the Directive Power of Magnets, fyc. 233 



Each of these expressions consists of a series of terms in ascend- 

 ing powers of -, which will be converging. 



We shall now seek to find X and Y for a galvanic current 

 traversing a wire coiled into the form of a hollow cylinder, of 

 which the internal radius is b, the external radius b + c, and the 

 length is 2/. We shall suppose the individual turns of the wire 

 to lie so close as that each may be regarded as an exact circle. 



Let A B be the axis of the coil, so that A and B are the 

 centres of its two faces; then AB = 2/. Let be the middle 

 point of A B. Let P be the attracted point, P M its perpendi- 

 cular distance p from A B. Let P A M = a, P B M = /3. 



Let C be the centre of any turn of the wire regarded as a 

 circle of radius a, CP = r, PCM = 0, OC = #; then it is readily 

 seen that for the whole cylindrical bobbin the forces X, Y are 

 given bv 



Ldx da, 



/* ~J -fJt 



y _ r+fr*+°. 



Mda: da, 



where L and M stand for the expressions on the right-hand side 

 of (1) and (2) respectively, and where fi depends on the strength 

 of the current. 



To perform the integrations for the length of the bobbin in 



