216 Proceedings of the Royal Society of Edinburgh. [Sess. 
sd > E if s>w.f , i.e. if s>3*4.10 -2 
and 
sbT>ac if s>wf , i.e. s>3 , 4.10~ 2 , 
which is so since s is a positive integer. Hence the quantity in the square 
bracket is positive. 
Symmetry of the investigation shows that in order to obtain the value 
for the atomic refractive index when the atoms are electro-negative to the 
extent s, we need only put — s for s in expression 1'33. 
1-34 
E + se — ( sd + E) 
s&T + ac 
RT 
Particular Cases. 
(i) s = 0. Neutral atom which has not lost any electrons by trans- 
ference. 
1*35 
WNp T 
p R^ 
(l - 
V RT/ 
(ii) s = l. Monovalent electro-positive atom. 
1-36 
A T 
A+1_ p *R 
E-e-(ri-E) 
6T — ac 
RT 
1-37 
(iii) s= — 1. Monovalent electro-negative atom. 
Wi\ 
A-! = 
„ , 7 ^.bT + ac 
E + e-(^ + E)- Mr 
At this stage it might be advisable to compare our formula with 
experimental values. 
, WK T _ 
A 0 = — u . E approx. 
P JAi 
For hydrogen 
W=1 
N 0 = 6 x 10 23 
T i 
g = 1 approx. 
A 0 = 6 . 10 23 . M. a = 10“ 8 
o 
= 2*4, 
which is of the same order of magnitude as the experimental values given 
in Bruhl’s paper in Zeitschrift fur physik. Chemie, 1891, p. 25, and in 
the usual text-books on physical chemistry, e.g. Smiles’ book on the 
Relation of Chemical Constitution to some Physical Properties. 
