XLI. On the Temperature and Physical Constitution of the Sun. By Professor F. ZÖLLNER*.

[With a Plate.]
§ 1.

AMONG the characteristic forms of the protuberances +

which the spectroscope used with wide slit now enables every one to examine, a considerable number convince the observer at once that we have here to do with enormous eruptions of incandescent hydrogen.

Without stepping beyond the range of known analogies, and therefore of conditions explanatory of cosmical phenomena, it is scarcely possible to find a cause for these eruptive protuberances other than that of a difference of pressure between the gases in

* Translated from a separate impression, communicated by the author, from the Proceedings of the Royal Saxon Society of Sciences, June 2, 1870. †The protuberances may be classed in two characteristic divisions, according to their shapes, viz. into the vapour- or cloud-forms, and the eruptive forms. The predominance of the one or of the other type appears to depend partly upon local conditions of the solar surface and partly upon periodic variation; so that at one time one type may prevail, whilst at another time the other type may be most strongly developed. It is easy to see why the cloudy prominences so closely correspond in form to terrestrial clouds and vapours, when we remember that the forms of our clouds depend not upon the suspended vesicles of water, but upon the mode in which different masses of heated and moving air are distributed. The vesicles in terrestrial clouds form only the material by means of which this difference in the masses of air is rendered visible. The clouds of the solar protuberances are rendered visible by the light emitted by the masses of glowing hydrogen,

Phil. Mag. S. 4. Vol. 40. No. 268. Nov. 1870.

Y

the interior and those on the surface of the sun. The possibility of such a difference of pressure, however, necessitates the existence of a zone of separation between the interior and exterior masses of hydrogen, the latter of which has been shown to form an essential portion of the solar atmosphere.

The supposition of such a layer of separation is so forcibly impressed on the mind on the first sight of such an eruptive protuberance, that it even suggests itself to observers who, like Respighi, suppose that electricity may be the cause of these solar volcanic phenomena.

If, however, we admit only the simpler and therefore more probable hypothesis of the difference of pressure, we have before us a phenomenon which, by the application of the mechanical theories of heat and of gases, may be made to yield us most important conclusions concerning the temperature and physical constitution of the sun. The object of the present communication is to exhibit the fertility of this mode of attacking the question.

The mechanical theory proves for perfect gases:

(1) The law of Mariotte and Gay-Lussac.

(2) The constant relation of specific heat with constant volume and with constant pressure.

These constants, determined by means of well-known methods for a given gas, must therefore, from the point of view of the mechanical theory of gases, be considered unalterable, in the same way as the atomic weight of the elements; and they certainly must not be placed in the category of other empirical constants, such as the conductive power of bodies for heat, or the coefficients of expansion of solid or liquid bodies. These constants only apply within the limits for which they have been ascertained by experiment, and altogether lose their significance when applied far beyond these limits.

Upon this assumption I consider the eruptive protuberances as a phenomenon of the issue of a gas from one space to another, in such a way that the pressure during the issue in both spaces is supposed to be constant, and so that no absorption or evolution of heat occurs.

Let A signify the heat-equivalent of the unit of work;

v the initial velocity of the gas in the plane of the outlet; 9 the intensity of gravity on the sun;

κ the relation of the specific heat of the gas with constant pressure and constant volume;

c the specific heat of the gas with constant volume reduced to an equal weight of water;

t; the absolute temperature of the gas in the interior space whence the gas issues;

to the absolute temperature of the issuing gas in the plane

of the outlet;

P. the pressure of the gas in the interior;"

Pa the pressure in the plane of the outlet.

Ρα

According to the mechanical theory of heat, and upon the above-mentioned hypotheses, the following relation holds good between these nine quantities*:

2g

(1).

(2)

Further, let

a, signify the mean height of the barometer in metres of

ρ

mercury;

the density of the gas under consideration at the temperature of melting ice, and under the pressure of the column a, on the earth's surface;

o the density of the gas in the interior space under the pressure p; and at the absolute temperature t1;

a the coefficient of expansion of the gas for 1° C.

