THE TEMPERATURE OF MARS--MR. LOWELL'S ESTIMATE.
We have now to consider a still more important and fundamental question,
and one which Mr. Lowell does not grapple with in this volume, the
actual temperatures on Mars due to its distance from the sun and the
atmospheric conditions on which he himself lays so much stress. If I am
not greatly mistaken we shall arrive at conclusions on this subject
which are absolutely fatal to the conception of any high form of organic
life being possible on this planet.
_The Problem of Terrestrial Temperatures._
In order that the problem may be understood and its importance
appreciated, it is necessary to explain the now generally accepted
principles as to the causes which determine the temperatures on our
earth, and, presumably, on all other planets whose conditions are not
wholly unlike ours. The fact of the internal heat of the earth which
becomes very perceptible even at the moderate depths reached in mines
and deep borings, and in the deepest mines becomes a positive
inconvenience, leads many people to suppose that the surface-
temperatures of the earth are partly due to this cause. But it is now
generally admitted that this is not the case, the reason being that all
rocks and soils, in their natural compacted state, are exceedingly bad
conductors of heat.
A striking illustration of this is the fact, that a stream of lava often
continues to be red hot at a few feet depth for years after the surface
is consolidated, and is hardly any warmer than that of the surrounding
land. A still more remarkable case is that of a glacier on the
south-east side of the highest cone of Etna underneath a lava stream
with an intervening bed of volcanic sand only ten feet thick. This was
visited by Sir Charles Lyell in 1828, and a second time thirty years
later, when he made a very careful examination of the strata, and was
quite satisfied that the sand and the lava stream together had actually
preserved this mass of ice, which neither the heat of the lava above it
at its first outflow, nor the continued heat rising from the great
volcano below it, had been able to melt or perceptibly to diminish in
thirty years. Another fact that points in the same direction is the
existence over the whole floor of the deepest oceans of ice-cold water,
which, originating in the polar seas, owing to its greater density sinks
and creeps slowly along the ocean bottom to the depths of the Atlantic
and Pacific, and is not perceptibly warmed by the internal heat of the
earth.
Now the solid crust of the earth is estimated as at least about twenty
miles in average thickness; and, keeping in mind the other facts just
referred to, we can understand that the heat from the interior passes
through it with such extreme slowness as not to be detected at the
surface, the varying temperatures of which are due entirely to solar
heat. A large portion of this heat is stored up in the surface soil, and
especially in the surface layer of the oceans and seas, thus partly
equalising the temperatures of day and night, of winter and summer, so
as greatly to ameliorate the rapid changes of temperature that would
otherwise occur. Our dense atmosphere is also of immense advantage to us
as an equaliser of temperature, charged as it almost always is with a
large quantity of water-vapour. This latter gas, when not condensed into
cloud, allows the solar heat to pass freely to the earth; but it has the
singular and highly beneficial property of absorbing and retaining the
dark or lower-grade heat given off by the earth which would otherwise
radiate into space much more rapidly. We must therefore always remember
that, very nearly if not quite, the _whole_ of _the warmth we experience
on the earth is derived from the sun._[8]
[Footnote 8: Professor J.H. Poynting, in his lecture to the British
Association at Cambridge in 1904, says: "The surface of the earth
receives, we know, an amount of heat from the inside almost
infinitesimal compared with that which it receives from the sun, and on
the sun, therefore, we depend for our temperature."]
In order to understand the immense significance of this conclusion we
must know what is meant by the _whole_ heat or warmth; as unless we know
this we cannot define what half or any other proportion of sun-heat
really means. Now I feel pretty sure that nine out of ten of the average
educated public would answer the following question incorrectly: The
mean temperature of the southern half of England is about 48° F.
Supposing the earth received only half the sun-heat it now receives,
what would then be the probable mean temperature of the South of
England? The majority would, I think, answer at once--About 24° F.
Nearly as many would perhaps say--48° F. is 16° above the freezing
point; therefore half the heat received would bring us down to 8° above
the freezing point, or 40° F. Very few, I think, would realise that our
share of half the amount of sun-heat received by the earth would
probably result in reducing our mean temperature to about 100° F. below
the freezing point, and perhaps even lower. This is about the very
lowest temperature yet experienced on the earth's surface. To understand
how such results are obtained a few words must be said about the
absolute zero of temperature.
