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§ 3.

I now begin the discussion of numerical values with formula (I.). The lowest value which can be assigned to t is clearly 0. Hence we obtain for the internal temperature t, the minimum value

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Considering that the density of the solar atmosphere is reduced to an almost infinitely small quantity at a very moderate distance from the sun's surface, and that the resistance thereby offered is very slight, we may for the sake of simplicity make the value of H equal to the mean height of the eruptive protube rances. A more exact discussion of the conditions under which this may be done will be given hereafter..

Protuberances are not unfrequently observed having an elevation of 3 minutes; but in order to be near the mark of a mean value, I will take H to be 15 minute.

The Heat-equivalent A I take to be equal to 424 expressed in metrical and centesimal units. The product xc is taken to equal 3.409 for hydrogen, from the latest researches of Regnault*. The value of for hydrogen is, according to Dulong, 1·411†.

A somewhat more detailed discussion is needed to obtain the numerical value of r. According to the preceding, this signifies the radius of the layer of separation through which the eruptions break out. The question is, does this value correspond with the radius of the sun, or, in other words, is this radius identical with that of the solar disk as we see it, or not?

The latest researches of Frankland and Lockyer, St.-Claire Deville, and Wüllner have shown that the discontinuous spectrum of hydrogen and other gases can be changed into a continuous bright one, the lines of the discontinuous spectrum undergoing a characteristic series of changes when the pressure is gradually increased, which consist essentially in the widening of the lines (as in the line Hs), and in a corresponding diminution of the distinctness of their boundaries. These changes render it possible to come to some conclusion respecting the amount of the pressure exerted at the given point; and Frankland and Lockyer have already drawn conclusions on this subject, since they say that "at the lower surface of the chromosphere itself the pressure is very far below the pressure of the earth's atmosphere".

* Pogg. Ann. vol. lxxxix.

† Ann. de Chim. et de Phys. vol. xli.

+ Proc. Roy, Soc. vol. xvii. pp. 288, 2 1.

From Wüllner's researches* we may, I believe, conclude that the pressure at the base of the chromosphere or at the outer edge of the luminous solar disk is equal to that of a column of mercury at the earth's surface from 50 millims. to 500 millims, in height+.

It is thus clear that it is not necessary, in order to explain the presence of the dark lines in the solar spectrum, to assume that the continuous spectrum is produced by the incandescence of a solid or liquid body; for we may with equal right consider that the continuous spectrum is produced by the glowing of a powerfully compressed gas.

This has indeed been experimentally proved by Wüllner for the sodium-lines, inasmuch as he remarks, " Under a pressure of 1230 millims. the maximum of light at Ha becomes less distinct, the whole spectrum is most dazzling, and the sodium-lines are seen as beautiful dark lines‡, so that the light of glowing hydrogen is intense enough to produce in an atmosphere of sodiumvapour a Fraunhofer-line-a proof that the light of a glowing solid is not requisite for this purpose.

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Hence it follows that the radius of the visible solar disk need not be necessarily identical with that of the supposed layer of separation, but that this latter may probably be assumed to lie below the point at which the hydrogen gas under compression evolves a continuous spectrum. The probability of these considerations is much increased by the phenomena of sun-spots. However different even now may be the theoretical speculations as to the nature of the spots, almost all observers agree in admitting that the umbra lies at a lower level than the surrounding parts §. The depth at which the umbra lies has been ascertained, parly by direct (De La Rue, Stewart, Loewy), partly by indirect observations (Faye), to be about 8" ||.

If, therefore, we consider the umbræ the products of a local cooling floating on the surface of a glowing liquid like islands on a glowing ocean, and the penumbra to be condensationclouds which surround these islands or cooler spaces at a certain

*Pogg. Ann. vol. cxxxvii. pp. 336-361.

† See Wüllner, loc. cit. pp. 340–345.

In consequence of the high temperature, the sodium of the glass is volatilized. At 1000 millims. pressure the sodium-lines are seen bright (loc. cit. p. 345).

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§ Spörer, on the contrary, says, we regard the spots as cloud-like forms floating above the bright surface of the sun. The penumbra is nothing more than a collection of small spots, through the interstices of which the bright surface above which the spot is situated can be seen" (Pogg. Ann. vol. cxxviii. (1866), p. 270).

Faye, by calculations from Carrington's observations, finds that this depth corresponds to 0.005-0009 of the sun's radius (Comptes Rendus, vol. lxi. pp. 1082–1090).

elevation*, it appears that the simplest supposition is that the liquid surface required by this theory of the sun-spots is identical with that out of which the protuberances burst forth. The radius of this surface r will be r=R-8" when R signifies the sun's radius expressed in seconds; or taking R at the mean distance of the sun to be 16', we have r=15′ 52". According to Hansen, the mean solar parallax is 8"-915; hence we have r=680,930,000 metres, or 8"=5,722,500 metres. In order, therefore, to be able to obtain a numerical value for the minimum temperature in the space from which an eruption of the height of 1.5 minute breaks out, we have only to substitute the following values in equation (5):

r=680,930,000,

H=64,370,000, A= =3·409.

