VOL. LIII.] PHILOSOPHICAL TRANSACTIONS. 721 



3. From water into glass. 

 Sin. incid. . s. refr. of the red :: 1 : O.863739 = s, 5g° 44' 20''4 

 Of the violet :: 1 : 0. 1 59966 = *, 59 18 45 



The difference is the greatest divergence O 25 354- 



4. From air into spirit of wine. 



Sin. incid. : s. refr. of the red :: 1 : 0.733400J = s. 47° lO' 20^2 



Of the violet :: 1 : O.7266366 = s. 46 36 18.6 



The difference is the greatest divergence O 34 1 .6 



5. From spirit of wine into glass. 



Sin. incid. : s. refr. of the red :: 1 : O.8853964 = *, 62° 18' O'^l 

 Of the violet :: 1 -.0.8821802 = 5, 61 54 24 



And their difference is the greatest divergence O 23 36 



These numbers are partly transcribed from Sir Isaac Newton, and partly com- 

 puted by a rule of Mr. Euler in the Phil. Trans. They are indeed carried on to 

 more decimal places than the experiments hitherto made can well bear : but it is 

 hoped that hereafter methods may be devised to measure the refractions of light 

 to a very great degree of precision. 



When a slender pencil sOj is refracted by the surface of a denser medium ot, 

 fig. 3, the extreme rays being ov the violet, and or the red ; we have seen that 

 the surface rvt, at which the rays pass again into the rarer medium, being pa- 

 rallel to the first surface ot, the extreme, and all the intermediate rays, will 

 emerge' parallel to each other, and to the pencil so. But if the last surface rvt 

 cut the former in a line perpendicular to the plane of refraction at the point r, 

 on the side of the radiant point s, then the extreme rays, being refracted at the 

 points V, R, will converge to some point f in the rarer medium : and if the light 

 be received on a screen at p, it will be colourless ; if nearer to the refracting 

 medium, or farther from it, it will be tinged, but on different sides. Thus, if 

 the denser medium be water, and the surrounding medium air ; the angle of in- 

 cidence LOS being 20°, the angle of divergence vor will be 7' 46''''. And ovp the 

 angle of incidence at the 2d refraction for the violet rays being taken of 30°, the 

 angle of convergence ufy will be 14' 26''''. 



On the contrary, if the plane VRt, fig. 4, which terminates the denser me- 

 dium, cut the first refracting plane on the other side of the perpendicular ol, the 

 rays will diverge from some pointy on the other side of the 2d surface: the 

 violet ray ov being more refracted from the perpendicular vp, than the red is 

 from the perpendicular Rj&. And it is evident, that if the distance (ot or ot) of 

 the point of incidence from the edge of a prism, the angle of incidence los, and 

 the angle of the prism (otv or otv,) be given, together with the refractive powers 

 of the media, the lines ov, or, will be given in magnitude and position. And 



VOL. XI. 4 Z 



