267 



sin^ (a + j3) [3 sin (m + v — 2 a) + sin (w— v)] 

 + 2^sin^/3(3sin2w-l)-- 0. 



sin^(a +j3) [3 sin (u 4-v + 2/3) + sin(«^-v)] 

 ^ + ^P sin^ a. sin w cos ui=.0, 

 in which a and /3 denote the angles bag and ABC, of the 

 triangle formed by the lines joining the three magnets ; 

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

 A and c, make with the line ab; and p 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, 

 .... ?w_i, mo, 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 

 ' • -.y-i.o' 2^6,0' 2/1, o» • • •> ^^^ ^^y ^^^1 small transversal 

 velocities . . . z/'_j q, ^/'^ „, ^'10, . . ., it is required to deter- 

 mine their displacements . . . «/_5^^, yo,/» 2^i,<j ... 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= «^, 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, 



