Oct. 5, 1871 | 

THE TEMPERATURE OF THE SUN 
HE increase of the volume of atmospheric air, under 
constant pressure, being directly proportional to the 
increment of temperature, while the coefficient of expan- 
sion is 0'00203 for 1° of Fahrenheit, it will be seen that a 
temperature of 3,272,000° Fah. communicated to the 
I 
664 
of the existing density. Accordingly, if we assume that 
the height of our atmosphere is only 42 miles, the eleva- 
tion of temperature mentioned would cause an expansion 
increasing its height to 6643 x 42 = 279,006 miles. This 
calculation, it should be observed, takes no cegnizance of 
the diminution of the earth’s attraction at great altitudes, 
which, if taken into account, would considerably increase 
the estimated height. Let us now suppose the atmosphere 
of the sun to be replaced by a medium similar to the 
terrestrial atmosphere raised to the temperature of 
3,272,000°, and containing the same quantity of matter as 
the terrestrial atmosphere for corresponding area. Evi- 
dently the attraction of the sun’s mass would under these 
conditions augment the density and weight of the supposed 
atmosphere nearly in the ratio of 279 : 1; hence its 
279,006 
ar 
terrestrial atmosphere would reduce its density to 
height would be reduced to = 10,000 miles, But 
if the atmosphere thus increased in density by the sun’s 
superior attraction consisted of a compound gas princi- 
pally hydrogen, say 1°4 times heavier than pure hydrogen, 
the height would be 10 X 10,000 = 100,000 miles. The 
pressure exerted by this supposed atmosphere at the 
surface of the photosphere would obviously be 14°7 X 2779 
= 410 pounds per square inch, nearly. Unless, therefore, 
the depth greatly exceeds 100,000 miles, and unless it can 
be shown that the mean temperature is less than 
3,272,000° Fah., the important conclusion must be ac- 
cepted that the solar atmosphere contains so small a 
quantity of matter that notwithstanding the great depth 
it will offer only an insignificant resistance to the pas- 
sage of the solar rays. Now, the assumed mean tempe- 
rature, 3,272;000°, so far from being too high, will be found 
to be considerably underrated. It will be recollected that 
the temperature at the surface of the photosphere, deter- 
mined by the ascertained intensity of solar radiation at 
the boundary of the earth’s atmosphere, somewhat exceeds 
4,035,000°. Consequently, as the diminution of intensity 
caused by the dispersion of the rays, will be inversely 
as the convex areas of the photosphere and the sphere 
formed by the boundary of the solar envelope, viz., 
1°52 ; 1, the temperature at the said boundary will be 
4,035,000° 
1°52 
The true mean, therefore, will be 3,344,800’, instead of 
,272,000° Fah., a difference which leads irresistibly to 
the inference that, either the solar atmosphere is more than 
100,000 miles in depth, or it contains less matter than the 
terrestrial atmosphere, for corresponding area. It will be 
demonstrated hereafter that the retardation of the rays pro- 
jected from the border of the photosphere consequent on 
the increased depth of the solar atmosphere (supposed to be 
the main cause of the observed diminution of energy near 
the sun’s limb), cannot appreciably diminish the intensity 
of the radiant heat. The ratio of diminution of the 
density of the gases composing the solar atmosphere at 
succeeding altitudes, is represented by Fig. 5, in which the 
length of the ordinates of the curve a @ 0 shows the degree 
of tenuity at definite points above the photosphere. This 
curve has been constructed agreeably to the theory that the 
densities at different altitudes, or what amountstothe same, 
the weight of the masses incumbent at succeeding points, 
decreases in geometrical progression as the height above 
the base increases in arithmetrical progression. The 
vertical line @ c has been divided into 42 equal parts, 
in order to facilitate comparisons with the terrestrial 
= 2,654,600° 
NATURE 

449 

atmosphere, the relative density of which, at corre- 
sponding heights, is obviously as correctly repre- 
sented by this diagram as that of the solar atmo- 
sphere. It is true that, owing to the greater height 
of the latter compared with the attractive force of 
the sun’s mass, the upper strata of the terrestrial atmo- 
sphere will be relatively more powerfully attracted than 
the upper strata of the vastly deeper solar atmosphere. 
The ordinates of the curve a @ 6 will therefore not repre- 
sent the density quite correctly in both cases. The dis- 
crepancy, however, resulting from the relatively inferior 
attraction of the sun’s mass at the boundary of its atmo- 
sphere, will be very nearly neutralised by the increased 
density towards that boundary, consequent on the great 
reduction of temperature—fully 1,380,000° Fah.—caused 
by the dispersion of the solar rays before entering space. 
It may be well to add that, in representing the relative 
height and pressure of the terrestrial atmosphere, a ¢ in 
our diagram indicates forty-two miles, while 4 c indicates 
a pressure of 14°7 pounds per square inch; and that in 
representing the solar atmosphere, @ ¢ indicates 100,000 
miles and 4 ¢ 410 pounds per square inch. Bearing in 
mind the high temperature and small specific gravity, the 
extreme tenuity in the higher regions of the solar atmo- 
sphere will be comprehended by mere inspection of our 
diagram. Already midway towards the assumed boundary, 
the density of the solar atmosphere is so far reduced that 
it contains only ;)555 of the quantity of matter contained 
in an equal volume of atmosphere at the surface of the 
earth. 
Let us now consider the diminution of intensity occa- 
sioned by the increased depth through which the heat rays 
pass which are projected from the receding surface of the 
photosphere. Fig. 6 represents the sun and its atmosphere 
extending j of the semi-diameter of the photosphere, 77 /, 
cg, &c., &c., being the heat rays projected towards the 
earth. The depth of the solar atmosphere at a distance 
of 32 of the radius from the centre of the luminary, 
will be seen to be only 2’0012 greater than the ver- 
tical depth. Now, careful actinometer observations 
enables us to demonstrate that when the zenith distance 
is under 60°, the radiant energy of the sun’s rays in pass- 
ing through the terrestrial atmosphere is very nearly in 
the inverse ratio of the cube root of the depth penetrated 
(see the previously published table). The increase of 
epth resulting from atmospheric refraction, it may be 
well to observe, is too small at moderate zenith distances 
to call for correction ; nor does the atmospheric density 
vary sufficiently during bright sunshine to affect the radiant 
intensity appreciably. The table adverted to shows that 
an increase of the sun’s zenith distance of 5’ in 60° occasions 
a diminution of temperature hardly amounting to 0'044° 
Fah. Adopting the same rate of retardation for the solar 
atmosphere as that observed in the terrestrial atmosphere, 
it will be found that the loss of radiant energy of the 
solar rays at x of the radius from the border of the 
photosphere will be only 1°26 greater than at its centre. 
According to the researches of Secchi and others, the loss 
is fully three times greater than that established by the 
rate of diminution which we have adopted. This circum- 
stance, in connection with the extreme tenuity of the solar 
atmosphere, rendering any considerable loss improbable, 
points to the fact that some other agency than increased 
depth is the true cause of the diminution of the tempera- 
ture under consideration. Accordingly, the writer some 
time ago instituted a series of experiments with incan- 
descent cast-iron spheres, for the purpose of ascertaining 
practically if the reduction of temperature could be 
accounted for solely on the ground that the obliquity of 
the rays diminishes their energy. Previous experiments 
had demonstrated that the accepted doctrine is quite in- 
correct, which teaches that heat rays emanating from the 
surface of incandescent radiators are projected with equal 
energy in all directions. It was, found during those 
