Popular Science Monthly/Volume 18/November 1880/The Sun's Heat
By Professor C. A. YOUNG.
OF PRINCETON, N. J.
THERE has been a prevailing idea for many years, founded upon Brewster's fallacious experiments, that thermal, luminous, and chemical rays are fundamentally different, though coexistent in the sunbeams. This is erroneous: it is true, indeed, that rays whose vibrations are too slow to be seen produce powerful heating effects, and that those which are invisible because they are too rapid have a strong influence in determining certain chemical and physical reactions; but it is also true that the visible rays are capable of producing the same effects to a greater or less degree, and there is some reason for thinking that certain animals can see by rays to which the human retina is insensible. There is absolutely no philosophical basis for distinction between the visible and invisible radiations of the sun, except in the one point of vibration-frequency—their pitch, to use the analogy of sound. The expressions thermal, luminous, and chemical rays are apt to be misleading. All the waves of solar radiation are carriers of energy, and when intercepted do work, producing heat, or vision, or chemical action, according to circumstances.
If the amount of solar light is enormous as compared with terrestrial standards, the same thing is still more true of the solar heat, which admits of somewhat more accurate measurement, since we are no longer dependent on a so unsatisfactory unit as the "candle-power," and can substitute thermometers and balances for the human eye.
It is possible to intercept a beam of sunshine of known dimensions, and make it give up its radiant energy to a weighed mass of water or other substance, to measure accurately the rise of temperature produced in a given time, and from these data to calculate the whole amount of heat given off by the sun in a minute or a day.
Pouillet and Sir John Herschel seem to have been the first fairly to grasp the nature of the problem, and to investigate upon the subject in a rational manner.
Herschel's experiments were made in 1838 at the Cape of Good Hope, where he was then engaged in his astronomical work. He proceeded in this way: A small tin vessel, containing about half a pint of water, carefully weighed, was placed on a light wooden support, touching it at only three points. This was put inside of a considerably larger cylinder, also of tinned iron; this outer cylinder having a double cover with a hole in it—the cover large enough to shade the sides of the vessel, and the hole a little less than three inches in diameter. A delicate thermometer was immersed in the water, with a sort of dasher of mica for the purpose of stirring it and keeping the temperature uniform throughout the mass. The apparatus was so placed and adjusted that the whole of the light and heat passing through the hole in the cover would fall upon the surface of the water, the sun at that time (December 31st) being within 12° of the zenith at noon.
This apparatus was placed in the sunshine and allowed to stand for ten minutes, shaded by an umbrella, and the slight rise in the temperature of the water was noted. Then the umbrella was removed and. the solar rays were allowed to fall upon the water for the same length of time, and the much larger rise of temperature was noted; finally, the apparatus was again shaded and the change for ten minutes again observed. The mean between the effects in the first and last ten-minute intervals can be taken as the measure of the influence of other causes besides the sun, and, deducting this from the rise during the ten minutes' insolation, we have the effect of the simple sunshine.
Herschel's figures for his first experiment run as follows:
The mean of the first and third is 0·17°, and this deducted from the second gives 3·73° Fahr. as the rise of temperature produced by a sunbeam three inches in diameter, absorbed by a mass of matter equivalent to 4,638 grains of water. (We do not indicate the minutiae of the process by which the weight of the tin vessel, thermometer, stirrer, etc., are allowed for.) Nothing more is now necessary to enable us to compute just how much heat is received by the earth in a day or a year, except, indeed, the determination of the very troublesome and somewhat uncertain correction for the absorption of heat by the earth's atmosphere; a correction deduced by means of observations made at varying heights of the sun above the horizon.
Herschel preferred to express his results in terms of melting ice, and put it in this way:
The amount of heat received on the earth's surface, with the sun in the zenith, would melt an inch thickness of ice in two hours thirteen minutes, nearly.
Since there is every reason to believe that the sun's radiation is equal in all directions, it follows that, if the sun were surrounded by a great shell of ice, one inch thick and 186,000,000 miles in diameter, its rays would just melt the whole in the same time.
