74 M. POUILLET ON SOLAR HEAT, 
The advantage there may be in resolving thus the problem 
will be better comprehended when we shall have shown the new 
relations which thence result between the unknown quantities 
which we seek to determine. Let us represent by z the zenithal 
temperature and preserve the same designation for the other 
quantities, namely,— 
/' for the temperature of space ; 
i for the mean temperature of the atmospheric column ; 
b for the absorbing power which the atmosphere exerts upon 
the terrestrial heat; and 
b! for the absorbing power which the atmosphere exerts upon 
the celestial heat. 
This being established, let us consider,— 
1. That during the unity of time the zenithal inclosure emits 
by the unity of surface a quantity of heat, 
Ba’; 
B being the same constant 1°146 of which we have previously 
spoken ; there is no coefficient relative to the radiating power, 
because we must suppose it equal to unity. 
2, That the atmosphere emits likewise a quantity of heat 
because its emissive power is equal to its absorbing power, which 
we have represented by 6. 
3. Lastly, that space emits a quantity of heat 
Ba‘, 
but that there is only one portion of it (1— 4’) which directly tra- 
verses the atmosphere to reach the ground, whence it follows that 
with relation to the thermometer which rests upon the ground, 
it is as if space had an emissive power 1— 0’, and as if it trans- 
mitted only a quantity of heat 
(1— 0) Ba’. 
Since the zenithal inclosure replaces the atmosphere and space, 
the quantity of heat which it emits with relation to the thermo- 
meter must be exactly equal to the sum of the quantities of heat 
emitted by the atmosphere and space. 
We have then 
Ba’ =Bba’ + (1 — 0) Ba’, 
@=ba +(1—#) eS. (4.) 
Such is the general relation which connects incessantly the ze- 
nithal temperature with the temperature of space, with the mean 
