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On the Measure of Temperature , 
[Oct, 
§ 1. On the Cooling Process in General. 
It is known, that when a body is exposed to the cooling process in a vacuum, its 
excess of heat is dissipated entirely by means of what is called radiation, and that 
when immersed in any medium gaseous or liquid, the cooling process is more ra- 
pid, in as much as the heat lost to the fluid is to be added to that dissipated by radi- 
ation. It is, therefore, necessary to distinguish between these two effects, and as 
they are, to all appearance, the results of two different laws, it is further necessary to 
study them separately. This is what we propose to do, treating of the cooling pro- 
cess first, in a vacuum ; and secondly, in an elastic medium. But as our method 
of proceeding is, in each case, founded on the same principles, it will be proper first 
to establish these. 
To obtain the elementary law of cooling, that is to say, the law which would be ob- 
served by a body, the dimensions of which should be so small, that we might safely 
assume all its parts to have at each instant the same temperature, it would be need- 
lesslv complicating the question, if not indeed rendering it altogether insoluable, 
to attempt the observation of the phenomena in a solid body ; since in this case 
an« additional element would be introduced, viz. the internal distribution of heat, 
which is of course a function of the eonductibility. Being thus confined to liquids 
by the very nature of the problem, the mercurial thermometer itself appeared the 
best suited to such experiments. But as it was necessary, in extending our enqui- 
ries to very high temperature 6 :, to employ a volume sufficiently large to prevent the 
cooling process acquiring a rapidity that should render it difficult to follow it with 
accuracy, it became essential, first, to determine what effect would be produced on 
the law of cooling, by the employment of a greater or lesser mass of liquid in the 
ball of the thermometer. Nor was it of less importance to examine whether this law 
depends at all upon the nature of the fluid, or on the nature, or even shape, of the 
vessel in which it is contained ; this preliminary enquiry lias been the subject of a 
series of experiments, of which we shall now proceed to give some account ; first, 
however, explaining the method of calculation used in reducing our observations to 
a common term of comparison. 
Suppose we have observed at certain intervals of time, equal amongst themselves, 
(every miuute for instance,) the excess of temperature of any body over that of the 
, surrounding medium, and that for the intervals 
m m m m m 
0 1 2 3 &c. to t 
these excesses have been found to be 
A B C D &c. to T : 
if the law of a geometrical progression were the true one, we should have 
B = Am ; C — Am 2 &c. to T = Amt 
m being a fraction which would be different for different bodies. This expression 
is not rigorously true, especially if the temperatures are high — but we may conceive 
the possibility of representing a certain number of terms belonging to the preced- 
ing series by an expression of the form t 2 determining properly the co- 
efficients m and (2. And we may, by the aid of this formula, calculate, with a consi- 
derable degree of approximation, the value of the time t corresponding to any excess 
of temperature 7 1 , provided this excess be included in the series which has served 
for interpolation. 
This same expression affords us the means of determining the quickness of the 
cooling process, corresponding to each excess of temperature, i. e. the number of 
degrees by which the temperature of the body would be lowered iu a minute, 
supposing the rate of cooling to be uniform during that minute. The expression 
of this rate will be, 
dT a 
= T («+ 2P t) log. m, 
d t 
this quantity ought, of course, always to exceed the actual loss of heat in that inter- 
val, because the rate diminishes continually, and this, however minute the interval 
is assumed. 
Our readers may well suppose, that it is not with any idea of correcting for the 
minute error just noticed, that we have adopted the course described, but rather 
with the view, that when a series is thus divided into several parts, each of which is 
represented by empirical formulae that answer exactly to the numbers given by o 
