THEORY OF ETHER 165 



Each portion of the bounding surface of two such media 

 upon which light is incident becomes a centre of disturbance, 

 from which minor waves are rectilinearly propagated in each 

 medium. The effect at a given point p in the one medium is 

 the resultant of all the disturbances which reach it ; and the 

 effect at a given point p is the resultant of all the disturbances 

 which reach that point through the other medium. Suppose 

 the incident wave-front be considered, for simplicity, as a 

 straight line a b cutting the surface in a. Draw b c perpendicular 

 to a b. \ For the clear understanding of the following, it is of the 

 greatest importance that the whole diagram should be accurately 

 copied step by step on a larger scale by the aid of compasses and 

 rulers.] Then from a as centre, and with b c as radius, describe the 

 partial circle d q. By the time the portion of the wave-front at 

 b has reached the surface at c the disturbance originated at a 

 will have spread to all parts of the curve d x. Take inter- 

 mediate points e and f on the wave-front a b, and draw perpen- 

 diculars to the surface, and from the points g and h describe 

 partial circles with radii equal to the distance which the 

 portion of the wave-front at b has yet to travel to the surface 

 after these intermediate points have reached it. These dis- 

 tances will bej c and k c, obtained by drawing parallels to the 

 wave-front from the points g and h. A tangent drawn to 

 these curves will now represent the reflected wave-front. 



Let us now take several points in the surface a c, such 

 that the displacements caused at the point m by the waves 

 from consecutive portions x, y, z are in opposite directions i.e. 

 the distance of these points from m must vary by half wave- 

 lengths. Then, as before demonstrated, the only effective 

 portion of the surface in illuminating the point .m is the small 

 area at g, the displacement at which has been caused by the 

 portion of the wave-front at e, the areas further away more 

 and more completely destroying one another. The same 

 reasoning applies to every other portion of the reflected wave- 

 front, and hence the light must be reflected in the direction d c, 

 all the other ether disturbances being neutralised. 



It is obvious from the construction that the reflected wave- 

 front is inclined at the same angle to the reflecting surface as 



