the two methods applied for its determination have yielded somewhat
unequal results. From the intensity of the radiation, Christiansen,
and afterwards Warburg, calculated a temperature of about 6000° Cent.
Wilson and Gray found for the centre of the sun 6200°, which they
afterwards corrected into 8000°. Owing to the absorption of light by
the terrestrial and the solar atmospheres, we always find too low
values. That applies, to a still greater extent, to any estimate based
upon the determination of that wave-length for which the heat emission
from the solar spectrum is maximum. Le Chatelier compared the intensity
of sunlight filtered through red glass with the intensities of light
from several terrestrial sources of fairly well-known temperatures
treated in the same way. These estimates yielded to him a solar
temperature of 7600° Cent. Most scientists reckon with an absolute
temperature of 6500°, corresponding to about 6200° Celsius. That is
what is known as the “effective temperature” of the sun. If the solar
rays were not partially absorbed, this temperature would correspond
to that of the clouds of the photosphere. Since red light is little
absorbed comparatively, Le Chatelier’s value of 7600°, and the almost
equal value of Wilson and Gray of 8000°, should approximately represent
the average temperature of the outer portions of the clouds of the
photosphere. The higher temperature of the faculæ is evident from
their greater light intensity, which, however, may partly be due to
their greater height. Carrington and Hodgson saw, on September 1,
1859, two faculæ break out from the edge of a sun-spot. Their splendor
was five or six times greater than that of the surrounding parts of
the photosphere. That would correspond to a temperature of about
10,000 or 12,000° Cent. The deeper parts of the sun which broke out on
these occasions evidently have a higher temperature, and this is not
unnatural, since the sun is losing heat by radiation from its outer
portions.
We know that the temperature of our atmosphere decreases with greater
heights. The movements of the air are concerned in this change. A
sinking mass of air is compressed by the increased pressure to which
it is being exposed, and its temperature rises, therefore, just as
the temperature rises in a pneumatic gas-lighter when the piston is
pressed down. If the air were dry and in strong vertical motion, its
temperature would change by 10° Cent. (18° F.) per km. If it stood
still, it would assume an almost uniform temperature; that is to say,
there would be no lowering of the temperature as we proceed upward. The
actual value lies between the two extremes. As the gravitation in the
photosphere of the sun is 27.4 times greater than on the surface of the
earth, we can deduce that, if the air on the sun were as dense as on
the earth, the temperature on the sun would vary 27.4 times as much as
on the earth with the increasing height—that is to say, by 270 degrees
per kilometre, provided its atmosphere were in violent agitation. Now,
the outer portions of the solar atmosphere are, indeed, in violent
motion, so that this latter assumption seems to be justified. But
this part consists essentially of hydrogen, which is 29 times lighter
than the air. We must, therefore, reduce the value at which we arrive
to one-twenty-ninth. As a result, the final temperature gradient per
kilometre would only be 9° Cent. (16.2° F.). But the radiation is
extremely powerful on the sun, and it tends to equalize the conditions.
Nine degrees per kilometre is therefore, without doubt, too high a
value. Further, in the interior of the sun the gases are much heavier.
At a small depth, however, they will be so strongly compressed by the
upper strata that their further compressibility will be limited, and
the calculation which we have just made loses its validity. Yet, in any
case, the temperature of the sun must increase as we penetrate nearer
to its centre. If we accept a temperature gradient per kilometre of
the value above indicated, 9°—it is three times greater in the solid
earth-crust—we should obtain for the centre of the sun a temperature
of more than six million degrees.
All substances melt and evaporate as their temperature is raised. If
the temperature exceeds a certain limit, the “critical temperature,”
the substance can no longer be condensed to a liquid, however high the
pressure may be pushed, and the substance will only exist as a gas.
