1819.} und on the Laws of the Communication of Heat. 175 
The first column contains the excess of the temperature of the 
thermometers above that of the surrounding air. The second 
exhibits the corresponding velocities of cooling of the thermo- 
meter A, the diameter of whose bulb was about two centimetres. 
These velocities were calculated from the observations by the 
method explained above. The third and fourth columns exhibit 
the velocities of the cooling of the thermometers B and C, caleu- 
lated in the same way for the excess of temperatures indicated 
in the first column. The diameter of the bulb of the thermo- 
meter B was about four centimetres ; that of. the thermometer 
C about seven. 
A simple inspection of this table shows us at once the inac- 
curacy of the law of Richmann ; for we see that the velocities 
of cooling increase according to a more rapid progression than 
the excesses of temperature. Now if we take the ratios of the 
corresponding numbers in the second and third columns, we shall 
find that they have varied as follows, beginning with the terms 
which correspond with the greatest excess of temperature : 
a Sec eo Leasing, SAIL, cg 5 oO Le bie Ms ate 
These numbers, which differ very little from each other, and 
which are alternately greater and less, inform us that the rate of 
cooling follows the same law in the two thermometers A and B. 
If we compare in the same way the numbers contained in the 
second and fourth columns, we obtain for their ratios : 
I Tr) RE a “gto Rea Br Sa 3°77 
The near approximation to equality in these numbers shows 
us that the law of cooling is likewise the same for the thermo- 
meters A and C; for the differences in the preceding numbers 
must be ascribed to unavoidable errors in the experiments ; and 
they are owing to inaccuracies merely of one hundredth of a 
degree in the velocities. 
We are entitled to conclude, from what precedes, that the law 
of cooling, observed in a mercurial thermometer, is independent 
of the size of its bulb, and of consequence that it is the element- 
ary law of cooling, of which we are in search; or, in some 
measure, the law of cooling of a point. 
We have not examined how the velocity of cooling varies with 
the extent of surface, in consequence of the little precision of 
measurement of which the surface of a ball of glass blown at 
the extremity of a tube is susceptible ; and because that research 
was foreign to the object which we had in view. However, it 
will be seen from the approximate measures which we have 
given of the diameters of the bulbs, that the velocities of cooling 
are nearly inversely as the diameters, as would be the case with 
a solid sphere of infinitely small size. 
Let us now proceed to the examination of the influence which 
the nature of the liquid in the vessel may have upon the law of 
6 
