Climatic Changes Part 14

Allied to the preceding hypothesis is Shapley's[113] nebular hypothesis.

At frequent intervals, averaging about once a year during the last thirty years, astronomers have discovered what are known as novae. These are stars which were previously faint or even invisible, but which flash suddenly into brilliancy. Often their light-giving power rises seven or eight magnitudes--a thousand-fold. In addition to the spectacular novae there are numerous irregular variables whose brilliancy changes in every ratio from a few per cent up to several magnitudes. Most of them are located in the vicinity of nebulae, as is also the case with novae. This, as well as other facts, makes it probable that all these stars are "friction variables," as Shapley calls them. Apparently as they pa.s.s through the nebulae they come in contact with its highly diffuse matter and thereby become bright much as the earth would become bright if its atmosphere were filled with millions of almost infinitesimally small meteorites. A star may also lose brilliancy if nebulous matter intervenes between it and the observer. If our sun has been subjected to any of these changes some sort of climatic effect must have been produced.

In a personal communication Shapley amplifies the nebular climatic hypothesis as follows:

Within 700 light years of the sun in many directions (Taurus, Cygnus, Ophiuchus, Scorpio) are great diffuse clouds of nebulosity, some bright, most of them dark. The probability that stars moving in the general region of such clouds will encounter this material is very high, for the clouds fill enormous volumes of s.p.a.ce,--e.g., probably more than a hundred thousand cubic light years in the Orion region, and are presumably composed of rarefied gases or of dust particles. Probably throughout all our part of s.p.a.ce such nebulosity exists (it is all around us, we are sure), but only in certain regions is it dense enough to affect conspicuously the stars involved in it. If a star moving at high velocity should collide with a dense part of such a nebulous cloud, we should probably have a typical nova. If the relative velocity of nebulous material and star were low or moderate, or if the material were rare, we should not expect a conspicuous effect on the star's light.

In the nebulous region of Orion, which is probably of unusually high density, there are about 100 known stars, varying between 20% and 80% of their total light--all of them irregularly--some slowly, some suddenly. Apparently they are "friction variables." Some of the variables suddenly lose 40% of their light as if blanketed by nebulous matter. In the Trifid Nebula there are variables like those of Orion, in Messier 8 also, and probably many of the 100 or so around the Rho Ophiuchi region belong to this kind.

I believe that our sun could not have been a typical nova, at least not since the Archeozoic, that is for perhaps a billion years. I believe we have in geological climates final proof of this, because an increase in the amount of solar radiation by 1000 times as in the typical nova, would certainly punctuate emphatically the life cycle on the earth, even if the cause of the nova would not at the same time eliminate the smaller planets. But the sun may have been one of these miniature novae or friction variables; and I believe it very probable that its wanderings through this part of s.p.a.ce could not long leave its mean temperature unaffected to the amount of a few per cent.

One reason we have not had this proposal insisted upon before is that the data back of it are mostly new--the Orion variables have been only recently discovered and studied, the distribution and content of the dark nebulae are hardly as yet generally known.

This interesting hypothesis cannot be hastily dismissed. If the sun should pa.s.s through a nebula it seems inevitable that there would be at least slight climatic effects and perhaps catastrophic effects through the action of the gaseous matter not only on the sun but on the earth's own atmosphere. As an explanation of the general climatic conditions of the past, however, Shapley points out that the hypothesis has the objection of being vague, and that nebulosity should not be regarded as more than "a possible factor." One of the chief difficulties seems to be the enormously wide distribution of as yet undiscovered nebulous matter which must be a.s.sumed if any large share of the earth's repeated climatic changes is to be ascribed to such matter. If such matter is actually abundant in s.p.a.ce, it is hard to see how any but the nearest stars would be visible. Another objection is that there is no known nebulosity near at hand with which to connect the climatic vicissitudes of the last glacial period. Moreover, the known nebulae are so much less numerous than stars that the chances that the sun will encounter one of them are extremely slight. This, however, is not an objection, for Shapley points out that during geological times the sun can never have varied as much as do the novae, or even as most of the friction variables. Thus the hypothesis stands as one that is worth investigating, but that cannot be finally rejected or accepted until it is made more definite and until more information is available.

