On Hygrometry . 
51 
is proportional to the evaporation, — a proposition which I have shown is untenable. 
It contains another error*, which is common to both investigations, and which I 
shall now proceed to explain. 
In considering the process which takes place, when a thermometer with mois- 
tened bulb is exposed to the power of evaporation, we at once perceive that it is not 
until the depression has attained its maximum, and is consequently stationary, that 
we can deduce any useful result. It is then that two forces or powers, the value 
of one of which we are seeking, are in equilibrio : this value we obtain in conse- 
quence of its equalitv with that which is known. For at this period of the experi- 
ment, it is evident, that the indefinitely small decrements of caloric, the effect of eva- 
poration, are balanced or neutralized by the indefinitely small increments arising 
from conduction and radiation in the equally small moments of time. By determin- 
ing the latter, we obtain an expression for the h$at lost by evaporation ; from which 
may be deduced the rate of evaporation ; thence the tension of the moisture in the 
air ; and lastly, its weight. 
Thus we see, that everything depends on our correctly estimating the incre- 
ments of heat, furnished by conduction and radiation to the moist bulb ther- 
mometer, depressed a certain number of degrees below the temperature of the air. 
Newton supposed that these increments were as the differences of temperature of 
the body to be cooled (or heated), and that of the medium. This hypothesis was 
shown by experiment to be incorrect, but it is only lately that MM. Dulong 
and Petit, by separating the effects of these two causes, have established the true 
law. With regard to radiation, the effect of it is so small in comparison with that 
of conduction, in the case we are considering, and being indeed easily got rid of 
altogether, we may leave it out of the question. The rate then, at which a body, 
cooled below the temperature of the atmosphere, receives caloric, is proportional, 
not to the 'simple difference of temperature, but to that difference raised to the 
1.233 power. Thus, when the depressions are as 1 : 2, the increments and con- 
sequently the decrements will be as 1 : 2 35 This very important law is entirely 
unnoticed in either of the solutions of which I have given an account. 
Notwithstanding the failure of both these attempts, the theoretical solution of the 
question appears to me sufficiently obvious. In applying it to practice is the sole 
difficulty, owing to our not having any correct determinations of the constants, or 
any senes of carefully conducted experiments of the cor responding dew points to 
various depressions of the moistened thermometer. In the hope of exciting the at- 
tention of inquirers, and of eliciting some valuable contributions to the subject, I 
shall terminate this paper, by giving what appears to me the most direct solution of 
the problem. The application of the thermometer to determine the moisture in 
the air, is every way so desirable, that no means should be neglected of fixing the 
subject on a secure basis. 
Let e = evaporation in grams from a surface of one square inch for one inch liy- 
grometric tension, and barometer 30 inches in one unit of time. 
For any other tension ( F' — J'),\ it will be e (¥ r — f), in which F' is the tension 
due to the indication of the moist thermometer ; and /, to that of the dew 
point. 
For any other surface s, it will be s e ( F' — f), and for any other barometer B 
30. s* (T r 
B 
Let w represent the weight in grains o f water of the mass to be cooled, .and L the 
proportional part to be evaporated of any mass of water at the temperature to pro- 
duce a fail of 1°, then will the evaporation of j— evidently produce a fall of 1° in 
the temperature of tv. 
Now let i = increment of caloric in the unit of time for depression D and ba- 
rometer B =c-f-r, where c is the effect of conduction, and ris that of radiation. 
Then will ■ express the amount of evaporation in grains, in the unit of time. 
But 
e (Y'—f) 30 
B 
was also found to be an expression for the same, therefore 
* It has, however, greatly the advantage of the other solution, by adopting the 
tension due to the temperature of the evaporating surface, instead of that due to 
the temperature of the air. 
t F' represents the tension of vapour due to the temperature of the moist ther- 
mometer j J as before, of that actually existing in the air. 
