000 Source: {\em Physical Review}, Vol. VIII, 1916, Of the Initial Condition of the Corona Discharge,'' Jakob Kunz, p. 30. Description: Electric force in volts/cm vs. radius of a wire in cm. Reference Relation: $y=k_{1}/x^{.5}+k_{2}$ Comments: The source says the reference relation does not hold for small radii and data for these have not been included. --------------------------------------------- Case 91b x y 0.00386 166000 0.00678 136000 0.00825 121000 0.01200 109000 0.01300 114000 0.02050 99000 0.03250 83000 0.03850 79000 0.05120 73000 0.06420 64000 Source: {\em Physical Review}, Vol. VIII, 1916, Of the Initial Condition of the Corona Discharge,'' Jakob Kunz, p. 30. Description: Electric force in volts/cm vs. radius of a wire in cm. Reference Relation: $y=k_{1}/x^{.5}+k_{2}$ Comments: The source says the reference relation does not hold for small radii and data for these have not been included. The graph above suggests that Kunz took a second measurement near $x=.0125$ when his first did not fit the reference relation. --------------------------------------------- Case 92 x y 53.2 18800 91.3 25000 173.5 36000 248.5 45100 334.8 54200 483.6 70800 616.6 82900 720.0 92800 746.0 95100 768.3 96700 Source: {\em Physical Review}, VIII, 1916, Of the Initial Condition of the Corona Discharge,'' Jakob Kunz, p. 35. Description: Electric force in volts/cm vs. pressure in mm. Reference Relation: $y=k_{1}/x^{.5}+k_{2}$ Comments: The source says the reference relation does not hold for small radii and data for these have not been included. --------------------------------------------- Case 93 x y -190 6925 -79 6930 18 6934 225 6952 300 6956 435 6969 540 6983 630 6995 845 7037 Source: {\em Physical Review}, Vol. VIII, 1916, The Effect of Temperature upon the Absorption Spectrum of a Synthetic Ruby,'' K. S. Gibson, p. 43. Description: Wavelength vs. temperature in Centigrade. Reference Relation: $\log (y-6900) =k_{1}x+k_{2}$ --------------------------------------------- Case 94 x y 1980 1.30e+09 1980 1.10e+09 2820 1.61e+09 3670 2.39e+09 4400 2.56e+09 4790 3.24e+09 5520 3.43e+09 5640 3.15e+09 Source: {\em Physical Review}, Vol. VIII, 1916, The Electromotive Force Produced by the Acceleration of Metals,'' Richard C. Tolman and T. Dale Stewart, p. 112. Description: Charge in coulombs vs. velocity in cm/sec. Reference Relation: $y=kx$ --------------------------------------------- Case 95 x y 15.240 0.0491 17.500 0.0726 18.030 0.0792 18.890 0.0930 19.580 0.1010 20.880 0.1247 21.505 0.1410 Source: {\em Physical Review}, Vol. VIII, 1916, Compton's Formula for the Temperature Variation of the Specific Heat of Solids,'' F. Schwers, p. 119. Description: Specific heat ($C_{v}$) vs. absolute temperature. Reference Relation: $y=kx^{3}$ Comments: A residual plot shows one outlying endpoint. --------------------------------------------- Case 96a x y 0.392 0.860 0.343 0.726 0.294 0.493 0.245 0.342 0.221 0.283 0.208 0.255 0.196 0.243 0.184 0.218 0.172 0.199 0.160 0.178 0.147 0.154 Source: {\em Physical Review}, Vol. VIII, 1916, The Law of Absorption of X-Rays at High Frequencies,'' Albert W. Hull and Marion Rice, p. 328. Description: Mass absorption coefficient vs. wavelength in angstroms; for aluminum. Reference Relation: $y=k_{1}x^{3}+k_{2}$ --------------------------------------------- Case 96b x y 0.294 3.84 0.245 2.24 0.221 1.70 0.208 1.39 0.196 1.27 0.184 1.07 0.172 0.91 0.160 0.79 0.147 0.71 Source: {\em Physical Review}, Vol. VIII, 1916, The Law of Absorption of X-Rays at High Frequencies,'' Albert W. Hull and Marion Rice, p. 328. Description: Mass absorption coefficient vs. wavelength in angstroms; for copper. Reference Relation: $y=k_{1}x^{3}+k_{2}$ --------------------------------------------- Case 97 x y 4880 249.0 5870 149.0 6780 101.0 7700 71.7 8860 47.3 9970 34.7 Source: {\em Physical Review}, Vol. VIII, 1916, The Absorption Coefficients of Soft X-Rays,'' C. D. Miller, p. 340. Description: Absorption coefficient vs. potential. Reference Relation: $yx^{2.77}=k$ Comments: The source says the reference relation holds for potentials of at least 4480 and only those are included here. --------------------------------------------- Case 98a x y 2.96 0.615 2.28 0.555 1.78 0.515 1.47 0.487 1.35 0.473 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 473. Description: Outside-inside brightness ratio vs. pitch of coiling in the filament. Measurements taken at 2300$^{\circ}$ Kelvin with light of wavelength .656 microns. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 98b x y 2.96 0.681 2.28 0.598 1.78 0.551 1.47 0.516 1.35 0.500 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 473. Description: Outside-inside brightness ratio vs. pitch of coiling in the filament. Measurements taken at 2300$^{\circ}$ Kelvin with light of wavelength .493 microns. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 98c x y 2.96 0.656 2.28 0.581 1.35 0.498 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 473. Description: Outside-inside brightness ratio vs. pitch of coiling in the filament. Measurements taken at 1900$^{\circ}$ Kelvin with light of wavelength .656 microns. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 98d x y 2.96 0.682 2.28 0.604 1.35 0.515 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 473. Description: Outside-inside brightness ratio vs. pitch of coiling in the filament. Measurements taken at 1900$^{\circ}$ Kelvin with light of wavelength .493 microns. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 99a x y 1360 49.6 1372 49.4 1473 55.4 1510 57.5 1558 60.1 1586 60.8 1589 60.9 1605 62.5 1635 64.2 1732 68.9 1778 70.5 1795 71.7 1798 72.3 1908 77.4 1987 81.8 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 477. Description: Resistance vs. absolute temperature for a helical filament. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 99b x y 1390 48.9 1413 48.5 1519 55.3 1524 55.4 1650 61.2 1695 63.0 1793 67.9 1795 68.2 1885 72.5 1948 75.8 Source: {\em Physical Review}, Vol. VIII, 1916, Temperature and Blackening Effects in Helical Tungsten Filaments,'' B. E. Shackelford, p. 477. Description: Resistance vs. absolute temperature; for a hairpin filament. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 100a x y 145 28 161 36 315 68 329 73 464 102 490 106 599 133 615 136 723 160 739 162 837 187 850 186 1037 226 1043 228 1200 261 1215 263 1331 288 1345 290 1465 317 1474 318 1532 331 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--507. Description: Demagnetization vs. magnetic flux in cgs units; for torsion of 1.5 degrees. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing x values. Eleven sets are given in the source; I have taken only the first four. --------------------------------------------- Case 100b x y 145 37 161 37 315 97 329 98 464 150 490 150 599 198 615 199 723 241 739 241 837 281 850 281 1037 351 1043 349 1200 397 1215 405 1331 451 1345 448 1465 494 1474 492 1532 513 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--507. Description: Demagnetization vs. magnetic flux in cgs units; for torsion of 2.4 degrees. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing x values. Eleven sets are given in the source; I have taken only the first four. --------------------------------------------- Case 100c x y 145 63 161 67 315 139 329 140 464 206 490 206 599 265 615 265 723 319 739 320 837 368 850 369 1037 453 1043 455 1200 524 1215 525 1331 580 1345 580 1465 634 1474 635 1532 661 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--507. Description: Demagnetization vs. magnetic flux in cgs units; for torsion of 3.6 degrees. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing x values. Eleven sets are given in the source; I have taken only the first four. --------------------------------------------- Case 100d x y 145 85 161 85 315 184 329 183 464 251 490 269 599 329 615 346 723 400 739 415 837 464 850 478 1037 574 1043 587 1200 666 1215 676 1331 740 1345 747 1465 816 1474 820 1532 854 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--507. Description: Demagnetization vs. magnetic flux in cgs units; for torsion of 5.2 degrees. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing x values. Eleven sets are given in the source; I have taken only the first four. --------------------------------------------- Case 101a x y 0.216 1.5 0.320 2.4 0.436 3.6 0.556 5.2 0.687 8.1 0.773 11.3 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--508. Description: Torsion angle in degrees vs. a factor determined from previous work; for Norway iron. Reference Relation: $k_{1}x=y(k_{2}-x^{2})$ --------------------------------------------- Case 101b x y 0.128 4.1 0.234 8.1 0.328 12.6 0.390 16.5 0.440 20.6 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, pp. 506--508. Description: Torsion angle in degrees vs. a factor determined from previous work; for Viking steel. Reference Relation: $k_{1}x=y(k_{2}-x^{2})$ --------------------------------------------- Case 102 x y 2 628 5 1319 8 1912 11 2437 14 2903 17 3321 23 4032 29 4571 35 4991 44 5403 56 5605 68 5400 77 4994 83 4585 89 4044 95 3352 98 2938 101 2471 104 1947 107 1354 110 671 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, p. 508, explanation on pp. 509--510. Description: Magnetic flux in cgs units vs. position in cm on a 112 cm rod where the measurement was taken. Reference Relation: $y=k_{1}x^{2}+k_{2}x+k_{3}$ Comments: I did not collect a similar set on p. 514. Residuals from the reference relation show clear lack of fit. --------------------------------------------- Case 103 x y 2366 0.272 5155 0.245 5605 0.234 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, p. 511, explanation in second full paragraph on p. 512. Description: Factor determined from previous work vs. magnetic flux measured in cgs units at the center of a 112 cm rod. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 104a x y 337 1.58 666 3.16 1019 4.74 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, p. 513. Description: Torsion angle in degrees vs. demagnetization at the center of a 112 cm rod clamped at the middle. Reference Relation: $y=kx$ --------------------------------------------- Case 104b x y 798 4.33 1125 6.08 1439 7.70 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, p. 513. Description: Torsion angle in degrees vs. demagnetization at the center of a 112 cm rod clamped at quarter length. Reference Relation: $y=kx$ --------------------------------------------- Case 105 x y 2 553 8 1754 14 2655 20 3361 26 3905 32 4308 38 4599 44 4746 50 4792 56 4712 62 4550 68 4337 74 4049 77 3882 80 3701 86 3275 92 2759 98 2134 104 1371 110 392 Source: {\em Physical Review}, Vol. VIII, 1916, On the Demagnetization of Iron and Steel Rods by Strain and Impact,'' Guy G. Becknell, p. 515. Description: Magnetic flux after torsion in cgs units vs. position in cm where measurement was taken on a 112 cm rod. Reference Relation: $(x+k_{1}y)^{2}+k_{2}x+k_{3}y+k_{4}=0$ Comments: The reference relation is a parabola with the axes rotated; the tangent of the angle of rotation ($k_{1}$), according to the source, is .00147. --------------------------------------------- Case 106a x y 100.0 33.78 84.0 40.96 75.9 45.31 48.0 57.44 33.1 64.47 17.4 71.11 Source: {\em Physical Review}, Vol. VIII, 1916, The Dielectric Constant of Aqueous Solutions,'' Elmer A. Harrington, p. 592. Description: Dielectric constant of a solution of methyl alcohol vs. its concentration. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 106b x y 0.1 77.64 0.2 76.73 0.4 75.53 0.5 75.05 0.6 74.46 0.7 73.84 0.9 72.52 1.0 71.84 1.2 70.36 1.4 68.67 Source: {\em Physical Review}, Vol. VIII, 1916, The Dielectric Constant of Aqueous Solutions,'' Elmer A. Harrington, p. 592. Description: Dielectric constant of a solution of sugar vs. its concentration. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 106c x y 0.5 80.22 1.0 81.51 1.5 82.81 2.0 83.98 2.5 85.16 3.0 86.17 Source: {\em Physical Review}, Vol. VIII, 1916, The Dielectric Constant of Aqueous Solutions,'' Elmer A. Harrington, p. 592. Description: Dielectric constant of a solution of urea vs. its concentration. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 107 x y 1 7.450e+11 2 1.395e+12 3 2.015e+12 4 2.620e+12 5 3.200e+12 6 3.680e+12 7 4.080e+12 Source: {\em Physical Review}, Vol. VIII, 1916, The Distribution of Angular Velocities among Diatomic Molecules,'' Edwin C. Kemble, p. 696. Description: Rotation frequency vs. ordinal position for the HCl molecule. Reference Relation: $y=kx$ Comments: Reference relation shows clearly patterned residuals; even more striking is a plot of $x/y$ vs. $x$. --------------------------------------------- Case 108a x y 0.0018 96.9 0.0041 93.8 0.0069 92.2 0.0081 91.7 0.0098 90.6 0.0115 89.8 0.0152 88.7 0.0169 88.7 0.0188 87.7 0.0205 87.1 0.0218 86.7 0.0275 85.7 0.0298 85.1 0.0322 84.8 0.0335 84.8 0.0355 84.2 0.0374 83.6 Source: {\em Physical Review}, Vol. IX, 1917. Counter Electromotive Force in the Aluminum Rectifier,'' Albert Lewis Fitch, pp. 23--25. Description: Counter electromotive force in volts vs. time in seconds. Reference Relation: $y=k_{1}+k_{2}k_{3}^{x}+k_{4}(1/k_{3})^{x}$ Comments: Ten data sets are given in the source; I have taken only the first four. --------------------------------------------- Case 108b x y 0.0028 96.4 0.0039 95.1 0.0065 93.5 0.0104 91.9 0.0111 91.4 0.0138 90.6 0.0157 89.8 0.0222 88.5 0.0238 88.3 0.0266 87.5 0.0309 86.7 0.0331 86.6 0.0350 86.1 0.0374 85.6 Source: {\em Physical Review}, Vol. IX, 1917. Counter Electromotive Force in the Aluminum Rectifier,'' Albert Lewis Fitch, pp. 23--25. Description: Counter electromotive force in volts vs. time in seconds. Reference Relation: $y=k_{1}+k_{2}k_{3}^{x}+k_{4}(1/k_{3})^{x}$ Comments: Ten data sets are given in the source; I have taken only the first four. --------------------------------------------- Case 108c x y 0.0074 97.9 0.0102 97.7 0.0129 97.5 0.0150 97.4 0.0156 97.2 0.0199 97.2 0.0220 97.1 0.0268 96.9 0.0287 96.4 0.0316 96.4 0.0340 96.1 0.0368 95.8 0.0384 95.8 Source: {\em Physical Review}, Vol. IX, 1917. Counter Electromotive Force in the Aluminum Rectifier,'' Albert Lewis Fitch, pp. 23--25. Description: Counter electromotive force in volts vs. time in seconds. Reference Relation: $y=k_{1}+k_{2}k_{3}^{x}+k_{4}(1/k_{3})^{x}$ Comments: Ten data sets are given in the source; I have taken only the first four. --------------------------------------------- Case 108d x y 0.0038 46.7 0.0063 45.9 0.0126 44.2 0.0142 43.6 0.0175 43.1 0.0197 42.6 0.0217 42.3 0.0232 42.0 0.0268 41.6 0.0287 41.4 0.0310 41.3 0.0332 40.8 0.0354 40.6 0.0384 40.1 Source: {\em Physical Review}, Vol. IX, 1917. Counter Electromotive Force in the Aluminum Rectifier,'' Albert Lewis Fitch, pp. 23--25. Description: Counter electromotive force in volts vs. time in seconds. Reference Relation: $y=k_{1}+k_{2}k_{3}^{x}+k_{4}(1/k_{3})^{x}$ Comments: Ten data sets are given in the source; I have taken only the first four. --------------------------------------------- Case 109 x y 1.66e+15 3.82 1.87e+15 4.32 2.40e+15 5.44 Source: {\em Physical Review}, Vol. IX, 1917, Photo-Electric Potentials for Extremely Short Wave-Lengths,'' P. E. Sabine, p. 214. Description: Applied voltage vs. frequency. