ITS EFFECT ON TEMPERATURE AND ITS PRESSURE ON SMALL BODIES. 535 
make some rough estimate of the amount conducted inwards from tlie Fourier 
equation, hut the problem is not an easy one. Perhaps we get the 1)est estimate by 
comparing the actual temperature with that above found. 
If the actual temperature is taken as about -f the upper limit, say 297° A, tlien 
the radiation outwards is of the order yf = OAl of that where no conduction 
exists. Then nearly | of the heat is probably conducted inwards. 
If the moon always turned the same face to the sun instead of to the earth, the 
upper limit would be approached. 
1 QTfij)€vcit'Li') d oj" ct SpliQ} iccil jA.hsovb'iTiy Solicl Body of the Ovd&r 1 coHtmi. tn dtct'inctcv 
at the Distance of the Earth from the Sun. 
The calculation of the temperature of such a body is interesting for two reasons. 
Firstly, the body will be at nearly the same temperature throughout, and secondly, 
as we shall show in the second part of this paper, the mutual repulsion of two sucli 
bodies, due to the pressure of their radiation, is of the same order as their gravitative 
attraction. 
If the radius of the body is a, its effective receiving area is ttcF, and it receives 
Tra^S ergs/sec. 
. Its radiating surface is 477cF, and therefore its average radiation per square 
centimetre in the steady state is 
7r«'S/47rfr = 
If we take S = 2-5 cal./niin. or 0-04 cal./sec., and if the conductivity is of the 
order of that of terresti'ial rock lying, say, between O'Ol and O'OOl, it is evident that 
a difference of temperature of only a few degrees between the receiving and tlie dark 
surfaces will convey heat sufficient to supply radiation, O'Ol cal./sec., equal to the 
average. Thus, if the conductivity is 0-001 and the diameter is 1 centim., a difference 
of temperature of 10° suffices. 
We may therefore take the temperature of the surface as approximately uniform 
when the steady state is reached. Let tlie temperature be d, and let the solar 
temperature he dg. Then we have 
-.Of = %-. 46,000 S 
4 
and 
e = , 
20-7 
If 
= 6200° A, 
0 = 300° A approximately. 
This will he the temperature of fully absorbing bodies smaller than 1 centim., so 
long as they are not too small to absorb the radiation falliiip: on them 
* 
