190 Mr. C. Bams on Maxwell's Theory of the 



the parts in question, on the index whose position is x = l', 

 will be 



4 L ?' e 0> 9 *£t> «££-.* 



where Z=L — V. 



Hence the motion of the index, i/r ? is 



^ = Z'((/> 1 ln^ + </>ln^+(/) 3 lnA)-^lny. 



Now, if the experiment is so conducted that 1 ==0 3 = 0' and 

 ^=^ = ^L, which implies uniformity of temper throughout the 

 wire from to L, then 



+ = /(*-*') In-| 



a 



which suggests the most convenient method of experiment. 

 If it is possible to heat the upper wire uniformly throughout 

 its length, this equation takes the simpler form 



>|r = /(0 -0') In 2. 



If 0' is negligible relatively to 0, this method leads to absolute 

 results. 



There is another case which facilitates experiment. Let 

 ^1 = 03, 0' = O, 1=1'. Then 



^ = /0! In 2 + l(<f>-<f) 1 ) In -. 



If the behaviour of the wires for = X (i. e. for the case in 

 which the upper wire has the uniform temperature corre- 

 sponding to 0,) be known, this equation is similar to the pre- 

 ceding. In general and intermediate cases correction members 

 must be investigated. 



If a series of detorsions, 0, be observed at 0°, and another 

 series, <3>, be observed at ©° ; if = O , F(0) and yp> = n/2R, 

 (Gauss's method of angular measurement), then 



where R is the distance between Gauss's mirror and scale in 

 centimetres, and where N and n are the scale-parts (centims.) 

 corresponding to ©°, 0°, respectively. Hence, whatever be 

 the function F, the distance of the individual curves for 0° 

 and 0° apart varies directly as O . This result, though simple 

 enough, has special bearing on certain data below. 



