584 PROFESSOR J. H. POYNTING ON RADIATION IN THE SOLAR SYSTEM; 
This, then, is the upper limit to the temperature ol the hottest part of au airless moon. 
For a surface at angle X with the line to the sun, 
6^ = 412 cos^ X. 
If we take this as the law of temperature of the side of the moon exposed to the 
sun, we can find the effective temperature of the full moon as seen from the earth, 
i.e., the uniform temperature of a flat disc of radius equal to that of the moon, 
sending: to us the same total radiation. 
If Nc/o) is the normal stream of radiation from I sq. centim. of surface of the 
moon immediately under the sun sent out through a cone angle dco, that sent out in 
direction X to the normal is N cos X dco. But 1 sq. centim. on the moon s surface 
inclined at X to the sun’s rays only receives cos X of the radiation received by the 
surface immediately under the sun. It therefore sends in the direction of fhe earfh, 
also at X to the normal, only N cos” kdco. Hence the total radiation to the earth, 
obtained by putting dco = 2 it sin 6 dO and integrating is 
TT 
p N cos” X 27rin” sin X dX 
I - ^ 
‘'o ' 
where m is the radius of the moon and r is its distance from the earth 
2-n- m~ 
'3 
N. 
Let Nd be the normal stream from the equivalent flat disc, then 
77 
and 
, nr 
j-TT — JN 
2N 
The effective temperature of the flat disc is therefore that of the surface 
immediately under the sun at the same distance from it. 
Then the eftective average = 412 x \/f = 412 X 0’9 = 371° A. The upper 
limit, then, to the average effective temperature of the moon’s disc is just below that 
of boiling water. 
This is very considerably above Langley’s estimate, that the surface of the full 
moon is a few degrees al)ove the freezing-point. There can be no doubt that a very 
appreciable amount of heat is conducted inwards. The observations during eclipses 
by Langley* and by Boeddicker show that some heat is still received from the 
moon’s surface when it has entered the full shadow, and that it takes time after the 
eclipse has passed to establish a steady temperature again. It mighd be possible to 
* “Third Memoir,’ p. 159. 
