THE GENERATION OF COSMICAL HEAT.
In the preceding Chapter we endeavoured to show how the action of
gravitation upon the particles of diffused primordial matter would
result in the formation, by condensation and aggregation, of a spherical
planetary body. We have now to consider another result of the
gravitating action, and for this we must call to our aid a branch of
scientific enquiry and investigation unrecognized as such at the period
of Laplace’s speculations, and which has been developed almost entirely
within the past quarter of a century.
The “great philosophical doctrine of the present era of science,” as the
subject about to engage our attention has been justly termed, bears the
title of the “Conservation of Force,” or—as some ambiguity is likely to
attend the definition of the term “Force”—the “Conservation of Energy.”
The basis of the doctrine is the broad and comprehensive natural law
which teaches us that the quantity of force comprised by the universe,
like the quantity of matter contained in it, is a fixed and invariable
amount, which can be neither added to nor taken from, but which is for
ever undergoing change and transformation from one form to another. That
we cannot create force ought to be as obvious a fact as that we cannot
create matter; and what we cannot create we cannot destroy. As in the
universe we see no new matter created, but the same matter constantly
disappearing from one form and reappearing in another, so we can find no
new force ever coming into action—no description of force that is not to
be referred to some previous manner of existence.
Without entering upon a metaphysical discussion of the term “force,” it
will be sufficient for our purpose to consider it as something which
produces or resists motion, and hence we may argue that the ultimate
effect of force is motion. The force of gravity on the earth results in
the motion or tendency of all bodies towards its centre, and, similarly,
the action of gravitation upon the atoms or particles of a primeval
planet resulted in the motion of those particles towards each other. We
cannot conceive force otherwise than by its effects, or the motion it
produces.
And force we are taught is indestructible; therefore motion must be
indestructible also. But when a falling body strikes the earth, or a
gunshot strikes its target, or a hammer delivers a blow upon an anvil,
or a brake is pressed against a rotating wheel, motion is arrested, and
it would seem natural to infer that it is destroyed. But if we say it is
indestructible, what becomes of it? The philosophical answer to the
question is this—that the motion of the mass becomes transferred to the
particles or molecules composing it, and transformed to molecular
motion, and this molecular motion manifests itself to us as heat. The
particles or atoms of matter are held together by cohesion, or, in other
words, by the action of molecular attraction. When heat is applied to
these particles, motion is set up among them, they are set in vibration,
and thus, requiring and making wider room, they urge each other apart,
and the well-known _expansion by heat_ is the result. If the heat be
further continued a more violent molecular motion ensues, every increase
of heat tending to urge the atoms further apart, till at length they
overcome their cohesive attraction and move about each other, and a
_liquid or molten condition_ results. If the heat be still further
increased, the atoms break away from their cohesive fetters altogether
and leap off the mass in the form of vapour, and the matter thus assumes
the _gaseous or vaporous form_. Thus we see that the phenomena of heat
are phenomena of motion, and of motion only.
This mutual relation between heat and work presented itself as an embryo
idea to the minds of several of the earlier philosophers, by whom it was
maintained in opposition to the _material theory_ which held heat to be
a kind of matter or subtle fluid stored up in the inter-atomic spaces of
all bodies, capable of being separated and procured from them by rubbing
them together, but not generated thereby. Bacon, in his “Novum Organum,”
says that “heat itself, its essence and quiddity, is motion and nothing
else.” Locke defines heat as “a very brisk agitation of the insensible
parts of an object, which produces in us that sensation from whence we
denominate the object hot; so what in our sensation is _heat_, in the
object is nothing but _motion_.” Descartes and his followers upheld a
similar opinion. Richard Boyle, two hundred years ago, actually wrote a
treatise entitled “The Mechanical Theory of Heat and Cold,” and the
ingenious Count Rumford made some highly interesting and significant
experiments on the subject, which are described in a paper read before
the Royal Society in 1798, entitled “An Inquiry concerning the Source of
Heat excited by Friction.” But the conceptions of these authors remained
isolated and unfruitful for more than a century, and might have passed,
meantime, into the oblivion of barren speculation, but for the impulse
which this branch of inquiry has lately received. Now, however, they
stand forth as notable instances of truth trying to force itself into
recognition while yet men’s minds were unprepared or disinclined to
receive it. The key to the beautiful mechanical theory of heat was found
by these searching minds, but the unclasping of the lock that should
disclose its beauty and value was reserved for the philosophers of the
present age.