Another suggested cause of solar variations is the relatively sudden contraction of the sun such as that which sometimes occurs on the earth when continents are uplifted and mountains upheaved. It seems improbable that this could have occurred in a gaseous body like the sun. Lacking, as it does, any solid crust which resists a change of form, the sun probably shrinks steadily. Hence any climatic effects thus produced must be extremely gradual and must tend steadily in one direction for millions of years.

Still another suggestion is that the tidal action of the stars and other bodies which may chance to approach the sun's path may cause disturbances of the solar atmosphere. The vast kaleidoscope of s.p.a.ce is never quiet. The sun, the stars, and all the other heavenly bodies are moving, often with enormous speed. Hence the effect of gravitation upon the sun must vary constantly and irregularly, as befits the geological requirements. In the case of the planets, however, the tidal effect does not seem competent to produce the movements of the solar atmosphere which appear to be concerned in the inception of sunspots. Moreover, there is only the most remote probability that a star and the sun will approach near enough to one another to produce a p.r.o.nounced gravitational disturbance in the solar atmosphere. For instance, if it be a.s.sumed that changes in Jupiter's tidal effect on the sun are the main factor in regulating the present difference between sunspot maxima and sunspot minima, the chances that a star or some non-luminous body of similar ma.s.s will approach near enough to stimulate solar activity and thereby bring on glaciation are only one in twelve billion years, as will be explained below. This seems to make a gravitational hypothesis impossible.

Another possible cause of solar disturbances is that the stars in their flight through s.p.a.ce may exert an electrical influence which upsets the equilibrium of the solar atmosphere. At first thought this seems even more impossible than a gravitational effect. Electrostatic effects, however, differ greatly from those of tides. They vary as the diameter of a body instead of as its ma.s.s; their differentials also vary inversely as the square of the distance instead of as the cube.

Electrostatic effects also increase as the fourth power of the temperature or at least would do so if they followed the law of black bodies; they are stimulated by the approach of one body to another; and they are c.u.mulative, for if ions arrive from s.p.a.ce they must acc.u.mulate until the body to which they have come begins to discharge them. Hence, on the basis of a.s.sumptions such as those used in the preceding paragraph, the chances of an electrical disturbance of the solar atmosphere sufficient to cause glaciation on the earth may be as high as one in twenty or thirty million years. This seems to put an electrical hypothesis within the bounds of possibility. Further than that we cannot now go. There may be other hypotheses which fit the facts much better, but none seems yet to have been suggested.

In the rest of this chapter the tidal and electrical hypotheses of stellar action on the sun will be taken up in detail. The tidal hypothesis is considered because in discussions of the effect of the planets it has. .h.i.therto held almost the entire field. The electrical hypothesis will be considered because it appears to be the best yet suggested, although it still seems doubtful whether electrical effects can be of appreciable importance over such vast distances as are inevitably involved. The discussion of both hypotheses will necessarily be somewhat technical, and will appeal to the astronomer more than to the layman. It does not form a necessary part of this book, for it has no bearing on our main thesis of the effect of the sun on the earth. It is given here because ultimately the question of changes in solar activity during geological times must be faced.

In the astronomical portion of the following discussion we shall follow Jeans[114] in his admirable attempt at a mathematical a.n.a.lysis of the motions of the universe. Jeans divides the heavenly bodies into five main types. (1) Spiral nebulae, which are thought by some astronomers to be systems like our own in the making, and by others to be independent universes lying at vast distances beyond the limits of our Galactic universe, as it is called from the Galaxy or Milky Way. (2) Nebulae of a smaller type, called planetary. These lie within the Galactic portion of the universe and seem to be early stages of what may some day be stars or solar systems. (3) Binary or multiple stars, which are extraordinarily numerous. In some parts of the heavens they form 50 or even 60 per cent of the stars and in the galaxy as a whole they seem to form "fully one third." (4) Star cl.u.s.ters. These consist of about a hundred groups of stars in each of which the stars move together in the same direction with approximately the same velocity. These, like the spiral nebulae, are thought by some astronomers to lie outside the limits of the galaxy, but this is far from certain. (5) The solar system.

