NUCLEAR CONDENSATION OF CERTAIN ORGANIC VAPOURS. 
457 
takes place before any condensation occurs; for otherwise, when the expansion 
reaches (say, for example) 1'34, drops will be formed on the natural ions present 
and the temperature will rise with the liberation of the latent heat of condensation, 
and this rise of temperature will be different in different apparatus. Since actually 
the final temperatures were the same, we conclude that there was no rise of 
temperature in this manner and the expansions were strictly adiabatic. 
(2) The formula 0 2 = 0\('i\/v 2 ) y ~ l is for air the expression of the observed results of 
Lummer and Pringsheim’s* * * § and Makower’sI' experiments, in which 0 2 , 6 U v u v 2 
were directly observed. With air in an engine cylinder Callendar^ has observed 
with a platinum thermometer a change of temperature of as large as 244° C., that is, 
from —34°'4 to 210° C. 
A more exact calculation will now be given of d 2 (for the conditions of experiment 
given in the next table) when air initially saturated with an organic vapour expands. 
Richarz calculated y for a mixture of gases. The following indicates how his§ result 
is obtained. Let the mixture and each component gas have the masses 1, 1—p, p, 
the densities (at 760 mm. and a common temperature) p, p, p", the specific heats at 
constant volume c, c', c", the ratio of specific heats, i. e. , C/c, y, y, y", and let P be 
the gas constant for a gram-molecule (M) of a gas. Then 
c = c'{ 1-p) + pc" = c' + p(c"-c'), . (3) 
and the specific volume of the mixture is 
1 1 /, v 1 1 /II 
- - ( 1 ~P) ~jr ~ —/ + P ( ~7t ~ —/1 > 
p p p p \p p 
C — c = = - k (k = const.), 
JM p v h 
since M is proportional to p, and P and J are constant. Whence 
1 > jij 1 a jhj 
-y = P cL » ~i 7 = pc k, —— = p c k . 
y— 1 y — i y — L 
By eliminating p in (3) and (4), and re-arranging terms 
pc(p"-p') = (p-p')p"c"+(p"-p)p'c'. 
Whence by (5) 
1 - P-P' 1 | P"~P 1 
7-1 p"-p'y"- 1 p"-p' 7-1 
* Smith, ‘ Cont. to Knowledge,’ 1903. 
t ‘Phil. Mag.,’ February, 1903, p. 226. 
\ ‘ Proc. Inst. Civil Eng.,’ 131, Pt. I., p. 170 (1897-8), 
§ Richarz, ‘Ann. d. Phys.,’ 19, 639 (1906). 
3 N 
(4) 
(5) 
VOL. CCVIII,—A 
