ee 
Oct. 27, 1870] 
NATURE E 
523 
becomes identical with the analogous one in (3), and, in conse- 
quence, of the second 
(2.) 
t=, 
The theoretical foundations and essential assumptions ne- 
cessary for the treatment of the phenomena in question on the sun’s 
surface having been explained, a reconstruction and simplification 
of the above equations, more suitable to the object in hand, may 
well follow. 
If H denote the height to which a body with the initial velocity 
wv on the sun’s surface is hurled up in a vertical direction, then, 
taking the diminution of gravity into account, we have : 
2? = ae _* 
Sega! 
or, 
ee ap 
2g r+H 
This value substituted for _ in Equation (t) gives : 
gf 
o> 
rHA 
i= ——_ + fa; 
* x¢\(r-+ 4H) st 
7HA 
“xeL(r + A) 
%, = 4, we obtain the following for Equation (1) : 
or ta’-ing = a, and, according to our assumption, 
&f=at+?e (1.) 
Further, let 
Se ee 
oa q 
aE AE 
aya 
£ = Mm 
1P1 
The Equations (2) (3) (4) become then converted into the following : 
Z. Di I 
Ses |f AES II. 
z es dh ee) 
c= 4 fi (111. ) 
4. 
h 
bm , 
oe EERE eS] 
In addit‘on there is obtained from these four equations by 
elimination the following : 
g 
i Bi, (2+4)6 bm 
a@+t zt 
rh 
(7 + A)t 
(v.) 
This equation, of course, expresses the density, , of the com- 
pressed mass of gas only as a function of the three magnitudes 4, 
h, and ¢; if, therefore, under the assumptions made, three out of the 
four values considered can be determined by observation, either 
positively or within certain degrees, the fourth can then be 
determined. And in fact, partly by spectroscopic, partly by other, 
observations, fixed extreme values can be obtained for the magni- 
tudes ¢, #,, and /, so that thus a limit for 4, that is to say, for the 
outer hydrogen atmosphere in the neighbourhood of the in- 
candescent liquid separating layer, is also obtained. This value 
substituted in Equation (1) the value of H being known, gives 
then at once a value for the inner temperature 4, and from 
(111.) and (tv.) fixed values for #; and f, can be obtained with equal 
ease. 
3 a Pas : 
Now to proceed, however, to the discussion of numerical | 
values, I will commence with Formula (I.) 
The lowest value which can be attached to ¢ is evidently o. 
We then obtain for the inner temperature 4 the minimum 
yalue : 
pe rHA (s) 
xe (r+ H) 5 
Having regard to the extreme tenuity, and therefore slight re- 
sistance, of the atmosphere even at a very moderate distance from 
the sun’s surface, the value of H may, for the sake of simplicity, be 
put as equal to the mean height of the eruptive protuberances. 
f= 
A more detailed discussion of the conditions under which this is 
allowable will be given later. 
Protuberances three minutes high are not of very rare occur 
rence ; to keep, however, as close as possible within the limit 
of an estimation of mean value, I will assume H to be only 1° 
minutes. 
Adopting the metre and centigrade degree as units, I take the 
heat equivalent A as zy. The product xe is, according to the 
latest researches of Regnault, for hydrogen 3°409. According to 
Dulong, the value of x for hydrogen is 1°411. 
The numerical value of requires a somewhat more detailed 
discussion. It is, according to the preceding, the radius of the 
separating layer from which the protuberances break forth, 
There then arises the question, whether this value agrees with 
that of the sun’s radius; that is, whether this separating layer 
coincides or not with the portion of the sun’s luminous disc, which 
we have made use of for our measurements. 
The late researches of Frankland and Lockyer, St. Claire, 
Deville, and Wiillner have proved that the discontinuous spec- 
trum of hydrogen and other gases can, by increase of pressure, 
be converted into a bright luminous and continuous spectrum, 
the bright lines of the discontinuous spectrum passing through a 
series of very characteristic changes, on the pressure being 
gradually raised, which principally, as for instance by the line 
HA, consist in a widening out and increasing indefiniteness of 
outline. 
These changes permit within certain limits an estimation of the 
intensity of the pressure on the spot in question, and Frankland 
and Lockyer have already hazarded such conclusions. They 
arrive at the result ‘‘ that at the lower surface of the chromo- 
sphere the pressure is very far below the pressure of the earth’s 
atmosphere.” : 
The researches of Wiillner, I believe, allow even the con- 
clusion that the pressure at the base of the chromosphere, or at the 
outer edge of the sun’s luminous disc, must lie between 50mm. and 
500mm. of a mercury barometer on the earths surface. 
According to this, the presence of dark lines on a continuous 
ground in the sun’s spectrum no longer compels the conclusion 
that this continuous spectrum is caused by the incandescence of 
a solid or liquid body. The continuous spectrum can equally well 
be considered as produced by the incandescence of a strongly 
compressed gas. 
Wiillner has, in fact, proved this for the sodium line; for in 
his account of the above-mentioned researches he remarks :— 
““At a pressure of 1230mm. the maximum at H, recedes 
still further ; the whole spectrum is truly dazzling; the sodium 
lines appear as beautiful dark bands ;* consequently, the light of 
hydrogen gas is sufficiently intense to produce a Fraunhofer’s 
line in a sodium atmosphere—a proof that the light of an incan- 
descent solid is not necessary.” 
From this it follows that the radius of the visible portion of the 
sun’s disc need not be considered as identical with that of the 
supposed separating layer, but that the latter probably must be 
looked upon as situated beneath the layer where, through in- 
creased pressure, the spectrum of the hydrogen atmosphere 
becomes continuous. This view is strongly supported by a con- 
sideration of the phenomena of the sun’s spots. 
However different the views as to the nature of the sun’s spots 
may be, almost all observers agree that the nuclei of the spots 
must lie deeper than the surrounding portion.+ Partly from 
direct (De La Rue, Stewart, Loewy), partly from indirect (Faye) 
observations the depth is assumed to be about 8”.¢ 
If, then, the nuclei of the sun’s spots are considered as scoria- 
ceous products of a local cooling down on an incandescent liquid 
surface and the penumbra as clouds of condensation, which at a 
certain height crown the coasts of these slag islands, the simplest 
assumption is, that the (according to this theory) necessarily 
liquid surface is identical with the surface of the separating layer 
in question from which the protuberances break forth. The 
radius 7 of this surface therefore, the observed semi-diameter of 
the sun being expressed in seconds, would be approximately— 
r=R-8" 
2 Toe 
* Tn consequence of the high temperature in the tubes, sodium volatilises 
out of the glass. At a pressure of 1ooomm. the sodium lines are still 
luminous. 
+ Spoerer says, however, “‘ We consider the spots to be cloudlike forma- 
tions far above the luminous surface of the sun’s body. The penumbra is 
simply a collection of smaller spots, through the spaces between which the 
luminous surface is visible above which the spot is situated.” (Comp. Pogg. 
Ann. Ixxviii. 270.) : : ? 
t From calculation of Carrington’s observations Faye finds this depth t 
be ‘oo5 — ‘oog of the sun’s radius. (Comp. Rend. Ixi. 270.) 
