From what has been said, it is clear that two observers standing beside each other, or one above the other, nay, that even the two eyes of the same observer, do not see exactly the same bow.  The position of the base of the cone changes with that of its apex.  And here we have no difficulty in answering a question often asked—­namely, whether a rainbow is ever seen reflected in water.  Seeing two bows, the one in the heavens, the other in the water, you might be disposed to infer that the one bears the same relation to the other that a tree upon the water’s edge bears to its reflected image.  The rays, however, which reach an observer’s eye after reflection from the water, and which form a bow in the water, would, were their course from the shower uninterrupted, converge to a point vertically under the observer, and as far below the level of the water as his eye is above it.  But under no circumstances could an eye above the water-level and one below it see the same bow—­in other words, the self-same drops of rain cannot form the reflected bow and the bow seen directly in the heavens.  The reflected bow, therefore, is not, in the usual optical sense of the term, the image of the bow seen in the sky.

Sec. 7. Analysis and Synthesis of Light.  Doctrine of Colours.

In the rainbow a new phenomenon was introduced—­the phenomenon of colour.  And here we arrive at one of those points in the history of science, when great men’s labours so intermingle that it is difficult to assign to each worker his precise meed of honour.  Descartes was at the threshold of the discovery of the composition of solar light; but for Newton was reserved the enunciation of the true law.  He went to work in this way:  Through the closed window-shutter of a room he pierced an orifice, and allowed a thin sunbeam to pass through it.  The beam stamped a round white image of the sun on the opposite wall of the room.  In the path of this beam Newton placed a prism, expecting to see the beam refracted, but also expecting to see the image of the sun, after refraction, still round.  To his astonishment, it was drawn out to an image with a length five times its breadth.  It was, moreover, no longer white, but divided into bands of different colours.  Newton saw immediately that solar light was composite, not simple.  His elongated image revealed to him the fact that some constituents of the light were more deflected by the prism than others, and he concluded, therefore, that white light was a mixture of lights of different colours, possessing different degrees of refrangibility.

Let us reproduce this celebrated experiment.  On the screen is now stamped a luminous disk, which may stand for Newton’s image of the sun.  Causing the beam (from the aperture L, fig. 7) which produces the disk to pass through a lens (E), we form a sharp image of the aperture.  Placing in the track of the beam a prism (P), we obtain Newton’s coloured image, with its red and violet ends, which he called a spectrum.  Newton divided the spectrum into seven parts—­red, orange, yellow, green, blue, indigo, violet; which are commonly called the seven primary or prismatic colours.  The drawing out of the white light into its constituent colours is called dispersion.