Part 7
If we paused on the words with which our last chapter closed, the reader might perhaps so far gather an impression that the whole all-important subject of the solar energy was involved in mystery and doubt. But if it be indeed a mystery when considered in its essence, so are all things; while regarded separately in any one of its terrestrial effects of magnetic or chemical action, or of light or heat, it may seem less so. Since there is not room to consider all these aspects, let us choose the last, and look at this energy in its familiar form of the _heat_ by which we live.
We, the human race, are warming ourselves at this great fire which called our bodies into being, and when it goes out we shall go too. What is it? How long has it been? How long will it last? How shall we use it?
To look across the space of over ninety million miles, and to try to learn from that distance the nature of the solar heat, and how it is kept up, seemed to the astronomers of the last century a hopeless task. The difficulty was avoided rather than met by the doctrine that the sun was pure fire, and shone because “it was its nature to.” In the Middle Ages such an idea was universal; and along with it, and as a logical sequence of it, the belief was long prevalent that it was possible to make another such flame here, in the form of a lamp which should burn forever and radiate light endlessly without exhaustion. With the philosopher’s stone, which was to transmute lead into gold, this perpetual lamp formed a prime object of research for the alchemist and student of magic.
We recall the use which Scott has made of the belief in this product of “gramarye” in the “Lay of the Last Minstrel,” where it is sought to open the grave of the great wizard in Melrose Abbey. It is midnight when the stone which covers it is heaved away, and Michael’s undying lamp, buried with him long ago, shines out from the open tomb and illuminates the darkness of the chancel.
“I would you had been there to see The light break forth so gloriously; That lamp shall burn unquenchably Until the eternal doom shall be,”
says the poet. Now we are at liberty to enjoy the fiction as a fiction; but if we admit that the art which could make such a lamp would indeed be a black art, which did not work under Nature’s laws, but against them, then we ought to see that as the whole conception is derived from the early notion of a miraculous constitution of the sun, the idea of an eternal self-sustained sun is no more permitted to us than that of an eternal self-sustained lamp. We must look for the cause of the sun’s heat in Nature’s laws, and we know those laws chiefly by what we see here.
Before examining the source of the sun’s heat, let us look a little more into its amount. To find the exact amount of heat which it sends out is a very difficult problem, especially if we are to use all the refinements of the latest methods in determining it. The underlying principle, however, is embodied in an old method, which gives, it is true, rather crude results, but by so simple a treatment that the reader can follow it readily, especially if unembarrassed with details, in which most of the actual trouble lies. We must warn him in advance that he is going to be confronted with a kind of enormous sum in multiplication, for whose general accuracy he may, however, trust to us if he pleases. We have not attempted exact accuracy, because it is more convenient for him that we should deal with round numbers.
The apparatus which we shall need for the attack of this great problem is surprisingly simple, and moderate in size. Let us begin by finding how much sun-heat falls in a small known area. To do this we take a flat, shallow vessel, which is to be filled with water. The amount it contains is usually a hundred cubic centimetres (a centimetre being nearly four-tenths of an inch), so that if we imagine a tiny cubical box about as large as a backgammon die, or, more exactly, having each side just the size of this (Fig. 53), to be filled and emptied into the vessel one hundred times, we shall have a precise idea of its limited capacity. Into this vessel we dip a thermometer, so as to read the temperature of the water, seal all up so that the water shall not run out, and expose it so that the heat at noon falls perpendicularly on it. The apparatus is shown in Fig. 54, attached to a tree. The stem of the instrument holds the thermometer, which is upside down, its bulb being in the water-vessel. Now, all the sun’s rays do not reach this vessel, for some are absorbed by our atmosphere; and all the heat which falls on it does not stay there, as the water loses part of it by the contact of the air with the box outside, and in other ways. When allowance is made for these losses, we find that the sun’s heat, if all retained, would have raised the temperature of the few drops of water which would fill a box the size of our little cube (according to these latest observations) nearly three degrees of the centigrade thermometer in one minute,--a most insignificant result, apparently, as a measure of what we have been told is the almost infinite heat of the sun! But if we think so, we are forgetting the power of numbers, of which we are about to have an illustration as striking in its way as that which Archimedes once gave with the grains of sand.
