32 



Mr. W. H. M. Christie on the 



[Mar. 1, 



examined absorb the blue and violet rays strongly, whilst crown glass 

 absorbs the red and green. Notwithstanding its yellow colour, very 

 dense flint (having a specific gravity of 5*0), when well made, actually 

 transmits considerably more light than the specimens of crown I have 

 met with. Thus I found that for a thickness of four inches the propor- 

 tion of the incident light transmitted in the case of flint (sp. gr. 5*0) and 

 crown was as follows, allowance being made for the loss by reflexion at 

 the surfaces : — 



Eed. Green. Blue, 



per cent. per cent. per cent. 



Flint 56 49 5 



Crown 40 39 21 



From these results it would appear that a thickness of 4 inches of flint 

 or 3 inches of crown would absorb half of the incident light, the glass 

 being in each case well made. 



The absorption in the case of a train of prisms can easily be calculated 

 as follows : — 



Let e~ fl , e~ ct be the coefficient of light transmitted through thicknesses 

 t, t' of flint and crown. 



h, lc the height and breadth of the half -prism. 



k the abscissa for any ray measured from the edge of the flint prism. 



nsin /3 



: q K , t' = q(k — k), where q = n tan a, q' = 



, n being the 



cos a COS ((j—yjs) 

 number of half -prisms. 



Putting B= Brightness of transmitted pencil, which is supposed to be 

 large enough to fill the whole of the prism, we have 



b= Ok /l e ^e^d K =Ch yv^-^«-^'A- dlc 



=— — , . {ef-^-^n, C being a constant. 

 -fq+cq J & 



For evaluating this expression the following Table of the values of the 

 negative exponential will be found convenient : — 



•95 



-0-051 



e 



•75 



-0-288 



e 



•55 



-0-598 



e 



1 -35 



-1-050 



e 



•15 



-1-897 



e 



•90 



-0-105 



e 



•70 



-0357 



e 



•50 



-0-693 



e 



•30 



-1-204 



e 



•10 



-2-303 



e 



•85 



-0-162 



e 



•65 



-0-431 



e 



•45 



-0-798 



e 



I -25 



-1-386 



e 



•05 



-2-996 



e 



•80 



-0-223 



•60 



-0-511 



•40 



-0-916 



1 -20 



-1-609 



•02 

 •01 



-3-912 



e \ 



e 



e 



e 



e 



-4-605 



e 



1, Simple Prism. 



2=0 



B=^.{1 



thus B increases with lc, rapidly at first, and then more and more slowly. 



Taking a prism of 60°, and putting /= 0*173, which would give an ab- 

 sorption of 50 per cent, for 4 inches, we have the following Table for the 



brightness - {1 

 n 



} (omitting the constant factor 



Ch 

 2/tan a 



