TEMPERATURE OF THE SUN
Newton was the first who attempted to measure the quantity of heat received by the earth from the sun. His object in making the experiment was to ascertain the temperature encountered by the comet of 1680 at its passage through perihelion. He found it, by multiplying the observed heating effects of direct sunshine according to the familiar rule of the "inverse squares of the distances," to be about 2,000 times that of red-hot iron.[698]
Determinations of the sun's thermal power, made with some scientific exactness, date, however, from 1837. A few days previous to the beginning of that year, Herschel began observing at the Cape of Good Hope with an "actinometer," and obtained results agreeing quite satisfactorily with those derived by Pouillet from experiments made in France some months later with a "pyrheliometer."[699] Pouillet found that the vertical rays of the sun falling on each square centimetre of the earth's surface are competent (apart from atmospheric absorption) to raise the temperature of 1·7633 grammes of water one degree Centigrade per minute. This number (1·7633) he called the "solar constant"; and the unit of heat chosen is known as the "calorie." Hence it was computed that the total amount of solar heat received during a year would suffice to melt a layer of ice covering the entire earth to a depth of 30·89 metres, or 100 feet; while the heat emitted would melt, at the sun's surface, a stratum 11·80 metres thick each minute. A careful series of observations showed that nearly half the heat incident upon our atmosphere is stopped in its passage through it.
Herschel got somewhat larger figures, though he assigned only a third as the spoil of the air. Taking a mean between his own and Pouillet's, he calculated that the ordinary expenditure of the sun per minute would have power to melt a cylinder of ice 184 feet in diameter, reaching from his surface to that of α Centauri; or, putting it otherwise, that an ice-rod 45·3 miles across, continually darted into the sun with the velocity of light, would scarcely consume, in dissolving, the thermal supplies now poured abroad into space.[700] It is nearly certain that this estimate should be increased by about two-thirds in order to bring it up to the truth.
Nothing would, at first sight, appear simpler than to pass from a knowledge of solar emission—a strictly measurable quantity—to a knowledge of the solar temperature; this being defined as the temperature to which a surface thickly coated with lamp-black (that is, of standard radiating power) should be raised to enable it to send us, from the sun's distance, the amount of heat actually received from the sun. Sir John Herschel showed that heat-rays at the sun's surface must be 92,000 times as dense as when they reach the earth; but it by no means follows that either the surface emitting, or a body absorbing those heat-rays must be 92,000 times hotter than a body exposed here to the full power of the sun. The reason is, that the rate of emission—consequently the rate of absorption, which is its correlative—increases very much faster than the temperature. In other words, a body radiates or cools at a continually accelerated pace as it becomes more and more intensely heated above its surroundings.
Newton, however, took it for granted that radiation and temperature advance pari passu—that you have only to ascertain the quantity of heat received from, and the distance of a remote body in order to know how hot it is.[701] And the validity of this principle, known as "Newton's Law" of cooling, was never questioned until De la Roche pointed out, in 1812,[702] that it was approximately true only over a low range of temperature; while five years later, Dulong and Petit generalised experimental results into the rule, that while temperature grows by arithmetical, radiation increases by geometrical progression.[703] Adopting this formula, Pouillet derived from his observations on solar heat a solar temperature of somewhere between 1,461° and 1,761° C. Now, the higher of these points—which is nearly that of melting platinum—is undoubtedly surpassed at the focus of certain burning-glasses which have been constructed of such power as virtually to bring objects placed there within a quarter of a million of miles of the photosphere. In the rays thus concentrated, platinum and diamond become rapidly vaporised, notwithstanding the great loss of heat by absorption, first in passing through the air, and again in traversing the lens. Pouillet's maximum is then manifestly too low, since it involves the absurdity of supposing a radiating mass capable of heating a distant body more than it is itself heated.
