342 
If we adopt 4 = 2,15 Mr. Perreau’s consecutive results give for D 
a ) 3395,0 b) 3393,9 c) 3394,3 
d) 3394,4 e) 3393,5 /) 3395,0 
The mean value is I) = 3394,3 so that from equation (12), § 16. ; 
if we were to apply it. we should get: K= 1,000884. Now the 
dielectric constant of C0 2 is decidedly greater than this: 
Boltzmann finds: K= 1,000945; Klemencic: 1,000985. 
The divergence can be readily accounted for in view of the well 
known fact 4 ) that carbon dioxide exhibits absorption bands of ex¬ 
ceptional breadth and intensity in the infra-red region of the spectrum. 
§ 22. In connection with the preceding results the question 
now arises in how far we are justified in substituting equation (3) 
of § 15. for equation (2) of the same section. Let us call 4* the 
value we should obtain- were we to apply formula (2), § 15., to 
a given pair of numerical data. Then if A is (as before) the value 
of the constant which we find when we make use of the approxi¬ 
mate expression (3), the ratio of the approximate and the exact va¬ 
lue is seen to be 
y> A*— 2 (v 1 -{-v. 2 ) 
therefore 
(9) A.— A * _ — i) — i) 
A* 
To get an idea of the magnitude of this correction let us take the 
case of carbon dioxide for which the fractional part of the index 
is greater than for any other gas hitherto considered. Over the 
range covered by the work of Perreau and of Mascart, v — 1 
for C0 2 has been seen to remain of the order 4,5.10~ 4 ; hence 
(3) (A — 4*)/4* 
1 ) Angstrom, Phys. Revue, Bd. 1, p. 606. 1892. 
Paschen, Annalen d. Phys. u. Ch., Bd. 50, p. 409. 1893; Bd. 51, p. 1. 
1894; Bd. 52, p. 209. 1894. 
Rubens u. Aschkinass, Annalen d. Phys. u. Ch., Bd. 64, p. 584. 1898. 
Rubens u. Ladenburg, Ve r h a n d 1. d. d. p h y s. G e s., Jahrg. 7 , p. 170. 1905 . 
