[164] PROFESSOR STOKES, ON THE 



the small size of the pupil, a portion at least of the system is seen distinctly when the image 

 of the luminous point is seen distinctly. Omitting further consideration of the conditions of 

 distinctness, let us regard the eye as a point, and investigate the form and character of the 

 rings. 



19. Let /, g, h be the co-ordinates of the eye. To find the retardation, it will be 

 sufficient, as in Art. 9, to write f, g, h for a, b', c, and take tv, y to denote the co-ordinates of 

 ' that point of the mirror on which a given point of a ring is seen projected. The whole retarda- 

 tion is the sum of the expressions in (5) and (ll) ; and making the above substitution we 

 find 



Hence the bands still form a system of concentric circles. If X, Y be the co-ordinates of 

 the centre of the system, 



f ( l 



h \h p) c \c p) 



(L _ l\(L + 1 _ -\ 



\h cj \h c pi 



X= P ' ° KC pJ (27) 



PI 

 and Y may be written down from symmetry. 



The equations of a line joining the eye and the luminous point are 



f-a t] -b £ - c 

 f- a g-b h - c' 



At the point in which this line cuts the mirror £=0, or at least is a very small quantity, 

 which may be neglected. Hence we have 



%=l J. (28) 



c h 



from whence t] may be written down if required. If £j, tj x denote the co-ordinates of the point 

 in which the line joining the eye and the image meets the mirror, £„ »;, may be obtained from 

 Ff r] by writing a„ 6„ c x for a, b, c, where a u b i} c 2 denote the co-ordinates of the image. 

 Observing that 



a, a 12 1 



we 



find 



C i C C, p c 



c h 



£ = — -— (29) 



> 1 1 2 



7 + 



h c p 



