1878.] 



of determining Ratio of Dispersions. 



493 



be a compound prism formed of two prisms of crown and flint glass 

 respectively, with their angles turned the same way), so as to fall 

 about midway between the glasses to be compared, and thereby divide 

 between them the irrationality which has to be encountered in the 

 observation. The observation of the azimuth of achromatism is most 

 accurate when there is little or no irrationality ; and, if preferred, the 

 crown glasses might be compared with a standard crown, and the 

 flint glasses with a standard flint, the primary prism being in the one 

 case any crown glass prism that happens to be at hand, and in the 

 other case a flint glass prism. The crown glass to be measured being 

 compared with the standard crown by using them in succession to 

 achromatize the same primary crown in the same position, and similarly 

 for the flint glass to be measured and the standard flint, we can 

 deduce the ratio of the dispersions of the crown and flint glasses to 

 be measured if we know, once for all, the ratio of the dispersions 

 of the standard crown and flint glasses. This may be determined by 

 a specially careful series of observations of the kind above described, 

 made once for all, or, if preferred, by the method of indices. 



The direct comparison of a crown and flint glass is, however, so 

 accurate, especially if a glass of intermediate quality be used for the 

 primary prism, that I feel satisfied it will suffice for practical pur- 

 poses. It is hardly necessary to observe that, if the primary prism be 

 of intermediate quality to the two compared, the right hand edge of 

 the aperture will be the fiducial edge in the one case, and the left 

 hand edge in the other. In saying this, I assume that we have not 

 extravagant inclinations or differences of angles to deal with, for there 

 is a g^^'-i rra tionality observed even when two prisms of the same 

 glass, but of different angles, achromatize each other, which is, how- 

 ever, ordinarily so small that it may be neglected in comparison with 

 the real irrationality of the media. 



By turning the primary prism into a different azimuth, or substi- 

 tuting a different primary prism, and repeating the observation, an 

 estimate may be formed of the degree of reliance that may be placed 

 on the results. 



To give an idea of the degree of accuracy of which the results are 

 susceptible, I subjoin a few numbers extracted from my note-book. 

 The prisms designated H 74, H 88, H 98, were experimental prisms 

 of phosphatic glass of different compositions. They were more or less 

 striated, but were good enough to show the principal fixed lines of the 

 spectrum. In the different determinations of the ratio of dispersions, 

 the primary prism was set at different azimuths. In the calculation 

 of (2) the indices for D were used. The differences from the means 

 are exhibited. 



H 74 to H 98, 1-882, 1'892; mean, 1*887; differences, - 0-005, + 

 0-005. 



