280 Prof. Challis on a Theory of the Dispersion of Light. 



which are of the same order as those between the different expe- 

 rimental determinations of /j,, sufficiently attest the accuracy of 

 the formula. 



I take occasion to advert here to a memoir by the Astronomer 

 Royal in the Philosophical Transactions for 1868 (part 1, p. 29), 

 the object of which is to calculate the wave-lengths correspond- 

 ing to KirchhofFs scale-measures of lines of the spectrum, in 

 order to increase the scientific value of these measures. The 

 calculations for this purpose are based upon DitscheineFs deter- 

 minations of the wave-lengths for the lines B, C, T), E, F, G. 

 KirchhofFs measure is expressed as a function of the correspond- 

 ing wave-length by a simple algebraical formula of interpolation 

 containing six constants, the values of which are found by means 

 of the scale-measures and wave-lengths of the above six lines. 

 Mr. Airy chose this method because he did " not know any phy- 

 sical reason for adopting one formula in preference to another." 

 The method appears not to have been successful, several of the 

 differences between the computed and observed wave-lengths in 

 the part of the spectrum between P and G ranging between 800 

 and 900, and in some cases exceeding the latter number. In 

 the Table given in this communication, the greatest difference 

 between the calculated and observed values of X in the case in 

 which the calculations were founded on the values of /x and A, 

 for only the three lines B, E, G is ]06, a few larger (evidently 

 affected by errors of observation) being excepted. The superior 

 accuracy of the results thus obtained is not to be attributed to 

 my calculations having been made with refractive indices instead 

 of KirchhofFs measures, because these are data of the same kind as 

 the others and equally trustworthy. My better success is rather to 

 be accounted for by the advantage I have taken of the indications 

 of the Undulatory Theory of Light, and may, I think, be justly 

 regarded as some evidence of the truth of the proposed theory of 

 Dispersion. Since KirchhofFs scale-measure is a function of /ul, 

 the results of the foregoing calculations made by assuming for 



fju 2 a series proceeding according to powers of -^, would seem to 



prove that, by the intervention of a like series for the scale- 

 measure, it would be possible to calculate the corresponding 

 wave-length with great accuracy, 



Cambridge, August 20, 1869. 



