CHAPTER XXI.

THE PROBABLE AGE AND ORIGIN OF THE SUN.

Gravitation Theory.-Amount of Heat emitted by the Sun-Meteoric Theory. -Helmholtz's Condensation Theory.-Confusion of Ideas.-Gravitation not the chief Source of the Sun's Heat.-Original Heat.-Source of Original Heat.-Original Heat derived from Motion in Space.--Conclusion as to Date of Glacial Epoch.--False Analogy.-Probable Date of Eocene and Miocene Periods.

Gravitation Theory of the Origin and Source of the Sun's Heat. -There are two forms in which this theory has been presented: the first, the meteoric theory, propounded by Dr. Meyer, of Heilbroun; and the second, the contraction theory, advocated by Helmholtz.

It is found that 83-4 foot-pounds of heat per second are incident upon a square foot of the earth's surface exposed to the perpendicular rays of the sun. The amount radiated from a square foot of the sun's surface is to that incident on a square foot of the earth's surface as the square of the sun's distance to the square of his radius, or as 46,400 to 1. Consequently 3,869,000 foot-pounds of heat are radiated off every square foot of the sun's surface per second- -an amount equal to about 7,000 horse power. The total amount radiated from the whole surface of the sun per annum is 8,340 x 1030 foot-pounds. To maintain the present rate of radiation, it would require the combustion of about 1,500 lbs. of coal per hour on every square foot of the sun's surface; and were the sun composed of that material, it would be all consumed in less than 5,000 years. The opinion that the sun's heat is maintained by combustion cannot be entertained for a single moment. A pound of coal falling into the sun from an infinite distance would produce by

its concussion more than 6,000 times the amount of heat that would be generated by its combustion.

It is well known that the velocity with which a body falling from an infinite distance would reach the sun would be equal to that which would be generated by a constant force equal to the weight of the body at the sun's surface operating through a space equal to the sun's radius. One pound would at the sun's surface weigh about 28 pounds. Taking the sun's radius at 441,000 miles,* the energy of a pound of matter falling into the sun from infinite space would equal that of a 28-pound weight descending upon the earth from an elevation of 441,000 miles, supposing the force of gravity to be as great at that elevation as it is at the earth's surface. upwards of 65,000,000,000 foot-pounds. A better idea of this enormous amount of energy exerted by a one-pound weight falling into the sun will be conveyed by stating that it would be sufficient to raise 1,000 tons to a height of 5 miles. It would project the Warrior, fully equipped with guns, stores, and ammunition, over the top of Ben Nevis.

It would amount to

Gravitation is now generally admitted to be the only conceivable source of the sun's heat. But if we attribute the energy of the sun to gravitation as a source, we assign it to a cause the value of which can be accurately determined. Prodigious as is the energy of a single pound of matter falling into the sun, nevertheless a range of mountains, consisting of 176 cubic miles of solid rock, falling into the sun, would maintain his heat for only a single second. A mass equal to that of the earth would maintain the heat for only 93 years, and a mass equal to that of the sun itself falling into the sun would afford but 33,000,000 years' sun-heat.

It is quite possible, however, that a meteor may reach the sun with a velocity far greater than that which it could acquire by gravitation; for it might have been moving in a direct line towards the sun with an original velocity before coming under

I have taken for the volume and mass of the sun the values given in Professor Sir William Thomson's memoir, Phil. Mag., vol. viii. (1854)

the sensible influence of the sun's attraction. In this case a greater amount of heat would be generated by the meteor than would have resulted from its merely falling into the sun under the influence of gravitation. But then meteors of this sort must be of rare occurrence. The meteoric theory of the sun's heat has now been pretty generally abandoned for the contraction theory advanced by Helmholtz.

