Mr. W. Sutherland on Molecular Refraction. 147 



the merits of Gladstone's and Lorenz's refraction-formulas will 

 be appropriate : — 



1. In all cases where the same specimen of a substance has 

 been examined with sufficient accuracy in the liquid and 

 vapour states, the Lorenz formula is markedly superior to 

 Gladstone's. 



2. Quincke has shown that, within the limits of experimental 

 error, Gladstone's formula is verified by his experiments with 

 compression, while Lorenz's fails. 



3. Landolt firds that in most cases both formulse hold with 

 considerable accuracy when applied to the change from solid 

 state to liquid, but that Gladstone's has the advantage. 



4. Landolt finds that Gladstone's formula leads to more 

 accurate results than Lorenz's when applied to the deduction 

 of the index of a mixture from those of its constituents. Thus 

 while the calculated values of (n — V)/d differ from the expe- 

 rimentally found values by '05 per cent, on the average, and 

 •16 per cent, in the worst case, {n^ — l)/{n? + 2)d departs on 

 the average from experiment by '16 per cent., and '6 percent, 

 in the worst case. Gladstone's formula is thus decidedly the 

 better of the two for chemical optical analysis. If it is used 

 to determine the amount of a particular substance dissolved 

 in a certain amount of solvent from the determined index and 

 density of the solution, it gives much more reliable results than 

 Lorenz's. 



5. Landolt showed that the general results as to refraction- 

 equivalents of the elements C, 0, H, and N, and the halogens 

 obtained by the study of the Gladstone expression, still held for 

 the Lorenz formula ; but Briihl was able to show that, from 

 the chemical point of view, Lorenz's formula is preferable, as 

 it allows of the calculation of the refraction-equivalent of a 

 molecule from those of its atoms with a smaller percentage 

 error. 



It is thus seen that neither formula is a complete expression 

 for all the physical facts, but that on the whole the Gladstone 

 formula is the nearer of the two to the truth. It will now be 

 shown that Gladstone's formula can be obtained as a first 

 theoretical approximation, and that a second approximation 

 gives an extension and improvement of Gladstone's formula, 

 rendering it capable of expressing the complete relation of 

 index to density. 



Consider the path of a ray in a medium composed of evenly 

 distributed atoms between which lies sether with all the 

 properties of free sether unaltered. The ray is supposed 

 capable of passing through the substance of an atom. This is 

 a natural supposition, seeing that the vibrations of matter are 



L2 