_The Zero of Temperature._
Heat is now believed to be entirely due to ether-vibration, which
produces a correspondingly rapid vibration of the molecules of matter,
causing it to expand and producing all the phenomena we term 'heat.' We
can conceive this vibration to increase indefinitely, and thus there
would appear to be no necessary limit to the amount of heat possible,
but we cannot conceive it to decrease indefinitely at the same uniform
rate, as it must soon inevitably come to nothing. Now it has been found
by experiment that gases under uniform pressure expand 1/273 of their
volume for each degree Centigrade of increased temperature, so that in
passing from 0° C. to 273° C. they are doubled in volume. They also
decrease in volume at the same rate for each degree below 0° C. (the
freezing point of water). Hence if this goes on to-273° C. a gas will
have no volume, or it will undergo some change of nature. Hence this is
called the zero of temperature, or the temperature to which any matter
falls which receives no heat from any other matter. It is also sometimes
called the temperature of space, or of the ether in a state of rest, if
that is possible. All the gases have now been proved to become, first
liquid and then (most of them) solid, at temperatures considerably above
this zero.
The only way to compare the proportional temperatures of bodies, whether
on the earth or in space, is therefore by means of a scale beginning at
this natural zero, instead of those scales founded on the artificial
zero of the freezing point of water, or, as in Fahrenheit's, 32° below
it. Only by using the natural zero and measuring continuously from it
can we estimate temperatures in relative proportion to the amount of
heat received. This is termed the absolute zero, and so that we start
reckoning from that point it does not matter whether the scale adopted
is the Centigrade or that of Fahrenheit.
_The Complex Problem of Planetary Temperatures._
Now if, as is the case with Mars, a planet receives only half the amount
of solar heat that we receive, owing to its greater distance from the
sun, and if the mean temperature of our earth is 60° F., this is equal
to 551° F. on the absolute scale. It would therefore appear very simple
to halve this amount and obtain 275.5° F. as the mean temperature of
that planet. But this result is erroneous, because the actual amount of
sun heat intercepted by a planet is only one condition out of many that
determine its resulting temperature. Radiation, that is loss of heat, is
going on concurrently with gain, and the rate of loss varies with the
temperature according to a law recently discovered, the loss being much
greater at high temperatures in proportion to the 4th power of the
absolute temperature. Then, again, the whole heat intercepted by a
planet does not reach its surface unless it has no atmosphere. When it
has one, much is reflected or absorbed according to complex laws
dependent on the density and composition of the atmosphere. Then, again,
the heat that reaches the actual surface is partly reflected and partly
absorbed, according to the nature of that surface--land or water, desert
or forest or snow-clad--that part which is absorbed being the chief
agent in raising the temperature of the surface and of the air in
contact with it. Very important too is the loss of heat by radiation
from these various heated surfaces at different rates; while the
atmosphere itself sends back to the surface an ever varying portion of
both this radiant and reflected heat according to distinct laws. Further
difficulties arise from the fact that much of the sun's heat consists of
dark or invisible rays, and it cannot therefore be measured by the
quantity of light only.
From this rough statement it will be seen that the problem is an
exceedingly complex one, not to be decided off-hand, or by any simple
method. It has in fact been usually considered as (strictly speaking)
insoluble, and only to be estimated by a more or less rough
approximation, or by the method of general analogy from certain known
facts. It will be seen, from what has been said in previous chapters,
that Mr. Lowell, in his book, has used the latter method, and, by taking
the presence of water and water-vapour in Mars as proved by the
behaviour of the snow-caps and the bluish colour that results from their
melting, has deduced a temperature above the freezing point of water, as
prevalent in the equatorial regions permanently, and in the temperate
and arctic zones during a portion of each year.
_Mr. Lowell's Mathematical Investigation of the Problem._
But as this result has been held to be both improbable in itself and
founded on no valid evidence, he has now, in the _London, Edinburgh, and
Dublin Philosophical Magazine_ of July 1907, published an elaborate
paper of 15 pages, entitled _A General Method for Evaluating the
Surface-Temperatures of the Planets; with special reference to the
Temperature of Mars_, by Professor Percival Lowell; and in this paper,
by what purports to be strict mathematical reasoning based on the most
recent discoveries as to the laws of heat, as well as on measurements or
estimates of the various elements and constants used in the
calculations, he arrives at a conclusion strikingly accordant with that
put forward in the recently published volume. Having myself neither
mathematical nor physical knowledge sufficient to enable me to criticise
this elaborate paper, except on a few points, I will here limit myself
to giving a short account of it, so as to explain its method of
procedure; after which I may add a few notes on what seem to me doubtful
points; while I also hope to be able to give the opinions of some more
competent critics than myself.
