A NEW ESTIMATE OF THE TEMPERATURE OF MARS.
When we are presented with a complex problem depending on a great number
of imperfectly ascertained data, we may often check the results thus
obtained by the comparison of cases in which some of the more important
of these data are identical, while others are at a maximum or a minimum.
In the present case we can do this by a consideration of the Moon as
compared with the Earth and with Mars.
_Langley's Determination of the Moon's Temperature._
In the moon we see the conditions that prevail in Mars both exaggerated
and simplified. Mars has a very scanty atmosphere, the moon none at all,
or if there is one it is so excessively scanty that the most refined
observations have not detected it. All the complications arising from
the possible nature of the atmosphere, and its complex effects upon
reflection, absorption, and radiation are thus eliminated. The mean
distance of the moon from the sun being identical with that of the
earth, the total amount of heat intercepted must also be identical; only
in this case the whole of it reaches the surface instead of one-fourth
only, according to Mr. Lowell's estimate for the earth.
Now, by the most refined observations with his Bolometer, Mr. Langley
was able to determine the temperature of the moon's surface exposed to
undimmed sunshine for fourteen days together; and he found that, even in
that portion of it on which the sun was shining almost vertically, the
temperature rarely rose above the freezing point of water. However
extraordinary this result may seem, it is really a striking confirmation
of the accuracy of the general laws determining temperature which I have
endeavoured to explain in the preceding chapter. For the same surface
which has had fourteen days of sunshine has also had a preceding
fourteen days of darkness, during which the heat which it had
accumulated in its surface layers would have been lost by free radiation
into stellar space. It thus acquires during its day a maximum
temperature of only 491° F. absolute, while its minimum, after 14 days'
continuous radiation, must be very low, and is, with much reason,
supposed to approach the absolute zero.
_Rapid Loss of Heat by Radiation on the Earth._
In order better to comprehend what this minimum may be under extreme
conditions, it will be useful to take note of the effects it actually
produces on the earth in places where the conditions are nearest to
those existing on the moon or on Mars, though never quite equalling, or
even approaching very near them. It is in our great desert regions, and
especially on high plateaux, that extreme aridity prevails, and it is in
such districts that the differences between day and night temperatures
reach their maximum. It is stated by geographers that in parts of the
Great Sahara the surface temperature is sometimes 150° F., while during
the night it falls nearly or quite to the freezing point--a difference
of 118 degrees in little more than 12 hours.[10] In the high desert
plains of Central Asia the extremes are said to be even greater.[11]
Again, in his _Universal Geography_, Reclus states that in the Armenian
Highlands the thermometer oscillates between 13° F. and 112°F. We may
therefore, without any fear of exaggeration, take it as proved that a
fall of 100° F. in twelve or fifteen hours not infrequently occurs where
there is a very dry and clear atmosphere permitting continuous
insolation by day and rapid radiation by night.
[Footnote 10: Keith Johnston's 'Africa' in _Stanford's Compendium._]
[Footnote 11: _Chambers's Encyclopaedia_, Art. 'Deserts.']
Now, as it is admitted that our dense atmosphere, however dry and clear,
absorbs and reflects some considerable portion of the solar heat, we
shall certainly underestimate the radiation from the moon's surface
during its long night if we take as the basis of our calculation a
lowering of temperature amounting to 100° F. during twelve hours, as not
unfrequently occurs with us. Using these data--with Stefan's law of
decrease of radiation as the 4th power of the temperature--a
mathematical friend finds that the temperature of the moon's surface
would be reduced during the lunar night to nearly 200° F. absolute
(equal to-258° F.).
_More Rapid Loss of Heat by the Moon._
Although such a calculation as the above may afford us a good
approximation to the rate of loss of heat by Mars with its very scanty
atmosphere, we have now good evidence that in the case of the moon the
loss is much more rapid. Two independent workers have investigated this
subject with very accordant results--Dr. Boeddicker, with Lord Rosse's
3-foot reflector and a Thermopile to measure the heat, and Mr. Frank
Very, with a glass reflector of 12 inches diameter and the Bolometer
invented by Mr. Langley. The very striking and unexpected fact in which
these observers agree is the sudden disappearance of much of the
stored-up heat during the comparatively short duration of a total
eclipse of the moon--less than two hours of complete darkness, and about
twice that period of partial obscuration.