Hence we find t;=40690°.

If we give H double the above value, or suppose an eruption of 3 minutes (as not unfrequently occurs) to take place, we have a minimum temperature t;=74910°.

We may, however, now inquire whether we are justified in taking the extreme heights of observed protuberances as values for H in our formula, H signifying the height to which a body thrown out from the sun's surface would rise without resistance. If we have really to do with rising masses of glowing hydrogen, as is indeed sufficiently proved, this rise may take place, according to Archimedes's principles, like air heated and made specifically lighter than the neighbouring parts. It is, however, clear that the two conditions of motion will produce a very different effect as regards the time in which the moving masses will reach a given height. Without going more specially into these conditions, it is plain that the time which a protuberance needs in order to rise to a given elevation H, by virtue of the principle of Archimedes, will under all circumstances be greater than that needed to rise to the same height H when moving under the influence of a certain initial velocity and encountering no resistance.

An exact observation of the length of time which a rising prominence takes to reach a given elevation will give a means of deciding whether or not the elevation is reached by the action of the first-mentioned cause; and unless this is proved to be likely, this elevation cannot be used as an integral part of the above formula.

According to the hypothesis which we have made, the outlet whence the protuberance emerges from the glowing layer of

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* I have mentioned this theory, five years ago, in my Photometrical Researches,' p. 245, and also in the Vierteljahrsschrift d. Astron. Ges. Jahrgang iv., H. 3. p. 172; and it is my intention to develope it in a special memoir.

liquid is situated at a depth of h=8" below the visible edge of the solar disk. H signifies the elevation of a protuberance reckoned from the plane of the outlet.

Let signify the time which the prominence requires to rise from the outlet to the height H;

T1 the time which the protuberance needs to rise from the height h (that is, from the visible limit of the photosphere) to the height H;

v the velocity at the outlet;

v1 the velocity at the height h.

Assuming the truth of the first hypothesis, and neglecting the diminution of the intensity of gravity (g), we obtain the following equations:

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√2 (H− h)

,

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v= √2gH, _v1= √2g(H—h).

If we now take

H=64,370,000 metres, h=5,722,600 metres, g=274.3 metres we have

T=11 minutes 25 seconds,

T1=10 minutes 54 seconds,

v = 187,900 metres 25.32 German geog. miles,

v1 = 179,400 metres =27.17 German geog. miles.

If, therefore, we observe in a protuberance an ascensional velocity equal to the above, we are entitled to employ in our equation the elevation which is reached in the above times. I have often observed such a velocity in a protuberance, and have drawn a representation (Plate II.) of a protuberance in which the rate of ascension agrees well with the calculated velocities.

As regards the enormous initial velocities of these eruptive movements, Lockyer, by his beautiful observations of the alteration of the refrangibility of light, came by direct observations to numbers of the same order. During the short period during which these observations have been made, Lockyer* has ascertained that the maximum values of the rate of motion, horizontal and vertical, of a current of hydrogen in the chromosphere reach 40 and 120 miles per second. The above values expressed in English miles are

v=123.1 miles, and v1=117·7 miles ;

and therefore they agree with Lockyer's observations.

* Proc. Roy. Soc. 1869, No. 115.

According to the mechanical theory of heat, such velocities in the case of hydrogen necessitate a difference of temperature amounting to 40690° C. The temperatures themselves may be approximately determined if we can succeed in obtaining any limiting value for t, the temperature of the outer atmosphere of hydrogen. This temperature, as has been already shown, may be taken to be nearly identical with that in the neighbourhood of the outlet.

$ 4.

A limiting value for t may be obtained from equation (V.),

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In this the density σ of the enclosed mass of gas is expressed as a function of the three values ph, h, and t. I shall now show that the value of σ cannot exceed a certain limit; and thus the value of t is also ascertained within a given limit, inasmuch as limits to the values pr and h have been already determined. It has been already pointed out that the explanation of the eruptive protuberances presupposes the existence of a layer of separation, dividing the space out of which the eruptions break forth from that into which they empty themselves. It is only by the existence of such a division that the required difference in pressure is rendered possible.

Respecting the physical constitution of this layer, the further assumption is necessary that it is in some other state than the gaseous. It may be either solid or liquid. In consequence of the high temperature the solid state is excluded; and we must therefore conclude that the layer of division consists of an incandescent liquid.

Respecting the mass of hydrogen enclosed by this liquid layer, two suppositions appear at first sight possible :

1. The whole interior of the sun is filled with glowing hydrogen, and our luminary would appear like a great bubble of hydrogen surrounded by an incandescent atmosphere.

2. The masses of hydrogen which are thrown out in these volcanic outbursts are local aggregations contained in hollow spaces formed near the surface of an incandescent liquid mass, and these burst through their outer shell when the increased pressure of the material in the interior reaches a certain point.

According to the first assumption, a state of stable equilibrium will only occur when the specific gravity of the liquid dividing layer is smaller than that of the gaseous layer which lies immediately underneath it. As, however, the density of a gaseous globe, whose particles obey the laws of Newton and Mariotte,

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