(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. * * * * *