Well! to maintain this source of heat it is only necessary that the rate of condensation should be such that the Sun’s diameter should decrease seventy-seven meters a year, or one kilometer in thirteen years. This contraction is so gradual that it would be wholly imperceptible. Nine thousand five hundred years would be required to reduce the diameter by one single second of arc. Even if the Sun be actually in a gaseous state, its temperature, so far from growing less, or even remaining stationary, would increase by the very fact of contraction; for if on the one hand the temperature of a gaseous body falls when it condenses, on the other hand the heat generated by contraction is more than sufficient to prevent a fall in temperature, and the amount of heat increases until a liquid state is reached. The Sun seems to have reached this stage.
The condensation of the Sun, whose density is only one-fourth that of the Earth, may thus of itself maintain for centuries, at least for ten million years, the light and heat of this brilliant star. But we have just spoken of a second source of heat: the fall of meteorites. One hundred and forty-six million meteorites fall upon the Earth yearly. A vastly greater number fall into the Sun, because of its greater attraction. If their mass equals about the one hundredth part of the mass of the Earth, their fall would suffice to maintain the temperature—not by their combustion, for if the Sun itself was being consumed it would not have lasted more than six thousand years, but by the sudden transformation of the energy of motion into heat, the velocity of impact being 650,000 meters per second, so great is the solar attraction.
If the Earth should fall into the Sun, it would make good for ninety-five years the actual loss of solar energy; Venus would make good this loss for eighty-four years; Mercury for seven; Mars for thirteen; Jupiter for 32,254; Saturn for 9652; Uranus for 1610; and Neptune for 1890 years. That is to say, the fall of all the planets into the Sun would produce heat enough to maintain the present rate of expenditure for about 46,000 years.
It is therefore certain that the fall of meteors greatly lengthens the life of the Sun. One thirty-third millionth of the solar mass added each year would compensate for the loss, and half of this would be sufficient if we admit that condensation shares equally with the fall of meteorites in the maintenance of solar heat; centuries would have to pass before any acceleration of the planets’ velocities would be apparent.
Owing to these two causes alone we may, therefore, admit a future for the Sun of at least twenty million years; and this period cannot but be increased by other unknown causes, to say nothing of an encounter with a swarm of meteorites.
The Sun therefore was the last living member of the system; the last animated by the warmth of life.
But the Sun also went out. After having so long poured upon his celestial children his vivifying beams, the black spots upon his surface increased in number and in extent, his brilliant photosphere grew dull, and his hitherto dazzling surface became congealed. An enormous red ball took the place of the dazzling center of the vanished worlds.
For a long time this enormous star maintained a high surface temperature, and a sort of phosphorescent atmosphere; its virgin soil, illumined by the light of the stars and by the electric influences which formed a kind of atmosphere, gave birth to a marvelous flora, to an unknown fauna, to beings differing absolutely in organization from those who had succeeded each other upon the worlds of its system.
But for the Sun also the end came, and the hour sounded on the timepiece of destiny when the whole solar system was stricken from the book of life. And one after another the stars, each one of which is a sun, a solar system, shared the same fate; yet the universe continued to exist as it does today.
Ψ
The science of mathematics tells us: “The solar system does not appear to possess at present more than the one four hundred and fifty-fourth part of the transformable energy which it had in the nebulous state. Although this remainder constitutes a fund whose magnitude confounds our imagination, it will also some day be exhausted. Later, the transformation will be complete for the entire universe, resulting in a general equilibrium of temperature and pressure.
“Energy will not then be susceptible of transformation. This does not mean annihilation, a word without meaning, nor does it mean the absence of motion, properly speaking, since the same sum of energy will always exist in the form of atomic motion, but the absence of all sensible motion, of all differentiation, the absolute uniformity of conditions, that is to say, absolute death.”
Such is the present statement of the science of mathematics.
Experiment and observation prove that on the one hand the quantity of matter, and on the other hand the quantity of energy also, remains constant, whatever the change in form or in position; but they also show that the universe tends to a state of equilibrium, a condition in which its heat will be uniformly distributed.
The heat of the Sun and of all the stars seems to be due to the transformation of their initial energy of motion, to molecular impacts; the heat thus generated is being constantly radiated into space, and this radiation will go on until every sun is cooled down to the temperature of space itself.
If we admit that the sciences of today, mechanics, physics and mathematics, are trustworthy, and that the laws which now control the operations of nature and of reason are permanent, this must be the fate of the universe.
Far from being eternal, the Earth on which we live has had a beginning. In
