Jour, of Frank. Inst. 
Zcellner’s Rpiral Prominence. 
Plate I. 
F. Zollner del. 
Longacre ft Co., Fhila. 
Geographical Miles. 
FIGURE I. 
Position 160° 
Time, 10* 22m 
1869, August 29. 
FIGURE a. 
The same Protuberance 
Time, 11* 20m F.ZOLLNER; ON THETEMPERATURE AND PHYSICAL CONSTITUTION 
OF THE SUN. 
[ Report of the Royal Saxonian Scientific Association. Mathematical and Physi- 
cal Class. Session of the 2d of June, 1870.] 
| Front tile Journal of the Franklin Institute.] 
Lehigh University, Sept. 15, 1870. 
To the Editors of the Journal of the Franklin Institute. 
GENTLEMEN:—Quite recently I have received from my friend, Prof. 
Zbllner, an important memoir “On the Temperature and Physical 
Constitution of the Sun,” a translation of which I forward you for 
publication in the Journal of the Franklin Institute, which has ever 
kept us so well informed of all that relates to solar physics. 
Prof. Zollncr’s memoir accompanied the following letter: 
“ Leipzig, July 30, 1870. 
To 1\rof. A. M. Mayer, Ph. D. 
“ My Dear Sir:—I have waited until to-day to fulfill the duty 
of answering your agreeable letter and tendering my thanks for 
the reception of the reports of your investigations. I hope you 
will excuse my delay. It was my intention to reciprocate your 
favor by sending you the accompanying report, the completion of 
which required a longer time than I had originally supposed. 
“ At the present time, when Germany is arming for a struggle of 
life and death, and when the waves of national enthusiasm surge 
even into the quiet workshops of science, successful investigations 
are out of the question. I am, therefore, doubly glad that I have 
finished the present work before the beginning of the great catas- 
trophe. It contains a sketch and the principal points of a longer, 
separate treatise upon the sun, which was to follow this report in a 
few months. Under the existing circumstances, however, I will 
probably want the necessary repose to finish it in so short a time. 
“ Receive the assurance of my especial esteem and favor again, 
with a few lines. 
“ Yours, sincerely, F. Zollner.” 
I.—Among the characteristic shapes of the protuberances,* which 
can now be observed at any time with a spectroscope having a 
widened slit, there is a considerable number which must convince 
♦The forms of the protuberances may be divided into two characteristic groups : 
vaporous or cloudy and eruptive. The preponderence of one or the other type 
seems to depend partially on local conditions of the solar surface and partially on 2 
every unprejudiced observer that they are due to violent eruptions 
of incandescent hydrogen. 
It is impossible, without passing beyond the well-known analo- 
gies necessary for the explanation of cosmical phenomena, to assign 
any other cause to these eruptions than the difference of pressure 
of the gases emanating from the interior and from the surface of 
the sun. To make such a difference of pressure possible it is neces- 
sary to admit the existence of a separating stratum between the 
inner and outer strata of hydrogen—the latter of which, as is well 
known, forms an important portion of the solar atmosphere. 
The admission of this separating layer seems inevitable at the 
first sight of the protuberances, even to those observers who, like 
Eespighi, do not deem it improbable that these eruptions are due to 
electrical causes. 
But if we retain the more simple, and, therefore, more natural ex- 
planation by difference of pressure, we will be able to draw import- 
ant conclusions in reference to the temperature and physical struc- 
ture of the sun by following out the mechanical theory of heat and 
of gases. 
From the premises of the mechanical theory for unliquifiable 
gases follow: 
1. Marriotte’s and Gay Lussac’s Laws. 
2. The constancy of the relation of specific heats under constant 
volume and constant pressure. 
This constant quantity, determined for a certain gas by well- 
known methods, must be considered as invariable (like the atomic 
weight of a body), according to the mechanical theory of gases, 
and must not be classified with other empirical constants, such as 
the power of conducting heat, or the coefficient of expansion of solids 
and liquids. These constants are true only within the limits for 
which they have been ascertained by observation, and lose their 
significance if these limits are considerably exceded. 
According to this assumption, I consider the eruptive protuber- 
the time, so that at certain times one or the other type may preponderate. The 
fact that the cloud-like formations remind us so vividly of terrestrial clouds and 
vapors is easily explained, if we consider that the forms of our clouds are not due 
to the vesicles of water suspended in them, but to the manner in which heated 
air in motion expands. 