Dr. Boeddicker was unable to detect any appreciable heat at the period
of greatest obscuration; but, owing to the extreme sensitiveness of the
Bolometer, Mr. Very ascertained that those parts of the surface which
had been longest in the shadow still emitted heat "to the amount of one
per cent. of the heat to be expected from the full moon." This however
is the amount of radiation measured by the Bolometer, and to get the
temperature of the radiating surface we must apply Stefan's law of the
4th power. Hence the temperature of the moon's dark surface will be the
[fourth root of (1 over 100)] = 1 over 3.2 [A] of the highest temperature
(which we may take at the freezing-point, 491° F. abs.), or 154° F. abs.,
just below the liquefaction point of air. This is about 50° lower than the
amount found by calculation from our most rapid radiation; and as this
amount is produced in a few hours, it is not too much to expect that,
when continued for more than two weeks (the lunar night), it might reach
a temperature sufficient to liquefy hydrogen (60° F. abs.), or perhaps
even below it.
[Note A: LaTex markup $\root 4 \of {1 \over 100} = {1 \over 3.2}$ ]
_Theory of the Moon's Origin._
This extremely rapid loss of heat by radiation, at first sight so
improbable as to be almost incredible, may perhaps be to some extent
explained by the physical constitution of the moon's surface, which,
from a theoretical point of view, does not appear to have received the
attention it deserves. It is clear that our satellite has been long
subjected to volcanic eruptions over its whole visible face, and these
have evidently been of an explosive nature, so as to build up the very
lofty cones and craters, as well as thousands of smaller ones, which,
owing to the absence of any degrading or denuding agencies, have
remained piled up as they were first formed.
This highly volcanic structure can, I think, be well explained by an
origin such as that attributed to it by Sir George Darwin, and which has
been so well described by Sir Robert Ball in his small volume, _Time and
Tide._ These astronomers adduce strong evidence that the earth once
rotated so rapidly that the equatorial protuberance was almost at the
point of separation from the planet as a ring. Before this occurred,
however, the tension was so great that one large portion of the
protuberance where it was weakest broke away, and began to move around
the earth at some considerable distance from it. As about 1/50 of the
bulk of the earth thus escaped, it must have consisted of a considerable
portion of the solid crust and a much larger quantity of the liquid or
semi-liquid interior, together with a proportionate amount of the gases
which we know formed, and still form, an important part of the earth's
substance.
As the surface layers of the earth must have been the lightest, they
would necessarily, when broken up by this gigantic convulsion, have come
together to form the exterior of the new satellite, and be soon adjusted
by the forces of gravity and tidal disturbance into a more or less
irregular spheroidal form, all whose interstices and cavities would be
filled up and connected together by the liquid or semi-liquid mass
forced up between them. Thence-forward, as the moon increased its
distance and reduced its time of rotation, in the way explained by Sir
Robert Ball, there would necessarily commence a process of escape of the
imprisoned gases at every fissure and at all points and lines of
weakness, giving rise to numerous volcanic outlets, which, being
subjected only to the small force of lunar gravity (only one-sixth that
of the earth), would, in the course of ages, pile up those gigantic
cones and ridges which form its great characteristic.
But this small gravitative power of the moon would prevent its retaining
on its surface any of the gases forming our atmosphere, which would all
escape from it and probably be recaptured by the earth. By no process of
external aggregation of solid matter to such a relatively small amount
as that forming the moon, even if the aggregation was so violent as to
produce heat enough to cause liquefaction, could any such
long-continued volcanic action arise by gradual cooling, in the absence
of internal gases. There might be fissures, and even some outflows of
molten rock; but without imprisoned gases, and especially without water
and water-vapour producing explosive outbursts, could any such amount of
scoriae and ashes be produced as were necessary for the building up of
the vast volcanic cones, craters, and craterlets we see upon the moon's
surface.
I am not aware that either Sir Robert Ball or Sir George Darwin have
adduced this highly volcanic condition of the moon's surface as a
phenomenon which can _only_ be explained by our satellite having been
thrown off a very much larger body, whose gravitative force was
sufficient to acquire and retain the enormous quantity of gases and of
water which we possess, and which are _absolutely essential_ for that
_special form of cone-building volcanic action_ which the moon exhibits
in so pre-eminent a degree. Yet it seems to me clear, that some such
hypothetical origin for our satellite would have had to be assumed if
Sir George Darwin had not deduced it by means of purely mathematical
argument based upon astronomical facts.
