Natural Radiation from Moving Bodies. 585 
owing to the shortening of the waves, the velocity in this 
vibration is changed, and therefore the volume- density of 
vibratory energy in the ether is modified as above. And 
the Lorentz transformation has shown us what is not so 
immediately obvious, that also on the electric view which 
considers the sources to be constituted of vibrating electrons, 
though their relative motions are not affected by the uniform 
translation as again Carnot’s principle demands, yet the 
vibratory energy “emitted from them is modified in the manner 
here described. 
Cambridge, September 21, 1903. 
| Note added Dec. 26.—As the intensity of the pressure 
of radiation depends on the instantaneous state of the adjacent 
medium, it may be expected te remain equal to the energy 
per unit volume, as above assumed, whether the body that it 
acts on is at rest or in motion. 
We may verify in detail for a plane-polarized wave-train 
with electric force (0, Q, 0), current (0, v, 0), and magnetic 
force (0, 0, y), incident directly on an absorbing face perpen- 
dicular to z. Then* the mechanical force in the absorber 
per unit volume is 
X= (v- Ly, 
dy dQ - =) : 
where 
alae Sak eae ae ieee Yo: 
and ‘e 
I~ tare” 
v being the velocity of the material medium, with which the 
axes of coordinates travel. Thus 
4 y | x, t vy dQ 3, 
I oo o Ane), 7 de at” 

i 
Let the slice between a, and «2 be an indefinitely thin one 
containing the absorbing interface ; as Q is continuous across 
it, dQ/dt is very small ‘outside it; thus, y being finite, the 
last term is negligible, and the mechanical force acting on the | 
slice is equal to the value of y’/87 just outside it, where Q is 
null; thus it is equal to the energy-density just outside, 
whether the absorber is in motion or not. 
From the way of considering the origin of this mechanical 
* * Ather and Matter,’ 1900, § 65. 