If we start from -273° as absolute zero, this critical temperature is
nearly one and a half times as high as the ebullition temperature of
the substance under atmospheric pressure. So far as our experience
goes, it does not appear probable that the critical temperature of any
substance could be higher than 10,000° or 12,000° Cent., the highest
values which we have calculated for the temperature of the faculæ. The
inner portions of the sun must hence be gaseous, and the whole sun
be a strongly compressed mass of gas of extremely high temperature,
which, owing to the high pressure, is at a density 1.4 times as great
as that of water, and which in many respects, therefore, will resemble
a liquid. It must, for instance, be extremely viscid, and that accounts
for the relatively great stability of the sun-spots (one sun-spot held
out for a year and a half in 1840 and 1841). The sun would thus have
to be regarded as a sphere of gas, in the outer portions of which a
certain amount of condensations of cloud character have taken place,
owing to radiation and to the outward movements of the gaseous masses.
The pressure in the photosphere—that is, in those parts in which these
clouds are floating—has been averaged at five or six atmospheres, a
figure which, considering the very high gravitation, would suggest
a layer of superposed gas above it corresponding to not more than a
fifth of our terrestrial atmosphere. At an approximately corresponding
height, 11,500 m. (38,000 ft.), there are floating in the terrestrial
atmosphere the highest cirrus clouds, to which the clouds of the
photosphere may in many respects be compared.
We turn back to the unanswered question whence the sun takes the
compensation for the heat which it constantly radiates into space. The
most powerful source of heat known to us is that of chemical reactions.
The most familiar reaction of daily life is the combustion of coal.
By burning one gramme of carbon we obtain 8000 calories. If the sun
consisted of pure carbon, its energy would not hold out more than 4000
years. It is not to be wondered at, therefore, that most scientists
soon abandoned the hope of solving the problem in this way. The French
astronomer Faye attempted to explain the replenishment of the losses of
heat by radiation from the sun by arguments in which he resorted to the
heat of a combination of the constituents of the sun. He said: “So high
a temperature must prevail in the interior of the sun that everything
there will be decomposed into its elementary constituents. When the
atoms afterwards penetrate into the outer layers, they are again
united, and they liberate heat.” Faye thus imagined that new masses of
elements would constantly rise from the interior of the sun and would
be reunited in chemical combination on the surface. But if new masses
are to penetrate upward to the surface, those which were at first above
must go back to the centre of the sun, in order to be re-decomposed
by the great heat there; and this re-decomposition would consume just
as much heat as was gained by the rising of the same masses to the
surface. This convection can therefore only help to transport the store
of heat from the interior to the surface. The total amount of heat
stored in the sun would in this way, supposing the mean temperature to
be six million degrees, be able to cover the heat expenditure for about
three million years.
We have, moreover, seen that the highest strata of the sun are
distinguished by line spectra, suggestive of simple chemical compounds,
while at greater depth in the sun-spots chemical combinations occur
which are characterized by band spectra. It is quite incorrect to
assert that high temperatures must necessarily decompose all chemical
compounds into their elements. The mechanical theory of heat teaches
us only that at rising temperatures products are formed whose
formation goes hand in hand with an absorption of heat. Thus, at a
high temperature, ozone is formed from oxygen, although ozone is more
complex in composition than oxygen, and by this reaction 750 calories
are consumed when one gramme of oxygen is transformed into one gramme
of ozone. We likewise know that in the electric arc, at a temperature
of about 3000°, a compound is formed under consumption of heat by the
oxygen and nitrogen of the atmosphere. A new method for the technical
preparation of nitric acid from the nitrogen of the air is based upon
this reaction. Again, the well-known compounds benzene and acetylene
are formed from their elements, carbon and hydrogen, under absorption
of heat. All these bodies can only be synthesized from their elementary
constituents at high temperatures. We further know from experience
that the higher the temperature at which a reaction takes place, the
greater, in general, the amount of heat which it absorbs.
