and the Communication of Heat. 
315 
1830.] 
servation the rate of cooling deduced from these formula:, for different excesses of 
temperature, is treed from those uncertainties and irregularities which are often 
found to accompany single results. 
Let us now return to the first comparison, of which we have spoken above, and 
let us enquire how the rate of cooling has varied in the three different series, the 
calculated results of which are given in the accompanying table. 
Excess of Tem- 
perature. 
Rate of Cooling of 
Thermometer A. 
Diam.=2centim. 
Rate of Cooling of 
Thermometer B- 
Diain.=4 centira. 
Rate of Cooling of 
Thermometer C. 
Diam.=.7 centitn. 
100° 
18°, 90 
8,07 
5,00 
80 
14 ,00 
6,60 
3,67 
60 
0 ,58 
4,56 
2,52 
40 
5 ,03 
2,80 
1,56 
20 
2 ,75 
1,30 
0,73 
The first column contains the excess of temperature of the thermometers over 
that of the surrounding medium ; in the next will be found the corresponding rates 
of cooling of the thermometer A, the bull) of which is about 2 centimetres ( ,788 
inch) in diameter. These rates have been calculated, according to the method 
just explained, from actual observation. The third and fourth columns contain the 
rates of the thermometers B &. C, calculated in the same way, and for the excess of 
temperature in the first Column. The bulb of the thermometer B is nearly 4 centi- 
metres (1,576 inches) in diameter ; that of the thermometer C 7 centimetres (2,758 
inches). 
A mere inspection of this table will he sufficient to show the inaccuracy of Rich- 
man’s law; for we see at once, that the rate of cooling increases faster than the 
excess of temperature. Now, if we enquire what is the ratio of the corresponding 
numbers in the second and third columns, we shall find that they are as follow, — 
beginning with those which correspond with the greatest excess of temperature. 
2,11 2,12 2,10 2,12 2,11 
These numbers, which diifer very little among themselves, and the differences of 
which appear to be accidental, enable us to infer, that the rate of cooling follows 
the same law in the two thermometers A & B, In the same way, comparing the 
numbers in the second and fourth columns, we shall find as their ratios, 
3,78 3,81 3,80 3,80 3,77 
These numbers being also nearly the same, we see that the law of Cooling is still 
the same for the thermometers A & C ; for the differences presented by the pre- 
ceding numbers ought to be attributed to the errors inseparable from the most 
careful experiments, and indeed amount to little more than the hundredth part of a 
degree on the rates. We are, therefore, justified in concluding, from all that precedes, 
that the law of cooling, for a mercurial thermometer, has no reference to the size 
of the bulb, and that it is consequently the elementary law we are seeking ; in other 
words, the law which the cooling of a material point would follow. 
We have not examined the question, how far the rate of cooling would be affec- 
ted by difference of surface, on account of the difficulty of measuring precisely the 
surface of a bulb of glass, blown at the extremity of a tube, as well as because this 
inquiry was distinct from the one we had undertaken. We may however see even 
in (lie approximate measures given of the bulbs, that the rap.d.ty of coohng is 
nearly in the ratio which would hold with spheres indefinitely small ; that is to say, 
in the inverse ratio of their diameters. . , f 
Let us now attend to the influence which the nature of the liquid of which the 
thermometer might be constructed would have on the law of cooling. On account 
of the difficulty of constructing thermometers of any other substance than mercury, 
a difficulty occasioned by the uncertainty which still e^elopes ^ ^ enclo^ 
in all other bodies, we determined to observe the cooling of 1 ffiese 
ingthem in a glass matras, in which should be immersed a mercurial eri JO, iet 
of great sensibility. We satisfied ourselves, that ie posi » temnerature of 
was a matter of indifference, and that at any particular instant ^ 
every part of the mass would be the same; which in< eet s .'. ' , which 
of that internal conduction, the result of the currents 
is therefore nearly perfect, at least for masses such as I > 
pertinents. 