_Mr. Lowell's Mode of Estimating the Surface-temperature of Mars._
The author first states, that Professor Young, in his _General
Astronomy_ (1898), makes the mean temperature of Mars 223.6° absolute,
by using Newton's law of heat being radiated in proportion to
temperature, and 363° abs. (=-96° F.) by Dulong and Petit's law; but
adds, that a closer determination has been made by Professor Moulton,
using Stefan's law, that radiation is as the _/4th_ power of the
temperature, whence results a mean temperature of-31° F. These estimates
assume identity of atmospheric conditions of Mars and the Earth.
But as none of these estimates take account of the many complex factors
which interfere with such direct and simple calculations, Mr. Lowell
then proceeds to enunciate them, and work out mathematically the effects
they produce:
(1) The whole radiant energy of the sun on striking a planet becomes
divided as follows: Part is reflected back into space, part absorbed by
the atmosphere, part transmitted to the surface of the planet. This
surface again reflects a portion and only the balance left goes to warm
the planet.
(2) To solve this complex problem we are helped by the _albedoes_ or
intrinsic brilliancy of the planets, which depend on the proportion of
the visible rays which are reflected and which determines the
comparative brightness of their respective surfaces. We also have to
find the ratio of the invisible to the visible rays and the heating
power of each.
(3) He then refers to the actinometer and pyroheliometer, instruments
for measuring the actual heat derived from the sun, and also to the
Bolometer, an instrument invented by Professor Langley for measuring the
invisible heat rays, which he has proved to extend to more than three
times the length of the whole heat-spectrum as previously known, and
has also shown that the invisible rays contribute 68 per cent, of the
sun's total energy.[9]
[Footnote 9: For a short account of this remarkable instrument, see my
_Wonderful Century_, new ed., pp. 143-145.]
(4) Then follows an elaborate estimate of the loss of heat during the
passage of the sun's rays through our atmosphere from experiments made
at different altitudes and from the estimated reflective power of the
various parts of the earth's surface--rocks and soil, ocean, forest and
snow--the final result being that three-fourths of the whole sun-heat
is reflected back into space, forming our _albedo_, while only
one-fourth is absorbed by the soil and goes to warm the air and
determine our mean temperature.
(5) We now have another elaborate estimate of the comparative amounts of
heat actually received by Mars and the Earth, dependent on their very
different amounts of atmosphere, and this estimate depends almost wholly
on the comparative _albedoes_, that of Mars, as observed by astronomers
being 0.27, while ours has been estimated in a totally different way as
being 0.75, whence he concludes that nearly three-fourths of the
sun-heat that Mars receives reaches the surface and determines its
temperature, while we get only one-fourth of our total amount. Then by
applying Stefan's law, that the radiation is as the 4th power of the
surface temperature, he reaches the final result that the actual heating
power at the surface of Mars is considerably _more_ than on the Earth,
and would produce a mean temperature of 72° F., if it were not for the
greater conservative or blanketing power of our denser and more
water-laden atmosphere. The difference produced by this latter fact he
minimises by dwelling on the probability of a greater proportion of
carbonic-acid gas and water-vapour in the Martian atmosphere, and thus
brings down the mean temperature of Mars to 48° F., which is almost
exactly the same as that of the southern half of England. He has also,
as the result of observations, reduced the probable density of the
atmosphere of Mars to 2-1/2 inches of mercury, or only one-twelfth of
that of the Earth.
_Critical Remarks on Mr. Lowell's Paper._
The last part of this paper, indicated under pars. 4 and 5, is the most
elaborate, occupying eight pages, and it contains much that seems
uncertain, if not erroneous. In particular, it seems very unlikely that
under a clear sky over the whole earth we should only receive at the
sea-level 0.23 of the solar rays which the earth intercepts (p. 167).
