746 
MR. A. McAULAY OX THE MATHEMATICAL 
477 -q = V - j 11 uqd<5 = — V j 11 Vuqds = V (1|| uVqds — j j udtq 'j. 
Now, on the present theory (by means of the equations 4ttC = VVH, [V<ASH]„ + b = 0, 
and by elimination of B from the equations B = H + 47rl, SVB = 0, [S /’2B] a + J = 0), 
VH = 4tt (C - SVI), [dtR\ + h = - 4tt [Sdtl] a + b . 
Hence substituting H for q, 
H = V (jj| uC ds - ||| wSVI + [f «S d%lj = V ( [|| uC ds + ||| SlVw ch ). 
This is equation (35). Again substituting A for q, and putting 
47 tw = 
wS VA d? — j j «S dtk, 
we get [equations (19), (20), § 26] 
4tt- (A - Vic) = V [ 11 uB cU = - 111 VVnB d? = 4 tt |f j YIVu d? + [ [j VRVu ds 
Also, 
|j| VHVfi d? = f j j wVVH ds — uY dt H = 4tt ||| uC d?. 
This proves equation (34). 
That the present theory (and Maxwell’s), so far as H and A depend upon I and C, 
thus leads exactly to the ordinary theory is of some importance. One consequence is, 
that the mechanical action between bodies carrying currents and the induction of 
currents by the variation of position and magnitude of other currents and magnets, 
must necessarily be independent of the nature of the medium separating them, so long 
as that medium is non-magnetic. This is in direct contrast with the known large 
influence the medium separating two charges of electricity has on the mutual actions 
of the bodies bearing the charges. On the present, as on Maxwell’s theory, this is 
simply owing to the fact that the ordinary theory of magnetism is in the points just 
mentioned, accurately true, whereas the ordinary theory (action-at-a-distance, with 
consequently no difference of specific inductive capacity for different media) of 
electrostatics is not even approximately true. [Whether or not the theory I have 
called the “ ordinary ” theory has actually ever been formulated is of little conse¬ 
quence. I have, in the above, accurately enough described what I mean by the 
term.] 