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 110 x y 0.5495 25.403 0.5893 21.739 0.6000 20.914 0.7000 15.139 0.8000 11.432 0.9000 8.873 1.0000 7.121 1.0800 6.123 1.1000 5.904 1.2000 4.918 1.3000 4.101 1.4000 3.515 1.4500 3.272 1.5000 3.030 1.6000 2.662 1.7000 2.348 1.7150 2.304 1.7700 2.153 1.8000 2.070 1.8200 2.020 1.9000 1.827 2.0000 1.614 2.1000 1.431 2.1400 1.372 Source: {\em Physical Review}, Vol. IX, 1917, Natural and Magnetic Rotary Dispersion in the Infra-Red Spectrum,'' L. R. Ingersoll, p. 262. Description: Natural rotation in degrees per mm vs. wavelength; for quartz at 20$^{\circ}$ Centigrade. Reference Relation: $y=11.6064/(x^{2}-.010627) + 13.42/(x^{2}-78.22) - 4.3685/x^{2}$ Comments: The source gives two different formulas, but notes the one given here attains exceedingly good'' agreement with observations using parameters determined in previous work. --------------------------------------------- Case 111a x y 25.403 0.3120 21.739 0.2694 20.914 0.2595 15.139 0.1860 11.432 0.1425 8.873 0.1119 7.121 0.0890 6.123 0.0752 5.904 0.0724 4.918 0.0603 4.101 0.0516 3.515 0.0448 3.272 0.0418 3.030 0.0389 2.662 0.0341 2.348 0.0303 2.153 0.0277 2.070 0.0266 2.020 0.0259 1.827 0.0234 1.614 0.0205 1.431 0.0179 1.372 0.0169 Source: {\em Physical Review}, Vol. IX, 1917, Natural and Magnetic Rotary Dispersion in the Infra-Red Spectrum,'' L. R. Ingersoll, pp. 262 and 265, explanation on p. 268. Description: Magnetic rotation vs. natural rotation, both in degrees per mm; for quartz at 20$^{\circ}$ Centigrade. Reference Relation: $y=kx$ --------------------------------------------- Case 111b x y 13.915 3.571 9.665 2.475 9.220 2.363 6.482 1.639 4.950 1.229 3.825 0.938 3.024 0.747 2.500 0.622 2.059 0.522 1.734 0.445 1.509 0.383 1.325 0.342 1.191 0.308 0.870 0.232 0.780 0.208 Source: {\em Physical Review}, Vol. IX, 1917, Natural and Magnetic Rotary Dispersion in the Infra-Red Spectrum,'' L. R. Ingersoll, pp. 262 and 265, explanation on p. 268. Description: Magnetic rotation vs. natural rotation, both in degrees per mm; for limonene at 22$^{\circ}$ Centigrade. Reference Relation: $y=kx$ Comments: Residuals for the reference relation show a beautiful decaying periodic pattern. --------------------------------------------- Case 111c x y 5.716 3.252 3.968 2.292 3.818 2.196 2.708 1.463 2.066 1.119 1.606 0.870 1.286 0.702 1.058 0.573 0.876 0.495 0.742 0.433 0.640 0.365 0.542 0.303 0.500 0.273 0.408 0.232 0.380 0.222 Source: {\em Physical Review}, Vol. IX, 1917, Natural and Magnetic Rotary Dispersion in the Infra-Red Spectrum,'' L. R. Ingersoll, pp. 262 and 265, explanation on p. 268. Description: Magnetic rotation vs. natural rotation, both in degrees per mm; for pinene at 22$^{\circ}$ Centigrade. Reference Relation: $y=kx$ Comments: Regression of $y$ on $x$ shows the intercept is highly significant. --------------------------------------------- Case 112a x y 41.700 0.00220 13.700 0.00170 2.520 0.00147 1.350 0.00118 0.900 0.00080 0.476 0.00070 0.201 0.00050 Source: {\em Physical Review}, Vol. IX, 1917, On the Phosphorescence of the Uranyl Salts,'' Edward L. Nichols and H. L. Howes, p. 301. Description: Duration vs. intensity of excitation; for process 1. Reference Relation: $\ln x =ky$ Comments: The source says that $\ln x$ and $y$ are proportional, but it seems very clear that an intercept is necessary. --------------------------------------------- Case 112b x y 41.700 0.00400 13.700 0.00310 2.520 0.00240 1.350 0.00198 0.900 0.00170 0.476 0.00146 0.201 0.00110 Source: {\em Physical Review}, Vol. IX, 1917, On the Phosphorescence of the Uranyl Salts,'' Edward L. Nichols and H. L. Howes, p. 301. Description: Duration vs. intensity of excitation; for process 1+2. Reference Relation: $\ln x =ky$ Comments: The source says that $\ln x$ and $y$ are proportional, but it seems very clear that an intercept is necessary. --------------------------------------------- Case 113a x y 11 11.951 12 9.915 13 8.362 14 7.136 15 6.168 16 5.360 17 4.730 19 3.747 20 3.363 21 3.030 22 2.751 23 2.509 24 2.293 25 2.103 26 1.938 27 1.798 28 1.662 29 1.549 30 1.445 39 0.841 40 0.800 41 0.750 42 0.716 44 0.641 46 0.587 47 0.562 48 0.535 49 0.511 50 0.485 51 0.449 56 0.383 57 0.373 Source: {\em Physical Review}, Vol. IX, 1917, On the Nuclear Charge of Atoms,'' Fernando Sanford, pp. 385, 386. Description: Wavelength for K radiation, $\alpha$ line vs. atomic number. Reference Relation: $1/y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 113b x y 12 9.477 13 7.954 14 6.744 15 5.808 16 5.018 17 4.394 19 3.456 20 3.090 21 2.778 22 2.516 23 2.294 24 2.086 25 1.860 26 1.756 27 1.629 28 1.506 29 1.402 30 1.306 39 0.757 40 0.718 42 0.631 44 0.569 46 0.522 47 0.499 48 0.471 49 0.448 50 0.427 51 0.396 56 0.334 57 0.326 Source: {\em Physical Review}, Vol. IX, 1917, On the Nuclear Charge of Atoms,'' Fernando Sanford, pp. 385, 386. Description: Wavelength for K radiation, $\beta$ line vs. atomic number. Reference Relation: $1/y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 113c x y 40 6.091 41 5.749 42 5.432 44 4.861 45 4.662 46 4.385 47 4.170 50 3.619 51 3.458 57 2.676 58 2.567 59 2.471 60 2.382 62 2.208 63 2.130 64 2.057 66 1.914 68 1.790 73 1.525 74 1.486 76 1.397 77 1.354 78 1.316 79 1.287 79 1.280 80 1.243 81 1.209 82 1.179 83 1.144 90 0.971 92 0.919 Source: {\em Physical Review}, Vol. IX, 1917, On the Nuclear Charge of Atoms,'' Fernando Sanford, pp. 385, 386. Description: Wavelength for L radiation, principal line vs. atomic number. Reference Relation: $1/y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 114 x y 211.32 166667.3 332.04 203646.8 427.47 228606.6 565.05 260599.3 827.56 312389.2 1528.71 420908.5 Source: {\em Physical Review}, Vol. IX, 1917, On the Effect of Distributed Capacity in Single Layer Solenoids,'' J. C. Hubbard, p. 534. Description: Period vs. capacity of condenser; capacity seems to be measured in cm. Reference Relation: $y^{2}=k_{1}x+k_{2}$ Comments: The source tabulates the square of the period; I have converted back to the presumed original data. --------------------------------------------- Case 115 x y 2537 4.89 2852 4.35 3076 4.04 3260 3.81 4227 2.94 4608 2.69 5536 2.24 Source: {\em Physical Review}, Vol. IX, 1917, A Note on the Relation between Ionizing Potentials and Atomic Charges,'' Fernando Sanford, p. 575. Description: Ionizing potential vs. wavelength of single-line spectra for various elements. Reference Relation: $y=k_{1}/x^{.5}+k_{2}$ Comments: The simple relation $xy=k$ fits much better here than the reference relation. The data has been rearranged in order of increasing $x$ values. --------------------------------------------- Case 116 x y 1500 5.7 1700 10.8 1900 18.8 2100 30.6 2300 47.2 2500 69.7 2700 98.9 Source: {\em Physical Review}, Vol. X, 1917, The True Temperature Scale of Tungsten and its Emissive Powers at Incandescent Temperatures,'' A. G. Worthing, p. 393, explanation on p. 394. Description: Radiation intensity in watts/cm$^{2}$ vs. absolute temperature. Reference Relation: $\log y =k_{1}(\log x)^{2}+k_{2}\log x +k_{3}$ --------------------------------------------- Case 117 x y 10 110 20 442 30 830 40 1263 50 1745 60 2235 70 2713 80 3213 90 3712 Source: {\em Physical Review}, Vol. X, 1917, Theory of Crystal Structure, with Application to Twenty Crystals Belonging to the Cubic of Isometric System,'' Albert C. Crehore, p. 443. Description: See source for details. Reference Relation: $y=kx^{5/3}$ Comments: The reference relation shows clear lack of fit. --------------------------------------------- Case 118 x y 22 4.780e-06 22 4.760e-06 24 4.600e-06 41 5.020e-06 48 5.140e-06 60 5.330e-06 83 5.200e-06 86 5.560e-06 102 5.660e-06 104 5.880e-06 111 6.050e-06 138 6.500e-06 164 6.440e-06 170 6.970e-06 178 7.330e-06 211 7.930e-06 244 7.680e-06 245 8.070e-06 262 8.360e-06 282 8.730e-06 292 8.850e-06 296 8.440e-06 310 9.040e-06 343 9.580e-06 358 9.950e-06 358 9.870e-06 374 1.030e-05 384 1.036e-05 390 1.045e-05 397 1.059e-05 451 1.112e-05 452 1.123e-05 480 1.128e-05 500 1.205e-05 518 1.230e-05 524 1.208e-05 563 1.305e-05 568 1.280e-05 600 1.388e-05 600 1.380e-05 605 1.400e-05 608 1.376e-05 Source: {\em Physical Review}, Vol. X, 1917, The Specific Resistance and Thermo-Electric Power of Metallic Calcium,'' C. L. Swisher, p. 604. Description: Specific resistance of calcium vs. Centigrade temperature. Reference Relation: $y=k_{1}x+k_{2}$ Comments: I have combined data for three specimens as Swisher's figure shows he does. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 119 x y 54.0 9.80 57.4 9.80 61.0 9.50 69.0 9.70 69.5 9.20 86.0 10.20 91.0 9.70 92.7 8.40 93.0 8.80 93.0 8.50 93.7 9.00 94.7 8.60 94.7 9.00 120.0 10.40 124.0 10.80 125.0 9.80 128.0 9.70 129.0 10.30 130.0 9.20 131.0 10.60 131.2 9.70 145.0 11.10 146.6 10.40 147.0 10.30 148.0 10.60 158.0 9.10 158.5 10.40 166.5 9.90 167.0 10.30 170.0 10.70 170.0 10.60 192.0 11.90 192.0 11.00 192.5 11.20 192.5 10.10 193.5 10.10 194.0 12.00 194.0 10.70 196.0 10.80 219.0 10.85 221.4 10.70 221.4 10.60 225.0 11.10 227.0 11.90 242.0 13.70 242.7 13.60 245.0 11.60 247.0 11.50 249.0 12.50 250.0 12.60 257.0 11.70 257.0 11.70 286.0 11.50 287.0 11.70 293.5 12.10 294.0 12.30 299.0 11.70 300.0 12.90 300.0 13.00 302.0 11.90 304.0 11.80 337.0 13.00 337.5 13.00 338.0 15.40 363.5 13.50 363.5 13.50 389.0 13.00 389.5 13.00 394.0 14.90 396.0 14.70 405.0 13.40 406.0 13.30 406.0 13.30 Source: {\em Physical Review}, Vol. X, 1917, The Specific Resistance and Thermo-Electric Power of Metallic Calcium,'' C. L. Swisher, pp. 606--607. Description: Thermoelectric power of calcium against lead vs. Centigrade temperature. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 120 x y 20 0.00 22 1.25 24 2.75 26 4.80 28 7.30 30 9.60 32 12.65 34 15.20 36 18.50 40 23.40 Source: {\em Physical Review}, Vol. X, 1917, A New Method of X-Ray Crystal Analysis,'' A. W. Hull, p. 665. Description: Intensity of the K-alpha radiation line for molybdenum vs. voltage in kilovolts. Reference Relation: $y=k_{1}(x-k_{2})^{1.5}$ Comments: The reference relation shows clear lack of fit. --------------------------------------------- Case 121 x y 1e-06 28.183829 1e-06 64.565423 1e-06 6.025596 1e-02 446.683592 1e-02 316.227766 1e-02 436.515832 1e-01 1513.561248 1e-01 549.540874 1e-01 602.559586 1e+00 1995.262315 1e+00 1995.262315 1e+00 1995.262315 10.0000 5754.399000 10.0000 5011.872000 10.0000 4168.694000 199.5262 7413.102000 199.5262 7079.458000 199.5262 10000.000000 575.4399 12882.496000 575.4399 11481.536000 575.4399 12302.688000 8128.3052 15135.612000 8128.3052 14454.398000 8128.3052 104712.855000 Source: {\em Physical Review}, Vol. XI, 1918, The Brightness Sensibility of the Retina,'' Julian Blanchard, p. 192. Description: Glare vs. field brightness, both in millilamberts. Reference Relation: $y=kx^{.32}$ Comments: The source gives logarithms of both variables; I converted to get the presumed original data. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 122a x y 1.12 746 1.12 746 1.12 752 1.25 742 Source: {\em Physical Review}, Vol. XI, 1918, The Mobilities of Gaseous Ions,'' Kia-Lok Yen, pp. 346, 354, 355. Description: Pressure vs. mobility of positive ions; for air, 60 cycles, 119 volts. Reference Relation: $xy=k$ Comments: The relation appears to be claimed for both positive and negative mobilities. I have taken only the data for positive mobilities and then only the first four of six sets. --------------------------------------------- Case 122b x y 1.57 750 1.57 746 1.64 752 1.64 749 1.82 692 2.26 558 Source: {\em Physical Review}, Vol. XI, 1918, The Mobilities of Gaseous Ions,'' Kia-Lok Yen, pp. 346, 354, 355. Description: Pressure vs. mobility of positive ions; for air, 14,758 cycles, 5,000 volts. Reference Relation: $xy=k$ Comments: The relation appears to be claimed for both positive and negative mobilities. I have taken only the data for positive mobilities and then only the first four of six sets. --------------------------------------------- Case 122c x y 5.51 748 5.51 746 5.92 748 8.20 518 14.94 290 14.94 300 Source: {\em Physical Review}, Vol. XI, 1918, The Mobilities of Gaseous Ions,'' Kia-Lok Yen, pp. 346, 354, 355. Description: Pressure vs. mobility of positive ions; for air, 14,758 cycles, 4,000 volts. Reference Relation: $xy=k$ --------------------------------------------- Case 122d x y 5.28 748 5.50 746 6.60 600 8.95 498 13.90 300 22.91 198 Source: {\em Physical Review}, Vol. XI, 1918, The Mobilities of Gaseous Ions,'' Kia-Lok Yen, pp. 346, 354, 355. Description: Pressure vs. mobility of positive ions; for hydrogen, 60 cycles, no voltage given. Reference Relation: $xy=k$ --------------------------------------------- Case 123 x y 20000 0.710 25000 0.620 30000 0.555 35000 0.520 40000 0.500 50000 0.470 Source: {\em Physical Review}, Vol. XI, 1918, An Experimental Investigation of the Energy in the Continuous X-Ray Spectra of Certain Elements,'' Clayton T. Ulrey, p. 408. Description: Wavelength of maximum energy in angstrom units vs. voltage in volts. Reference Relation: $yx^{.5}=k$ --------------------------------------------- Case 124 x y 20000 0.615 25000 0.490 30000 0.405 35000 0.355 40000 0.310 50000 0.250 Source: {\em Physical Review}, Vol. XI, 1918, An Experimental Investigation of the Energy in the Continuous X-Ray Spectra of Certain Elements,'' Clayton T. Ulrey, p. 408. Description: Wavelength $\lambda_{0}$ in angstrom units vs. voltage in volts. Reference Relation: $xy=k$ --------------------------------------------- Case 125a x y 71.2 0.040 61.5 0.063 52.3 0.084 42.7 0.104 33.2 0.125 Source: {\em Physical Review}, Vol. XII, 1918, The Relation between the Specific Inductive Capacity of an Electrolyte and the Electric Potential of a Metal Placed in It,'' Dayton L. Ulrey, pp. 54--55. Description: Electromotive force in volts vs. specific inductive capacity; for solutions of methyl alcohol and water. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source cites a relation between $80.9-x$ and $y$, but $x$ is given here as the original measured quantity. The relation is the same in either case. --------------------------------------------- Case 125b x y 81.51 0.046 83.98 0.060 86.17 0.071 Source: {\em Physical Review}, Vol. XII, 1918, The Relation between the Specific Inductive Capacity of an Electrolyte and the Electric Potential of a Metal Placed in It,'' Dayton L. Ulrey, pp. 54--55. Description: Electromotive force in volts vs. specific inductive capacity; for solutions of urea and water. