2819.] and on the Laws of the Communicutiun of Heat. 251 
and beeause it is probable that it is more, than compensated, 
from the stem of the thermometer employed by Laroche 
not being completely plunged into the mercury. 
Instead of taking each of the series which is given by this 
philosopher, we have taken in some measure the mean of them, 
assisted by the formula by which M. Biot has represented these 
observations—a formula inserted in page 634 of the fourth 
volume of his Traité de Physique. The numbers which we give 
as the result of observation are then deduced from the formula 
of M. Biot. To represent them by means of our law, we must 
make V, which here represents the radiation, equal to 
4:24 (a' — 1) 
t bemg the excess of the temperature of the crucible, and aa 
constant quantity, which we have found precisely equal to 1-0077. 
Values of ¢. Values of V observed. Values of V calculated. 
TROOP AWS agesutivaw: 15 ASH ode ahh aati 15-29° 
VSO SNS oN ets Seis ahs 12 Bilbanedts as. teadsoe 12°52 
EGOS saseesns ab buiietegy 10°09 stajdgrache’s 10°15 
TAQ A Lf votes wick) Se BOA Preiss aid prise peureih 811 
N20 Sisrapeesicvaey bn wag O BOD. brig fadiever's 6°36 
LOQH6s: Ry asibibaak ods ArSAny iactdine aglgees 4°86 
80 ee ee MG) -iiigau -uisis Bhuvt 3°58 
Gin’ sda ae de alee Pb. thin F< amare. 2°47 
This last series furnishes by its agreement with our law, a new 
proof that the number a depends neither upon the mass nor on 
the state of the surface of the body. Since we find it here to 
hhave the same value as in our experiments on cooling vitreous 
and silvered surfaces in vacuo. 
From the expression of the velocity of cooling in vacuo, we 
ean easily deduce the relation which connects the temperatures 
and the times. If we denote the time by 7, we have 
V=-=M@'-) 
M being a constant coefficient which depends solely on the 
temperature of the surrounding medium. From this we conclude 
—dt 
dt = w@at 
and > 
} a—1 . 
r:= Wie. (log. —-) + a constant quantity. 
The arbitrary constant quantity and the number M will be 
determined in each particular case, when we have observed the 
values of ¢ corresponding to two known values of the time z. 
If we supposed ¢ so small that, considering the smallness of 
the logarithm of a, we could confine ourselves to the terms of 
the first power in the development of a‘, we should obtain the 
Newtonian law. 
{To be continued.) 
