VOL. XXII.] PHILOSOPHICAL TRANSACTIONS. 531 



the sun is taken in this sense. And this is to be observed every where in 

 the rest. 



The tliird rainbow is lost in opposition to the sun, when the ratio of refrac- 

 tion is as 1 to 0,91855. And thence recurs to the sun in the ratio of 1 to 

 0,6825. Whence again, the order of the colours being restored, in the ratio 

 of 4 to 1, orofcA to Cf, it ceases opposite to the sun. But the fourth iris 

 beginning from the sun in the ratio of equality, passes over in opposition to it 

 in the ratio of 1 to 0,94805, and thence returns to the sun, if the ratio be as 

 5 to 4. Hence again it is spread to the sun's opposition, in the ratio of 1 to 

 0,50337. And in this space are included the known refractions of all fluids. 

 Lastly, the ratio being as 5 to 1, or as ca to cn, it vanishes in the sun itself: 

 the colours being every where inverted as to sight in the return to the sun, but 

 direct in the egress from it. Hence in watery clouds, the primary and fourth 

 iris object their scarlet colours to the sun, but the secondary and third, their 

 purple. 



But whence the different refractive virtue of fluids arises, is a problem of no 

 small difficulty, and may very justly be reckoned among the secrets of nature, 

 not yet discovered by our senses, or our argumentation. For, among fluids, 

 pure water is found to refract the rays of light least of all. But imbued by any 

 salts dissolved in it, the refraction is increased according to the quantity of the 

 salts, and its own weight. And corrosive spirits, which are much heavier than 

 water, turn aside the rays of light much more. Nor is it a wonder, since they 

 are denser bodies, and therefore may be conceived the more to obstruct the pas- 

 sage of light. But it does not appear by a like argument, why so great a refraction 

 is found in any ardent spirits or oils, especially in spirit of turpentine or wine, 

 since they are very light fluids in respect of water, and consist much of ethereal 

 particles. This seems to require a very intimate knowledge of the nature of 

 light, as also of matter. 



Now from the given distance of the iris from the sun, to deduce the ratio of 

 refraction, supplies the curious with an occasion of observing very accurately, 

 and with little trouble, the refraction of any fluid whatever. For if a drop of 

 any transparent fluid hangs at the lower part of a small glass tube, and the sun 

 being near the horizon, but shining clearly, it be observed under what angle 

 with the opposite place to the sun the colours of the iris are seen in the drop ; 

 the ratio required may be had by a little calculation. The equation arising 

 is cubic explicable but by one root, by which the ratio is computed from 

 having the primary iris given. The equation is t" — SttI .... 4rrt = O, 

 where x is the tangent of the angle of incidence required, and t the tangent of 

 half the distance of the iris from the point opposite to the sun, to radius r = i. 



3 Y 2 



