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 Heilbronn; 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 × 10^{30} 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,[201] 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. It would amount to 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 5½ miles. It would project the _Warrior_, fully equipped with guns, stores, and ammunition, over the top of Ben Nevis.

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 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,[202]

3 _r_^{2}M^{2} Work of condensation = — × ———————————— × _g_ 5 R_m_

M is the mass of the sun, _m_ the mass of the earth, R the sun’s radius, and _r_ the earth’s radius. Taking M = 4230 × 10^{27} lbs., _m_ = 11,920 × 10^{21} 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,

3 (20,889,272·5)^2 × (4230 × 10^{27})^2 Work = — × ————————————————————————————————————— 5 2,328,500,000 × 11,920 × 10^{21}

= 168,790 × 10^{36} 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 specific heat. If we simply consider the sun as an incandescent body 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 be its specific heat.

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, 234·5 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 95·7 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, 95·7 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 1° 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 possesses in the form of temperature; but in the latter case it has, in addition to this, to part with the energy bestowed upon its molecules by the descending piston. While the temperature of the gas is sinking 1°, 95·7 foot-pounds of energy in the form of heat are being imparted to it by the descending piston; and these have to be got rid of before the temperature is lowered by 1°. Consequently 234·5 foot-pounds of the heat given out previously existed in the air under the form of temperature, and the remaining 95·7 foot-pounds given out were imparted to the air by the descending piston while the gas was losing its temperature. 234·5 foot-pounds represent the energy or heat which the air previously possessed, and 95·7 the energy or heat of condensation.

In the case of the cooling of the sun from a nebulous mass, there would of course be no external force or pressure exerted on the mass analogous to that of the piston on the air; but there would be, what is equivalent to the same, the gravitation of the particles to each other. There would be the pressure of the whole mass towards the centre of convergence. In the case of air, and all perfect gases cooling under pressure, about 234 foot-pounds of the original heat possessed by the gas are given out while 95 foot-pounds are being generated by condensation. We have, however, no reason whatever to believe that in the case of the cooling of the sun the same proportions would hold true. The proportion of original heat possessed by the mass of the sun to that produced by condensation may have been much greater than 234 to 95, or it may have been much less. In the absence of all knowledge on this point, we may in the meantime assume that to be the proportion. The total quantity of heat given out by the sun resulting from the condensation of his mass, on the supposition that the density of the sun is uniform throughout, we have seen to be equal to 20,237,500 years’ sun-heat. Then the quantity of heat given out, which previously existed in the mass as original temperature, must have been 49,850,000 years’ heat, making in all 70,087,500 years’ heat as the total amount.

The above quantity represents, of course, the total amount of heat given out by the mass since it began to condense. But the geological history of our globe must date its beginning at a period posterior to that. For at that time the mass would probably occupy a much greater amount of space than is presently possessed by the entire solar system; and consequently, before it had cooled down to within the limits of the earth’s present orbit, our earth could not have had an existence as a separate planet. Previously to that time it must have existed as a portion of the sun’s fiery mass. If we assume that it existed as a globe previously to that, and came in from space after the condensation of the sun, then it is difficult to conceive how its orbit should be so nearly circular as it is at present.

Let us assume that by the time that the mass of the sun had condensed to within the space encircled by the orbit of the planet Mercury (that is, to a sphere having, say, a radius of 18,000,000 miles) the earth’s crust began to form; and let this be the time when the geological history of our globe dates its commencement. The total amount of heat generated by the condensation of the sun’s mass from a sphere of this size to its present volume would equal 19,740,000 years’ sun-heat. The amount of original heat given out during that time would equal 48,625,000 years’ sun-heat,—thus giving a total of 68,365,000 years’ sun-heat enjoyed by our globe since that period. The total quantity may possibly, of course, be considerably more than that, owing to the fact that the sun’s density may increase greatly towards his centre. But we should require to make extravagant assumptions regarding the interior density of the sun and the proportion of original heat to that produced by condensation before we could manage to account for anything like the period that geological phenomena are supposed by some to demand.

The question now arises, by what conceivable means could the mass of the sun have become possessed of such a prodigious amount of energy in the form of heat previous to condensation? What power could have communicated to the mass 50,000,000 years’ heat before condensation began to take place?

_The Sun’s Energy may have originally been derived from Motion in Space._—There is nothing at all absurd or improbable in the supposition that such an amount of energy might have been communicated to the mass. The Dynamical Theory of Heat affords an easy explanation of at least _how_ such an amount of energy _may_ have been communicated. Two bodies, each one-half the mass of the sun, moving directly towards each other with a velocity of 476 miles per second, would by their concussion generate in a _single moment_ the 50,000,000 years’ heat. For two bodies of that mass moving with a velocity of 476 miles per second would possess 4149 × 10^{38} foot-pounds of energy in the form of _vis viva_; and this, converted into heat by the stoppage of their motion, would give an amount of heat which would cover the present rate of the sun’s radiation, for a period of 50,000,000 years.

