and Voltmeter with a Long Scale. 211 



fig. 10 the other coil. Let r ± = 6 in the first case, and let 

 the depth of the coil be 1. In the second, let r 2 = | and the 

 depth of the coil = 6. Considered alone, the two coils are 



Fier. 9. 



rVi 





1 



- 



< t.*= 6 => 



1 





therefore similar in all respects. They are moreover supposed 

 to be suspended in two fields of equal intensity, and to convey 

 the same current. 



Fig. 10. 



Sr*\-6 



For the sake of symmetry the wire in figs. 8 and 9 has to 

 be divided between two rectangles, which, however, does not 

 affect the argument. 



The suspension in both cases having to bear the same load, 

 the relative sensibilities of the two arrangements for con- 

 tinuous currents will therefore be as their deflecting-moments 

 directly. 



For fig. 9 the moment 



M 1 = incH/r 1 , 



and for fig. 10 



so that 



M 2 = 2rccH 



a 



2r. 



Mi 

 Mo 



lr^ 



= 7 



therefore M 1 = 7M 2 for steady currents. 