A similar law applies to the influence of pressure. When the pressure
is increased, such processes will be favored as will yield products of
a smaller volume. If we imagine that a mass of gas rushes down from a
higher stratum of the sun into the depths of the sun’s interior, as
gases do in sun-spots, complex compounds will be produced by virtue
of the increased pressure. This pressure must increase at an immense
rate towards the interior of the sun, by about 3500 atmospheres
per kilometre. The gases which dissociate into atoms at the lower
pressures and the higher temperatures of the extreme solar strata above
the photosphere clouds enter into chemical combination in the depths
of the spots, as we learn from spectroscopic examination. Owing to
their high temperatures, these compounds absorb enormous quantities of
heat in their building up, and these quantities of heat are to those
which are concerned in the chemical processes of the earth in the same
ratio as the temperature of the sun is to that at which the chemical
reactions are proceeding on the earth. As these gases penetrate
farther into the sun, temperature and pressure are still more and more
increased, and there will result products more and more abounding in
energy and concentration. We may, therefore, imagine the interior
of the sun charged with compounds which, brought to the surface of
the sun, would dissociate under an enormous evolution of heat and an
enormous increase of volume. These compounds have to be regarded as
the most powerful blasting agents, by comparison with which dynamite
and gun-cotton would appear like toys. In confirmation of this view,
we observe that gases when penetrating into the photosphere clouds are
able to eject prominences at a stupendous velocity, obtaining several
hundred kilometres per second. This velocity surpasses that of the
swiftest rifle-bullet about a thousandfold. We may hence ascribe to
the explosives which are confined in the interior of the sun energies
which must be a million times greater than the energy of our blasting
agents. (For the energy increases with the square of the velocity.)
And yet these solar blasting agents have already given up a large part
of their energy during their passage from the sun’s interior. It thus
becomes conceivable that the solar energy—instead of holding out for
4000 years, as it would if it depended upon the combustion of a solar
sphere made out of carbon—will last for something like four thousand
million years. Perhaps we may further extend this period to several
billions.
That there are such energetic compounds we have learned from the
discovery of the heat evolution of radium. According to Rutherford,
radium is decomposed by one-half in the space of about 1300 years. In
this decomposition a quantity of about a million calories is evolved
per gramme and per year, and we thus find that the decomposition of
radium into its final products is accompanied by a heat evolution of
about two thousand millions of calories per gramme—about a quarter of
a million times more heat than the combustion of one gramme of carbon
would yield.
In chemical respects as well, then, the earth is a dwarf compared to
the sun, and we have every reason to presume that the chemical energy
of the sun will be sufficient to sustain the solar heat during many
thousand millions and possibly billions of years to come.
IV
THE RADIATION PRESSURE
Next to simple measuring and simple calculations, astronomy appears
to be the most ancient science. Yet, though man has worshipped the
sun from the most remote ages, it was not fully comprehended before
the middle of the past century that the sun is the source of all life
and of all motion. Part of the veneration for the sun was transferred
to the moon, with its mild light, and to the smaller celestial
lights. It did not escape notice that their positions in the sky
were always changing simultaneously with the annual variations in
the weather, and all human undertakings depended upon the weather
and the seasons. The moon and the stars were worshipped—we know
now, without any justification whatever—as ruling over the weather,
and consequently over man’s fate.[6] Before anything was undertaken
people attempted first to assure themselves of the favorable aspect
of the constellations, and since the most remote ages astrologers
have exercised a vast influence over the ignorant and superstitious
multitude.
[Footnote 6: The moon strongly, and more than any other agent,
influences the tides. Apart from this effect the position of
the moon has only a feeble influence upon the air pressure and
upon atmospheric electricity and terrestrial magnetism. The
influence of the stars is imperceptible.]
In spite of the vehement enunciation of Giordano Bruno (1548-1600),
this superstition was still deeply rooted when Newton succeeded in
proving, in 1686, that the movements of the so-called wandering stars,
or planets, and of their moons could be calculated with the aid of
one very simple law: that all these celestial bodies are attracted
by the sun or by their respective central bodies with a force which
is proportional to their own mass and to the mass of the central
body and inversely proportional to the square of their distance from
that central body. Newton’s contemporary, Halley, applied the law of
gravitation also to the mysterious comets, and calculating astronomy
has since been based upon this, its firmest law, to which there has
not been found any exception. The world was thus at once rid of
the paralyzing superstition which exacted belief in a mysterious
ruling of the stars. The contemporaries of Newton, as well as their
descendants, have rightly valued this discovery more highly than any
other scientific triumph of this hero’s. According to Newton’s law, all
material bodies would tend to become more and more concentrated and
united, and the development of the universe would result in the sucking
up of the smaller celestial bodies—the meteorites, for instance—by
the larger bodies.
