212 Prof. G-. M. Minchin on the Magnetic 



cross-section of the wire. If, however, we assume that at any 

 point, Q (fig. 2), it varies inversely as the distance of the 

 point from the axis OV of the current, its value at Q may be 



written a - 3 where cr is a constant and a and a have the 

 a 



meanings already given to them"*. If we put, as before, i for 

 the total current traversing the section, we have 



era I — =i, (48 a) 



which gives <r= -J , where A is the area of the cross-section. 

 The resultant conical angle subtended now at P will be 



ife-JS, (48*) 



where £1 has the value given in (32) ; and since, to the second 

 order, 



- = 1 (Ecos — m cos g/>) H — ^(Ecos 0—mcos c/>) 2 , (48 c) 



to the expression for fUdS given in (43) must be added the 

 correction 



ft | - - (E cos e—m cos (j>) + - 2 (E cos 0—m cos </>) 2 j tfS. (48 d) 



The term of the second order in O in (32) will, of course, 

 contribute nothing to this correction, while the term of the 

 first order in XI is to be taken with the term 



— - (E cos 0—m cos <p) 



only, so that the expression for the correction is 



^((^-^/---(Ecos^-mcos^ + ^Ecos^-mcosci)) 2 "!^ 



+ ^. LEsin<9(Ecos0--mcosci>)a 7 S. . (48 e) 



Putting 0=<£ — x, as before, the only terms of new form that 

 present themselves are 



E 2 1 



-I- ^ sin 2</> . % sin 2 % j HdRd x ; 



* The necessity for considering this case was pointed out to me by 

 Professor Perry. J 



