336 Mr. W. Hibbert on the Gladstone 



5. The value of ft given by a liquid enables us to apply 

 the Gladstone formula (amended) during the transition 

 from the liquid to the gaseous state. 



6. There are grounds for believing that the value of ft is 

 related to other volume-relationships of the substance, 

 as, for example, the specific volume at the boiling- 

 point. 



7. In some cases there may be a connexion between ft and 

 the coefficient of thermal expansion. 



A further argument for the introduction of the quantity ft 

 is the fact that it will remove certain anomalies in molecular 

 refractions, bringing the value for hydrogen, chlorine, &c. 

 into harmony with that given by the gaseous elements. This 

 point, together with others of a like nature, is reserved for 

 another paper. 



So far as the suggestions thrown out are probable, it would 

 appear that " the actual volume of the particles " is not 

 a correct expression for ft. In the case of water, ft has a 

 varying value, which is attributed to the resolution of its 

 complex molecule into simpler forms. But such resolution 

 could not diminish the volume of the particles, unless we 

 mean by this phrase " the true volume of the atoms -f the 

 inter-atomic space." If we imagine a surface drawn to enclose 

 the molecule, it will include such space as lies between the 

 atoms in that molecule. Similarly, when two molecules 

 coalesce to form one of greater complexity the space occupied 

 by the two is greater than before. They do not actually 

 touch, so that the enclosing surface has a greater volume 

 than twice that which encloses one molecule. 



The results obtained so far show that the modified Glad- 

 stone expression promises to cover all ranges of density*. 

 This wide range of applicability is obtained by emphasizing 

 the volume-relationships involved in the formula — a fact 

 which acquires further significance when we remember that 

 it is as a measure of a volume that the Gladstone expression 

 has proved so useful. For the specific refraction of a sub- 

 stance, (fi — l)v, is evidently a fractional part of the specific 

 volume v. Moreover, both Dufet (Jburn. de Phys. 1885) 

 and Sutherland (Phil. Mag. 1888), in developing a theo- 

 retical basis for the Gladstone law, have shown that u volume 

 of molecules " is involved, though the exact definition of the 

 phrase is not arrived at. 



* Except perhaps in the case of certain solids. See data for refraction 

 of solids collected in the paper by Dr. Gladstone and myself already 

 mentioned, Chem. Soc. Trans. 1895, p. 831. 