If, now, we suppose this shell to shrink in diameter, retaining, however, the same quantity of ice by increasing its thickness, it would still be melted in the same time. Let the shrinkage continue until the inner surface touches the photosphere, and it would constitute an envelope more than a mile in thickness, through which the solar fire would still thaw out its way in the same two hours and thirteen minutes; at the rate, according to Herschel's determinations, of more than forty feet a minute. Herschel continues that, if this ice were formed into a rod 45·3 miles in diameter, and darted toward the sun with the velocity of light, its advancing point would be melted off as fast as it approached, if by any means the whole of the solar rays could be concentrated upon it. Or, to put it differently, if we could build up a solid column of ice from the earth to the sun, two miles and a quarter in diameter, spanning the inconceivable abyss of ninety-three millions of miles, and if then the sun should concentrate his power upon it, it would dissolve and melt, not in an hour nor a minute, but in a single second; one swing of the pendulum, and it would be water; seven more, and it would be dissipated in vapor.
In formulating this last statement we have, however, employed, not Herschel's figures, but those resulting from later observations, which increase the solar radiation about twenty-five per cent., giving fifty feet, and not forty feet, as the thickness of the ice-crust which the sun would melt off of his own surface in a minute. An easy calculation shows that to produce this amount of heat by combustion would require the hourly burning of a layer of anthracite coal about sixteen feet (five metres) thick over the entire surface of the sun—four fifths of a ton per hour on each square foot of surface—at least eight times as much as the consumption of the most powerful blast-furnace known to art. It is equivalent to a continuous evolution of more than seven thousand horse-power on every square foot of the sun's whole area. As Sir William Thomson has shown, the sun, if it were composed of solid coal and produced its heat by combustion, would burn out in less than six thousand years.
Of this enormous outflow of heat the earth of course intercepts only a small portion, about 2200000. But even this minute fraction is enough to melt yearly at the equator a layer of ice something over one hundred and ten feet thick. If we choose to express it in terms of "power," we find that this is equivalent, for each square foot of surface, to more than sixty tons raised to the height of a mile; and, taking the whole surface of the earth, the average energy received from the sun is over fifty mile-tons yearly; or one horse-power, continuously acting, to every thirty square feet of the earth's surface. Most of this, of course, is expended merely in maintaining the earth's temperature; but a small portion, perhaps 1000 of the whole, as estimated by Helmholtz, is stored away by animals and vegetables, and constitutes an abundant revenue of power for the whole human race.
If we inquire what becomes of that principal portion of the solar heat which misses the planet, and passes off into space, no certain answer can be given.Fig. 1.Remembering, however, that space is full of isolated particles of matter (which we encounter from time to time as shooting-stars), we can see that nearer or more remotely in its course each solar ray is sure to reach a resting-place. Some have attempted to maintain that the sun sends heat only toward its planets; that the action of radiant heat, like that of gravitation, is only between masses. But all scientific investigation so far shows that this is not the case. The energy radiated from a heated globe is found to be alike in all directions, and wholly independent of the bodies which receive it, nor is there the slightest reason to suppose the sun any way different in this respect from every other incandescent mass.
Pouillet's experiments were made about the same time as Herschel's, but with a different apparatus, though based on the same principles. He named his instrument the pyrheliometer, or measurer of solar fire. Fig, 1 represents it. The little snuffbox-like vessel, a b, of silver-plated copper, blackened on the upper surface, contains a weighed quantity of water, and a thermometer is immersed in it, the mercury in its stem being visible at d. The disk e e makes it easy to point the instrument squarely to the sun by directing it so that the shadow of a falls concentrically upon this disk. The button at the lower end is for the purpose of agitating the water in the vessel a a, by simply turning the whole thing on its axis in the collar c c. The instrument is much more convenient than Herschel's apparatus, but hardly as accurate, except under very careful manipulation.
Tyndall has modified it by filling the upper vessel with mercury, which is a better conductor of heat than water.