Suppose, with Helmholtz, that the sun originally existed as a nebulous mass, filling the entire space presently occupied by the solar system and extending into space indefinitely beyond the outermost planet. The total amount of work in foot-pounds performed by gravitation in the condensation of this mass to an orb of the sun's present size can be found by means of the following formula given by Helmholtz,*

Work of condensation = 3 -2M2

5 Rm

M is the mass of the sun, m the mass of the earth, R the sun's radius, and the earth's radius. Taking M = 4230 × 1027 lbs., m = 11,920 x 1021 lbs., R = 2,328,500,000 feet, and r = 20,889,272 feet; we have then for the total amount of work performed by gravitation in foot-pounds,

The amount of heat thus produced by gravitation would suffice for nearly 20,237,500 years.

These calculations are based upon the assumption that the density of the sun is uniform throughout. But it is highly probable that the sun's density increases towards the centre, in which case the amount of work performed by gravitation would be somewhat more than the above.

Some confusion has arisen in reference to this subject by the introduction of the question of the amount of the sun's specifio heat. If we simply consider the sun as an incandescent body Phil. Mag., § 4, vol. xi., p. 516 (1856).

in the process of cooling, the question of the amount of the sun's specific heat is of the utmost importance; because the absolute amount of heat which the sun is capable of giving out depends wholly upon his temperature and specific heat. In this case three things only are required: (1), the sun's mass; (2), temperature of the mass; (3), specific heat of the mass. But if we are considering what is the absolute amount of heat which could have been given out by the sun on the hypothesis that gravitation, either according to the meteoric theory suggested by Meyer or according to the contraction theory advocated by Helmholtz, is the only source of his heat, then we have nothing whatever to do with any inquiries regarding the specific heat of the sun. This is evident because the absolute amount of work which gravitation can perform in the pulling of the particles of the sun's mass together, is wholly independent of the specific heat of those particles. Consequently, the amount of energy in the form of heat thus imparted to the particles by gravity must also be wholly independent of specific heat. That is to say, the amount of heat imparted to a particle will be the same whatever may its specific heat.

be

Even supposing we limit the geological history of our globe to 100 millions of years, it is nevertheless evident that gravitation will not account for the supply of the sun's heat during so long a period. There must be some other source of much more importance than gravitation. What other source of energy greater than that of gravitation can there be? It is singular that the opinion should have become so common even among physicists, that there is no other conceivable source than gravitation from which a greater amount of heat could have been derived.

The Origin and Chief Source of the Sun's Heat.-According to the foregoing theories regarding the source of the sun's heat, it is assumed that the matter composing the sun, when it existed in space as a nebulous mass, was not originally possessed of temperature, but that the temperature was given to it

as the mass became condensed under the force of gravitation. It is supposed that the heat given out was simply the heat of condensation. But it is quite conceivable that the nebulous mass might have been possessed of an original store of heat previous to condensation.

It is quite possible that the very reason why it existed in such a rarefied or gaseous condition was its excessive temperature, and that condensation only began to take place when the mass began to cool down. It seems far more probable that this should have been the case than that the mass existed in so rarefied a condition without temperature. For why should the particles have existed in this separated form when devoid of the repulsive energy of heat, seeing that in virtue of gravitation they had such a tendency to approach to one another? But if the mass was originally in a heated condition, then in condensing it would have to part not only with the heat generated in condensing, but also with the heat which it originally possessed, a quantity which would no doubt much exceed that produced by condensation. To illustrate this principle, let us suppose a pound of air, for example, to be placed in a cylinder and heat applied to it. If the piston be so fixed that it cannot move, 2345 foot-pounds of heat will raise the temperature of the air 1° C. But if the piston be allowed to rise as the heat is applied, then it will require 330-2 foot-pounds of heat to raise the temperature 1° C. It requires 957 foot-pounds more heat in the latter case than in the former. The same amount of energy, viz., 234-5 foot-pounds, in both cases goes to produce temperature; but in the latter case, where the piston is allowed to move, 957 foot-pounds of additional heat are consumed in the mechanical work of raising the piston. Suppose, now, that the air is allowed to cool under the same conditions: in the one case 234-5 foot-pounds of heat will be given out while the temperature of the air sinks 1o C.; in the other case, where the piston is allowed to descend, 330-2 foot-pounds will be given out while the temperature sinks 1° C. In the former case, the air in cooling has simply to part with the energy which it pos