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,[Pg 217] 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[Pg 218] 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)[Pg 219] 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][Pg 220] 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.

From a series of experiments carefully conducted at Daramona, Ireland, with a delicate thermal balance, of the kind invented by Boys and designated a "radio-micrometer," Messrs. Wilson and Gray arrived in 1893, with the aid of Stefan's Law, at a photospheric temperature of 7,400° C.,[718] reduced by the first-named investigator in 1901 to 6,590°.[719] Dr. Paschen, of Hanover, on the other hand, ascribed to the sun a temperature of 5,000° from comparisons between solar radiative intensity and that of glowing platinum;[720] while F. W. Very showed in 1895[721] that a minimum value of 20,000° C. for the same datum resulted from Paschen's formula connecting temperature with the position of maximum spectral energy.

A new line of inquiry was struck out by Zöllner in 1870. Instead of tracking the solar radiations backward with the dubious guide of empirical formulæ, he investigated their intensity at their source. He showed[722] that, taking prominences to be simple effects of the escape of powerfully compressed gases, it was possible, from the known mechanical laws of heat and gaseous constitution, to deduce minimum values for the temperatures prevailing in the area of their development. These came out 27,700° C. for the strata lying immediately above, and 68,400° C. for the strata lying immediately below the photosphere, the former being regarded as the region into which, and the latter as the region from which the eruptions took place. In this calculation, no prominences exceeding 40,000 miles (1·5′) in height were included. But in 1884, G. A. Hirn of Colmar, having regard to the enormous velocities of projection observed in the interim, fixed two million degrees Centigrade as the lowest internal temperature by which they could be accounted for; although admitting the photospheric condensations to be incompatible with a higher external temperature than 50,000° to 100,000° C.[723]

This method of going straight to the sun itself, observing what goes on there, and inferring conditions, has much to recommend it; but its profitable use demands knowledge we are still very far from possessing. We are quite ignorant, for instance, of the actual circumstances attending the birth of the solar flames. The assumption that they are nothing but phenomena of elasticity is a purely gratuitous one. Spectroscopic indications, again, give hope of eventually affording a fixed point of comparison with terrestrial[Pg 221] heat sources; but their interpretation is still beset with uncertainties; nor can, indeed, the expression of transcendental temperatures in degrees of impossible thermometers be, at the best, other than a futile attempt to convey notions respecting a state of things altogether outside the range of our experience.

A more tangible, as well as a less disputable proof of solar radiative intensity than any mere estimates of temperature, was provided in some experiments made by Professor Langley in 1878.[724] Using means of unquestioned validity, he found the sun's disc to radiate 87 times as much heat, and 5,300 times as much light as an equal area of metal in a Bessemer converter after the air-blast had continued about twenty minutes. The brilliancy of the incandescent steel, nevertheless, was so blinding, that melted iron, flowing in a dazzling white-hot stream into the crucible, showed "deep brown by comparison, presenting a contrast like that of dark coffee poured into a white cup." Its temperature was estimated (not quite securely)[725] at about 2,000° C.; and no allowances were made, in computing relative intensities, for atmospheric ravages on sunlight, for the extra impediments to its passage presented by the smoke-laden air of Pittsburgh, or for the obliquity of its incidence. Thus, a very large balance of advantage lay on the side of the metal.

A further element of uncertainty in estimating the intrinsic strength of the sun's rays has still to be considered. From the time that his disc first began to be studied with the telescope, it was perceived to be less brilliant near the edges. Lucas Valerius, of the Lyncean Academy, seems to have been the first to note this fact, which, strangely enough, was denied by Galileo in a letter to Prince Cesi of January 25, 1613.[726] Father Scheiner, however, fully admitted it, and devoted some columns of his bulky tome to the attempt to find its appropriate explanation.[727] In 1729 Bouguer measured, with much accuracy, the amount of this darkening; and from his data, Laplace, adopting a principle of emission now known to be erroneous, concluded that the sun loses eleven-twelfths of his light through absorption in his own atmosphere.[728] The real existence of this atmosphere, which is totally distinct from the beds of ignited vapours producing the Fraunhofer lines, is not open to doubt, although its nature is still a matter of conjecture. The separate effects of its action on luminous, thermal, and chemical rays were carefully studied by Father Secchi, who in 1870[729] inferred the total absorption to be 88/100 of all radiations taken together, and added the important observation that the light from the limb is no[Pg 222] longer white, but reddish-brown. Absorptive effects were thus seen to be unequally distributed; and they could evidently be studied to advantage only by taking the various rays of the spectrum separately, and finding out how much each had suffered in transmission.

