HELMHOLTZ ON THE CONSERVATION OF FORCE. 155 



bodies liable to be changed by induction, will, on the contrary, as 

 in the case of electricity, be measured by the alterations of the sum 



V+i{W,+W,), 



where V denotes the potential of the bodies towards each other, 

 W and W. those of the bodies UDon themselves. If B be 



a o * 



an unchangeable steel magnet, the approximation of a body with 

 changeable magnetism generates a vis viva equal to the increase 



of the sum V+iw„. 



3. It is known that the exterior action of a magnet can always 

 be represented by a certain distribution of its fluids over its 

 surface ; we can therefore for the potential of the magnet, sub- 

 stitute the potentials of such surfaces ; we then find, as in the 

 case of conducting electric surfaces, for a perfectly soft mass of 

 iron A, which is magnetized by a magnet B, the gain C in vis 

 viva for the unit of quantity of the positive magnetism, during 

 the passage from the surface of the iron to an infinite distance, 

 given by the equation 



~ac=v+w„. 



Now as every magnet contains equal quantities of north and south 

 magnetism, hence Q in each =0, it follows for such a piece of 

 iron, or for a piece of steel of the same form, position, and dis- 

 tribution of magnetism, whose magnetism therefore is com- 

 pletely bound by the magnet B, that 



v=-w,. 



4. But V is the vis viva generated by a steel magnet during 

 its approximation until its magnetism is completely bound; 

 according to this equation it must be the same no matter what 

 may be the magnet to which it approaches, provided always that 

 the approximation is continued till the magnetism is completely 

 bound, for W„ remains always the same. The vis viva of a piece 

 of iron, on the contrary, which has been approximated till the 

 same distribution is effected, is, as shown above, 



hence only half as great as that of the already magnetized mass. 

 It is to be remembered that W is in itself negative, hence —-W 

 always positive. 



