VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIONS. 737 



by refraction, only that the former is inverted, and the different rays have 

 reflexibilities that are inversely as their refrangibilities. 



Having settled this point, I proceeded to inquire into the absolute reflexibility 

 of the extreme colours ; for if this be known, the angle of incidence being given, 

 the angle of reflection of all the different rays may be found. For a solution of 

 which problem I made the following experiment. 



Obs. 10. The sun shining strongly through the small hole in the window- 

 shut, and the rays diverging into a cone, whose base fell on an horizontal chart 

 2i feet from the hole, between the hole and chart I placed a screen, which had 

 a plate and small hole in it ; the rays passing through this, fell on a small pin, 

 so placed that the images formed might be at right angles to the shadow ; one 

 of these I measured, together with its distance from the shadow, the distance of 

 the shadow from the hole, the breadth of the shadow, and the diameter of the 

 pin ; these measures were as follow. In fig. 7, c is the centre, and Ben the cir- 

 cumference of the pin, gm the chart, and gd a line in it, being the axis of all 

 the images, at right angles to cd, the distance of c from d the centre of the sha- 

 dow, and also to the shadow itself; ge is the p:irallel side of the image, g being 

 red, E violet, and f the confine of the green and blue ; ce is a radius parallel to 

 ED, and CA another drawn through b, the point where ob is incident, at the 

 angle oba, to which, by what was before shown, abf is equal. By measurement 

 GE is -f of an inch, cb V^, cd 44. ; now the shadow being lessened by a penum- 

 bra, this added to half the shadow, and their sum to the distance between the 

 penumbra and the violet, give ed ^^ of an inch. Whence it is easy to calcu- 

 late, that the angle of incidence being 77° 20', the angle of the red's reflection 

 abg is 75° 50', and that of the violet's 78° 51'. Now the natural sines of 77" 

 20', 75° 50', and 78° 51', are as 9756, 9695, and 98II ; or as 250, 248, and 

 251 ; which are very nearly as 77-I-, 77, and 78; and making an allowance for 

 the omissions made in the reductions, the errors in the operations and measure- 

 ments, they may be accounted as accurately in the above proportion. Now 

 these extremes 77 and 78, are the very proportions of the red's refrangibility 

 to the violet's. Optics, book 1, part 1, prop. 7. So that the reflexibility of the 

 red is to that of the violet as the refrangibilities inversely. But it is obvious that 

 the sine of incidence is not the same in the two cases ; for in the one it is equal 

 to that of the mean ray's reflection, while in the other none of the rays are re- 

 fracted at an angle equal to that of incidence, otherwise they would not be re- 

 fracted at all. This however being a consequence of the essential distinction in 

 the circumstances, does not impair the beautiful analogy which we have seen is 

 preserved in the two operations, and which proves them to be different exertions 

 of the same power. Now we may find, from the data obtained, the sines of all 

 the rays in the spectrum, by adding to 77 the lengths of the spaces into which 

 it is divided, and which are without any sensible error as the difierences of those 



VOL. XVII 5 B 



