426 
LORD RAYLEIGH AHD MRS. H. SIDGWICK OX THE 
a correction is required for the finite dimensions of the sections. The quadruple 
integration over the two areas may be effected by suitably combining various values 
of f corresponding to the central turn of one section and to the middle of one of the 
linear boundaries of the other. (See Maxwell’s ‘Electricity,’ 2nd edition, § 706, 
Appendix II.) We find 
f(A + h,ci,B) = -9927191 
f(A—h, a, B) =1-098740J 
sum 2’091459 
/(A, a Ah', B)= 1-1585761 
/(A, a—li, B) = -937866] 
sum 2 "096442 
/(A, a, B + £) =1-0246121 
/(A, a, B— Jc) =1-059526] 
sum 2-084138 
/(A, a, B+F) = 1-0263061 
/(A, a, B—//) = ] -058569 J 
sum 2 - 084875 
The sum of the eight values is 8 - 356914. From this we subtract 2 Xf( A, a, B), viz., 
2"089152, and divide by 6; whence for the mean value of f applicable to the sections 
as a whole 
/= 1-044627, 
differing, as it turns out, extremely little from/"(A, a, B). 
From the values given we see that f increases very sensibly as B diminishes, so 
that, as was expected, the distance between the fixed and the suspended coil, or 
between the two fixed coils, is too great to realise fully the advantageous condition 
of things described as the ideal, in wdfich f would be approximately independent of 
variations in B. 
To express the actual variations of f as a function of A, a, B, we write 
<v = 
f 
dA da dB 
and we obtain sufficiently accurate values of X, /x, v from those of f already given. 
Thus 
f(A + h, a, B)— /(A— h, a, B) 
/(A, a, B) 
■2h 
A 
= -1-95. 
In like manner /x= + 2"23, v= — "28 ; so that 
dB 
B* 
