﻿for Measurement of Resistances and Capacities, 309 



This proposition gives a simple means of determining the 

 equality in practice. The commutator position 8= \ may be 

 easily and accurately obtained (see footnote, p. 302) once for 

 all, or we may obtain it and adjust to the equality (II) by 

 proceeding as follows. Short circuit Rand H, then r=k=0^ 

 and the galvanometer deflexion will be zero only when $ = },. 

 Turn the commutator while the axle is still in rotation until 

 the deflexion becomes zero, fix it in this position, give H its 

 original value, and balance the resulting galvanometer de- 

 flexion by adjustment of R. 



Balances corresponding to p = k, and p = r. — "When p = k, 

 and = in (9) we get for the corresponding value 8 2 of 8 

 •the equation 



<rt**-i>= ™* h y* sr , .... (12) 



cosh ! 2 zt 

 •and when/) = r, U=0, and 8 = 8 3 , 



Tft-ott-wfo-*)}- C cosh^r T > • • (13) 



with similar equations in the region where 8 < -J- or >-g-. The 

 leads 8 2 and S ;; are each functions of zt only. 8 2 varies from 

 _-J- to 0, and 8 d from 1 to -J , as zt increases from to co . The 

 course of these functions is shown in the curves of fig. 5 

 (II. & III. give 8 2 and S s with zt, from zt = up to zt = 4:, 

 II a. & Ilia, give 8 2 and 8 3 with 1 /zt, from 1/-t = up to 

 1/zt = 0'4z, to include the region where zt is too great to 

 admit of direct plotting). The X 's are experimental values 

 obtained by simply arbitrarily making the corresponding 

 equality and turning the commutator until the galvanometer 

 deflexion becomes zero. 



Two practical methods for adjusting to the equalities may 

 be deduced from these results. They depend on the fact 

 that although 



1 / 1 1\ R s . K 



*=h+sVh + k> r =ir+-$> amU= KTH> 



are all functions of the same variables, the ratios r and k 

 may be altered as much as we please without affecting z, so 



long as R + S, and |^j+^i, i.e. the total resistance and 



capacity of the branch BDC, remain unaltered. E. g., if 

 H be transferred from the arm BD to a position in series 

 with SK in the arm CD (in fig. 1 this may be easily done 

 by transferring the battery-lead making contact at D to 

 the junction between R and H) we make k = without 