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source cites a relation between $80.9-x$ and $y$, but $x$ is given here as the original measured quantity. The relation is the same in either case. --------------------------------------------- Case 126a x y 13.4 0.300 23.0 0.393 37.5 0.500 57.0 0.610 76.0 0.710 96.0 0.790 115.0 0.880 140.0 0.960 Source: {\em Physical Review}, Vol. XII, 1918, Polarization Measurements of Wire Cathodes in Separately Ionized Bases,'' C. A. Skinner, p. 137; comments on limits of applicability, p. 137 and p. 138. Description: Current density vs. applied potential in volts; for plates. Reference Relation: $x=ky^{2}$ --------------------------------------------- Case 126b x y 6.5 0.405 12.8 0.580 22.0 0.780 36.3 0.980 55.5 1.180 75.0 1.380 94.0 1.560 113.5 1.700 133.0 1.900 Source: {\em Physical Review}, Vol. XII, 1918, Polarization Measurements of Wire Cathodes in Separately Ionized Bases,'' C. A. Skinner, p. 137; comments on limits of applicability, p. 137 and p. 138. Description: Current density vs. applied potential in volts; for wires. Reference Relation: $x=ky^{2}$ --------------------------------------------- Case 127a x y 0.160 140.0 0.210 159.0 0.255 171.0 0.305 180.0 0.350 188.0 0.400 195.0 0.445 200.0 0.495 205.0 0.550 208.0 0.585 209.5 0.630 210.0 Source: {\em Physical Review}, Vol. XII, 1918, Simplified Theory of the Cathode Fall in Bases with Application to Plates and Wires,'' C. A. Skinner, p. 151. Description: Potential drop between cathode and point, considered in volts, vs. radial distance from the axis of a wire in cm. Reference Relation: $y=k_{1}+k_{2}[\ln ((1+\sqrt{1-(x/k_{3})^{2}})/ (1-\sqrt{1-(x/k_{3})^{2}}))$$- \sqrt{1-(x/k_{3})^{2}}] Comments: More data sets are given than the three taken. --------------------------------------------- Case 127b x y 0.160 162.0 0.210 183.0 0.255 198.0 0.305 207.0 0.350 216.0 0.400 223.0 0.445 228.0 0.495 232.0 0.550 233.5 0.585 235.0 Source: {\em Physical Review}, Vol. XII, 1918, Simplified Theory of the Cathode Fall in Bases with Application to Plates and Wires,'' C. A. Skinner, p. 151. Description: Potential drop between cathode and point, considered in volts, vs. radial distance from the axis of a wire in cm. Reference Relation: y=k_{1}+k_{2}[\ln ((1+\sqrt{1-(x/k_{3})^{2}})/ (1-\sqrt{1-(x/k_{3})^{2}}))$$- \sqrt{1-(x/k_{3})^{2}}]$ Comments: More data sets are given than the three taken. --------------------------------------------- Case 127c x y 0.160 179.0 0.210 200.0 0.255 214.0 0.305 226.0 0.350 234.0 0.400 240.0 0.445 244.0 0.495 246.0 0.520 246.5 Source: {\em Physical Review}, Vol. XII, 1918, Simplified Theory of the Cathode Fall in Bases with Application to Plates and Wires,'' C. A. Skinner, p. 151. Description: Potential drop between cathode and point, considered in volts, vs. radial distance from the axis of a wire in cm. Reference Relation: $y=k_{1}+k_{2}[\ln ((1+\sqrt{1-(x/k_{3})^{2}})/ (1-\sqrt{1-(x/k_{3})^{2}}))$$- \sqrt{1-(x/k_{3})^{2}}]$ Comments: More data sets are given than the three taken. --------------------------------------------- Case 128a x y 20 0.0001301 60 0.0001151 120 0.0000982 180 0.0000855 240 0.0000756 300 0.0000678 Source: {\em Physical Review}, Vol. XII, 1918, The Magnetic Properties of some Rare Earth Oxides as a Function of Temperature,'' E. H. Williams, p. 161. Description: Magnetic susceptibility per unit mass vs. Centigrade temperature; for gadolinium oxide. Reference Relation: $(x+k_{1})y=k_{2}$ --------------------------------------------- Case 128b x y 20 0.0001891 60 0.0001672 120 0.0001426 180 0.0001244 240 0.0001101 300 0.0001022 Source: {\em Physical Review}, Vol. XII, 1918, The Magnetic Properties of some Rare Earth Oxides as a Function of Temperature,'' E. H. Williams, p. 161. Description: Magnetic susceptibility per unit mass vs. Centigrade temperature; for erbium oxide. Reference Relation: $(x+k_{1})y=k_{2}$ --------------------------------------------- Case 128c x y 20 0.0002341 60 0.0002074 120 0.0001767 180 0.0001539 240 0.0001366 300 0.0001226 Source: {\em Physical Review}, Vol. XII, 1918, The Magnetic Properties of some Rare Earth Oxides as a Function of Temperature,'' E. H. Williams, p. 161. Description: Magnetic susceptibility per unit mass vs. Centigrade temperature; for dysprosium oxide. Reference Relation: $(x+k_{1})y=k_{2}$ --------------------------------------------- Case 128d x y 23.0 2.93e-05 103.4 2.37e-05 179.4 1.98e-05 283.0 1.66e-05 Source: {\em Physical Review}, Vol. XII, 1918, The Magnetic Properties of some Rare Earth Oxides as a Function of Temperature,'' E. H. Williams, p. 161. Description: Magnetic susceptibility per unit mass vs. Centigrade temperature; for neodymium oxide. Reference Relation: $(x+k_{1})y=k_{2}$ --------------------------------------------- Case 129a x y 28.2 -6.0 38.2 -8.0 50.2 -10.6 59.2 -12.6 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 185. Description: Grid voltage vs. plate voltage; both in volts. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 129b x y 59.5 3.0 69.5 1.0 81.0 -1.2 90.0 -3.0 100.0 -5.0 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 185. Description: Grid voltage vs. plate voltage; both in volts. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 129c x y 830 0.00 905 -0.31 950 -0.48 1025 -0.80 1070 -0.98 1140 -1.28 1200 -1.54 1275 -1.85 1350 -2.15 1420 -2.45 1491 -2.75 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 185. Description: Grid voltage vs. plate voltage; both in volts. Reference Relation: $y=k_{1}x+k_{2}$ Comments: Second $y$ value corrected from .31 to $-.31$. It seems clear that this is a transcription or typographical error. --------------------------------------------- Case 130a x y 400 0.00044 500 0.00150 600 0.00310 650 0.00405 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 187. Description: Current in amps vs. voltage between filament and anode. Reference Relation: $y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 130b x y 140 0.00105 160 0.00250 180 0.00465 200 0.00705 210 0.00840 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 187. Description: Current in amps vs. voltage between filament and anode. Reference Relation: $y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 130c x y 160 0.00056 200 0.00240 220 0.00370 240 0.00525 260 0.00690 Source: {\em Physical Review}, Vol. XII, 1918, Theory of the Thermionic Amplifier,'' H. J. van der Bijl, p. 187. Description: Current in amps vs. voltage between filament and anode. Reference Relation: $y^{.5}=k_{1}x+k_{2}$ --------------------------------------------- Case 131a x y 1.780 867 1.800 858 1.838 847 1.911 810 Source: {\em Physical Review}, Vol. XII, 1918, On the Effect of a Transverse Magnetic Field on the Discharge through a Geissler Tube,'' James E. Ives, p. 301. Description: Potential in volts vs. current in milliamps for various magnetic field and resistance conditions. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 131b x y 1.800 854 1.800 861 1.854 824 1.935 775 Source: {\em Physical Review}, Vol. XII, 1918, On the Effect of a Transverse Magnetic Field on the Discharge through a Geissler Tube,'' James E. Ives, p. 301. Description: Potential in volts vs. current in milliamps for various magnetic field and resistance conditions. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 131c x y 1.792 863 1.800 852 1.841 819 1.898 765 Source: {\em Physical Review}, Vol. XII, 1918, On the Effect of a Transverse Magnetic Field on the Discharge through a Geissler Tube,'' James E. Ives, p. 301. Description: Potential in volts vs. current in milliamps for various magnetic field and resistance conditions. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 132 x y .1200 161.3333 .1362 163.2000 .1500 165.5000 .1525 166.5000 .2490 168.6333 .2830 171.9500 .3410 171.2000 .3970 174.1167 .4360 174.0833 .4570 175.7000 .4810 174.0000 .5500 174.9333 Source: {\em Physical Review}, Vol. XII, 1918, Law of Motion of a Droplet Moving with Variable Velocity in Air,'' Raymond B. Abbott, p. 387. Description: Angle of lead of electromotive force ahead of a falling droplet in degrees vs. wavelength. Reference Relation: $\tan y =k/x$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 133 x y 0.0861 1.1 0.1084 2.3 0.1250 3.4 0.1380 3.6 0.1820 6.4 0.2430 11.2 0.2460 12.8 0.3170 21.7 0.3500 24.2 0.3630 27.0 0.3810 31.4 0.4250 39.4 0.4510 42.3 0.4690 47.0 0.5200 56.8 0.6020 72.0 0.6120 73.5 0.7100 93.0 0.8120 120.1 0.9100 139.3 0.9110 141.0 1.0820 173.5 1.1810 195.0 1.3890 240.5 1.7150 317.8 1.9500 373.0 Source: {\em Physical Review}, Vol. XII, 1918, Law of Motion of a Droplet Moving with Variable Velocity in Air,'' Raymond B. Abbott, p. 392. Description: Distance fallen in cm vs. time of fall in seconds for a light sphere falling in air. Reference Relation: $y=k_{1}x+k_{2}(e^{-k_{3}x}-1)$ Comments: Next to last $y$ value corrected from 217.8 to 317.8 on the basis of a graph in the source. --------------------------------------------- Case 134a x y 0.1670 24.0 0.1410 21.5 0.1230 19.2 0.1120 17.5 0.1020 15.5 0.0972 14.5 0.0917 12.6 0.0907 11.8 Source: {\em Physical Review}, Vol. XIII, 1919, The Emission and Absorption of Photoelectrons by Platinum and Silver,'' Otto Stuhlman, Jr., p. 132. Description: Volume of metal in micron$^{2}$ (sic) vs. coefficient of absorption in cm$^{-1}$-micron$^{-2}$; for platinum. Reference Relation: $y^{3}=k_{1}x+k_{2}$ --------------------------------------------- Case 134b x y 0.099 29.5 0.083 26.0 0.070 23.0 0.059 20.0 0.050 17.5 0.043 12.8 Source: {\em Physical Review}, Vol. XIII, 1919, The Emission and Absorption of Photoelectrons by Platinum and Silver,'' Otto Stuhlman, Jr., p. 132. Description: Volume of metal in micron$^{2}$ (sic) vs. coefficient of absorption in cm$^{-1}$-micron$^{-2}$; for silver. Reference Relation: $y^{3}=k_{1}x+k_{2}$ --------------------------------------------- Case 135a x y 20 222.9 38 801.3 56 1690.5 88 4858.0 Source: {\em Physical Review}, Vol. XIII, 1919, The Logarithmic Law Connecting Atomic Number and Frequency Differences in Spectral Series,'' Gladys A. Anslow, p. 329. Description: Frequency difference vs. atomic number. Reference Relation: $\log y =k_{1}\log x +k_{2}$ Comments: The source gives ten sets; I have taken the first four. Note that, though $k_{1}$ is near 2, Anslow is not proposing $y=kx^{2}$. --------------------------------------------- Case 135b x y 20 105.99 38 394.44 56 878.40 88 2016.60 Source: {\em Physical Review}, Vol. XIII, 1919,The Logarithmic Law Connecting Atomic Number and Frequency Differences in Spectral Series,'' Gladys A. Anslow, p. 329. Description: Frequency difference vs. atomic number. Reference Relation: $\log y =k_{1}\log x +k_{2}$ Comments: The source gives ten sets; I have taken the first four. Note that, though $k_{1}$ is near 2, Anslow is not proposing $y=kx^{2}$. --------------------------------------------- Case 135c x y 12 92.00 30 872.40 48 2484.10 80 9835.06 Source: {\em Physical Review}, Vol. XIII, 1919, The Logarithmic Law Connecting Atomic Number and Frequency Differences in Spectral Series,'' Gladys A. Anslow, p. 329. Description: Frequency difference vs. atomic number. Reference Relation: $\log y =k_{1}\log x +k_{2}$ Comments: The source gives ten sets; I have taken the first four. Note that, though $k_{1}$ is near 2.5, Anslow is not proposing $y=kx^{2.5}$. --------------------------------------------- Case 135d x y 12 40.95 30 338.91 48 1171.05 80 4630.31 Source: {\em Physical Review}, Vol. XIII, 1919, The Logarithmic Law Connecting Atomic Number and Frequency Differences in Spectral Series,'' Gladys A. Anslow, p. 329. Description: Frequency difference vs. atomic number. Reference Relation: $\log y =k_{1}\log x +k_{2}$ Comments: The source gives ten sets; I have taken the first four. Note that, though $k_{1}$ is near 2.5, Anslow is not proposing $y=kx^{2.5}$. --------------------------------------------- Case 136a x y 0.792 4.67 0.599 3.48 0.311 1.63 0.241 1.18 Source: {\em Physical Review}, Vol. XIII, 1919, The Joule-Thompson Effect for Air at Moderate Temperatures and Pressures,'' L. G. Huxton, p. 467. Description: Bridge reading (which indicates a temperature drop) vs. pressure drop in meters. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives many data sets; I have taken the first four. --------------------------------------------- Case 136b x y 0.697 3.98 0.631 3.59 0.298 1.60 0.199 0.94 Source: {\em Physical Review}, Vol. XIII, 1919, The Joule-Thompson Effect for Air at Moderate Temperatures and Pressures,'' L. G. Huxton, p. 467. Description: Bridge reading (which indicates a temperature drop) vs. pressure drop in meters. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives many data sets; I have taken the first four. --------------------------------------------- Case 136c x y 0.726 4.07 0.620 3.46 0.310 1.63 0.255 1.32 Source: {\em Physical Review}, Vol. XIII, 1919, The Joule-Thompson Effect for Air at Moderate Temperatures and Pressures,'' L. G. Huxton, p. 467. Description: Bridge reading (which indicates a temperature drop) vs. pressure drop in meters. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives many data sets; I have taken the first four. --------------------------------------------- Case 136d x y 0.747 4.12 0.653 3.54 0.343 1.84 0.264 1.39 Source: {\em Physical Review}, Vol. XIII, 1919, The Joule-Thompson Effect for Air at Moderate Temperatures and Pressures,'' L. G. Huxton, p. 467. Description: Bridge reading (which indicates a temperature drop) vs. pressure drop in meters. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives many data sets; I have taken the first four. --------------------------------------------- Case 137 x y 10.0 1.9 13.0 4.1 16.1 6.2 19.0 8.1 22.2 9.9 25.0 12.0 27.9 13.9 30.0 16.0 33.7 18.4 36.6 19.4 39.5 22.0 Source: {\em Physical Review}, Vol. XIV, 1919, The Variation in Sound Intensity of Resonators and Organ Pipes with Blowing Pressure,'' Beryl F. Love and Margaret K. Dawson, p. 52. Description: Resonator deflection vs. water pressure, both measured in cm. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 138a x y 50 2.889 59 1.933 60 1.775 63 1.590 64 1.558 65 1.470 66 1.418 67 1.365 68 1.316 70 1.223 71 1.183 Source: {\em Physical Review}, Vol. XIV, 1919, Some Nuclear Charges Calculated for L-Radiation,'' Fernando Sanford, p. 177. Description: Wavelength of shortest line in L-radiation band for various elements vs. atomic number. Reference Relation: $x=k_{1}/y^{.5}+k_{2}$ --------------------------------------------- Case 138b x y 90 4.131e-08 83 5.125e-08 82 5.302e-08 81 5.471e-08 79 5.847e-08 78 6.058e-08 77 6.276e-08 76 6.508e-08 74 7.007e-08 73 7.272e-08 71 7.856e-08 70 8.162e-08 68 8.813e-08 67 9.168e-08 66 9.556e-08 Source: {\em Physical Review}, Vol. XIV, 1919, Formula for the Wave-Lengths of M-Radiation,'' Fernando Sanford, p. 276. Description: Wavelength of alpha-line of M-radiation band for various elements vs. atomic number. Reference Relation: $x=k_{1}/y^{.5}+k_{2}$ Comments: The observation for uranium is not included, since Sanford says it does not fit the reference relation. --------------------------------------------- Case 139 x y 598 2.8 1270 7.6 1820 16.3 2000 20.1 Source: {\em Physical Review}, Vol. XIV, 1919, The Bunsen Aspirating Pump and the Bernoulli Principle,'' Will C. Baker, p. 230. Description: Pressure in excess of atmospheric in cm of mercury vs. velocity in cm/sec. Reference Relation: $y=k_{1}x^{2}+k_{2}$ Comments: The relation $y=k_{1}x^{2.5}+k_{2}$ fits much better. --------------------------------------------- Case 140 x y 0.052 1.58 0.075 3.30 0.095 5.14 0.115 7.72 0.143 11.50 0.172 16.35 0.197 21.50 0.218 26.35 0.223 27.60 Source: {\em Physical Review}, Vol. XIV, 1919, A Note on the Comparison of Inductances, or of an Inductance and a Capacity by an Electromotor Method,'' Alva W. Smith, p. 358. Description: Deflection in cm vs. current in amps. Reference Relation: $y=kx^{2}$ --------------------------------------------- Case 141 x y 0.100 9.80 0.133 7.35 0.143 6.83 0.167 5.90 0.200 4.95 0.250 3.90 0.300 3.25 0.700 1.39 0.900 1.10 Source: {\em Physical Review}, Vol. XIV, 1919, A Note on the Comparison of Inductances, or of an Inductance and a Capacity by an Electromotor Method,'' Alva W. Smith, p. 358. Description: Deflection in cm vs. capacity in microfarads. Reference Relation: $xy=k$ --------------------------------------------- Case 142 x y 7 2.00 15 4.22 20 5.70 30 8.37 40 11.19 50 13.97 60 16.77 70 19.47 75 20.97 Source: {\em Physical Review}, Vol. XIV, 1919, A Note on the Comparison of Inductances, or of an Inductance and a Capacity by an Electromotor Method,'' Alva W. Smith, p. 358. Description: Deflection in cm vs. inductance in millihenrys. Reference Relation: $y=kx$ --------------------------------------------- Case 143 x y 100 0.00797 75 0.02400 50 0.09240 35 0.21400 20 0.48900 10 0.88600 0 1.86000 Source: {\em Physical Review}, Vol. XIV, 1919, Studies of the Adsorption of Gases by Charcoal. II.'' Harvey B. Lemon and Kathryn Blodgett, p. 399. Description: Final pressure vs. percentage oxygen in an oxygen-nitrogen mixture. Reference Relation: $\log y =k_{1}x+k_{2}$ Comments: Source notes a slight concavity (i.e. lack of fit) in the log-linear plot, but still concludes that the relation is very nearly exponential.'' --------------------------------------------- Case 144a x y 5.510e-06 90.0 3.746e-05 83.3 4.601e-05 81.8 5.419e-05 80.3 6.199e-05 79.0 Source: {\em Physical Review}, Vol. XIV, 1919, The Reflection Factors of Tungsten at Incandescent Temperatures,'' W. Weniger and A. H. Pfund, p. 427. Description: Reflection factor (a percentage) vs. resistivity in ohm-cm. