267 
sin’ (a + () [3 sin(u +v—2a) + sin (wu—v)] 
+ 2qsin*P (3sin?u—1) = 0. 
sin®(a +3) [3 sin (u +v +2) + sin(u—v)] 
+6psin’a. sinucosu=0. 
in which a and B denote the angles Bac and asc, of the 
triangle formed by the lines joining the three magnets; 
uand v, the angles which the directions of the magnets, 
a and c, make with the line an; 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- 
mulz to some remarkable cases,—as, when the three mag- 
nets are in the same right line; when the line joiming two 
of them is in the magnetic meridian, or perpendicular to it; 
&e. 
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. 
Asa 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, 
sees My Moy M ++, 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 
+ Y1,09 Yo, Yi,09 °°"? and any very small transversal 
velocities .-. 419 Yoo Y',0 °° 
mine their displacements .--¥_4. %,» Ye -** for any 
other time ¢; each particle being supposed to attract the 
one which immediately precedes or follows it in the series, 
with an energy = a’, and to have no sensible influence on 
., it is required to deter- 
any of the more distant particles. This problem may be 
considered as equivalent to that of integrating generally the 
equation in mixed differences, 
aS +." ~~ = 
