the Absurdity of Diamagnetic Polarity. 269 



A similar result would follow for a gas, provided the mass- 

 density be nearly uniform. 



In air or a gas, 



I'=£F, 

 or 



Po 

 and, therefore, along a line of force in air, 



Pi *Po 



or 



Pi 



or approximately, since k is very small, 



that is, nearly, 



Pi 2p 



P,-i>i=|(F 2 2 -F,'). 



(?) 



In a liquid, I = kF, and therefore, along a line of force 



and therefore 



, 7 rfF, 71? dF _ 



dp = L — ds ■= kb ~ ds, 

 1 ds ds 



p,-ih=-^-^). 



.... (7') 



The important simplification effected by putting ^ constant 

 makes it easy to determine the abrupt change which takes 

 place in the force when we pass from 

 one soft body to another. For let F a -pis 9 



be the force just inside a soft body A 

 and F b the force just inside another 

 soft body B, near any point P of 

 their common surface ; and let a , 9 b 

 be the angles F a and F b make with 

 the common normal at P, drawn from 

 A to B. Then the density at P of 

 the surface-laver of A will be I cos 6 

 and of the layer of B, — I 6 cos 6 b . Hence, in passing from 

 A to B, we have 



F 6 cos0 6 -F a cos0 a = 47r. 



I 6 co 



5 0, + L cos 6 }, 



o ' a at 



