on anew Electro-dynamic Experiment. 41 
by integrating it with relation to s between two points whose 
distances to the element ds! may be 1’ and 7, we have 
* 1 1 
—failsds! a ar) 
which may be written thus 
ifs 1 dx’ 1 dw 
— ! FTE tae 20. yet 
bai (— ae ds eas ee) 
of which the integral, taken for the first term of r/' to r,|', and 
for the second of 7/ to 7;/, gives 
I y ZF ( a a a + a ) 
2? Tr ee pe: Rey) 
r 4 nf! rf! ry rj 
so that the action sought is precisely the same as if it were 
produced by four forces equal to 47 7', directed according to 
the right lines which join two by two the extremities of the con- 
ductors, two of these forces being attractive and the other two 
repulsive. : 
If there be required the momentum of rotation impressed in 
the case which we are here examining, by ore of the two 
rectilinear conductors on the other conductor around an axis 
parallel to the first, and whose shortest distance to the line 
which we have named a be represented by , it will be ne- 
cessary to multiply the component parallel to a of the mutual 
action of the two elements by s'— 4, and then integrate in the 
same manner: as s' is constant in the first integration, it will 
suffice to perform this multiplication after it has been executed ; 
thus we shall have two terms of the same form to integrate 
anew, the first will be 
—Laii — : = diss 
and there will come, by integrating partially, 
rear. s'—b Gas yok ds’ 
zit! —— pail [” So 
But it is easy to see that by naming c the value of s which 
corresponds to 7’, and which is a constant in the actual inte- 
gration, we have 
gi MAE, ee V a+c cot B", ds'= Bree dp", 
sin B! ? sin? p// 
ds Gh" _ 7 tanga’ , 
= Te oy) ih. ohadued oY 
the second term will be integrated in the same manner, and 
we shall have at last, for the momentum of rotation sought, 
7 ‘rt —t ‘—b fane + Bit B 
a 8/—b — s,/—b a, 5, y fang + B/' tang. 4 B/ 
ny Ts Mir ey ig tang b} vf tang t B,/ j 
In the case where the axis of rotation parallel to the right 
line s passes by the point of intersection of the two right lines 
Vol. 67. No. 333. Jan. 1826. F a and 
