IN THE INTERIOR OF TRANSPARENT BODIES. 425 



now this value of a shews that the particles vibrate according to the 

 cycloidal law. Hence it follows, that if the velocity of propagation be 

 constant, the particles of ether must vibrate according to the cycloidal 

 law. This conclusion is also true, if we account for dispersion by means 

 of M. Cauchy's hypothesis of finite intervals, neglecting the action of 

 the material upon the etherial particles; for then we shall have an 

 equation of the form 



d a a _ d 2 a „ d'a 



dF = mB drf +mB d* : 



treating this equation in the same manner as we have just treated the 

 equations 



cPa -n d'a „ 



-j^r = mB-rr - mta, 

 dP du< 



we may arrive at the same result as that just obtained. 



§ 34. If we consider the manner in which light may be produced 

 by combustion, I think it is not very likely that the particles always 

 vibrate according to the cycloidal law. Let us, for example, take the 

 case of oxygen and hydrogen, and suppose the two gases mixed to- 

 gether in the proper proportion to form water. They will remain in a 

 state of stable equilibrium* so long as we keep the temperature below 

 a certain point, but if we raise the temperature above that point, the 

 equilibrium will become unstable, and on the slightest disturbance the 

 particles will rush together to assume new positions of equilibrium. 

 Now they will evidently be unable to assume their positions of equi- 

 librium immediately, but will as it were shoot beyond them, and oscillate 

 backwards and forwards for a little time before they come to rest, the 

 consequence of this will be, that an oscillatory motion will be com- 

 municated to the etherial particles which surround them, and it may be 

 in this manner that waves of light are produced. Now it is clear, that 

 the material particles will in general communicate their own peculiar 

 kind of vibration, whatever that may be, to the etherial particles, and 



• I speak here of chemical forces, on the supposition that they are the same in kind as 

 common forces, for if this supposition be not true, the results arrived at in the present 

 paper, and all similar results depending upon molecular action, are useless. 



