of Luminous IVaves in Transpareiit Bodies. 203 



Fig. 1 represents what we may conceive to be the arrange- 

 ment of the particles of tether and matter*, supposing that 

 there are fewer of the former than of the latter, the larger dots 

 representing the particles of matter and the smaller those of 

 aether. 



Fig. 2 represents the case where there are just as many 

 particles of aether as of matter. 



Fig. 3 represents a case (and, as we shall hereafter show, 

 a very probable case) in which there are more aethereal than 

 material particles, and yet the circumstances are exactly the 

 same as in fig. 2 : it is that case in which the particles of mat- 

 ter exercise so strong a repulsive force on the aethereal parti- 

 cles as to gather them into globules, which may be regarded 

 as each one particle. 



Fig. 4 represents the case first described, in which each 

 particle of matter is surrounded by many particles of aether, 

 which are not gathered into globules as in fig. 3, but spread 

 over the whole space between the particles of matter. 



It is evident from these figures, that we have two very dif- 

 ferent cases to consider in applying the equations of motion 

 to the vibrations of aether as it exists in the interior of trans- 

 parent bodies: 1st, that case which is represented by fio-ures 

 1, 2, and 3, in which (as will be shown) the equations oV mo- 

 tion will be linear equations with constant coefficients ; and 

 2ndly, that case which is represented by fig. 4, in which the 

 equations of motion will be linear equations with variable co- 

 efficients. My object in the present investigation is to 

 examine the circumstances of propagation of waves in both 

 these cases, confining myself entirely to the consideration of 

 plane waves propagated with a uniform velocity, both for the 

 sake of simplicity and because similar results to those deduced 

 in the case of plane waves may be obtained in a similar man- 

 ner in the case of any other species of waves. 



The following is a brief outline of the course I have pur- 

 sued and the results I have arrived at. 



In the fjrst place, I have investigated the general equations 

 of vibratory motion of a system of material particles sur- 

 rounded by nethereal particles. 



I have then simplified these equations by assuming that the 

 arrangement of the tethereal particles is such as is represented 

 in figures 1, 2, or 3, and applied the equations thus simpli- 

 fied to the case of plane waves propagated with a uniform 

 velocity. 



• We here suppose the particles of matter to be placed at the corners 

 of cubes ; but our reasoning will be e(|ually true for any other arran^'enicnt 

 of the |)articlcs, provided it be perfectly symmetrical and homogeneous. 



