SIR a GREEXHILL ON ELECTROMAGNETIC INTEGRALS. 
(iO 
Ill making these verifications use must be made of the differentiation formulas 
given in the ‘American Journal of Mathematics’ (‘A. J.M.’), 1910, p. 392, where 
D denoting = (A^ + «^+6^)^ —4AW, 
(3) 
_ = _PA-^^+Q„—g— 
(4) 
dP d 7 A" + cr + />^ , .-V i 2ah 4(du-]E 
„ = -i’h — y - +CA -j- = . 
(5) 
dP i dP , dP 
''da ^dk ' db 
P + « 
cm 
dh 
(f) 
(7) 
dQA ^d^ 
dk 
dh 
dh 
= ^7ri = 
dk 
. PrtA 
I) 
I) 
- P« A ^ + (,)A^> 
with the check formulas 
( 8 ) 
d^_kh^_h — - Q 
"dA ^dA 
dP 
«_A — 6 — — 0 
" dh dh ' dh ~ 
dP i dQ 7 dQ „ 
ct — - k-A —h — == 0, 
da da da 
Wi-qk-iih = w, 
(h) 
dW 
dA 
-y, = -V 
dh 
dW 
da 
Reviewing these calculations it will be noticed that the S.F. again shows generally 
a marked superiority over the P.F. in its analytical simplicity. 
This N in (l), § 18, is the expression which gives the potential energy (P.E.) of 
the two co-axial helical currents, or their equivalent current sheet solenoids, investi¬ 
gated by V. Jones, ‘Roy. Soc. Proc.,’ 1897, or the mutual P.E. of the two pairs of 
equivalent end plates (‘A.M.S.,’ 1907, § 59). 
But as it is the force only between the two currents which is required, and this is 
given by dN/d?> = L, we need only calculate the end values of L for measurement 
in the current weigher. 
20 . As another illustration of the extra analytical simplicity of the S.F., take the 
calculations of Bromwich (‘L.M.S.,’ 1912), where the results are expressed in a series 
for the attraction and P.F. of a circular disc, the circle on AB, where the surface 
density is a- = hid, varying as the power of the distance y from the centre 0. 
