Mr. Louis Schweiidler on Differential Galvanometers, 271 



2nd case. — When the battery resistance /cannot be neglected 

 against either iv or w\ but when the two resistances at which 

 balance is arrived at are invariably equal. 



Thus, substituting in the general equation 



we get 



W = w' = lVj 



2=g ! =$=-^+lS4w* + Sfw+p, . , (a,b) 



P* = h • • ■ • (e) 



C=l (d) 



Srd case. — When the conditions given under 1 and 2 are both 

 fulfilled, or 



w = w' = w 



and 



f=0; 

 then we have 



ff=9'=ff= l %> (a, 5) 



P s =ii w 



C=l, (d) 



the very same result which was obtained by direct reasoning at 

 the beginning of this paper. 



Applications. — Though the problem in its generality has now 

 been entirely solved, it will not perhaps be considered irrelevant 

 to add here some applications. 



For our purpose differential galvanometers may be conveni- 

 ently divided into two classes, viz. those in which the resistances 

 to be measured vary within narrow limits, and those where these 

 limits are extremely wide. 



To the first class belong the differential galvanometers which 

 are used for indicating temperature by the variation of the re- 

 sistance of a metallic wire exposed to the temperature to be 

 measured — as, for instance, C. W. Siemens' s resistance ther- 

 mometer for measuring comparatively low temperatures^ or his 

 electric pyrometer for measuring the high temperature in 

 furnaces. 



It is clear that for such instruments the law of maximum 

 sensitiveness should best be fulfilled for the average resistance 

 to be measured, which average resistance under given circum- 

 stances is always known. 



To the second class belong those differential galvanometers 

 which are used for testing telegraph-lines, at present the most 

 important application of these instruments. In this case each 



