VOL. LIII.] PHILOSOPHICAL TRANSACTIONS. 7^3 



face of air at an angle of incidence of about 47° 32'-!-, the divergence of the ex- 

 treme rays will be about 2° Sl'^-: a small difference of sines answering to a con- 

 siderable difference of the angles when they approach to 90°: the ultimate differ- 

 ence to which they converge, being (from water into air) ^^ 26'^. 



Let a pencil of the solar light so, fig. 6, fall on the surface of water bc, the 

 extreme rays being refracted into ov, or; it is required to assign the glass prism 

 PNw (whose section pnw is an isosceles triangle) such, that the base nw being 

 parallel to so, and the surface of the water ac being inclined to the base nw in 

 the same angle as the surface bc; the extreme rays, in their passage through 

 the glass prism, shall be parallel ; and all the rays shall emerge colourless in the 

 line soo* ; that is, in the incident ray produced through both the media. The 

 angle sob, and the refractions from air into water being given, the angles von, 

 RON, and their diftererice vor, are given. Draw therefore, by the lemma, the 

 line OG, making the sine of rog to that of vog, as the sine of refraction of a red 

 ray, in passing from glass into water, is to the sine of refraction of a violet ray, 

 their angles of incidence being equal, then pn, perpendicular to og, will be the 

 intersection of the plane of refraction with the side of the prism that is required. 



Thus, the angle sob being 30", vor will be 18' 12 4-, vog = 50° 38' A"\, rog 

 = 50° 19' 52"-!-, whose sines are as the sines of refraction of the violet and the 

 red, in passing from glass into water at a common angle of incidence. And 

 therefore the angles of the emergence of the rays ov, or, in passing from water 

 into glass, will be equal, that is w will in its passage through the glass prism, 

 be parallel to Rr, and the rays meeting with equal and contrary refractions at the 

 points v, r, 0, as they suffered at v, r, o, will emerge colourless at o. 



Yet we must not be surprized if the pencil os is not absolutely pure light (even 

 supposing the matter, the figure, and the disposition, of the media to be fault- 

 less) because (1°) perhaps the refractive powers have not been determined with 

 sufficient exactness. (2°) If the glass plate which contains the water be not very 

 thin, the light will have received a slight tincture in passing through it at o : this 

 however may be remedied by confining the water between two glass prisms. 

 And (3°) it is scarcely possible to make experiments of this kind with a pencil of 

 light so slender as the theory prescribes. But proper allowances being made on 

 these accounts, and the refracting planes adjusted as the lemma directs, the light 

 will emerge sufficiently pure to justify the theory. And the refractions of either 

 medium being given, it will appear from the experiments whether those of the 

 other medium have been determined with sufficient accuracy. Observe also, 

 that as in practice we must fit the water to the glass, not the glass to the water, 

 we are to begin by assuming vr of a convenient magnitude; and supposing the 

 rays vr, Rr, &c. to be parallel within the glass, find the point o to which they 



4 z 2 



