u Law " in Physical Optics. 325 



and let /3 have the meaning suggested, then 



and (^! — 1)^ — Qa 2 — l)v 2 



f^l — ^2 



This equation shows that the measure of J3 will depend 

 on differences which we know to be small, and it is at once 

 evident that the best experiments only will be serviceable. 

 Thus, a table of results for carbon disulphide gives the follow- 

 ing figures for the temperatures of 0° and 40° Centigrade ; 

 the data are Ketteler's : — 



/*! = 1-64375, fi 2 = l-6U$7 ; ^ = -77314, u 2 = -81103. 



Therefore 



0-497709-0-496245 Q-Q01464 _ 

 ^~ 0-03188 0-03188 - u " U45y - 



Here the difference between the two terms of the numerator 

 Is only s^q of either, and as each term involves only the 

 fractional part of the index, any error in //, is multiplied 

 about 900 times in its effect on /3. 



This makes it imperative to attach weight only to those 

 experiments where special appliances have been adopted to 

 keep the temperature constant during the observations. For 

 this reason I simply allude to the few results I have myself 

 obtained in a few preliminary experiments, reserving data for a 

 fuller discussion. The results here presented depend almost 

 entirely on the work of three sets of observers, namely, Nasini 

 and Bernheimer, Perkin, and Ketteler. It would be in- 

 vidious for me to single out one of these as more accurate 

 than the others ; their papers show that all the experiments 

 are of a high order of accuracy. It is doubtful, however, 

 whether Perkin's data are not the most serviceable for our 

 present purpose, if only for the reason that the interval of 

 temperature he employed is greater, with the consequence 

 that the differences on which /3 depends become more marked, 

 and thereby afford greater accuracy. 



Table I. is drawn up from a paper by Nasini and Bern- 

 heimer"*. They were the first to use a jacketed prism, so 

 that their results are the earliest of those suitable for deducing 

 (o. One substance in their list — bromonaphthalene — has been 

 omitted, as it stands alone in giving an increase in (fju — l)v 

 on heating. It is probable that the limit of experimental 

 error is reached with that substance. 



Column 2 gives the temperatures, 3 the densities, and 

 * Gaz. Chim. Ital. xv., 1885. 



