These remarks hold for the "outer corona," while the inner portion, the so-called "inner corona," shines in a more uniform light. The spectroscopic examination demonstrates that the light consists mainly of hydrogen gas and of an unknown gas designated coronium, which particularly seems to occur in the higher parts of the inner corona. The outer streamers of the corona, on the contrary, yield a continuous spectrum which shows that the light is radiated by solid or liquid particles. In the spectrum of the coronal rays at an extreme distance from the disk, astronomers have sometimes fancied that they discerned dark lines on a bright ground, just as in the spectrum of the photosphere. It has been assumed that this light is reflected sunlight, originating from small solid or liquid particles of the outer corona. It must be reflected, because it is partly polarized. The radiating disposition of the outer corona indicates the action of a force, the radiation pressure, which drives the smaller particles away from the centre of the sun.
As regards the temperature of the sun, we have already seen that the two methods applied for its determination have yielded somewhat unequal results. From the intensity of the radiation, Christiansen, and afterwards Warburg, calculated a temperature of about 6000° Cent. Wilson and Gray found for the centre of the sun 6200°, which they afterwards corrected into 8000°. Owing to the absorption of light by the terrestrial and the solar atmospheres, we always find too low values. That applies, to a still greater extent, to any estimate based upon the determination of that wave-length for which the heat emission from the solar spectrum is maximum. Le Chatelier compared the intensity of sunlight filtered through red glass with the intensities of light from several terrestrial sources of fairly well-known temperatures treated in the same way. These estimates yielded to him a solar temperature of 7600° Cent. Most scientists reckon with an absolute temperature of 6500°, corresponding to about 6200° Celsius. That is what is known as the "effective temperature" of the sun. If the solar rays were not partially absorbed, this temperature would correspond to that of the clouds of the photosphere. Since red light is little absorbed comparatively, Le Chatelier’s value of 7600°, and the almost equal value of Wilson and Gray of 8000°, should approximately represent the average temperature of the outer portions of the clouds of the photosphere. The higher temperature of the faculæ is evident from their greater light intensity, which, however, may partly be due to their greater height. Carrington and Hodgson saw, on September 1, 1859, two faculæ break out from the edge of a sun-spot. Their splendor was five or six times greater than that of the surrounding parts of the photosphere. That would correspond to a temperature of about 10,000 or 12,000° Cent. The deeper parts of the sun which broke out on these occasions evidently have a higher temperature, and this is not unnatural, since the sun is losing heat by radiation from its outer portions.
We know that the temperature of our atmosphere decreases with greater heights. The movements of the air are concerned in this change. A sinking mass of air is compressed by the increased pressure to which it is being exposed, and its temperature rises, therefore, just as the temperature rises in a pneumatic gas-lighter when the piston is pressed down. If the air were dry and in strong vertical motion, its temperature would change by 10° Cent. (18° F.) per km. If it stood still, it would assume an almost uniform temperature; that is to say, there would be no lowering of the temperature as we proceed upward. The actual value lies between the two extremes. As the gravitation in the photosphere of the sun is 27.4 times greater than on the surface of the earth, we can deduce that, if the air on the sun were as dense as on the earth, the temperature on the sun would vary 27.4 times as much as on the earth with the increasing height—that is to say, by 270 degrees per kilometre, provided its atmosphere were in violent agitation. Now, the outer portions of the solar atmosphere are, indeed, in violent motion, so that this latter assumption seems to be justified. But this part consists essentially of hydrogen, which is 29 times lighter than the air. We must, therefore, reduce the value at which we arrive to one-twenty-ninth. As a result, the final temperature gradient per kilometre would only be 9° Cent. (16.2° F.). But the radiation is extremely powerful on the sun, and it tends to equalize the conditions. Nine degrees per kilometre is therefore, without doubt, too high a value. Further, in the interior of the sun the gases are much heavier. At a small depth, however, they will be so strongly compressed by the upper strata that their further compressibility will be limited, and the calculation which we have just made loses its validity. Yet, in any case, the temperature of the sun must increase as we penetrate nearer to its centre. If we accept a temperature gradient per kilometre of the value above indicated, 9°—it is three times greater in the solid earth-crust—we should obtain for the centre of the sun a temperature of more than six million degrees.
All substances melt and evaporate as their temperature is raised. If the temperature exceeds a certain limit, the "critical temperature," the substance can no longer be condensed to a liquid, however high the pressure may be pushed, and the substance will only exist as a gas. If we start from -273° as absolute zero, this critical temperature is nearly one and a half times as high as the ebullition temperature of the substance under atmospheric pressure. So far as our experience goes, it does not appear probable that the critical temperature of any substance could be higher than 10,000° or 12,000° Cent., the highest values which we have calculated for the temperature of the faculæ. The inner portions of the sun must hence be gaseous, and the whole sun be a strongly compressed mass of gas of extremely high temperature, which, owing to the high pressure, is at a density 1.4 times as great as that of water, and which in many respects, therefore, will resemble a liquid. It must, for instance, be extremely viscid, and that accounts for the relatively great stability of the sun-spots (one sun-spot held out for a year and a half in 1840 and 1841). The sun would thus have to be regarded as a sphere of gas, in the outer portions of which a certain amount of condensations of cloud character have taken place, owing to radiation and to the outward movements of the gaseous masses. The pressure in the photosphere—that is, in those parts in which these clouds are floating—has been averaged at five or six atmospheres, a figure which, considering the very high gravitation, would suggest a layer of superposed gas above it corresponding to not more than a fifth of our terrestrial atmosphere. At an approximately corresponding height, 11,500 m. (38,000 ft.), there are floating in the terrestrial atmosphere the highest cirrus clouds, to which the clouds of the photosphere may in many respects be compared.