There is a treatise of his extant, in which he remarks (I cite from memory) that as some people believe it possible for numbers to express a quantity as great as that of the grains of sand upon the sea-shore, while others deny this, he will show that they can express one even larger. To prove this beyond dispute, he begins by taking a small seed, beside which he ranges single grains of sand in a line, till he can give the number of these latter which equal its length. Next he ranges seeds beside each other till their number makes up the length of a span; then he counts the spans in a stadium, and the stadia in the whole world as known to the ancients, at each step expressing his results in a number certainly _greater_ than the number of sand-grains which the seed, or the span, or the stadium, or finally the whole world, is thus successively shown to contain. He has then already got a number before his reader’s eyes demonstrably larger than that of all the grains of sand on the sea-shore; yet he does not stop, but steps off the earth into space, to calculate and express a number _greater_ than that of all the grains of sand which would fill a sphere embracing the earth and the sun!
We are going to use our little unit of heat in the same way, for (to calculate in round figures and in English measure) we find that we can set over nine hundred of these small cubes side by side in a square foot, and, as there are 28,000,000 feet in a square mile, that the latter would contain 25,000,000,000 of the cubes, placed side by side, touching each other, like a mosaic pavement. We find also, by weighing our little cup, that we should need to fill and empty it almost exactly a million times to exhaust a tank containing a ton of water. The sun-heat falling on one square mile corresponds, then, to over seven hundred and fifty tons of water raised _every minute_ from the freezing-point to boiling, which already is becoming a respectable amount!
But there are 49,000,000 square miles in the cross-section of the earth exposed to the sun’s rays, which it would therefore need 1,225,000,000,000,000,000 of our little dies to cover one deep; and therefore in each _minute_ the sun’s heat falling on the earth would raise to boiling 37,000,000,000 tons of water.
We may express this in other ways, as by the quantity of ice it would melt; and as the heat required to melt a given weight of ice is 79/100 of that required to bring as much water from the freezing to the boiling point, and as the whole surface of the earth, including the night side, is four times the cross-section exposed to the sun, we find, by taking 526,000 minutes to a year, that the sun’s rays would melt in the year a coating of ice over the whole earth more than one hundred and sixty feet thick.
We have ascended already from our small starting-point to numbers which express the heat that falls upon the whole planet, and enable us to deal, if we wish, with questions relating to the glacial epochs and other changes in its history. We have done this by referring at each step to the little cube which we have carried along with us, and which is the foundation of all the rest; and we now see why such exactness in the first determination is needed, since any error is multiplied by enormous numbers. But now we too are going to step off the earth and to deal with numbers which we can still express in the same way if we choose, but which grow so large thus stated that we will seek some greater term of comparison for them. We have just seen the almost incomprehensible amount of heat which the sun must send the earth in order to warm its oceans and make green its continents; but how little this is to what passes us by! The earth as it moves on in its annual path continually comes into new regions, where it finds the same amount of heat already pouring forth; and this same amount still continues to fall into the empty space we have just quitted, where there is no one left to note it, and where it goes on in what seems to us utter waste. If, then, the whole annual orbit were set close with globes like ours, and strung with worlds like beads upon a ring, each would receive the same enormous amount the earth does now. But this is not all; for not only along the orbit, but above and below it, the sun sends its heat in seemingly incredible wastefulness, the final amount being expressible in the number of _worlds_ like ours that it could warm like ours, which is 2,200,000,000.
We have possibly given a surfeit of such numbers, but we cannot escape or altogether avoid them when dealing with this stupendous outflow of the solar heat. They are too great, perhaps, to convey a clear idea to the mind, but let us before leaving them try to give an illustration of their significance.
Let us suppose that we could sweep up from the earth all the ice and snow on its surface, and, gathering in the accumulations which lie on its Arctic and Antarctic poles, commence building with it a tower greater than that of Babel, fifteen miles in diameter, and so high as to exhaust our store. Imagine that it could be preserved untouched by the sun’s rays, while we built on with the accumulations of successive winters, until it stretched out 240,000 miles into space, and formed an ice-bridge to the moon, and that then we concentrated on it the sun’s whole radiation, neither more nor less than that which goes on every moment. In _one_ second the whole would be gone, melted, boiled, and dissipated in vapor. And this is the rate at which the solar heat is being (to human apprehension) _wasted_!
Nature, we are told, always accomplishes her purpose with the least possible expenditure of energy. Is her purpose here, then, something quite independent of man’s comfort and happiness? Of the whole solar heat, we have just seen that less than 1/2,000,000,--less, that is, than the one twenty-thousandth part of one per cent,--is made useful to us. “But may there not be other planets on which intelligent life exists, and where this heat, which passes us by, serves other beings than ourselves?” There _may_ be; but if we could suppose all the other planets of the solar system to be inhabited, it would help the matter very little; for the whole together intercept so little of the great sum, that all of it which Nature bestows on man is still as nothing to what she bestows on some end--if end there be--which is to us as yet inscrutable.
