206 Sir William Thomson [Feb. 2, 



that of the ether surrounding it. The motion that the ether had in 

 virtue of the exciting beam of light alone, before the spherules came 

 into existence, may be regarded as being compounded with the motion 

 of the ether relatively to each spherule, to produce the whole resultant 

 motion experienced by the ether when the beam of light passes along 

 the tube, and azure light is seen proceeding from it laterally. Now 

 this second component motion is clearly the same as the whole motion 

 of the ether would be, if the exciting light were annulled and each 

 spherule kept vibrating in the opposite direction, to and fro through 

 the same range as that which the ether in its place had, in virtue of 

 the exciting light, when the spherule was not there. 



Supposing now, for a moment, that without any exciting beam at all, 

 a large number of minute spherules are all kept vibrating through 

 very small ranges * parallel to one line. If you place your eye in 

 the plane through the length of the tube and i)erpendicular to that 

 line, you will see light from all parts of the tube, and this light which 

 you see will consist of vibrations parallel to that line. But if you 

 place you eye in the line of the vibration of a spherule, situated about 

 the middle of the tube, you will see no light in that direction ; but 

 keeping your eye in the same position, if you look obliquely towards 

 either end of the tube, you will see light fading into darkness, as you 



* In the following question of the recent Smith's Prize Examination at 

 Cambridge (paper of Tuesday, Jan. 30, 1883), the dynamics of the subject, and 

 particularly the motion of the ether produced by keeping a single spherule 

 embedded in it vibrating to and fro in a straight line, are illustrated in parts 

 (a) and (d): — 



" 8. (a) From the known phenomenon that the light of a cloudless blue sky, 

 viewed in any direction perpendicular to the sun's direction, is almost wholly 

 polarised in the plane througli the sun, assuming that tliis light is due to particles 

 of matter of diameters small in comparison with the wave-length of light, prove 

 that tlie direction of the vibrations of plane polarised light is perpendicular to the 

 plane of polarisation. 



" (6) Show that the equations of motion of a homogeneous isotropic elastic solid 



of unit density, are 



cPa ,, ^dS 



57^ = ^'^ + ^")^^ + '^^°' 



d^y dS 



JF = (* + *"> JT+»^=^' 



where k denotes the modulus of resistance to compression ; n the rigidity-modulus ; 

 a, )8, 7, the components of displacement at (x, y, z, t) ; and 



da d fi dy 



S = ^ h -^ r T~' 



d X d !i a z 



o? d^ d' 



- = (^k + \n)—+nv'P, 



d x^ dy"^ dz^ 



" (c) Show that every possible solution is included in the following : — 



c?0 dih d (b 



a = -r^ + u, ^ = -— + v, 7 = -— -f ?p, 

 dx dy ' ' dz 



