IN THE INTERIOR OF TRANSPARENT BODIES. 421 



the relation thus established between v and X will be the dispersion of 

 light; but it is very important to inquire whether the dispersion that 

 would be produced by this relation, if true, follows the same law as 

 that which really takes place. 



In the above formula as \ increases v increases (supposing C positive), 



and therefore the index of refraction ^ (which varies as -) diminishes: 



now as we pass from the violet to the red rays we know that \ increases, 

 hence our formula for v gives an index of refraction diminishing as we 

 pass from violet to red ; and so far it agrees with experiment. If C 

 be negative, of course the reverse is the case ; it is easy to see that Cs 

 being positive or negative depends on the law of force, and that there 

 are a variety of different laws which will make it positive. (See § 26). 



§ 29- To estimate what effect the motion of the material particles 

 has upon the velocity of propagation. 



To do this, we must add to the equations (2?) in Article (6) the 

 equations of motion of the material particles, which, if we denote the 

 force of one particle of matter on another by m l r, ^ (/",), will evidently be 





+ 'Em\(p{r')Aa i + -<p'(r) A a?, (A a?, A a, + A^Aft + A* A7,)l 

 and similar expressions for ~~ and -~!j % 



(-»,)• 



Now it is easy to see that the six equations (B) and (S t ) may be 

 satisfied by assuming 



o = a cos k (vt — u), /3 =£cos k(vt— it), y = c cos k (vt—u), 



a^a^oskivt—u), fi t = b t cosk(i)t — u), y = c / cosk{vt-u / ), 



where u =px + qy + r%, u, =px i + qy t + r%,, and a b c, a, b t c t , are dis- 

 posable constants, which we may determine so that the vibrations of the 

 particles shall be wholly transversal : this will appear by substituting 

 as follows these values for a /3 y, a, /3, 7,, and supposing the vibrations 

 transversal. 



Vol. VII. Part III. SB 