The vesicles of vapor in terrestrial clouds only form the means through which 
the above-mentioned differences of masses of air become visible. The clouds of the 
protuberances are made visible by the incandescence of glowing hydrogen. 3 
ances as a phenomenon, duo to the flow of a gas from one space into 
another, while the pressure in both is constant, and neither commu- 
nication nor absorption of heat is assumed. 
Let A — the equivalent of heat for a unit of work; 
v — tho velocity of the flow of the gas in the plane of the 
opening; 
g _ the intensity of gravitation on the sun; 
x — the relation of the specific heats of tho gas under con- 
stant pressure and constant volume; 
c — the specific heat of the gas under constant volume, in its 
relation to an equal weight of water; 
t, — the absolute temperature of the gas in the inner space 
from which it emanates; 
— tho absolute temperature of the emanating gas in the 
plane of the opening through which it flows; 
pi — the pressure of the gas in the inner space; 
/>» — the pressure in the plane of the opening. 
According to the mechanical theory of heat these nine mag. 
nitudes bear to each other the following relations:* 
Kt„=xc (*'— <•)> .... [i.] 
' • • • • [2-] 
Furthermore, let a, — be the mean height of the barometer in 
metres of mercury; 
p — the density of the gas at the temperature 
of melting ice under the pressure of the 
column of mercury a, and on the surface 
of the earth; 
n — the density of the gas in the inner space 
under the pressure p\ and at the absolute 
temperature t\; 
a the coefficient of expression of the gas for 
1° C. 
According to Marriotte’s and Gay Lussac’s Law, we have— 
- [3.] 
The pressure pk in the plane of emanation may be considered 
* Zeuner, Elements of the Mechanical Theor}* of Heat. Second edition : 1866, 
p. 165. 4 
equal to the pressure of the solar atmosphere at the level of the 
above-mentioned separating stratum (i. e. at the base of the atmos- 
phere). Then let 
pa = be the pressure at the base of the atmosphere; 
h = a certain height above the base; 
ph = the pressure at this height; 
t =. the absolute temperature of the atmosphere assumed as con- 
stant—the law of temperature not being known ; 
y = the gravity of the sun at the base of the atmosphere; 
r = the radius of the separating stratum ; 
Pj =the specific gravity of mercury at the temperature of melt- 
ing ice; 
y j = the intensity of gravity on the surface of the earth ; 
=the mean height of the barometer; 
P = the density of the gas of the atmosphere at the temperature 
of melting ice and under the influence of the magnitudes 
y, and a 
Then we have by a well-known process: 
log. nat. ( — \ = p g yf , • • • [4.] 
\ / p, y, at (r + hy 
In order to combine this equation with the three preceding ones 
we must assume : 
1. That the principal component of the solar atmosphere, which 
produces the , consists of the same gas which emanates 
from the interior of the sun to form the eruptive protuberances. 
2. That the absolute temperature t, of the atmosphere is equal to 
the absolute temperature at the plane of the opening through 
which the gas passes. 
The first of these assumptions I consider amply justified, because 
the discovery of the so-called chromosphere furnishes the proof 
that the whole surface of the sun is actually enveloped by a consid- 
erable atmosphere of hydrogen. 
I am led to the second assumption by the fact that there is 
scarcely any difference in the brilliancy of the basis of all eruptive 
protuberances from that of the chromosphere. If we consider, 
moreover, that the constant mean temperature t, in formula [4], 
which has been substituted for the temperatures decreasing for the 5 
height h (because the law of the decrease is not known), must cor- 
respond to that of a stratum near the base,* then this temperature 
approaches that of the outer surface of the separating stratum. 
According to the first supposition, P in formula [4] becomes iden- 
tical with that in [3], and according to the second 
t = L. 
IT.—After explaining the theoretical principles necessary to the 
consideration of the solar phenomena, we will now simplify the 
above equations. 
If h is the height to which a body will ascend perpendicularly 
with an initial velocity v on the surface of the sun, we have, con- 
sidering the decrease of gravity : 
v2 = 2 n H —:—, 
J r -f H 
v2 r H 
°r* 2y==r + ll* 
Substituting this value of in formula [1], we have 
_ r H A 
1 x c (r + ll) + k * 
r H A 
or if = a, and according to our supposition /„ «= t, we 
3* C ( V r t A j 
get for formula [I] t{ = a + t. [I.] 
