on anew Electro-dynamic Experiment. 43 
d* M ye d2q adsds’ : 
qray dsds'= $22 arg dsds' @perayy |? 
adsds’ 
(a2 + s? + s*)3 
integrated first with relation to s, so that the integral becomes 
null with s, gives 
so that 
the quantity 
atsds’ 
@+s)yaepers 
that it remains to integrate by only varying s', the most simple 
means to come there is to make 
VY@+s+s*=/u—s, 
which gives 
ae u—a?—s? ds’ mn 
Balan eee 
2 2 (u-a?—s*)?+4atu _ (w+ at — s*)?+ 4a®s? 
a +s ——) ee ha Be mei — 4u , 
and changes the quantity to integrate into 
adu 
2as 
(u+a2— s2)29 
1 a7 4a? s® 
of which the integral, taken so that it vanishes when s= 0 is 
(+ fe PPB ta—s 
2Qas 
a arc tang — arc tang = 9 
which becomes reduced, by executing the indicated operations 
and in calculating by the formula known the tangent of the 
difference of the two arcs, to : 
ss 
af a+ s+ 8? 
We have then for the value of the momentum M of rotation, in 
the case where the two electric currents, of which the lengths 
are s and s', depart from points where their directions meet the 
right line which measures the shortest distance from it, 
M= Lil(q-a arc tang +), 
q 
a arc tang = a arc tang —- 
when a =0, we have evidently M = 377'q, that which agrees 
with the value M = 427'p which we have already found (page 
382), because then g becomes the perpendicular which was then 
distinguished by p. If we suppose a infinite, M becomes null, 
as it should be, because that in this case a arc tang 7 = 9, 
If we name z the angle of which the tangent is 
ss! 
a Japeps™ 
EK? we 
