So that upon the whole, we shall find that the reason of the Phænomena seems to depend upon the obliquity of the orbicular pulse, to the Lines of Radiation, and in particular, that the Ray cd which constitutes the Scarlet has its inner parts, namely those which are next to the middle of the luminous body, precedent to the outermost which are contiguous to the dark and unradiating skie. And that the Ray ef which gives a Blue, has its outward part, namely, that which is contiguous to the dark skie precedent to the pulse from the innermost, which borders on the bright area of the luminous body.

We may observe further, that the cause of the diluting of the colours towards the middle, proceeds partly from the wideness of the hole through which the Rays pass, whereby the Rays from several parts of the luminous body, fall upon many of the same parts between c and f as is more manifest by the Figure: And partly also from the nature of the refraction it self, for the vividness or strength of the two terminating colours, arising chiefly as we have seen, from the very great difference that is betwixt the outsides of those oblique undulations & the dark Rays circumambient, and that disparity betwixt the approximate Rays, decaying gradually: the further inward toward the middle of the luminous body they are remov’d, the more must the colour approach to a white or an undisturbed light.

Upon the calculation of the refraction and reflection from a Ball of Water or Glass, we have much the same Phænomena, namely, an obliquity of the undulation in the same manner as we have found it here. Which, because it is very much to our present purpose, and affords such an Instancia crucis, as no one that I know has hitherto taken notice of, I shall further examine. For it does very plainly and positively distinguish, and shew, which of the two Hypotheses, either the Cartesian or this is to be followed, by affording a generation of all the colors in the Rainbow, where according to the Cartesian Principles there should be none at all generated. And secondly, by affording an instance that does more closely confine the cause of these Phænomena of colours to this present Hypothesis.

And first, for the Cartesian, we have this to object against it, That whereas he says (Meteorum Cap. 8. Sect. 5.) Sed judicabam unicam (refractione scilicet) ad minimum requiri, & quidem talem ut ejus effectus aliâ contrariâ (refractione) non destruatur: Nam experientia docet si superficies NM & NP (nempe refringentes) Parallelæ forent, radios tantundem per alteram iterum erectos quantum per unam frangerentur, nullos colores depicturos; This Principle of his holds true indeed in a prisme where the refracting surfaces are plain, but is contradicted by the Ball or Cylinder, whether of Water or Glass, where the refracting surfaces are Orbicular or Cylindrical. For if we examine the passage of any Globule or Ray of the primary Iris, we shall find it to pass out of the Ball or Cylinder again, with the same inclination and refraction that it enter’d in withall, and that that last refraction by means of the intermediate reflection shall be the same as if without any reflection at all the Ray had been twice refracted by two Parallel surfaces.

And that this is true, not onely in one, but in every Ray that goes to the constitution of the Primary Iris; nay, in every Ray, that suffers only two refractions, and one reflection, by the surface of the round body, we shall presently see most evident, if we repeat the Cartesian Scheme, mentioned in the tenth Section of the eighth [Schem. 6.]
Fig. 3. Chapter of his Meteors, where EFKNP in the third Figure is one of the Rays of the Primary Iris, twice refracted at F and N, and once reflected at K by the surface of the Water-ball. For, first it is evident, that KF and KN are equal, because KN being the reflected part of KF they have both the same inclination on the surface K that is the angles FKT, and NKV made by the two Rays and the Tangent of K are equal, which is evident by the Laws of reflection; whence it will follow also, that KN has the same inclination on the surface N, or the Tangent of it XN that the Ray KF has to the surface F, or the Tangent of it FY, whence it must necessarily follow, that the refractions at F and N are equal, that is, KFE and KNP are equal. Now, that the surface N is by the reflection at K made parallel to the surface at F, is evident from the principles of reflection; for reflection being nothing but an inverting of the Rays, if we re-invert the Ray KNP, and make the same inclinations below the line TKV that it has above, it will be most evident, that KH the inverse of KN will be the continuation of the line FK, and that LHI the inverse of OX is parallel to FY. And HM the inverse of NP is Parallel to EF for the angle KHI is equal to KNO which is equal to KFY, and the angle KHM is equal to KNP which is equal to KFE which was to be prov’d.

So that according to the above mentioned Cartesian principles there should be generated no colour at all in a Ball of Water or Glass by two refractions and one reflection, which does hold most true indeed, if the surfaces be plain, as may be experimented with any kind of prisme where the two refracting surfaces are equally inclin’d to the reflecting; but in this the Phænomena are quite otherwise.

The cause therefore of the generation of colour must not be what Des Cartes assigns, namely, a certain rotation of the Globuli ætherei, which are the particles which he supposes to constitute the Pellucid medium, But somewhat else, perhaps what we have lately supposed, and shall by and by further prosecute and explain.

But, First I shall crave leave to propound some other difficulties of his, notwithstanding exceedingly ingenious Hypothesis, which I plainly confess to me seem such; and those are,

First, if that light be (as is affirmed, Diopt. cap. 1. §. 8.) not so properly a motion, as an action or propension to motion, I cannot conceive how the eye can come to be sensible of the verticity of a Globule, which is generated in a drop of Rain, perhaps a mile off from it. For that Globule is not carry’d to the eye according to his formerly recited Principle; and if not so, I cannot conceive how it can communicate its rotation, or circular motion to the line of the Globules between the drop and the eye. It cannot be by means of every ones turning the next before him; for if so, then onely all the Globules that are in the odd places must be turned the same 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 præterea 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.