228 
Proceedings of the Royal Society 
But, by Ampere’s result, that two closed circuits act on one another 
as two magnetic shells, it should be 
ff is-JfdsS . U V S . Ui/ V 
= ff ds iff ds '( S.UVJV + 3 SaUv'SaUi/, -j-g) . 
Comparing, we have 
giving 
Ta a 
=s Ta<£' 
. 1^3 
® = — — , <p — . 
Ta 3 ’ Ta 4 ’ 
which are consistent with one another, and which lead to 
V ,Q = _ J_ 
Ta + ^ Ta 3 
Hence, if we put 
we get 
Q = 
P 
1 - n 
2wTa 3 1 
1 -\-n 
' 2^Ta’ 
and the mutual potential of two elements is of the form 
which is the expression employed by Helmholtz in his recent 
paper. (Ueber die Bewegungsgleichungen der Rlectricitdt, Crelle, 
1870, p. 76.) 
