32 Mr. L. Scbvvendler on the Galvanometer Resistance 



T> 



As S is to be constant for all wires, -^ expresses for a given 



space and constant conductivity a constant electrical resistance, 

 which may be w ; and putting 



IT 1 



we 



have 



and U developed, we arrive at 



But as U, the number of convolutions in a given definite 

 space, cannot increase indefinitely with g, because 8,;the radial 

 thickness of the insulating covering, is always larger than zero, 

 we have here to adopt the minus sign of the square ro 



U 



= 4 + \/f-\/l\/f + 6- 



If we now call Y the magnetic moment of the branch, of 

 which g is the resistance and U the number of convolutions, we 

 have 



v f U 

 i = const. r ; 



g + k' 



or by substituting for U its value, and putting 



V g=x, &c, 

 we obtain 



„2 



% w Vv V ^TTJ 4>w 2 

 Y = const = »— — ; 



and the question now is, which value of x raises Y to its maxi- 

 mum ? It is 



Sx 2 . x 3 ~\ 



X , 1 W \/~ W 2 



s-i* + +H 



W s/ v 



2 / "" ^ — 



V w \/y 4w 2 -^ 



2*{|1 + JL - \Z-£j= + ^-i) =0; 



