1877.] 



Refractive Indices of Glass. 



291 



If / be the focal distance of a compound lens for line F, / ' ; / ", &c. 

 of the component lenses, then 



f fW T fir) . fir) 



J Jo Jo Jo 



f being the focal length for the ray denoted by cc. 

 If there be two lenses in the combination 



1 1,1 b'b" , , „. 2 

 — = — + (c — c )ar. 



since the effect of changing the ray to be denoted by zero does not sen- 

 sibly change the value of the coefficient ^ (V — c"), this may be taken 



b —b 



as a measure of the irrationality of the combination. 



Let there be three glasses (1), (2), (3); no combination free from 

 secondary dispersion and of finite focal length can be made with these 

 glasses if 



1, 1, 1 =0. 



b\ b\ b'" 

 b'c', b"c", b"'c"' 



Again, if the secondary chromatic aberration of (2) (1) is the same as 

 that of (3) (1), then that of (2) (3) has also the same value, and the 

 three glasses satisfy the above condition. 



Prof. Stokes has expressed the character of glasses in the following 

 manner : — Let a prism of small angle i be perfectly achromatized by two 

 prisms of standard glasses with angles i', i" taken algebraically as regards 

 sign, then 



ai+a'i' + a"i" = deviation of any ray, 

 abi -f - a'b'i' -f- a"b"i" = 0, 

 abci -f- a'b'c'i' + a"b"c' '%" = ; 



hence 



c a"b' 



i c — c' a'b' 



If c=c" this ratio is zero, but if c=c' it is infinite; let 4r=tan0, 



then the angle $ may be taken with a and b as a complete specification 

 of the optical properties of the glass. Prof. Stokes's method has a great 

 advantage in the close correspondence between the values of i, i', i" and 

 the powers of the component lenses of a perfectly achromatic object-glass, 

 and also in the rapidity with which a determination can be made. The 

 method adopted in this paper is convenient in the fact that a single 

 standard glass is alone required. 



The determinations were made with a spectrometer supplied to Messrs. 

 Chance Bros. & Co. by Mr. Howard Grubb. The telescope and collimator 

 are 2 inches aperture ; the circle is 15 inches diameter, is graduated to 10', 

 and reads by two verniers to 10". 



The lines of the spectrum observed were generally A, B, C, D, E, b, F, 

 (Gr), G, 7i, H 1 . D is the more refrangible of the pair of sodium lines, b 



