42 Sequel of M. Ampére’s Memoir 
a and s', we have b = 0; and if we suppose, besides, that the 
current which flows along s' departs from this point of inter- 
section, we shall moreover have 
yas ped Ras tet 
s/= 0, B/ = ->> B)' = => 
so that the value of the momentum of rotation will be reduced 
mn Si a tang $6," 
to 1qit(4- —-*— gs -). 
r r tang 3G, 
“ “ 
We have just seen that when the directions of the two rec- 
tilinear conductors of which we seek the mutual action, form a 
right angle, that of the two elements of s and s' becomes r-. 
Be 1 
duced to —iitrsdsid —s 
and that we have, in the same case, 
La @ PS aes 
then this elementary action may be thus written, 
—lLitsdd Vf a@+ s+ s%d (a+ s+ s!t)73 
2 
ss'dsds’ ; 
= 527 ——— ‘ 
2 (a2+ st si2)2 
As it acts in the direction of the right line 7, it is necessary, to 
find the momentum of rotation which results from it around the 
right line a, to multiply it by the sine of the angle contained be- 
tween its direction and that of this right line, which is equal to 
Jerse 
/ets+se 
and by the shortest distance 
ss’ 
Sep s? 
that is to say, that the force must be multiplied by the quantity 
ss! 
Japs + se 
which I shall represent by g, which gives 
d?M -. Ss2dsds 
pees woe eg ee 
dsdsi= 3% (ope eyy 
dsds’ 
This value at first does not appear easy to integrate; but if 
we distinguish the value of g once with relation to s, and the 
other by varying s', we have 
a7 so ples 2 s’ st - a?s' + s'3 
ds A at} st + 52 (a+ s+ s2)3 (ats? s)3? 
. ja q me a? + 3s'2 7 3(a? + s’%) 52 
dsds (a? + s? +#9)3 (a? + s?-+ s'2)5 a 
at 352 32 
+ 
@+eF EE @ TET ou 
