sappear as a CAUSE when its effects are
produced in the shape of motion, expansion, or raising of weight.

"In water-mills the continual diminution in bulk which the earth
undergoes, owing to the fall of the water, gives rise to motion, which
afterwards disappears again, calling forth unceasingly a great quantity
of heat; and, inversely, the steam-engine serves to decompose heat again
into motion or the raising of weights. A locomotive with its train may
be compared to a distilling apparatus; the heat applied under the boiler
passes off as motion, and this is deposited again as heat at the axles
of the wheels."

Mayer then closes his paper with the following deduction: "The solution
of the equations subsisting between falling force and motion requires
that the space fallen through in a given time--e. g., the first
second--should be experimentally determined. In like manner, the
solution of the equations subsisting between falling force and motion on
the one hand and heat on the other requires an answer to the question,
How great is the quantity of heat which corresponds to a given quantity
of motion or falling force? For instance, we must ascertain how high a
given weight requires to be raised above the ground in order that its
falling force maybe equivalent to the raising of the temperature of
an equal weight of water from 0 degrees to 1 degrees centigrade. The
attempt to show that such an equation is the expression of a physical
truth may be regarded as the substance of the foregoing remarks.

"By applying the principles that have been set forth to the relations
subsisting between the temperature and the volume of gases, we find
that the sinking of a mercury column by which a gas is compressed is
equivalent to the quantity of heat set free by the compression; and
hence it follows, the ratio between the capacity for heat of air under
constant pressure and its capacity under constant volume being taken as
= 1.421, that the warming of a given weight of water from 0 degrees to
equal weight from the height of about three hundred and sixty-five
metres. If we compare with this result the working of our best
steam-engines, we see how small a part only of the heat applied under
the boiler is really transformed into motion or the raising of weights;
and this may serve as justification for the attempts at the profitable
production of motion by some other method than the expenditure of the
chemical difference between carbon an