9. THERE is a farther appearance in the rainbow particularly described about five years ago[333], which is, that under the upper part or the inner bow there appears often two or three orders of very faint colours, making alternate arches of green, and a reddish purple. At the time this appearance was taken notice of, I gave my thoughts concerning the cause of it[334], which I shall here repeat. Sir ~ISAAC NEWTON~ has observed, that in glass, which is polished and quick-silvered, there is an irregular refraction made, whereby some small quantity of light is scattered from the principal reflected beam[335]. If we allow the same thing to happen in the reflection whereby the rainbow is caused, it seems sufficient to produce the appearance now mentioned.
10. LET A B (in fig. 162.) represent a globule of water, B the point from whence the rays of any determinate species being reflected to C, and afterwards emerging in the line C D, would proceed to the eye, and cause the appearance of that colour in the rainbow, which appertains to this species. Here suppose, that besides what is reflected regularly, some small part of the light is irregularly scattered every way; so that from the point B, besides the rays that are regularly reflected from B to C, some scattered rays will return in other lines, as in B E, B F, B G, B H, on each side the line B C. Now it has been observed above[336], that the rays of light in their passage from one superficies of a refracting body to the other undergo alternate fits of easy transmission and reflection, succeeding each other at equal intervals; insomuch that if they reach the farther superficies in one sort of those fits, they shall be transmitted; if in the other kind of them, they shall rather be reflected back. Whence the rays that proceed from B to C, and emerge in the line C D, being in a fit of easy transmission, the scattered rays, that fall at a small distance without these on either side (suppose the rays that pass in the lines B E, B G) shall fall on the surface in a fit of easy reflection, and shall not emerge; but the scattered rays, that pass at some distance without these last, shall arrive at the surface of the globule in a fit of easy transmission, and break through that surface. Suppose these rays to pass in the lines B F, B H; the former of which rays shall have had one fit more of easy transmission, and the latter one fit less, than the rays that pass from B to C. Now both these rays, when they go out of the globule, will proceed by the refraction of the water In the lines F I, H K, that will be inclined almost equally to the rays incident on the globule, which come from the sun; but the angles of their inclination will be less than the angle, in which the rays emerging in the line C D are inclined to those incident rays. And after the same manner rays scattered from the point B at a certain distance without these will emerge out of the globule, while the intermediate rays are intercepted; and these emergent rays will be inclined to the rays incident on the globule in angles still less than the angles, in which the rays F I and H K are inclined to them; and without these rays will emerge other rays, that shall be inclined to the incident rays in angles yet less.