40 Sequel of M. Ampére’s Memoir 
because in one case 8 augments with s', and diminishes in the 
other; for then the angle ! is a right angle, and the angle 6" 
is comprised between a chord and a tangent formed by the 
extremity, whence it is easy to conclude 
r=2asnf, J=c—2af,ds= —2ad8, 
; : dy dg 
which gives Penis —F anpe 
and for the value of the momentum sought 
1aayl cost? 6d 
eee Kf sng ? 
which is precisely the same form as that of the force in the 
case of the rectilinear conductor, and is integrated precisely 
in the same manner. The reason of this analogy between 
these two cases, otherwise so different, is found in this circum- 
stance,—that in that of the rectilinear conductor we had 
Bats ee oPag pe 
r= spss —acotf,ds' = sat 
whence we obtain avy _ 46 
r sing? 
which differs only by the signs of the value of — in the case 
of. the circular conductor; which ought to be so, because in 
the first, 8 diminishes when s’ augments, and because it aug- 
ments with s’ in the second. 
Let us now consider two rectilinear conductors the direc- 
tions of which form a right angle, but may not be situated in 
the same plane, by naming a the right line which measures the 
distance of these directions, and by taking the points where 
they are met by the right line a for the origin of s and of s', we 
Z d 
have P= 4S EST = ds’= sds’, 
dr s 
and csf=—- a= - > 
But we have seen (vol. Ixvi. page 381) that the mutual action 
of the two elements ds and ds! is generally equal to 
T gine Os: cos? 6 
azz 1 3 
cos 6 r 
it may then be written thus, 
iiilrs dsid—; 
and as this force must be multiplied by — to haye its com- 
ponent parallel to the right line a, the value of this component 
is found to be —taitsdsd—, 
by 
- 
