MOLECULAR REFRACTION. 43 



density should be tlie same for all bodies, and he found it to be 

 approximatly so. Laplace shewed that on the emission theory and 

 according to his treatment of molecular force (n^-l)/d ought to 

 be the same for a given substance whatever the density is, and in 

 the case of gases (n--l)jd was found experimentally to be constant. 

 But on the establishment of the undulatory theory, the theoretical 

 foundations of the above relation between index and density fell 

 to the ground. Gladstone and Dale, however, devoted themselves 

 to the study of the relation from its purely empirical side, and 

 found that when the density of a liquid is caused to change by 

 variation of temperature (n-'-l)/d does not approach so nearly as 

 {n-l)ld to constancy. The empirical relation (?i-l)/c? = constant is 

 known as Gladstone's law. 



If M is the molecular weight of a substance then M (n-l)/d is 

 the molecular refraction, and was shewn in a large number of 

 cases, by Landolt, to be the sum of certain definite refraction 

 equivalents for the elementary atoms in the molecule. Gladstone 

 shewed that structure in certain cases influenced this molecular 

 refraction, and Briihl discovered a certain measurable connection 

 between the amount of the molecular refraction of a molecule, 

 and the linkings of the polyvalent atoms. 



But the large jaumber of researches undertaken by chemists on 

 this subject, all depended on the pui'ely empirical law of 

 Gladstone, no corresponding connection between index and 

 density having been deduced from this undulatory theory, when 

 Lorenz of Copenhagen, and Lorentz of Amsterdam brought out a 

 theoretical deduction from the undulatory theory according 

 to which {71- -l)/(n- + 2)d is constant for a given substance. 

 Lorenz obtains this result by applying to the discontinuous 

 distribution of molecules and ether a differential equation for the 

 vibratory motion, which involves the idea of variable amplitude, 

 but invariable wave length, namely, the mean wave length 

 in this medium. His investigation involves integration through- 

 out a single molecule; but as the mean wave length may 

 be very different from the actual wave length in a molecule, this 

 application of a mean wave length in a region where it does not 

 actually hold may lead to invalid results. Lorenz applied a 

 very strict test to his formula by comparing the liquid and vapour 

 states of several substances, in each case (n- — 1 )/(?i" + '2)d proved 

 to be the same for the two states, whereas (n-l)/d varied as 

 much as 10 per cent. But soon after Quincke submitted the 

 Newton, Gladstone, and Lorenz formulae to a comparative test by 

 measuring the change of index of various liquids with pressure, 

 and found that Gladstone's law is the only one which expi'esses 

 the actual facts. It is, therefore, only fortuitously that Lorenz's 

 fox'mvila bridges so accurately the great change of state from 

 liquid to vapour, and on the whole from an experimental point of 

 view Gladstone's is the preferable statement. 



