522 
NATURE 
PROF, ZOELLNER ON THE SUN’S TEMPERATURE 
AND PHYSICAL CONSTITUTION * 
AMONG the characteristic forms of the protuberances + the 
observation of which the spectroscope with widened slit has 
rendered possible at all times, is to be found a not inconsiderable 
number of such, whose appearance at once conveys the con- 
viction to every impartial observer that we have hereto deal 
with vast eruptions of incandescent hydrogen masses. 
It is probably impossible, without quitting the range of known 
analogous occurrences and at the same time the conditions ex- 
planatory of cosmical phenomena, to assume any other cause of 
these eruptions than the difference of pressure of the issuing gas 
in the interior and on the surface of the sun, The possibility of 
such a difference of pressure presupposes, necessarily, the ex- 
istence of a separating layer between the inner and outer masses of 
hydrogen, the latter of which, as is known, form an essential 
constituent of the sun’s atmosphere. 
The assumption of the existence of such a separating layer is, 
at first sight of the above-mentioned protuberance phenomena, 
so cogent that it even foices itself as undeniable upon observers 
who, like Respighi, do not hold it to be improbable that electrical 
forces could be the cause of such eruptions. 
Keeping, however, to the more simple and therefore more 
natural assumption of a difference of pressure, we have to deal 
with a phenomenon which, on the application of the mechanical 
theory of heat and gases, is capable of yielding most important 
information as to the temperature and physical constitution of 
the sun. 
For perfect gases the mechanical theory infers from its pre- 
mises, —firstly, the law of Mariotte and Gay-Lussac ; secondly, 
the constancy of the relation of the specific heats at constant 
volume and constant pressure. 
This constant, therefore, when determined according to known 
methods for a definite gas, must, from the point of view of the 
mechanical theory of gases, be considered, similarly to the 
atomic weight of a body, as invariable, and must on no account 
be placed in the category of other empirical constants, such as 
the conducting power of bodies for heat, or the co-efficient of 
expansion of solid and liquid bodies, &c. These constants only 
hold good within those limits within which they are determined 
by observation, and lose their significance when employed far 
beyond those limits. 
Under this supposition I consider the eruptive protuberances as a 
phenomenon of the efflux of a gas from one space into another, the 
pressure in both spaces during the discharge being assumed constant, 
and neither a communication nor an abstraction of heat as taking 
place. 
Let A be the heat-equivalent of the unit of work, 
v the velocity of efflux of the gas in the plane of the opening, 
g the intensity of gravity on the sun, 
x the relation of the specific heats of the gas at constant pres- 
sure and constant volume, 
c the specific heat of the gas at constant volume referred to an 
equal weight of water, 
z, the absolute temperature of the gas in the inner space, 
from which the efflux takes place, 
z, the absolute temperature of the issuing gas in the plane of 
the discharge opening, 
; the pressure of the gas in the inner space, 
?, the pressure in the plane of the discharge opening. 
Then, according to the dynamical theory of heat, we have, under 
the assumptions which have been made, the following two rela- 
tionst between these nine magnitudes :— 
* T. Ziliner. Ueber die Temperatur und physische Beschaffenheit der 
Sonne. Werichte Kén, Sachs, Gesellschaft der Wissenschaften. Sitzung 
am 2 Juni, 1870. 
+ The forms of the protuberances may be divided into two characteristic 
groups—into the vapour- or cloud-like and into the eruptive formations. The 
preponderance of the one or the other type appears partly to be dependent 
on local conditions on the surface of the sun, partly on the time, so that at 
particular periods the one, at others the other, type preponderates. The 
striking resemblance of the cloud-like formations to terrestrial clouds is 
readily explained, when it is considered that the forms of our clouds are due, 
not to the particles of water suspended in them, but essentially to the 
nature and manner in which the differently heated and agitated masses 
of air are spread out. The particles of aqueous vapour are, in terrestrial 
clouds, simply the material by means of which the above-mentioned differ- 
ences between the masses of air are rendered evident tous. The glow of 
the incandescent masses of hydrogen is the cause of the visibility of the 
clouds of the protuberances. 
} Zeuner, Grundziige der mechanischen Warmetheorie. 2 Au 1°66, p. 165. 
gu 2 — 
ae = xe( 4 4.) (1) 
Z Bi — 
4, Ba a 
Further, let 2, be the mean height of the barometer in metres 
of mercury, 
p the density of the gas under consideration at the tempera- 
ture of melting ice, and under the pressure a, on the 
earth’s surface, 
o the density of the gas contained‘in the inner space under 
the pressure ;, and at the absolute temperature 4, 
a the coefficient of expansion of tle gas for 1° C. 
Conformably to the law of Mariotte and Gay-Lussac, we 
then have also the following relation :— 
a 
Le ies (3) 
a,a 
The pressure p, in the plane of the discharge opening may, 
under the suppositions made, be considered as identical with 
the pressure which the atmosphere of the sun exercises at. the 
niveau of the above-mentioned separating layer, z¢., at its 
base. 
Let, in this case, 
f, be the pressure at the base of the atmosphere, 
A acertain height above the base, 
py the pressure at this height, 
¢ the absolute temperature in the atmosphere, which, in 
consequence of insufficient knowledge of the law of tem- 
perature is assumed to be everywhere constant, 
g the gravity of the sun at the base of the atmosphere, 
y the radius.of the separating layer, 
p, the specific gravity of mercury at the temperature of 
melting ice, 
g, the intensity of gravity on the earth’s surface, 
a, the mean height of the barometer, 
p the density of the gas composing the atmosphere at the 
temperature of melting ice, and under the influence of the 
quantities g, and a, ; 
we then obtain, by a known method of deduction, the following 
relation, 
x 
Pa BL h ( 4) 
Pn /481a, at (7 + h) 
In order to combine this with the three previous equations, a 
double assumption must be made : 
First, that the essential constituent of the sun’s atmosphere, 
which produces the pressure /,, consists of the same gas as 
escapes from the interior of the sun during eruptive pro- 
tuberances. 
Secondly, that the absolute temperature ¢ of the atmosphere, 
may be considered as essentially agreeing with the absolute tem- 
perature at the zzveau of the opening during the discharge. 
Having regard to the object of the present memoir, I con- 
sider the admissibility of the first assumption as_ sufficiently 
established by observations, since the discovery of the so-called 
chromosphere has given the proof that the whole surface of the 
sun is surrounded by an atmosphere of hydrogen of very con- 
siderable extent. 
The correctness of the second assumption I infer from the 
luminosity of the base of all eruptive protuberances not differing to 
any extent from that of the chromosphere. _\Nhen it is considered 
that the constant mean temperature ¢ in Formula (4), which, in 
consequence of the want of knowledge of the law governing the 
decrease of temperature, is substituted for the temperatures fall- 
ing with the height 4, evidently must correspond to a layer near 
the base,* this temperature becomes at the same time approxi- 
mated to that belonging to the outer surface of the separating 
layer. 
By virtue of the first assumption, the value p in Formula (4) 
log. nat. 
* With regard to the increasing density of the layers of air towards the 
base, the temperature introducediinto Formula (4) must, apart from the special 
law for the decrease of temperature, always agree with the temperature of a 
layer which lies deeper than “ This difference, which, as a simple calcu- 
2 
lation shows, is in general a very considerable one, seems to me to be 
entirely disregarded in the barometrical estimation of heights, in which, as 
is known, the mean temperature of the two stations is made use of, and to 
give a simple explanation of certain periodical phenomena which have lately 
been urged, 
