PRESSURE ON RESISTANCE OF METALS. 583 



which depart Httle from Hnearity, the departure is symmetrical about 

 the mean pressure, and may be represented within the hmits of error 

 by a second degree equation of the form Ap (12000 — p). In these 

 cases the manner of departure from Hnearity is entirely specified by 

 giving the maximum departure. The initial slope of the pressure- 

 resistance curve is the average slope plus four times the maximum 

 percentage deviation, and the final slope is the average slope minus 

 four times the maximum deviation. The departure from linearity is 

 of course a function of temperature. The experimental values of the 

 departure were plotted against temperature and smooth curves drawn 

 through the points. In the tables the smoothed values of maximum 

 departure are given as functions of temperature, and in a diagram 

 the experimental values are given, from which the accuracy of the 

 departure from linearity may be estimated. 



For most substances, however, the departure from linearity is not 

 s;yTnmetrical, and the relation between pressure and change of resist- 

 ance cannot be represented by a second degree equation. Further- 

 more, the manner of variation from linearity is different for difterent 

 metals, so that it is not possible to represent the behavior of all metals 

 by a formula containing only two constants. Lisell ^ and Beckman ^ 

 found a two constant formula sufficient. Lisell's formula was a simple 

 second degree expression, R = Ro(l + yp + 5p"), and Beckman's 

 was exponential, R = Roe"P+''P'. Any formula, however, must give 

 correctly at least the average coefficient, the maximum deviation from 

 linearity and the pressure of maximum deviation. At higher pressures 

 all three of these data are unrelated, so that two constants will cer- 

 tainly not suffice. It might be possible to find a three constant 

 formula which would work for all the metals within the limits of error, 

 but I have preferred to exhibit graphically the deviations from linear- 

 ity of each substance. The deviation curves are functions of tempera- 

 ture, so that to completely represent the data within my range a 

 curve at each one of the five temperatures is necessary. The deviation 

 curves have been smoothed as follows. First, smooth deviation curves 

 were drawn through the experimental points at each temperature. 

 The maximum deviation and the pressure of maximum deviation 

 were next each plotted against temperature and smooth curves drawn 

 through these points. These smoothed maximum deviations and 

 pressures of maximum deviation are listed in the Tables, and the 

 experimental values of maximum deviation are shown in the curves 

 as functions of temperature. The smoothed deviation curves for 

 each temperature were then further adjusted graphically so that the 