For relative measurements, as for instance a comparison of the amounts of heat received from the sun at different hours of the day, Crova employs a slightly different instrument, of which Fig. 2, copied from his paper in the "Annales de Chimie" for February, 1880, is a representation.
An exceedingly sensitive alcohol thermometer, shown separately at T, with a large bulb carefully blackened, is inclosed in a double-walled sphere B, nickel-plated on the outside. An opening in the walls of the sphere, carefully aligned with a similar opening in a double screen E, allows a beam of light to fall upon the thermometer-bulb, the beam being about two thirds the diameter of the bulb. Theis constructed with a supplementary reservoir, r, at the lower end, by means of which the end of the indicating column can be made to fall near the middle of the scale at any temperature, the object being to measure only changes of temperature, not absolute temperatures. The bulb and tube are so proportioned that a degree on the scale is nearly half an inch long, thus permitting great accuracy of reading.
In order, however, to determine just how much heat is required to raise the thermometer of this instrument 1°, it is necessary to compare it with one of the standard instruments, by exposing it to the sun at the same time.
This method of procedure, by which we determine the rate at which a sunbeam of given dimensions communicates heat to a measured mass of matter, is known as the dynamic method; it is somewhat inconvenient in requiring considerable time and a number of readings.
There is a different process for deducing the same results, which has been employed by Waterston, Ericsson, Secchi, Violle, and others, and may be called the statical method. It consists essentially in observing how much the sun will raise the temperature of a body, exposed to its rays, above that of the inclosure in which it is placed, this inclosure being kept at a fixed and known temperature by the circulation of water, or some such means.
Instruments based on this principle are called actinometers. Of these probably the most complete in its arrangements is that of Violle, described in his paper upon the mean temperature of the sun's surface, published in the "Annales de Chimie" in 1877. We give a diagram of the instrument (Fig. 3). It consists of two concentric spheres of thin metal; the outer, twenty-three centimetres in diameter, the inner, fifteen centimetres. The outer is polished on the outside, the inner is blackened on the inside. The space between the two spheres is filled with water, which is kept at a uniform temperature, either by mixing snow or ice with it, or else by a current circulated through it by means of the stopcocks tt. A sensitive thermometer, T, has its blackened bulb placed in the center of the inner sphere, the stem reaching outside through a tubulure provided for the purpose. Two opposite openings, shown in the figure, allow a beam of sunlight to pass through the globes. A perforated screen at D limits its diameter so that none of it shall touch the walls of the vessel, though the thermometer-bulb is entirely covered by it. A small screen at M allows the observer to see the shadow of the thermometer-bulb, and so to perceive whether the tube through which the light enters is properly directed. If the apparatus is mounted upon what is called an equatorial stand, like a telescope, and provided with clock-work, the whole labor of observation will consist merely in reading the thermometer. The difference between its temperature and that of the water in the surrounding shell gives the necessary data for calculating the intensity of the solar radiation at the time of reading; since the heat received by the thermometer from the sun and shell together must just equal that radiated back by the thermometer-bulb to the shell, after allowing for the orifices.
Fig. 2.—Crova's Pyrheliometer.
Violle found that at noon, on a fair day, the thermometer of this apparatus generally stood, when exposed to the sun, from 10∙5° to 12∙5° centigrade (i. e., 18∙9° to 22∙5° Fahr.) above the temperature of the shell when the latter was filled with ice-water. If it were filled with boiling water, as in some of his experiments, the difference became about 1° C. less.
The results obtained with instruments of this class of course agree very closely with those reached by the dynamic method.
