[166] PROFESSOR STOKES, ON THE 



joining L and L 3 , when the image of the eye is in this line the bands necessarily become rings, 

 having the image for their centre. Hence the theory of the rings or bands, which it is the object 

 of the experiment to compare with observation, is not involved in the assumption that the image 

 of the eye was in the line LL^ when the system of rings appeared arranged symmetrically 

 around the image of the luminous point. By moving the head a little to one side, and 

 observing whether the centre of the system of rings then lay to the right or left of the image, 

 it was easy to compare theory with observation as to the direction of curvature. 



There was no difficulty in telling when the virtual image of the eye coincided with the 

 image of the luminous point, since in that case the latter image expanded indefinitely. The 

 phenomena observed offered no direct test of the coincidence of the virtual image of the eye 

 with the luminous point, except what arose from the appearance of the bands themselves. I 

 did not think it worth while to take any measures, but contented myself with observing that 

 when the eye was in the expected position, or thereabouts, the rings expanded indefinitely 

 when the image was kept in the centre of the system, and the bands formed when the image was 

 allowed to pass to one side changed curvature as the head moved backwards and forwards. 



21. The bands may be considered as completely characterized by the position and 

 magnitude of the achromatic line, and by the value of the numerical quantity which has been 

 already defined as the central order. A simple geometrical construction has already been given 

 for determining the achromatic circle. Substituting X, Y for ce, y in (26), and denoting the 

 resulting value of R by - n \, we find 



t \h\c~ p) " c U ~ p) J + \h \c ~ p) " c \h " p I f 



n °~ n\ n _ i\ n i _ t\ * (30) 



\h c) \h c p) 



In the application of this formula n Q is to be taken positively. 



Denoting as before the radius of the achromatic circle by v, we find from (28), (29), and 

 the formulae thence derived which give tj, r\ x , 



\h\c pi c\h p)) \h\c pi c\h pi) 



\h c) \h c p) 



When the bands are nearly straight, instead of the central order it is more convenient to 

 consider the mean breadth of a fringe. According to the definition of /3, 



v + (Zdn : v :: \/(n + dn ) : \/n , 



since the radii of the several rings are as the square roots of their orders. We have therefore 



»-k < 38 > 



22. In the case of a concave mirror, if a small flame be so placed as to coincide with its 

 image, and be then moved a little towards the mirror, or from it, it is possible to see a single 



