of Edinburgh, Session 1871-72. 787 
Returning to the electrodynamic integral, note that it may be 
written 
-/v • (dpV) \ , 
so that, by the corrected formula just quoted, its value as a surface 
integral is 
yys.u.v . V * cZs -ff Ui/V 2 ~ ds. 
Of this the last term vanishes, unless the origin is in, or infinitely 
near to, the surface over which the double integration extends. 
The value of the first term is seen (by what precedes) to be the 
vector-force due to uniform normal magnetisation of the same 
surface. 
Also, since 
we obtain at once 
whence, by differentiation, or by putting p + a for p, and expanding 
in ascending powers of Ta (both of which tacitly assume that the 
origin is external to the space integrated through, i.e ., that Tp no¬ 
where vanishes), we have 
- VffW * ■ "-/f-w ■ 
and this, again, involves 
s • u ^ 5 • 
The interpretation of these, and of more complex formulas of a 
similar kind, leads to many curious theorems in attraction and in 
potentials. Thus, from (a) we have 
# 5 * 1 *. 
