70 REPORT—1840. 
at the surface, and B determines the common ratio of the geo- 
metrical progression according to which the range diminishes. 
From observations with two thermometers at different depths, 
A and B may be obtained @ posteriori. 
94. Now when we consult M. Poisson’s work, we find that his 
equation (23.), page 497, whichis equivalent to the preceding one, 
is thus composed. The quantity A, on which the superficial 
range depends, contains (1) astronomical constants of climate y, 
&, &, @ already mentioned; (2) a temperature A depending on 
the mean force of the solar rays which have traversed the atmo- 
sphere and entered into combination with the earth’s surface by 
absorption at a given place*; (3) the constant of conductivity 4, 
and of specific heat ce. 
95. The co-efficient B, on which the rate of diminution of the 
range depends, is fortunately a very simple quantity, involving 
neither astronomical constants, nor those proper to the superficies. 
It is, in fact, an absolute number multiplied by, / a. and from 
a knowledge of it (by observations with two or more thermome- 
ters) this quantity may be very readily and accurately deter- 
mined ; and it affords the only unexceptionable manner of ascer- 
taining the conductivity of the earth’s crust on a large scale. 
Observations to this effect have, from time to time, been made 
by thermometers plunged more or less below the soil; first, by 
Ott of Zurich, in 1762+; secondly, by Leslie near Edinburgh ; 
thirdly, by Herrenschneider at Strasbourg}; fourthly, by Muncke 
at Heidelberg§; fifthly, by Rudberg at Upsala; sixthly, by 
Arago at Paris; seventhly, by Quetelet at Brussels. An ad- 
* Poisson, p. 480, where the definition of / is “ Une température constante 
proportionelle & l’intensité de la chaleur solaire, telle qu'elle est a la distance 
moyenne de la terre au soleil et aprés avoir traversée l’'atmosphére pour arriver 
au point O.” It must not, however, be forgotten, that it includes ¢, a constant 
of superficial absorption, and therefore varies from one point to another. See 
Poisson, p. 500. The quantity / is one of the most troublesome clearly to ap- 
prehend, and the dispersion (and sometimes permutation) of symbols throughout 
so large a work contributes to the ambiguity. I will therefore add, that in the 
ce SET: = x) a? ¢ is a constant of absorption for a 
given soil, but which may vary with the incidence of the rays (p. 474) ; S is the 
product of an element of surface, and a quantity of heat in the condition in 
which the atmosphere has transmitted it (p. 475); a and a, denote the proper 
superficial radiating power of the point O under consideration, and the cooling 
effect due to the contact of air (p. 849). The product of h by Q (see Art. 105, 
note) measures the thermometric efficiency of the solar rays in raising the 
climateric temperature of the spot (p. 518). 
+ Lambert's Pyrométrie, p. 356. } Imperfect; only one thermometer. 
§ Gives only the epochs. 
value of h, page 480, namely, 
