on some of the leading doctrines of caloric > & c. 353 
If we make, for example, n — 100, we shall have the elastic 
force at 100 degrees below the boiling point, or at the tem- 
perature of melting ice. We thus obtain 
Log. F n = 1.4771213 — 2.1778831 = — 0.7007618. 
Or employing negative indices in order to make use of the 
ordinary logarithmic tables. 
Log. F„ = T. 2932382, whence 
F n = o. 19917 inches; and observation 
gives us o. 200. 
The error is obviously insensible ; and we may adopt, says 
M. Biot, our formula as representing the experiments of 
Mr. Dalton. To introduce the Fahrenheit degrees into 
the formula, calling them/, and counting from 212®, we have 
a/ = n ; and substituting this value of n in the preceding 
formula, we obtain 
a — — o. 00834121972 
b = o. 00002081091 
c = -f- o. 00000000380, 
whence Log. F/ = 1.4771213 + qf + bf 2 + cf\ f being 
the number of degrees of Fahrenheit, reckoning them from 
212 0 , positive below and negative above this point of de- 
parture. 
By the above formula, thus elaborately investigated by 
M. Biot, I have computed the elastic forces of steam at the 
three successive temperatures of 232 0 , 262° and 312 0 , or 20°, 
30° and ioo°, above the boiling point of Fahrenheit's scale. 
In the first case we have/ = — ■ 20 and of -j- bf* -j- cf s = 
20 + 400 b — 8000 c ; / is negative, being above the point 
of departure 212 0 , and, consequently, the products */and cj\ 
are positive, while 6/ 2 becomes negative. 
3 A 
MDCCCXVIII. 