Then let — = —p— = b and —— = m. Then will for- 
* 0 ’ «i “ 
mu las [2], [3] and [4] become 
M*): • • • • m 
* = 67’;, [HI-] 
j,.=Pne bm • • [IV.] 
* In reference to thu incieasing of the air towards the base, the tempe- 
rature in formula [4] (independently of the special law for decrease of tempera- 
ture), must correspond to the temperature of a layer which is lower than-n. This 
difference, which is generally very considerable, as is shown by a simple calcula- 
tion, seems to be generally neglected in determining heights by the barometer (in 
which the moan temperaturo of the two stations is used); and this circumstance 
teems to explain periodical phenomena, observed lately, in a very simple manner. 6 
Prom these we obtain by elimination: 
„ = A& ffL+JVe" . . . [V.] 
a +1\ t '/ 
This equation, therefore, expresses the density a of the com- 
pressed gas only as a function of the three magnitudes y>„, h and t. 
If, therefore, under the above suppositions, we can determine three 
of the four magnitudes by observation or keep them within limits, 
we can obtain the fourth. Now, by means of spectroscopic and 
other observations a, y>h and h can be actually determined within 
certain limits, so that we may also limit t, the temperature of the 
outer hydrogen atmosphere near the glowing liquid separating 
stratum. Substituting this value in [I.] (h being known), we obtain 
a value for the inner temperature t:, and [III.] and [IV.] also yield 
values for p\ andy>a . 
III.—In the discussion of numerical values, I will begin with 
formula [I]. 
The lowest value assignable to t is, of course, 0. Then t\ becomes 
a minimum: 
j rHA 
On account of the fact that the density of the atmosphere almost 
becomes zero, even at a moderate distance from the surface and the 
resulting slight resistance, H may for simplicity be made equal to 
the mean height of the protuberances. The conditions necessary 
for this will be discussed further on. 
Not unfrequently the protuberances attain the height of 3 
minutes. In order to keep within the bounds of a mean value, I 
will take H at T5 minutes. Assuming the metre and degree cen- 
tigrade as units, the equivalent of heat a = ?£5. The product, 
x c, according to the latest researches of Eegnault (Pogg. Ann. 89 
vol.) equals 3*409 for hydrogen. According to Dulong (Ann. de 
Cliem. et de Plugs, t. 41) the value of x for hydrogen equals 1*411. 
The numerical value of r requires a somewhat longer discussion. 
This is the radius of the separating stratum, from which the pro- 
tuberances emanate. Here the question arises whether this value 
coincides with that of the solar radius, i. e.t whether this stratum 
coincides with the boundary of the luminous solar disc used for our 
measurements. 
The latest investigations of Frankland and Lockyer, St. Claire-  7 
Deville and Wiillner liave proved that the broken spectrum of 
hydrogen and other gases may be changed to a continuous brilliant 
one by increasing the pressure. When this is done the bright lines 
of the broken speotum undergo very characteristic changes, which 
consist principally, us in the line II.5, in a widening and increasing 
blurring of outline. 
From these changes we may, within certain limits, draw conclu- 
sions concerning the amount of pressure, as Frankland and Lockyer 
have indeed done. They believe “ that at the lower surface of the 
chromosphere itself the pressure is very far below the pressure of 
the earth’s surface.” 
The investigations of Wiillner, I believe, even justify the as- 
sumption that the pressure at the base of the chromosphere or at 
the extreme edge of the luminous solar disc must be between 
50 mm. and 500 mm. of a mercury barometer on the earth’s surface. 
For this reason the presence of dark lines in the solar spectrum 
on a continuous ground does not necessitate the assumption that 
this continuous spectrum is caused by the incandescence of a solid 
or liquid; for we may with equal right assume that it is due to the 
incandescence of a more highly compressed gas. 
Wiillner has even proved this experimentally for the sodium 
line, and he makes the following observations: 
“At a pressure of 1,230 mm. the maximum at ira falls back still 
further ; the whole spectrum becomes dazzling, and the sodium- 
lines appear as beautiful dark lines;* a proof that the light of 
hydrogen is intense enougli to produce a Fraunhofer’s line in an 
atmosphere of sodium, and that the light of an incandescent solid 
is not necessary.” 
