418 PROCEEDINGS OP THE AMERICAN ACADEMY 



then the same as that of the known line in the spectrum of the liquid 

 used for comparison; for we have for each case 



sin ^{P + D) , sin i (P + D') 

 n = ^--^—p '- n' = ^-—p •' 



sin — sin — 



and, since P is constant, and D' = D, it follows that n' = n. 



By this method, the index of refraction of a given liquid may be 

 determined for a single line ; as, for instance, for D. This is sufficient 

 for the optical analysis in the form in which it has been developed by 

 Landolt. Two objections to this method present themselves at once. 

 The first is the necessity of finding by tentative processes a comparison- 

 liquid which shall have about the same mean index of refraction as 

 the liquid an index of which is to be determined. I admit the force 

 of the objection, but it must not be estimated too highly. Whole 

 classes of liquids agree pretty nearly in their optical characters ; as, 

 for instance, the oils of the C^g H^^ series, the ethers of the fatty acids, 

 hydrocarbons and saline solutions. The second objection is that, with 

 liquids of low dispersive powers, it is not easy to distinguish the spec- 

 tral lines with absolute certainty. This difficulty is easily avoided by 

 using a second prism, with a high dispersive power, placed next to the 

 collimator so as to form a long spectrum, which shall fall upon the 

 trial-prism. The final dispersion is then the sum of the dispersions of 

 the two prisms, and no difficulty will be found in distinguishing the 

 spectral lines. It is, of course, necessary that the subsidiary prism 

 shall have the same position in both cases. Two or more subsidiary 

 prisms either of flint-glass or of carbonic disulphide may be used with 

 great advantage, but one will usually be found sufficient. The indices 

 of refraction of the comparison-liquids being known for at least three 

 lines, the values of the constants rt, h, and c in Cauchy's formula 



« = ^ + p + r4 



may be determined. It then only remains to compute the index of 

 refraction of the line which has been found to have the same index as 

 the line /), for instance, of the liquid examined. This is easily done 

 when the line in question has been identified by means of KirehhofT's 

 chart so that its wave-length is known. It will, of course, often hap- 

 pen that no line in the comparison-liquid exactly corresponds with the 

 line D selected for the liquid examined. In this case the index of 

 the nearest line may be employed instead, when great accuracy is not 

 required and when subsidiary prisms are used, or we may use a filar 



