364 Miscellanies. 
proposed, more or less exact, representing the law of elastic force: 
that of La Place, as stated in the Traité de Physique of Biot, has 
the form, F =760" x 10% + bi? + ci? +, &e. 
in which F designates the elastic force estimated in millimetres ; 
760 the height of the column of quicksilver supported by atmos- 
pheric pressure, and a, b, c, &c. constant coefficients which M. De 
la Place endeavored to determine by experiment: he found a= 
0.154547, 6= — 0.00625826. &c. Such a formula is obviously 
rather complicated, and to apply it to high temperatures, the terms 
2°, 14, &c. would be requisite ; ¢ representing the excess of the tem- 
perature over 212°. But a more simple one may be found, by ob- 
serving that the elastic force of the vapor increases for each element 
of the temperature, by a quantity which is in the compound ratio of 
the existing elastic force, and the increments of what I call the ex- 
pansive heat, (chaleur expansive) and which is proportional to the 
product of the temperature by the density which it would give to 
steam, or to the quotient of that temperature by the volume which 
it tends to give to steam agreeably to the law of dilatation laid down 
by Gay Lussac. Thus, then the true law will be, that the elastic 
force increases in geometrical progression, while the expansive heat 
increases in arithemetical progression, and as this expansive heat, 
designating by x the excess of temperature above 100 reuee 
100 +2 100+ 03 
8+0.03(100+2)  11+0. eeaes Og 
being the —— of the dilatation or increase of volume for each 
00+ 100 Tre 
frome ai ir Pos 
would be proportional to 
degree): and as —_— 
we may regard 
X- 
the increments as proportional to the quotient => ll rs a 032 and e 
press the elastic force by the formula, 
F=760” x10 = - Te 5032" 
nm being a constant coefficient, and 760” the atmospheric pressure- 
This Semale i in taking the logarithms, oe 
poe log- F = log..160 Sire opis 
if F be known by experiment, we shall find m in resolving the 
preceding “oe! in n, which will give, 
_1 0.032 
—- (log. F — log. 760”). 