It follows from this that the radius of the visible solar disc is 
not necessarily identical with that of the assumed separating 
stratum, but that the latter probably lies below that stratum, where 
the spectrum of the hydrogen atmosphere becomes continuous by 
increased pressure. • This view is supported by the appearance of 
solar spots. 
Nearly all observers, however different their theoretical opinions 
about the nature of the solar spots, agree in that the nucleus of 
* In consequence of the high temperature of the tube, sodium from the glass 
becomes vaporized. At a pressure of 1 ,< OJ mm. the sodium lines arc still bright, 
(1. c. p. 345.) 8 
these spots must be deeper than their surroundings.* This depth 
is taken at about 8", partially from direct (De la Rue, Steward, 
Loewy) and partially from indirect observations (Faye).f 
If the nucleus of the solar spots is considered as a scoriaceous 
product of local cooling on a liquid surface, and the penumbrse as 
clouds of condensation, which surround at a certain height the 
coasts of these islands of slag,;]: then the simplest supposition is 
that the liquid surface (necessary to support this theory) is iden- 
tical with the surface of the separating stratum in question, from 
which the protuberances burst forth. If e represents the observed 
solar radius in seconds, then the radius r of this surface would be 
approximately, 
r = r — 8". 
Or R at 16' at the mean distance of the sun, r= 15' 52". 
If the mean parallax of the sun is taken at 8" *915, according to 
Hansen, then 
r = 680,930,000 metres; 
therefore, 8" = 5,722,500 “ 
In order to determine numerically the absolute minimum tempe- 
rature in the space, from which an eruption of T5 minutes height 
takes place, we must substitute the following values in fomula [5]: 
r = 680,930,000; 
h = 61,370,000; 
= 1 
A , 421’ 
xc= 3*109. 
Then we will find that 
ti = 40690°. 
If we substitute for H double the above value, whfch would cor* 
* SpSrer, however, says: We consider the spots as cloud-formations above the 
luminous surface of the sun. The penumbra is nothing more than an aggregation 
of small spots, the spaces between which allow the luminous surface to shine 
through, above which the spot is situated.—Pogg. Ann. vol. 128, (1866.) 
f Faye, by computations based on the observations of Carrington, finds that this 
depth is 0 005 — 0 009 of the solar radius.—Comptes. Rendus, LXI., 1082—1090. 
J This theory has been indicated by me in my photometric observations, p. 245, 
five years ago, and further developed last year in the quarterly report of the 
A-strom. Soc., year IV., No. 3, p. 172. I reserve a still further development and 
explanation by means of the spectroscopic observations on solar spots, for a paper 
soon to be published. 9 
respond to a protuberance of 3 minutes height, then the minimum 
value of 
U = 74910°. 
Here, however, the question arises, whether we have a right to 
substitute the extremes of the observed heights of protuberances 
in our formulae for H, which stands for the distance to which a 
body, thrown up vertically from the sun, would rise without resist- 
ance. If we actually have to do with burning masses of hydrogen, 
as observation proves beyond a doubt, their rising may be due 
equally well to Archimedes’ principle, like that of heated gases in 
a chimney, by becoming specifically lighter than the surrounding 
atmosphere. These two causes would, however, differ materially 
in the time necessary for the gaseous masses to reach a certain 
height. Without entering into a special discussion of this point, 
it is clear that the time needed by a protuberance to rise to a given 
height, by Archimedes’ principle, must in all cases be greater than 
by a force throwing it vertically up to the same height without 
resistance and with a certain initial velocity. 
Therefore an observation made as accurately as possible on the 
time required by a protuberance to reach a certain height will 
decide whether this height is due to the former cause, and in that 
case only can the light be used as an integrating component of the 
above formulae. 
According to the supposition, the opening through which the 
protuberances pass, lies in the liquid incandescent separating stra- 
tum at a depth h— 8" under the visible limit of the solar disk. 
H, in the above formula, meant the height of a protuberance from 
the plane of the opening. 
Let * — the time required by the protuberance to reach the 
height, II, from the opening. 
r j = the time required by the protuberance to reach H from h, 
the outer limit of the photosphere. 
v — the velocity at the opening. 