It need hardly be said that the amount of heat received from the sun in a minute by a given area exposed to its radiation varies widely according to the altitude of the sun and the condition of the air; indeed, the most difficult part of the experimental problem lies in the determination of the corrections to be applied on account of the absorption of the earth's atmosphere. It would take us too far to discuss the formulæ and methods of calculation which have been proposed. They are necessarily very complicated—those, at any, rate which are tolerably accurate in their results—because they have to take into account the meteorological conditions, especially the hygrometric state of the air. Besides this, the absorption varies greatly for radiations of different pitch; so that the violet rays, which are photographically the most active, suffer more than the green and yellow, which are most effective in the growth of plants; and these more than the red; and the red, in their turn, much more than the low-pitched, slowly vibrating waves which, though invisible, are still the chief carriers of energy, and do more to warm and vivify the earth than all the others.
Speaking loosely, it may be estimated that at the sea-level, in fair weather, neither excessively moist nor dry, about thirty per cent, of the solar radiation is absorbed when the sun is at the zenith, and at least seventy-five per cent, at the horizon. Of the rays striking the upper surface of the atmosphere, between forty-five and fifty per cent., therefore, are generally intercepted in the air, even when there are no clouds.
Of course, it does not follow that the heat absorbed in our atmosphere is lost to the earth. Far from it: the air itself becomes warmed and communicates its heat to the earth; and, since the atmosphere intercepts a large proportion of the heat which the earth would radiate into space, if not thus blanketed, the temperature of the earth is kept much higher than it would be if there were no air.
It is now generally customary to express the intensity of the solar radiation in a somewhat different way from that which has been indicated. Instead of stating how much ice would be melted in a minute by a given sunbeam, we give the number of calories received per minute by one square metre exposed perpendicularly to the sun's rays at the upper surface of the atmosphere. This number is called the solar constant, and according to different experimenters ranges from Pouillet's estimate, 17·6, to that of Forbes, who found 28·2. The most reliable recent determinations by Crova and Violle set it at 23·2 and 25·4 respectively. Probably 24 is very near the truth, though there remains a considerable amount of uncertainty, since the results obtained by the same observer on different days, after all possible pains is taken with the corrections, are even more discordant than the numbers given above. A continued series of observations at some very elevated station would improve the data.
Experiments with the thermopile show that the heat radiated by the solar disk varies, like the light, very considerably from the center to the edges. The first observations of this kind were made by Professor Henry, at Princeton, in 1845, and have since been repeated by many others, Secchi and Langley especially. According to Langley, the heat emitted from a point about 20" from the limb is only one half that from the same extent of surface at the center of the disk; the diminution of heat being notably less than that of light, as shown by Vogel's observations. Langley's table runs as follows, the first column giving the distance from the center of the disk, and the second the intensity of radiation shown by the thermopile:
Besides this regular variation of the radiation from center to edge, Secchi in 1852 found, or thought he found, a notable difference between the radiation from the equator of the sun and that from the higher latitude, the difference being at least one sixteenth between the equator and latitude 30°. The northern hemisphere he also found to be a little hotter than the southern. Later investigators (Langley especially) have failed to find any such difference; and on the whole it seems probable that Secchi was mistaken; though this is not certain, as it would be quite unsafe to assert that the actual condition of the sun's surface may not have changed between 1852 and 1876.
In connection with the absorption of the solar atmosphere, Langley has ventured some interesting speculations. After showing that variations in the number and magnitude of sun-spots can not directly produce any sensible effect upon terrestrial temperatures, he calls attention to the fact that even slight changes in the depth and density of the sun's absorbing layer would make a great difference; and he raises the question whether we may not find here the explanation of glacial and carboniferous periods in the earth's history. It is quite certain that, were the envelope removed, the solar radiation would be at least doubled, and perhaps increased in a much higher ratio; while any considerable increase of its thickness would so diminish our heat-supply as to give us perpetual winter.
As yet our means of observation have not sufficed to detect with certainty any variations in the amount of heat emitted by the sun at different times. That there are such variations is almost certain, since the nuclei of sun-spots radiate much less heat as well as light than neighboring regions of the solar surface, and the faculæ more; this has been directly determined with the thermopile. The whole amount of variation in the total heat-supply has, however, proved too small for measurement with our present instruments, and science waits anxiously for apparatus and methods of delicacy adequate to deal with the problem. We are as yet entirely uncertain whether, at the time of a sun-spot maximum, the solar radiation is more or less powerful than ordinary.
