200 Royal Society :— 



the matter of whicli the motions constitute heat. Whether this 

 matter is or is not electricity, whether it is a continuous fluid inter- 

 permeating the spaces between molecular nuclei, or is itself niolecu- 

 larly grouped ; or whether all matter is continuous, and molecular 

 heterogeneousness consists in finite vortical or other relative motions 

 of contiguous parts of a body ; it is impossible to decide, and per- 

 haps in vain to speculate, in the present state of science. 



I append the solution of a dynamical problem for the sake of the 

 illustrations it suggests for the two kinds of effect on the plane of 

 polarization referred to above. 



Let the two ends of a cord of any length be attached to two 

 2)oints at the ends of a horizontal arm made to rotate round a ver- 

 tical axis through its middle point at a constant angidar velocity, 

 b), and let a second cord bearing a weight be attached to the middle 

 of the first cord. The two cords being each perfectly light and 

 flexible, and the weight a material point, it is required to determine 

 its motion when infinitely little disturbed from its position of equi- 

 libriutn*. 



Let I be the length of the second cord, and m the distance from 

 the weight to the middle point of the arm bearing the first. Let x 

 and y be, at any time t, the rectangular coordinates of the position 

 of the weight, referred to the position of equilibrium O, and two rec- 

 tangular lines OX, OY, revolving uniformly in a horizontal plane in 

 the same direction, and with the same angular velocity as the bearing 

 arm ; then, if we choose OX parallel to this arm, and if the rotation 

 be in the direction with OY preceding OX, we have, for the equa- 

 tions of motion, 



d-x „ n dy g 



— lO^X — 2o)-f- = —%;X, 



dt- dt I 



dt;' '' dt ni' 

 If for brevity we assume 



2\l^mJ 2\l ml 



we find, by the usual methods, the following solution : — 



a;= A cos {[w'+wH(X' + 4wV )*]*<-}-«} 



+ Bcos{[<o= + ?j=-(X^+4ttV)*]^-^+/3}, 



2a)2-\-+(\'* + 4reV)^ . 2(o--\2-(X^ + 4hV)5 



!/= ; — 7~, „ n, 1-1 A sin d) — :; ;: — „ „. i-,i B sinvZ/. 



2w[w- + ?J- + (X^-h4?i-w-)^]-f ^ 2w[w- + w^ — (\^ + 4>ra>-)^]^ ^ 



where A, a, B, /3 are arbitrary constants, and ^ and ^ are used for 

 brevity to denote the arguments of the cosines appearing in the 

 expression for x. 



* By means of this arrangement, but without the rotation of the bearing arm, 

 a very beautiful experiment, due to Professor Blackburn, may be made by attach- 

 ing to the weight a bag of sand discharging its contents thiough a fine aperture. 