-zq = the velocity at h. > 
Assuming the former cause, and neglecting the decrease of grav- 
ity (g\ we have: 
_ 2 h , 2 (h — h) 
* g 
1=v// — A.) 10 
Assigning the following values: 
h = 64,370,000 in. 
h = 5,722,600 “ 
g = 274-3 “ 
we have 
r = 11 min. 25 sec.; tx = 10 min. 54 sec. 
v = 187,900 m., or 25-32 geogr. miles. 
v, = 179,400 m., = 24*17 “ “ 
If, therefore, we observe such a velocity in a protuberance, we 
are justified in substituting the corresponding height in our formu- 
lae. I have observed such a velocity frequently, and take the 
liberty of placing before you the drawing of a protuberance whose 
velocity corresponds very well with the above. (Figs. 1 and 2, 
Plate I.) 
Lockyer’s* beautiful observation of the change of the refrangi- 
bility of light led him directly to exactly similar magnitudes. He 
found the maximum velocities of streams of gas moving vertically 
or horizontally in the chromosphere to be 40 and 120 English miles 
a second. The above values, reduced to English miles, become 
v — 123T, and v, = 117*7, 
and therefore correspond to those of Lockyer. 
According to the mechanical theory of heat, such velocities of 
hydrogen necessitate differences of temperature amounting to 
40690° C. We may, therefore, ascertain the temperature itself, if 
we can assign certain limits to the temperature, t, of the outer 
atmosphere of hydrogen. It has already explained why this tem- 
perature has been assumed as approximating that of the openings 
through which protuberances pass. 
4. A limit for t may be found from formula Y. 
&Ph fa + t\q bm(.r+b)t 
a~a + t \ t ) e 
In this the density a of the confined masses of gas is expressed as a 
function of j)h, h and t. I shall now show that a cannot exceed a 
certain value, and that, therefore, t is also limited to a certain value, 
jph and h having already been determined. 
It has been shown before that the explanation of eruptive pro- 
tuberances necessitates the existence of a separating stratum between 
the space from which they emanate and the space into which they 
pass. Nothing else would make the differences of pressure possible. 
* Proceed. R. S, No. 115 (1869), and Comp. Rend., T. 69, p. 123. 11 
In reference to its physical condition, we must furthermore assume 
that it cannot be gaseous, and must, therefore, .be either solid or 
liquid. The former being improbable, on account of the high tem- 
perature, we must conclude that the separating stratum consists of 
an incandescent liquid. 
In reference to the inner masses of hydrogen bounded by that 
stratum, two suppositions are possible, viz.:* 
1. The whole interior of the sun is filled with incandescent hy- 
drogen gas, which would make the sun an immense bubble of 
hydrogen surrounded by a liquid glowing envelope. 
2. The masses of hydrogen, bursting out into protuberances, are 
local collections in bubble-like caverns, which form in the superfi- 
cial layers of a liquid glowing mass, and burst through when the 
presence of the confined gas increases. 
Under the first supposition, stablo equilibrium could only exist 
if the specific gravity of the outer layer is less than that of the gas 
below it. Since the density of a globe of gas whose particles are 
subject to Newton’s and Mariotte’s laws increases towards its cen- 
tre, the specific gravity of the outer bounding layer must necessar- 
ily be less than the mean specific gravity of the sun. But if we 
take the mean specific gravity of the sun as the maximum of liquid 
outer layer, we would be obliged to assume that all deeper layers, 
including the gaseous one immediately below, have the same spe- 
cific gravity. 
Then the interior of the sun could not consist of a gas, but of an 
incompressible fluid. All these properties are clearly a neces- 
sary consequence of the supposition that the specific gravity a of 
the compressed gases forming the protuberances reaches as its 
maximum the mean specific gravity of the sun. 
In that case, we must suppose, secondly, that the sun consists of 
an incompressible liquid, near whose surface there are collections 
of glowing masses of hydrogen, which break through bubble-like 
caverns as eruptive protuberances under certain differences of 
pressure. 
However small these caverns may be in special cases, the speci- 
fic gravity of the enclosed gases cannot be greater than that of the 
* The phenomenon of tho formation of bubbles cannot be adduced as an argu- 
ment ngainst this, because tho conditions are entirely different, since the molecular 
attraction of the envelope keeps the confined gases in equilibrium, and the gravi- 
tation of the particles disappears. In the above case, the very opposite takes 
place. The molecular attraction is insignificant, compared with the gravity of 
the mass. 12 
surrounding liquid, because, otherwise the compressed gases would 
sink towards the interior of the sun. 
The specific gravity of the sun, according to the latest determi- 
nations, is T46. If this is substituted for o, 40690 for a in (Form. 