We turn back to the unanswered question whence the sun takes the compensation for the heat which it constantly radiates into space. The most powerful source of heat known to us is that of chemical reactions. The most familiar reaction of daily life is the combustion of coal. By burning one gramme of carbon we obtain 8000 calories. If the sun consisted of pure carbon, its energy would not hold out more than 4000 years. It is not to be wondered at, therefore, that most scientists soon abandoned the hope of solving the problem in this way. The French astronomer Faye attempted to explain the replenishment of the losses of heat by radiation from the sun by arguments in which he resorted to the heat of a combination of the constituents of the sun. He said: "So high a temperature must prevail in the interior of the sun that everything there will be decomposed into its elementary constituents. When the atoms afterwards penetrate into the outer layers, they are again united, and they liberate heat." Faye thus imagined that new masses of elements would constantly rise from the interior of the sun and would be reunited in chemical combination on the surface. But if new masses are to penetrate upward to the surface, those which were at first above must go back to the centre of the sun, in order to be re-decomposed by the great heat there; and this re-decomposition would consume just as much heat as was gained by the rising of the same masses to the surface. This convection can therefore only help to transport the store of heat from the interior to the surface. The total amount of heat stored in the sun would in this way, supposing the mean temperature to be six million degrees, be able to cover the heat expenditure for about three million years.
We have, moreover, seen that the highest strata of the sun are distinguished by line spectra, suggestive of simple chemical compounds, while at greater depth in the sun-spots chemical combinations occur which are characterized by band spectra. It is quite incorrect to assert that high temperatures must necessarily decompose all chemical compounds into their elements. The mechanical theory of heat teaches us only that at rising temperatures products are formed whose formation goes hand in hand with an absorption of heat. Thus, at a high temperature, ozone is formed from oxygen, although ozone is more complex in composition than oxygen, and by this reaction 750 calories are consumed when one gramme of oxygen is transformed into one gramme of ozone. We likewise know that in the electric arc, at a temperature of about 3000°, a compound is formed under consumption of heat by the oxygen and nitrogen of the atmosphere. A new method for the technical preparation of nitric acid from the nitrogen of the air is based upon this reaction. Again, the well-known compounds benzene and acetylene are formed from their elements, carbon and hydrogen, under absorption of heat. All these bodies can only be synthesized from their elementary constituents at high temperatures. We further know from experience that the higher the temperature at which a reaction takes place, the greater, in general, the amount of heat which it absorbs.
A similar law applies to the influence of pressure. When the pressure is increased, such processes will be favored as will yield products of a smaller volume. If we imagine that a mass of gas rushes down from a higher stratum of the sun into the depths of the sun’s interior, as gases do in sun-spots, complex compounds will be produced by virtue of the increased pressure. This pressure must increase at an immense rate towards the interior of the sun, by about 3500 atmospheres per kilometre. The gases which dissociate into atoms at the lower pressures and the higher temperatures of the extreme solar strata above the photosphere clouds enter into chemical combination in the depths of the spots, as we learn from spectroscopic examination. Owing to their high temperatures, these compounds absorb enormous quantities of heat in their building up, and these quantities of heat are to those which are concerned in the chemical processes of the earth in the same ratio as the temperature of the sun is to that at which the chemical reactions are proceeding on the earth. As these gases penetrate farther into the sun, temperature and pressure are still more and more increased, and there will result products more and more abounding in energy and concentration. We may, therefore, imagine the interior of the sun charged with compounds which, brought to the surface of the sun, would dissociate under an enormous evolution of heat and an enormous increase of volume. These compounds have to be regarded as the most powerful blasting agents, by comparison with which dynamite and gun-cotton would appear like toys. In confirmation of this view, we observe that gases when penetrating into the photosphere clouds are able to eject prominences at a stupendous velocity, obtaining several hundred kilometres per second. This velocity surpasses that of the swiftest rifle-bullet about a thousandfold. We may hence ascribe to the explosives which are confined in the interior of the sun energies which must be a million times greater than the energy of our blasting agents. (For the energy increases with the square of the velocity.) And yet these solar blasting agents have already given up a large part of their energy during their passage from the sun’s interior. It thus becomes conceivable that the solar energy—instead of holding out for 4000 years, as it would if it depended upon the combustion of a solar sphere made out of carbon—will last for something like four thousand million years. Perhaps we may further extend this period to several billions.
That there are such energetic compounds we have learned from the discovery of the heat evolution of radium. According to Rutherford, radium is decomposed by one-half in the space of about 1300 years. In this decomposition a quantity of about a million calories is evolved per gramme and per year, and we thus find that the decomposition of radium into its final products is accompanied by a heat evolution of about two thousand millions of calories per gramme—about a quarter of a million times more heat than the combustion of one gramme of carbon would yield.
In chemical respects as well, then, the earth is a dwarf compared to the sun, and we have every reason to presume that the chemical energy of the sun will be sufficient to sustain the solar heat during many thousand millions and possibly billions of years to come.