in Transparent Substances. 225 



passing through the centre of the sphere. But, on the other 

 hand, the point m f , which is symmetrical with the point m, also 

 gives rise to waves of equal intensity formed of horizontal vibra- 

 tions parallel to the pencil ; only there will be a difference of 

 phase of half a wave-length between the waves arising from the 

 point m' and those from the point m. In fact the incident wave 

 formed of vertical vibrations reaches the points m and m' in 

 the same phase. Hence, if the molecules of aether in the in- 

 cident vibration approach the reflecting surface at in, they are 

 at the same time moving away from this surface atm'; hence the 

 motion will be from right to left in the vibration reflected by 

 the point m, while it will be from left to right in the vibration 

 reflected by the point m'. The reflected waves will therefore be 

 in opposite phases, and will destroy each other in all points at 

 equal distance from m and m' — that is to say, in all points of 

 the horizontal plane passing through the centre of the sphere : 

 thus the eye placed in this plane will not be affected by the ho- 

 rizontal vibrations proceeding from m and m'. In other corre- 

 sponding points the effect will be the same (excepting that it 

 will not be to the whole of the reflected vibrations, but merely 

 to the horizontal component parallel to the beam that the rea- 

 soning applies). In fine, the horizontal components parallel to 

 the luminous pencil proceeding from the illuminated part of the 

 sphere situated above the plane of vision will be destroyed by 

 interference with the same components proceeding from the part 

 of the sphere which is below the plane of vision. 



The same reasoning applies to the third components, horizon- 

 tal and perpendicular to the pencil of light. Thus the effect 

 produced by the point n will be destroyed by that of the cor- 

 responding point n 1 for the eye placed in the horizontal plane 

 passing through the centre of the sphere. 



In short, the eye in the position in question only receives 

 light formed by the first components — that is, composed of 

 vertical vibrations. In other words, the light is polarized in a 

 horizontal plane. 



It is easy to understand that, if the spherical corpuscles arc 

 small enough, this destruction by interference will be produced 

 even outside the horizontal plane which passes through the 

 centre of the sphere, provided the observer is not too far off. 

 Thus when the plane of vision coincides with the plane of polar- 

 ization of the pencil of light (which I will suppose to be very 

 thin), all the illuminated corpuscles will transmit to the eye 

 light consisting only of vertical vibrations. This is confirmed 

 by experiment. 



V. Always assuming that the corpuscles are spherical, let us 

 examine what ensues when the horizontal pencil of light is 



Phil. Mag. S. 4. Vol. 39. No. 260. March 1870. Q 



