for the Measurement of a particular Resistance. 287 



In this case the number of turns of wire in the coil of the 

 galvanometer has a considerable influence on the result, and 

 hence comparison between the sensibility in one case and 

 that in another when the galvanometer has been changed is 

 difficult. I have assumed in the present investigation that the 

 galvanometers are all such that they will give deflections 

 = AGVc/, where A is a constant, which must be the same for 

 each instrument. „ . 



From equation (3) we may express p /- in the form 

 jjjj _ ci + c 2 g 



a ^g %^g 



for a minimum 



-j where c 1? c 2 , c 3 are constants; 



K c a aJtl 



_ (B + 2f)'Rac + Ba 2 (q +/) + ac 2 (R +/) + o?cR 

 ~ 2acR + acf+ aR(a +f) + cU(c +/) + c 2 f 



__ (R + c){/(R + c) + E(a + c)} 



a 



(a + c){f(R + c) + B,(a + c)} 



= a*±l (14) 



a + c v ' 



We have now to combine this value of g with the values of 

 a and c previously found, namely 



«*=/&, (12) 



c - n+f > {1S) 



^ a ^Tc (14) 



From (12) and (14) we get 



r c + R. 

 a—j — — > 

 •a + c 



and 



fU-a? 