Returning now to the problem of the moon's temperature, I think the
phenomena this presents may be in part due to the mode of formation here
described. For, its entire surface being the result of long-continued
gaseous explosions, all the volcanic products--scoriae, pumice, and
ashes--would necessarily be highly porous throughout; and, never having
been compacted by water-action, as on the earth, and there having been
no winds to carry the finer dust so as to fill up their pores and
fissures, the whole of the surface material to a very considerable depth
must be loose and porous to a high degree. This condition has been
further increased owing to the small power of gravity and the extreme
irregularity of the surface, consisting very largely of lofty cones and
ridges very loosely piled up to enormous heights.
Now this condition of the substance of the moon's surface is such as
would produce a high specific heat, so that it would absorb a large
amount of heat in proportion to the rise of temperature produced, the
heat being conducted downwards to a considerable depth. Owing, however,
to the total absence of atmosphere radiation would very rapidly cool the
surface, but afterwards more slowly, both on account of the action of
Stefan's law and because the heat stored up in the deeper portions could
be carried to the surface by conduction only, and with extreme slowness.
_Very's Researches on the Moon's Heat._
The results of the eclipse observations are supported by the detailed
examination of the surface-temperature of the moon by Mr. Very in his
_Prize Essay on the Distribution of the Moon's Heat_ (published by the
Utrecht Society of Arts and Sciences in 1891). He shows, by a diagram of
the 'Phase-curve,' that at the commencement of the Lunar day the surface
just within the illuminated limb has acquired about 1/7 of its maximum
temperature, or about 70° F. abs. As the surface exposed to the
Bolometer at each observation is about 1/30 of the moon's surface, and
in order to ensure accuracy the instrument has to be directed to a spot
lying wholly within the edge of the moon, it is evident that the surface
measured has already been for several hours exposed to oblique sunshine.
The curve of temperature then rises gradually and afterwards more
rapidly, till it attains its maximum (of about +30 to 40° F.) a few
hours _before_ noon. This, Mr. Very thinks, is due to the fact that the
half of the moon's face first illuminated for us has, on the average, a
darker surface than that of the afternoon, or second quarter, during
which the curve descends not quite so rapidly, the temperature near
sunset being only a little higher than that near sunrise. This rapid
fall while exposed to oblique sunshine is quite in harmony with the
rapid loss of heat during the few hours of darkness during an eclipse,
both showing the prepotency of radiation over insolation on the moon.
Two other diagrams show the distribution of heat at the time of
full-moon, one half of the curve showing the temperatures along the
equator from the edge of the disc to the centre, the other along a
meridian from this centre to the pole. This diagram (here reproduced)
exhibits the quick rise of temperature of the oblique rim of the moon
and the nearly uniform heat of the central half of its surface; the
diminution of heat towards the pole, however, is slower for the first
half and more rapid for the latter portion.
It is an interesting fact that the temperature near the margin of the
full-moon increases towards the centre more rapidly than it does when
the same parts are observed during the early phases of the first
quarter. Mr. Very explains this difference as being due to the fact that
the full-moon to its very edges is fully illuminated, all the shadows of
the ridges and mountains being thrown vertically or obliquely _behind
them._ We thus measure the heat reflected from the _whole_ visible
surface. But at new moon, and somewhat beyond the first quarter, the
deep shadows thrown by the smallest cones and ridges, as well as by the
loftiest mountains, cover a considerable portion of the visible surface,
thus largely reducing the quantity of light and heat reflected or
radiated in our direction. It is only at the full, therefore, that the
maximum temperature of the whole lunar surface can be measured. It must
be considered a proof of the delicacy of the heat-measuring instruments
that this difference in the curves of temperature of the different parts
of the moon's surface and under different conditions is so clearly
shown.
