way with the first, namely, the 3. 5. 7. 9. 11, &c. but all the Globules interposited between them in the even places; namely, the 2. 4. 6. 8. 10. &c. must be the quite contrary, whence, according to the Cartesian Hypothesis, there must be no distinct colour generated, but a confusion. Next, since the Cartesian Globuli are suppos'd (Principiorum Philosoph. Part. 3. §. 86.) to be each of them continually in motion about their centers, I cannot conceive how the eye is able to distinguish this new generated motion from their former inherent one, if I may so call that other wherewith they are mov'd or turbinated, from some other cause than refraction. And thirdly, I cannot conceive how these motions should not happen sometimes to oppose each other, and then, in stead of a rotation, there would be nothing but a direct motion generated, and consequently no colour. And fourthly, I cannot conceive, how by the Cartesian Hypothesis it is possible to give any plausible reason of the nature of the Colours generated in the thin laminæ of these our Microscopical Observations; for in many of these, the refracting and reflecting surfaces are parallel to each other, and consequently no rotation can be generated, nor is there any necessity of a shadow or termination of the bright Rays, such as is suppos'd (Chap. 8. §. 5. Et preterea observavi umbram quoque, aut limitationem luminis requiri: and Chap. 8. §. 9.) to be necessary to the generation of any distinct colours; Besides that, here is oftentimes one colour generated without any of the other appendant ones, which cannot be by the Cartesian Hypothesis.
There must be therefore some other propriety of refraction that causes colour. And upon the examination of the thing, I cannot conceive any one more general, inseparable, and sufficient, than that which I have before assign'd. That we may therefore see how exactly our Hypothesis agrees also with the Phænomena of the refracting round body, whether Globe or Cylinder, we shall next subjoyn our Calculation or Examen of it.
And to this end, we will calculate any two Rays:Schem. 6.
Fig. 3. as for instance; let EF be a Ray cutting the Radius CD (divided into 20. parts) in G 16. parts distant from C, and ef another Ray, which cuts the same Radius in g 17. parts distant, these will be refracted to K and k, and from thence reflected to N and n, and from thence refracted toward P and p; therefore the Arch F f will be 5.d 5'. The Arch F K 106.d 30'. the Arch f k 101.d 2'. The line F G 6000. and f g 5267. therefore h f. 733. therefore F c 980, almost. The line F K 16024. and f k 15436. therefore N d 196. and n o 147 almost, the line N n 1019 the Arch N n 5.d 51'. therefore the Angle N n o is 34.d 43'. therefore the Angle N o n is 139.d 56'. which is almost 50.d more than a right Angle.