There has been a great deal of pretty vigorous discussion as to the temperature of the sun, and that the subject is a difficult one is evident enough from the wide discrepancy between the estimates of the highest authorities. For instance, Secchi originally contended for a temperature of about 18,000,000° Fahr. (though he afterward lowered his estimate to about 250,000); Ericsson puts the figure at 4,000,000
Fig. 3.—Violle's Actinometer.
or 5,000,000; Zöllner, Spoerer, and Lane name temperatures ranging from 50,000° to 100,000° Fahr.; while Pouillet, Vicaire, and Deville have put it as low as between 3,000° and 10,000° Fahr. The intensest artificial heat may perhaps reach 4,000° Fahr.
The difficulty is twofold. In the first place, the sun can not properly be said to have a temperature, any more than the earth's atmosphere can. The temperature of different portions of the solar envelope must vary enormously, increasing fast as we descend below the surface; so that in all probability there may be a difference of thousands of degrees between the temperature at the upper surface of the photosphere and that at the sun's center, or even at the depth of a few thousand miles.
We may, however, partially evade this difficulty by substituting as the object of inquiry the sun's effective temperature: i. e., instead of seeking to ascertain the actual temperature of different parts of the sun's surface, we may inquire what temperature would have to be given to a uniform surface of standard radiating power (a surface covered with lampblack is generally taken as this standard) and of the same size as the sun, in order that it might emit as much heat as the sun actually does. In this way we obtain a perfectly definite object of investigation. But the problem still remains very difficult, and has obtained as yet no entirely satisfactory solution. The difficulty lies in our ignorance as to the laws which connect the temperature of a surface with the amount of heat radiated per second. So long as the temperature of the radiating body does not much exceed that of surrounding space, the heat emitted is very nearly proportional to the excess of temperature. The extremely high values of the solar temperature asserted by Secchi and Ericsson depend upon the assumption of this law (known as Newton's) of proportionality between the heat radiated and the temperature of the radiating mass; a law which direct experiment proves to be untrue as soon as the temperature rises a little. In reality, the amount of heat radiated increases much faster than the temperature.
More than forty years' ago the French physicists Dulong and Petit, by a series of elaborate experiments, deduced an empirical formula, which answered pretty satisfactorily for temperatures up to a dull-red heat. By applying this formula, Pouillet and Vicaire and others arrived at the low solar temperatures assigned by them. It is, however, evidently unsafe to apply a purely empirical formula to circumstances so far outside the range of the observations upon which it was founded, and, in fact, within a few years several experimenters, Rosetti especially, have shown that it needs modification even in the investigation of artificial temperatures, like that of the electric arc. Rosetti, from his observations, has deduced a different law of radiation, and by its application finds 10,000° Cent, or 18,000° Fahr. as the effective temperature of the sun; a result which, all things considered, seems more reasonable and better founded than any of the earlier estimates. He considers that this is also pretty nearly the actual temperature of the upper layers of the photosphere. The radiating power of the photospheric clouds, to be sure, can hardly be as great as that of lampblack, but on the other hand their radiation is supplemented by that of other layers, both above and below.
Besides the data as to the intensity of the solar temperature obtained by calculation from the measured emission of heat, we have also direct evidence of a very impressive sort. When heat is concentrated by a burning-glass, the temperature at the focus can not rise above that of the source of heat, the effect of the lens being simply to move the object at the focus virtually toward the sun; so that, if we neglect the loss of heat by transmission through the glass, the temperature at the focus should be the same as that of a point placed at such a distance from the sun that the solar disk would seem just as large as the lens itself viewed from its own focus.
The most powerful lens yet constructed thus virtually transports an object at its focus to within about 250,000 miles of the sun's surface, and in this focus the most refractory substances—platinum, fireclay, the diamond itself—are either instantly melted or dissipated in vapor. There can be no doubt that, if the sun were to come as near us as the moon, the solid earth would melt like wax.
