A numerical solution of the relation between heat and work was what
Mayer aimed at, and towards the end of his first paper he makes the
attempt. It was known that a definite amount of air, in rising one
degree in temperature, can take up two different amounts of heat. If
its volume be kept constant, it takes up one amount: if its pressure
be kept constant it takes up a different amount. These two amounts
are called the specific heat under constant volume and under constant
pressure. The ratio of the first to the second is as 1: 1.421. No
man, to my knowledge, prior to Dr. Mayer, penetrated the significance
of these two numbers. He first saw that the excess 0.421 was not, as
then universally supposed, heat actually lodged in the gas, but heat
which had been actually consumed by the gas in expanding against
pressure. The amount of work here performed was accurately known, the
amount of heat consumed was also accurately known, and from these data
Mayer determined the mechanical equivalent of heat. Even in this
first paper he is able to direct attention to the enormous discrepancy
between the theoretic power of the fuel consumed in steam-engines, and
their useful effect.

Though this paper contains but the germ of his further labours, I
think it may be safely assumed that, as regards the mechanical theory
of heat, this obscure Heilbronn physician, in the year 1842, was in
advance of all the scientific men of the time.

Having, by the publication of this paper, secured himself against what
he calls 'Eventualitaeten,' he devoted every hour of his spare time
to his studies, and in 1845 published a memoir which far transcends
his first one in weight and fulness, and, indeed, marks an epoch in
the history of science. The title of Mayer's first paper was,
'Remarks on the Forces of Inorganic Nature.' The title of his second
great essay was, 'Organic Motion in its Connection with Nutrition.' In
it he expands and illustrates the physical principles laid down in his
first brief paper.

He goes fully through the calculation of the mechanical equivalent of
heat. He calculates the performances of steam-engines, and finds that
100 lbs. of coal, in a good working engine, produce only the same
amount of heat as 95 lbs. in an unworking one; the 5 missing lbs.
having been converted into work. He determines the useful effect of
gunpowder, and finds nine per cent. of the force of the consumed
charcoal invested on the moving ba