the Electro-magnetic PoTtw by Schweigger's Multiplier. 4-13 



electro-magnetic power acts at the same time inversely as the 

 distance (comp. ^'lot Precis de Physique, torn. ii. p. 122. Han- 

 steen in Gilbert's Annals, bd. Ixx. p. 175. Schmidt ibid. 

 p. S^S), therefore inversely as DE. But DE = sin. c. is for 

 the length of the needle, which I have fixed above as = 1 . 

 The aggregate powei', with which the electro-magnetism and 

 the magnetism of the needle act upon each other is therefore 



ECOS. C. ~f^ 



m— =E?«. cot. c. 



sin. r. 



Now if the needle is stationary in ns, then the electro-mag- 

 netism and the terrestrial magnetism balance each other ; it is 

 tlierefore 



M?;z sin. f = Ew. cot. c. and from tliis 



E= 



M= sin. c. tang;, c. M. 



(A] 



The same equation is likewise applicable, when the electric 

 .stream jiasses from N. to S., only that the repulsion of the 

 north pole is then a westerly one. 



b) When the connect- 

 ing wire does not pass 

 through the magnetic 

 meridian, but makes an 

 angle with it NCK = </. 

 Here two cases are to 

 be distinguished. 



a) Let the connecting 

 wire intersect the mag- 

 netic meridian in such a 

 manner that the north 

 pole of the wire and the 

 south pole of the needle 

 are opjiosite to each odier. Here the magnetism of the con- 

 necting wire acts so strongly upon the needle, that the north 

 pole of the latter is at first *drawn as far as to the wire, then 

 passes on below it, and is next repelled again on the other side, 

 so that the needle remains at rest in ns, where <^NC« = c is 

 put. If one again changes here DE = E into DG and GE, 

 then is DG = E. cos. KCG = E. cos. [c — d). 



The aggregate power with which the needle and die con- 

 necting wire react on each other is therefore 



r, cos.(c — (/) ri , ,, , 



= ^'« nn.(c-d) ~ ' *'°'* ('""")' consequently 

 Mm sin. c=E;«. cot. (c— ^Z), therefore 

 E= sin. r. (ang. [r — d) M. (R) 



•i K 2 Bui 