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ --------------------------------------------- Case 144b x y 5.510e-06 93.8 3.746e-05 86.6 4.601e-05 85.0 5.419e-05 83.5 6.199e-05 82.3 Source: {\em Physical Review}, Vol. XIV, 1919, The Reflection Factors of Tungsten at Incandescent Temperatures,'' W. Weniger and A. H. Pfund, p. 427. Description: Reflection factor (a percentage) vs. resistivity in ohm-cm. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ --------------------------------------------- Case 145a x y 58 3.0680e-09 57 3.1880e-09 56 3.3070e-09 55 3.4440e-09 53 3.7370e-09 52 3.8960e-09 51 4.0650e-09 50 4.2420e-09 49 4.4340e-09 48 4.6320e-09 47 4.8500e-09 46 5.0750e-09 45 5.3300e-09 44 5.5840e-09 42 6.1800e-09 41 6.5030e-09 40 6.8720e-09 39 7.2550e-09 38 7.6960e-09 37 8.1430e-09 35 9.1790e-09 34 9.7900e-09 33 1.0435e-08 32 1.1146e-08 31 1.1902e-08 30 1.2963e-08 29 1.3785e-08 28 1.4890e-08 27 1.6018e-08 26 1.7396e-08 25 1.8892e-08 Source: {\em Physical Review}, Vol. XIV, 1919, On the X-Ray Absorption Frequencies Characteristic of the Chemical Elements,'' William Duane and Kang-Fuh-Hu, p. 520. Description: Wavelength vs. atomic number. Reference Relation: $1/y=(k_{1}+k_{2}x)/\sqrt{1-k_{3}(k_{1}+k_{2}x)^{2}}$ --------------------------------------------- Case 145b x y 24 2.067e-08 22 2.490e-08 20 3.072e-08 19 3.446e-08 17 4.391e-08 16 5.014e-08 15 5.804e-08 14 6.755e-08 13 7.982e-08 12 9.471e-08 Source: {\em Physical Review}, Vol. XIV, 1919, On the X-Ray Absorption Frequencies Characteristic of the Chemical Elements,'' William Duane and Kang-Fuh-Hu, p. 521. Description: Wavelength vs. atomic number. Reference Relation: $1/y=(k_{1}+k_{2}x)/\sqrt{1-k_{3}(k_{1}+k_{2}x)^{2}}$ --------------------------------------------- Case 146 x y 18 1.74 80 8.40 14 1.50 14 1.39 Source: {\em Physical Review}, Vol. XV, 1920, Studies with the Ionization Gage. II. Relation between Ionization Current at Constant Pressure and Number of Electrons per Molecule of Gas,'' S. Dushman and C. G. Found, p. 134. Description: Factor relating ionization current and unit electron current vs. number of electrons per molecule. Reference Relation: $y=kx$ --------------------------------------------- Case 147 x y 152.0 175 94.0 115 86.0 102 73.6 84 68.0 77 Source: {\em Physical Review}, Vol. XV, 1920, Cathode Fall in Neon,'' Arthur H. Compton and C. C. Van Voorhis, p. 496. Description: Minimum potential drop vs. normal cathode fall, both variables measured in volts. Reference Relation: $y=kx$ --------------------------------------------- Case 148a x y 2.240925 0.41 4.349561 0.95 6.418063 1.55 7.554219 1.85 9.749875 2.56 11.888232 3.36 12.981640 3.78 14.033686 4.22 14.714906 4.50 15.050000 4.75 15.872843 5.00 16.276777 5.28 17.305612 5.80 18.533440 6.20 19.429423 6.90 20.594347 7.20 Source: {\em Physical Review}, Vol. XVI, 1920, Ionization Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen and Mercury and Iodine Vapors,'' Clifton G. Found, p. 45. Description: Current in milliamps vs. voltage; for argon at very low pressure. Reference Relation: $y=k(x+.95)^{1.5}$ Comments: The source tabulates $(x+.95)^{1.5}$; I converted back to the presumed original data. --------------------------------------------- Case 148b x y 1.605453 0.31 3.816066 0.74 5.970312 1.29 8.120873 1.92 10.321545 2.68 12.562419 3.43 13.009683 3.64 13.537223 3.84 14.140924 4.08 14.732896 4.32 15.231621 4.52 15.722843 4.74 16.366876 5.00 16.842201 5.20 Source: {\em Physical Review}, Vol. XVI, 1920, Ionization Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen and Mercury and Iodine Vapors,'' Clifton G. Found, p. 45. Description: Current in milliamps vs. voltage; for nitrogen at very low pressure. Reference Relation: $y=k(x+1.1)^{1.5}$ Comments: The source tabulates $(x+1.1)^{1.5}$; I converted back to the presumed original data. --------------------------------------------- Case 148c x y 2.201927 0.57 4.400386 1.19 6.632008 1.96 8.768272 2.80 10.982761 3.68 12.652451 4.55 13.186609 4.85 13.883686 5.10 14.396010 5.40 14.900000 5.55 15.396173 5.82 16.526029 6.60 17.620754 7.38 Source: {\em Physical Review}, Vol. XVI, 1920, Ionization Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen and Mercury and Iodine Vapors,'' Clifton G. Found, p. 45. Description: Current in milliamps vs. voltage; for carbon monoxide at very low pressure. Reference Relation: $y=k(x+1.1)^{1.5}$ Comments: The source tabulates $(x+1.1)^{1.5}$; I converted back to the presumed original data. --------------------------------------------- Case 148d x y 2.489268 0.48 4.625504 0.95 6.751424 1.52 8.874100 2.18 10.596071 2.75 12.107709 3.32 13.186609 3.74 13.710961 3.96 14.226189 4.17 14.732896 4.38 15.066236 4.52 15.559908 4.72 16.366876 5.06 18.383440 5.92 Source: {\em Physical Review}, Vol. XVI, 1920, Ionization Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen and Mercury and Iodine Vapors,'' Clifton G. Found, p. 45. Description: Current in milliamps vs. voltage; for hydrogen at very low pressure. Reference Relation: $y=k(x+1.1)^{1.5}$ Comments: The source tabulates $(x+1.1)^{1.5}$; I converted back to the presumed original data. --------------------------------------------- Case 149 x y 2 0.0600 4 0.0420 6 0.0290 8 0.0260 12 0.0230 16 0.0200 22 0.0160 32 0.0120 45 0.0090 58 0.0075 70 0.0065 Source: {\em Physical Review}, Vol. XVI, 1920, The Existence of Homogeneous Groups of Large Ions,'' Oswald Blackwood, p. 98. Description: Mobility vs. age. Reference Relation: $xy^{3/2}=k$ --------------------------------------------- Case 150 x y 1630 6.25 1670 5.90 1740 5.50 1818 5.15 1890 4.85 1925 4.70 Source: {\em Physical Review}, Vol. XVI, 1920, Arcing Temperatures in Mercury as a Function of the Temperature of the Cathode,'' T. C. Hebb, p. 382. Description: Absolute temperature of cathode vs. striking voltage . Reference Relation: $y=k_{1}x+k_{2}$ Comments: Reference relation shows strong lack of fit. --------------------------------------------- Case 151 x y 340.0 19.35 407.6 15.35 564.3 10.20 883.0 5.12 2133.0 0.00 Source: {\em Physical Review}, Vol. XVI, 1920, Variation with Pressure of the Residual Ionization due to the Penetrating Radiation,'' K. Melvina Downey, p. 429. Description: Pressure in excess of atmospheric, measured in atmospheres, vs. time in seconds, an apparent proxy for ionization. Reference Relation: $y=k_{1}/x+k_{2}$ Comments: The source tabulates time in minutes and seconds; I converted to equivalent seconds. --------------------------------------------- Case 152a x y 64 0.021 128 0.023 256 0.026 512 0.032 1024 0.040 2048 0.052 4096 0.070 Source: {\em Physical Review}, Vol. XVI, 1920, The Absorption of Sound by Rigid Walls,'' Paul E. Sabine, p. 516. Description: Sound absorption coefficient vs. frequency; for 18 inch walls of hard brick set in mortar, unpainted. Reference Relation: $y=k_{1}x+k_{2}x^{.5}+k_{3}$ --------------------------------------------- Case 152b x y 128 0.0092 256 0.0097 512 0.0120 1024 0.0150 2048 0.0190 4096 0.0280 Source: {\em Physical Review}, Vol. XVI, 1920, The Absorption of Sound by Rigid Walls,'' Paul E. Sabine, p. 516. Description: Sound absorption coefficient vs. frequency; for 18 inch walls of hard brick set in mortar, standard gypsum plaster covering after 1 year. Reference Relation: $y=k_{1}x+k_{2}x^{.5}+k_{3}$ --------------------------------------------- Case 152c x y 128 0.0079 256 0.0084 512 0.0104 1024 0.0144 2048 0.0174 4096 0.0250 Source: {\em Physical Review}, Vol. XVI, 1920, The Absorption of Sound by Rigid Walls,'' Paul E. Sabine, p. 516. Description: Sound absorption coefficient vs. frequency; for 18 inch walls of hard brick set in mortar, standard gypsum plaster covering after 3 months. Reference Relation: $y=k_{1}x+k_{2}x^{.5}+k_{3}$ --------------------------------------------- Case 153a x y 0.314 0.176 0.373 0.195 0.422 0.218 0.471 0.228 Source: {\em Physical Review}, Vol. XVII, 1921, The Mass Absorption and Mass Scattering Coefficients for Homogeneous X Rays of Wavelength between .13 and 1.05 Angstrom Units in Water, Lithium, Carbon, Nitrogen, Oxygen, Aluminum, and Iron,'' C. W. Hewlett, p. 292, explanation of applicable range on p. 294. Description: Wavelength in angstrom units vs. absorption coefficient; for lithium. Reference Relation: $y=k_{1}x^{3}+k_{2}$ Comments: The source says the reference relation holds for wavelengths between .2 and .5 and only this data is collected here. The source gives seven data sets; I have taken the first four. --------------------------------------------- Case 153b x y 0.210 0.176 0.228 0.178 0.241 0.185 0.252 0.188 0.265 0.191 0.290 0.200 0.324 0.206 0.373 0.229 0.422 0.250 0.471 0.280 Source: {\em Physical Review}, Vol. XVII, 1921, The Mass Absorption and Mass Scattering Coefficients for Homogeneous X Rays of Wavelength between .13 and 1.05 Angstrom Units in Water, Lithium, Carbon, Nitrogen, Oxygen, Aluminum, and Iron,'' C. W. Hewlett, p. 292, explanation of applicable range on p. 294. Description: Wavelength in angstrom units vs. absorption coefficient; for carbon. Reference Relation: $y=k_{1}x^{3}+k_{2}$ Comments: The source says the reference relation holds for wavelengths between .2 and .5 and only this data is collected here. The source gives seven data sets; I have taken the first four. --------------------------------------------- Case 153c x y 0.203 0.178 0.252 0.195 0.301 0.225 0.350 0.251 Source: {\em Physical Review}, Vol. XVII, 1921, The Mass Absorption and Mass Scattering Coefficients for Homogeneous X Rays of Wavelength between .13 and 1.05 Angstrom Units in Water, Lithium, Carbon, Nitrogen, Oxygen, Aluminum, and Iron,'' C. W. Hewlett, p. 292, explanation of applicable range on p. 294. Description: Wavelength in angstrom units vs. absorption coefficient; for nitrogen. Reference Relation: $y=k_{1}x^{3}+k_{2}$ Comments: The source says the reference relation holds for wavelengths between .2 and .5 and only this data is collected here. The source gives seven data sets; I have taken the first four. --------------------------------------------- Case 153d x y 0.210 0.204 0.228 0.213 0.241 0.213 0.265 0.228 0.309 0.251 0.373 0.301 0.422 0.360 0.471 0.444 Source: {\em Physical Review}, Vol. XVII, 1921, The Mass Absorption and Mass Scattering Coefficients for Homogeneous X Rays of Wavelength between .13 and 1.05 Angstrom Units in Water, Lithium, Carbon, Nitrogen, Oxygen, Aluminum, and Iron,'' C. W. Hewlett, p. 292, explanation of applicable range on p. 294. Description: Wavelength in angstrom units vs. absorption coefficient; for water. Reference Relation: $y=k_{1}x^{3}+k_{2}$ Comments: The source says the reference relation holds for wavelengths between .2 and .5 and only this data is collected here. The source gives seven data sets; I have taken the first four. --------------------------------------------- Case 154 x y -181 213 -88 300 -16 378 26 425 Source: {\em Physical Review}, Vol. XVII, 1921, Note on the Characteristics of the New Singing Tube,'' Charles T. Knipp, p. 533. Description: Vibrations per second vs. Centigrade temperature at point B in Knipp's apparatus. Reference Relation: $y=k_{1}x+k_{2}$ Comments: Knipp's last observation is omitted here, since he says he is not sure it fits the reference relation. --------------------------------------------- Case 155 x y 60.0 12.00 63.9 9.30 65.1 8.90 66.1 8.45 68.4 7.80 71.1 7.10 74.4 6.30 78.1 5.45 80.9 5.00 84.2 4.70 88.5 4.30 93.6 3.85 100.4 3.40 109.9 2.95 123.0 2.50 141.0 2.00 168.0 1.55 205.0 1.10 Source: {\em Physical Review}, Vol. XVII, 1921, A Study of the Photo-Active Electrolytic Cell, Platinum-Rhodamine-B-Platinum,'' Carleton C. Murdock, p. 640. Description: Corrected galvanometer reading in cm vs. time of exposure in seconds. Reference Relation: $y=12-(x-60)/(.0844x+1.28)$ Comments: The source says the reference relation holds for the decay portion of the data $(x\geq60)$ and only this is included here. --------------------------------------------- Case 156 x y 503 0.000561 553 0.002270 605 0.009310 608 0.011200 652 0.061400 700 0.173000 Source: {\em Physical Review}, Vol. XVIII, 1921, Vapor Pressure of Metallic Calcium,'' Norman B. Pilling, p. 367. Description: Pressure in mm of mercury vs. Centigrade temperature. Reference Relation: $\log y =k_{1}/(273+x)+k_{2}$ Comments: The $R^{2}$ is higher for the simpler relation $\log y =k_{1}x+k_{2}$. --------------------------------------------- Case 157 x y 1000 0.57 1500 5.64 2000 24.20 2500 69.80 3000 161.00 3500 317.00 Source: {\em Physical Review}, Vol. XVIII, 1921, Total Emissive Powers and Resistivities of Tungsten at Incandescence,'' A. G. Worthing and W. E. Forsythe, p. 146. Description: Emissive power in watts/cm$^{2}$ vs. absolute temperature. Reference Relation: $\log y =k_{1}\log x +k_{2}/x+k_{3}$ Comments: A regression of $\log y$ on $\log x$ and $1/x$ shows both are significant. Contrast this with Case 49. --------------------------------------------- Case 158a x y 0.1 22.9 1.0 77.7 10.0 225.0 Source: {\em Physical Review}, Vol. XVIII, 1921, Conductivity of Flames Containing Salt Vapors,'' A. B. Bryan, p. 281. Description: Conductivity vs. concentration. Reference Relation: $y=k_{1}x^{.435}+k_{2}$ Comments: The source says the reference relation holds for high'' conductivities and only this data is included here. To determine what Bryan considered high, I consulted an associated graph in the source with a curve broken very clearly into a curved portion and a straight portion and took only points lying on the straight portion. --------------------------------------------- Case 158b x y 5e-03 1.69 2e-02 3.31 1e-01 6.36 1e+00 14.55 1e+01 37.70 5e+01 75.00 Source: {\em Physical Review}, Vol. XVIII, 1921, Conductivity of Flames Containing Salt Vapors,'' A. B. Bryan, p. 281. Description: Conductivity vs. concentration; for Na$_{2}$CO$_{3}$. Reference Relation: $y=k_{1}x^{.435}+k_{2}$ --------------------------------------------- Case 158c x y 0.04 12.25 0.40 55.00 4.00 155.50 Source: {\em Physical Review}, Vol. XVIII, 1921, Conductivity of Flames Containing Salt Vapors,'' A. B. Bryan, p. 281. Description: Conductivity vs. concentration; for CsCl. Reference Relation: $y=k_{1}x^{.435}+k_{2}$ Comments: The source says the reference relation holds for high'' conductivities and only this data is included here. To determine what Bryan considered high, I consulted an associated graph with a curve broken very clearly into a curved portion and a straight