According to Jeans this seems to be unique. It does not fit into the general mathematical theory by which he explains spiral nebulae, planetary nebulae, binary stars, and star cl.u.s.ters. It seems to demand a special explanation, such as is furnished by tidal disruption due to the pa.s.sage of the sun close to another star.

The part of Jeans' work which specially concerns us is his study of the probability that some other star will approach the sun closely enough to have an appreciable gravitative or electrical effect, and thus cause disturbances in the solar atmosphere. Of course both the star and the sun are moving, but to avoid circ.u.mlocution we shall speak of such mutual approaches simply as approaches of the sun. For our present purpose the most fundamental fact may be summed up in a quotation from Jeans in which he says that most stars "show evidence of having experienced considerable disturbance by other systems; there is no reason why our solar system should be expected to have escaped the common fate." Jeans gives a careful calculation from which it is possible to derive some idea of the probability of any given degree of approach of the sun and some other star. Of course all such calculations must be based on certain a.s.sumptions. The a.s.sumptions made by Jeans are such as to make the probability of close approaches as great as possible. For example, he allows only 560 million years for the entire evolution of the sun, whereas some astronomers and geologists would put the figure ten or more times as high. Nevertheless, Jeans' a.s.sumptions at least show the order of magnitude which we may expect on the basis of reasonable astronomical conclusions.

According to the planetary hypothesis of sunspots, the difference in the effect of Jupiter when it is nearest and farthest from the sun is the main factor in starting the sunspot cycle and hence the corresponding terrestrial cycle. The climatic difference between sunspot maxima and minima, as measured by temperature, apparently amounts to at least a twentieth and perhaps a tenth of the difference between the climate of the last glacial epoch and the present. We may suppose, then, that a body which introduced a gravitative or electrical factor twenty times as great as the difference in Jupiter's effect at its maximum and minimum distances from the sun would cause a glacial epoch if the effect lasted long enough. Of course the other planets combine their effects with that of Jupiter, but for the sake of simplicity we will leave the others out of account. The difference between Jupiter's maximum and minimum tidal effect on the sun amounts to 29 per cent of the planet's average effect.

The corresponding difference, according to the electrical hypothesis, is about 19 per cent, for electrostatic action varies as the square of the distance instead of as the cube. Let us a.s.sume that a body exerting four times Jupiter's present tidal effect and placed at the average distance of Jupiter from the sun would disturb the sun's atmosphere twenty times as much as the present difference between sunspot maxima and minima, and thus, perhaps, cause a glacial period on the earth.

On the basis of this a.s.sumption our first problem is to estimate the frequency with which a star, visible or dark, is likely to approach near enough to the sun to produce a _tidal_ effect four times that of Jupiter. The number of visible stars is known or at least well estimated. As to dark stars, which have grown cool, Arrhenius believed that they are a hundred times as numerous as bright stars; few astronomers believe that there are less than three or four times as many. Dr. Shapley of the Harvard Observatory states that a new investigation of the matter suggests that eight or ten is probably a maximum figure. Let us a.s.sume that nine is correct. The average visible star, so far as measured, has a ma.s.s about twice that of the sun, or about 2100 times that of Jupiter. The distances of the stars have been measured in hundreds of cases and thus we can estimate how many stars, both visible and invisible, are on an average contained in a given volume of s.p.a.ce. On this basis Jeans estimates that there is only one chance in thirty billion years that a visible star will approach within 2.8 times the distance of Neptune from the sun, that is, within about eight billion miles. If we include the invisible stars the chances become one in three billion years. In order to produce four times the tidal effect of Jupiter, however, the average star would have to approach within about four billion miles of the sun, and the chances of that are only one in twelve billion years. The disturbing star would be only 40 per cent farther from the sun than Neptune, and would almost pa.s.s within the solar system.