In 1878 Professor Langley made a careful comparison between the radiation of the sun and that of the molten metal in a Bessemer "converter" when at its greatest heat. By a very ingenious arrangement he brought the solar heat and that from the metal to confront each other upon the faces of a thermopile; and he found that, even neglecting all corrections for the loss of solar heat by transmission through the smoky atmosphere of Pittsburgh, and by the reflections which brought it to his apparatus, the sun's radiation was eighty-seven times as powerful as that from the converter, surface for surface. Had the just corrections been ascertained and applied (a matter, however, of extreme difficulty, and even impossible under the circumstances), the ratio would be increased from eighty-seven to more than one hundred certainly, and perhaps to one hundred and fifty.
As to the temperature of the metal in the converter. Professor Langley considers that it must have been above that of the fusion of platinum, because platinum wire held over the mouth of the converter just before pouring, or in the stream of metal, melts immediately. There may be some question, however, whether the melting of the wire really indicates quite so high a temperature, since fluid iron and its vapor attack platinum in something the same way as mercury and its vapor attack gold and silver. Similar conclusions as to the intensity of the solar temperature follow from investigations by Soret and others, as to the penetrating power of the sun's rays; and from a comparison with artificial sources of heat in respect to the relative proportion of the rays of different wave-lengths in the total radiation. A body of low temperature emits an enormous proportion of slowly vibrating, invisible vibrations, while, as the temperature rises, the shorter waves become proportionally more and more abundant. Thus, in the composition of a body's radiation, we get some clew to its temperature. Hitherto all such tests concur in putting the sun's temperature high above that of any known terrestrial flame.
And now we come to questions like these: How is such a heat maintained? How long has it lasted already—how long will it continue—are there any signs of either increase or diminution?—questions to which, in the present state of science, only somewhat vague and unsatisfactory replies are possible.
As to progressive changes in the amount of the solar heat, it can be said, however, that there is no evidence of anything of the sort since the beginning of authentic records. There have been no such changes in the distribution of plants and animals within the last two thousand years, as must have occurred if there had been within this period any appreciable alteration in the heat received from the sun. So far as can be made out, with few and slight exceptions, the vine and olive grow just where they did in classic days, and the same is true of the cereals and the forest-trees. In the remoter past there have been undoubtedly great changes in the earth's temperature, evidenced by geological records; carboniferous epochs, when the temperature was tropical in almost arctic latitudes; and glacial periods, when our now temperate zones were cased in sheets of solid ice, as northern Greenland is at present. Even as to these changes, however, it is not yet certain whether they are to be traced to variations in the amount of heat emitted by the sun, or to changes in the earth herself or in her orbit. So far as observation goes, we can only say that the outpouring of the solar heat, amazing as it is, appears to have gone on unchanged through all the centuries of human history.
What, then, maintains the fire? It is quite certain, in the first place, that it is not a case of mere combustion. As has been said only a few Images back, it has been shown that even if the sun were made of solid coal, burning in pure oxygen, it could only last about six thousand years—it would have been nearly one third consumed since the beginning of the Christian era. Nor can the source of its heat lie simply in the cooling of its incandescent mass. Huge as it is, its temperature must have fallen more than perceptibly within a thousand years if this were the case.
Two different theories have been proposed, which are probably both true to some extent. One of them finds the chief source of the solar heat in the impact of meteoric matter, the other in the slow contraction of the sun. As to the first, it is quite certain that some of the solar heat is produced in that way; but the question is, whether the supply of meteoric matter can be sufficient to account for any great proportion of the whole. As to the second, on the other hand, there is no question as to the adequacy of the hypothesis to account for the whole supply of solar heat; but there is as yet no direct evidence whatever that the sun is really shrinking.
