aU known Substances to the Magnetic Injliience, i^c. 109 



whole force of the nearer focus of the bar which would act on 

 the needle in the position n s. nylft *>iU 



Again, the distances of the remote focus F's and F'n being 

 each = 2, both their influences will be inversely as 2', that 

 is 4 or j; the reciprocal of which, i-, represents the respective 

 forces. And ^ + ^ = j represents the counteracting force operat- 

 ing on the needle in the }X)sition n s, at the distance 2. Hence 

 J- — 7 = f- represents the resultant influence of both foci, or 

 of the whole bar in the given position. 



Secondly, As to the actual influence exerted by the mag- 

 net in the deflected position of the needle s' n'. 



The distances F sf and F 7i' being ^^ and ^ = 4 and -^ , tlieir 



squares, representing the inverse power of their action, are ^ and 



^. Hence the reciprocal representing the attractive force is ^ ; 



and the reciprocal representing the repulsive force is ^. Then 



U + l = m+t.= '^ or ^^, which represents the whole in- 

 fluence of the nearer fo>cus in the actual position, s' n\ assumed 

 by the needle *. 



Again, the distance F^ s\ in the case before us, was found to 

 be If,, and that of Fn' = 2^^, or Ji and | = | and 'i the 

 squares of which are |J and ^. 



Hence the reciprocal representing the attractive foi'ce is ^; 



and the reciprocal representing the repuhive action is ^. Then 



fl + ^ = S + S = S = the whole influence of the ren^e 

 fomis, or counteracting forces, in the actual position, s' n\ as- 

 sumed by the needle. 



Hence ^ — ^ - ?^^ — ^^^soo _ 2453125 repre^^ents the re 

 xxciicc j^ gjjpj — j_jjj3^ un^M: — 1411341 reprebeuTS me re- 

 sultant influence of both foci in the deviated or actual position 

 assumed by the needle, whilst the excess of this above the as- 

 sumed force in the position n ,s = | , indicates the quantity of 

 power gained by the magnet in consequence of the length of the 

 compass needle. 



• It is here assumed that the attractive and repulsive forces are parallel to 

 each other, which is not the case ; hence the results obtained, though suffi- 

 ciently near for our present object, can only be considered as approximations. 



