IN THE INTERIOR OF TRANSPARENT BODIES. 409 



that all colours are propagated with the same velocity in vacuum, the 

 particles of ether cannot exercise any sensible force at the distance X. 



If this be correct, the explanation of the phenomenon of dispersion 

 by the hypothesis of finite intervals falls to the ground ; for if the 

 particles of ether in the interior of transparent bodies are placed at 

 intervals not extremely small compared with X, they must exercise 

 very little force upon each other, and therefore the ethereal medium 

 in the interior of transparent bodies must be almost devoid of elasticity, 

 which evidently cannot be the case. But even supposing the hypothesis 

 of finite intervals to be true, I may in the present investigation neg- 

 lect the terms of the equation involving fourth and higher differential 

 coefficients ; for experiment shews that the dispersion of a ray is 

 small compared with the whole deviation produced by refraction; there- 

 fore these terms (if not quite insensible) must be small compared with 

 those involving second differential coefficients. Now it is not my 

 object to investigate that part of the dispersion (if there be any) 

 which arises from these terms, but that which arises from other terms; 

 namely, those introduced into the equations in consequence of the in- 

 fluence exerted by the particles of matter on those of ether; therefore, 

 in accordance with a well-known principle, I may neglect the former 

 terms in investigating the effect of the latter. 



$13. Neglecting, then, the terms in the equation which involve 

 fourth and higher differential coefficients for the reasons just stated, 

 we have the following equations of motion for any particle of ether, 

 (writing down the two other equations for the motion parallel to the 

 axes of y and «;) 



(d*a d i a\ . ' d /dfi dy\^ 



m c?f dx- * \dif r dz 2 ) "" " J dx \dy 



m dt : " dy' \dx< dz*) ' dy \dx + dz) 



dy \dx< dz-) ' dy \dx dz) 



m ~di> = A dtf + B \d& + df) + {A " B) di \£ + ~dy 



1 (C). 



