194 



Mr. C. Coleridge Farr. Some Expressions for 



These relations may all be proved (as was done originally by the 

 author) by induction, using the well known relation 



-TV 2<r 1 cr 1 ^ 



PO- = -- COS(9Po-i- - Po-2. 

 <T CT 



Assuming them to be true for PO i and PO 2, they may then be shown 

 to be true for P,,. ; and trial establishes the equality in the case of P 2 

 and P r Professor T. K. Lyle has, however, given me a much shorter 

 and neater proof by means of the relations 



(a) (l-/**)Fr= oP^x- 



(6) (o-+l)P (7+1 



(c) ,,P> o-P. + P 



(d) F^i-PV-i = 



where, as usual, PL = r-^, u 



dp 



if I denote the half-length of the coil. Since 



, l-z 



cos u = , 



r 



r = 



we have 



dr_ 



dz 



dr_ 

 dx 



-t* 



0, 



A single example is sufficient. Taking the case of equation (3) we 

 have 



Expressions for the components of the magnetic force in that region 

 of a long coil for which r and r' are both greater than S. 



ofx. 



