1819.] and on the Laws of the Communication of Heat. 245 
Y@) ,@ F@ 8 F" © 
¢@) =t-— ae ais = 33° a 
And as this equation must hold good for all values of ¢, we thust 
have 
| Sighs a 
n being an indeterminate number ; whence we deduce : 
F (6) =m.ai + aconstant quantity. 
Making, for the sake of shortness, jerk = m, we get 
F (¢ + 6) = m.a't+® + a constant quantity. 
We have then finally for the value of the velocity, 
V=m.a} (a'— 1) 
an equation which contains the law of cooling in vacuo. 
If we suppose @ constant, the coefficient m a? will be so like- 
wise, and the preceding law may be announced in this manner. 
When a body cools in vacuo, surrounded by a medium whose 
temperature is constant, the velocity of cooling for excess of tem- 
perature in arithmetical progression, increases as the terms of a 
geometrical progression, diminished by a constant quantity. 
The ratio a of this progression is easily found for the thermo- 
meter, whose cooling we have observed ; for when # augments 
by 20°, ¢ remaining the same, the velocity of cooling is’ then 
multiplied by 1-165, the mean of all the ratios determined above. 
We have then 
h a= \/ 1165 = 10077. 
It only remains, in order to verify the accuracy of this law, to 
compare it with the different series contained in the table inserted 
above. Let us begin with that in which the surrounding medium 
was 0°. We find in this case that itis necessary to make m = 
2:037 ; we have then for this case, 
V = 2:087 (a‘ — 1) 
in which a = 1:0077.*. 
Excesses of temp, or Values of V ob- Values of V cal- 
values of ¢. served. culated, 
Ben nxn nrertea Senate tOOy 2. 26. iste ates 10°68° 
SERED 015 inie ‘ain plot me ett ORI) Gi ae 8°89 
eS peril A (0 A a 7:34 
| Re a Fick RE ruck ewes as 6-03 
Se re BED os wie eons 4:87 
140 cnen aaaKs “hc ET ere 3°89 
Es 6653, 058 Gal ah i Se ee a 3°05 
ry BUD". sohucvenaaiee 2°33 
ee ‘TL: Sane Bete Mear Io 1-72 
* To recollect the value of the coefficient -O01T, we may remark, that it is 
nearly eqnal to the square of the coefficient of the dilatation of the gases. 
