334 Dulong and Petit onthe Measure of Temperatures, (May, 
values of v. The remainders will evidently be the velocities of 
cooling owing to radiation, or, which comes to the same thing, 
those which would have taken place in vacuo. 
We give here the numbers thus determined for the thermo- 
meter with its bulb naked; we join to them the velocities 
deduced from the law of cooling in vacuo. The velocity in this 
case is expressed by 
m(a’ — 1); 
t representing the excess of temperature of the body, m a con- 
stant coefficient which must be determined in each case, and 
which is here equal to 2°61; a denoting the exponent 1-0077 
common to all bodies. 
locities Pp Acer de- lociti yu 
Excesses of temp. Velocities of cooling in vacuo de Velocities of cooling in 
duced from observations in air. vacuo by calculation. 
2 na eres eae : ie Rias dina gieiiate ele 3 16°40° 
240... 5 eh « papas 13; Tektiir cei es Siete - locus of 13°71 
ad) ee eee os bie 1d:3 Lgsite- evenias wore te ae le 
2) i O'BBim sats eceranrnese 9-42 
ie » sic bi osane ie miedts 7°85 wreath Cis dopa 77) 
Cr he hate ee ee oy 6:25 
0 ee et 5°02 ark i oom ono Ame 
Bsa adnate | eee ee 4 eae rng Oe 
| aE ee ge re 3°04 sy, Migr asthe 2a9 
Bs, bs a puns tial a hlidicost Denyse wia’s sips inejats ea 2°20 
We see, from the example which we have just given, that it 
is possible, by immediate observations of cooling im air, to esti- 
mate separately the losses of heat due to contact and to radia- 
tion ; and that it is necessary for this to observe the cooling of 
the same body under two different conditions of surface. But: 
this mode of calculation depends on the one side on the suppo- 
sition that the quantity of heat carried off by the air is indepen- 
dent of the nature of the surface of the body ; and on the other 
on this principle, that bodies of a different nature preserve at all 
temperatures the same ratio between their radiating powers. 
These two propositions are rigorously true, but can only be 
constated by direct experiments, such as those which we have 
stated above ; and though Mr. Leslie has adopted them in the 
use which he has made of the principle which we have just 
explained, his results have not all the accuracy that could be 
desired, because he has always calculated the velocities of cool- 
ing according to the Newtonian law. 
The laws relative to each of these two effects which concur to 
_ the cooling of a body plunged into a fluid being separately esta- 
blished, it is merely necessary to unite them i order to deduce 
the law of total, cooling. 
The velocity v of this cooling for an excess ¢ of temperature 
will be then expressed by the formula 
m(at—lh4 nt’. 
