244 Dulong and Petit on the Measure of Temperatures, [ArRiz, 
results which it contains lead us to a very simple approximation 
which discovers the law of cooling in vacuo. If we compare 
the corresponding numbers of the second and third column; that 
is to say, the velocities of cooling for the same excess of temper- 
ature, the surrounding medium being successively at 0° and at 
20°, we find that the ratios of these velocities vary as follows : 
Po) Pe PIS ES Pe PP ee tee le. . hee 
These numbers, which differ very little from each other without 
showing any regularity, in their variations, require to be rendered 
equal changes im the velociiies vbserved, which would scarcely 
amount to one per cent. 
Let us now compare the velocities observed when the sur- 
rounding medium was at 20° and 40°. We shall find for the 
ratios of these velocities : 
116 2016.01°16 «1716: BYE EG. I se ee ee 
When the surrounding medium is at 40° and 60°, the ratios 
are : 
hiss. IG 6. F166. vel TR bigs aes. ks 
‘When the surrounding medium is at 60° and 80°, the ratios 
are : 
bbges Ps TGP, 2. 16 Job, bees ie 
These last three comparisons lead us to the same conclusion 
as the first, and inform us, besides, that the constant ratio 
between two consecutive series has remained always the same 
when the surrounding medium was heated from 0° to 20°; from 
20° to 40°; from 40° to 60° ; and from 60° to 80°. The preced- 
ing experiments then prove the following law: The velocity of 
cooling of a thermometer in vacuo Avi a constant excess of temper- 
ature, increases in a geometrical progression, when the tempera- 
ture of the surrounding medium increases in an arithmetical 
progression. The ratio of this geometrical progression is the same 
whatever be the excess of temperature considered. 
This first law, which applies solely to the variation of temper- 
ature of the surrounding medium, enables us to put the expres- 
sion found formerly of the velocity of cooling in vacuo, 
E¢ +19 —F'@ 
under the form 
gt + ag. 
a being a constant quantity, and ¢ (#) a function of the vanable 
t only, and which we must endeavour to discover. 
The two expressions of the velocity of cooling being equal, 
we have 
F(t + 6)—F(6 
Cr Se 
Whence by developing the series 