Even though Jeans holds that the frequency of the mutual approach of the sun and a star was probably much greater in the distant past than at present, the figures just given lend little support to the tidal hypothesis. In fact, they apparently throw it out of court. It will be remembered that Jeans has made a.s.sumptions which give as high a frequency of stellar encounters as is consistent with the astronomical facts. We have a.s.sumed nine dark stars for every bright one, which may be a liberal estimate. Also, although we have a.s.sumed that a disturbance of the sun's atmosphere sufficient to cause a glacial period would arise from a tidal effect only twenty times as great as the difference in Jupiter's effect when nearest the sun and farthest away, in our computations this has actually been reduced to thirteen. With all these favorable a.s.sumptions the chances of a stellar approach of the sort here described are now only one in twelve billion years. Yet within a hundred million years, according to many estimates of geological time, and almost certainly within a billion, there have been at least half a dozen glaciations.

Our use of Jeans' data interposes another and equally insuperable difficulty to any tidal hypothesis. Four billion miles is a very short distance in the eyes of an astronomer. At that distance a star twice the size of the sun would attract the outer planets more strongly than the sun itself, and might capture them. If a star should come within four billion miles of the sun, its effect in distorting the orbits of all the planets would be great. If this had happened often enough to cause all the glaciations known to geologists, the planetary orbits would be strongly elliptical instead of almost circular. The consideration here advanced militate so strongly against the tidal hypothesis of solar disturbances that it seems scarcely worth while to consider it further.

Let us turn now to the electrical hypothesis. Here the conditions are fundamentally different from those of the tidal hypothesis. In the first place the electrostatic effect of a body has nothing to do with its ma.s.s, but depends on the area of its surface; that is, it varies as the square of the radius. Second, the emission of electrons varies exponentially. If hot glowing stars follow the same law as black bodies at lower temperatures, the emission of electrons, like the emission of other kinds of energy, varies as the fourth power of the absolute temperature. In other words, suppose there are two black bodies, otherwise alike, but one with a temperature of 27 C. or 300 on the absolute scale, and the other with 600 on the absolute scale. The temperature of one is twice as high as that of the other, but the electrostatic effect will be sixteen times as great.[115] Third, the number of electrons that reach a given body varies inversely as the square of the distance, instead of as the cube which is the case with tide-making forces.

In order to use these three principles in calculating the effect of the stars we must know the diameters, distances, temperature, and number of the stars. The distances and number may safely be taken as given by Jeans in the calculations already cited. As to the diameters, the measurements of the stars thus far made indicate that the average ma.s.s is about twice that of the sun. The average density, as deduced by Shapley[116] from the movements of double stars, is about one-eighth the solar density. This would give an average diameter about two and a half times that of the sun. For the dark stars, we shall a.s.sume for convenience that they are ten times as numerous as the bright ones. We shall also a.s.sume that their diameter is half that of the sun, for being cool they must be relatively dense, and that their temperature is the same as that which we shall a.s.sume for Jupiter.

As to Jupiter we shall continue our former a.s.sumption that a body with four times the effectiveness of that planet, which here means with twice as great a radius, would disturb the sun enough to cause glaciation. It would produce about twenty times the electrostatic effect which now appears to be a.s.sociated with the difference in Jupiter's effect at maximum and minimum. The temperature of Jupiter must also be taken into account. The planet is supposed to be hot because its density is low, being only about 1.25 that of water. Nevertheless, it is probably not luminous, for as Moulton[117] puts it, shadows upon it are black and its moons show no sign of illumination except from the sun. Hence a temperature of about 600C., or approximately 900 on the absolute scale, seems to be the highest that can reasonably be a.s.signed to the cold outer layer whence electrons are emitted. As to the temperature of the sun, we shall adopt the common estimate of about 6300C. on the absolute scale. The other stars will be taken as averaging the same, although of course they vary greatly.