Why may not the sun have been composed of two such bodies? And why may not the original store of heat possessed by him have all been derived from the concussion of these two bodies? Two such bodies coming into collision with that velocity would be dissipated into vapour by such an inconceivable amount of heat as would thus be generated; and when they condensed on cooling, they would form one spherical mass like the sun. It is perfectly true that two such bodies could never attain the required amount of velocity by their mutual gravitation towards each other. But there is no necessity whatever for supposing that their velocities were derived from their mutual attraction alone. They might have been approaching towards each other with the required velocity wholly independent of gravitation.

We know nothing whatever regarding the absolute motion of bodies in space. And beyond the limited sphere of our observation, we know nothing even of their relative motions. There may be bodies moving in relation to our system with inconceivable velocity. For anything that we know to the contrary, were one of these bodies to strike our earth, the shock might be sufficient to generate an amount of heat that would dissipate the earth into vapour, though the striking body might not be heavier than a cannon-ball. There is, however, nothing very extraordinary in the velocity which we have found would be required in the two supposed bodies to generate the 50,000,000 years’ heat. A comet, having an orbit extending to the path of the planet Neptune, approaching so near the sun as to almost graze his surface in passing, would have a velocity of about 390 miles per second, which is within 86 miles of the required velocity.

But in the original heating and expansion of the sun into a gaseous mass, an amount of work must have been performed against gravitation equal to that which has been performed by gravitation during his cooling and condensation, a quantity which we have found amounts to about 20,000,000 years’ heat. The total amount of energy originally communicated by the concussion must have been equal to 70,000,000 years’ sun-heat. A velocity of 563 miles per second would give this amount. It must be borne in mind, however, that the 563 miles per second is the velocity at the moment of collision; about one-half of this velocity would be derived from the mutual attraction of the two bodies in their approach to each other. Suppose each body to be equal in volume to the sun, and of course one-half the density, the amount of velocity which they would acquire by their mutual attraction would be 274 miles per second, consequently we have to assume an original or projected velocity of only 289 miles per second.

If we admit that gravitation is not sufficient to account for the amount of heat given out by the sun during the geological history of our globe, we are compelled to assume that the mass of which the sun is composed existed prior to condensation in a heated condition; and if so, we are further obliged to admit that the mass must have received its heat from some source or other. And as the dissipation of heat into space must have been going on, in all probability, as rapidly before as after condensation took place, we are further obliged to conclude that the heat must have been communicated to the mass immediately before condensation began, for the moment the mass began to lose its heat condensation would ensue. If we confine our speculations to causes and agencies known to exist, the cause which has been assigned appears to be the only conceivable one that will account for the production of such an enormous amount of heat.

The general conclusion to which we are therefore led from physical considerations regarding the age of the sun’s heat is, that the entire geological history of our globe must be comprised within less than 100 millions of years, and that consequently the commencement of the glacial epoch cannot date much farther back than 240,000 years.

The facts of geology, more especially those in connection with denudation, seem to geologists to require a period of much longer duration than 100 millions of years, and it is this which has so long prevented them accepting the conclusions of physical science in regard to the age of our globe. But the method of measuring subaërial denudation already detailed seems to me to show convincingly that the geological data, when properly interpreted, are in perfect accord with the deductions of physical science. Perhaps there are now few who have fairly considered the question who will refuse to admit that 100 millions of years are amply sufficient to comprise the whole geological history of our globe.

_A false Analogy supposed to exist between Astronomy and Geology._—Perhaps one of the things which has tended to mislead on this point is a false analogy which is supposed to subsist between astronomy and geology, viz., that geology deals with unlimited _time_, as astronomy deals with unlimited _space_. A little consideration, however, will show that there is not much analogy between the two cases.

Astronomy deals with the countless worlds which lie spread out in the boundless infinity of space; but geology deals with only one world. No doubt reason and analogy both favour the idea that the age of the material universe, like its magnitude, is immeasurable; we have no reason, however, to conclude that it is eternal, any more than we have to infer that it is infinite. But when we compare the age of the material universe with its magnitude, we must not take the age of one of its members (say, our globe) and compare it with the size of the universe. Neither must we compare the age of all the presently existing systems of worlds with the magnitude of the universe; but we must compare the past history of the universe as it stretches back into the immensity of bygone _time_, with the presently existing universe as it stretches out on all sides into limitless _space_. For worlds precede worlds in time as worlds lie beyond worlds in space. Each world, each individual, each atom is evidently working out a final purpose, according to a plan prearranged and predetermined by the Divine Mind from all eternity. And each world, like each individual, when it serves the end for which it was called into existence, disappears to make room for others. This is the grand conception of the universe which naturally impresses itself on every thoughtful mind that has not got into confusion about those things called in science the Laws of Nature.[203]

But the geologist does not pass back from world to world as they stand related to each other in the order of _succession in time_, as the astronomer passes from world to world as they stand related to each other in the order of _coexistence in space_. The researches of the geologist, moreover, are not only confined to one world, but it is only a portion of the history of that one world that can come under his observation. The oldest of existing formations, so far as is yet known, the Laurentian Gneiss, is made up of the waste of previously existing rocks, and it, again, has probably been derived from the degradation of rocks belonging to some still older period. Regarding what succeeds these old Laurentian rocks geology tells us much; but of the formations that preceded, we know nothing whatever. For anything that geology shows to the contrary, the time which may have elapsed from the solidifying of the earth’s crust to the deposition of the Laurentian strata—an absolute blank—may have been as great as the time that has since intervened.

