64 



NATURE 



{Nov. 15, 1888 



in virtue of previous assumptions, to be extremely large rela- 

 tively to electrical vibrations. The path described by an ether 

 particle originally lying in the axis must therefore be regarded 

 as an alternating electric current of finite length perpendicular 

 to the axis. It must therefore be a current of varying velocity, 

 the velocity having its maximum value when the particle is cross- 

 ing the axis, and becoming zero at the extremities of its path. 

 Such a current will be deflected by the north pole of the solenoid 

 with a force proportional to the velocity, and therefore the half- 

 vibration will assume the form of a semicircular arc as in the 

 case of an electric arc deflected by a magnet, the ends of the 

 arc coinciding with the ends of the original rectilinear path. 

 The particle during the second half of the vibrations will be 

 deflected in the opposite direction, and therefore will return 

 along the other half of the circle. The effect of the electric 

 current in the solenoid will therefore be to transform the plane- 

 polarized ray of light into a circularly-polarized ray.^ 



The circular motion of the ether particles v/ill be in the oppo- 

 -site direction to that of the current in the solenoid ; the small 

 circular current will therefore correspond to a small magnet with 

 its south pole directed towards the origin. The north pole 

 of the solenoid will therefore attract these circular currents, and 

 diminish the rate of propagation of the wave of light along the 

 axis, as each of the circles will tend to approach the north pole 

 of the solenoid. The effect of this motion, again, will be to 

 .produce an induction current in the circle in the opposite direc- 

 tion to the former one, and the circle will come to rest in a new 

 position determined by the condition that these two currents 

 shall be in equilibrium. The induced current will be repelled 

 from the north pole, and all these induced currents will form a 

 second ray circularly polarized in the opposite direction to the 

 former one, and having a greater rate of propagation than the 

 original plane-polarized ray. 



To obtain a mathematical representation of these results, sup- 

 pose that we are looking from the origin along the axis of X 

 with the axis of Y horizontally to the right and the axis of Z 

 vertically upwards. The plane of XY may be taken as the 

 plane of vibration of the incident ray, which will therefore be 

 represented by the expression — 



(37) 



The electric current, consisting in the circular motion of one of 

 the ether particles, will be of a special kind, as its velocity will 

 be variable, the effect of which will be to increase its self-induc- 

 tion. Any one of these circles will be acted on by the other 

 circles, which are indefinitely near to it, and the resulting 

 attractive and repulsive forces will affect the elastic force of the 

 ether which originally determined the vibrations, so that a current 

 of variable velocity must be considered as equivalent to a series 

 of distinct currents following each other in succession, and 

 having their velocities determined by the corresponding accelera- 

 tions. To investigate this action, consider the two rectilmear 

 components (38) of each of the circular currents. The induction 

 of any rectilinear element on the parallel elements can be 

 neglected, as the actions on each side of any element will be 

 equal in amount, so that it will only be necessary to consider 

 the vertical component of the induction. This is proportional 

 to the change in dzjcit — that is, to cf^zldfi. The elastic force on 

 the point x in the direction x + dx is therefore no longer of the 

 form P . dyjdx, but of the form P . dyjdx - B . dHfdC-, and 

 therefore the force in the opposite direction obtained by replacing 

 xhy x - dx is — 



J = a sin --(:*: - vt) ^ a sin 27r/'f - l\ 



This is equivalent to two opposite circularly-polarized rays of 

 equal wave-length determined by the equations — 



;.,=.sin2.(£-i,). 



[x t\ 

 0, = - a cos 27r - - - I ; 



a cos 2ir( £ - - ). 



Va t^ 



Owing to the change in the velocity of propagation, \ will be 

 altered, and therefore also T if the medium is isotropic ; so that 

 it will be more accurate to put— 



jt'j = a sin 2ir/ 



and 



and 



<^0 



.,= -«C0S2.(^^^-^J 



^, = «sin2.(^^-;^), 



(38) 



Since the stationary node of the ray remains unaffected, we 

 shall have — 



(39) 



' A circularly-polarized ray will therefore behave like a solenoid, and 

 deflect a magnetic needle, affording an example of a direct action of light 

 upon magnetism. 



dx dx^ 



dx' 



^dH_ 



dxdt^ 



So that the differential equation of the light-vibrations will be- 



^df' 



,dh 



dxdt' 



This equation will, however, be modified by the action of the 

 molecules on the light-vibrations, and introducing the corre- 

 sponding term from (6) (August 23, p. 405), we have — 



d;'v ^ £y 

 ^dt' dx'- 



and similarly — 



+ 47rVi(;«:i - y) 



d-z d'^z , 9 1/1 



'dt^ 



'dx"' 



B d^z 



B J^y 

 27r dxdfi 



(40) 



(40a) 





(42) 



The action of the molecule is the same along both the axes , 

 so we may put r.^ = c^, and Xy/y — \p{T) - x-^fz, where i|'(T) is a 

 known function of T^ determined from equation (4) (August 23, 

 p. 405). 



Both the above equations will be satisfied by the functions /^ 

 and Zi of (38), provided— 



And J2 ^'^^ ^2 will also be solutions of — 



l4=_P-f '^l(;f(T2) 

 "2" ^ 



The quantities A.^, \.^. T^, Tg, are determined by the four 

 equations (39), (41), and (42). 



The two waves (38) give together a new wave determined by 

 the equations — 



■n = yx + y-i = 2a cos <?> . sin 27r ^£ - ^, 



■ ■ (43) 

 ^ = z^ + Z2 — -2a sin <p . sin 2ir / — - - j, 



where d>=:ir(— - -- -- -f tv; )• 



This new vibration will take place in the plane — 

 rj sin (|) + C cos ^ = o, 



which makes an angle - <p with the plane of XY — that is, with 

 the plane of the original vibration. 



If, therefore, d be the length of the solenoid, the plane of 

 vibration will be rotated in the positive direction through the 

 angle — 



-(.i-.i)-"(;.-y- 



As the plane is determined by the value of tan <p, this 

 equation shows that as the time increases \li will oscillate 

 between certain fixed limits, the period of which being equal 

 to i/Ti - 1/T2 will be too small to be observed. For all 