The basis of the meteoric theory is simply this: If a moving body be stopped, either suddenly or gradually, a quantity of heat is generated, which may be expressed, in calories, by the formula 850' in which m is the mass of the body in kilogrammes, and v its velocity in metres per second: a body weighing 850 kilogrammes and moving one metre per second would, if stopped, develop just one calory of heat—i. e., enough to heat one kilogramme of water from freezing-point to 1° centigrade; if it were moving 500 metres per second (about the speed of a cannon-ball), it would produce 250,000 times as much heat, or enough to raise the temperature of a mass of water equal to itself nearly 300° C. If it were moving, not 500 metres per second, but about 700,000 (approximately the velocity with which a body would fall into the sun from any planetary distance), the heat produced would be 1,400 x 1,400, or nearly 2,000,000 times as great—sufficient to bring a mass of matter many thousand times greater than itself to most vivid incandescence, and immensely more than could be produced by its complete combustion under any conceivable circumstances. With reference to this theory, Sir William Thomson has calculated the amount of heat which would be produced by each of the planets in falling into the sun from its present orbit. The results are as follows, the heat produced being expressed by giving the number of years and days through which it would maintain the sun's present expenditure of energy:
That is, the collapse of all the planets upon the sun would generate sufficient heat to maintain its supply for nearly 46,000 years.
A quantity of matter equal to only about one one hundredth of the mass of the earth, falling annually upon the solar surface, would therefore maintain its radiation indefinitely. Of course, this increase of the sun would cause an acceleration of the motion of all the planets—a shortening of their periods; since, however, the mass of the sun is 330,000 times that of the earth, the yearly addition would be only one thirty-three millionth of the whole, and it would require centuries to make the effect sensible. The only question, then, is whether any such quantity of matter can be supposed to reach the sun. While it is impossible to deny this dogmatically, it on the whole seems improbable, for astronomical reasons. If so large a quantity of matter annually falls upon the solar surface, it is necessary to suppose a vastly greater quantity circulating around the sun, between it and the planet Mercury. The process by which the orbit of a meteoric body is so changed as to make it enter the solar atmosphere is a very slow one; so that only a very small proportion of the whole could be caught in any given year. But, if there were near the sun any considerable quantity of meteoric matter—anything like the mass of the earth, for instance—it ought to produce a very observable effect upon the motions of the planet Mercury—an effect not yet detected.
For this reason astronomers generally, while conceding that a portion, and possibly a considerable fraction, of the solar heat may be accounted for by this hypothesis, are disposed to look further for their explanation of the principal revenue of solar energy. They find it in the probable slow contraction of the sun's diameter, and the gradual liquefaction and solidification of the gaseous mass. The same total amount of heat is produced when a body moves against a resistance which brings it to rest gradually, as if it had fallen through the same distance freely and been suddenly stopped. If, then, the sun does contract, heat is necessarily produced by the process; and that in enormous quantity, since the attracting force at the solar surface is more than twenty-seven times as great as gravity at the surface of the earth, and the contracting mass is so immense.
In this process of contraction, each particle at the surface moves inward by an amount equal to the whole diminution of the solar radius, while a particle below the surface moves less, and under a diminished gravitating force; but every particle in the whole mass of the sun, excepting only that at the exact center of the globe, contributes something to the evolution of heat. To calculate the precise amount of heat developed, it would be necessary to know the law of increase of the sun's density from the surface to the center; but Helmholtz, who first suggested the hypothesis, in 1853, has shown that, under the most unfavorable suppositions, a contraction of about 250 feet a year in the sun's diameter—a mile in twenty-one years—would account for its whole annual heat-emission. This contraction is so slow that it would be quite imperceptible to observation. It would require 9,500 years to reduce the diameter a single second of arc (since 1" equals 450 miles at the sun's distance), and nothing less would be certainly detectable.
Of course, if the contraction is more rapid than this, the mean temperature of the sun must be actually rising notwithstanding the amount of heat it is losing. Observation alone can determine whether this is so or not.
