fi Law " in Physical Optics. 33? 



It seemed worth while asking whether this fractional part 

 of the volume had a physical meaning. If the quantity /5 

 may be regarded as a measure of true molecular volume, and 

 there still remain a certain element of volume to be measured, 

 it will most probably be found by accepting a well-known 

 kinetic constitution for the liquids. If temperature be con- 

 stant, we may assume that each molecule of a liquid vibrates 

 as a whole over a certain region called its domain, the centre 

 of this region being defined as the centre of the molecule 

 when in its mean position. 



The extent of the domain, and the relation between it and 

 the total volume, will depend on the energy of molecular 

 motion, and on the law of molecular force with regard to 

 distance. 



Thus the apparent volume is made up of fractional parts, 

 one of which may be called the sum of the volumes of the 

 molecules, another the sum of the volumes of the domains, 

 and a third the interstitial spaces. A satisfactory theory 

 for evaluating these can perhaps not be found till more is 

 known of the magnitude and law of the molecular forces, but 

 an empirical examination suggested that (fi — l)v might pos- 

 sibly serve as a basis for finding the domain. At any rate it 

 gives by transposition a part of v which fairly answers to the 

 only criterion of the domain which I can lay down. 



Nothing is known as to possible change of the dimensions 

 of the molecules themselves, but it seems highly probable that 

 the domain of a given substance will most certainly differ 

 under different physical conditions. Still further does it 

 seem probable that the domain of different substances, heated 

 between the same temperature-limits, may change in the 

 same ratio. Figures in the tables which follow will prove 

 this for the new expression, to what may be called a first 

 approximation. 



The transformation referred to is 



(/4-l)fl = ^W--^|, 



the value of the square bracket on the right being equal to 



. v. 



It was evident to me, and will be to any one familiar with 

 the data given by molecular refractions, that this last expres- 

 sion gives a fraction of v tolerably near that obtained by the 

 use of the other well-known expression 



. v. 



fi 2 + 2 

 Phil Mag. S. 5. Vol. 40. No. 245. Oct. 1895. 2 A 



