VOL. LIII.] PHILOSOPHICAL TRANSACTIONS. 725 



The other cases in which refracted light may recover its whiteness, though it 

 emerges not parallel to the incident, or may be tinged though parallel to it, Sir 

 Isaac does not treat of ; the experiment he had made, being sufficient for the pur- 

 poses to which he applies it. But he assures his readers, that if they will argue 

 truly on his theory, trying all things with good instruments and sufficient cir- 

 cumspection, the expected event will not be wanting. And the fact is, that in all 

 the experiments which have been made, if none of the necessary data are want- 

 ing, the appearance of the emerging light may be certainly predicted. 



Remark '2. When a slender pencil of light is refracted at the surface of any 

 medium, the extreme rays, the violet and red, and the several intermediate rays, 

 each of its particular degree of refrangibility, will all diverge from, or converge to 

 the same physical point : or when that point, by altering the position of the 

 plane, is thrown to an infinite distance, will all of them become parallel. And it 

 appears from the foregoing solution, that such parallelism may always be effected 

 whatever be the refracting power of the medium pnw, provided that, in a given 

 medium, the quantities m, n, &c. of the lemma, which represent the sines of 

 refraction of the several sorts of rays, to a common sine of incidence, continue 

 to be in constant ratios to one another. Conversely if, from experiments such as 

 that which Sir Isaac Newton made, it follows that, whatever be the refractive 

 powers of the media, and the angle of incidence of the light, the pencils s o, so, 

 may be made to reciprocate with each other, while all the sorts of rays, in passing 

 or repassing through the prism p n w, become parallel; if I say, this is confirmed 

 by experiments, it is a proof that, for any given medium, the ratios of those quan- 

 ties m, n, &c. are invariable. 



Remark 3. And hence Sir Isaac deduces the two theorems subjoined to his 

 8th experiment ; by the first of which he contrives to make the ratios of the sines 

 of refraction belonging to the several sorts of rays, to a common sine of inci- 

 dence, when they pass from glass into air, to serve for finding the like ratios for 

 the rays passing from water into air, without the trouble of new experiments. 



His first theorem may be deduced in this manner ; Let all the sorts of rays, 

 whether united in a pencil of light, or separated parallelwise by refraction, have 

 the same angle of incidence, whose sign is i, when they pass from a denser into a 

 rarer medium ; and let v and r stand for the sines of refraction of the extreme 

 (or any two sorts of) rays. Then seeing, by the experiments, the ratio of v to i, 

 is given, as also that of r to i ; the ratio of v — i to i, as also (invert.) that of i 

 to R ~ I, and (ex aequo) that of v — i to r — i are given ; for this last write the 

 ratio of 1 top. 



In like manner, let the refractive power of the medium from which the rays 

 emerge into the same medium as before, be increased or diminished, as also the 

 common angle of incidence ; and we need only write other marks v and r for the 



