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.
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.
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.
(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, cæteris 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."
- October 19, 1907.