the Elect ro-mag7ietic Po-joer hy Schvoeigger' s Multiplier. 445 



the above, may be very easily developed in the following man- 

 ner. I have here the case in view, 

 in which the connecting wire 

 passes thi'ough the magnetic meri- 

 dian. Let KZ be the wire, NS the 

 direction of the magnetic meri- 

 dian, and the original situation of 

 the needle, which now stands in 

 ns in equilibrium with the terre- 

 strial magnetism, and moves in 

 the plane D'EG. Now let DD' 

 be the distance of the wire from 

 the plane, in which the needle 

 moves, which distance we will 

 state =X. Now DE is=E; if* 

 we divide this power into DG and 

 EG, then we have 



DG = E. COS. EDG = E. cos. ED'G = E. cos. c. 

 Now the electro-magnetic power acts inversely as the di- 

 stance DE. But it is 



DE= V (DD'-'4-r)'E^)= v(^-'-|-sin.^ c). 

 The needle and the electro-magnetism act on each other, 

 therefore, with the power 



And because 



Mjm sin. r = 



Em COS. c 



,V^ir' + sin.'' c) ' 



Eto cos. c 



Then is E = '— ^/{x^ + s\n^c) M. 



COS. c ^ 



The equations BCD change in the same manner into the 

 followiniJ: : 



(AO 



E^ _±L£_ ^(';r^+ sin.^ {c-d))M 

 E=£^^)^/(-^+sin.Mc+.)). 



M 



(B') 

 (C) 

 (DO 



COS. (c + d) 



4) The distance of the connecting wire from the horizontal 

 plane, in which the needle moves, can be very easily measured 

 in a mechanical manner ; every one may as easily perceive, 

 however, that this method promises little precision. The 

 equations themselves fortunately offer the ineans of determin- 



inp- 



