COLOURS OF THICK PLATES. [157] 



point from the axis, be denoted by ■y/ n o> 4 ^ e ra ^" OI " ^ e bright fringes of the first, second,.., 

 orders will be denoted, on the same scale, by ^/{n ± l), <y/( OT o =*= 2) ... and those of the dark 

 rings by ^/ (« ± \), ^/n ± |) ... 



The manner in which the rings open out from the centre as the luminous point is moved 

 sideways out of the axis is very striking, and has been accurately described by Newton. The 

 explanation of it is obvious. It may be remarked that the system of rings, regarded as in- 

 definite, is formed on the same scale whatever be the distance of the luminous point from the 

 axis, but the portion of the indefinite system which alone is visible, in consequence of the 

 coincidence or approximate coincidence of the maxima and minima of intensity corresponding 

 to the several colours, depends altogether upon that distance. Since in passing from the 

 interior to the exterior boundary of a given fringe the square of the radius receives a given 

 increase, it follows that the area of the fringe is constant, that is, independent of the per- 

 pendicular distance of the luminous point from the axis. Hence the breadth of the fringe 

 continually decreases as the diameter of the circle which forms either boundary increases. 

 When a small flame is used for the source of light, and is moved sideways from the axis, the 

 fringes soon become confused, because a flame which does very well for forming the broad 

 fringes of comparatively small radius seen near the axis, will not answer for the fine fringes of 

 large radius which are formed at a distance from the axis. But on using for the source of 

 light the image of the sun in the focus of a small concave mirror belonging to a microscope 

 apparatus, I found that the fringes were formed quite distinctly even when their diameters 

 became very large and consequently their breadths very small. 



Section II. 

 Bands formed by a plane mirror, and viewed directly by the eye. 



8. In the case of a plane mirror p = 03 ; and if R be the retardation of the stream 

 scattered at emergence relatively to the stream scattered at entrance, R will be obtained by 

 adding together the second members of equations (5) and (ll). Hence we have 



R--^jA^-ay+{y~br}- l -{{x-ay + {y-bf]\ . . . (15) 



It is to be remembered that in this formula a, b, c denote the co-ordinates of the luminous 

 point ; x, y those of any point in the dimmed surface ; a', b\ c those of any point M of space 

 towards which the eye is directed, and for distinct vision of which it is adapted ; and that the 

 formula is only approximate, the approximation depending both upon the smallness of the 

 obliquity, and upon the smallness of the thickness t of the glass in comparison with the dis- 

 tances of the luminous point and the point M from the mirror. 



As regards the illumination at a given point M, we are evidently concerned with so much 



