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 a.s.sume, 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 pa.s.sage 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 pa.s.sage: "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 quant.i.ty than in our own air at corresponding barometric pressure." I cannot understand this pa.s.sage 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 a.s.sume some quality in his atmosphere entirely different from any found in our own atmosphere."

J.H. POYNTING. October 19, 1907.

CHAPTER VI.

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 acc.u.mulated in its surface layers would have been lost by free radiation into stellar s.p.a.ce. 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 112F. 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. Boedd.i.c.ker, with Lord Rosse's 3-foot reflector and a Thermopile to measure the heat, and Mr. Frank Very, with a gla.s.s 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. Boedd.i.c.ker 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 const.i.tution 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 quant.i.ty 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 ma.s.s 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 quant.i.ty 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 a.s.sumed 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 quant.i.ty 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, acc.u.mulates 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 a.s.sociation 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 a.s.sures 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 a.s.sume 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 acc.u.mulator 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 c.u.mulative 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 ent.i.tled to dwell upon, but the second--the presence of large quant.i.ties 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 c.u.mulative effect, as is strikingly shown by the comparison with the actual temperature conditions of the moon. This c.u.mulative 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 gla.s.s 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 acc.u.mulate 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 acc.u.mulation 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, acc.u.mulates there for weeks and months together, and can only slowly escape. It is this great c.u.mulative 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 c.u.mulative agencies are not present.[12]

[Footnote 12: The effects of this 'c.u.mulative' power of a dense atmosphere are further discussed and ill.u.s.trated in the last chapter of this book, where I show that the universal fact of steadily diminishing temperatures at high alt.i.tudes is due solely to the diminution of this c.u.mulative 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!]