110 Prof. Stokes on the Occurrence of Abnormal Figures in 



the rings become less distinct than with homogeneous rays, and 

 presently there takes place a sort of dislocation amounting to 

 half an order, that is, the bright rings beyond a certain point, 

 or in other words, outside the circle determined by a certain value 

 of r, correspond, in regard to the series formed by their radii, 

 with the dark rings inside this circle, and vice versd. At some 

 distance beyond that at which the dislocation takes place the 

 rings become very distinct again ; but it is useless to trace further 

 the variations of the expression for I, because the circumstances 

 supposed to exist in forming that expression are too remote from 

 those of actual experiment to allow the interpretation of the 

 formula to be carried far. 



According to the numerical values of m and m',a dark ring might 

 be converted, by the change of sign of the factor cos (m— m')r 2 , 

 into a bright ring, or a bright ring into a dark ring, or a ring of 

 either kind might be rendered broader or narrower than it would 

 regularly have been. The coalescence of the fourth and fifth 

 bright rings in Mr. Crookes's photographs when bromide of 

 silver was used seems to be merely an effect of this nature. 



But in order that a dislocation of the kind above explained 

 should take place, it is not essential that two kinds only of rays 

 should act, nor even that the curve of photographic intensity 

 should admit of two distinct maxima within the spectrum. 

 Suppose that rays of all refrangibilities lying within certain 

 limits pass through the crystal and fall on the plate. For the 

 sake of obtaining an expression which admits of being worked 

 out numerically without too much trouble, and yet results from 

 a hypothesis not very remote from the circumstances of actual 

 experiment, I will suppose the total photographic power of the 

 rays whose parameters lie between m and m -i dm to be propor- 

 tional to sin mdm between the limits m=27r andm = 37r, and to 

 vanish beyond those limits. Since m is very nearly proportional 

 to the reciprocal of the wave-length, and the ratio 3tt to 2ir or 

 3 to 2 is nearly that of the wave-lengths of the fixed lines D, H, 

 this assumption corresponds to the supposition that the rays less 

 refrangible than D are inefficient, that the action there com- 

 mences, then increases according to a certain law, attains a maxi- 

 mum, decreases, and finally vanishes at H. The action would 

 really terminate at H if a bath of a solution of sulphate of qui- 

 nine of a certain strength were used. On this assumption, and 

 supposing, as before, that the rays of different refrangibilities act 

 independently of each other, we have 



= I sin 2 (mr 2 ) sin mdm. 



J27T 