_Probable Date of the Eocene and Miocene Periods._—If we take into consideration the limit which physical science assigns to the age of our globe, and the rapid rate at which, as we have seen, denudation takes place, it becomes evident that the enormous period of 3 millions of years comprehended in the foregoing tables must stretch far back into the Tertiary age. Supposing that the mean rate of denudation during that period was not greater than the present rate of denudation, still we should have no less than 500 feet of rock worn off the face of the country and carried into the sea during these 3 millions of years. This fact shows how totally different the appearance and configuration of the country in all probability was at the commencement of this period from what it is at the present day. If it be correct that the glacial epoch resulted from the causes which we have already discussed, those tables ought to aid us in our endeavour to ascertain _how_ much of the Tertiary period may be comprehended within these 3 millions of years.

We have already seen (Chapter XVIII.) that there is evidence of a glacial condition of climate at two different periods during the Tertiary age, namely, about the middle of the Miocene and Eocene periods respectively. As has already been shown, the more severe a glacial epoch is, the more marked ought to be the character of its warm inter-glacial periods; the greater the extension of the ice during the cold periods of a glacial epoch the further should that ice disappear in arctic regions during the corresponding warm periods. Thus the severity of a glacial epoch may in this case be indirectly inferred from the character of the warm periods and the extent to which the ice may have disappeared from arctic regions. Judged by this test, we have every reason to believe that the Miocene glacial epoch was one of extreme severity.

The Eocene conglomerate, devoid of all organic remains, and containing numerous enormous ice-transported blocks, is, as we have seen, immediately associated with nummulitic strata charged with fossils characteristic of a warm climate. Referring to this Sir Charles Lyell says, “To imagine icebergs carrying such huge fragments of stone in so southern a latitude, and at a period immediately preceded and followed by the signs of a warm climate, is one of the most perplexing enigmas which the geologist has yet been called upon to solve.”[204]

It is perfectly true that, according to the generally received theories of the cause of a glacial climate the whole is a perplexing enigma, but if we adopt the Secular theory of change of climate, every difficulty disappears. According to this theory the very fact of the conglomerate being formed at a period immediately preceded and succeeded by warm conditions of climate, is of itself strong presumptive evidence of the conglomerate being a glacial formation. But this is not all, the very highness of the temperature of the preceding and succeeding periods bears testimony to the severity of the intervening glacial period. Despite the deficiency of direct evidence regarding the character of the Miocene and Eocene glacial periods, we are not warranted, for reasons which have been stated in Chapter XVII., to conclude that these periods were less severe than the one which happened in Quaternary times. Judging from indirect evidence, we have some grounds for concluding that the Miocene glacial epoch at least was even more severe and protracted than our recent glacial epoch.

By referring to Table I., or the accompanying diagram, it will be seen that prior to the period which I have assigned as that of the glacial epoch, there are two periods when the eccentricity almost attained its superior limit. The first period occurred 2,500,000 years ago, when it reached 0·0721, and the second period 850,000 years ago, when it attained a still higher value, viz., 0·0747, being within 0·0028 of the superior limit. To the first of these periods I am disposed to assign the glacial epoch of Eocene times, and to the second that of the Miocene age. With the view of determining the character of these periods Tables II. and III. have been computed. They give the eccentricity and longitude of perihelion at intervals of 10,000 years. It will be seen from Table II. that the Eocene period extends from about 2,620,000 to about 2,460,000 years ago; and from Table III. it will be gathered that the Miocene period lasted from about 980,000 to about 720,000 years ago.

In order to find whether the eccentricity attained a higher value about 850,000 years ago than 0·0747, I computed the values for one or two periods immediately before and after that period, and satisfied myself that the value stated was indeed the highest, as will be seen from the subjoined table:—

851,000 0·07454 850,000 0·074664 849,500 0·07466 849,000 0·07466

How totally different must have been the condition of the earth’s climate at that period from what it is at present! Taking the mean distance of the sun to be 91,400,000 miles, his present distance at midwinter is 89,864,480 miles; but at the period in question, when the winter solstice was in perihelion, his distance at midwinter would be no less than 98,224,289 miles. But this is not all; our winters are at present shorter than our summers by 7·8 days, but at that period they would be longer than the summers by 34·7 days.

At present the difference between the perihelion and aphelion distance of the sun amounts to only 3,069,580 miles, but at the period under consideration it would amount to no less than 13,648,579 miles!