portion and took only points lying on the straight portion. --------------------------------------------- Case 159a x y 5 1.63 10 1.84 20 2.32 40 2.77 70 3.12 Source: {\em Physical Review}, Vol. XVIII, 1921, Conductivity of Flames Containing Salt Vapors,'' A. B. Bryan, p. 290. Description: Concentration vs. conductivity; for Al$_{2}$Cl$_{6}$. Reference Relation: $y^{2}-1=kx^{2/3}$ --------------------------------------------- Case 159b x y 5 1.46 10 1.71 20 1.90 30 1.99 Source: {\em Physical Review}, Vol. XVIII, 1921, Conductivity of Flames Containing Salt Vapors,'' A. B. Bryan, p. 290. Description: Concentration vs. conductivity; for H$_{3}$BO$_{3}$. Reference Relation: $y^{2}-1=kx^{2/3}$ --------------------------------------------- Case 160 x y 16.0 1.33333 17.0 1.33325 18.0 1.33317 19.0 1.33308 20.0 1.33298 22.0 1.33284 24.0 1.33262 26.0 1.33241 28.0 1.33220 30.0 1.33190 40.0 1.33049 44.0 1.32992 48.0 1.32928 50.0 1.32894 52.0 1.32858 55.0 1.32807 56.0 1.32799 58.0 1.32758 60.0 1.32716 62.0 1.32678 65.0 1.32616 70.0 1.32510 73.0 1.32444 77.0 1.32354 80.0 1.32284 81.0 1.32259 82.5 1.32218 85.0 1.32172 87.0 1.32123 90.0 1.32042 93.0 1.31973 95.0 1.31922 97.0 1.31878 98.4 1.31828 Source: {\em Physical Review}, Vol. XX, 1922, The Variation of the Index of Refraction of Water, Ethyl Alcohol, and Carbon Bisulphide, with the Temperature,'' Elmer E. Hall and Arthur R. Payne, p. 253. Description: Index of refraction of pure, gas-free water relative to air for sodium light vs. Centigrade temperature. Reference Relation: $y=k_{1}x^{4}+k_{2}x^{3}+k_{3}x^{2}+k_{4}x+k_{5}$ Comments: The source calls the reference relation an empirical formula, but rejects earlier empirical formulas as inadequate. --------------------------------------------- Case 161a x y 14 1.36290 16 1.36210 18 1.36129 20 1.36048 22 1.35967 24 1.35885 26 1.35803 28 1.35721 30 1.35639 32 1.35557 34 1.35474 36 1.35390 38 1.35306 40 1.35222 42 1.35138 44 1.35054 46 1.34969 48 1.34885 50 1.34800 52 1.34715 54 1.34629 56 1.34543 58 1.34456 60 1.34368 62 1.34279 64 1.34189 66 1.34096 68 1.34004 70 1.33912 72 1.33820 74 1.33728 76 1.33626 Source: {\em Physical Review}, Vol. XX, 1922, The Variation of the Index of Refraction of Water, Ethyl Alcohol, and Carbon Bisulphide, with the Temperature,'' Elmer E. Hall and Arthur R. Payne, p. 257. Description: Index of refraction of ethyl alcohol, relative to air, for sodium light vs. Centigrade temperature. Reference Relation: $y=k_{1}x^{3}+k_{2}x^{2}+k_{3}x+k_{4}$ Comments: The source calls the reference relation empirical. A residual plot shows that the data is not linear. --------------------------------------------- Case 161b x y 15 1.62935 16 1.62858 18 1.62704 20 1.62546 22 1.62387 24 1.62226 26 1.62064 28 1.61902 30 1.61740 32 1.61577 34 1.61413 36 1.61247 38 1.61080 40 1.60914 42 1.60748 44 1.60582 45 1.60499 Source: {\em Physical Review}, Vol. XX, 1922, The Variation of the Index of Refraction of Water, Ethyl Alcohol, and Carbon Bisulphide, with the Temperature,'' Elmer E. Hall and Arthur R. Payne, p. 257. Description: Index of refraction of carbon bisulfide, relative to air, for sodium light vs. Centigrade temperature. Reference Relation: $y=k_{1}x^{3}+k_{2}x^{2}+k_{3}x+k_{4}$ Comments: The source calls the reference relation empirical. A residual plot shows that the data is not linear. --------------------------------------------- Case 162 x y 118.99 2.64 119.66 2.90 143.34 3.34 144.06 3.31 168.36 3.88 169.33 3.98 187.19 4.34 196.01 4.45 196.98 4.63 222.03 5.12 223.28 5.31 234.83 5.51 235.88 5.57 273.91 6.43 275.29 6.49 Source: {\em Physical Review}, Vol. XXXI, 1910, The Rotary Power of Quartz, Cinnobar, and Nicotine at Low Temperature,'' F. A. Molby, pp. 295--6. Description: Decrease in rotation at $-188^{\circ}$ Centigrade vs. rotation at 20$^{\circ}$ Centigrade. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source calls observations for wavelengths of 404.7 and 670.8 uncertain and they are not included here. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 163 x y 0.0107 0.125 0.0126 0.162 0.0180 0.232 0.0307 0.385 0.0349 0.414 0.0372 0.448 0.0448 0.576 0.0467 0.563 0.0522 0.637 0.0674 0.807 Source: {\em Physical Review}, Vol. XXXI, 1910, Studies in Luminescence. XII. The Absorption of Alcoholic Solutions of Eosin and Resorufin,'' Edward L. Nichols and Ernest Merritt, p. 379. Description: Coefficient of absorption for resorufin in a concentrated solution vs. the coefficient in a dilute solution. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 164 x y 4.10 5.333 2.96 5.321 2.30 5.313 1.80 5.308 1.19 5.296 1.07 5.295 0.91 5.292 0.75 5.290 0.68 5.290 0.58 5.288 0.50 5.287 0.41 5.286 Source: {\em Physical Review}, Vol. XXXI, 1910, A Study of some of the Elastic Properties of a Platinum-Iridium Wire,'' L. P. Sieg, p. 442. Description: Period in seconds vs. amplitude in degrees. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source's data table includes the point (1.3,5.288), which seems to be an error. It would fit the reference relation neatly if corrected to (1.3,5.298), but since the observation also appears to have been dropped from an accompanying graph in the article, I have chosen to omit it rather than guess at a correction. --------------------------------------------- Case 165 x y 36.90 192.7 37.24 207.4 38.17 213.1 40.18 210.5 143.60 776.1 233.40 1188.0 308.60 1633.0 313.00 1693.0 349.80 1948.0 372.80 1941.0 380.60 1927.0 382.00 2042.0 384.50 2049.0 463.10 2535.0 525.40 2705.0 530.70 2740.0 710.00 3825.0 Source: {\em Physical Review}, Vol. XXXI, 1910, A Study of some of the Elastic Properties of a Platinum-Iridium Wire,'' L. P. Sieg, p. 454. Description: Torque in cgs units vs. torsional strain in degrees. Reference Relation: $y=kx$ --------------------------------------------- Case 166a x y 0.5302 0.380 0.5420 0.426 0.5720 0.549 0.5965 0.660 0.6130 0.760 0.6280 0.820 0.6420 0.880 0.6620 0.975 0.6790 1.070 0.6930 1.140 0.7076 1.220 0.7310 1.350 Source: {\em Physical Review}, Vol. XXXI, 1910, On the Initial Velocity of Electrons as a Function of the Wave-Length in the Photoelectric Effect,'' Jakob Kunz, p. 539. Description: Potential difference in volts vs. frequency. Reference Relation: $y=k_{1}x^{2}+k_{2}$ --------------------------------------------- Case 166b x y 0.5320 0.380 0.5420 0.428 0.5570 0.490 0.5710 0.550 0.5870 0.620 0.6010 0.682 0.6140 0.742 0.6310 0.824 0.6425 0.880 0.6570 0.955 0.6740 1.040 0.6810 1.080 0.6970 1.160 0.7070 1.210 0.7225 1.310 0.7310 1.350 Source: {\em Physical Review}, Vol. XXXI, 1910, On the Initial Velocity of Electrons as a Function of the Wave-Length in the Photoelectric Effect,'' Jakob Kunz, p. 539. Description: Potential difference in volts vs. frequency. Reference Relation: $y=k_{1}x^{2}+k_{2}$ --------------------------------------------- Case 167 x y 6.56e-05 24.76 6.28e-05 18.86 6.04e-05 14.88 5.83e-05 11.28 5.65e-05 8.65 5.48e-05 6.86 5.34e-05 5.90 5.22e-05 4.82 5.09e-05 4.20 4.98e-05 3.70 4.87e-05 2.84 4.77e-05 2.10 Source: {\em Physical Review}, Vol. XXX, 1910, Some Photo-Electric Properties of the Alkali Metals. III. The Dependence of Photo-Electric Current on the Wave-Length of the Incident Light,'' F. K. Richtmyer, p. 385. Description: Relative energy vs. wavelength. Reference Relation: $\log (x^{5}y) =k_{1}/x+k_{2}$ --------------------------------------------- Case 168 x y 750.0 2.07 547.4 2.79 316.0 4.93 215.3 7.49 Source: {\em Physical Review}, Vol. XXX, 1910, The Effect of Changes in the Pressure and Temperature of Gases upon the Mobility of the Negative Ions Produced by Ultraviolet Light,'' Alois F. Kovarik, p. 435. Description: Mobility vs. pressure. Reference Relation: $xy=k$ Comments: Only a small portion of the total range of the data---the portion for which the source says the reference relation holds---is included here. --------------------------------------------- Case 169 x y 698.0 5.600 648.0 5.500 570.0 4.480 540.0 4.350 503.0 4.020 468.0 3.940 463.0 3.730 428.0 3.680 416.0 3.380 409.0 3.320 388.0 2.920 378.0 2.770 360.0 2.640 340.0 2.620 335.0 2.500 300.0 2.100 296.0 2.050 268.0 1.800 237.0 1.540 202.0 1.130 180.0 0.870 149.0 0.622 84.5 0.222 Source: {\em Physical Review}, Vol. XXX, 1910, The Effect of Changes in the Pressure and Temperature of Gases upon the Mobility of the Negative Ions Produced by Ultraviolet Light,'' Alois F. Kovarik, p. 443. Description: Mobility at 760 mm vs. temperature. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 170a x y -25 11.030 -20 11.250 -15 11.475 -10 11.700 -5 11.935 0 12.173 5 12.420 10 12.660 15 12.920 20 13.173 25 13.435 30 13.700 35 13.965 40 14.240 45 14.520 50 14.800 55 15.080 60 15.385 65 15.690 70 16.000 75 16.320 Source: {\em Physical Review}, Vol. XXX, 1910, Note on the Relation between the Temperature and the Resistance of Nickel,'' C. F. Martin, p. 523. Description: Resistance vs. Centigrade temperature. Reference Relation: $\log y =k_{1}x+k_{2}$ Comments: I have taken only two of three data sets tabulated in the source, since Martin says the third fits the reference relation poorly. Note that Martin explictly states that he does not yet have enough evidence to claim a general law. He does seem to believe that the reference relation holds for the two data sets I have collected, however. The reference relation shows clear lack of fit. --------------------------------------------- Case 170b x y -27.70 70.72 -27.60 70.74 -24.60 71.64 -23.60 72.34 -23.60 71.92 -18.40 73.57 -12.90 75.39 -7.04 77.29 -5.95 77.65 8.40 82.42 8.80 82.54 9.00 82.61 9.20 82.70 11.38 83.44 23.76 87.70 24.05 87.82 Source: {\em Physical Review}, Vol. XXX, 1910, Note on the Relation between the Temperature and the Resistance of Nickel,'' C. F. Martin, p. 523. Description: Resistance vs. Centigrade temperature. Reference Relation: $\log y =k_{1}x+k_{2}$ Comments: I have taken only two of three data sets tabulated in the source, since Martin says the third fits the reference relation poorly. Note that Martin explictly states that he does not yet have enough evidence to claim a general law. He does seem to believe that the reference relation holds for the two data sets I have collected, however. --------------------------------------------- Case 171a x y 0.00366 3.4 0.00218 6.3 0.00217 6.6 0.00211 6.2 0.00205 6.9 0.00197 6.4 0.00195 7.9 0.00194 7.1 0.00191 8.5 0.00181 10.1 0.00178 8.0 0.00172 8.2 0.00169 8.8 0.00167 9.9 0.00165 10.6 0.00165 11.1 0.00156 11.4 0.00151 12.2 0.00147 11.4 0.00146 12.4 0.00145 13.4 0.00142 13.3 0.00130 15.6 0.00130 15.7 0.00124 16.8 0.00121 17.4 0.00119 13.0 0.00119 16.6 0.00117 13.6 0.00113 21.1 0.00105 22.5 0.00087 32.6 0.00075 47.3 0.00070 54.4 0.00069 54.9 0.00067 61.9 0.00067 62.7 0.00066 57.1 0.00064 60.6 0.00059 67.8 0.00058 75.8 0.00054 82.5 0.00050 97.3 0.00049 105.0 0.00049 113.0 0.00048 116.0 0.00046 120.0 0.00045 118.0 0.00044 152.0 0.00042 135.0 0.00041 144.0 0.00039 166.0 0.00038 184.0 0.00036 191.0 0.00035 166.0 0.00035 227.0 0.00035 231.0 Source: {\em Physical Review}, Vol. XXX, 1910, The Terminal Velocity of Fall of Small Spheres in Air,'' John Zeleny and L. W. McKeehan, pp. 551, 554 and 555. Description: Time of fall in seconds vs. radius of falling sphere of black wax in cm. Reference Relation: $yx^{2}=k$ --------------------------------------------- Case 171b x y 0.001075 1.6 0.001030 1.6 0.000880 3.2 0.000830 1.9 0.000826 2.5 0.000736 4.0 0.000640 5.7 0.000640 4.7 0.000508 10.6 0.000506 7.0 0.000465 9.8 0.000449 11.3 0.000437 12.4 0.000428 10.5 0.000428 10.8 0.000422 13.8 0.000413 13.0 0.000370 20.8 0.000349 23.3 0.000338 12.5 0.000324 25.6 0.000324 25.6 0.000322 25.5 0.000318 20.9 0.000314 25.8 0.000314 21.0 0.000309 20.7 0.000277 35.4 0.000275 28.3 0.000274 25.8 0.000273 28.3 0.000267 25.8 0.000267 30.3 0.000254 28.3 0.000252 30.2 0.000239 47.0 0.000238 47.1 0.000234 61.8 0.000233 44.4 0.000225 33.4 0.000223 62.3 0.000222 48.1 0.000216 38.0 0.000215 52.1 0.000205 83.6 0.000194 41.5 0.000188 80.7 0.000186 64.1 0.000185 67.6 0.000181 48.7 0.000179 58.3 0.000177 56.8 0.000174 89.9 0.000170 82.3 0.000165 76.3 0.000164 64.7 0.000159 55.2 Source: {\em Physical Review}, Vol. XXX, 1910, The Terminal Velocity of Fall of Small Spheres in Air,'' John Zeleny and L. W. McKeehan, pp. 551, 554 and 555. Description: Time of fall in seconds vs. radius of falling sphere of mercury in cm. Reference Relation: $yx^{2}=k$ --------------------------------------------- Case 171c x y .004150 1.50 .003720 3.20 .003690 2.50 .003540 3.40 .003430 3.75 .003280 2.65 .003270 3.80 .003240 4.10 .003170 3.50 .003130 3.30 .003090 3.20 .003070 4.15 .003020 3.90 .003000 3.00 .002785 3.80 .002780 3.85 .002780 4.30 .002740 5.30 .002720 5.30 .002670 4.75 .002600 3.75 .002560 4.90 .002560 1.80 .002550 4.80 .002470 5.30 .002470 5.90 .002440 6.70 .002420 5.10 .002400 5.85 .002300 5.25 .002230 6.60 .002210 6.30 .002200 6.50 .002160 7.30 .002140 6.70 .002060 7.30 .002020 8.55 .002000 7.43 .002000 7.40 .001800 8.70 .001790 9.05 .001725 10.95 .001645 10.05 .001630 10.60 .001610 11.50 .001570 12.50 .001554 12.1 .001535 11.3 .001520 14.2 .001420 15.2 .001400 15.6 .001350 18.8 .001230 18.1 .001220 22.5 .001170 21.3 .001160 20.7 .001160 20.2 .001145 24.6 .001090 27.3 .001060 25.7 .001035 29.6 .000965 30.4 .000862 45.7 .000850 38.6 .000665 77.7 .000579 92.1 .000527 106.0 .000500 123.2 Source: {\em Physical Review}, Vol. XXX, 1910, The Terminal Velocity of Fall of Small Spheres in Air,'' John Zeleny and L. W. McKeehan, pp. 551, 554 and 555. Description: Time of fall in seconds vs. radius of falling sphere of paraffin in cm. Reference Relation: $yx^{2}=k$ --------------------------------------------- Case 172 x y 0 -0.248 1 -0.217 2 -0.172 3 -0.126 4 -0.080 5 -0.044 7 0.039 8 0.080 9 0.117 Source: {\em Physical Review}, Vol. XXX, 1910, The Dependence of the Photo-Electric Current on Light Intensity,'' F. K. Richtmyer, p. 77. Description: Rate of charge at electrical zero in mm/sec vs. potential difference in arbitrary units. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 173a x y 0.0100 0.318 0.0236 0.646 0.0400 1.033 0.0625 1.573 0.0816 2.055 0.1110 2.682 0.1310 3.200 0.1600 3.930 0.1970 4.800 0.2970 7.510 0.3870 9.790 0.7600 18.530 Source: {\em Physical Review}, Vol. XXIX, 1909, The Dependence of Photo-Electric Current on Light Intensity,'' F. K. Richtmyer, p. 80. Description: Photoelectric current in deflections/sec vs. light intensity. Reference Relation: $y=kx$ --------------------------------------------- Case 173b x y 19 5.90e-09 30 8.70e-09 45 1.25e-08 63 1.64e-08 84 2.26e-08 118 3.14e-08 155 3.88e-08 210 5.26e-08 304 7.95e-08 375 9.75e-08 475 1.23e-07 620 1.60e-07 Source: {\em Physical Review}, Vol. XXIX, 1909, On the Photo-Electric Effect with the Alkali Metals. II. The Dependence of Photo-Electric Current on Light Intensity,'' F. K. Richtmyer, p. 407. Description: Photoelectric current in amps vs. light intensity in foot-candles. Reference Relation: $y=kx$ --------------------------------------------- Case 174 x y 1.90 4.38 2.50 5.78 3.20 7.60 3.22 7.91 3.80 8.96 5.05 12.40 5.05 12.27 5.08 12.15 5.08 12.15 5.10 12.25 5.10 12.30 6.55 16.15 7.78 18.18 10.25 24.60 Source: {\em Physical Review}, Vol. XXIX, 1909, A Systematic Study of Vibrators and Receivers for Short Electrical Waves,'' Harold W. Webb and L. E. Woodman, p. 106. Description: Wavelength in cm vs. length of rod in cm. Reference Relation: $y=kx$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 175 x y 1.27 8.9 1.59 10.4 1.91 11.4 2.22 12.8 2.54 14.7 3.18 17.8 Source: {\em Physical Review}, Vol. XXIX, 1909, A Systematic Study of Vibrators and Receivers for Short Electrical Waves,'' Harold W. Webb and L. E. Woodman, p. 110. Description: Wavelength vs. diameter of sphere, both in cm. