746 PHILOSOl'HICAL TRANSACTIONS. [aNNO I7g6. 



the images, I made in one of the blades, with a file, a small dent, which, on 

 the chart, cast an elliptic or semi-circular outline; then I observed that the 

 images of both blades were disturbed by it, and wound round the edges of the 

 semi-circle; and they were all affected in precisely the same manner and degree. 

 So then the 1st knife deflected the images formed by the 2d, in precisely the 

 same degree that it inflected those images which itself formed, and so of the 

 other knife; otherwise the effect of the dent would have been different on the 

 two sets of images. We may therefore conclude, that the angles or sines of 

 inflection and deflection, bear the same ratio to the angle or sine of incidence, 

 and that they are equal to each other. My next object was to determine this 

 ratio in one of these cases, and consequently in both; and it was very agreeable 

 to find data for the solution of this problem in Newton's measurements of the 

 images and shadow: since this philosopher's well-known accuracy in such matters, 

 besides the singular ingenuity of the methods he employed, made me more 

 satisfied with these than any experiment I could make on the subject. In fig. 

 11, cs is the line perpendicular to the chart su, and passing through the centre 

 of the body, whose half is cd or se; eb is parallel to cs, and ai a ray incident 

 at D; ADB or edi is the angle of incidence; edr that of the red's deflection; 

 EDv that of the violet's; and edg that of the intermediate's. According to 

 Newton, cd was ^-^ of an inch, de 6 inches, si -^ of an inch, kv -,-fj., and 

 consequently kg j-i-o ; gs was J^; whence the angles ide, edv, edg, and edr, 

 will be found to be 4-^', 5', 7', and 9', respectively. Now the natural sines of 

 4V) 5', 7', and 9', are as the numbers ISOQ, 1454, 20354-, and 2617, which 

 are as the sines of incidence, deflection, and inflection of the violet, green, and 

 red. Thus the angles of flexion of the extreme and mean rays being given, 

 those of the other rays are found by dividing the difference between 1454 and 

 2617 in the harmonical ratio: for then the red will be equal to 145-I-; the 

 orange 87tV; the yellow ISS-r^.; the green 193|; tlie blue igSf; the indigo 

 129-1^; and the violet 258-^; and by adding to the number 1454 the violet, and 

 to their sum the indigo, and so on, we get the flexibility of the red, from 26 17 

 to 247 If ; of the orange, from 247 l-f- to 2384-|-; of the yellow, from 2384f to 

 2229-J; of the green, from 2229-i- to 2035^; of the blue, from 2035^ to I841f; 

 of the indigo, from 1841-| to 171'2a; and of the violet, from 1712a to 1454; 

 the common sine of incidence being 1309. It is therefore evident, that the 

 flexibility of the red is not to that of the violet as the refrangibility of the violet 

 to that of the red; and a little attention will convince us that we had no reason 

 to expect the analogy should be kept up in this respect; for the refrangibility of 

 the rays depends on the species of the refracting medium, and follows no general 

 rule; whereas our calculation has been made concerning the action of the bend- 

 ing power at a certain distance, greater than that at which the particles of media 

 act on the rays in refracting them. It was observed, in the mathematical pro- 



