ITS EFFECT ON TEMPERATURE AND ITS PRESSURE ON S^IALL BODIES. 539 
Putting d(o = 271 sin B cW and integrating over the hemisphere, we get 
Total normal pressure = p (N cos^ 6 . '2rr sin BdBj'U) = Stt-N/SU = 2R/3U, 
.'o 
Total tangential stress = 0, since the radiation is symmetrical about the normal. 
If the surface is receiving radiation, let us suppose that the stream is a parallel 
pencil S per second per square centimetre held normal to the stream, and that it is 
inclined at 6 to the normal to the receiving surface. The momentum received 
per second is S cos d/U. This produces 
Normal pressure = S cos" 0/\J. 
Tangential stress = S cos 0 sin 6/\J. 
If the stream is entirely absoiTed both these forces exist. 
If the stream is entirely reflected, the reflected pencil exerts an equal normal force 
and an equal and opposite tangential force, and we have only normal pressure of 
amount 2S cos" 6j\J. 
If only a fraction /x is reflected, the incident and reflected streams will give 
Normal pressure = (1 + /x) S cos‘^ d/U. 
Tangential stress = (I — /x) S cos 6 sin d/U. 
To the normal pressure must l;)e added the pressure due to the radiation emitted 
from the surface. 
Radiation Pressure in Fidl Sunlight. 
If a full absorber is exposed normally to the solar radiation at the distance of the 
0‘175xl0^ 
earth the pressure on it is S/U, or —^ -77^ — = 5'8 X I0““ dyne/sq. centim. 
The Radiation Pressures Between Small Bodies. Comparison with, their 
mutual Gravitation. 
It is well known that the radiation force on a small body, exposed to solar radiation, 
does not decrease so rapidly as gravitative pull on the body as its size decreases. If 
the body is a sphere of radius a and density p, and with a fully absorbing surface, and 
if it is so small that it is practically at one temperature all through, it is receiving a 
stream of momentum 
7r«2S/U 
directed from the sun. Its own radiation outwards being equal in all directions lias 
zero resultant pressure. 
