486 



Prof. Stokes on an accurate Method 



[June 20, 



that is to say, the indices for several fixed lines in each glass, it still 

 becomes a question what it is best to do with them so as to produce 

 the best result. 



Fraunhofer proposed an empirical rule for combining the results,* 

 but remarked that the number thus obtained was not exactly that 

 which answered best in practice. I have elsewhere shown reason to 

 think that the rule may be taken to be simply that the ratio of dis- 

 persions to be chosen is that for an infinitely small portion of the 

 spectrum at its brightest part;f or in other words, that the focal 

 length of the combination of two glasses must be made a maximum or 

 minimum (it is practically a minimum) at the brightest part of the 

 spectrum. 



The refractive index of one glass may be expressed in terms of that 

 of another, or of some standard glass, by an interpolation formula 

 with three, or at most four, terms. The most accurate observations 

 with prisms are only just sufficient to show that a fourth term is 

 needed, and for the practical purpose of the construction of object- 

 glasses, where in consequence of irrationality the ends of the spectrum 

 are sure to be a good deal out of focus, it will be amply sufficient to 

 confine ourselves to three terms. The three coefficients in the inter- 

 polation formula may be determined by observing in each glass the 

 indices of refraction for three selected lines, though it is well to 

 observe more than three lines, and combine the results. 



The angular extent of the spectrum being but small in practical 

 cases, the necessity of determining three constants by observations 

 made in it requires great delicacy of measurement. Small errors of 

 observation would easily produce an error in the deduced ratio which 

 would be sensible, or even material, in practice. 



For the actual construction of an object-glass we require, as has 

 been already remarked, the knowledge of only a single constant relat- 

 ing to the dispersion, not of two ; and if we can find some test whereby 

 to know when the required condition is satisfied, we may dispense with 

 such extreme accuracy in the angular measurements. 



Such a test is afforded by the secondary tints, which change with 

 extreme rapidity when the refracting angle of one of the mutually 

 achromatizing prisms, or the position of one of them in azimuth, is 

 altered. If a moderately narrow object with vertical sides, black on a 

 white ground, or white on a black ground, be viewed through opposed 

 prisms, one of crown and one of flint glass, with a small telescope, 

 and the prisms be set to achromatize each other as nearly as may 

 be, it will be found that the slightest touch altering one of the prisms 

 in azimuth alters notably the secondary tints. 



The secondary tints in an objective are readily shown by directing 



* " Denkschriften der K. Akad. der Wiss. zu Munchen," vol. v, p. 215. 

 f " Report of the British Association for 1855," part ii, p. 14. 



