210 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the actions going on in the separate atoms of a molecule or mixture 
are to a large extent mutually independent. For if they were not, the 
refractive index of a compound would be determined principally by 
the interaction between the atoms, and not, as it is, by their individual 
properties. 
The assumptions made throughout this paper are at best rough 
approximations to the true state of things ; but as they have enabled 
H. A. Lorentz to deduce the additive law for atomic refractive indices, 
and Sir J. J. Thomson to give an indication of the discrepancies which 
might be expected to occur in this law, a further analysis along similar 
lines may not be considered undesirable. 
In Part I of this paper we shall discuss the value of the atomic refrac- 
tive index in the case of atoms from which electrons have been transferred, 
ignoring the contribution to this value arising from fields of electrical force 
due to the vicinity of other atoms or groups of atoms. 
In Part II we shall endeavour to obtain a formula for the molecular 
refractive index of a diatomic molecule, which will allow for the contribu- 
tion due to electrical action between the atoms of the molecule. 
Part I. 
(a) Atomic Refractive Index of a Collection of Atoms each of which 
is electro-positive to the extent s. 
In this discussion we consider each atom to have lost s electrons by 
transference to other atoms with which it has become combined. 
Each atom will therefore be positively charged to the extent se where e 
is the charge carried by each negative electron. 
We shall neglect the action of the fields of force set up by this chemical 
combination or by the vicinity of electrical fields due to hydroxyl groups 
and groups containing multiple bonds. 
Let pr = (g r ?i £,.) = Displacement of r th electron from its position of 
equilibrium at time t , when an electro-magnetic 
field acts upon it. 
r = ( x , y , z) = Displacement of centre of sphere of positive electrifi- 
cation. 
F = (X, Y, Z) = Force due to incident electro-magnetic field. 
F' = (X', Y', Z') = Electric force arising from the polarisation which is 
due to displacement of electrons. 
Hence, assuming that the atom consists of a sphere of positive electrifi- 
