34 



Mr. W. H. M. Christie on the 



[Mar. I, 



suppose fq=xcq\ 



(x — l)cq 



which gives the limiting breadth 7c. 



The condition e~ cq ' k =xe~ fqk may be expressed hi words thus : — When 

 the brightness is a maximum, the light transmitted through the thickest 

 parts of the train of crown prisms must be x times that through the 

 thickest parts of the train of flint prisms, x being the thickness of crown 

 (expressed in terms of the total thickness corresponding to 1 inch breadth 

 of prism) which gives the same absorption as the total thickness of flint 

 corresponding to 1 inch breadth. The thickness is in each case that tra- 

 versed by the ray. 



"When x=l or fq = cq', the formula becomes indeterminate; the 

 absorption is then the same for all rays of the pencil, and 



B=ChJce- fqk = ChJce- c «' k . 

 Putting — = as before, we have 



CifC 



7 1 1 



£=_or — ; 



or, when the brightness is a maximum, the breadth of the prisms must 

 be such that the whole absorption is the absorption in passing through 



the crown being supposed equal to that in the flint. This will be ap- 

 proximately true in the case of the direct-vision prism, for which there- 

 fore the thickness of glass traversed (flint and crown combined) should 

 not exceed 5-8 inches, if we take /=• 173, as found by experiment for a 

 very good specimen of flint. With less pure glass, such as is frequently 

 used, this limiting thickness may be much smaller ; in one piece of very 

 dense flint which I examined it would be only 1*5 inch ; but the ab- 

 sorption of the crown being here considerably less than that of the flint, 

 the formula just given would no longer apply. Further, for the blue end 

 of the spectrum / would be much larger, being, in fact, about *78 for the 

 yellow flint, whilst c is about *34 for the crown, so that the total thick- 

 ness for photographic work should certainly not exceed 3 inches, the 

 limit being fixed by the absorption of the crown. 



These numerical results, however, are given more as illustrating the 

 principles on which spectroscopes should be constructed than as general 

 rules applicable in all cases ; for there is such great diversity in glass that, 

 by a judicious selection, it is quite possible that a considerably greater 

 thickness might prove to be admissible for the photographic rays. Fur- 

 ther, the observations on which the values of the coefficients of absorption 

 are based are liable to a small uncertainty on account of the difficulty of 

 allowing for want of perfect polish in the two surfaces of the plate. They 

 may be taken, however, as useful approximations to the truth. 