According to Mariotte and Gay-Lussac's law we have, therefore, the following relation,

The pressure pa in the plane of the outlet may, according to our assumptions, be considered to be equal to that exerted by the solar atmosphere at the level of the layer of separation, or at the lowest point of the atmosphere.

Let pa signify the pressure at the lowest point of the atmosphere; h a given height above this point;

Ph the

pressure at this height;

t the absolute temperature of this atmosphere assumed to be constant throughout in the absence of knowledge of the laws of temperature;

g.the gravity of the sun at the bottom of its atmosphere; r the radius of the layer of separation;

P1 the specific gravity of mercury at the temperature of melting ice;

9, the intensity of gravity at the earth's surface;

a the mean height of the barometer;

p the density of the gas forming the atmosphere at the temperature of melting ice and under the action of g

and a1.

* Zeuner, Grundzüge der mechanischen Wärmetheorie, 2te Aufl. 1866,

p. 165.

We then have the following relation :

log nat (Pa) =

pgrh
Pigia,at (r+h)*

(4)

In order to connect this equation with the three previous ones, a twofold hypothesis must be made:

(1) That the chief constituent of the solar atmosphere exerting the pressure pa consists of the same gas which issues from the interior of the sun during the activity of the eruption.

(2) That the absolute temperature t of the atmosphere may be supposed mainly to correspond with the absolute temperature ta at the level of the point from which the gas issues.

I consider that the first of these assumptions is sufficiently proved by observation to allow of its use for the purposes of the present memoir, inasmuch as the discovery of the chromosphere has proved that the whole surface of the sun is surrounded by a very considerable atmosphere of hydrogen gas. The admissibility of the second assumption I deduce from the fact that in general the intensity of the light of the base of all the eruptive prominences is not essentially different from that of the chromosphere.

If it be remembered that the constant mean temperature t in formula (4) (which, owing to our ignorance of the law of decrease of temperature, has been substituted for the temperatures sinking to the elevation h)* must nearly coincide with that of the lowest portions of the atmosphere, it will be seen that this temperature must nearly approach that of the outer surface of the dividing layer.

According to the first supposition, the value p in the fourth formula will become identical with the corresponding value in formula (3); and according to the second supposition we have t=ta.

$ 2.

Having in the foregoing stated the theoretical basis and the most essential hypotheses upon which the phenomena under consideration are to be treated, it will now be advisable to look to

h

2

* With reference to the increasing density of the air as the lowest layer is approached, the temperature expressed in formula (4) must, independently of the particular law of diminution of temperature, always agree with that of a layer lying deeper than This difference, which, as a simple calculation shows, is generally very considerable, appears to me to have been lost sight of in barometric measurements of heights where the mean temperature of both stations has been used; and this circumstance may suffice to explain simply many periodic phenomena which have been lately insisted on.

a simplification and alteration of the above formula rendering them more suitable for the question under consideration.

If H represent the height to which a body possessing the initial velocity v can be thrown up vertically from the sun's surface, we have

v2 TH r+H' 2gr+H

=

kc(r+H)

=a and, according to our hypothesis, t。=t, we

the equations (2), (3), and (4) will read as follows:

=-> =b, =m,

9

(I.)

rh

bmht.
(r+h)t.

This equation therefore expresses the density σ of the compressed gas as a function of the three values ph, h, and t. If, therefore, three of these four magnitudes can be ascertained by observation, or if certain limits can be assigned to their values, the fourth can be determined. In fact it is possible, partly by spectroscopic and partly by other means of observation, to determine certain limiting values for σ, ph, and h; so that a limit can also be obtained for the value of t—that is, for the temperature of the outer atmosphere of hydrogen in the neighbourhood of the glowing liquid layer of separation. This value, substituted in equation (I.), then gives, when H is known, a value for the internal temperature t; and in the same way the values of Pi and Pa can be obtained from equations (III.) and (IV.).