THE TEMPERATURE OF AIR AND THE PROBLEM OF AN ICE AGE.

I beg permission to briefly review the assumptions upon which Section II., III. of "the Cause dell' Era Gladale" (Pavia, 1865) is based. And which the reviewer of the book in Nature (No. 1348, Vol. LII p. 412 ) judged as far from satisfactory.- Luigi De Marchi.

THE mean temperature t of the air is determined by the balance of radiations received from the sun and from the soil with that given up towards the sky, and is ruled by the action of meteorological factors. According to Maurer's and Trabert's discussion of nocturnal temperatures, air radiation in the atmosphere is a linear function of its temperature; so radiations from soil and towards sky are expressed as proportional to the differences [{t_s - t), (t - t_c)] of t from the mean temperature t_s, of soil, and from the mean temperature t_c, of an ideal stratum, the radiations of which would be equivalent to that of the whole atmosphere and of all the celestial bodies except the sun. This temperature t_c I call temperature of the sky.

Similarly, the mean temperature t, of soil is determined (if we abstract from meteorological agents, that is in solar climate) by the balance of its radiation towards the sky [which is proportional to (t_s - t_c)] with that fraction of mean solar heat which is bestowed upon heating the surface considered. The mean annual solar heat received by unity of surface at the limits of the atmosphere (which is 0.305 of the solar constant at the equator) diminishes with the latitude λ, not as cos λ, but, according to Wiener's computations, as the cosine of an auxiliary angle ζ, which is 0° at the equator, and 65° 31′ at the poles, and which represents zenithal distance of a fixed sun, the intensity of which would be 3/10 of the true intensity, and the annual effect of which would be equivalent to that of the true sun. At sea· level this quantity of solar heat is supposed to reduce itself, according to Bouguer's law, from 1 to p^{sec ζ}, where p is the mean transparence of the atmosphere.

Upon these assumptions, the annual solar temperature of the air on a continental globe is expressed (omitting here a little term for diffused heat) by a formula t₁ = t_c + k_s cos ζ ^{(p sec ζ)/m_s} where m_s m_s is the transparence of the atmosphere for the earth's radiations, and k_s is a coefficient proportional to the heating power of solar radiation for soil, and depends then upon the physical constitution of the latter. On the sea the effect of solar heat is most complicated, but abstracting from currents, arguments are given for accepting on oceanic globe a formula t_o = t_c + k_a (p sec ζ)/m_a, where m_a, k_a are the analogues of m_s, k_s for sea. Forbes expresses the mean temperature of each parallel by t = t₀, + x (t₁ - t₀), when x is the fraction of parallel occupied by continents; but the same formula may express the mean temperature of every point on continents, if x means its continentality, whose expression by annual range e (x = (e - e₀) / (e₁ - e₀) is discussed.

The calculation of coefficients in the complex formulae so obtained is very much simplified by comparison with known empirical formulae. Mendeleef's formula for vertical distribution of temperature leads to the fundamental fact that the mean temperature of the sky, t_c, is a constant for all points at sea-level, and from evaluations of Mendeleef's constant by Woeikof I assume it as - 45,4 °C. ( - 49,7 °F.). So is numerically expressed what Mr. Culverwell calls the blanketing function of atmosphere, and its function of conforming temperature on the earth's surface; and Croll's fallacy of evaluating effects of solar heat by differences from a hypothetical temperature of space is placed in evidence. Values of t₀, t₁ at equator, discussed from Forbes' formulae, give values of k_s/m_s, k_a/m_a; p is assumed as 0,60.

Solar temperatures so obtained give a very satisfactory representation of facts: their differences from true temperatures are a striking reflex of the distribution of meteorological and physical agents (sea and air currents, convective motions, shore-ice, &c.) not accounted for in deduction of formulae.

An attempt is made for a theory of annual range, where Wilson's principle of the constancy of nocturnal cooling of bodies, whatever may be the temperature of the air, allows the assumption that the temperature of the sky follows in its variations temperature of soil. Comparison of theory with facts indicates the enormous smothering influence of meteorological agents.

Discussions of astronomical and geographical theory of an Ice Age, in the light of the formulae given, accounts for variability of physical and meteorological agents. None seems to me to satisfy either the theory or the actual conditions for variation of climates, as developed on facts by Brückner's classical work on "Klimaschwankungen." These conditions seem to the author to be satisfied by the suggestion of a small diminution in the transparence p, attended by a proportional, or by a smaller, diminution of m_s, m_a. So the difference t - t_c is diminished, less at low latitudes, more at higher. above all at 70° Lat., the variation diminishing further. Diminution is greater on sea and less on continent, so diminishing at high latitudes thermic difference het ween earth and sea, what is, according to Brüickner's demonstration, the capital condition for a rainy period on continents, and indirectly fur glaciers pushing forward. Abo the difference between equator and poles is strengthened.

lnversely, an increase of p and m_s, m_a would bring, as in Tertiary periods, a more equal distribution of temperature between equator and poles, by increasing for several degrees the temperature in higher latitudes. Mars is probably in a similar condition, as polar ice-caps do dissolve, notwithstanding that the intensity of sun is there much less than on earth ; but the Martian atmosphere is extraordinarily more transparent than ours. Annual range would be strengthened ; but the flora of East Siberia suggests that also Heer's polar floras might have sustained severe winter, provided that summer's heat was sufficient to support them, and that abrupt variations were avoided.

Quelle: Luigi De Marchi, Nature Vol. 53, No. 1373, Feb. 20, 1896, p. 376.