1819.] and onthe Laws of the Communication of Heat. 181 
nication between the balloon and the glass tube was rendered 
very free by the openings, a and 6, made in the plate near the 
central opening. 
If the cooling was to be observed, in vacuo, the process was 
stopped when the machine ceased to dilate the air, and we 
measured immediately the tension of what remained in the 
balloon. The stop-cock was then shut, and the observations 
commenced. When the experiment was to be conducted in air, 
that of the balloon was at first dilated, in order to facilitate the 
contact of surfaces, and then the proper quantity was allowed to 
enter. When the cooling was to be observed in a gas, the 
balloon was first emptied of air, gas was then allowed to enter, 
and a vacuum was again made, after which the requisite quantity 
of gas was introduced. By this contrivance, it was mixed with 
only an inappreciable quantity of air. , 
We shall terminate this description by saying, that the dimen- 
sions of the thermometer had been calculated, so that the obser- 
vation of the cooling could begin at about 300°. The experiments 
in air and in the gases require rather a longer preparation, and 
cannot be commenced with safety till the equilibrium is restored 
through the whole extent of fluid. The series of observations 
belonging to them commence at about 250°. 
The experiment for cooling in vacuo, or in gases, being thus 
prepared, it remained merely to observe the rate of cooling by 
means of a watch with a second’s hand at equal intervals of time. 
But these temperatures require two corrections, which we shall 
point out. In the first place, it is obvious, from the nature of 
our apparatus, that after a short time the stem of the thermo- 
meter was cooled down to the temperature of the surrounding 
air. Every temperature observed, therefore, was too low, by a 
number of degrees equal to that to which the mercury in the 
stem would dilate, when heated from the temperature of the 
surrounding atmosphere to that of the bulb. This correction 
was easily calculated, and was applied to all the temperatures 
observed. The object of the second correction was to reduce 
the indications of the mercurial thermometer to that of the air 
thermometer. For this we employed the table given in the first 
part of this memoir. 
Having thus obtained a series of consecutive temperatures of 
the thermometer, it only remained to apply to that series the 
mode of calculation which we have explained above. We 
divided it then into two parts, which were represented each by 
expressions of the form m. a*‘+@* in which ¢ denotes the time 3 
and these formulas served to calculate the velocity of cooling for 
the different excesses of temperature; but these velocities 
required a diminution easily determined in each case. That it 
may be conceived in what this consists, we must remark, that the 
cooling of the bulb of the thermometer, arising from the loss of 
heat which takes place at the surface, is always a little 
7 
