.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. Itis vain to say, with M. Poisson, “ Les lois 
d’absorption de la chaleur solaire & travers l’atmosphere, les variations diurnes et annuelles 
sont également inconnues, et l’on peut seulement supposer qu’ elles sont peu considérables.” 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-twen- 
tieth part. We know, indeed, that the difference of the direct effect 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 sunshine 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 (&) 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 adapted 
for laboratory experiments ; M. ELIE DE BEAUMONT has assigned 0:5614 for the value of ¢ 
(that of an equal bu/k of water being=1), proper to the soil at the Observatory at Paris. 
“ To obtain the conductivity of the soil @ 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 p 
be expressed by A,; then 
log AA=A+Bp 
in which A of course denotes the log. range when p = 0 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 a 
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, u, «, » already 
mentioned ; (2) a temperature 4, depending on the 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 &, and of specific heat c. 
* The coefficient B, on which the rad of diminution of the range depends, is fortunately a 
very simple quantity, involving neither astronomical constants, nor those proper to the super- 
ficies. Itis, in fact, an absolute number multiplied b ca and from a knowledge of it (by 
P aay g M) 
VOL. XVI. PART II. o kK 
