ACTION OF A CIRCULAR CURRENT OUTSIDE THE AXIS. 9! 



The successive derivatives satisfy the equations 



/?---% /;"=-2y;, 

 (31) /;'=-4%, /;"=-4^, 



The coefficients to be used, when the powers of y are higher 

 than the fourth, will be expressed by the aid of the following 

 differentials : 



du x 



~T~ ~ ~~ ' 



ax u 



_ - a 



32) = 



If we limit the expansion to the fourth powers of the ordinate 

 y, the components of the force are 



3 4* 2 -fl 2 7 2 3.5 



" 1 " + 



(33) 



2.4 



y 



737. When the ratio - is very small, the value of the component 

 Y is an infinitely small quantity of the first order in respect of X. 