How is this heat maintained? Not by the miracle of a perpetual self-sustained flame, we may be sure. But, then, by what fuel is such a fire fed? There can be no question of simple burning, like that of coal in the grate, for there is no source of supply adequate to the demand. The State of Pennsylvania, for instance, is underlaid by one of the richest coal-fields of the world, capable of supplying the consumption of the whole country at its present rate for more than a thousand years to come. If the source of the solar heat (whatever that is) were withdrawn, and we were enabled to carry this coal there, and shoot it into the solar furnace fast enough to keep up the known heat-supply, so that the solar radiation would go on at just its actual rate, the time which this coal would last is easily calculable. It would not last days or hours, but the whole of these coal-beds would demonstrably be used up in rather less than one one-thousandth of a second! We find by a similar calculation that if the sun were itself one solid block of coal, it would have burned out to the last cinder in less time than man has certainly been on the earth. But during historic times there has as surely been no noticeable diminution of the sun’s heat, for the olive and the vine grow just as they did three thousand years ago, and the hypothesis of an actual burning becomes untenable. It has been supposed by some that meteors striking the solar surface might generate heat by their impact, just as a cannon-ball fired against an armor-plate causes a flash of light, and a heat so sudden and intense as to partly melt the ball at the instant of concussion. This is probably a real source of heat-supply so far as it goes, but it cannot go very far; and, indeed, if our whole world should fall upon the solar surface like an immense projectile, gathering speed as it fell, and finally striking (as it would) with the force due to a rate of over three hundred miles a second, the heat developed would supply the sun for but little more than sixty years.[4]
[4] These estimates differ somewhat from those of Helmholtz and Tyndall, as they rest on later measures.
It is not necessary, however, that a body should be moving rapidly to develop heat, for arrested motion always generates it, whether the motion be fast or slow, though in the latter case the mass arrested must be larger to produce the same result. It is in the slow settlement of the sun’s own substance toward its centre, as it contracts in cooling, that we find a sufficient cause for the heat developed.
This explanation is often unsatisfactory to those who have not studied the subject, because the fact that heat is so generated is not made familiar to most of us by observation.
Perhaps the following illustration will make the matter plainer. When we are carried up in a lift, or elevator, we know well enough that heat has been expended under the boiler of some engine to drag us up against the power of gravity. When the elevator is at the top of its course, it is ready to give out in descending just the same amount of power needed to raise it, as we see by its drawing up a nearly equal counterpoise in the descent. It can and must give out in coming down the power that was spent in raising it up; and though there is no practical occasion to do so, a large part of this power could, if we wished, be actually recovered in the form of heat again. In the case of a larger body, such as the pyramid of Ghizeh, which weighs between six and seven million tons, all the furnaces in the world, burning coal under all its engines, would have to supply their heat for a measurable time to lift it a mile high; and then, if it were allowed to come down, whether it tell at once or were made to descend with imperceptible slowness, by the time it touched the earth the same heat would be given out again.
Perhaps the fact that the sun is gaseous rather than solid makes it less easy to realize the enormous weight which is consistent with this vaporous constitution. A cubic mile of hydrogen gas (the lightest substance known) would weigh much more at the sun’s surface than the Great Pyramid does here, and the number of these cubic miles in a stratum one mile deep below its surface is over 2,000,000,000,000! This alone is enough to show that as they settle downward as the solar globe shrinks, here is a _possible_ source of supply for all the heat the sun sends out. More exact calculation shows that it _is_ sufficient, and that a contraction of three hundred feet a year (which in ten thousand years would make a shrinkage hardly visible in the most powerful telescope) would give all the immense outflow of heat which we see.
There is an ultimate limit, however, to the sun’s shrinking, and there must have been some bounds to the heat he can already have thus acquired; for--though the greater the original diameter of his sphere, the greater the gain of heat by shrinking to its present size--if the original diameter be supposed as great as possible, there is still a finite limit to the heat gained.
Suppose, in other words, the sun itself and all the planets ground to powder, and distributed on the surface of a sphere whose radius is infinite, and that this matter (the same in amount as that constituting the present solar system) is allowed to fall together at the centre. The actual shrinkage cannot possibly be greater than in this extreme case; but even in this practically impossible instance, it is easy to calculate that the heat given out would not support the _present_ radiation over eighteen million years, and thus we are enabled to look back over past time, and fix an approximate limit to the age of the sun and earth.
