267 



siu 3 (a ■+- |3) [3 sin (u + v — 2 a) + sin (u— v)] 

 + 2?sin 3 j3 (3sin 2 e<— 1) := 0. 



sin 3 (a +/3) [3 sin (w + v + 2/3) + sin (a— v)] 

 , + 6^> sin 3 a. sin w cos w = 0. 



in which a and /3 denote the angles bac and abc, of the 

 triangle formed by the lines joining the three magnets ; 

 u and v, the angles which the directions of the magnets, 

 a and c, make with the line ab; and^j and q the ratios of 

 the forces of the magnets a and b to that of the third mag- 

 net c, at the unit of distance. 



The paper concluded with the application of the for- 

 mulae to some remarkable cases, — as, when the three mag- 

 nets are in the same right line ; when the line joining two 

 of them is in the magnetic meridian, or perpendicular to it ; 

 &c. 



The Chair having been taken, pro tempore, by his Grace 

 the Archbishop of Dublin, V. P., the President continued 

 his account of his researches in the theory of light. 



As a specimen of the problems which he had lately con- 

 sidered and resolved, the following question was stated : — 

 An indefinite series of equal and equally distant particles, 

 .... m—i, m , mi, . . . , situated in the axis of x, at the 

 points .... — 1, 0, + 1, .... , being supposed to receive, 

 at the time 0, any very small transversal displacements 

 • • • V—x o' I/o o' Vt o» • • * » an ^ anv ver y sma M transversal 

 velocities . . . y'_ x «, y 0i0 , y 1>0 , .-., it is required to deter- 

 mine their displacements . . . y_ ht , y %t > y 1>t > . • • for any 

 other time t ; each particle being supposed to attract the 

 one which immediately precedes or follows it in the series, 

 with an energy r= a 2 , and to have no sensible influence on 

 any of the more distant particles. This problem may be 

 considered as equivalent to that of integrating generally the 

 equation in mixed differences, 