Less demonstrably, but scarcely less surely, Mr. J. J. Waterston, who attacked the problem in 1860, erred in the opposite direction. Working up, on Newton's principle, data collected by himself in India and at Edinburgh, he got for the "potential temperature" of the sun 12,880,000° Fahr.,[704] equivalent to 7,156,000° C. The phrase potential temperature (for which Violle substituted, in 1876, effective temperature) was designed to express the accumulation in a single surface, postulated for the sake of simplicity, of the radiations not improbably received from a multitude of separate solar layers reinforcing each other; and might thus (it was explained) be considerably higher than the actual temperature of any one stratum.
At Rome, in 1861, Father Secchi repeated Waterston's experiments, and reaffirmed his conclusion;[705] while Soret's observations, made on the summit of Mont Blanc in 1867,[706] furnished him with materials for a fresh and even higher estimate of ten million degrees Centigrade.[707] Yet from the very same data, substituting Dulong and Petit's for Newton's law, Vicaire deduced in 1872 a provisional solar temperature of 1,398°.[708] This is below that at which iron melts, and we know that iron-vapour exists high up in the sun's atmosphere. The matter was taken into consideration on the other side of the Atlantic by Ericsson in 1871. He attempted to re-establish the shaken credit of Newton's principle, and arrived, by its means, at a temperature of 4,000,000° Fahrenheit.[709] Subsequently, an "underrated computation," based upon observation of the quantity of heat received by his "sun motor," gave him 3,000,000°. And the result, as he insisted, followed inevitably from the principle that the temperature produced by radiant heat is proportional to its density, or inversely as its diffusion.[710] The principle, however, is demonstrably unsound.
In 1876 the sun's temperature was proposed as the subject of a prize by the Paris Academy of Sciences; but although the essay of M. Jules Violle was crowned, the problem was declared to remain unsolved. Violle (who adhered to Dulong and Petit's formula) arrived at an effective temperature of 1,500° C., but considered that it might actually reach 2,500° C., if the emissive power of the photospheric clouds fell far short (as seemed probable) of the lamp-black standard.[711] Experiments made in April and May, 1881, giving a somewhat higher result, he raised this figure to 3,000° C.[712]
Appraisements so outrageously discordant as those of Waterston, Secchi, and Ericsson on the one hand, and those of the French savants on the other, served only to show that all were based upon a vicious principle. Professor F. Rosetti,[713] accordingly, of the Paduan University, at last perceived the necessity for getting out of the groove of "laws" plainly in contradiction with facts. The temperature, for instance, of the oxy-hydrogen flame was fixed by Bunsen at 2,800° C.—an estimate certainly not very far from the truth. But if the two systems of measurement applied to the sun be used to determine the heat of a solid body rendered incandescent in this flame, it comes out, by Newton's mode of calculation, 45,000° C.; by Dulong and Petit's, 870° C.[714] Both, then, are justly discarded, the first as convicted of exaggeration, the second of undervaluation. The formula substituted by Rosetti in 1878 was tested successfully up to 2,000° C.; but since, like its predecessors, it was a purely empirical rule, guaranteed by no principle, and hence not to be trusted out of sight, it was, like them, liable to break down at still higher elevations. Radiation by this new prescription increases as the square of the absolute temperature—that is, of the number of degrees counted from the "absolute zero" of -273° C. Its employment gave for the sun's radiating surface an effective temperature of 20,380° C. (including a supposed loss of one-half in the solar atmosphere); and setting a probable deficiency in emission (as compared with lamp-black) against a probable mutual reinforcement of superposed strata, Professor Rosetti considered "effective" as nearly equivalent to "actual" temperature. A "law of cooling," proposed by M. Stefan at Vienna in 1879,[715] was shown by Boltzmann, many years later, to have a certain theoretical validity.[716] It is that emission grows as the fourth power of absolute temperature. Hence the temperature of the photosphere would be proportional to the square root of the square root of its heating effects at a distance, and appeared, by Stefan's calculations from Violle's measures of solar radiative intensity, to be just 6,000° C.; while M. H. Le Chatelier[717] derived 7,600° from a formula, conveying an intricate and unaccountable relation between the temperature of an incandescent body and the intensity of its red radiations.