_The Application of the Preceding Results to the Case of Mars._
This somewhat lengthy account of the actual state of the moon's surface
and temperature is of very great importance in our present enquiry,
because it shows us the extraordinary difference in mean and extreme
temperatures of two bodies situated at the same distance from the sun,
and therefore receiving exactly the same amount of solar heat per unit
of surface. We have learned also what are the main causes of this almost
incredible difference, namely: (1) a remarkably rugged surface with
porous and probably cavernous rock-texture, leading to extremely rapid
radiation of heat in the one; as compared with a comparatively even and
well-compacted surface largely clad with vegetation, leading to
comparatively slow and gradual loss by radiation in the other: and (2),
these results being greatly intensified by the total absence of a
protecting atmosphere in the former, while a dense and cloudy atmosphere
with an ever-present supply of water-vapour, accumulates and equalises
the heat received by the latter.
The only other essential difference in the two bodies which may possibly
aid in the production of this marvellous result, is the fact of our day
and night having a mean length of 12 hours, while those of the moon are
about 14-1/2 of our days. But the altogether unexpected fact, in which
two independent enquirers agree, that during the few hours' duration of
a total eclipse of the moon so large a proportion of the heat is lost by
radiation renders it almost certain that the resulting low temperature
would be not very much less if the moon had a day and night the same
length as our own.
The great lesson we learn by this extreme contrast of conditions
supplied to us by nature, as if to enable us to solve some of her
problems, is, the overwhelming importance, first, of a dense and
well-compacted surface, due to water-action and strong gravitative
force; secondly, of a more or less general coat of vegetation; and,
thirdly, of a dense vapour-laden atmosphere. These three favourable
conditions result in a mean temperature of about +60° F. with a range
seldom exceeding 40° above or below it, while over more than half the
land-surface of the earth the temperature rarely falls below the
freezing point. On the other hand, we have a globe of the same materials
and at the same distance from the sun, with a maximum temperature of
freezing water, and a minimum not very far from the absolute zero, the
monthly mean being probably much below the freezing point of
carbonic-acid gas--a difference entirely due to the absence of these
three favourable conditions.
_The Special Features of Mars as influencing Temperature._
Coming now to the special feature of Mars and its probable temperature,
we find that most writers have arrived at a very different conclusion
from that of Mr. Lowell, who himself quotes Mr. Moulton as an authority
who 'recently, by the application of Stefan's law,' has found the mean
temperature of this planet to be-35° F. Again, Professor J.H. Poynting,
in his lecture on 'Radiation in the Solar System,' delivered before the
British Association at Cambridge in 1904, gave an estimate of the mean
temperature of the planets, arrived at from measurements of the sun's
emissive power and the application of Stefan's law to the distances of
the several planets, and he thus finds the earth to have a mean
temperature of 17° C. (=62-1/2° F.) and Mars one of-38° C. (=-36-1/2°
F.), a wonderfully close approximation to the mean temperature of the
earth as determined by direct measurement, and therefore, presumably, an
equally near approximation to that of Mars as dependent on distance from
the sun, and '_on the supposition that it is earth-like in all its
conditions._'
But we know that it is far from being earth-like in the very conditions
which we have found to be those which determine the extremely different
temperatures of the earth, and moon; and, as regards each of these, we
shall find that, so far as it differs from the earth, it approximates to
the less favourable conditions that prevail in the moon. The first of
these conditions which we have found to be essential in regulating the
absorption and radiation of heat, and thus raising the mean temperature
of a planet, is a compact surface well covered with vegetation, two
conditions arising from, and absolutely dependent on, an ample amount of
water. But Mr. Lowell himself assures us, as a fact of which he has no
doubt, that there are no permanent bodies of water, great or small, upon
Mars; that rain, and consequently rivers, are totally wanting; that its
sky is almost constantly clear, and that what appear to be clouds are
not formed of water-vapour but of dust. He dwells, emphatically, on the
terrible desert conditions of the greater part of the surface of the
planet.
That being the case now, we have no right to assume that it has ever
been otherwise; and, taking full account of the fact, neither denied nor
disputed by Mr. Lowell, that the force of gravity on Mars is not
sufficient to retain water-vapour in its atmosphere, we must conclude
that the surface of that planet, like that of the moon, has been moulded
by some form of volcanic action modified probably by wind, but not by
water. Adding to this, that the force of gravity on Mars is nearer that
of the moon than to that of the earth, and we may r reasonably conclude
that its surface is formed of volcanic matter in a light and porous
condition, and therefore highly favourable for the rapid loss of surface
heat by radiation. The surface-conditions of Mars are therefore,
presumably, much more like those of the moon than like those of the
earth.
