OK a neis) Electro-dynamic Expenmeni. 381 



which these two conductors will be the sides ; so that if it be 

 supposed that their length be increased or diminished in the 

 same proportion, the momentum of rotation will also be in- 

 creased or diminished in the same proportion. 



The result we have just obtained is but a particular case of 

 the general value of the momentum of rotation resulting from 

 the mutual action of two rectilinear conductors L'L", L^L;, 

 (fig. -t), situated in the same plane, in order to make each other 

 revolve round the point of intersection O of their directions. 

 In order to calculate more easily the value of this momentum, 

 which we shall call M, we shall place that of the mutual ac- 

 tion of the two elements ds, ds' under this form, 



= ^* COST. ^ V r /' 



which results immediately from the circumstance that the com- 

 ponent of this action, in the direction of the element d 5', be- 

 comes Lii'didij^y 



as we have just seen, in making k =■ — \ and n = 2. 



If we take the point of intersection of the dii'ections of 

 the two conductors for the origin of the distances OM = s, 

 OM' = s', we shall have s' sin /3 for the perpendicular OP 

 lowered from this point on the right line which joins the cen- 

 ti-es of the two elements, and for the value of the elementary 

 momentum of rotation, 



-|lM,d.d.'=i»Vd.'tang/3d(^), 

 whence it is cojicluded. 



But according to the manner in which the angles have been 

 taken in the formula representing the mutual action of the two 

 elements of voltaic conductors, the angle /3 is external to the 

 triangle OMM' ; and by calling e the angle MOM' comprised 

 between the directions of the two currents, the third angle 

 OMM', equal to «, will also be so to /3 — e, which gives 



y sin I 

 ' ~ "sin(/3-0' 



we have therefore 



-^ds' = ifi'^[cos/3sin/3sin(/3-£) + cos (/3-e) H-C]. 



Replacing in this value cos (/3 — e) by 



cos^ |3 cos ((3 — g) + sin" /3 cos (/3— e), 

 it will easily be seen that it is reduced to 



-jp- d s'= 5 ii' -.— [cos e cos /3 -f sui- (i cos (^ — e) + C], 



which 