It must, however, be remarked that Newton’s great precursor, Kepler,
observed in 1618 that the matter of the comets is repelled by the sun.
Like Newton, he believed in the corpuscular theory of light. The sun
and all other luminous bodies radiated light, they thought, because
they ejected minute corpuscles of light matter in all directions.
If, now, these small corpuscles hit against the dust particles in
the comets’ tails, the dust particles would be carried away with
them, and their repulsion by the sun would become intelligible. It
is characteristic that Newton would not admit this explanation of
Kepler’s, although he shared Kepler’s opinion on the nature of light.
According to Newton, the deviation of the tails of comets from his
law of general attraction was only apparent. The tails of comets, he
argued, behaved like the columns of smoke rising from a chimney, which,
although the gases of combustion are attracted by the earth, yet ascend
because they are lighter than the surrounding air. This view, which has
been characterized by Newcomb as no longer to be seriously taken into
consideration, demonstrates the strong tendency of Newton to explain
everything with the aid of his law.
The astronomers followed faithfully in the footsteps of their
inimitable master, Newton, and they brushed aside every phenomenon
which would not fit into his system. An exception was made by the
famous Euler, who, in 1746, expressed the opinion that the waves of
light exerted a pressure upon the body upon which they fell. This
opinion, however, could not prevail against the criticisms with which
others, and especially De Mairan, assailed it. That Euler was right,
however, was proved by Maxwell’s great theoretical treatise on the
nature of electricity (1873). He showed that rays of heat—and the
same applies, as Bartoli established in 1876, to radiations of any
kind—must exercise a pressure just as great as the amount of energy
contained in a unit volume, by virtue of their radiation. Maxwell
calculated the magnitude of this pressure, and he found it so small
that it could hardly have been demonstrated with the experimental means
then at our disposal. But this demonstration has since been furnished,
with the aid of measurements obtained in a vacuum, by the Russian
Lebedeff and by the Americans Nichols and Hull (1900, 1901). They have
found that this pressure, the so-called radiation pressure, is exactly
as great as Maxwell predicted.
In spite of Maxwell’s great authority, astronomers quite overlooked
this important law of his. Lebedeff, indeed, tried in 1892 to apply it
to the tails of comets, which he regarded as gaseous; but the law is
not applicable in this case. As late as the year 1900, shortly before
Lebedeff was able to publish his experimental verification of this
law, I attempted to prove its vast importance for the explanation of
several celestial phenomena. The magnitude of the radiation pressure
of the solar atmosphere must be equivalent to 2.75 milligrammes if the
rays strike vertically against a black body one square centimetre in
area. I also calculated the size of a spherule of the same specific
gravity as water, such that the radiation pressure to which it would be
exposed in the vicinity of the sun would balance the attraction by the
sun. It resulted that equilibrium would be established if the diameter
of the sphere were 0.0015 mm. A correction supplied by Schwarzschild
showed that the calculation was only valid when the sphere completely
reflects all the rays which fall upon it. If the diameter of the
spherule be still smaller, the radiation pressure will prevail over
the attraction, and such a sphere would be repelled by the sun. Owing
to the refraction of light, this will, according to Schwarzschild,
further necessitate that the circumference of the spherule should be
greater than 0.3 times the wave-length of the incident rays. When the
sphere becomes still smaller, gravitation will once more predominate.
But spherules whose sizes are intermediate between these two limits
will be repelled. It results, therefore, that molecules, which have far
smaller dimensions than those mentioned, will not be repelled by the
radiation pressure, and that therefore Maxwell’s law does not hold for
gases. When the circumference of the spherule becomes exactly equal to
the wave-length of the radiation, the radiation pressure will act at
its maximum, and it will then surpass gravity not less than nineteen
times. These calculations apply to all spheres, totally reflecting
the light, of a specific gravity like water, and to a radiation and
attraction corresponding to that of the sun. Since the sunlight is not
homogeneous, the maximum effect will somewhat be diminished, and it
is nearly equal to ten times the gravity for spheres of a diameter of
about 0.00016 mm.[7]
[Footnote 7: One centimetre of water contains 470 billions of
these spheres. Such a little drop of water, again, contains 96
millions of molecules, and there are probably organisms which
are smaller than these drops. Compare the experiments with
ultra-microscopic organisms by E. Raehlmann, N. Gaidukow, and
others.]
