\ 
Natural Radiation yrom Moving Bodies. 583 
in its direction to the velocity of light*. Thus, when the 
enclosure is moving as well as the reflector, the energy of 
the incident stream coming from its receding walls is in defect 
by twice the ratio of these velocities, and that of the reflected 
stream is in excess by twice the same ratio. This_ latter 
factor therefore also expresses the excess in the volume- 
density of natural radiation coming from a perfect radiator 
that is produced by its own advancing motion; but in a 
detailed specification of this radiation the modification of the 
wave-lengths in accordance with the Doppler principle is also 
to be borne in mind.. 
A different and generalized mode of treatment may also be 
adopted, based on Lorentz’s transformation for passing from 
the field of activity of a stationary electrodynamic material 
system to that of one moving with uniform velocity of trans- 
lation through the ether. If (f, g, A) and (a, 6, c) represent 
the field of a material system at rest in the ether, then to 
the first order of v/c, 
u v 
(/: fe Arc?” a Amc? ) 
and (a, b—Amvh, c+47vq) 
represent the values of the same vectors, say (/4, 91, 4) and 
(ay, b,, ¢), for a system in motion parallel to w with velocity 
v; aud the positions and magnitudes, and therefore relative 
velocities, of the electrons which produce these fields in the 
surrounding ether in the two cases are identical at each 
instant, so that the fields belong to the same material system ft. 
An enclosing material boundary is supposed to form part 
of the system, so as to retain the radiant energy at uniform 
density. Let us compare the densities E and EH, of energy 
in the two cases of rest and translation, as given by 
Maxwell’s formula 
E=2707( f? +9? +h?) + = (+P +e). 
We obtain, neglecting (u/c)? as before, 
E,=E+2u(gce—hb). 
* The Maxwellian formula for the pressure of radiation may be based 
(doc. cit.) on this result, in connexion with the conservation of the energy ; 
or conversely, the value of that pressure being assumed on other grounds, 
this result for the intensity of the reflexion may be based upon it. 
+ Cf. ‘ Ather and Matter, p. 169. [The change to “local time” 
merely introduces the Doppler effect. ] 
