422 



DR. T. R. LYLE ON THE SELF-INDUCTANCE OF 



Let these two circles be filaments A and B in the rectangular conductor whose 

 section is PQRS, fig. 1. Then, if x and y be the co-ordinates of B relative to axes 

 through A parallel to the sides of the rectangle, 



and on substitution in the above we obtain, as ROSA and COHEN* have done, 



y 



2a 16a a 

 = M say, 



where a is the radius of the circle A and i^ = 



48* 



6144a 4 



Fig. 1. 



If the co-ordinates of the A circle, referred to axes through the centre of the 

 rectangle, be X and Y, then a in the above expression for M becomes a + Y where a 

 now and in what follows is the mean radius of the coil. 



This substitution is most easily carried out by aid of TAYLOR'S Theorem. Thus the 

 complete expression for M is given by 



M = M + Y + 7+&c. 



da 1.2 da 2 



1 Bull, Bureau Standards,' vol. 2, p. 364, 1900, 



