44 M. Ampére on a new Electro-dynamic Experiment. 
~ 
é as 19 cat SUNS 
we shall have M = $72 g(a aes) 
it is the value of the momentum of rotation which would be 
produced by a force equal to 
Tech — z 
ze? (a ape? 
acting according to the right line which joins the two extremi- 
ties of the conductors opposed to those where they are met by 
the right line which measures the shortest distance of it. 
It is, for the rest, easy to see that if, instead of supposing 
that the two currents depart from the point where they meet the 
right, we had made the calculations for what limits soever, we 
should have found a value of M composed of four terms of 
the form of that which we have obtained in this particular 
case, two of these terms being positive and two negative. 
By combining the last result which we have just obtained 
with that which we found immediately before, it is easy to cal- 
culate the momentum of rotation resulting from the action of a 
conductor having for its form the perimeter of a rectangle, and 
acting on a moveable conductor around one of the sides of a 
rectangle, when the direction of this conductor is perpendi- 
cular to the plane of the rectangle, whatever in otherrespects be 
its distance from the other sides of the rectangle, and the di- 
mensions of this one. In determining by experiment the in- 
stant when the moveable conductor is in equilibrium between 
the opposed actions of the two rectangles situated in the same 
plane, but of different sizes and at different distances of the 
moveable conductor, we have a very simple means of pro- 
curing verifications of my formula susceptible of great preci- 
sion: it is that which we may easily make with the instrument 
of which I spoke above, by conveniently modifying the fixed 
conductors which make a part of it. 
The same calculations may be made for any value whatso- 
ever of the angle of the directions of the two rectilinear con- 
ductors: by naming this angle «, we have 
r= Vaiss + s?— ss! cose, 
. . . $$ 
and in always rae gpoe. 5 by g the ny —, we find that 
the force parallel to the right line a is equal to 
ri (% fee) 
2 (- + a cose ff" = ~ 
The momentum of rotation around the right line a is then equal 
If). 
to 1 74! i : z 
sit \(qsme—rcote — — 
a sin: 
As 