Y.) and 8" in metres for 7i, then, if 
ph = 0-500 m. t — 29500° 
and if = 0-050 m. t — 26000° 
mean value, t = 27700°. 
If equation (5) is differentiated with respect to t, then becomes 
negative, i. e., a decreases for increasing values of t. Hence it fol- 
lows that the above values for t are also minima. 
From this mean value of t, for the temperature of the solar atmo- 
sphere, the value of^h is found to be 0T80 m. These values are 
the basis of the following calculations:— 
The temperature found is about 8 times higher than that result- 
ing from the combustion of an explosive mixture, (Bunsen “On the 
Temperature of Carbonic Oxide and Hydrogen Flames,” Pog. An., 
CXXXI., p. 172,) and iron must exist, as a permanent gas, in the 
solar atmosphere. 
With the value t = 27700°, the inner temperature in formula (I) 
becomes U = 68400°. 
If the values of t\ and t are substituted in formula (II) we obtain 
—= 22-1, 
Pa 
i. e., the pressure in the interior of the space from which the pro- 
tuberances emanate is 22*1 times greater than the pressure at the 
surface of the liquid separating layer. If the value of t is substi- 
rp 
tuted in formula (IV) and h is taken at 6" as before, — = 766,000, 
' Ph 
the relation of the pressure on the liquid surface of the sun to that 
at the height, A, where the hydrogen spectrum begins to become 
continuous on account of the pressure. 
If, for ph we substitute the above value of 0 180 metres of mer- 
cury, get 
y>a= 184,000 atmospheres, 
and p-i = 4,070,000 
If we calculate the depth at which the maximum pressure of 
pi would be reached in the liquid solar mass of 1'46 specific gravity 
in consequence of hydrostatic pressure alone, we will find that it 13 
will take place at a depth of 139 geographical miles below the sur- 
face, t. e., in a depth of 146 seconds of arc, or eJ8 of the suns 
radius. 
Even if we neglect to consider the liquid state, and calculate that 
depth where the atmospheric pressure becomes equal to the inter- 
nal pressure, />,, assuming a much greater atmospheric envelope of 
hydrogen, we will find, even with a temperature of 68,400°, that it 
will be only 27" under the visible edge of the solar disk, or about 
s'a of the apparent solar radius. 
This shows how rapidly the pressure must increase towards the 
interior of the sun, and justifies the assumption, that even at such 
enormous temperatures permanent gases, as, for instance, hydrogen, 
can only exist in a liquid glowing state in the interior of the sun. 
5. An interesting result is obtained if we calculate the pressure 
in an atmosphere of nitrogen and oxygen,equal in weight and tem- 
perature to the above hydrogen atmosphere, at the height where 
the hydrogen spectrum'becomes continuous. If we suppose the 
pressure of the three atmospheres of h, o and N, to be equal, (pH=. 
1S4,000 atmospheres, which would correspond to the above value 
of pi,,) at a depth of 8" under the visible edge of the solar disk, i. e., 
at the level of the supposed separating stratum, when at the calcu- 
lated temperature of 27,000°, the pressure of each of the three 
atmospheres on the surface of the visible solar disk would be as 
follows: 
Hydrogen, p,, — 180 millimetres. 
Nitrogen, ph — 323 “ 
Oxygen, ph «= 124 —g “ 
Hence it follows, that under the above suppositions, the quantity 
of the last two gases must be considered as extremely small, com- 
pared with that of hydrogen, in that stratum where the spectrum 
of hydrogen becomes continuous. This would even be so if we 
should assume the weight of the two atmospheres as many million 
times greater, although, according to their specific gravities of 
the quantity of nitrogen and 1,g of oxygen would suffice to make 
the density of these gases at the base equal to that of hydrogen. 
The mean specific gravity of the sun would Lave to be taken as 
the maximum of density at the base of these atmospheres, and we 
can easily calculate from formula (III) and the known specific 14 
weights of oxygen and nitrogen what the weight of these atmo- 
spheres would have to be in order to reach that maximum. 
The result shows that the weight of the atmosphere of oxygen 
would only have to be 0 56, and of nitrogen 0'64 that of the hydro- 
gen atmosphere. 
If we suppose the simultaneous presence of all three gases on 
the surface of the sun, and neglect for the present the influence of 
the motion of the atmosphere, the rays emanating from these strata 
which give a continuous hydrogen spectrum, would pass through 
so slight a quantity of glowing oxygen and nitrogen that the ab- 
sorption would be insignificant, and the presence of o and N would 
not be indicated by dark lines in the spectrum, as is actually the 
case. 
