TTS EFFECT OX TEMPPTtATURE AND EPS FRESRURE OX SMALL BODIES. 551 
motion, whereas it appears, it the following inode ot treatineiit is correct, that the 
pressure on a radiating surface moving forward is only 1 — of the energy density 
of the radiation emitted. 
Let us suppose that a surface A, a full radiator, is moving with velocity u towards 
a full absorber B, which, with the surroundings, we will suppose at 0° A. Consider 
for simplicity a parallel pencil issuing normal from A with velocity U towards B. 
Let tlie energy density in the stream from A he E wlien A is at rest, and E' when it 
is moving. Let the pressure on A he = E when it is at rest, and p' when it is 
moving. When moving, A is emitting a stream of momentum p per second and this 
momentum ultimately falls on B. Let A start radiating and moving at the same 
instant; let it move a distance d towards B, and then let it stop radiating and 
moving. It emits momentum p' per second for a time <l/u and therefore emits total 
momentum p'diu. Since B is at rest, the pressure on it, the momentum which it 
receives per second, is E^ But since A is following up the stream sent out, B does 
not receive through a period as long as dju, hut for a time less by i//U. If we assume 
that the total momentum received by B is equal to the total sent out by A, we have 
p'dju = E' {d/u - d/U), 
or 
y/ = E'(l - n/U). 
To find E^ in terms of E we must make some assumption as to the eftect ot the 
motion on tlie radiation emitted. In the paper I have assumed that the emitting 
surface converts the same amount of its internal energy per second into radiant energy 
as when it is at rest, hut that p'u of the energy of motion of the radiating mass is 
also converted into radiant energy. Since the radiation emitted in one second is 
contained in length U — w, we have 
E' (U - u) = EU + p'u = EU + E' (^ “''j ?/, 
whence 
The same result is obtained if we assume that the amplitude of the emitted waves 
is the same whether the surface is moving or not, and that the energy density is 
inversely as the square of the wave-length for given amplitude. 
We have, therefore, if the above application of the equality of action and reaction 
is justified. 
In a similar way we can find the effect of motion of an absorber on the pressure 
against it due to the incident radiation. 
