386 M. Ampere on a new Electro-dynamic Experiment. 



suring, the angles which a rectirmear conductor, moveable 

 round its centre, forms, in the situation of equihbrium, with 

 two fixed conductors, the directions of which are through this 

 centre, and one of which is traversed several times by the elec- 

 tric current, which traverses the other but once. It is thus 

 we obtain the relation which ought to subsist between the mo- 

 mentum of rotation ; and we vei'ify it easily if the value of 

 these momenta, calculated after my formula, agrees with ex- 

 perience. 



If the conductor, the length of which has been designated 

 by b, were to extend ad hifinitum, the other, whose length is 

 always 2 a and its middle situated on the direction of the first, 

 we should have 



p :=z p ■= a sin £,>■' — ?• = 2 « cos e, 

 and the value of the momentum of rotation 



^a i i' \_p + p' + (r' — r) cot e] 



would become a i i' I sin s + ~^^ = "^^71* 



When the fixed conductor is indefinite in its two direc- 

 tions we must double this value, and we have 

 2 a Of 

 sin t 



for the momentum of rotation which it gives to the moveable 

 conductor 2 a. This momentum is therefore reciprocally pro- 

 portional to the sine of the angle e formed by the directions of 

 the two conductors. 



im • • •/ 1 ,/sin/3cos/3 /"d/J \ 



The expression ^ it a ^ y ; — ^ l^r )■> 



which I gave (in 1822) in my Recueil, page 331, for the value 

 of the component perpendicular to the element d s', may serve 

 to calculate very easily the mutual action of two parallel con- 

 ductors; for, by calling a the distance of these two con- 



a 



ductors, we have first r = -^j^j 



which gives, for the value of the preceding integral between 

 the limits /3', /3", 



els' 



A i i'-^ (cos /3" sin^ /3" + cos /3" — cos /3' sin- /3' — cos /3'), 

 then at each limit, presenting the values of 5 by b' and b", 



. , , a d /2" a d /3" 



s! ==&' -a cot/3" = i' - a cot/3', dsf= -^^-^, = -^-^,. 



By substituting these values and integrating agam between 



the 



