394 ON MAGNETS. 



Biot arrived at this formula by comparing the magnet to a Volta's 

 pile, which he considered as being itself a series of plates in which 

 the electricities of the terminal plates A and B dissimulate quantities 

 of electricity of opposite signs which vary in geometrical progression 

 with the number of plates. If N be the total number of plates, the 

 positive electricity of A dissimulates in the n th plate a quantity of 

 negative electricity expressed by #a n , and the negative electricity of 

 B dissimulates, in the same element, a quantity of positive electricity 

 tfa N - n , so that the quantity of free electricity in this element, sup- 

 posing the terminal charges to be equal, is 



We may get the previous formula from this by putting N = 2/^, and 

 therefore n = xp, p being the number of pairs for unit length, and 

 taking p = a*, 



It seems difficult to discuss a mode of reasoning which has for 

 its basis only the vague notion of dissimulated electricity. 



It may be observed that if we take the origin of the co-ordinates 

 in the centre of the bar, instead of at one end, equation (3) may be 

 written 



421. Green, starting from a particular conception of the coercive 

 force, found that, for a circular cylinder placed in a uniform field 

 parallel to the axis, the linear density at a distance x from the 

 middle of a bar whose length is 2/, and radius a, might be expressed 

 by the formula 



(4) \ ~ 



+e a 



or putting - = 



