vol,. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 531 



for the difference of refrangibility, by the difference of velocity in the rays of 

 light; which, if it really agreed with the observations, would give a great sim- 

 plicity to the theory of refraction, as reducing it under the same laws as the 

 theory of gravity; whereas on the hypothesis, in which the particles of light are 

 endowed with tendencies different from each other, we are obliged to multiply 

 the properties of matter. 



Messieurs de Courtivron and Melvil went so far the same ways, as to examine, 

 whether the immersions and emersions of Jupiter's satellites could not afford the 

 means of distinguishing the difference of velocities between the rays of several 

 colours. In fact, if", according to that hypothesis, the red rays were swifter than 

 the others, it possibly might happen that the satellite would appear of a reddish 

 colour in the beginning of the emersion ; viz. before the full time required for 

 the whole transmission of light from the satellite to us. As to the examination 

 of the number of seconds between the propagation of the red and violet rays, 

 the two authors differ widely; and M. Clairaut thinks, that Mr. de Courtivron's 

 calculations are more surely grounded than the others. 



Mr. Melvil supposes, that the difference of velocity between two sorts of rays 

 must be very nearly as the difference of their sines of refraction, when their sines 

 of incidence are the same. Whence he concludes that, as the sine of refraction 

 of the red rays is about y^ greater than the sine of refraction of the violet ones, 

 the velocity of the first rays must also exceed the velocity of the second by about 

 -Jy. He indeed gives those proportions as only being nearly the same; for, says 

 he further, to know exactly the ratio of the velocities from the sines of refiac- 

 tion, the following problem should be resolved, which he proposes to the learned: 

 " If two bodies fall, in equal angles of incidence, on a space terminated by 

 parallel planes, in which any power acts perpendicularly to the planes (according 

 to the hypothesis in prop. Q4, lib. 1, of the Principia), the ratio of the sines of 

 the emergence to the common sine of incidence, and consequently to each other, 

 being given, to determine the proportion of their velocities at the time of their 

 incidence on the first plane." 



But as the investigation of the curve described by the rays of light, in any 

 hypothesis of attractive power, has been published long ago (at least by M. 

 Claraut in 1738), and by such a method as leads to the solution of Mr. Mclvil's 

 problem, he doubts not but if he had seen that method, he would have resolved 

 the problem which he proposes, and perceived what a considerable difference there 

 is between the proportion of the velocities, and that of the sines of refraction. 



M. de Courtivron, who has made use of M. Claraut's solution, arrive*! at the 

 following result: If /; denote the ratio of the sines of incidence to the sine of 

 refraction for one of the colours, and q the same ratio for any other, then 

 y I — qq to \/ 1 — pp will express the ratio which the velocity of the first rays 



3 Y 2 



