UNIFORM CIRCULAR LAYER. 133 



7T 



and for 6 = - , or /x = 0, 



..... 

 2 "~ 2. 4 ...2 



2. 4 . ..2* 



767. UNIFORM CIRCULAR LAYER. The potential U of a 

 uniform circular layer (367) of density equal to unity, and of radius a 

 at a distance r from the centre, may be expressed by one or other of 

 the two series, 



(25) r 3 



i a i.i a 3 



U = 27ra\ 3 



J_2 r 2.4 r* 



2.4...(2+2; 



according as we have r $. a. 



We will consider more particularly the second of these expressions, 

 and, calling the bracket <(0), we shall write 



The components X and Y of the action of the layer on a point P, 

 the co-ordinates of which in respect of the axis and a perpendicular 

 to the axis are x and y, have the value 



X = - 2ira 

 Y = 2ira 



Since we have 



~br <)0 sin 



x = r cos 0, = cos 0, = 



<h; (h; r 



^r W cos 