We say “present” rate of radiation, because, so long as the sun is purely gaseous, its temperature rises as it contracts, and the heat is spent faster; so that in early ages before this temperature was as high as it is now, the heat was spent more slowly, and what could have lasted “only” eighteen million years at the present rate might have actually spread over an indefinitely greater time in the past; possibly covering more than all the æons geologists ask for.
If we would look into the future, also, we find that at the present rate we may say that the sun’s heat-supply is enough to last for some such term as four or five million years before it sensibly fails. It is certainly remarkable that by the aid of our science man can look out from this “bank and shoal of time,” where his fleeting existence is spent, not only back on the almost infinite lapse of ages past, but that he can forecast with some sort of assurance what is to happen in an almost infinitely distant future, long after the human race itself will have disappeared from its present home. But so it is, and we may say--with something like awe at the meaning to which science points--that the whole future radiation cannot last so long as ten million years. Its probable life in its present condition is covered by about thirty million years. No reasonable allowance for the fall of meteors or for all other known causes of supply could possibly at the present rate of radiation raise the whole term of its existence to sixty million years.
This is substantially Professor Young’s view, and he adds:--
“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 ... 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 as yet have no conception, by which the energy apparently lost in space may be returned. But the whole course and tendency of Nature, so far as science now makes out, points backward to a beginning and forward to an end. The present order of things seems to be bounded both in the past and in the future by terminal catastrophes which are veiled in clouds as yet inscrutable.”
There is another matter of interest to us as dwellers on this planet, connected not with the amount of the sun’s heat so much as with the degree of its temperature; for it is almost certain that a very little fall in the temperature will cause an immense and wholly disproportionate diminution of the heat-supply. The same principle may be observed in more familiar things. We can, for instance, warm quite a large house by a very small furnace, if we urge this (by a wasteful use of coal) to a dazzling white heat. If we now let the furnace cool to half this white-heat temperature, we shall be sure to find that the heat radiated has not diminished in proportion, but out of all proportion,--has sunk, for instance, not only to one-half what it was (as we might think it would do), but to perhaps a twentieth or even less, so that the furnace which heated the house can no longer warm a single room.
The human race, as we have said, is warming itself at the great solar furnace, which we have just seen contains an internal source for generating heat enough for millions of years to come; but we have also learned that if the sun’s internal circulation were stopped, the surface would cool and shut up the heat inside, where it would do us no good. The _temperature_ of the surface, then, on which the rate of heat-emission depends, concerns us very much; and if we had a thermometer so long that we could dip its bulb into the sun and read the degrees on the stem here, we should find out what observers would very much like to know, and at present are disposed to quarrel about. The difficulty is not in measuring the heat,--for that we have just seen how to do,--but in telling what temperature corresponds to it, since there is no known rule by which to find one from the other. One certain thing is this--that we cannot by any contrivance raise the temperature in the focus of any lens or mirror beyond that of its source (practically we cannot do even so much); we cannot, for instance, by any burning-lens make the image of a candle as hot as the original flame. Whatever a thermometer may read when the candle-heat is concentrated on its bulb by a lens, it would read yet more if the bulb were dipped in the candle-flame itself; and one obvious application of this fact is that though we cannot dip our thermometer in the sun, we know that if we could do so, the temperature would at least be greater than any we get by the largest burning-glass. We need have no fear of making the burning-glass too big; the temperature at its solar focus is _always_ and necessarily lower than that of the sun itself.
For some reason no very great burning-lens or mirror has been constructed for a long time, and we have to go back to the eighteenth century to see what can be done in this way. The annexed figure (Fig. 55) is from a wood-cut of the last century, describing the largest burning-lens then or since constructed in France, whose size and mode of use the drawing clearly shows. All the heat falling on the great lens was concentrated on a smaller one, and the smaller one concentrated it in turn, till at the very focus we are assured that iron, gold, and other metals ran like melted butter. In England, the largest burning-lens on record was made about the same time by an optician named Parker for the English Government, who designed it as a present to be taken by Lord Macartney’s embassy to the Emperor of China. Parker’s lens was three feet in diameter and very massive, being seven inches thick at the centre. In its focus the most refractory substances were fused, and even the diamond was reduced to vapor, so that the temperature of the sun’s surface is at any rate higher than _this_.