60 M. POUILLET ON SOLAR HEAT, 
loses a quantity of heat pc, and as it loses it by one surface s, 
each unity of surface loses 
pe 
s 
but since the body requires a time @ to fall 1°, it follows that 
in a time 1 it falls 
. 
b] 
yA 
zB 
Thus in the unity of time, the unity of surface loses a quantity 
of heat expressed by 
pe ml! a 7 
eer oS Nae 
For another body which should have the same initial tempera- 
ture T’, the loss would be 
pe, tla 
ait -™ « nat a. 
As these losses must be proportional to the radiating powers f 
and f' of the two bodies, we should have 
i HGS 
m” s.f'.pe 
that is to say, the coefficients m and m! are in fact in a direct 
ratio to the surfaces and the radiating powers, and in an inverse 
ratio to the masses and the capacities. 
14. The formule (2) and (3) contain the laws of cooling in 
absolute cold; they may be employed to solve a great number 
of questions. 
The first shows, for example, that under the equator, where 
the temperature of the earth is on an average 30°, each square 
centimetre loses in unities of heat, 
1:44 in 1, 
1037°00 in 12 hours ; 
whence it follows, that in a column of water 10 metres in 
depth, there would in twelve hours be only a lowering of 1°, if 
by its upper surface that column lost its heat in absolute cold 
without receiving compensation for what it loses, either by its 
free surface or by its sides. 
The second shows that in absolute cold the thermometer of 
MM. Dulong and Petit would take 
34''14 to fall from 100° to 0, 
74'-66 to fall from 0 to —100°; 
