174 MR W. J. M. RANKINE ON THE 
Now this quantity, which I shall denote by H, is the total heat required to 
raise unity of weight of liquid from +, to 7, of absolute temperature, and to evapo- 
rate it at the latter temperature. Therefore dhe total heat of evaporation, where the 
vapour may be treated as a perfect gas, increases sensibly at an uniform rate with the 
temperature of evaporation ; and the coefficient of its increase with temperature is 
equal to the apparent specific heat of the vapour at constant pressure, * (1+N). 
(20.) There have never been any experiments from which the apparent spe- 
cific heat of steam under constant pressure can be deduced in the manner in which 
that of permanent gases has been ascertained. 
The experiments of M. RreGnauur, however, prove that the total heat of 
evaporation of water increases uniformly with the temperature from 0° to 200° 
centigrade, and thus far fully confirm the results of this theory. 
The coefficient of increase is equal to 
Ky x 0:305 
Its mechanical value is consequently 
(34.) 
116:4 metres=382 feet per centigrade degree, or 
212 feet per degree of Fahrenheit. 
Although the principle of the conservation of vis viva has thus enabled us to 
ascertain the law of increase of the total heat of evaporation, it does not enable us 
to calculate @ priori the constant L, of the formula, being the latent heat of eva- 
poration at the fixed temperature from which the total heat is measured; for the 
changes of molecular arrangement which constitute evaporation are unknown. 
When the fixed temperature is that of melting ice, M. Regnavtt’s experi- 
ments give 606°5 centigrade degrees, applied to liquid water as the value of this 
constant; so that 
H=K,, (606°-5 + -305 T°) 
For the centigrade scale, 
H=K,, (1091%7 + 305 (T° — 32°) ) J 
For Fahrenheit’s scale. 
(35.) 
is the complete expression for the heat required to raise unity of weight of water 
from the temperature of melting ice to T’ above the ordinary zero, and to evapo- 
rate it at the latter temperature. This formula has been given by M. Recnau.r 
as merely empirical; but we have seen that it closely represents the physical law, 
when quantities depending on the expansion of water are neglected. 
It must be remarked, that the unit of heat in M. Recnavuut’s tables is not 
precisely the specific heat of water at 0° centigrade, but its mean specific heat 
between the initial and final temperatures of the water in the calorimeter. The 
utmost error, however, which can arise from this circumstance, is less than 7999 
of the total heat of evaporation, so that it may safely be neglected. 
Os 4 re ee a tee i 
