THE THEEMAL EFEECTS OE ELHIDS IN MOTION. 
589 
tions from the gaseous laws are so small, for common air, that very small absolute errors 
in observations of so heterogeneous a character as those of Eegnault on the law of 
compression and on the changes produced by pressure in the coefficients of expansion, 
and our own on the thermo-dynamic property on which we have experimented, may 
readily present us with results either absolutely inconsistent with one another, or only 
reconcileable by very strained assumptions. It is satisfactory now to find, when we have 
succeeded in extending our observations through a considerable range of temperature, 
that they lead to so simple a law ; and it is probable that the formula we have been led 
to by these observations alone, will give the deviations from Boyle’s law, and the changes 
produced by pressure in the coefficients of expansion, with more accuracy than has 
hitherto been attained in attempts to determine these deviations by direct observation. 
We must, however, reserve for a future communication the comparison between such 
results of our theory and experiments and Eeonault’s direct observations. In the 
mean time we conclude by putting the integral equation of elasticity into a more con- 
venient form, by taking C=]^, where lb denotes the “ height of the homogeneous atmo- 
sphere ” for the gas under any excessively small pressure, at any temperature and 
taking to denote the absolute temperature of freezing water, in which case we shall 
have, as nearly as observations hitherto made allow us to determine. 
t =273°-7. 
o 
Then, in terms of this notation, and of that above explained, in which p, v denote 
absolute temperature, pressure in pounds weight per square foot, and volume in cubic 
feet of one pound of air, the equation of elasticity investigated above becomes 
Ib^ 1 A TIT 
v —~ — ^AJK 
pto ^ 
where A denotes the amount of the thermal effect per pound per square foot, deter- 
mined by our observations, reckoned positive when it is a depression of temperature. 
