[160] PROFESSOR STOKES, ON THE 



other to its image. Hence we have the following construction : join the eye with the luminous 

 point and with its image, and produce the former line to meet the mirror ; the middle point 

 of the line joining the two points in which the mirror is cut by the two lines drawn from 

 the eye will be the centre of the system. 



Hence if the luminous point be placed to the right of the perpendicular let fall from 

 the eye on the plane of the mirror, and between the mirror and the eye, the concavity 

 of the fringes will be turned to the right. If the luminous point, lying still on the right, 

 be now drawn backwards, so as to come beside the eye, and ultimately fall behind it, the 

 curvature will decrease till the fringes become straight, after which it will increase in the 

 contrary direction, the convexity being now turned towards the right. This agrees with 

 observation. 



12. The expression for R shews that the circle which forms the achromatic line of 

 the system passes through the two points mentioned in the last paragraph but one. This 

 is always observed to be true in experiment as far as regards the image, and is found to be 

 true of the luminous point also when it is in front of the eye, so as to be seen along 

 with the fringes, provided the fringes reach so far. 



Denoting by n^K the value of R at the centre of the system of circles, taken positively, 

 we get from (21) and (22) 



n ° %xff-^) (23) 



The numerical quantity n may conveniently be called the central order, since when it 

 lies between i -\ and i + ^, where i is any integer, the colour at the centre belongs to the 

 bright ring of the i th order. If v be the radius of the central fringe, v will be equal to 

 the semi-difference of the quantities ah(h + c)~ l and ah(h - c)~\ whence 



ach 



V»r* w 



Having found the centre of the system of circles and the projection of the image, 

 or the point where the line joining the eye and the image cuts the mirror, describe a circle 

 passing through this projection. This will be the central line of the bright fringe of the 

 order 0, and its radius will be equal to v. Now describe a pair of circles whose radii are 

 to v as \/( w o ± to \/ n o- These will be the central lines of the two bright fringes of 

 the first order, for the particular colour to which the assumed value of X relates. The 

 central lines of the two bright fringes of the second order will be a pair of circles with 

 radii proportional to •y/C^o ± 2 )» anc * so on * The fringes will be broader on the concave than 

 on the convex side of the central white fringe. When the fringes become straight, n 

 becomes infinite, and the system becomes symmetrical with respect to the central fringe. 

 This agrees with observation. 



13. When the luminous point is situated in a line drawn through the eye perpendicular 

 to the mirror a = 0, and we have simply 



B .<±*' ( , + y). 