When Jeans' method of calculating the probability of a mutual approach of the sun and a star is applied to the a.s.sumptions given above, the results are as shown in Table 5. On that basis the dark stars seem to be of negligible importance so far as the electrical hypothesis is concerned. Even though they may be ten times as numerous as the bright ones there appears to be only one chance in 130 billion years that one of them will approach the sun closely enough to cause the a.s.sumed disturbance of the solar atmosphere. On the other hand, if all the visible stars were the size of the sun, and as hot as that body, their electrical effect would be fourfold that of our a.s.sumed dark star because of their size, and 2401 times as great because of their temperature, or approximately 10,000 times as great. Under such conditions the theoretical chance of an approach that would cause glaciation is one in 130 million years. If the average visible star is somewhat cooler than the sun and has a radius about two and one-half times as great, as appears to be the fact, the chances rise to one in thirty-eight million years. A slight and wholly reasonable change in our a.s.sumptions would reduce this last figure to only five or ten million.

For instance, the earth's mean temperature during the glacial period has been a.s.sumed as 10C. lower than now, but the difference may have been only 6. Again, the temperature of the outer atmosphere of Jupiter where the electrons are shot out may be only 500 or 700 absolute, instead of 900. Or the diameter of the average star may be five or ten times that of the sun, instead of only two and one-half times as great. All this, however, may for the present be disregarded. The essential point is that even when the a.s.sumptions err on the side of conservatism, the results are of an order of magnitude which puts the electrical hypothesis within the bounds of possibility, whereas similar a.s.sumptions put the tidal hypothesis, with its single approach in twelve billion years, far beyond those limits.

The figures for Betelgeuse in Table 5 are interesting. At a meeting of the American a.s.sociation for the Advancement of Science in December, 1920, Michelson reported that by measurements of the interference of light coming from the two sides of that bright star in Orion, the observers at Mount Wilson had confirmed the recent estimates of three other authorities that the star's diameter is about 218 million miles, or 250 times that of the sun. If other stars so much surpa.s.s the estimates of only a decade or two ago, the average diameter of all the visible stars must be many times that of the sun. The low figure for Betelgeuse in section D of the table means that if all the stars were as large as Betelgeuse, several might often be near enough to cause profound disturbances of the solar atmosphere. Nevertheless, because of the low temperature of the giant red stars of the Betelgeuse type, the distance at which one of them would produce a given electrical effect is only about five times the distance at which our a.s.sumed average star would produce the same effect. This, to be sure, is on the a.s.sumption that the radiation of energy from incandescent bodies varies according to temperature in the same ratio as the radiation from black bodies.

Even if this a.s.sumption departs somewhat from the truth, it still seems almost certain that the lower temperature of the red compared with the high temperature of the white stars must to a considerable degree reduce the difference in electrical effect which would otherwise arise from their size.

TABLE 5

THEORETICAL PROBABILITY OF STELLAR APPROACHES

--------------------------------------------------------------------- 1 2 3 4 _Average _Dark Stars_ _Sun_ Star_ _Betelgeuse_ --------------------------------------------------------------------- A. Approximate radius in miles 430,000 860,000 2,150,000 218,000,000 B. a.s.sumed temperature above absolute zero. 900 C. 6300 C. 5400 C. 3150 C. C. Approximate theoretical distance at which star would cause solar disturbance great enough to cause glaciation (billions[118] of miles). 1.2 120 220 3200 D. Average interval between approaches close enough to cause glaciation if all stars 130,000,000,000 were of given [119] type. Years. 130,000,000 38,000,000 700,000 ---------------------------------------------------------------------