This was done by H. C. Vogel in 1877.[730] Using a polarising photometer, he found that only 13 per cent. of the violet rays escape at the edge of the solar disc, 16 of the blue and green, 25 of the yellow, and 30 per cent. of the red. Midway between centre and limb, 88·7 of violet light and 96·7 of red penetrate the absorbing envelope, the abolition of which would increase the intensity of the sun's visible spectrum above two and a half times in the most, and once and a half times in the least refrangible parts. The nucleus of a small spot was ascertained to be of the same luminous intensity as a portion of the unbroken surface about two and a half minutes from the limb. These experiments having been made during a spot-minimum when there is reason to think that absorption is below its average strength, Vogel suggested their repetition at a time of greater activity. They were extended to the heat-rays by Edwin B. Frost. Detailed inquiries made at Potsdam in 1892[731] went to show that, were the sun's atmosphere removed, his thermal power, as regards ourselves, would be increased 1·7 times. They established, too, the practical uniformity in radiation of all parts of his disc. A confirmatory result was obtained about the same time by Wilson and Rambaut, who found that the unveiled sun would be once and a half times hotter than the actual sun.[732]

Professor Langley, now of Washington, gave to measures of the kind a refinement previously undreamt of. Reliable determinations of the "energy" of the individual spectral rays were, for the first time, rendered possible by his invention of the "bolometer" in 1880.[733] This exquisitely sensitive instrument affords the means of measuring heat, not directly, like the thermopile, but in its effects upon the conduction of electricity. It represents, in the phrase of the inventor, the finger laid upon the throttle-valve of a steam-engine. A minute force becomes the modulator of a much greater force, and thus from imperceptible becomes conspicuous. By locally raising the temperature of an inconceivably fine strip of platinum serving as the conducting-wire in a circuit, the flow of electricity is impeded at that point, and the included galvanometer records a disturbance of the electrical flow. Amounts of heat were thus[Pg 223] detected in less than ten seconds, which, expended during a thousand years on the melting of a kilogramme of ice, would leave a part of the work still undone; and further improvements rendered this marvellous instrument capable of thrilling to changes of temperature falling short of one ten-millionth of a degree Centigrade.[734]

The heat contained in the diffraction spectrum is, with equal dispersions, barely one-tenth of that in the prismatic spectrum. It had, accordingly, never previously been found possible to measure it in detail—that is, ray by ray. But it is only from the diffraction, or normal spectrum that any true idea can be gained as to the real distribution of energy among the various constituents, visible and invisible, of a sunbeam. The effect of passage through a prism is to crowd together the red rays very much more than the blue. To this prismatic distortion was owing the establishment of a pseudo-maximum of heat in the infra-red, which disappeared when the natural arrangement by wave-length was allowed free play. Langley's bolometer has shown that the hottest part of the normal spectrum virtually coincides with its most luminous part, both lying in the orange, close to the D-line.[735] Thus the last shred of evidence in favour of the threefold division of solar radiations vanished, and it became obvious that the varying effects—thermal, luminous, or chemical—produced by them are due, not to any distinction of quality in themselves, but to the different properties of the substances they impinge upon. They are simply bearers of energy, conveyed in shorter or longer vibrations; the result in each separate case depending upon the capacity of the material particles meeting them for taking up those shorter or longer vibrations, and turning them variously to account in their inner economy.

A long series of experiments at Allegheny was completed in the summer of 1881 on the crest of Mount Whitney in the Sierra Nevada. Here, at an elevation of 14,887 feet, in the driest and purest air, perhaps, in the world, atmospheric absorptive inroads become less sensible, and the indications of the bolometer, consequently, surer and stronger. An enormous expansion was at once given to the invisible region in the solar spectrum below the red. Captain Abney had got chemical effects from undulations twelve ten-thousandths of a millimetre in length. These were the longest recognised as, or indeed believed, on theoretical grounds, to be capable of existing. Professor Langley now got heating effects from rays of above twice that wave-length, his delicate thread of platinum groping its way down nearly to thirty ten-thousandths of a millimetre,[Pg 224] or three "microns." The known extent of the solar spectrum was thus at once more than doubled. Its visible portion covers a range of about one octave; bolometric indications already in 1884 comprised between three and four. The great importance of the newly explored region appears from the fact that three-fourths of the entire energy of sunlight reside in the infra-red, while scarcely more than one-hundredth part of that amount is found in the better known ultra-violet space.[736] These curious facts were reinforced, in 1886,[737] by further particulars learned with the help of rock-salt lenses and prisms, glass being impervious to very slow, as to very rapid vibrations. Traces were thus detected of solar heat distributed into bands of transmission alternating with bands of atmospheric absorption, far beyond the measurable limit of 5·3 microns.

