738 PHILOSOPHICAL TRANSACTIONS. [aNNO 179^. 



sines. Tlie sines of the red will be from 77 to 77-i- ; the orange from 77-1- to 

 77^- ; the yellow from 77-r to IT^ ; the green from TT\ to 'n\ ; the blue from 

 77^- to 771- ; the indigo from 774- to TT\; the violet from Ti\ to 78. So 

 that, the sine of incidence being given, that of the reflection of all the ditt'erent 

 rays may be found ; and the angle of incidence being 50° 48', the angles of re- 

 flection are as follows : of the extreme red oO° 1\' ; of the orange 50° 27 ; of 

 the yellow 50° 32' ; of the green 50° Sg' ; of the blue 50° 48' ; of the indigo 

 50° 57'; of the violet 51° 3'; and of the extreme violet 51° 15'. 



I shall conclude this part of the subject with a k\v remarks on the physical cause 

 of reflexibility. As light is reflected by a power extending to some distance from 

 the reflecting surface, the different reflexibility of its parts arises from a consti- 

 tutional disposition of these to be acted on differently by the power. And as 

 these parts are of different sizes, those which are largest will be acted on most 

 strongly. I shall not hesitate to go a step farther. In fig. 8. let ec be the re- 

 flecting surface, dh the perpendicular, and ab a ray incident at b, and produced 

 to F, and reflected into gb; draw gh parallel to fb, and gf to hb. Then hb : 

 (hg) bf ;: sin. hgb : sin. hbg, or :: sin. gbf : sin. hbg. But gbp is the supple- 

 ment of gba, the sum of the angles of reflection and incidence; therefore hb : 

 bf :: the sine of the sum of the angles of reflection and incidence, to the sine 

 of the angle of reflection : so that if i be the angle of incidence, r that of re- 

 flection, V the velocity of light, and f the reflecting force; p = sin^jR — i;^ 



By accommodating this formula to the different cases, we obtain f in all the rays; 



and the ratio of f in one set to f in another being required, we have, by strik- 



1 • 1 • . . , sin. (r + i) sin. (r' + i') o , , 



ing out V which is constant, p : f :: — . : -. — . buppose we would 



° sm. R sm. It '^^ 



know f and p' in the red and violet respectively; i = 50° 48', r = 50° 2l', and 



, o / ,1 / sin. 101° 9' sin. 10'2°a' „ ^ • ^, ,- ■ • 



R = I 15 ; then f : f :: -. — — :s"— -, : -. — tv^^—'- r^erforming the division in each 



sin. 50 21 sm. 51 lo ° 



by logarithms, and finding the natural sines corresponding to the quotients; f : 

 f':: 1275 : 1253. But the force exerted on the red is to that exerted on the 

 violet, as the size of the red to the size of the violet, by hypothesis; therefore 

 the red particles are to the violet as 1275 to 1253. This may be extended to all 

 the other colours, by similar calculations; their sizes lying between 1273 and 

 1253, which are the extreme red and extreme violet; thus the red will be from 

 1275 to 1272.^; the orange from 1272-i- to 127O; the yellow from 1270 to 1267; 

 the green from 1267 to 1264; the blue from 12(J4 to 12C)0; the indigo from 

 1260 to 1258; and the violet from 1258 to 1253. 



All this follows mathematically, on the supposition that the parts of light are 

 acted on in proportion to their sizes; and to say the trutli, I see no other proportion 

 in which we can reasonably suppose them to be influenced; for such an action is 

 not only conformable to the universal laws of attraction and repulsion, but also 

 to the following arguments. If the action be not in the simple ratio, it must 



