of the Rays of Light considered theoretically. 173 



being produced. Whatever hypothesis be adopted respecting 

 the density of the aether in the interior of mediums, it will be 

 proper to inquire in what manner the motions of the aethereal 

 particles are modified by the presence of the atoms of the 

 mediums ; and this inquiry is peculiarly necessary on the sup- 

 position that the density is the same in mediums as in free 

 space (which is the hypothesis we have selected, and is the 

 simplest that can be made) ; for on this supposition the dimi- 

 nution of the velocity of propagation in mediums must be 

 solely owing to the obstacle which their numerous and closely 

 arranged atoms oppose to the free motion of the aethereal par- 

 ticles. Wherever the continuity or homogeneity of the me- 

 diums is interrupted, sensible reflection will take place; but in 

 the interior of a uniform medium the cause of retardation will 

 act uniformly, and its mean effect, on the supposition of uniform 

 propagation, will be, to make the condensation corresponding 

 to a given velocity greater in a certain proportion than in free 

 space, and to diminish the velocity of propagation in the same 

 proportion. This may be inferred from an investigation relative 

 to this subject, which I gave in the Philosophical Magazine and 

 Annals of Philosophy for May 1830; in which it was also 

 shown, by reasoning on the above hypothesis, and on the sin- 

 gle assumption of the uniformity of propagation, that the ratio 

 m of the velocity of propagation in free space to that in a me- 

 dium, may be found from the equation 



^=1 = H, 



in which g is the density of the medium, and H a constant 

 proportional to the mean retardation of a given number of its 

 atoms supposed immoveable. Hence if the atoms be suscep- 

 tible of motion, so that when drawn a little from their posi- 

 tions of rest they tend to return by forces varying as the di- 

 stances from these positions (and various phaenomena make it 

 probable that this is actually the case), the quantity H, in so 

 far as the retardation is proportional to the reflective power 

 of the atoms, should be multiplied by cos <$>. For, without 

 stopping to inquire the manner of reflection from a single 

 atom, we may presume that the quantity of reflection from a 

 given number thickly disposed in a plane superficies, will 

 have a given proportion to the reflection from a continuous 

 superficies of equal magnitude, and susceptible of the same 

 kind of motion as the atoms. Hence, 



m Q — 1 T , 



== H cos <p 



m g ' 



rr 1 a 2 



— n 



Now, cot = — - — - — , and as -— —, which is a quantity 

 — re — immensely 