Thus far in our attempt to estimate the distance at which a star might disturb the sun enough to cause glaciation on the earth, we have considered only the star's size and temperature. No account has been taken of the degree to which its atmosphere is disturbed. Yet in the case of the sun this seems to be one of the most important factors. The magnetic field of sunspots is sometimes 50 or 100 times as strong as that of the sun in general. The strength of the magnetic field appears to depend on the strength of the electrical currents in the solar atmosphere. But the intensity of the sunspots and, by inference, of the electrical currents, may depend on the electrical action of Jupiter and the other planets. If we apply a similar line of reasoning to the stars, we are at once led to question whether the electrical activity of double stars may not be enormously greater than that of isolated stars like the sun.

If this line of reasoning is correct, the atmosphere of every double star must be in a state of commotion vastly greater than that of the sun's atmosphere even when it is most disturbed. For example, suppose the sun were accompanied by a companion of equal size at a distance of one million miles, which would make it much like many known double stars. Suppose also that in accordance with the general laws of physics the electrical effect of the two suns upon one another is proportional to the fourth power of the temperature, the square of the radius, and the inverse square of the distance. Then the effect of each sun upon the other would be sixty billion (6 10^{10}) times as great as the present electrical effect of Jupiter upon the sun. Just what this would mean as to the net effect of a pair of such suns upon the electrical potential of other bodies at a distance we can only conjecture. The outstanding fact is that the electrical conditions of a double star must be radically different and vastly more intense than those of a single star like the sun.

This conclusion carries weighty consequences. At present twenty or more stars are known to be located within about 100 trillion miles of the sun (five pa.r.s.ecs, as the astronomers say), or 16.5 light years. According to the a.s.sumptions employed in Table 5 an average single star would influence the sun enough to cause glaciation if it came within approximately 200 billion miles. If the star were double, however, it might have an electrical capacity enormously greater than that of the sun. Then it would be able to cause glaciation at a correspondingly great distance. Today Alpha Centauri, the nearest known star about twenty-five trillion miles, or 4.3 light years from the sun, and Sirius, the brightest star in the heavens, is about fifty trillion miles away, or 8.5 light years. If these stars were single and had a diameter three times that of the sun, and if they were of the same temperature as has been a.s.sumed for Betelgeuse, which is about fifty times as far away as Alpha Centauri, the relative effects of the three stars upon the sun would be, approximately, Betelgeuse 700, Alpha Centauri 250, Sirius 1.

But Alpha Centauri is triple and Sirius double, and both are much hotter than Betelgeuse. Hence Alpha Centauri and even Sirius may be far more effective than Betelgeuse.

The two main components of Alpha Centauri are separated by an average distance of about 2,200,000,000 miles, or somewhat less than that of Neptune from the sun. A third and far fainter star, one of the faintest yet measured, revolves around them at a great distance. In ma.s.s and brightness the two main components are about like the sun, and we will a.s.sume that the same is true of their radius. Then, according to the a.s.sumptions made above, their effect in disturbing one another electrically would be about 10,000 times the total effect of Jupiter upon the sun, or 2500 times the effect that we have a.s.sumed to be necessary to produce a glacial period. We have already seen in Table 5 that, according to our a.s.sumptions, a single star like the sun would have to approach within 120 billion miles of the solar system, or within 2 per cent of a light year, in order to cause glaciation. By a similar process of reasoning it appears that if the mutual electrical excitation of the two main parts of Alpha Centauri, regardless of the third part, is proportional to the apparent excitation of the sun by Jupiter, Alpha Centauri would be 5000 times as effective as the sun. In other words, if it came within 8,500,000,000,000 miles of the sun, or 1.4 light years, it would so change the electrical conditions as to produce a glacial epoch. In that case Alpha Centauri is now so near that it introduces a disturbing effect equal to about one-sixth of the effect needed to cause glaciation on the earth. Sirius and perhaps others of the nearer and brighter or larger stars may also create appreciable disturbances in the electrical condition of the sun's atmosphere, and may have done so to a much greater degree in the past, or be destined to do so in the future.

