158 UNDULATORY THEORY OF LIGHT. 



all the int(!rvals which separate the particles of ponderable bodies ; as well of 

 those which are opaque as of those which are transparent. It is furthermore 

 necessary to suppose that within these bodies it is possessed of a density or of 

 an elasticity different from that which belongs to it in free space ; or that the 

 molecules of the bodies themselves, in some manner, retard its movements 

 among them. Assuming for the present the first of these suppositions to be 

 the true one, it will follow that when a luminous wave encounters the surface of 

 a ponderable medium, its velocity of progress must undergo a change. The 

 nature of the change may be best understood by referring once more to the laws 

 which govern the impact of elastic solids. If a non-elastic ball impinge upon 

 another equal to it at rest in the line which joins their centres, it will divide 

 with the latter its motion, and the two will go on together with half the origi- 

 nal velocity of the first. But if the balls are elastic they will be in a state of 

 compression at the instant in which the motion is equally divided, and the re- 

 coil from this compression, acting with a force equal to that of the impact 

 v/hich produced it, will destroy the remaining half of the velocity of the first, 

 and cominunicatc an equal addition to the velocity of the second, so that the 

 latter Avill proceed with the entire velocity which belonged to the impinging 

 ball, and this will remain at rest. But if the impinging ball be heavier or 

 lighter than the other, the motion will not be equally divided at the moment 

 when the impact brings them to a common velocity — that is to say, at the mo- 

 ment when, if non-elastic, they would begin to move together ; and the recoil, 

 which doubles the efi'ect of impact, will destroy less or more than the entire 

 motion of the first and Avill add an equal amount to the motion of the second. 

 If less than the entire motion of the first is destroyed, that body will continue 

 to advance ; if more, it will move in a contrary direction, or rebound. If the 

 second, at the moment of maximum compression, has received less than half 

 the motion of the impinging body, (in which case it is the lighter of the two,) 

 the joint velocity with which both tend to advance together will be greater than 

 half the original velocity ; and as this will be doubled for the body originally 

 at rest, by the recoil, the second body will go on with a velocity greater than 

 that of the impinging body. But if the .second in the collision receives more 

 than half the motion of the impinging body, (in which case it will be the heavier,) 

 the joint velocity will be less than half the original velocity, and accordingly 

 the final velocity of the second will not be so great as that with which the first 

 encountered it. 



Regarding the successive strata of the ether in a luminous wave as clastic 

 bodies, it will follow that so long as they are equal in mass (which will be the 

 case when the density is uniform) the passage of an undulation or tremor will 

 leave all the ether behind it at rest. But if, at any given point, a stratum of 

 greater mass (that is, an ether of different density) be encountered, there will 

 be a movement of return as well as a movement of advance ; that is to say, there 

 will be a refiected undulation which, in the view we are now taking, will be an 

 imdulation by condensation. If the change of density be from denser to rarer, 

 then the advaiice movement of the impinging tremor will not be entirely arrested, 

 and there will be a reflected undulation by rarefoction. We have here sup- 

 posed the impinging wave to be in that phase in which the molecules are mov- 

 ino- in the same direction as the wave itself. But the consequences will be 

 entirely analogous if we suppose it to be in the opposite phase : only that, on 

 that supposition, the phases of the rejected waves will also be the reverse of 

 what is stated above. 



It appears, therefore, that at any surface at which the luminiferous ether 

 undergoes a change of density, an impinging wave will, in general, be divided 

 into two parts, one of which will be propagated beyond the surface, while the 

 other will be reflected from it. It remains to be considered what should be the 

 laws governing the directions in which these two waves will proceed. 



