68 REPORT—1840. 
87. The work in which the rigorous comparison of theory with 
experience in this most intricate inquiry has been most insisted 
on, is that of M. Poisson, of whose mathematical attainments 
it would be equally unnecessary and unbecoming in me to 
speak ; any criticisms I have to offer will therefore be confined 
to the second of the heads I have noticed above; and to his 
writings * I will chiefly confine my attention. 
88. So far as the effect of soLAR HEAT is concerned, the a pri- 
ort solution of the problem of the temperature of any part of the 
earth’s surface may be thus imagined :—(1.) The whole quantity 
of sunshine which falls on any part of the earth’s surface in 
the course of a year is to be found, and also the law of its 
variation of force at different seasons. (2.) The part of this 
heat which becomes effective in heating the earth’s crust is to 
be found by multiplying the amount by a constant depending 
upon the absorbent power of the surface. (3.) This quantity 
of heat thus reduced is propagated towards the interior, accord- 
ing to the laws of conduction, which again pre-suppose the 
knowledge of two constants proper to each soil, namely, the 
Conductivity and the Specific Heat. 
89. (1.) The measure of the quantity of sunshine received by 
any place in a year, and its distribution at different seasons, has 
been a favourite problem with mathematicians+. In ultimate 
analysis, it depends of course on the astronomical elements 
which affect the progress of the seasons, viz. the obliquity of 
the ecliptic(y), the latitude of the place(u), the excentricity of 
the earth’s orbit(a), and the longitude of the sun’s perigee(a) ft. 
But there are also elements quite as important as any of these ; 
the imperfect transparency of the air and its varying thickness, 
owing to differences of obliquity of the transmitted rays, and 
the condition of opacity depending on the weather. Neither of 
these are insignificant, neither of them compensatory; both 
may be considered as functions of the hour-angle and fraction 
of the year, and the second is besides subjected to the most 
capricious changes. Yet of these elements theory has hitherto 
taken no account, and consequently the expression for the 
quantity of sunshine obtained, in terms of astronomical con- 
stants, 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 4 travers l’at- 
mosphere, les variations diurnes et annuelles sont également 
* Théorie Mathématique de la Chaleur, 4to. Paris, 1835, chap. xii. Sup- 
plément, 4to, 1837, and Comptes Rendus, iv. 137. 
+ See a list in Kamtz, Lehrbuch, i. 60. 
t In Poisson’s Notation. § Théorie, p. 475. 
