Heat produced by Emission of Ions from Hot Bodies. 629 



fraction it of the latter flows down the high resistance arms 

 FDC. The heating current i is thus 



t=(l-w)t 1 = fl-w)V/R . 



The resistance of x when shunted by y is *~ and the 

 change in R due to switching on the shunt is 



3Eo= — a?l(x + y). 

 The current when the resistance is thus altered is 



«i+a»i= v/tRo+aig =v/Ro(i- *' ' 



Thus to the first order of small quantities 



3i l =* 1 V/V(*+y) (3) 



t = (l — W)t l9 a*=(l-w)Bh=(l~ W) y ' + y 



and BE may be written 



9 B=(1-.)V{2R^+BR}. 



To find BR from the deflexions D E of the galvanometer it 

 is necessary to consider the theory of the Wheatstone's 

 bridge circuit. If the resistances of CD, DF, FE, and EC- 

 are b, a, /3, and a. respectively and z is the current through 

 the galvanometer G-, then 



i 1= = i G(a + 6 + a + /3) + (& + a)(a + iST^-, 



where A is the usual determinant *, and 



.=(«-<= rf V-s(f-f-) 



1 + 77+ 7- + — 



to the first order in it. Thus if the Wheatstone's bridge is in 

 adjustment when /? = R, the increments B- and B/3( = BR) 

 due to a change of %i from % x to z'i + B«i will be related by the 

 equation 



v 1 7 Gr + all + 7r+- J 



where k is the insensibility of the galvanometer. In our 

 * J. J. Thomson's 'Elements of Electricity and Magnetism,' p. 306. 