Before we had recourse to the radiation pressure for the explanation
of the repulsion phenomena such as have been observed in the tails of
comets, it was generally believed with Zöllner that the repulsion was
due to electrical forces. Electricity undoubtedly plays an important
part in these phenomena, as we shall see. The way in which it acts
in these instances was explained by a discovery of C. T. R. Wilson
in 1899. Gases can in various ways be transformed into conductors of
electricity which as a rule they do not conduct. The conducting gases
are said to be ionized—that is to say, they contain free ions, minute
particles charged with positive or negative electricity. Gases can be
ionized, among other ways, by being radiated upon with Röntgen rays,
kathode rays, or ultra-violet light, as well as by strong heat. Since
the light of the sun contains a great many ultra-violet radiations, it
is indisputable that the masses of gases in the neighborhood of the sun
(_e.g._, probably in comets when they come near the sun) will partly
be ionized, and will contain both positive and negative ions. Ionized
gases are endowed with the remarkable capability of condensing vapors
upon themselves. Wilson showed that this property is possessed to a
higher degree by the negative ions than by the positive ions (in the
condensation of water vapor). If there are, therefore, water vapors in
the neighborhood of the sun which can be condensed by cooling, drops of
water will, in the first instance, be condensed upon the negative ions.
When these drops are afterwards repelled by the radiation pressure,
or when they sink, owing to gravity, as drops of rain sink in the
terrestrial atmosphere, they will carry with them the charge of the
negative ions, while the corresponding positive charge will remain
behind in the gas or in the air. In this way the negative and positive
charges will become separated from each other, and electric discharges
may ensue if sufficiently large quantities of opposite electricity have
been accumulated. By reason of these discharges the gases will become
luminescent, although their temperature may be very low. Stark has even
shown that low temperatures are favorable for the display of a strong
luminosity in electric discharges.
We have stated that Kepler, as early as the beginning of the
seventeenth century, came to the conclusion that the tails of comets
were repelled by the sun. Newton indicated how we might, from the shape
of the comets’ tails, calculate their velocity. The best way, however,
is to determine this velocity by direct observation. The comets’ tails
are not so uniform in appearance as they are generally represented in
illustrations, but they often contain several luminous nuclei (Fig.
33), whose motions can be directly ascertained.
[Illustration: Fig. 33.—Photograph of Roerdam’s comet (1893
II.), suggesting several strong nuclei in the tail]
From a study of the movements of comets’ tails, Olbers concluded,
about the beginning of the last century, that the repulsion of the
comets’ tails by the sun is inversely proportional to the square of
their distance—that is to say, that the force of the repulsion is
subject to the same law as the force of gravitation. We can, therefore,
express the repulsion effect in units of solar gravitation, and this
has generally been done. That the radiation pressure will in the same
manner change with the distance is only natural. For the radiation
against the same surface is also inversely proportional to the square
of the distance from the radiating body, the sun.
[Illustration: Fig. 34.—Photograph of Swift’s comet (1892 I.)]
In the latter part of the past century the Russian astronomer Bredichin
conducted a great many measurements on the magnitude of the forces with
which comets’ tails are repelled by the sun. He considered himself,
on the strength of these measurements, justified in dividing comets’
tails into three classes. In the first class the repulsion was 19 times
stronger than gravitation; in the second class, from 3.2 to 1.5 times
stronger; and in the third class, from 1.3 to 1 times stronger. Still
higher values have, however, been deduced for several comets. Thus
Hussey found for the comet of 1893 (Roerdam’s comet, 1893 II., Fig. 33)
a repulsion 37 times as strong as gravitation; and Swift’s comet (1892
I.) yields the still higher value of 40.5 (Fig. 34). Some comets show
several tails of different kinds, as the famous comet of Donati (Fig.
35). Its two almost straight tails would belong to the first class, and
the more strongly developed and curved third tail to the second class.
[Illustration: Fig. 35.—Donati’s comet at its greatest
brilliancy in 1858]