7. Although this difference is small, yet the former value would
have reduced his result about 0.7 of a foot pound.

Again, he uses 0.1686 for the specific heat of air at constant volume.
The value of this constant has never been found to any degree of
accuracy by direct experiment, and we are still dependent upon the
method established by La Place and Poisson, according to which the
constant ratio of the specific heat of a gas at constant pressure to
that at constant volume is found by means of the velocity of sound in
the gas. The value of the ratio for air, as found in the days of La
Place, was 1.41, and we have 0.2377 / 1.41 = 0.1686, the value used by
Clausius, Hanssen, and many others. But this ratio is not definitely
known. Rankine in his later writings used 1.408, and Tait in a recent
work gives 1.404, while some experiments give less than 1.4, and
others more than 1.41.

An error of one foot in a thousand in determining the velocity of
sound will affect the third decimal figure one or two units. A small
difference in the assumed weight of a cubic foot of air also affects
the result. M. Hanssen gives 0.080743 pound as the weight at 32 deg. F.
under the pressure of one atmosphere; while Rankine gives 0.080728
pound. In my own computations I use 1.406 as a more probable value of
the constant sought. This will give for the specific heat of air at
constant pressure

0.2375 / 1.406 = 0.1689

This is only 0.0003 of a unit greater than the value used by Hanssen,
but it would have given him nearly 775, instead of 771.89.

Again, he uses 491.4 deg. F. for the absolute temperature of melting ice.
The exact value of this constant is unknown; but the mean value as
determined by Joule and Thomson, in their celebrated experiments with
porous plugs, was 492.66 deg. F. This value would slightly change his
result. It will be seen from the above that a small change in the
constants used may affect by several units the computed value of the
mechanical equivalent. I have computed it, using 1.406 for the ratio
of the specific heat of air at constant pressure to that at constant
volume, 491.13 deg. F. as the temperature of melting ice above the zero of
the _air_ thermometer, 26,214 feet for the height of a homogeneous
atmosphere, and 0.2375 for the specific heat of air, and I find, by
means of these constants, 778. If computed from the zero of the
absolute scale, 492.66 deg. F., I find 777 to the nearest integer.
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