﻿304 Dr. S» R. Milner on the Use of the Secohmmeter 



result from (2) in its general form become complicated by 

 the presence in them of F and/, the resistances of the battery 

 and galvanometer arms; and it is only by assuming certain 

 simplifications in (2) that results which are practically useful 

 are obtained. The most useful simplification, and that on 

 which the methods described below are based, is that in 

 which F is supposed to be arbitrarily made very large and f 

 very small, compared with the combinations, and in the 

 following these conditions are assumed to be complied with*. 

 Equation (2) then becomes 



PS'-QR' E 

 (P + Q)(R'+S')F 5 



or if we write 



- P r_ lV 



we get the very simple form 



C=(p-r')| (i) 



If we put 



R , K 





R + !3 

 we get by (3) 



*~K + H- ~-R + SVH + k]' 





and (4) becomes on multiplying up to eliminate reciprocals 

 ofD, 



(D+*)C={(p-r)D+<p-*>}}. . . (5) 



When the variations of E/F are those given by the battery 

 commutator of the secohmmeter, and represented in curve I 

 (fig. 2), this equation gives the " unreversed " current C 

 through the galvanometer branch (i. e. previous to the second 

 set of reversals). In any period of time during which E/F 



* Practical considerations on the necessary magnitudes of F and/ are 

 given later, p. 313, In order to avoid clashing with these conditions it is 

 theoretically necessary to situate the " breaking " commutator X in the 

 high-resistance arm F, and the short-circuiting commutator Y in the 

 low-resistance arm / (i. e. in the arrangement of tig. 1, X, in that of 

 fig. 3, Y, should be the battery commutator, as shown in the figures). In 

 practice the rather more convenient use of X as the battery commutator 

 in all cases makes, however, no appreciable difference to the results. 



