35° D/\ Ure*s experimental researches 
apparently through a considerable range with experiment, 
and yet be inaccurate when farther extended. 
Dissatisfied, therefore, with this approximation, I prosecuted 
the inquiry, and had the happiness to discover a very simple 
and beautiful ratio, which will actually apply through an 
extensive scale of temperature, and is incomparably easier in 
practice than the preceding rule. The elastic force at 212°= 
30 inches being divided by 1.23, will give the force for 10^ 
below; this quotient divided by 1.2^, will give that for io° 
lower ; and so on progressively. To obtain the forces above 
212 0 , we have merely to multiply 30 by the ratio, 1.23 for 
the force at 222 0 ; this product by 1.22 for that at 232 0 , and 
thus for each successive interval of io° above the boiling 
point. 
Thus 30 x 1.23 = F 222 ». 30 x 123 x 1.22 = F 232% 
using F to denote the force at any temperature n y according 
to the notation of Laplace. 
By departing from the point of 210° F., we shall obtain 
results equally accurate, but more convenient for comparison 
with the experimental table. The following numbers exhibit 
the correspondence of this ratio with actual observation. 
