ON THE COLOURS OF THICK PLATES. 159
the flame must be seen distinctly, so that a short-sighted person requires an eye-glass or spectacles.
A concave mirror prepared with milk and water is well adapted for performing Newton's experiment in his manner, or rather by substituting, as in the Duke de Chaulnes's experiments, the image of the sun in the focus of a convex lens for the small hole employed by Newton. The experiment may however be varied in the following manner. Whatever appearance is presented on a screen may be seen without a screen by receiving the rays directly into the eye, and adapting it for distinct vision of an object at the distance of the screen. Accordingly, in order to see the rings which in Newton's experiment were thrown on a screen, it is sufficient to place a small flame in front of the mirror, in such a position as to coincide with its inverted image, when a remarkably beautiful system of rings is seen in air, surrounding the flame. Not the least striking circumstance connected with these rings is their apparent corporeity, since they seem to have a definite position in space like an actual object. The striking and beautiful phenomena so accurately described by Newton in his tenth and eleventh Observations may be seen in this manner by moving the flame sideways. By altering in various ways the positions of the flame and of the eye, both in this experiment and in that with a plane mirror, the rings or bands seen in the two cases may be perceived, independently of any theory, to be evidently of the same nature. It is unnecessary here to describe at length the various appearances presented, since they are noticed in the body of the paper, in connexion with the theory.
The first section contains the theory of the rings formed in Newton's manner. The investigation, though differing a little in the mode in which it is conducted, is the same in principle as that given by Sir John Hcrschel, but is somewhat more general, inasmuch as the curvatures of the two surfaces are supposed to be any whatsoever, and the luminous point is not supposed to be situated in the axis. The distance, too, of this point from the axis is at first supposed to be arbitrary, in order to investigate under what circumstances the rings can be formed most distinctly on a screen. The second section contains the theory of the bands and rings formed by a plane mirror. The expression for the retardation is deduced as a particular case from the formula