332 



CONSTITUTION OF MAGNETS. 



350. Let us, for instance, impose the condition on this force, that 

 it shall be directed along the right line which joins the elements, so 

 that we have 



x y z 



it follows that 



or 



Q " \ I ' 



X X 



In order that the second members of these two latter equations 

 shall be exact differentials of a function of the co-ordinates, we must 

 have 



and, therefore, 



- 

 r 3 



x r 



3 / ' 



The components of the elementary force will then be 



(30) 



The force itself may be determined by the ratio 



which gives 



r ./x-\ 2a\ . 3-^rl 2a\"6x $xl>r~\ 

 f=a-d( \= \ dx---dr\^ \ - ---- \ 



x \^ 3 / ^ 2 L 2 r r L 2 r J 



ds . 



