Royal Society. 387 



the limits /3/, /3^/ and /3/', /3,/', we have, for the value of the 

 force sought for, 



§ i ^ Ain /3;/' — sin (3/' — sin /3„' + sin j3/ 



L_ + _-L_ + _1 _i_\ 



sin /3„" — sin |3/' sin /3^/ sin /3/ /' 



or 



If the two conductors are of the same length, and perpen- 

 dicular to the right lines which join by pairs their extremities 

 on the same side, we have 



rj = r,l' = a, and r,/ = r/' = c. 



Calling c the diagonal line of the rectangle formed by these 

 two right lines and the direction of the two currents, the fore- 

 going expression then becomes 



i i' (J. -^\ = ILL. 



\ a c / ac 



Calling / the length of the conductors, and this rectangle be 



i i' 



commg a square, we have — ir for the value of the force 



finally, if we suppose one of the conductors indefinite in the 

 two directions, and that I be the length of the other, the terms 

 in which r/, r,l, rj'^ r,l' are in the denominator, will disappear, 

 we shall have 



and the expression of the force will become 



JLLi 



a 



which is reduced to i i' when the length / is equal to the di- 

 stance a, 



[To be continued.] 



LXI. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



THE meetings of this Society for the session 1825-6 wei't. 

 resumed on the 1 7th instant ; when the following papers, 

 were read : — On the changes that have taken place in some 

 ancient alloys of copper, by John Davy, M.D. F.R.S. — Ob- 

 servations on the apparent positions and distances of 468 

 double and triple fixed stars, made at the observatory at 

 3 C 2 Passy, 