The next condition favourable to the storing up of heat--a covering of
vegetation--is almost certainly absent from Mars except, possibly, over
limited areas and for short periods. In this feature also the surface of
Mars approximates much nearer to lunar than to earth-conditions. The
third condition--a dense, vapour-laden atmosphere--is also wanting in
Mars. For although it possesses an atmosphere it is estimated by Mr.
Lowell (in his latest article) to have a pressure equivalent to only
2-1/2 inches of mercury with us, giving it a density of only one-twelfth
part that of ours; while aqueous vapour, the chief accumulator of heat,
cannot permanently exist in it, and, notwithstanding repeated
spectroscopic observations for the purpose of detecting it, has never
been proved to exist.
I submit that I have now shown from the statements--and largely as the
result of the long-continued observations--of Mr. Lowell himself, that,
so far as the physical conditions of Mars are known to differ from those
of the earth, the differences are all _unfavourable_ to the conservation
and _favourable_ to the dissipation of the scanty heat it receives from
the sun--that they point unmistakeably towards the temperature
conditions of the moon rather than to those of the earth, and that the
cumulative effect of these adverse conditions, acting upon a
heat-supply, reduced by solar distance to less than one-half of ours,
_must_ result in a mean temperature (as well as in the extremes) nearer
to that of our satellite than to that of our own earth.
_Further Criticism of Mr. Lowell's Article._
We are now in a position to test some further conclusions of Mr.
Lowell's _Phil. Mag._ article by comparison with actual phenomena. We
have seen, in the outline I have given of this article, that he
endeavours to show how the small amount of solar heat received by Mars
is counterbalanced, largely by the greater transparency to light and
heat of its thin and cloudless atmosphere, and partially also by a
greater conservative or 'blanketing' power of its atmosphere due to the
presence in it of a large proportion of carbonic acid gas and aqueous
vapour. The first of these statements may be admitted as a fact which he
is entitled to dwell upon, but the second--the presence of large
quantities of carbon-dioxide and aqueous vapour is a pure hypothesis
unsupported by any item of scientific evidence, while in the case of
aqueous vapour it is directly opposed to admitted results founded upon
the molecular theory of gaseous elasticity. But, although Mr. Lowell
refers to the conservative or 'blanketing' effect of the earth's
atmosphere, he does not consider or allow for its very great cumulative
effect, as is strikingly shown by the comparison with the actual
temperature conditions of the moon. This cumulative effect is due to the
_continuous_ reflection and radiation of heat from the clouds as well as
from the vapour-laden strata of air in our lower atmosphere, which
latter, though very transparent to the luminous and accompanying heat
rays of the sun, are opaque to the dark heat-rays whether radiated or
reflected from the earth's surface. We are therefore in a position
strictly comparable with that of the interior of some huge glass house,
which not only becomes intensely heated by the direct rays of the sun,
but also to a less degree by reflected rays from the sky and those
radiated from the clouds, so that even on a cloudy or misty day its
temperature rises many degrees above that of the outer air. Such a
building, if of large size, of suitable form, and well protected at
night by blinds or other covering, might be so arranged as to accumulate
heat in its soil and walls so as to maintain a tolerably uniform
temperature though exposed to a considerable range of external heat and
cold. It is to such a power of accumulation of heat in our soil and
lower atmosphere that we must impute the overwhelming contrast between
our climate and that of the moon. With us, the solar heat that
penetrates our vapour-laden and cloudy atmosphere is shut in by that
same atmosphere, accumulates there for weeks and months together, and
can only slowly escape. It is this great cumulative power which Mr.
Lowell has not taken account of, while he certainly has not estimated
the enormous loss of heat by free radiation, which entirely neutralises
the effects of increase of sun-heat, however great, when these
cumulative agencies are not present.[12]
[Footnote 12: The effects of this 'cumulative' power of a dense
atmosphere are further discussed and illustrated in the last chapter of
this book, where I show that the universal fact of steadily diminishing
temperatures at high altitudes is due solely to the diminution of this
cumulative power of our atmosphere, and that from this cause alone the
temperature of Mars must be that which would be found on a lofty plateau
about 18,000 feet higher than the average of the peaks of the Andes!]
