62 M. POUILLET ON SOLAR HEAT, 
equal to the sum of the quantities of heat which it receives, and 
this gives a first equation, 
2e's'! = bes+ hes! sin?a. 
We obtain in the same manner for the globe and for the inclo- 
sure, two other equations which result from the equality between 
the quantities of heat received and lost, namely, 
es=e's! + (1—8) e's! sin? a, 
és! sin?'w =e’ s+ (1—JD) es. 
It is easy to see that these three equations are reducible to 
two, because the first is a consequence of the two last, and might 
be deduced from them. 
If we now suppose the radius of the envelope to be sensibly 
equal to the radius of the globe, as is nearly the case with the 
atmosphere around the earth, the equations become 
e=e' + (1—J) ed, 
é=e!l + (1—d)e, 
and this leads to the three following relations : 
e 2-3 
a WEG? 
e oun Dae 
ee 64+0—b0" 
é 2—5 
b+ 0-6" 
If, now, we designate by ¢, ¢", 7’ the temperatures of the globe, 
of the envelope and of the inclosure; by f, f",/’ their emissive 
powers, we shall have, in virtue of the principle above esta- 
blished, the three other equations: 
e=B.a', 
é=B.a", 
e'=B.f" age 
on the supposition we have made, to simplify the matter, that 
the globe and the inclosure have maximum emissive powers. 
These equations, combined with the preceding ones, give— 
eet 
fey hee 
a mii ait 
oH 
t—t" =| fir _ ene 
i I a ETF" 
ea 
ent So see ai 
IE AE ROW 