If the sun were wholly gaseous, we could assert positively that it must be growing hotter; for it is a most curious, and at first sight paradoxical, fact, first pointed out by Lane in 1870, that the temperature of a gaseous body continually rises as it contracts from loss of heat. By losing heat it contracts, but the heat generated by the contraction is more than sufficient to keep the temperature from falling. A gaseous mass, losing heat by radiation, must, therefore, at the same time, grow both smaller and hotter, until the density becomes so great that the ordinary laws of gaseous expansion reach their limit, and condensation into the liquid form begins. The sun seems to have arrived at this point, if, indeed, it were ever wholly gaseous, which is questionable. At any rate, so far as we can now make out, the exterior portion—i. e., the photosphere—appears to be a shell of cloudy matter, precipitated from the vapors which make up the principal mass, and the progressive contraction, if it is indeed a fact, must result in a continual thickening of this shell and the increase of the cloud-like portion of the solar mass.
This change from the gaseous to the liquid form must also be accompanied by the liberation of an enormous quantity of heat, sufficient to materially diminish the amount of contraction needed to maintain the solar radiation.
Of course, if this theory of the source of the solar heat is correct, it follows that in time it must come to an end; and, looking backward, we see that there must also have been a beginning: time was when there was no such solar heat as now, and the time must come when it will cease.
We do not know enough about the amount of solid and liquid matter at present in the sun, or of the nature of this matter, to calculate the future duration of the sun with great exactness, though an approximate estimate can be made. The problem is a little complicated, even on the simplest hypothesis of purely gaseous contraction, because, as the sun shrinks, the force of gravity increases, and the amount of contraction necessary to generate a given amount of heat becomes less and less; but this difficulty is easily met by a skillful mathematician. According to Newcomb, if the sun maintains its present radiation, it will have shrunk to half its present diameter in about five millions of years, at the longest. As it must, when reduced to this size, be eight times as dense as now, it can hardly then continue to be mainly gaseous, and its temperature must have begun to fall. Newcomb's conclusion, therefore, is, that it is hardly likely that the sun can continue to give sufficient heat to support life on the earth (such life as we now are acquainted with, at least) for ten millions of years from the present time.
It is possible to compute the past of the solar history upon this hypothesis somewhat more definitely than the future. The present rate of contraction being known, and the law of variation, it becomes a purely mathematical problem to compute the dimensions of the sun at any date in the past, supposing its heat-radiation to have remained unchanged. Indeed, it is not even necessary to know anything more than the present amount of radiation and the mass of the sun, to compute how long the solar fire can have been maintained at its present intensity by the process of condensation. No conclusion of geometry is more certain than that the contraction of the sun, from a diameter even many times larger than that of Neptune's orbit to its present dimensions, if such a contraction has actually taken place, has furnished about eighteen million times as much heat as the sun now supplies in a year; and, therefore, that the sun can not have been emitting heat at the present rate for more than that length of time, if its heat has been generated in this manner. If it could be shown that the sun has been shining as now for a longer time than that, the theory would be refuted; but, if the hypothesis be true, as it probably is in the main, we are inexorably shut up to the conclusion that the total life of the solar system, from its birth to its death, is included in some such space of time as thirty millions of years: no reasonable allowances for the fall of meteoric matter, based on what we are now able to observe, or for the development of heat by liquefaction, solidification, and chemical combination of dissociated vapors, could raise it to sixty millions.
At the same time it is, of course, impossible to assert that there has been no catastrophe in the past—no collision with some wandering star, endued, as Croll has supposed, like some of those we know of now in the heavens, with a velocity far surpassing that to be acquired by a fall, under the sun's attraction, even from infinity—producing a shock which might in a few hours, or moments even, restore the wasted energy of ages. Neither is it wholly safe to assume that there may not be ways of which we yet have no conception, by which the energy apparently lost in space may be returned, and burned-out suns and run-down systems restored; or, if not restored themselves, be made the germs and material of new ones to replace the old.
But the whole course and tendency of things, so far as science now makes out, points backward to a beginning and forward to an end. The present order of things appears to be limited in either direction by terminal catastrophes, which are veiled in clouds as yet impenetrable.