of the Interference of Homogeneous Light. 93. 



For y = 50 inches, 

 •00001 12091 x*+ '003760774 ar^ '03045574 x 2 — 36*35336 x 

 + 877-2895 = 0. 



I have sought the roots of these equations which have the 

 values nearest to that of x 1 on the line a n\ for the correspond- 

 ing values ofy, by the method of approximation ; and accord- 

 ingly, y = 41 gives x = 19*78 inches 



y = 45 x = 22*86 



y - 50 x = 26-92 



The points on the line a n' for these ordinates are found 

 by the equation x 1 = y tan i. 



Hence y = 41 gives x 1 = 19*515 inches 



y = 45 x 1 = 21-419 



^ = 50 x> = 23799 



We see that the points at which interference should take 

 place according to the Newtonian hypothesis, — that light moves 

 with a velocity in passing through refracting substances, 

 which is directly as the refractive index, — are still further from 

 the truth than according to the undulatory theory. The 

 central band ought to have been seen, according to this hy- 

 pothesis, following a direction similar to t u, fig. 5. 



This investigation is not, however, entirely lost labour; for in 

 addition to knowing the effect of the view we have followed, 

 we see also where we must seek for the true solution ; and it 

 is clear that these phenomena can only arise by light really 

 moving still slower in passing through refracting substances, 

 than it is supposed to do even on the undulatory theory. 



The experiment of Professor Powell must be allowed to be 

 an important as well as an elegant one, drawing a clear 

 boundary between the claims of rival theories, and pointing 

 with an analysing precision to the true theory, which no re- 

 ference to measurement alone would probably ever have dis- 

 covered. 



Since I learned the tendency of the Newtonian theory of re- 

 fraction, I have examined the displacement of the coloured 

 bands produced by causing one of the pencils to pass through 

 a very thin slip of mica, and the displacement is undoubtedly 

 in the direction which indicates the light to have passed 

 through it with diminished velocity, and which, if we knew the 

 exact thickness of the slip, might be determined. Perhaps the 

 only resource will finally be, — either the method which M. 

 Arago practised, of causing the pencils to pass through tw® 

 similar pieces of glass of which he knew the inclinations to the 

 directions of the pencils, and consequently the difference of 

 the thickness passed through by the rays ; or a method analo- 

 gous to this. 



M. Arago believed that he found the relative velocity in glass 



