Prof. A. Schuster's Electrical Notes. 



1?9 



10 ohms resistance each. By joining them in multiple arc or 

 series, we may change the internal resistance from 2*5 to 40 

 ohms, and conduct measurements of resistances lying between 

 half an ohm and 200 ohms with considerable accuracy. 



We have obtained a value for the smallest change of re- 

 sistance which it is possible to measure with any arrangement, 

 but have not discussed how closely we may approximate to 

 the theoretical value by any of the known methods. The 

 simplect arrangement, in many ways, is that in which a 

 differential galvanometer is used, as in fig. 1. The two 

 nearly equal resistarces to be compared 

 are p and p f , while G and Gr 7 denote 

 the two coils of the galvanometer. If 

 balance is obtained with a current i m 

 passing through the resistances, it is 

 required to determine the change Sp 

 which will produce the smallest observ- 

 able change of current 8y in the galva- 

 nometer. Equation (1) will be rpplicable if the internal 

 resistance of the battery b is small compared to p + q ; for 

 in that case a small change of resistance 8p will not disturb 

 appreciably the current in Gr 7 , and will produce the maximum 

 effect in its own branch. 



In order that this arrangement shall be workable, it is 

 necessary, however, that the maximum current i m which can 

 pass p shall also be able to pass through the galvanometer 

 without overheating it. Calling y m the greatest current which 

 the instrument will stand, we have as a necessary condition that 



As a second case, we take a differential galvanometer, but 

 place it in parallel circuit with the resistance p. The arrange- 

 ment is diagrammatically represented in rig. 2. 



In order that an electromotive force 



iSp shall produce a current — — in 



p+g 



the galvanometer-branch G, it is ne- 

 cessary that 6 should be large com- 

 pared with the combined resistance of 

 p and g. The current through the 



galvanometer will be — ; and hence 



with this arrangement it is necessary 

 that 



y m >i m p/g> 



Fi-. 2. 



E - 



N2 



