of the Earth and the Luminiferous ^Ether. 459 



niferous aether, it must be small ; quite small enough entirely 

 to refute Fresnel's explanation of aberration. Stokes has 

 given a theory of aberration which assumes the aether at the 

 earth's surface to be at rest with regard to the latter, and only 

 requires in addition that the relative velocity have a potential ; 

 hut Lorentz shows that these conditions are incompatible. 

 Lorentz then proposes a modification which combines some 

 ideas of Stokes and Fresnel, and assumes the existence of a 

 potential, together with Fresnel's coefficient. If now it were 

 legitimate to conclude from the present work that the aether 

 is at rest with regard to the earth's surface, according to 

 Lorentz there could not be a velocity potential, and his own 

 theory also fails. 



Supplement. 



It is obvious from what has gone before that it would be 

 hopeless to attempt to solve the question of the motion of the 

 solar system by observations of optical phenomena at the sur- 

 face of the earth. But it is not impossible that at even 

 moderate distances above the level of the sea, at the top of 

 an isolated mountain-peak, for instance, the relative motion 

 might be perceptible in an apparatus like that used in these 

 experiments. Perhaps if the experiment should ever be tried 

 under these circumstances, the cover should be of glass, or 

 should be removed. 



It may be worth while to notice another method for multi- 

 plying the square of the aberration sufficiently to bring it 

 within the range of observation which has presented itself 

 during the preparation of this paper. This is founded on the 

 fact that reflexion from surfaces in motion varies from the 

 ordinary laws of reflexion. 



Let ab (fig. l,p. 461) be a plane wave falling on the mirror 

 mn at an incidence of 45°. If the mirror is at rest, the 

 wave-front after reflexion will be ac. 



Now suppose the mirror to move in a direction which 

 makes an angle a with its normal, with a velocity co. Let V 

 be the velocity of light in the aether, supposed stationary, and 

 let cd be the increase in the distance the light has to travel 

 to reach d. In this time the mirror will have moved a 



distance — — . 



s/ 2 cos ol 



We have cd co v/ 2 cos a 



which put = r, and ac _ -, 



ad 

 ad 



