196 HOLTZMANN ON THE HEAT AND ELASTICITY 
bin it a 
In the same manner 7 is for atmospheric air, calculated from 
1 
the velocity of sound, = 1°415, also under the pressure of one 
atmosphere. Consequently 0°267 = 1°415 ¢, and c, = 0°189, 
; ka 
whence ¢ — ¢,, that is, there results, according to (IV.), x 
= 0°078. 
a ees 
But k is = anes) 
At the same time p is the pressure on 17 and ¢ the weight of 
1”¢* atmospheric air under that pressure and at the temperature 
t°.. Now we have for the pressure of one atmosphere p = 10333 
kil., and for the temperature of the freezing-point @ = 1°299 kil. 
Consequently 
__ 10333 
~ 1-299 
a is, according to Magnus, equal to 0°003668. With these num- 
bers we obtain i 7955 x 0003668 _ ad 
0:078 oe ' 
This result indicates that the heat which warms 1 kil. water 
1° C. is capable of raising 374 kilogrammes 1 metre. Clapeyron 
obtained the same result, but gives it in more complicated 
numbers. 
I will now attempt to determine how far this value of a is trust- 
worthy. The extreme values which were obtained for 6 are, ac- 
cording to Dela Roche and Bérard, 0°290 and 0°250, and the re- 
sults of other experimenters likewise fall within these limits. Gay~ 
= 7955 3 
Lussac and Welter found for the relation — the value 1°372, 
1 
which we may regard as the lowest limit of the probable values 
for this relation. By combination of these numbers we obtain 
as the smallest value a = 343, and as the highest value 429, 
whence it results that 374 is, it is true, a mean value, but may 
possibly be erroneous about 40. 
§ 2. Heat and Elasticity of Gases. 
9. If a gas be brought from the pressure p under the pressure 
p! without heat escaping, the temperature and density are altered. 
These changes may now be calculated from the formulz 
fogging ie AUbchiae) ghee 
a Po 
* Denoting one metre cube. 
