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% + 622 + 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, b= — 0.00625826. &c. Such a formula is obviously 
rather complicated, and to apply it to high temperatures, the terms 
43,74, &c. would be requisite ; 2 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 2 the excess of temperature above 100 centigrade 
100 +a 100-4201 aos 
8+0.03(100+2) ° 1140.03a Og 
being the coefficient of the dilatation or increase of volume for each 
100+e 100 eye 
11400327 (1 © 114 008m Cee 
would be proportional to 
depree)): and as = 
© 
the increments as proportional to the quotient 7; 0.032 and ex- 
press the elastic force by the formula, 
F=760" X10 =. ean 1.032" 
m being a constant coefficient, and 760” the atmospheric pressure. 
This formula in taking the logarithms, becomes 
Ne 
log. F = log. 760 + 114.0.032° 
if F be known by experiment, we shall find n in resolving the 
receding equation in , which will give 
B give, 
11+0.03zx 
oe — (log. F — log. 760”). 
n= 
