492 



Prof. Stokes on an accurate Method 



[June 20, 



achromatism, we get the angle of incidence in the position of achro- 

 matism. 



This angle, yfr, having been determined by either of the above 

 methods, we have, by the known formula — 



where the letters with the suffix ( refer to the second prism. For the 

 prisms would achromatize each other, as is supposed in the deduction of 

 the above formula in treatises on optics, under the same circumstances 

 in which they would achromatize, in succession, the same spectrum. 

 In the application of the formula, it is to be remembered that, of the 

 two angles 0, yjs, the former is that which lies on the side of the white 

 light, and is, therefore, the angle of incidence for the first, but of 

 emergence for the second, of two prisms which mutually achromatize 

 each other. 



In the application of the formula (2) the angles 0', ^ belong, 

 strictly speaking, to the brightest part of the spectrum, which for 

 shortness I will call M, for which the value of the differential co- 

 efficient dfx t : dju. is supposed to be sought. But the distance of 

 M from D is so small that it will hardly make any sensible error if we 

 use the values of the angles belonging to D, for not only is the cor- 

 rection to the product cos <p' cos yjr for either prism very small, but 

 the two corrections are in the same direction, and therefore tend to 

 neutralise each other in the ratio of the products, with which alone we 

 are concerned. If, however, we care to introduce the correction, it can 

 be done at the expense of a little additional calculation. In a crown 

 glass the index for M may be taken as greater by 0*001 than that 

 for D, and in a flint glass as greater by ; 001 multiplied by a 

 rough value of djx t : d/i. The angle of emergence may be taken to 

 be the same for M as for D. For the deviation, regarded as the func- 

 tion of the index, is a maximum or minimum for M ; and D being so 

 near M, the difference of deviations for D and M will be quite in- 

 sensible compared with the errors of observation of the azimuth of 

 achromatism, with which it is associated. Let the letters '/a, '\Jr, &c, 

 refer to M, while / a, yjr, &c, refer to D. y is obtained by observation, 

 and \Js', 0' must, in any case, be calculated from thence by the known 

 values of fi and i. We have now merely to calculate the '0' and 'yjr 

 for each glass from the formulas 



7 • • • (2), 



cosec i cos <p' cos yjr cosec i t cos 0/ cos yr y ' 



sin'0' = ; — sin0', 'y/ = i — '0', sin 'Y r =V sin 'y/, 



and substitute these values in the equation (2) instead of those belong- 

 ing to the line D. 



The primary prism had best be made of very low flint glass (or else 



