430 Mr. OBRIEN, ON THE PROPAGATION OF LUMINOUS WAVES 



If therefore the emergent light be received on a screen, several spots 

 of light, forming a line of light, will be seen instead of a single spot 

 of light. 



I believe that in general these spots will be too close together for 

 the eye to perceive them distinct from each other, therefore nothing 

 but a line of light will be seen. But these spots will in many cases 

 lie closer together in some parts of the line than at others, and, con- 

 sequently, a variation of the intensity of the light along the line, more 

 or less considerable, will be perceptible. 



In what has been said t has been supposed constant : it is easy to 

 see what the effect of the variation of / will be ; the values of <p' which 

 satisfy the equation (1) will suffer an extremely small periodical variation 

 as t increases ; for if we add to t any small increment less than that 

 which causes f to recur, then we may add to <p' another small increment 

 less than that which causes,/ to recur, just sufficient to leave f((p't) un- 

 altered, and at the same time not to make any sensible change in sin <£', 

 (for the increment which makes f recur cannot produce any sensible change 

 in <p'), and thus the equation (1) will still be satisfied; which shews that 

 as t increases the values of <p' which satisfy (1) suffer an extremely small 

 periodical variation, going through all values, when t increases by that 

 increment which makes f recur. 



Hence the spots on the screen will perform extremely small and 

 rapid oscillations; this will only spread them into minute lines of im- 

 perceptible length. Hence it is evident that the variation of t will pro- 

 duce no sensible alteration in the emergent light. 



That the variation of the intensity of light along the line on the 

 screen, taking into account the mixture of different colours, will in 

 many cases be sufficient to produce the appearance of decided inter- 

 ruptions, I hope to shew in a future paper. 



What has been said is sufficient, I think, to prove that if the vibra- 

 tions be not cycloidal, there must be a dispersion of homogeneous light 

 in passing through a prism. 