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source says the reference relation holds for wavelengths between 7 and 20 cm and only this data has been included. --------------------------------------------- Case 176a x y 15.8 207 12.2 114 9.1 62 7.7 51 Source: {\em Physical Review}, Vol. XXIX, 1909, A Systematic Study of Vibrators and Receivers for Short Electrical Waves,'' Harold W. Webb and L. E. Woodman, p. 114. Description: Energy vs. wavelength; for a rod vibrator. Reference Relation: $y/x^{2}=k$ --------------------------------------------- Case 176b x y 17.8 440 12.8 210 10.4 180 8.9 110 Source: {\em Physical Review}, Vol. XXIX, 1909, A Systematic Study of Vibrators and Receivers for Short Electrical Waves,'' Harold W. Webb and L. E. Woodman, p. 114. Description: Energy vs. wavelength; for a Righi vibrator. Reference Relation: $y/x^{2}=k$ --------------------------------------------- Case 177 x y 527.0 166.00 512.5 181.50 494.5 200.90 465.0 234.03 454.0 248.40 443.0 263.20 429.0 279.00 420.0 286.50 Source: {\em Physical Review}, Vol. XXIX, 1909, On the Photoelectric Effect of Sodium-Potassium Alloy and its Bearing on the Structure of the Ether,'' Jakob Kunz, p. 226. Description: Potential of alloy vs. wavelength. Reference Relation: $y=k_{1}x+k_{2}$ Comments: I have corrected the second $x$ value from 712.5 to 512.5 on the basis of an accompanying graph. The source says the reference relation holds up to about'' $\lambda=520$; this appears to correspond to the observations for which the source compares observed and calculated values and only these have been included here. --------------------------------------------- Case 178a x y 9050 0.00169 10100 0.00211 10900 0.00246 11750 0.00293 13750 0.00389 Source: {\em Physical Review}, Vol. XXIX, 1909, Dispersion of Magnetic Double Refraction in Liquids Compared with that of Electric Double Refraction,'' C. A. Skinner, p. 543. Description: Retardation vs. field; for nitro benzol, wavelength=500 microns. Reference Relation: $y/x^{2}=k$ --------------------------------------------- Case 178b x y 9000 0.00115 9950 0.00138 10900 0.00163 11750 0.00196 13750 0.00257 Source: {\em Physical Review}, Vol. XXIX, 1909, Dispersion of Magnetic Double Refraction in Liquids Compared with that of Electric Double Refraction,'' C. A. Skinner, p. 543. Description: Retardation vs. field; for nitro toluol, wavelength=500 microns. Reference Relation: $y/x^{2}=k$ --------------------------------------------- Case 178c x y 8900 0.00171 10050 0.00219 10850 0.00260 11750 0.00304 13800 0.00415 Source: {\em Physical Review}, Vol. XXIX, 1909, Dispersion of Magnetic Double Refraction in Liquids Compared with that of Electric Double Refraction,'' C. A. Skinner, p. 543. Description: Retardation vs. field; for a-mono-bromo-napthalene, wavelength=500 microns. Reference Relation: $y/x^{2}=k$ Comments: I have corrected the decimal point in two observations where it appears to be a clear typographic error. --------------------------------------------- Case 179a x y 22.6 .0001848 23.0 .0001849 23.7 .0001845 24.0 .0001835 24.8 .0001845 25.3 .0001915 25.7 .0001829 220.2 .0002735 347.0 .0003008 479.3 .0003222 481.7 .0003519 489.4 .0003562 496.9 .0003607 498.0 .0003551 501.2 .0003606 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Coefficients of Gas Viscosity. II,'' Willard J. Fisher, p. 104. Description: Viscosity vs. Centigrade temperature; for air. Reference Relation: $y^{1.5}/(x+273)=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 179b x y 25.0 .0001498 26.2 .0001517 75.8 .0001739 141.6 .0001970 183.1 .0002161 224.4 .0002348 289.9 .0002610 413.6 .0003073 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Coefficients of Gas Viscosity. II,'' Willard J. Fisher, p. 104. Description: Viscosity vs. Centigrade temperature; for N$_{2}$O. Reference Relation: $y^{1.5}/(x+273)=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 180 x y 116.2 1.672 112.5 1.662 106.8 1.643 102.1 1.630 100.0 1.623 97.5 1.621 97.1 1.614 96.7 1.610 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Dispersion of Electric Double Refraction,'' T. H. Havelock, p. 138. Description: Index of refraction vs. dispersion of double refraction. Reference Relation: $xy/(y^{2}-1)^{2}=k$ Comments: A simple linear relationship fits just as well. --------------------------------------------- Case 181a x y 0 1.0000 2 0.9738 42 0.9970 87 0.9828 107 0.9626 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Effect of Torsion on Thermal and Electrical Conductivity,'' Newland F. Smith, pp. 434--436. Description: Ratio of thermal conductivity after twist to conductivity before vs. angle of twist in degrees; for a steel bar. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. The source gives many data sets; I have taken the first for each material. --------------------------------------------- Case 181b x y 0 1.0000 24 0.9951 45 0.9971 58 0.9890 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Effect of Torsion on Thermal and Electrical Conductivity,'' Newland F. Smith, pp. 434--436. Description: Ratio of thermal conductivity after twist to conductivity before vs. angle of twist in degrees; for an iron bar. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. The source gives many data sets; I have taken the first for each material. --------------------------------------------- Case 181c x y 0 1.0000 29 0.9950 72 0.9856 112 0.9799 134 0.9756 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Effect of Torsion on Thermal and Electrical Conductivity,'' Newland F. Smith, pp. 434--436. Description: Ratio of thermal conductivity after twist to conductivity before vs. angle of twist in degrees; for a copper bar. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. The source gives many data sets; I have taken the first for each material. --------------------------------------------- Case 181d x y 0 1.0000 25 0.9807 47 0.9874 107 0.9626 118 0.9626 Source: {\em Physical Review}, Vol. XXVIII, 1909, The Effect of Torsion on Thermal and Electrical Conductivity,'' Newland F. Smith, pp. 434--436. Description: Ratio of thermal conductivity after twist to conductivity before vs. angle of twist in degrees; for a brass bar. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The data have been rearranged in order of increasing $x$ values. The source gives many data sets; I have taken the first for each material. --------------------------------------------- Case 182a x y 312000 2.0 356000 2.5 378000 3.0 390000 3.5 420000 5.2 Source: {\em Physical Review}, Vol. XXVII, 1908, The Frequency of the Singing Arc,'' George W. Nasmyth, pp. 134--135. Description: Arc current vs. frequency. Reference Relation: $x^{2}=k_{1}/y^{2}+k_{2}$ Comments: The source gives six tables; I have taken the first four. --------------------------------------------- Case 182b x y 315000 2.1 356000 2.8 365000 3.0 379000 3.5 Source: {\em Physical Review}, Vol. XXVII, 1908, The Frequency of the Singing Arc,'' George W. Nasmyth, pp. 134--135. Description: Arc current vs. frequency. Reference Relation: $x^{2}=k_{1}/y^{2}+k_{2}$ Comments: The source gives six tables; I have taken the first four. --------------------------------------------- Case 182c x y 316000 4.2 355000 5.0 371000 5.8 Source: {\em Physical Review}, Vol. XXVII, 1908, The Frequency of the Singing Arc,'' George W. Nasmyth, pp. 134--135. Description: Arc current vs. frequency. Reference Relation: $x^{2}=k_{1}/y^{2}+k_{2}$ Comments: The source gives six tables; I have taken the first four. --------------------------------------------- Case 182d x y 217000 1.0 236000 1.5 263000 2.0 274000 2.5 289000 3.0 295000 4.0 Source: {\em Physical Review}, Vol. XXVII, 1908, The Frequency of the Singing Arc,'' George W. Nasmyth, pp. 134--135. Description: Arc current vs. frequency. Reference Relation: $x^{2}=k_{1}/y^{2}+k_{2}$ Comments: The source gives six tables; I have taken the first four. --------------------------------------------- Case 183a x y 525 4.972 551 4.931 565 4.911 593 4.869 615 4.836 Source: {\em Physical Review}, Vol. XXVII, 1908, On the Conductance and Fluidity of Fused Salts,'' H. M. Goodwin and H. T. Kalmus, pp. 324--325. Description: Density of PbCl$_{2}$ referred to H$_{2}$O at 4$^{\circ}$ Centigrade vs. temperature. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 183b x y 373 5.820 398 5.779 420 5.738 488 5.609 Source: {\em Physical Review}, Vol. XXVII, 1908, On the Conductance and Fluidity of Fused Salts,'' H. M. Goodwin and H. T. Kalmus, pp. 324--325. Description: Density of PbBr$_{2}$ referred to H$_{2}$O at 4$^{\circ}$ Centigrade vs. temperature. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 183c x y 411 2.289 433 2.274 477 2.246 510 2.216 Source: {\em Physical Review}, Vol. XXVII, 1908, On the Conductance and Fluidity of Fused Salts,'' H. M. Goodwin and H. T. Kalmus, pp. 324--325. Description: Density of K$_{2}$Cr$_{2}$O$_{7}$ referred to H$_{2}$O at 4$^{\circ}$ Centigrade vs. temperature. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 184 x y 12.99 0.1188 14.47 0.1258 15.70 0.1328 16.92 0.1407 18.19 0.1514 19.41 0.1567 20.66 0.1664 21.88 0.1774 22.45 0.1892 24.41 0.2022 26.19 0.2158 27.09 0.2322 Source: {\em Physical Review}, Vol. XXVII, 1908, On the Conductance and Fluidity of Fused Salts,'' H. M. Goodwin and H. T. Kalmus, p. 317. Description: Equivalent fluidity vs. equivalent conductance. Reference Relation: $y=kx$ Comments: In the source, $x/y$ is tabulated and found to be relatively constant; hence, this is an example of real scientists using a Bacon-style invariant. --------------------------------------------- Case 185 x y 37.3 0.70 70.5 3.09 96.9 5.70 Source: {\em Physical Review}, Vol. XXVII, 1908, An Investigation of the Electric Intensities and Electric Displacement Produced in Insulators by their Motion in a Magnetic Field,'' S. J. Barnett, p. 461. Description: Deflection in units of 2 cm vs. speed in rotations per second. Reference Relation: $y=kx^{2}$ --------------------------------------------- Case 186a x y 337.0 39.4 353.0 43.6 356.0 43.8 357.0 44.1 385.2 50.2 406.0 56.2 495.0 75.7 Source: {\em Physical Review}, Vol. XXVI, 1908, On the Density, Electrical Conductivity and Viscosity of Fused Salts and their Mixtures,'' H. M. Goodwin and R. D. Mailey, pp. 48ff. Description: Fluidity vs. temperature; for sodium nitrate. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 186b x y 347 35.8 371 42.5 377 43.5 396 46.7 418 52.9 462 62.9 506 74.4 Source: {\em Physical Review}, Vol. XXVI, 1908, On the Density, Electrical Conductivity and Viscosity of Fused Salts and their Mixtures,'' H. M. Goodwin and R. D. Mailey, pp. 48ff. Description: Fluidity vs. temperature; for potassium nitrate. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 186c x y 259.0 17.9 269.0 19.6 274.0 20.6 284.0 22.2 310.0 27.1 317.5 28.6 319.0 28.7 320.0 28.8 344.0 34.0 Source: {\em Physical Review}, Vol. XXVI, 1908, On the Density, Electrical Conductivity and Viscosity of Fused Salts and their Mixtures,'' H. M. Goodwin and R. D. Mailey, pp. 48ff. Description: Fluidity vs. temperature; for lithium nitrate. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 186d x y 244.0 26.5 265.5 30.5 275.0 32.8 309.0 38.3 342.0 43.5 Source: {\em Physical Review}, Vol. XXVI, 1908, On the Density, Electrical Conductivity and Viscosity of Fused Salts and their Mixtures,'' H. M. Goodwin and R. D. Mailey, pp. 48ff. Description: Fluidity vs. temperature; for silver nitrate. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 187a x y 3000 2.8 4000 13.6 5000 28.3 6000 50.9 7000 73.5 8000 104.5 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 131. Description: Current in $10^{-7}$ amps vs. potential in volts. Reference Relation: $y=k_{1}x(x+k_{2})$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 187b x y 3000 2.3 3500 6.8 4000 13.6 5000 28.8 6000 50.3 7000 76.3 8000 104.5 8500 125.4 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 131. Description: Current in $10^{-7}$ amps vs. potential in volts. Reference Relation: $y=k_{1}x(x+k_{2})$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 187c x y 3500 5.7 4000 11.9 5000 26.6 6000 49.2 7000 73.5 8000 101.7 8350 118.1 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 131. Description: Current in $10^{-7}$ amps vs. potential in volts. Reference Relation: $y=k_{1}x(x+k_{2})$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 187d x y 3500 4.5 4000 10.7 5000 26.0 6000 47.5 7000 73.4 8000 102.3 9000 141.2 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 131. Description: Current in $10^{-7}$ amps vs. potential in volts. Reference Relation: $y=k_{1}x(x+k_{2})$ Comments: The source gives six data sets; I have taken the first four. --------------------------------------------- Case 188 x y 0.060 2825 0.107 3125 0.336 4500 0.464 5000 0.640 5850 1.090 7525 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 140. Description: Minimum potential to start flow of current, in volts, vs. diameter of point in mm. Reference Relation: $y=k_{1}+k_{2}x^{2/3}$ --------------------------------------------- Case 189 x y 0.0068 2615 0.0120 2665 0.0550 2860 0.0960 2985 0.1980 3505 0.3640 4320 Source: {\em Physical Review}, Vol. XXVI, 1908, The Discharge of Electricity from Pointed Conductors,'' John Zeleny, p. 134. Description: Minimum potential to start flow of current, in volts, vs. diameter of point in mm. