150 Louis Schwendler — On Differential Galvanometers. [No. 2, 



which equation with the other 



gives all that is required to determine g and g ', and the values thus ohtained 



gl + W <—p *UL (g + w ) — A = 1 



v9 



dw' { N N 2 j 



.-. Sa=K j^-A^Uu,' 



( N N 2 ) 



Thus the variation of a is always directly proportional to Q, a known function of g 

 and g', and to make 8a for any dw' as large as possible, we have to make <p a maxi- 

 mum with respect to g and g', while g and g' are connected by the following equation 



A=a'+ w' — p — — (g -f. w) I 



jp being a constant with respect to g and g ', as also is A. 



We have, therefore, to deal here with a relative maximum, and in accordance with 

 well known rules, we have to form the following partial differential coefficients : 



d<p lx-2gU_ E^/aiA 

 — A — = dgr dg 



<*N , „ 



R = - — ; =zg + w + f 

 dw 



S = 





s/g /an 2K T -\ 



'? A M) — g J3 x/fif ' 



d ST gr 2 *Jg 



d A 2 s/g s/g' — p (g + w) 



d g' 2 sjg *Jg' 



At or near balance when A is = 0, or very small, the terms A S and A S' in the re- 

 spective differential coefficients are to be neglected, because neither S nor S' become 

 infinite for any finite values of g and g'. 

 Thus we have approximately : 



N-22UL Ev/gii 



d g d 9 = P — Q 



dg 2 Jg N 2 N s 



