COLOURS OF THICK PLATES. [155] 



(- + ) (ax+by), 



\o c pi 



and the second line in the expression for A/? becomes 



2t n_ 



fXC \c c pi 



which vanishes since c satisfies the second of equations (12). If a screen be held in a direction 

 perpendicular to the axis of the mirror, at such a distance as to receive a distinct image of the 

 luminous point, and if a, b\ c' be now taken to denote the co-ordinates, not of the image 

 itself, but of a point of the screen very near the image, the part of AR which involves the 

 squares of x and y will continue to vanish, inasmuch as c remains the same as before, and the 

 part which contains first powers, though not absolutely evanescent, will be very small ; and 

 therefore a portion of the system of rings in the neighbourhood of the image will be formed 

 distinctly. 



5. This agrees with observation. In repeating Newton's experiment in his way, except 

 that a lens of short focus was employed instead of a small hole, and that the surface of the 

 glass was purposely dimmed with milk and water, I found that when the mirror was placed at 

 a distance from the luminous point widely different from its radius of curvature, and inclined a 

 little, so as to allow of receiving the image on a sheet of paper without stopping the incident 

 light, and when the paper was held at such a distance from the mirror as to receive a distinct 

 image of the luminous point, the image was accompanied by very distinct arcs of rings. 



Whatever appearance is presented on a screen may be seen without a screen, by placing the 

 eye in such a position as to receive the rays, and adapting it to distinct vision of an object at 

 the distance of the screen in its former position. It is found universally that when the image 

 of the luminous point is seen distinctly it is accompanied by a portion, more or less extensive, 

 of a system of coloured rings or bands. In this way the rings may be seen when the image is 

 virtual, in which case they cannot, of course, be thrown on a screen. 



In the experiment described in the introduction, in which a small flame is placed in such a 

 position as to coincide with its inverted image, and viewed directly, the rings seen are 

 remarkable for their fixity, appearing like a bodily object surrounding the flame, and having a 

 definite parallax, whether judged of by the motion of the head, or by the convergence of the 

 axes of the two eyes. The same is true of the system of rings formed when the flame 

 is moved sideways out of the position above mentioned. The reason of this fixity is, that 

 inasmuch as the retardation is independent of x and y, a given point of an imaginary plane 

 drawn through the flame perpendicular to the axis of the mirror belongs to a ring of the 

 same order, whatever be the point of the mirror against which it is seen projected. 



6. Having investigated the conditions of distinctness, let us now proceed to consider 

 the magnitude and character of the rings, supposing the luminous point to be situated at 

 a distance p from the mirror, and the rings to be thrown on a screen at the same distance, or 

 else viewed in air. In this case c = c = p; and if the luminous point be in the axis e = 0, 

 which reduces (5) to 





44—5 