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 190a x y 2.049 129.9 1.750 264.1 1.550 341.1 1.500 381.0 1.280 491.2 0.637 743.0 0.493 808.0 0.291 920.0 Source: {\em Physical Review}, Vol. XXVI, 1908, The Heat Dilution of Aqueous Salt Solutions,'' F. L. Bishop, p. 174. Description: Total heat absorbed when that quantity of solution containing one mol was diluted from the highest concentration to the one in question (Col. IX in the source's data table) vs. concentration of solution after adding water (Col. IV). Reference Relation: $y=k_{1}x+k_{2}$ Comments: Bishop explicitly states that he does not believe the relation will hold outside the given range of concentrations. Also, his comments and a graph suggest he does not believe the relation holds even within the given range for potassium chloride, which was therefore not taken. This is for potassium nitrate. --------------------------------------------- Case 190b x y 0.400 594.0 0.409 581.0 0.593 507.0 1.040 355.0 1.500 189.2 1.510 185.1 Source: {\em Physical Review}, Vol. XXVI, 1908, The Heat Dilution of Aqueous Salt Solutions,'' F. L. Bishop, p. 174. Description: Total heat absorbed when that quantity of solution containing one mol was diluted from the highest concentration to the one in question (Col. IX in the source's data table) vs. concentration of solution after adding water (Col. IV). Reference Relation: $y=k_{1}x+k_{2}$ Comments: Bishop explicitly states that he does not believe the relation will hold outside the given range of concentrations. Also, his comments and a graph suggest he does not believe the relation holds even within the given range for potassium chloride, which was therefore not taken. This is for sodium nitrate. --------------------------------------------- Case 190c x y 0.137 450 0.191 409 0.286 319 0.360 170 0.503 153 0.506 144 0.510 138 Source: {\em Physical Review}, Vol. XXVI, 1908, The Heat Dilution of Aqueous Salt Solutions,'' F. L. Bishop, p. 174. Description: Total heat absorbed when that quantity of solution containing one mol was diluted from the highest concentration to the one in question (Col. IX in the source's data table) vs. concentration of solution after adding water (Col. IV). Reference Relation: $y=k_{1}x+k_{2}$ Comments: Bishop explicitly states that he does not believe the relation will hold outside the given range of concentrations. Also, his comments and a graph suggest he does not believe the relation holds even within the given range for potassium chloride, which was therefore not taken. This is for barium nitrate. --------------------------------------------- Case 191 x y 80.0 12 60.0 27 50.0 39 40.0 51 30.0 68 25.0 79 20.0 93 12.5 117 Source: {\em Physical Review}, Vol. XXVI, 1908, Radioactivity of a Smoke Laden Atmosphere,'' S. J. Allen, p. 489. Description: Time in minutes to reach various given intensities vs. the intensities as a percent of intensity at time zero Reference Relation: $x=k_{1}k_{2}^{y}$ Comments: Many curves are given in the source, but this is singled out as the only one which is truly exponential.'' --------------------------------------------- Case 192 x y 372.12 96.00 371.00 95.75 293.00 73.35 273.00 67.61 83.00 11.99 77.50 10.47 Source: {\em Physical Review}, Vol. XXVI, 1908, Coefficient of Linear Expansion at Low Temperatures,'' Herbert G. Dorsey, p. 93. Description: Resistance in ohms vs. absolute temperature. Reference Relation: $y=k_{1}x^{2}+k_{2}x+k_{3}$ Comments: The source makes clear that this is just an empirical curve to be used for interpolation. --------------------------------------------- Case 193 x y 16.80 32.5 15.50 29.5 14.20 28.2 12.50 24.2 10.90 21.2 9.40 17.2 7.40 14.7 5.40 11.0 2.75 6.0 0.65 1.6 Source: {\em Physical Review}, Vol. XXV, 1907, A Study of the Propagation and Interception of Energy in Wireless Telegraphy. Part I,'' Charles A. Culver, p. 211. Description: Galvanometer deflection vs. length of horizontal receiving antenna in meters. Reference Relation: $y=kx$ Comments: This data set seems easy, but neither E* nor B*(10) proposes the reference relation. --------------------------------------------- Case 194a x y 0.024 1620 0.039 1980 0.091 2470 0.174 3050 0.244 3400 0.500 4650 Source: {\em Physical Review}, Vol. XXV, 1907, The Discharge of Electricity from Pointed Conductors Differing in Size,'' John Zeleny, p. 315. Description: Minimum voltage in volts to start current flowing vs. diameter of point in mm; for positive discharge from cylindrical points with hemispherical ends 1 cm from plate. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ Comments: I have taken the first four of the data sets in the source. --------------------------------------------- Case 194b x y 0.73 5530 1.13 6770 2.00 9250 Source: {\em Physical Review}, Vol. XXV, 1907, The Discharge of Electricity from Pointed Conductors Differing in Size,'' John Zeleny, p. 315. Description: Minimum voltage in volts to start current flowing vs. diameter of point in mm; for positive discharge from cylindrical points with hemispherical ends 1 cm from plate. Reference Relation: $y=k_{1}x^{.5}$ Comments: I have taken the first four of the data sets in the source. The reference relation here is different than in the other sets making up Case 194, but the data is the second half of a table, the first half of which makes up the data for Case 194a, and the reference relation here differs only in excluding the intercept. Hence, it seemed unreasonable to count this as a separate case. --------------------------------------------- Case 194c x y 0.088 2440 0.197 3175 0.267 3550 0.466 4475 0.516 4750 Source: {\em Physical Review}, Vol. XXV, 1907, The Discharge of Electricity from Pointed Conductors Differing in Size,'' John Zeleny, p. 319. Description: Minimum voltage in volts to start current flowing vs. diameter of point in mm; for positive discharge from cylindrical points with plane ends 1.5 cm from plate. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ Comments: I have taken the first four of the data sets in the source. The source says different values of $k_{1}$ and $k_{2}$ must be used for values of $x$ above and below .7. Hence, I have split this data into two sets. See Case 194d. --------------------------------------------- Case 194d x y 0.808 5750 1.170 6800 1.680 8015 2.180 9050 Source: {\em Physical Review}, Vol. XXV, 1907, The Discharge of Electricity from Pointed Conductors Differing in Size,'' John Zeleny, p. 319. Description: Minimum voltage in volts to start current flowing vs. diameter of point in mm; for positive discharge from cylindrical points with plane ends 1.5 cm from plate. Reference Relation: $y=k_{1}x^{.5}+k_{2}$ Comments: I have taken the first four of the data sets in the source. See comment for Case 194c. --------------------------------------------- Case 195a x y 20 1.60 30 1.11 40 0.83 50 0.64 60 0.54 71 0.46 80 0.40 91 0.35 100 0.32 Source: {\em Physical Review}, Vol. XXIV, 1907, The Capacity and Resistance of Aluminum Anode Films,'' C. McCheyne Gordon, p. 65. Description: Capacity vs. formation voltage; for HNaNH$_{4}$PO$_{4}$ solution. Reference Relation: $xy=k$ --------------------------------------------- Case 195b x y 10 3.80 20 1.95 40 0.95 81 0.48 90 0.42 100 0.38 Source: {\em Physical Review}, Vol. XXIV, 1907, The Capacity and Resistance of Aluminum Anode Films,'' C. McCheyne Gordon, p. 65. Description: Capacity vs. formation voltage; for K$_{2}$Cr$_{2}$O$_{7}$ solution. Reference Relation: $xy=k$ --------------------------------------------- Case 196a x y 75.54 3.49 69.69 4.20 52.86 5.03 22.14 12.53 15.79 17.72 Source: {\em Physical Review}, Vol. XXIV, 1907, The Absorption of Alpha Rays in Gases and Vapors,'' E. P. Adams, p. 112. Description: Maximum distance in cm between polonium and screen vs. pressure in cm of mercury; for air in test tube. Reference Relation: $xy=k$ --------------------------------------------- Case 196b x y 9.60 8.74 8.65 9.43 7.65 10.67 7.20 11.33 Source: {\em Physical Review}, Vol. XXIV, 1907, The Absorption of Alpha Rays in Gases and Vapors,'' E. P. Adams, p. 112. Description: Maximum distance in cm between polonium and screen vs. pressure in cm of mercury; for ethyl iodide in test tube. Reference Relation: $xy=k$ --------------------------------------------- Case 196c x y 70.15 4.03 59.30 4.70 44.15 6.09 34.07 7.87 18.60 14.33 15.60 16.06 Source: {\em Physical Review}, Vol. XXIV, 1907, The Absorption of Alpha Rays in Gases and Vapors,'' E. P. Adams, p. 112. Description: Maximum distance in cm between polonium and screen vs. pressure in cm of mercury; for oxygen in test tube. Reference Relation: $xy=k$ --------------------------------------------- Case 196d x y 22.8 2.38 21.0 2.53 17.9 2.97 16.6 3.53 14.1 4.29 9.5 5.97 6.4 8.58 4.5 11.58 Source: {\em Physical Review}, Vol. XXIV, 1907, The Absorption of Alpha Rays in Gases and Vapors,'' E. P. Adams, p. 112. Description: Maximum distance in cm between polonium and screen vs. pressure in cm of mercury; for nickel carbonyl in test tube. Reference Relation: $xy=k$ --------------------------------------------- Case 197a x y 0.560 1.68 1.025 3.59 1.585 5.21 1.995 7.05 Source: {\em Physical Review}, Vol. XXIV, 1907, The Elastic Modulus for Small Loads at the Elastic Limit,'' Henry W. Bearce, p. 192. Description: Deflection in wavelengths of sodium light vs. mass in grams; for an iron bar. Reference Relation: $y=kx$ --------------------------------------------- Case 197b x y 0.560 1.34 1.025 2.44 1.585 3.67 1.995 5.01 Source: {\em Physical Review}, Vol. XXIV, 1907, The Elastic Modulus for Small Loads at the Elastic Limit,'' Henry W. Bearce, p. 192. Description: Deflection in wavelengths of sodium light vs. mass in grams; for a steel bar. Reference Relation: $y=kx$ --------------------------------------------- Case 197c x y 0.560 1.35 1.025 2.74 1.585 4.54 1.995 5.92 Source: {\em Physical Review}, Vol. XXIV, 1907, The Elastic Modulus for Small Loads at the Elastic Limit,'' Henry W. Bearce, p. 192. Description: Deflection in wavelengths of sodium light vs. mass in grams; for a copper bar. Reference Relation: $y=kx$ --------------------------------------------- Case 197d x y 0.560 1.35 1.025 2.68 1.585 4.02 1.995 5.51 Source: {\em Physical Review}, Vol. XXIV, 1907, The Elastic Modulus for Small Loads at the Elastic Limit,'' Henry W. Bearce, p. 192. Description: Deflection in wavelengths of sodium light vs. mass in grams; for a brass bar. Reference Relation: $y=kx$ --------------------------------------------- Case 198 x y 0 2.437e-06 4 2.604e-06 6 2.665e-06 8 2.749e-06 Source: {\em Physical Review}, Vol. XXIV, 1907, On the Susceptibilities of Mixtures of Salt Solutions,'' J. C. McLennan and C. S. Wright, p. 283. Description: Susceptibility vs. amount of copper sulphate added to solution in cc. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 199a x y 4 45 8 75 20 200 40 455 Source: {\em Physical Review}, Vol. XXIV, 1907, On the Magnetic Behavior of Certain Nickel Alloys,'' Bruce V. Hill, p. 329. Description: Depression of transformation point in Centigrade degrees vs. percent copper in alloy. Reference Relation: $y=kx$ --------------------------------------------- Case 199b x y 5 37 10 72 15 110 Source: {\em Physical Review}, Vol. XXIV, 1907, On the Magnetic Behavior of Certain Nickel Alloys,'' Bruce V. Hill, p. 329. Description: Depression of transformation point in Centigrade degrees vs. percent tin in alloy. Reference Relation: $y=kx$ --------------------------------------------- Case 200a x y -21.50 0.0001249 14.05 0.0001421 53.55 0.0001606 100.30 0.0001829 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, pp. 387, 388. Description: Viscosity coefficient vs. Centigrade temperature; for nitrous oxide. Reference Relation: $x=k_{1}(x+273)^{1.5}/y + k_{2}$ Comments: Of the data sets given in the source, I have taken the first four with at least three observations. --------------------------------------------- Case 200b x y -21.5 0.0000851 20.6 0.0000989 53.5 0.0001096 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, pp. 387, 388. Description: Viscosity coefficient vs. Centigrade temperature; for ethylene oxide. Reference Relation: $x=k_{1}(x+273)^{1.5}/y + k_{2}$ Comments: Of the data sets given in the source, I have taken the first four with at least three observations. --------------------------------------------- Case 200c x y -21.50 .0001278 14.25 .0001449 53.50 .0001638 102.30 .0001858 162.40 .0002143 222.00 .0002385 240.00 .0002458 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, pp. 387, 388. Description: Viscosity coefficient vs. Centigrade temperature; for carbon oxide. Reference Relation: $x=k_{1}(x+273)^{1.5}/y + k_{2}$ Comments: Of the data sets given in the source, I have taken the first four with at least three observations. --------------------------------------------- Case 200d x y -20.6 .0000819 15.0 .0000889 99.2 .0001059 182.4 .0001215 302.0 .0001392 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, pp. 387, 388. Description: Viscosity coefficient vs. Centigrade temperature; for hydrogen. Reference Relation: $x=k_{1}(x+273)^{1.5}/y + k_{2}$ Comments: Of the data sets given in the source, I have taken the first four with at least three observations. --------------------------------------------- Case 201 x y 2.016 79.0 2.016 71.7 2.016 72.2 2.016 83.0 4.000 72.2 4.000 80.3 28.080 113.0 28.080 110.6 28.080 110.3 28.080 114.4 28.080 103.6 32.000 127.0 32.000 138.0 32.000 128.2 39.900 169.9 39.900 150.2 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, p. 293. Description: Intercept in Sutherland's equation vs. molecular weight. Reference Relation: $y=k_{1}x^{2}+k_{2}$ --------------------------------------------- Case 202 x y 2.016 71.7 28.080 113.0 32.000 138.0 39.900 169.9 Source: {\em Physical Review}, Vol. XXIV, 1907, The Temperature Coefficients of Gas Viscosity,'' Willard J. Fisher, p. 293. Description: Proportionality constant in Sutherland's equation vs. molecular weight. Reference Relation: $y=k_{1}x^{1.5}+k_{2}$ Comments: Helium is omitted, as the source says it does not conform to the reference relation. Several values are given for the proportionality constant; I have collected the ones Fisher used in his Figure 3. --------------------------------------------- Case 203 x y 1 1.32 2 2.68 3 3.93 4 5.30 5 6.58 6 7.84 7 9.16 8 10.48 9 11.71 10 12.80 Source: {\em Physical Review}, Vol. XXIII, 1906, Note on the Vibration Galvanometer,'' Roy T. Wells, p. 506. Description: Amplitude of vibration vs. distance in mm between points of galvanometer connection, a proxy for impressed potential difference. Reference Relation: $y=kx$ --------------------------------------------- Case 204a x y -59 36.3 -42 33.5 -32 31.9 -22 30.8 0 27.9 5 27.7 10 27.0 15 26.5 20 26.2 25 25.8 30 25.3 40 24.8 50 24.1 75 22.8 100 21.5 125 20.3 150 19.4 175 18.2 200 17.4 225 16.8 250 16.0 300 15.1 Source: {\em Physical Review}, Vol. XXII, 1906, The Equal Arm Balance,'' H. V. Carpenter and Zella E. Bisbee, pp. 38, 40. Description: Deflection in scale divisions vs. load in grams. Reference Relation: $1/y=k_{1}x+k_{2}$ --------------------------------------------- Case 204b x y -42 20.5 0 26.4 50 37.8 100 78.1 Source: {\em Physical Review}, Vol. XXII, 1906, The Equal Arm Balance,'' H. V. Carpenter and Zella E. Bisbee, pp. 38, 40. Description: Deflection in scale divisions vs. load in grams. Reference Relation: $1/y=k_{1}x+k_{2}$ --------------------------------------------- Case 204c x y 0 16.80 25 18.26 50 20.40 75 24.50 100 29.10 Source: {\em Physical Review}, Vol. XXII, 1906, The Equal Arm Balance,'' H. V. Carpenter and Zella E. Bisbee, pp. 38, 40. Description: Deflection in scale divisions vs. load in grams. Reference Relation: $1/y=k_{1}x+k_{2}$ --------------------------------------------- Case 204d x y 0 11.08 100 16.30 200 25.20 Source: {\em Physical Review}, Vol. XXII, 1906, The Equal Arm Balance,'' H. V. Carpenter and Zella E. Bisbee, pp. 38, 40. Description: Deflection in scale divisions vs. load in grams. Reference Relation: $1/y=k_{1}x+k_{2}$ --------------------------------------------- Case 205 x y 0.61 1252 0.66 1170 0.72 1079 0.80 980 0.89 891 1.00 799 Source: {\em Physical Review}, Vol. XXII, 1906, On the Conditions for Sparking at the Break of an Inductive Circuit,'' J. C. Hubbard, p. 139. Description: Capacitance vs. reading of screw from zero position. Reference Relation: $1/y=k_{1}x+k_{2}$ --------------------------------------------- Case 206a x y 101 0.63 81 0.83 61 1.38 41 1.84 21 3.25 11 4.95 6 7.42 Source: {\em Physical Review}, Vol. XXII, 1906, Studies in Luminescence. VI. The Decay of Phosphorescence in Sidot Blende,'' Edward L. Nichols and Ernest Merritt, pp. 284--285. Description: Time in seconds to fall to a given intensity vs. intensity. Reference Relation: $y=k_{1}/\sqrt{x}+k_{2}$ Comments: Of the data given in the source, I have taken the four curves at $\lambda=.512$ microns as those which the source most clearly indicates as following the reference relation. The source goes on to say that the extrapolation definitely does not hold. --------------------------------------------- Case 206b x y 61 0.72 41 1.24 21 2.42 11 4.03 6 6.22 Source: {\em Physical Review}, Vol. XXII, 