_Temperature on Polar Regions of Mars._
There is also a further consideration which I think Mr. Lowell has
altogether omitted to discuss. Whatever may be the _mean_ temperature
of Mars, we must take account of the long nights in its polar and
high-temperate latitudes, lasting nearly twice as long as ours, with the
resulting lowering of temperature by radiation into a constantly clear
sky. Even in Siberia, in Lat. 67-1/2°N. a cold of-88°F. has been
attained; while over a large portion of N. Asia and America above 60°
Lat. the _mean_ January temperature is from-30°F. to-60°F., and the
whole subsoil is permanently frozen from a depth of 6 or 7 feet to
several hundreds. But the winter temperatures, _over the same latitudes_
in Mars, must be very much lower; and it must require a proportionally
larger amount of its feeble sun-heat to raise the surface even to the
freezing-point, and an additional very large amount to melt any
considerable depth of snow. But this identical area, from a little below
60° to the pole, is that occupied by the snow-caps of Mars, and over the
whole of it the winter temperature must be far lower than the
earth-minimum of-88°F. Then, as the Martian summer comes on, there is
less than half the sun-heat available to raise this low temperature
after a winter nearly double the length of ours. And when the summer
does come with its scanty sun-heat, that heat is not accumulated as it
is by our dense and moisture-laden atmosphere, the marvellous effects of
which we have already shown. Yet with all these adverse conditions, each
assisting the other to produce a climate approximating to that which the
earth would have if it had no atmosphere (but retaining our superiority
over Mars in receiving double the amount of sun-heat), we are asked to
accept a mean temperature for the more distant planet almost exactly the
same as that of mild and equable southern England, and a disappearance
of the vast snowfields of its polar regions as rapid and complete as
what occurs with us! If the moon, even at its equator, has not its
temperature raised above the freezing-point of water, how can the more
_distant_ Mars, with its _oblique_ noon-day sun falling upon the
snow-caps, receive heat enough, first to raise their temperature to 32°
F., and then to melt with marked rapidity the vast frozen plains of its
polar regions?
Mr. Lowell is however so regardless of the ordinary teachings of
meteorological science that he actually accounts for the supposed mild
climate of the polar regions of Mars by the absence of water on its
surface and in its atmosphere. He concludes his fifth chapter with the
following words: "Could our earth but get rid of its oceans, we too
might have temperate regions stretching to the poles." Here he runs
counter to two of the best-established laws of terrestrial climatology--
the wonderful equalising effects of warm ocean-currents which are the
chief agents in diminishing polar cold; the equally striking effects of
warm moist winds derived from these oceans, and the great storehouse of
heat we possess in our vapour-laden atmosphere, its vapour being
primarily derived from these same oceans! But, in Mr. Lowell's opinion,
all our meteorologists are quite mistaken. Our oceans are our great
drawbacks. Only get rid of them and we should enjoy the exquisite
climate of Mars--with its absence of clouds and fog, of rain or rivers,
and its delightful expanses of perennial deserts, varied towards the
poles by a scanty snow-fall in winter, the melting of which might, with
great care, supply us with the necessary moisture to grow wheat and
cabbages for about one-tenth, or more likely one-hundredth, of our
present population. I hope I may be excused for not treating such an
argument seriously. The various considerations now advanced, especially
those which show the enormous cumulative and conservative effect of our
dense and water-laden atmosphere, and the disastrous effect--judging by
the actual condition of the moon--which the loss of it would have upon
our temperature, seem to me quite sufficient to demonstrate important
errors in the data or fallacies in the complex mathematical argument by
which Mr. Lowell has attempted to uphold his views as to the temperature
and consequent climatic conditions of Mars. In concluding this portion
of my discussion of the problem of Mars, I wish to call attention to the
fact that my argument, founded upon a comparison of the physical
conditions of the earth and moon with those of Mars, is dependent upon a
small number of generally admitted scientific facts; while the
conclusions drawn from those facts are simple and direct, requiring no
mathematical knowledge to follow them, or to appreciate their weight and
cogency. I claim for them, therefore, that they are in no degree
speculative, but in their data and methods exclusively scientific. In
the next chapter I will put forward a suggestion as to how the very
curious markings upon the surface of Mars may possibly be interpreted,
so as to be in harmony with the planet's actual physical condition and
its not improbable origin and past history.