ELASTIC FORCES OF AQUEOUS VAPOUR. 597 
The next object is to calculate a formula of interpolation which 
shall represent all the observations in a satisfactory manner, and 
by means of which, we can determine the force of aqueous va- 
pour corresponding to any given temperature. 
A great number of different formulz have been proposed to 
express the elastic force of aqueous vapour in functions of the 
temperature. Some of the formulz were given as simple for- 
mulz of interpolation, others were presented with greater pre- 
tensions, as really explanatory of the physical law of the phe- 
nomenon. 
De Prony first proposed an expression of the form 
e=aad+bPii+cy/+de; 
and he gave a general method for calculating, by means of ob- 
servations, the values of the coefficients a, 6, c, d, and the bases 
of the exponents «, B, y, *. 
Dr. Young proposed the formula adopted by many philoso- 
phers, e= (a + bt). 
MM. Dulong and Arago adopted an expression of the same 
form. The formula e= (1+0°715372)°, calculated by these illus- 
trious philosophers, contains only one constant quantity obtained 
from a single one of their observations, from that one made 
_ at the highest pressure. 
Roche proposed the formula 
t 
— m+nt 
e=a@a > 
_ which he gives, not as a simple formula of interpolation, but as 
_ formula has been since reintroduced by several natural philoso- 
_phers, namely, by M. August}; it represents sufficiently well 
_ my own observations between the limits which served to calculate 
the constant quantities. I had occasion to settle that point in 
t 
the mathematical expression of the phenomenon. The same 
calculating the three constant quantities by means of the tensions 
“at 0°, at 50°, and at 100°; but it is easy to see that it does not 
express the mathematical law of the phzenomenon, and that it 
ought only to be considered as a formula of interpolation; the 
function is discontinuous, and represents a curve with two 
branches. In the case of «>1, one of these branches, which 
ought to represent the observed tensions, terminates where 
* Journal de l’ Ecole Polytechnique, 2° cahier, p. 1. 
+ Poggendorff’s Annalen, vols. xiii. and lviii. The same formula has been 
adopted by M. Magnus in the paper mentioned in the Note to page 575. 
2u2 
