Lord Rayleigh's Investigations in Optics. 273 



where t and t' denote the respective thicknesses traversed, and 

 Sfi, h[j/ the corresponding variations of refractive index. 



The relation between hfi and h\ may generally be obtained 

 with sufficient approximation from Cauchy's formula 



fi = A + B\~ 2 (7) 



Thus 



S/x=-2B\- 3 S\ (8) 



The value of B varies of course according to the material of 

 the prisms. As an example I will take Chance's " extra-dense 

 flint." The indices for C and the more refrangible D are* 



so that 

 Also 



fi D = 1-650388, fie = 1-644866 ; 



/a d -/a c = -005522 ....... (9) 



X D = 5-889 x 10 -5 , X c =6-562 x 10~ 5 , 



the unit of length being the centimetre ; whence by (7), 



B=-984xl0- 10 (10) 



Thus by (5) and (8), 



*■',._*_ JffV (11) 



2B8X 1-968 fix. K ' 



For the soda-line, 



\ = 5-889 x 10" 5 , S\=-006 x 10 -5 ; 



and thus the thickness necessary to resolve this line is given by 



* = 1'02 centimetres (12) 



The number of times the power of a spectroscope exceeds that 

 necessary to resolve the soda-lines might conveniently be taken 

 as its practical measure. We learn from (12) that, according 

 to this definition, the power of an instrument with simple 

 prisms of "extra-dense glass " is expressed approximately by 

 the number of centimetres of available thickness. 



In order to confirm this theory, I have made some observa- 

 tions on the thickness necessary to resolve the soda-lines. 

 The prism was of extra-dense glass of refractive index very 

 nearly agreeing with that above specified, and had a refracting 

 angle of 60°. Along one face sliding screens of cardboard 

 were adapted, by which the horizontal aperture could be ad- 

 justed until, in the judgment of the observer, the line was 



* HppHnson, Proc. Boy. Soc. June 1877. 



