396 ON MAGNETS. 



long cylinder it reduces sensibly to ira^k ; the flow from the ends 

 may then be neglected. 



If we assume that the abscissa of the centre of gravity of this 

 area determines the position of the pole, we shall obtain the distance 

 2d of the two poles by dividing the moment m by the mass S ; we 

 shall thus obtain 



(6) 



for very long needles, this expression reduces to 2U-J =2U- 

 that is to say, that the poles are at a distance - from the ends. 



q 



422. M. Jamin obtained an analogous expression. If y is the 

 tension at each point, or the density, / and s the perimeter and 

 section of the bar, and A and c two constants, M. Jamin, in 

 comparing the phenomenon to the propagation of heat, finds, by 

 Fourier's laws, the following formula, which agrees with the results 

 of his experiments: 



If the section of the bar is circular and of radius a, we have 

 * /- = A /-> and putting ^ = 1$, the formula becomes 



/= 



V" 



it becomes identical with that of Green if we put 



q 27T#F 



^ = cinCi JTi. = - = 



