VOL. LXXXVI.] VHILOSOPHICAL TRANSACTIONS. 745 



which sound the notes in an octave, ttt, re, mi, sol, la, fa, si, ut. But as the 

 measures in these experiments were very minute, and the operations of conse- 

 quence liable to inaccuracy, I thought proper to try the thing by another test. 



Obs. 13, The sun shining into the room as before, I placed at the hole a 

 hollow prism made of fine plate-glass, and filled with pure water, its refracting 

 angle being 55°; the spectrum was thrown on an horizontal chart 8 feet from 

 the window, and at 4 feet from the prism there was placed, in the rays, a rough 

 black pin ^ of an inch in diameter. The shadow in the spectrum was bounded 

 by hyperbolic sides, as before described; and drawing a line, which might be 

 the axis of the shadow, and pass precisely through its middle, I marked on one 

 side 6 or 8 points of the shadow's outline, in each set of rays; and this being 

 often repeated, at different distances and in different shadows, the position of 

 the axis remaining the same, the curves formed by joining the points were all 

 parallel: which shows that each sine of inflection taken apart has a given ratio 

 to the sine of incidence. I afterwards divided the axis according to the musical 

 intervals, and thus found where each colour of the spectrum had terminated, in 

 what colour each part of the shadows had been, and by what ra) s formed. Then 

 I joined the parts that I had marked, and obtained a curve, which I took to be, 

 either nearly or accurately, an hyperbola of the 4th order. I next measured 

 the ordinates (the axis of the spectrum and shadow being the axis of the curve) 

 at the confines of each colour; first, the ordinate at the extremity of the recti- 

 linear red, then that at the confine of the red and orange, and so on to that at 

 the extreme rectilinear violet; to each of these ordinates I added the greatest 

 one, or that in the violet, which, in fig. 10, is vv'; that is, I produced tv to 

 v', so that vv' is equal to tv; and through v' I drew vV parallel to the axis vr, 

 and produced ga to g', and rR to k'; then from v' I set oft' \'g' equal to G'g, 

 and vV equal to rV, and the other ordinates in like manner; and I found, ac- 

 cording to the method before described, that vv' was divided inversely, after the 

 manner of the musical intervals. It is therefore evident that the inflexibilities of 

 the rays are directly as their deflexibilities and reflexibililies, but inversely as 

 their refrangibilities. The same may be proved, by measuring and dividing the 

 images made in the inside of the shadows: these I have found to be, at equal 

 incidences and distances, equal to the images on the outside, both in breadth, 

 in distance from the edge of the shadow, and in the relation which their divi- 

 sions bear to each other: therefore, whatever be the ratio of the angle of in- 

 flection to that of incidence, the same is the ratio of the angle of deflection to 

 that of incidence: so that the angle of deflection is equal to the angle of in- 

 flection. For further proof of this proposition I give the following experiment 

 and observation. 



Obs. 14. When 2 knife blades were placed by each other in a beam of light 

 which entered the dark room, so that the one might form and the other distend 



VOL. XV 11. 5 C 



