[Footnote 661: Thollon's estimate (_Comptes Rendus_, t. xcvii., p. 902) of 300,000 _kilometres_, seems considerably too low. Limiting the "average prominence region" to a sh.e.l.l 54,000 miles deep (2' of arc as seen from the earth), the visual line will, at mid-height (27,000 miles from the sun's surface), travel through (in round numbers) 320,000 miles of that region.]

[Footnote 662: Liveing and Dewar, _Phil. Mag._, vol. xvi. (5th ser.), p.

407.]

[Footnote 663: _Chemistry of the Sun_, p. 260.]

[Footnote 664: _Nature_, October 14, 1886.]

[Footnote 665: The normal spectrum is that depending exclusively upon wave-length--the fundamental constant given by nature as regards light.

It is obtained by the interference of rays, in the manner first exemplified by Fraunhofer, and affords the only unvarying standard for measurement. In the refraction spectrum (upon which Kirchhoff's map was founded), the relative positions of the lines vary with the material of the prisms.]

[Footnote 666: Scheiner, _Die Spectrala.n.a.lyse der Gestirne_, p. 168.]

[Footnote 667: _Phil. Mag._, vol. xxvii., p. 479.]

[Footnote 668: _Astr. and Astrophysics_, vol. xii., p. 321; Frost-Scheiner, _Astr. Spectr._, p. 363.]

[Footnote 669: Published in _Astroph. Jour._, vols. i. to vi.]

[Footnote 670: _Astr. and Astrophysics_, vol. xi., p. 793.]

[Footnote 671: _Astroph. Jour._, vol. vi., p. 95.]

[Footnote 672: _Annales de l'Observatoire de Nice_, t. iii., 1890.]

[Footnote 673: _Trans. Royal Society of Edinburgh_, vol. x.x.xvi., p. 99.]

[Footnote 674: Rev. A. L. Cortie, _Astr. and Astrophysics_, vol. xi., p.

401. Specimens of his photographs were given by Ranyard in _Knowledge_, vol. xiii., p. 212.]

[Footnote 675: _Ann. d. Phys._, Bd. cxvii., p. 296.]

[Footnote 676: _Comptes Rendus_, t. lxiii., p. 647.]

[Footnote 677: _Ibid._, t. lx.x.xvi., p. 317. Some half dozen of these identifications have proved fallacious.]

[Footnote 678: _Chemistry of the Sun_, p. 143.]

[Footnote 679: _Amer. Jour. of Science_, vol. x.x.xiv., p. 348.]

[Footnote 680: _Berlin Abhandlungen_, 1889.]

[Footnote 681: _Amer. Jour. of Science_, vol. xli., p. 243. See Appendix, Table II.]

[Footnote 682: _Astrophy. Jour._, vol. ix., p. 219; Fowler, _Knowledge_, vol. xxiii., p. 11.]

[Footnote 683: _Amer. Jour, of Science_, vol. xiv., p. 89; _Nature_, vol. xvi., p. 364; _Month. Not._, vol. x.x.xix., p. 440.]

[Footnote 684: _Month. Not._, vol. x.x.xviii., p. 473; Trowbridge and Hutchins, _Amer. Jour. of Science_, vol. x.x.xiv., p. 263.]

[Footnote 685: Scheiner, _Die Spectrala.n.a.lyse_, p. 180.]

[Footnote 686: _Comptes Rendus_, t. lxvii., p. 1123.]

[Footnote 687: Rev. A. L. Cortie, _Month. Not._, vol. li., p. 18.]

[Footnote 688: Young, _The Sun_, p. 135; Hale, _Astr. and Astrophysics_, vol. xi., p. 312 Buss, _Jour. Brit. Astr. a.s.s._, vol. ix., p. 253.]

[Footnote 689: _Phil. Trans._, vol. clxx., p. 46.]

[Footnote 690: _Comptes Rendus_, t. xcvii., p. 555; t. ci., p. 1145.]

[Footnote 691: Liveing and Dewar, _Astr. and Astrophysics_, vol. xi., p.

705.]

[Footnote 692: _Comptes Rendus_, t. lx., p. 213; t. lxiii., p. 289.]

[Footnote 693: _Ibid._, t. cviii., p. 1035.]

[Footnote 694: _Ibid._, t. cxi., p. 431.]

[Footnote 695: _Astroph. Jour._, vols. iv., p. 317; vi., p. 426.]

[Footnote 696: _Trans. Roy. Soc. Edin._, vol. x.x.xii., p. 452.]

[Footnote 697: _Comptes Rendus_, t. cxi., p. 941; Huggins, _Proc. Roy.

Soc._, vol. xlvi., p. 168.]

CHAPTER V

_TEMPERATURE OF THE SUN_

Newton was the first who attempted to measure the quant.i.ty 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 pa.s.sage 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 17633 grammes of water one degree Centigrade per minute. This number (17633) 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 3089 metres, or 100 feet; while the heat emitted would melt, at the sun's surface, a stratum 1180 metres thick each minute. A careful series of observations showed that nearly half the heat incident upon our atmosphere is stopped in its pa.s.sage through it.

Herschel got somewhat larger figures, though he a.s.signed 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 Alpha Centauri; or, putting it otherwise, that an ice-rod 453 miles across, continually darted into the sun with the velocity of light, would scarcely consume, in dissolving, the thermal supplies now poured abroad into s.p.a.ce.[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 pa.s.s from a knowledge of solar emission--a strictly measurable quant.i.ty--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 pa.s.su_--that you have only to ascertain the quant.i.ty 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 Pet.i.t 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 surpa.s.sed at the focus of certain burning-gla.s.ses 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 pa.s.sing 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 ma.s.s 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 subst.i.tuted, in 1876, _effective temperature_) was designed to express the acc.u.mulation in a single surface, postulated for the sake of simplicity, of the radiations not improbably received from a mult.i.tude of separate solar layers reinforcing each other; and might thus (it was explained) be considerably higher than the _actual_ temperature of any one stratum.