In 1894, Langley described at the Oxford Meeting of the British Association[738] his new "bolographic" researches, in which the sensitive plate was substituted for the eye in recording deflections of the galvanometer responding to variations of invisible heat. Finally, in 1901,[739] he embodied in a splendid map of the infra-red spectrum 740 absorption-lines of determinate wave-lengths, ranging from 0·76 to 5·3 microns. Their chemical origin, indeed, remains almost entirely unknown, no extensive investigations having yet been undertaken of the slower vibrations distinctive of particular substances; but there is evidence that seven of the nine great bands crossing the "new spectrum" (as Langley calls it)[740] are telluric, and subject to seasonal change. Here, then, he thought, might eventually be found a sure standing-ground for vitally important previsions of famines, droughts, and bonanza-crops.

Atmospheric absorption had never before been studied with such precision as it was by Langley on Mount Whitney. Aided by simultaneous observations from Lone Pine, at the foot of the Sierra, he was able to calculate the intensity belonging to each ray before entering the earth's gaseous envelope—in other words, to construct an extra-atmospheric curve of energy in the spectrum. The result showed that the blue end suffered far more than the red, absorption varying inversely as wave-length. This property of stopping predominantly the quicker vibrations is shared, as both Vogel and[Pg 225] Langley[741] have conclusively shown, by the solar atmosphere. The effect of this double absorption is as if two plates of reddish glass were interposed between us and the sun, the withdrawal of which would leave his orb, not only three or four times more brilliant, but in colour distinctly greenish-blue.[742]

The fact of the uncovered sun being blue has an important bearing upon the question of his temperature, to afford a somewhat more secure answer to which was the ultimate object of Professor Langley's persevering researches; for it is well known that as bodies grow hotter, the proportionate representation in their spectra of the more refrangible rays becomes greater. The lowest stage of incandescence is the familiar one of red heat. As it gains intensity, the quicker vibrations come in, and an optical balance of sensation is established at white heat. The final term of blue heat, as we now know, is attained by the photosphere. On this ground alone, then, of the large original preponderance of blue light, we must raise our estimate of solar heat; and actual measurements show the same upward tendency. Until quite lately, Pouillet's figure of 1.7 calories per minute per square centimetre of terrestrial surface, was the received value for the "solar constant." Forbes had, it is true, got 2.85 from observations on the Faulhorn in 1842;[743] but they failed to obtain the confidence they merited. Pouillet's result was not definitely superseded until Violle, from actinometrical measures at the summit and base of Mont Blanc in 1875, computed the intensity of solar radiation at 2.54,[744] and Crova, about the same time, at Montpellier, showed it to be above two calories.[745] Langley went higher still. Working out the results of the Mount Whitney expedition, he was led to conclude atmospheric absorption to be fully twice as effective as had hitherto been supposed. Scarcely 60 per cent., in fact, of those solar radiations which strike perpendicularly through a seemingly translucent sky, were estimated to attain the sea-level. The rest are reflected, dispersed, or absorbed. This discovery involved a large addition to the original supply so mercilessly cut down in transmission, and the solar constant rose at once to three calories. Nor did the rise stop there. M. Savélieff deduced for it a value of 3.47 from actinometrical observations made at Kieff in 1890;[746] and Knut Ångström, taking account of the arrestive power of carbonic acid, inferred enormous atmospheric absorption, and a solar constant of four calories.[747] In other words, the sun's heat reaching the outskirts of our atmosphere is capable[Pg 226] of doing without cessation the work of an engine of four-horse power for each square yard of the earth's surface. Thus, modern inquiries tend to render more and more evident the vastness of the thermal stores contained in the great central reservoir of our system, while bringing into fair agreement the estimates of its probable temperature. This is in great measure due to the acquisition of a workable formula by which to connect temperature with radiation. Stefan's rule of a fourth-power relation, if not actually a law of nature, is a colourable imitation of one; and its employment has afforded a practical certainty that the sun's temperature, so far as it is definable, neither exceeds 12,000° C., nor falls short of 6,500° C.

