530 PROFESSOR J. H. POYXTING ON RADIATION IN THE SOLAR SYSTEM I; 
thirds of the earth’s surface, the daily range is very small, of the order of 1° or 2° C., 
while even on the land it is, in extreme cases, not more than 15° C., which is not 
a large fraction of the al^sohite temperature. 
3. That the surface and the atmosphere over it at any one point have one effective 
temperature as a full radiator. This is no doubt a departure from reality. How 
wide a departure we have no present means of estimating. 
4. That there is no convection of heat from one latitude to another. 
This is a very wide departure from reality. But, as we shall see below, the mean 
temperature of the planet is very little affected by convection, even if we assume that 
it is so extensive as to make the surface of uniform temperature. 
5. That the reflexion at each point is i^oth of the radiation received. 
This is probably of the order of the actual reflexion from tne earth. According to 
Langley"' the moon reflects about -g-th of the radiation received. The earth certainly 
reflects less. The temperatures determined liereafter are proportional to the 4th root 
of the coefficient of absorption. Even if this coefficient is as low as 0'9 its 4th root 
is 0’974. Hence if the actual value is anywhere between 0'9 and 1, the assumed 
value of 0-9 will not make an error of more than 2|- per cent, in the value of the 
temperature. 
6. Hiat the planet ultimately radiates out all the heat received from the sun, no 
more and no less. 
This ao’ain is very near the condition of the real earth, which, on the vhole, 
radiates out rather more than it receives—perhaps on the average a caloiie pei 
square centimetre in three days. 
Making these six suppositions, let us calculate the temperature of various parts of 
this ideal planet. 
Consider a hand between latitudes X and 
X + dX. The area receiving heat from the sun 
•P • . 1 n X 4.1 rcosAdJ^—y 
at any instant, if projected normaffy to the r 
stream of solar radiation, is (fig. 2) 
2'r cos X rdX cos X = 2r" cos" XdX, 
where r is the radius of the planet. 
If S is the solar constant, this band is 
absorbing, with coefficient 0'9, 
0’9S X 2r"cos"XdX. 
But the band all round the globe is radiating 
equally, according to the second supposition, and the radiating area is 
Fig. 2. 
27rr cos X . rdX = cos Xr/X. 
* “ Third IMemoir oil the Temperature of the Moon.” ‘ National Academy of Sciences,’ vol. 4, Part 2, 
p. 197. 
