PROFESSOR FORBES ON THE TEMPERATURE OF THE EARTH. 221 



ments theory has hitherto taken no account, and consequently the expression for the quantity 

 of sunshine obtained, in terms of the astronomical constants, with so much labour, we must 

 hold to be nearly useless as a physical datum. It is vain to say, with M. PoissON, " Les lois 

 d' absorption de la chaleur solaire a travers I'atmosphere, les variations diumes et annuelles 

 sent egalement inconnues, et Ton peut seulement supposer gazelles sontpeu considerables ." We 

 know, on the contrary, that they are so considerable, that, estimating the loss of radiant heat 

 by a vertical passage through the atmosphere at only twenty-five per cent., at an angle of 

 elevation of 25" the force of the solar rays would be reduced to a half, and at 5° to one-tmen-' 

 tieth part. "We know, indeed, that the difference of the direct efi"ect of a vertical and a hori- 

 zontal sun is due to this cause alone, exaggerated, of course, immensely by the variable me- 

 teorological state of the atmosphere, which again is a function of the latitude. 



" (2.) The receptive power of the surface is a datum which we find it very difficult directly 

 to determine, and which, since the quantity of sun.shine cannot (as we have seen) possibly be 

 directly computed, must be inextricably mixed up with it. It might be a question, whether, 

 by covering a tolerably extensive surface of soil, in which thermometers are inserted, with a 

 composition of known superficial conductivity, this element might not become known. 



" (3.) The specific heat (c) and conductivity (Ji) of the soil are also inextricably mixed up 

 together in the analysis ; but either becoming known, the other may be inferred from ther- 

 mometric observations carried below the surface. The specific heat seems that best a,dapted 

 for laboratory experiments ; M. Elie de Beaumont has assigned 0-5614 for the value of c 

 (that of an equal hulk of water heing = l), proper to the soil at the Observatory at Paris. 



" To obtain the conductivity of the soil a posteriori, it is fortunately not necessary that the 

 preceding theoretical estimation of the distribution of sunshine should be correct; but there 

 are other estimates into which it essentially enters, and which must therefore be received 

 with corresponding caution. To facilitate reference to M. Poisson's work, I will shew how 

 the simple and very satisfactory observation of maximum and minimum temperature of the 

 earth's crust at given small depths (above the invariable stratum) may be made to yield a 

 knowledge of some of the constants above referred to. 



" Let the excess of the annual maximum above annual minimum temperature at a depth j?) 

 be expressed by A^, ; then 



log Ap = A -t- B jB 

 in which A of course denotes the log. range when jo = or at the surface, and B determines 

 the common ratio of the geometrical progression according to which the range diminishes. 

 From observations with two thermometers at different depths, A and B may be obtained d 

 posteriori. 



" Now when we consult M. Poisson's work, we find that his equation (23.), page 497, 

 which is equivalent to the preceding one, is thus composed. The quantity A, on which the 

 superficial range depends, contains (1) astronomical constants of climate y, /i, a, u already 

 mentioned ; (2) a temperature A, depending on tlie mean force of the solar rays which have 

 traversed the atmosphere and entered into combination with the earth's surface by absorp- 

 tion at a given place ; (3) the constant of conductivity k, and of specific heat c. 



" The coefficient B, on which the rate of diminution of the range depends, is fortunately a 

 very simple quantity, involving neither astronomical constants, nor tliose proper to the super- 

 ficies. It is, in fact, an absolute number multiplied by /-r-, and from a knowledge of it (by 

 VOL. XVI. PART II. 3 K 



