on some of the leading doctrines of caloric , (sfc. 353 
At these high heats, it is very possible that the experiment 
may be in error by 1 inch, which is the whole difference here. 
About half a degree of Fahrenheit misnoted, would give this 
deviation. 
Such a correspondence, therefore, of observation with the 
calculated results, shows that we have found a rule of perfect 
accuracy for all purposes of engineering, &c. If I am asked 
whether this formula coincides at every link with the chain of 
nature, I freely acknowledge, that I do not imagine it strictly 
so to do. But still it affords approximations such, that within 
moderate limits, I cannot tell whether to place more confi- 
dence in them, or in those found by experiment. It has 
moreover the rare advantage of being extremely simple, and 
level to the capacity of all practical men. 
In Biot’s excellent work above quoted, where many of the 
hitherto vague disquisitions of physical science have been 
happily brought within the pale of geometry, this celebrated 
philosopher has deduced, from Mr. Dalton’s experiments on 
the force of steam, a general formula for determining its 
elasticity at any temperature. 
In investigating this formula, he represents the decrease of 
the logarithms of the elastic forces by a series of terms of the 
form an -j- bn 12 + cn s ; abc being constant coefficients. 
Thus, Log. F„ = Log. 30 -f- an + bn 2 -f- cn 3 
It is unnecessary to employ powers of n higher than the 
cube, because their coefficients would be insensible, as the 
calculation will show. To determine the coefficients abc, he 
makes use of the elastic forces, observed at the temperatures 
on the centigrade scale of loo 0 , 75 0 , 50°, and 25 0 ; whence 
result these conditions, 