Although the motion of the gases would tend to diminish the 
above differences, the existence of the chromosphere proves the 
slightness of this influence in consequence of the intensity of gravi' 
tation and the great height of the stratum in question. (Compare 
Form. 4.) 
In order, however, to explain the absence of lines of two such 
universally diffused bodies as N and o in the solar spectrum, we 
must also consider the slight emissive power of permanent gases 
as compared to that of vaporized solids. 
If we consider the emissive power of different gases at the same 
temperature, and for rays of the same refrangibility, with reference 
to very small quantities of these gases,* the above experiment of 
Wiillner, in which the slight quantity of sodium vaporized from 
the glass of a Geissler’s tube emitted more light than hydrogen 
under 1,000 mm. pressure, furnishes the most beautiful proof of 
the exceedingly great difference in the emission and (according to 
Kirchhoff’s law of the) absorbing power of different gases at the 
same temperature. This will answer the objection to the above 
explanation of the absence of N and 0 lines, that the solar spec- 
trum contains the lines of bodies, the density of whose vapors is 
much greater, in consequence of their relation to the atomic weights, 
than that of oxygen and nitrogen. 
From these considerations we obtain either directly or indirectly, 
by deductions, the explanation of which I reserve for another place, 
the following conclusions: 
* We assume here the perfect transparency of the gas for the rays emitted by 
it; an assumption which comes nearer the truth the smaller the compared quan- 
tities of gas are. 15 
1. The absence of lines in the spectrum of a self-luminous star 
does not prove the absence of the corresponding bodies. 
2. The stratum, in which the reversion of the spectrum takes 
place, is different for every body, and lies the nearer to the centre 
of a star the greater the density of the vapor and the less the emis- 
sive power of the body is. 
3. In different stars this stratum, other things being equal, lies 
the nearer the centre the greater the intensity of gravitation. 
4. The distances of the strata of reversion for different bodies 
from the centre of the star and from each other increase with the 
temperature. 
o. The spectra of different stars contain the more lines, under 
similar circumstances, the less their temperature and-the greater 
their mass is. 
6. The great difference of intensity in the dark lines of the spec- 
trum of the sun and other fixed stars depends not only on the dif- 
ferences of absorption but also on the different depths at which the 
reversion of the spectra takes plase. 
In conclusion, I may be permitted to make a few remarks con- 
cerning the application of experiments with rarified gases to the 
heavenly bodies. Lecoq de Boisbaudran (Comp)t. Rcncl., t. 70, p. 
1091, 10 Mai, 1870,) has recently stated (with reference to Wiill- 
ner's investigations of rariability of spectra by pressure and in- 
crease of temperature,) that we should be cautious in applying the 
results so obtained to the consideration of the solar atmosphere, 
because the changes of the spectra were due far more to tempera- 
ture than to pressure. Even supposing that this would be verified 
by experiment, it would only slightly influence the results in the 
present dissertation. For, the nature of formula [5], by which the 
temperature of the atmosphere was obtained, is such that the pres- 
sure pllt at which the spectrum of hydrogen becomes continuous, 
may be very considerably changed without greatly changing the 
temperature. We have seen that pressures standing to each other 
as 1: 10 would produce values of temperature standing as 1: T15. 
Nevertheless, the separation of the influences exercised by pres- 
sure and temperature on the spectra of luminous gases must be con- 
sidered as a problem, whose solution is of the highest importance. 
Perhaps we shall be able by application of the well-known law 
of the heating power of galvanic currents and the law of Gay Lus* 
sac so to regulate the pressure of the gas by changing the level of 16 
mercury that the increase of pressure produced by the temperature 
during a stronger discharge is compensated by a diminution of 
pressure produced previous to the discharge. In this way the 
pressure would be kept constant, and we would be able to inves- 
tigate the effect of changes of.temperature on the spectrum without 
knowing the temperature itself. In this we would neglect the loss 
of heat caused by conduction and radiation during the short space 
of the discharge, and make the heat developed in the current ap- 
proximately proportional to the temperature of the glowing gas. 
If the mass of the gas is known we can calculate the maximum ab- 
solute temperature of the glowing gas from the time and tempera- 
ture of the discharge.