of a Circular Current of given Aperture Sfc. 303 



o : -'{«(»-«-**(-*+^r)+5s?[ w <*-« 



-^(6L-5K + ^+^J>sin2^]]-. .(6) 



Now the normal force at any point on the anchor-ring is the 



value of r~ with m = c ; it is therefore 



am 



<{(lHD^ + I5?<^- 17 >**}* - (7) 



If P is any point on the anchor-ring, the distance of P 

 from OY is a — ccos <£, and the area of a narrow circular strip 

 of the ring parallel to the plane of the aperture of the ring is 

 27r(a — c cos <fi) . cdcf> ; and this multiplied by (7) is the normal 

 flux of force through the strip. Integrating the product from 

 $ = to </> = 7r, we get the flux through the whole of the 

 upper half of the ring. The result is simply 



(Jj — j) 1 (a—ccos(j))sm(j^d(j), 



the second term in (7) being neglected because it gives a 

 term of the third order. Thus this part of the flux is 



W ( L ~i) (8) 



Adding this to (5), we have the whole flux sought, divided 

 by i, equal to 



w |4a(L-2) + 2 c (L-^- I J(2L + 19)J, . (9) 



Ha 

 where L = log e — . This, then, is the Coefficient of Self- 



G 



Induction. If in this expression a and c are taken in centi- 

 metres, the result is the coefficient measured in absolute units; 

 and if this is divided by 10 9 , we have the coefficient of self- 

 induction in secohms. 



Thus, for example, a circular current running in a wire the 

 diameter of whose cross-section is 2 millim., while the diameter 

 of its central filament is 2 centim., has a coefficient of self- 



59*207 



induction of about 59*207 absolute units, or 5 — secohms : 



10 b 



and if the dimensions of the cross-section were neglected, this 



number would be 58*866. 



Clerk Maxwell (Elec. and Mag. vol. ii. art. 704) gives the 



