148 Mr. W. Sutherland on Molecular Eef Taction. 



communicated to sether and the vibrations of sether are taken 

 up by matter. But the ray travels more slowly in matter 

 than in sethor, so that, for every portion of matter passed 

 through in a certain path, the ray loses time as compared 

 with its time along a similar path in pure sether. Now what- 

 ever the shape of the atoms may be, if we imagine them to be 

 very small and very numerous, there is a certain mean distance 

 in the atom which we can in every case imagine the ray to 

 traverse, and on account of the numerousness of the atoms 

 this mean distance is the same for all experimentally possible 

 distributions of the molecules. It is possible that the mean 

 distance may alter with temperature, but, within the limits of 

 refraction-experiments as yet carried out, we may assume the 

 mean distance to be independent of temperature. Under 

 these circumstances we imagine that every encounter of a ray 

 with an atom means the traversing of this fixed mean distance 

 in matter instead of in tether, and a corresponding loss of time. 

 The total loss of time along a path will be proportional to the 

 mean number of encounters, which is directly proportional to 

 the length of path travelled, to the mean sectional area of an 

 atom, and to the number of atoms in unit volume ; thus 

 calling s the length of the path considered, I the mean distance 

 through an atom, a its mean sectional area, m its mass, and d 

 the density of the substance, so that the number of atoms in 

 unit volume is proportional to d/m, the number of encounters 

 varies as sadjm. If v be the velocity of light in free sether 

 and V in the matter of an atom, then the loss of time in an 

 atom is l/Y — l/v. Hence we can write the total loss of time 



kslad /I 1 \ 

 as [^ . 



But if v' is the mean velocity of light in the atom-strewn 

 medium, the loss of time is equal to s/v'—s/v. 



s s _ kslad /I In 

 ' ' v' V m \V V J' 



i. e. {n—l)-j =^/a(N — I) = constant ; 



where n is the index of the medium and N is the index of re- 

 fraction of the matter of the atom. This is Grladstone's law. 



Now la is the volume of the atom, and regarding m/d as 

 the actual measure of the domain of the atom (usually called 

 the atomic volume), and calling these volumes u and U, we 



