3. THE external rainbow is formed by two reflections made between the incidence and emergence of the rays; for it is to be noted, that the rays _g h, g k, g l_, at the points _h, k, l_, do not wholly pass out of the drop, but are in part reflected back; though the second reflection of these particular rays does not form the outer bow. For this bow is made by those rays, which after their entrance into the drop are by the refraction of it united, before they arrive at the farther surface, at such a distance from it, that when they fall upon that surface, they may be reflected in parallel lines, as is represented in fig. 161; where the rays _a b, c d, e f_, are collected by the refraction of the drop into the point _g_, and passing on from thence strike upon the surface of the drop in the points _h, k, l_, and are thence reflected to _m, n, o_, passing from _h_ to _m_, from _k_ to _n_, and from _l_ to _o_ in parallel lines. For these rays after reflection at _m, n, o_, will meet again in the point _p_, at the same distance from these points of reflection _m, n, o_, as the point _g_ is from the former points of reflection _h, k, l_. Therefore these rays in passing from _p_ to the surface of the drop will fall upon that surface in the points _q, r, s_ in the same angles, as these rays made with the surface in _b, d, f_, after refraction. Consequently, when these rays emerge out of the drop into the air, each ray will make with the surface of the drop the same angle, as it made at its first incidence; so that the lines _q t, r v, s w_, in which they come from the drop, will be parallel to each other, as well as the lines _a b, c d, e f_, in which they came to the drop. By this means these rays to a spectator commodiously situated will become visible. But all the other rays, as well those nearer the center of the drop _x y_, _z_ α, as those more remote from it β γ, δ ε, will be reflected in lines not parallel to the lines _h m, k n, l o_; namely, the ray _x y_, in the line ζ η, the ray ϰ α in the line θ ϰ, the ray β γ in the line λ μ, and the ray δ ε in the line ν χ. Whence these rays after their next reflection and subsequent refraction will be scattered from the forementioned rays, and from one another, and by that means become invisible. 4. IT is farther to be remarked, that if in the first case the incident rays _a b, c d, e f_, and their correspondent emergent rays _h m, k n, l o_, are produced till they meet, they will make with each other a greater angle, than any other incident ray will make with its corresponding emergent ray. And in the latter case, on the contrary, the emergent rays _q t, r v, s w_ make with the incident rays an acuter angle, than is made by any other of the emergent rays.