Simultaneously and independently, and without even the knowledge of each
other, three men, far removed from probable intercourse, conceived the
same ideas and worked out nearly similar results concerning the
mechanical theory of heat. Seeing that motion was convertible into heat,
and heat into motion, it became of the utmost importance to determine
the exact relation that existed between the two elements. The first who
raised the idea to philosophic clearness was Dr. Julius Robert Mayer, a
physician of Heilbronn in Germany. In certain observations connected
with his medical practice it occurred to him that there must be a
necessary equivalent between work and heat, a necessary numerical
relation between them. “The variations of the difference of colour of
arterial and venous blood directed his attention to the theory of
respiration. He soon saw in the respiration of animals the origin of
their motive powers, and the comparison of animals to thermic machines
afterwards suggested to him the important principle with which his name
will remain for ever connected.”
Next in order of publication of his results stands the name of Colding,
a Danish engineer, who about the year 1843 presented a series of memoirs
on the steam engine to the Royal Society of Copenhagen, in which he put
forth views almost identical with those of Mayer.
Last in publication order, but foremost in the importance of his
experimental treatment of the subject, was our own countryman, Dr. Joule
of Manchester. “Entirely independent of Mayer, with his mind firmly
fixed upon a principle, and undismayed by the coolness with which his
first labours appear to have been received, he persisted for years in
his attempts to prove the invariability of the relation which subsists
between heat and ordinary mechanical power.” (We are quoting from
Professor Tyndall’s valuable work on “Heat considered as a Mode of
Motion.”) “He placed water in a suitable vessel, agitated the water by
paddles, and determined both the amount of heat developed by the
stirring of the liquid and the amount of labour expended in its
production. He did the same with mercury and sperm oil. He also caused
discs of cast iron to rub against each other, and measured the heat
produced by their friction, and the force expended in overcoming it. He
urged water through capillary tubes, and determined the amount of heat
generated by the friction of the liquid against the sides of the tubes.
And the results of his experiments leave no shadow of doubt upon the
mind that, under all circumstances, the quantity of heat generated by
the same amount of force is fixed and invariable. A given amount of
force, in causing the iron discs to rotate against each other, produced
precisely the same amount of heat as when it was applied to agitate
water, mercury, or sperm oil. * * * * _The absolute amount of heat_
generated by the same expenditure of power, was in all cases the same.”
“In this way it was found that the quantity of heat which would raise
one pound of water one degree Fahrenheit in temperature, is exactly
equal to what would be generated if a pound weight, after having fallen
through a height of 772 feet, had its moving force destroyed by
collision with the earth. Conversely, the amount of heat necessary to
raise a pound of water one degree in temperature, would, if all applied
mechanically, be competent to raise a pound weight 772 feet high, or it
would raise 772 pounds one foot high. The term ‘foot pounds’ has been
introduced to express in a convenient way the lifting of one pound to
the height of a foot. Thus the quantity of heat necessary to raise the
temperature of a pound of water one degree Fahrenheit being taken as a
standard, 772 foot-pounds constitute what is called the _mechanical
equivalent_ of heat.”
By a process entirely different, and by an independent course of
reasoning, Mayer had, a few months previous to Joule, determined this
equivalent to be 771·4 foot-pounds. Such a remarkable coincidence
arrived at by pursuing different routes gives this value a strong claim
to accuracy, and raises the Mechanical Theory of Heat to the dignity of
an exact science, and its enunciators to the foremost place in the ranks
of physical philosophers.
In linking together the labours of the two remarkable men above alluded
to, Prof. Tyndall remarks, that “Mayer’s labours have in some measure
the stamp of profound intuition, which rose however to the energy of
undoubting conviction in the author’s mind. Joule’s labours, on the
contrary, are an experimental demonstration. Mayer _thought_ his theory
out, and rose to its grandest applications. Joule _worked_ his theory
out, and gave it the solidity of natural truth. True to the speculative
instinct of his country, Mayer drew large and mighty conclusions from
slender premises; while the Englishman aimed above all things at the
firm establishment of facts.... To each belongs a reputation which will
not quickly fade, for the share he has had, not only in establishing the
dynamical theory of heat, but also in leading the way towards a right
appreciation of the general energies of the universe.”
But from these generalities we must pass to the application of the
mechanical theory of heat to our special subject. We have learnt that
every form of motion is convertible into heat. We know that the falling
meteor or shooting star, whose motion is impeded by friction against the
earth’s atmosphere, is heated thereby to a temperature of incandescence.
