366. =Circumstances under which Rainbows are Seen.=--A rainbow is seen when the spectator stands between the sun and falling rain. This commonly can not be the case, except in the latter part of the day. It sometimes, though very rarely, happens that a shower passes from the east to the west in the morning, and then a rainbow can be seen in the west. Fig. 255 is intended to show under what circumstances a rainbow is seen. Let a horizontal line be drawn from O, the observer, to P, a point directly under the middle point of the arch. If this line were extended backward from the observer it would be precisely in the direction of the sun from him. That is, the sun is directly opposite the middle of the bow. Now if the drop at A reflect a red ray to the eye of the spectator all other drops similarly situated in the arch will reflect red rays. So if B reflect a green ray all other drops similarly situated will do the same. And so of C, reflecting the violet ray. For the sake of clearness there are only three reflections represented, but the same is true of all the seven colors. In the secondary bow the arrangement of the colors is reversed, the red being at the inner part of the bow and the violet at the outer part. The double reflections are manifest in the drops D, E, and F. What I have described as taking place in a few drops takes place in countless multitudes of them in forming the bow. As the exact place of the rainbow depends not only upon the direction of the rays of the sun but also the position of the spectator, it is clear that no two spectators see precisely the same bow, for the drops that form it for the one are not the same drops that form it for the other. This is very obvious if the two be quite distant from each other; but it is equally true if they are very near together, although in this case the bow for the one would be very nearly coincident with the bow for the other. It is also true that the rainbow of one moment is not the rainbow of the next, for as the drops that reflect it are falling drops there must be a constant succession of them in any part of the bow. 367. =Colors in Dew-Drops and Ice-Crystals.=--We often see something very analogous to the rainbow in the dew. As the sun rises, if, with our backs to it, we look at the dew-drops, we see all the colors of the rainbow glistening every where before us, as if the grass were filled with gems of every hue. Here we have the same refraction and reflection in drops of water, and the resemblance fails only in the regularity of arrangement which the rainbow presents. We see the same thing also if the ground is strewed with bits of ice which have fallen from the branches of the trees, and the sun shines aslant upon them.