Prof. A. Schuster's Electrical Notes. 181 



If, further, q is large compared with p, and therefore r large 

 compared with s, we obtain the fundamental equation, 



p + g 



If all resistances are equal, which is often supposed to be 

 the most favourable arrangement, the smallest detectable 

 change of resistance hp is given by 



Bp _ 4&y m 



P i m ' 



that is to say, we only obtain half the maximum sensibility. 



In the general case the best galvanometer- resistance is 

 found to be 



r{p + s) t 



y (r + s) ' 

 and by introducing this value into equation (4), we obtain 



Sp=2(p + s)fy. 



Also 



a. V r + s 





s/ g \/ rs/ p + s 

 Hence 



p V V q/\ pji m 



This equation shows what we lose in sensitiveness by 

 making s too large or q too small. If Carey Foster's method 

 is adopted, p = q, and the sensitiveness is necessarily reduced 

 in the ratio of ^2:1. 



The results here obtained are valid so long as we have 

 sufficient battery-power at our command. If we are limited 

 to a fixed and insufficient electromotive force, the conditions 

 are altogether different, and in that case the problem has 

 been fully discussed by Mr. 0. Heaviside (Phil. Mag. 1873, 

 xlv. p. 114). 



M. Ch. Eug. Guye*, in a valuable paper, has discussed 

 the best arrangement of a Wheatstone-bridge for bolometer 

 measurements, but he only considered the special case of the 

 equality between two and two of the four resistances. His 

 results are in agreement with those given above. 



In comparing the different methods of measuring resist- 

 ance, we see that there is really no theoretical advantage of 



* Archives des Sciences physiques et naturelles, January 1892, 