Let us then suppose that myriads of such cosmical particles came into
collision from the effect of their mutual attraction, or that the
component atoms of a vast nebulous mass violently converged under the
like influence. What would follow? Obviously the generation of an
intense heat by the arrest of converging motion, such a heat as would
result in the fusion of the whole into one mass. Mayer, in one of his
most remarkable papers (“Celestial Dynamics”) remarks that the
“Newtonian theory of gravitation, whilst it enables us to determine,
from its present form, the earth’s state of aggregation in ages past, at
the same time points out to us a source of heat powerful enough to
produce such a state of aggregation—powerful enough to melt worlds: it
teaches us to consider the molten state of a planet as the result of the
mechanical union of cosmical masses, and to derive the radiation of the
sun and the heat in the bowels of the earth from a common origin.”
And the same laws that governed the formation of the earth, governed
also the formation of the moon: the variations of Nature’s operations
are _quantitative_ only and not _qualitative_. The Divine Will that made
the earth made the moon also, and the means and mode of working were the
same for both. The geological phenomena of the earth afford
unmistakeable evidence of its original fluid or molten condition, and
the appearance of the moon is as unmistakeably that of a body once in an
igneous or molten state. The enigma of the earth’s primary formation is
solved by the application of the dynamical theory of heat. By this
theory the generation of cosmical heat is removed from the quicksands of
conjecture and established upon the firm ground of direct calculation:
for the absolute amount of heat generated by the collision of a given
amount of matter is (of course, with some little uncertainty) deducible
from a mathematical formula. Mayer has computed the amount of heat that
the matter of the earth would have generated, if it had been formed
originally of only two parts drawn into collision by their mutual
attraction, and has found that it would be from 0 to 32,000 or 47,000[1]
Centigrade degrees, according as one part was infinitely small as
compared with the other, or as the two parts were of equal size.
Professor Helmholtz, another labourer in the same field of science, has
computed the amount of heat generated by the condensation of the whole
of the matter composing the solar system: this he finds would be
equivalent to the heat that would be required to raise the temperature
of a mass of water equal to the sum of the masses of all the bodies of
the system to 28,000,000 (twenty-eight million) degrees of the
Centigrade scale.
These examples afford abundant evidence of sufficient heat having been
generated by the aggregation of the matter of the moon to reduce it to a
state of fusion, and so to produce, from a nebulous chaos of diffused
cosmical matter, a molten body of definite outline and size.
It is requisite here to remark that fusion does not necessarily imply
combustion. It has been frequently asked, How can a volcanic theory of
the lunar phenomena be upheld consistently with the condition that it
possesses no atmosphere to support Fire? To this we would reply that to
produce a state of incandescence or a molten condition it is _not_
necessary that the body be surrounded by an atmosphere. The intensely
rapid motion of the particles of matter of bodies, which the dynamical
theory shows to be the origin of the molten state, exists quite
independently of such external matter as an atmosphere. The complex
mixture of gases and vapours which we term “air,” has nothing whatever
to do with the fusion of substances, whatever it may have to do with
their combustion. Combustion is a chemical phenomenon, due to the
combination of the oxygen of that air with the heated particles of the
combustible matter: oxygen is the sole supporter of combustion, and
hence combustion is to be regarded rather as a phenomenon of oxygen than
as a phenomenon of the matter with which that oxygen combines. The
greatest intensity of heat may exist without oxygen, and consequently
without combustion. In support of this argument it will be sufficient to
adduce, upon the authority of Dr. Tyndall, the fact that a platinum wire
can be raised to a luminous temperature and actually _fused_ in a
perfect vacuum.
But while the mass of condensing cosmical matter was thus accumulating
and forming the globe of the moon, the heat consequent upon the
aggregation of its particles was suffering some diminution from the
effect of radiation. So long as the radiated heat lost fell short of the
dynamical heat generated, no effect of cooling would be manifest; but
when the _vis viva_ of the condensing matter was all converted into its
equivalent of heat, or when the accession of heat fell short of that
radiated, a necessary cooling must ensue, and this cooling would be
accompanied by a solidification of that part of the mass which was most
free to radiate its heat into surrounding space: that part would
obviously be the outer surface.
With the solidification of this external crust began the “year one” of
selenological history.
The phenomena attendant upon the cooling of the mass we will consider in
the next Chapter.