1830.] 
and the Communication of Heat. 
317 
scale becomes, on the contrary, the less rapid in the upper part. Thus, in the series 
above given, the ratios inscribed in the last column diminish, as we consider greater 
excess of temperature ; they would increase again, if the series were continued suffi- 
siently tar ; and agreeably to the property common to all quantities, the differences of 
'which change their sign, these ratios would continue much the satne throughout a 
sufficiently extensive part of the thermometric scale. This is one of the most im- 
portant results of the theory of cooling. If we have not deceived ourselves, as to 
the correctness of the laws we have arrived at, we shall be able to give, in the sequel 
of this memoir, a very simple explanation of this remarkable fact, which could only 
have been brought to light, in observing, as vve have done, the progressof cooling at 
very high temperatures. 
It is from the want of such experiments that Messrs. Dalton and Leslie have 
arrived at conclusions so much at variance with truth, on the subject of which we 
are treating. The first misled by the idea, that the law of Richman was true with- 
in the range of his thermometric scale, and having, at the same time, neglected to 
compare the cooling of different substances within a sufficient range, adopted the 
conclusion, that the law of cooling for all bodies was the same. Mr. Leslie again, 
who had remarked, that the law changes with the nature of the surface, but not hav- 
ing included in his experiments sufficiently elevated temperatures, supposed that 
the difference observed, would increase as the temperature increased, which error 
has involved him in many other inaccurate conclusions, to which we shall have 
hereafter occasion to refer. We will here content ourselves with one remark, which 
is, that we are surprised to find Mr. Leslie, who had observed the difference in the 
law of cooling, occasioned by the different natures of bodies, and had thence conclud- 
ed rightly, that the law of Ricliraan could not be true, employing notwithstanding 
that very law pretty generally, in calculating the results of his experiments. 
We have concluded these preliminary researches, by observing the cooling of 
water in three vessels of tinned plate, having the same capacity ; the first spherical ; 
the sect nd cylindrical, the height being double the diameter of the base ; the third 
cylindrical also, the height being only half the diameter of the base. 
Excess of 
Tempera- 
ture. 
Rateof Cool 
ing of the 
sphere. 
Rate of Cool- 
ing of the Cy- 
linder, No.l. 
Rate of Cool- 
ing of the Cy- 
linder, No. 2. 
Ratio of the 
3d column to 
the 2d. 
Ratio of the 
4th column 
to the 2d. 
60 
0,90 
1,11 
1,01 
1,23 
1,12 
50 
0,73 
0,89 
0,80 
1,22 
1,10 
40 
0,54 
0,66 
0,60 
1,22 
1,11 
80 
0,38 
0,47 
0,43 
1,23 
1,13 
20 
0,21 
0,26 
0,23 
1,24 
1,10 
The law of cooling is then the same for the three vessels of different shapes, as 
indicated by the uniformity of value of the ratios in the fourth and fifth columns. 
The shape of the vessel has, therefore, no sensible influence on the law of cooling ; 
and what confirms this conclusion, is that the ratios between the above rates of cool- 
ing, are pretty nearly those of the surfaces of the three vessels, as any one may easily 
satisfy himself. We may recapitulate the results just established, by saying that 
the law of cooling of any liquid mass depends upon the nature and condition of the 
surface of the vesssel in which it is contained, but is alto ^ e / he !L. , ? dere .“ de ^ i ^; t ‘^ 
nature of the liquid, and of the shape and size of the vessel. This is the principle 
we proposed to establish in this introduction, and which must serve as a foundation 
to the researches we are now about to give an account ot. 
§ 2. Apparatus for the experiments on cooling • 
The bodies, the cooling of which we have observed, have been cor iformahly to 
the principles just established ; thermometers having a volume such, tb.il thi dej res- 
sion of temperature could be easily observed with precision. We cowt^c^d o, 
the bulbs of which were about, the one, 6 centimetres in d lameter first, 
containing about three pounds of mercury was used in observations on h gh tempe. 
mures ; the smaller one being employed for the lower 
shorten the period of the experiments. The results obtained 
easily reduced to what the other would have given, had n • \ i« 
ciently prolonged ; to do this, it was sufficient to commence observing w the small 
one at a higher temperature, than that at which the o sem ions ^ ^ 
one were to terminate. The ratio of the rates of cooli 0 b 
