CASE OF A SINGLE POLE. 567 



The distance of the two lines along B'B is uSt, and, along the 

 common perpendicular, RS/ sin a. Lastly, the density of each of 

 them is 



m 



Let us draw the right line AQ parallel to the magnetic trails; 

 let a and a' be the angles of the arcs bq and b'q' which correspond 

 to them, h and h' the perpendiculars AP and AT'. The actions 

 f and f of these two lines are respectively directed along the 

 bisections of the angles a and a', and in opposite directions ; they 



<x 

 make with the perpendicular, angles respectively equal to - and 



a -- , and we have 



2m a 



2m 



The components Z and X of the resultant force, measured 

 perpendicularly, and parallel to the sheet, the first upwards, and 

 the second in the direction of the motion of the movable pole, are 



a 



Z =/ cos 



F 2 sin cos (a )~| 



a / a\ WSina 2 \ 2/ 



"/COS (a --)=__!_ __ _J 



a .a' / a'\ _ 



sin 2 - sin sin I a 



(a\ 2m 2 2 \ 2/ 



-/"uiL-F 1 -a J- 



X=/sin--/' sin 



2 



We have further 

 h = 2C sin a, 

 h' h 



or, disregarding the infinitely small quantities of the second order, 



