2. THERE appears most frequently two rainbows; both of which are caused by the foresaid reflection of the sun-beams from the drops of falling rain, but are not produced by all the light which falls upon and are reflected from the drops. The inner bow is produced by those rays only which enter the drop, and at their entrance are so refracted as to unite into a point, as it were, upon the farther surface of the drop, as is represented in fig. 160; where the contiguous rays _a b_, _c d_, _e f_, coming from the sun, and therefore to sense parallel, upon their entrance into the drop in the points _b, d, f_, are so refracted as to meet together in the point _g_, upon the farther surface of the drop. Now these rays being reflected nearly from the same point of the surface, the angle of incidence of each ray upon the point g being equal to the angle of reflection, the rays will return in the lines _g h, g k, g l_, in the same manner inclined to each other, as they were before their incidence upon the point _g_, and will make the same angles with the surface of the drop at the points _b, k, l_, as at the points _b, d, f_, after their entrance; and therefore after their emergence out of the drop each ray will be inclined to the surface in the same angle, as when it first entered it; whence the lines _b m, k n, l o_, in which the rays emerge, must be parallel to each other, as well as the lines _a b, c d, e f_, in which they were incident. But these emerging rays being parallel will not spread nor diverge from each other in their passage from the drop, and therefore will enter the eye conveniently situated in sufficient plenty to cause a sensation. Whereas all the other rays, whether those nearer the center of the drop, as _p q, r s_, or those farther off, as _t u, w x_, will be reflected from other points in the hinder surface of the drop; namely, the ray _p q_ from the point _y, r s_ from _z, t v_ from α, and _w x_ from β. And for this reason by their reflection and succeeding refraction they will be scattered after their emergence from the forementioned rays and from each other, and therefore cannot enter the eye placed to receive them copious enough to excite any distinct sensation.