1906, Studies in Luminescence. VI. The Decay of Phosphorescence in Sidot Blende,'' Edward L. Nichols and Ernest Merritt, pp. 284--285. Description: Time in seconds to fall to a given intensity vs. intensity. Reference Relation: $y=k_{1}/\sqrt{x}+k_{2}$ Comments: Of the data given in the source, I have taken the four curves at $\lambda=.512$ microns as those which the source most clearly indicates as following the reference relation. The source goes on to say that the extrapolation definitely does not hold. --------------------------------------------- Case 206c x y 81.4 1.06 61.4 1.35 31.4 2.98 11.4 6.47 Source: {\em Physical Review}, Vol. XXII, 1906, Studies in Luminescence. VI. The Decay of Phosphorescence in Sidot Blende,'' Edward L. Nichols and Ernest Merritt, pp. 284--285. Description: Time in seconds to fall to a given intensity vs. intensity. Reference Relation: $y=k_{1}/\sqrt{x}+k_{2}$ Comments: Of the data given in the source, I have taken the four curves at $\lambda=.512$ microns as those which the source most clearly indicates as following the reference relation. The source goes on to say that the extrapolation definitely does not hold. --------------------------------------------- Case 206d x y 81.4 0.45 61.4 0.69 21.4 2.60 11.4 4.48 7.4 5.97 Source: {\em Physical Review}, Vol. XXII, 1906, Studies in Luminescence. VI. The Decay of Phosphorescence in Sidot Blende,'' Edward L. Nichols and Ernest Merritt, pp. 284--285. Description: Time in seconds to fall to a given intensity vs. intensity. Reference Relation: $y=k_{1}/\sqrt{x}+k_{2}$ Comments: Of the data given in the source, I have taken the four curves at $\lambda=.512$ microns as those which the source most clearly indicates as following the reference relation. The source goes on to say that the extrapolation definitely does not hold. --------------------------------------------- Case 207 x y 5875 95.0 5866 36.0 5857 23.0 5839 9.5 5821 5.0 5803 3.0 Source: {\em Physical Review}, Vol. XXI, 1905, The Magnetic Rotation of Sodium Vapor,'' R. W. Wood and H. W. Springsteen, p. 50. Description: Rotary dispersion in degrees vs. wavelength. Reference Relation: $y=k_{1}x^{2}/(x^{2}-k_{2})^{2}$ Comments: Two presumed typographical errors have been corrected: $x_{2}$ from 5886 to 5866 and $x_{3}$ from 5875 to 5857. The revised values fit the relation better and, more important, can be derived by working backward from the calculated'' column in the source's data table using the hypothesized formula. --------------------------------------------- Case 208 x y 2.07 101 2.14 102 7.23 364 7.29 367 7.40 375 11.77 596 11.80 601 11.81 601 18.78 965 21.20 1087 21.24 1087 21.27 1091 25.91 1335 25.96 1336 26.03 1337 31.59 1625 31.72 1635 31.91 1644 99.52 5276 Source: {\em Physical Review}, Vol. XXI, 1905, The Joule-Thompson Effect in Carbon-Dioxide. I. Experimental,'' Frederick E. Kester, p. 272. Description: Electromotive force in microvolts vs temperature in degrees. Reference Relation: $y=k_{1}x+k_{2}x^{2}$ Comments: One point marked (?) in the source's data table has been omitted. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 209a x y 0.300 1.000 0.213 0.480 0.141 0.142 0.071 0.048 Source: {\em Physical Review}, Vol. XXI, 1905, Experiments on Resonance in Wireless Telegraph Circuits, Part III,'' George W. Pierce, p. 377. Description: Relative deflection of dynamometer vs. coefficient of coupling for second station. Reference Relation: $y=kx^{2}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 209b x y 0.300 1.000 0.213 0.590 0.141 0.260 0.071 0.068 Source: {\em Physical Review}, Vol. XXI, 1905, Experiments on Resonance in Wireless Telegraph Circuits, Part III,'' George W. Pierce, p. 377. Description: Relative deflection of dynamometer vs. coefficient of coupling for second station. Reference Relation: $y=kx^{2}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 209c x y 0.300 1.000 0.213 0.600 0.141 0.255 0.071 0.076 Source: {\em Physical Review}, Vol. XXI, 1905, Experiments on Resonance in Wireless Telegraph Circuits, Part III,'' George W. Pierce, p. 377. Description: Relative deflection of dynamometer vs. coefficient of coupling for second station. Reference Relation: $y=kx^{2}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 209d x y 0.300 1.000 0.213 0.660 0.141 0.300 0.071 0.087 Source: {\em Physical Review}, Vol. XXI, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part III,'' George W. Pierce, p. 377. Description: Relative deflection of dynamometer vs. coefficient of coupling for second station. Reference Relation: $y=kx^{2}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 210 x y 7.5 2.23 8.0 2.85 9.0 4.89 10.0 8.80 11.0 16.50 12.0 29.90 12.5 38.40 13.0 52.00 Source: {\em Physical Review}, Vol. XX, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part II,'' George W. Pierce, p. 225. Description: Average deflection in cm vs. micrometer reading. Reference Relation: $y=k_{1}((16-x)^{2}+25)^{3}$ --------------------------------------------- Case 211 x y 0 41.8 2.74 27.3 5.63 20.4 8.10 15.8 10.90 12.3 18.70 7.1 Source: {\em Physical Review}, Vol. XX, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part II,'' George W. Pierce, p. 229. Description: Deflection in cm vs. added resistance. Reference Relation: $y=k_{1}/(x+k_{2})^{2}$ --------------------------------------------- Case 212a x y 23.8 92 20.8 94 17.8 100 15.8 106 14.8 115 13.8 130 12.8 165 Source: {\em Physical Review}, Vol. XX, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part II,'' George W. Pierce, pp. 233, 234, 241. Description: Resonant capacity in the receiving side circuit vs. height of antenna in meters. Reference Relation: $(x-11.8)(y-84.6)=k$ --------------------------------------------- Case 212b x y 23.3 50.0 22.3 55.0 21.3 57.0 20.3 60.0 18.3 63.0 16.3 65.0 14.3 69.0 12.3 71.0 10.3 72.5 8.3 74.0 6.3 75.0 4.3 76.5 2.3 77.0 Source: {\em Physical Review}, Vol. XX, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part II,'' George W. Pierce, pp. 233, 234, 241. Description: Resonant capacity in the receiving side circuit vs. height of antenna in meters. Reference Relation: $(x-30)(y-84.6)=k$ --------------------------------------------- Case 212c x y 22.0 89 19.0 91 16.0 96 14.0 102 12.0 115 11.0 140 9.0 45 8.5 50 8.0 55 7.5 60 7.0 62 6.5 66 6.0 68 Source: {\em Physical Review}, Vol. XX, 1905, Experiments on Resonance in Wireless Telegraph Circuits. Part II,'' George W. Pierce, pp. 233, 234, 241. Description: Resonant capacity in the receiving side circuit vs. height of antenna in meters. Reference Relation: $(x-10)(y-85)=k$ --------------------------------------------- Case 213a x y 900 1.97 1000 2.51 1100 3.11 1200 3.70 1300 4.28 1400 4.89 1500 5.46 Source: {\em Physical Review}, Vol. XX, 1905, The Conduction Losses from Carbon Filaments when Heated to Incandesence in Various Gases,'' L. W. Hartman. Description: Conduction loss in watts vs. temperature. Reference Relation: $y=k_{1}x+k_{2}x^{2}$ Comments: I have taken only two of the data sets given, because I was not confident I understood how to extract data from the remaining tables. --------------------------------------------- Case 213b x y 900 0.42 1000 0.56 1100 0.70 1200 0.82 1300 0.90 1400 0.95 1500 0.96 Source: {\em Physical Review}, Vol. XX, 1905, The Conduction Losses from Carbon Filaments when Heated to Incandesence in Various Gases,'' L. W. Hartman. Description: Conduction loss in watts vs. temperature. Reference Relation: $y=k_{1}x+k_{2}x^{2}$ Comments: I have taken only two of the data sets given, because I was not confident I understood how to extract data from the remaining tables. --------------------------------------------- Case 214a x y 0.009 30 0.010 38 0.020 59 0.020 68 0.038 107 0.040 102 0.044 108 0.050 126 0.053 135 Source: {\em Physical Review}, Vol. XX, 1905, The Dielectric Strength of Double-Refracting Crystals,'' John Almy, p. 392. Description: Spark potential in cgs units vs. thickness of plate in cm; for selenite. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. The data have been rearranged in order of increasing $x$ values. The value for $x_{3}$ has been corrected from .92 to .02, which is derived by working backward from the value calculated by the source on the basis of the reference relation. --------------------------------------------- Case 214b x y 0.006 40 0.016 96 0.017 90 0.020 102 0.030 117 0.032 120 0.037 125 Source: {\em Physical Review}, Vol. XX, 1905, The Dielectric Strength of Double-Refracting Crystals,'' John Almy, p. 392. Description: Spark potential in cgs units vs. thickness of plate in cm; for quartz cut parallel to the optic axis. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 214c x y 0.0045 30 0.0080 44 0.0150 59 0.0200 76 0.0280 87 0.0300 90 0.0390 117 Source: {\em Physical Review}, Vol. XX, 1905, The Dielectric Strength of Double-Refracting Crystals,'' John Almy, p. 392. Description: Spark potential in cgs units vs. thickness of plate in cm; for quartz cut normal to the optic axis. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 214d x y 0.070 76 0.075 72 0.095 109 0.100 81 0.115 111 Source: {\em Physical Review}, Vol. XX, 1905, The Dielectric Strength of Double-Refracting Crystals,'' John Almy, p. 392. Description: Spark potential in cgs units vs. thickness of plate in cm; for aragonite cut parallel to the optic axis. Reference Relation: $y=k_{1}x+k_{2}$ Comments: The source gives six data sets; I have taken the first four. The data have been rearranged in order of increasing $x$ values. --------------------------------------------- Case 215 x y 91 9.0 96 16.0 102 46.0 107 75.0 113 45.0 120 16.5 130 7.5 Source: {\em Physical Review}, Vol. XIX, 1904, Experiments on Resonance in Wireless Telegraph Circuits,'' George W. Pierce, p. 213. Description: Deflection vs. localized capacity. Reference Relation: $y=k_{1}/(1+k_{2}(k_{3}/x-1)^{2})$ Comments: The source says the reference relation holds for $x$ between 91 and 130, and only this data is included here. E* reports the clearly spurious relationship $y=k/\sqrt{x}$ for this case. The problem is that, while the distinction of this power proportionality is extremely low, the intercept $k_{2}$ in $y=k_{1}/\sqrt{x}+ k_{2}$ is even more highly insignificant. This is a bug in E* which could be corrected simply by limiting the effect of $t$ in E*'s criterion for evaluating power proportionalities. --------------------------------------------- Case 216 x y 5.60 14.28 7.90 19.22 8.16 20.04 15.80 31.90 Source: {\em Physical Review}, Vol. XVIII, 1904, A Study of the Radiations Emitted by a Righi Vibrator,'' Harley R. Willard and L. Elmer Woodman, p. 19. Description: Wavelength vs. resonator length. Reference Relation: $y=k_{1}x+k_{2}$ --------------------------------------------- Case 217 x y 752 20.80 652 19.84 548 18.30 444 15.80 347 14.90 238 10.60 142 6.80 49 2.70 19 1.36 Source: {\em Physical Review}, Vol. XVIII, 1904, On the Character of the Radiation from Ordinary Metals,'' E. F. Burton, p. 190. Description: Current vs. pressure. Reference Relation: $y=kx$ Comments: The source says conductivity is almost exactly proportional to the pressure,'' but the plot above shows very clear lack of fit. --------------------------------------------- Case 218a x y 1245 0.537 1420 0.575 1607 0.611 1825 0.649 2068 0.694 2345 0.738 2658 0.785 3000 0.834 3395 0.888 3823 0.940 4305 0.998 4842 1.056 5443 1.125 6102 1.188 6870 1.260 Source: {\em Physical Review}, Vol. XVII, 1903, Diffusion and Supersaturation in Gelatine,'' Harry W. Morse and George W. Pierce, pp. 138, 147. Description: Distance from bottom of tube at which a disc of precipitate appears vs. time in seconds; temperature=15.7, silver nitrate $N$, potassium chromate $N/75$. Reference Relation: $y=kx^{.5}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 218b x y 1732 0.687 1920 0.723 2350 0.801 2596 0.845 2865 0.888 3170 0.934 3505 0.982 3870 1.032 4315 1.083 4900 1.139 Source: {\em Physical Review}, Vol. XVII, 1903, Diffusion and Supersaturation in Gelatine,'' Harry W. Morse and George W. Pierce, pp. 138, 147. Description: Distance from bottom of tube at which a disc of precipitate appears vs. time in seconds; temperature=16.0, silver nitrate $2N$, potassium chromate $N/75$. Reference Relation: $y=kx^{.5}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 218c x y 1625 0.672 1805 0.705 2000 0.742 2215 0.782 2450 0.822 2710 0.866 2995 0.910 3300 0.955 3645 1.003 4020 1.051 4430 1.107 4885 1.162 5365 1.220 5895 1.280 Source: {\em Physical Review}, Vol. XVII, 1903, Diffusion and Supersaturation in Gelatine,'' Harry W. Morse and George W. Pierce, pp. 138, 147. Description: Distance from bottom of tube at which a disc of precipitate appears vs. time in seconds; temperature=16.3, silver nitrate $2N$, potassium chromate $N/75$. Reference Relation: $y=kx^{.5}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 218d x y 1705 0.684 1885 0.719 2083 0.760 2300 0.798 2540 0.842 3090 0.930 3405 0.976 3740 1.023 4110 1.077 4525 1.128 Source: {\em Physical Review}, Vol. XVII, 1903, Diffusion and Supersaturation in Gelatine,'' Harry W. Morse and George W. Pierce, pp. 138, 147. Description: Distance from bottom of tube at which a disc of precipitate appears vs. time in seconds; temperature=16.3, silver nitrate $2N$, potassium chromate $N/75$. Reference Relation: $y=kx^{.5}$ Comments: I have taken the first four of the data sets given in the source. --------------------------------------------- Case 219 x y 6.9 7.9 9.1 10.5 12.2 14.5 17.0 19.9 22.8 27.5 29.9 35.3 Source: {\em Physical Review}, Vol. XVII, 1903, Energy in the Visible Spectrum of the Hefner Standard,'' Knut {\AA}ngstr\"{o}m, p. 306. Description: Intensity of Hefner lamp vs. intensity of glow lamp. Reference Relation: $y=kx$ --------------------------------------------- Case 220 x y 0.75 1.87e-07 0.70 1.04e-07 0.65 5.44e-08 0.60 2.61e-08 0.55 1.17e-08 0.50 3.40e-09 Source: {\em Physical Review}, Vol. XVII, 1903, Energy in the Visible Spectrum of the Hefner Standard,'' Knut {\AA}ngstr\"{o}m, p. 312. Description: Total energy vs. wavelength. Reference Relation: $y=.016e^{-z}(z^{3}+3z^{2}+6z+6)/7.85^{4}$ where $z=7.85/x$ Comments: I have corrected the exponent on the third $z$ from 3 to 1. This completes the series of descending exponents in the obvious way and also causes the formula to check with the calculated'' column in the source's data table. --------------------------------------------- Case 221 x y 2.85 0.140056 2.93 0.140085 4.42 0.139927 18.37 0.139459 24.52 0.139182 25.00 0.138980 27.40 0.138990 28.00 0.139000 31.68 0.138890 32.14 0.138873 32.41 0.138846 36.59 0.138753 45.00 0.138447 53.39 0.138225 65.22 0.137942 83.89 0.137479 Source: {\em Physical Review}, Vol. XVI, 1903, Note on the Variation of the Specific Heat of Mercury with Temperature. Experiments by the Continuous-Flow Method of Calorimetry,'' H. T. Barnes and H. L. Cooke, p. 67, 68. Description: {\em Js} vs. mean temperature. Reference Relation: $y=k_{1}x^{2}+k_{2}x+k_{3}$ Comments: I have combined data from two tables here, as the source does in an accompanying figure. --------------------------------------------- Case 222 x y 0 4.36 99 2.12 192 1.56 257 1.30 320 1.13 377 1.02 453 0.92 507 0.82 Source: {\em Physical Review}, Vol. XVI, 1903, The Radiant Efficiency of the Mercury Arc,'' William P. Geer, p. 99. Description: Galvanometer throw vs. time in seconds. Reference Relation: $1/y=k_{1}x+k_{2}$