382 ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



move so that portions of greater inductivity shall be drawn into 

 the field. If on the other hand the potential of the condenser 

 plates is maintained constant, the charge is directly proportional 

 to the inductivity, so that the energy is also directly pro- 

 portional. 



We have seen in 140 that in this case the energy tends to 

 increase, so that again the forces tend to bring substance of greater 

 inductivity into the field. These properties of the energy should 

 not be confused with the maximum property mentioned in 119, 

 180, for there the variation was in F, tending to make it differ 

 from the values necessitated by the differential equation 



a / dv\ d ( dv\ a / 9F\ 



~- fju ^ + 5- [fA -^ -f sr I f* ~o~ = ~" ^TP ; 



dx V 9# / ty \ ty J ^z \ fa J 



/ju being unvaried. Here the variation is in //,, and may be made 

 to depend on geometrical parameters fixing the position of the 

 polarizable bodies, precisely as in 140 we had changes in 

 geometrical parameters, and in this case the variations of F must 

 be such as are consistent with the above differential equation. 



We may look at the matter from a slightly different point 

 of view. Since we found in 140 that the capacity tends to 

 increase when the forces of the system produce motion, the system 

 will move so as to increase //,. The capacity will be increased 

 when a body of greater inductivity moves into stronger parts of the 

 field, consequently magnetic bodies are drawn into the strong parts 

 of the field, while diamagnetic bodies are repelled from the stronger 

 portions to the weaker portions. This property was correctly 

 stated by Faraday, and was demonstrated by Lord Kelvin. It 

 is this tendency of diamagnetic bodies to move to the weaker 

 parts of the field that often makes them set themselves across 

 the field, instead of along it as they should do in a uniform field. 



We may calculate the mechanical forces experienced by unit 

 of volume of a substance by the proposition that the work done 

 by the forces in a displacement is equal to the loss of energy 

 of the system. Let us call the force per unit volume 5, H, Z. 

 Then if a body is displaced so that a point x, y, z comes into 

 the position x + Sac, y + By, 2 + Sz, and the corresponding change 

 in W be STT, we have 



(i) BW = - JJJ(S&B + 1% + Z&) dr. 



