204- The Rev. M. O'Brien aii the Propagatioii 



I have then deduced the following results : — 



1st. That the velocity of pi-opagation is in general different 

 for tran&ver&al and for direct vibrations, and that consequently 

 any arbitrary disturbance will give rise to two waves, propa- 

 gated with different velocities, one consisting of transversal 

 and the other of direct vibrations. 



2ndly. That plane waves cannot be propagated with a uni- 

 form velocity, unless the particles vibrate according to the 

 cijcloidal law. 



Srdly. That if v be the velocity of propagation, and \ the 

 length of the wave, then there is the following relation be- 

 tween and X {quite independently of the hypothesis offnite 

 intervals), viz. 



4^ ^ 



A2 - o2 - B' 



supposing the particles of matter absolutely fixed in space; 

 and 



4- tt" C C^ 



~w ^ 0^^^ + ir - b; 



supposing the pai'ticles of matter capable of motion (as they 

 must be). 



In these formulae B is a certain constant depending on the 

 law of force of one particle of tether on another ; B^ a similar 

 constant with reference to particles of matter; and C C^ two 

 constants depending on the mutual action of matter and aether 

 on each other. B and B, are not the same for transversal and 

 direct vibrations. 



These residts show that the dispersion of light may be com- 

 pletely accounted for without having recourse to the hypothesis 

 of finite intervals. Indeed a more general value of K than 

 that just given may be obtained in the following form, viz. 



4 TT^ C C| Cg Cg . 



IF ~ ^F'^^ + J^'^B, "^ u^^^b:, ^ tj'^ - B3 + ^^• 



by supposing that the particles of transparent bodies are com- 

 pound (as they must be in many cases), consisting of several 

 essentially different atoms, there being a term in the above 

 equation for each difl^erent atom. Of course with such a re- 

 lation as this we may make the different corresponding values 

 of ju. and X agree with their actual values obtained by obser- 

 vation as nearly as we please. 



Lastly. I have shown that, though it appears at first sight 

 almost impossible to solve the differential equations in the 

 case represented by fig. 4, yet there is a peculiar circumstance 

 in the case of luminous waves which enables us to get over 