These data largely depend on observations made in California and other
parts of the southern United States, where the lower atmosphere is
exceptionally dust-laden. Till we have similar observations made in the
tropical forest-regions, which cover so large an area, and where the
atmosphere is purified by frequent rains, and also on the prairies and
the great oceans, we cannot trust these very local observations for
general conclusions affecting the whole earth. Later, in the same
article (p. 170), Mr. Lowell says: "Clouds transmit approximately 20 per
cent. of the heat reaching them: a clear sky at sea-level 60 per cent.
As the sky is half the time cloudy the mean transmission is 35 per
cent." These statements seem incompatible with that quoted above.
The figure he uses in his calculations for the actual albedo of the
earth, 0.75, is also not only improbable, but almost self-contradictory,
because the albedo of cloud is 0.72, and that of the great cloud-covered
planet, Jupiter, is given by Lowell as 0.75, while Zollner made it only
0.62. Again, Lowell gives Venus an albedo of 0.92, while Zollner made it
only 0.50 and Mr. Gore 0.65. This shows the extreme uncertainty of these
estimates, while the fact that both Venus and Jupiter are wholly
cloud-covered, while we are only half-covered, renders it almost
certain that our albedo is far less than Mr. Lowell makes it. It is
evident that mathematical calculations founded upon such uncertain data
cannot yield trustworthy results. But this is by no means the only case
in which the data employed in this paper are of uncertain value.
Everywhere we meet with figures of somewhat doubtful accuracy. Here we
have somebody's 'estimate' quoted, there another person's 'observation,'
and these are adopted without further remark and used in the various
calculations leading to the result above quoted. It requires a practised
mathematician, and one fully acquainted with the extensive literature of
this subject, to examine these various data, and track them through the
maze of formulae and figures so as to determine to what extent they
affect the final result.
There is however one curious oversight which I must refer to, as it is a
point to which I have given much attention. Not only does Mr. Lowell
assume, as in his book, that the 'snows' of Mars consist of frozen
water, and that therefore there _is_ water on its surface and
water-vapour in its atmosphere, not only does he ignore altogether Dr.
Johnstone Stoney's calculations with regard to it, which I have already
referred to, but he uses terms that imply that water-vapour is one of
the heavier components of our atmosphere. The passage is at p. 168 of
the _Philosophical Magazine._ After stating that, owing to the very
small barometric pressure in Mars, water would boil at 110° F., he adds:
"The sublimation at lower temperatures would be correspondingly
increased. Consequently the amount of water-vapour in the Martian air
must on that score be relatively greater than our own." Then follows
this remarkable passage: "Carbon-dioxide, because of its greater
specific gravity, would also be in relatively greater amount so far as
this cause is considered. For the planet would part, _caeteris paribus_,
with its lighter gases the quickest. Whence as regards both water-vapour
and carbon-dioxide we have reason to think them in relatively greater
quantity than in our own air at corresponding barometric pressure." I
cannot understand this passage except as implying that 'water-vapour and
carbon-dioxide' are among the heavier and not among the lighter gases of
the atmosphere--those which the planet 'parts with quickest.' But this
is just what water-vapour _is_, being a little less than two-thirds the
weight of air (0.6225), and one of those which the planet _would_ part
with the quickest, and which, according to Dr. Johnstone Stoney, it
loses altogether.
* * * * *
Note on Professor Lowell's article in the _Philosophical Magazine_; by
J.H. Poynting, F.R.S., Professor of Physics in the University of
Birmingham.
"I think Professor Lowell's results are erroneous through his neglect of
the heat stored in the air by its absorption of radiation both from the
sun and from the surface. The air thus heated radiates to the surface
and keeps up the temperature. I have sent to the _Philosophical
Magazine_ a paper in which I think it is shown that when the radiation
by the atmosphere is taken into account the results are entirely
changed. The temperature of Mars, with Professor Lowell's data, still
comes out far below the freezing-point--still further below than the
increased distance alone would make it. Indeed, the lower temperature on
elevated regions of the earth's surface would lead us to expect this. I
think it is impossible to raise the temperature of Mars to anything like
the value obtained by Professor Lowell, unless we assume some quality in
his atmosphere entirely different from any found in our own atmosphere."
J.H. POYNTING. October 19, 1907.