Thus an electrical hypothesis of solar disturbances seems to indicate that the position of the sun in respect to other stars may be a factor of great importance in determining the earth's climate.

FOOTNOTES:

[Footnote 112: H. H. Turner: On a Long Period in Chinese Earthquake Records; Mon. Not. Royal Astron. Soc., Vol. 79, 1919, pp. 531-539; Vol.

80, 1920, pp. 617-619; Long Period Terms in the Growth of Trees; _idem_, pp.793-808.]

[Footnote 113: Harlow Shapley: Note on a Possible Factor in Geologic Climates; Jour. Geol., Vol. 29, No. 4, May, 1921; Novae and Variable Stars, Pub. Astron. Soc. Pac., No. 194, Aug., 1921.]

[Footnote 114: J. H. Jeans: Problems of Cosmogony and Stellar Dynamics, Cambridge, 1919.]

[Footnote 115: This fact is so important and at the same time so surprising to the layman, that a quotation from The Electron Theory of Matter by O. W. Richardson, 1914, pp. 326 and 334 is here added.

"It is a very familiar fact that when material bodies are heated they emit electromagnetic radiations, in the form of thermal, luminous, and actinic rays, in appreciable quant.i.ties. Such an effect is a natural consequence of the electron and kinetic theories of matter. On the kinetic theory, temperature is a measure of the violence of the motion of the ultimate particles; and we have seen that on the electron theory, electromagnetic radiation is a consequence of their acceleration. The calculation of this emission from the standpoint of the electron theory alone is a very complex problem which takes us deeply into the structure of matter and which has probably not yet been satisfactorily resolved.

Fortunately, we can find out a great deal about these phenomena by the application of general principles like the conservation of energy and the second law of thermodynamics without considering special a.s.sumptions about the ultimate const.i.tution of matter. It is to be borne in mind that the emission under consideration occurs at all temperatures although it is more marked the higher the temperature.... The energy per unit volume, _in vacuo_, of the radiation in equilibrium in an enclosure at the absolute temperature, T, is equal to a universal constant, A, multiplied by the fourth power of the absolute temperature. Since the intensity of the radiation is equal to the energy per unit volume multiplied by the velocity of light, it follows that the former must also be proportional to the fourth power of the absolute temperature.

Moreover, if E is the total emission from unit area of a perfectly black body, we see from p. 330 that E=A'T^{4}, where A' is a new universal constant. This result is usually known as Stefan's Law. It was suggested by Stefan in the inaccurate form that the total radiant energy of emission from bodies varies as the fourth power of the absolute temperature, as a generalization from the results of experiments. The credit for showing that it is a consequence of the existence of radiation pressure combined with the principles of thermodynamics is due to Bartoli and Boltzmann."]

[Footnote 116: Quoted by Moulton in his Introduction to Astronomy.]

[Footnote 117: Introduction to Astronomy.]

[Footnote 118: The term billions, here and elsewhere, is used in the American sense, 10^{9}.]

[Footnote 119: The a.s.sumed number of stars here is ten times as great as in the other parts of this line.]

CHAPTER XV

THE SUN'S JOURNEY THROUGH s.p.a.cE

Having gained some idea of the nature of the electrical hypothesis of solar disturbances and of the possible effect of other bodies upon the sun's atmosphere, let us now compare the astronomical data with those of geology. Let us take up five chief points for which the geologist demands an explanation, and which any hypothesis must meet if it is to be permanently accepted. These are (1) the irregular intervals at which glacial periods occur; (2) the division of glacial periods into epochs separated sometimes by hundreds of thousands of years; (3) the length of glacial periods and epochs; (4) the occurrence of glacial stages and historic pulsations in the form of small climatic waves superposed upon the larger waves of glacial epochs; (5) the occurrence of climatic conditions much milder than those of today, not only in the middle portion of the great geological eras, but even in some of the recent inter-glacial epochs.