192 DR CARGILL G. KNOTT ON THE 



Table of Successive Differences of Thin Nickel Resistances. 



Temperature. Resistance. 1st Differences. 2nd Differences. 



0' 1-914 



• 275 



50° 2-189 -091 



-366 



100° 2-555 -045 



-411 



150° 2-966 -050 



-461 



200° 3-427 -084 



•545 

 250° 3-972 



Although it is impossible to get a single parabolic equation to apply all 

 through, we may calculate parabolic equations to apply to successive over- 

 lapping, segments of a hundred degrees' range, taking as initial points the 

 successive temperatures 0°, 50°, 100°, 150°. We thus obtain four equations, 

 which will be found to agree closely with the observations. To compare these 

 equations with those for other metals, such as platinum and palladium, would 

 then be an easy matter. 



It is to be remembered, however, that the usual method of representing 

 observations by an empirical formula of ascending powers of the one variable 

 has rarely any deep significance. What is of real importance in all such 

 investigations is to know, first, what the value of a certain quantity is, and, 

 second, how it varies under given conditions ; and in many instances the latter 

 is the main object of research. It is so in the present inquiry. It should be 

 our object, then, to tabulate our results in such a manner that the rate of change 

 of resistance per degree of temperature may be evident at a glance for all tem- 

 peratures. The usual equation is of the form 



R = Ro(l + at +/3t 2 ), 



from which we may almost at once calculate dH/dt for any temperature. 



What we wish, however, is not so much this quantity as the quantity 'R- 1 dR/dt, 



which is the real rate of change of resistance. 



In the following table this quantity is calculated for the four series of 



observations already given, so that the peculiarities of nickel may be readily 



indicated. The quantities are estimated for the temperatures 50°, 100°, 150°, 



200°, since for these alone can be safely estimated the rates of change in the 



case of the nickel. The necessary calculation is most readily effected by means 



of the formula — 



1 dR, 1 A 



li, dt " ll t ~\ 



where Ax A 2 are the first and second differences in the series of resistances, 



