ITS EFFECT ON TEMPERATITRE AND ITS PRESSURE ON SMALL BODIES. 545 
motion alters the rate at which the surface is emitting radiation, but it appears worth 
while to trace consecpiences on the assumption that the radiation goes on as if the 
surface weie at rest,^ but that it is crowded up into less space or spread over more, 
and that we can superpose on this the energy given out to, or taken from, the stream by 
the work done by or on the moving surface Ipy the radiation jiressure. This work can 
evidently be calculated to the first order of approximation liy supposing the jiressure 
equal to its value when the surface is at rest. 
Let us draw from A as centre a sphere of radius U, equal to tlie velocity of radiation, 
fhe ener^\ Avlnch, in a system at rest, would be radiated into a cone with A as vertex, 
length U, and solid angle dw, in the direction AP making y with the direction of 
motion AB, will now be crowded up into a cone of length U — u cos y, since u cos y 
is the velocity of A in the direction AP. We shall suppose that n/U is very small. 
Hence the energy density in the cone is increased in the ratio U -f- u cos y : U or by 
the factor 1 4- u cos y/U. 
Considering now the effect of the work done, the force on A due to the stream in 
d(o is N cos dc/oj/U, and the work done in one second is (N cos dc/o/U) X u cos y. 
AVhen A is at rest the energv in this cone is 
N cos 6 doj. 
When A is moving it is increased to 
>T n j I N cos 6 d(x) 
jN cos u do) -j- .0. u cos y, 
that is 
N cos 9 doi{ I ^). 
Thus the effect of the work done is equal to that of the crowding and the energy 
density on the whole is increased in the ratio 
1 + 
2n cosy 
U ' 
The pressure is increased in the ratio of the energy density. Then the force on A 
due to the radiation through doj is increased from 
N cos 9 d(j} 
U 
to 
211 cos 
U 
* Adfled August 20, 1903.—Since the above was written Professor Ij.4RM0R has pointed out to me that 
the results obtained in the text from this assumption, along with the hypothesis of crowding of the 
radiation and its increase by an amount equivalent to the work of the radiation pressure, can lie justified 
by an argument based on the following considerations. A perfect reflector moving with uniform speed in 
an enclosure, itself also moving at that speed, and so in a steady state, must send back as much radiation 
of every kind as a full radiator in its place. Now the electrodyiiamics of perfect reflexion are known; 
hence the effect of motion of a full radiator on the amount of its radiation can lie determined. The result 
is equivalent to the statement that the amplitudes of the excursions of the optical Dbrators are the same 
at the same temperature whether the source to which they belong is moving or not. 
YOL. ecu.-A. 4 A 
