516 Mr. B,. H. M. Bosanquet on the 



all cases in which residual blue has been observed, the diffract- 

 ing matter has been in the state of vapour, and the particles 

 would be spherical.) Now the relative oscillation of a sphere 

 through a space equal to its own diameter in a medium not en- 

 tirely penetrable by it must give rise to a displacement of the 

 medium, some part of which will be at right angles to the direc- 

 tion of oscillation of the sphere ; and it is evident that the prin- 

 cipal term of this displacement will have a periodic time equal 

 to half that of the sphere itself. (The relation has some resem- 

 blance to that between the vibrations of a tuning-fork and of a 

 string attached to it at right angles to its length.) Under 

 these circumstances a certain proportion of the incident red and 

 ultra-red rays would give rise to diffracted light of halved perio- 

 dic time, i. e. to ultra-violet and violet negatively polarized. 

 This transformation, however, would soon disappear as the par- 

 ticles increased further in size. 



The second point I propose to allude to is as follows. It ap- 

 pears to me that it is impossible that the inertia of the material 

 particles can in general be the source of the diminished velocity 

 of light within transparent bodies. For if the inertia of the par- 

 ticles acts in this way, they must, whether they oscillate them- 

 selves or not, absorb energy in the manner of a friction-brake; 

 it is impossible that they should act as loads to the sether, and 

 not themselves absorb energy; and the energy so absorbed 

 must be converted into heat. It should therefore always be the 

 case that the greater refractive index corresponds to the greater 

 absorption, if it be true that the inertia of the particles is always 

 the source of the refraction. But this is not the case. For 

 instance, in glass the absorption of rays of high refrangibility is 

 very small ; whereas the heat-rays of low refrangibility are almost 

 entirely absorbed. Other similar instances will occur to every 

 one. 



A few words may be said as to the formula 

 sin *== tan (45° -It). 



a. is the neutral angle, sin 2R the polarization of light emitted 



normally. 



Let A be the mean amplitude of the diffracted light in the 



plane normal to the beam, B parallel to the axis of the beam. 



In the first stage B = 0; in the second B increases up toB = A, 



which marks the termination of the second stage. 



A 2 — B 2 B 



The normal polarization is -r§ — ^ =cos 2<fi, where - = tan ; 



and if we define II by the condition that polarization = sin 2R, 

 we have at once 2(/> = 90 o — 2R, or = 45° — R. (Brewster's </>is 