FOOTNOTES:

[698] Principia, p. 498 (1st ed.).

[699] Comptes Rendus, t. vii., p. 24.

[700] Results of Astr. Observations, p. 446.

[701] "Est enim calor solis ut radiorum densitas, hoc est, reciproce ut quadratum distantiæ locorum a sole."—Principia, p. 508 (3d ed., 1726).

[702] Jour. de Physique, t. lxxv., p. 215.

[703] Ann. de Chimie, t. vii., 1817, p. 365.

[704] Phil. Mag., vol. xxiii. (4th ser.), p. 505.

[705] Nuovo Cimento, t. xvi., p. 294.

[706] Comptes Rendus, t. lxv., p. 526.

[707] The direct result of 5-1/3 million degrees was doubled in allowance for absorption in the sun's own atmosphere. Comptes Rendus, t. lxxiv., p. 26.

[708] Ibid., p. 31.

[709] Nature, vols. iv., p. 204; v., p. 505.

[710] Ibid., vol. xxx., p. 467.

[711] Ann. de Chim., t. x. (5th ser.), p. 361.

[712] Comptes Rendus, t. xcvi., p. 254.

[713] Phil. Mag., vol. viii., p. 324, 1879.

[714] Ibid., p. 325.

[715] Sitzungsberichte, Wien, Bd. lxxix., ii., p. 391.

[716] Wiedemann's Annalen, Bd. xxii., p. 291; Scheiner, Strahlung und Temperatur der Sonne, p. 27.

[717] Comptes Rendus, March 28, 1892; Astr. and Astrophysics, vol. xi., p. 517.

[718] Phil. Trans., vol. clxxxv., p. 361.

[719] Proc. Roy. Society, December 12, 1901.

[720] Scheiner, Temp. der Sonne, p. 36.

[721] Astroph. Jour., vol. ii., p. 318.

[722] Astr. Nach., Nos. 1,815-16.

[723] L'Astronomie, September, 1884, p. 334.

[724] Amer. Jour. of Science, vol. i. (3rd ser.), p. 653.

[725] Young, The Sun, p. 310.

[726] Op., t. vi., p. 198.

[727] Rosa Ursina, lib. iv., p. 618.

[728] Méc. Cél., liv. x., p. 323.

[729] Le Soleil (1st ed.), p. 136.

[730] Monatsber., Berlin, 1877, p. 104.

[731] Astr. Nach., Nos. 3,105-6; Astr. and Astrophysics, vol. xi., p. 720.

[732] Proc. Roy. Irish Acad., vol. ii., No. 2, 1892.

[733] Am. Jour. of Sc., vol. xxi., p. 187.

[734] Amer. Jour. of Science, vol. v., p. 245, 1898.

[735] For J. W. Draper's partial anticipation of this result, see Ibid. vol. iv., 1872, p. 174.

[736] Phil. Mag., vol. xiv., p. 179, 1883.

[737] "The Solar and the Lunar Spectrum," Memoirs National Acad. of Science, vol. xxxii.; "On hitherto Unrecognised Wave-lengths," Amer. Jour. of Science, vol. xxxii., August, 1886.

[738] Astroph. Jour., vol. i., p. 162.

[739] Annals of the Smithsonian Astroph. Observatory, vol. i.; Comptes Rendus, t. cxxxi., p. 734; Astroph. Jour., vol. iii., p. 63.

[740] Phil. Mag., July, 1901.

[741] Comptes Rendus, t. xcii., p. 701.

[742] Nature, vol. xxvi., p. 589.

[743] Phil. Trans., vol. cxxxii., p. 273.

[744] Ann. de Chim., t. x., p. 321.

[745] Ibid., t. xi., p. 505.

[746] Comptes Rendus, t. cxii., p. 1200.

[747] Wied. Ann., Bd. xxxix., p. 294; Scheiner, Temperatur der Sonne, pp. 36, 38.

article by Agnes Mary Clerke

from The Project Gutenberg eBook of A Popular History of Astronomy During the Nineteenth Century