580 Dr. J. Larmor on the 



of the independent sporadic shocks transmitted through the 

 aether from the impacts of the separate and independent 

 cathode particles. Both kinds of disturbance are resolvable 

 by Fourier's principle into trains of simple waves. But if 

 we consider the constituent train having wave-length variable 

 between A, and \ + 8\, i. e. varying irregularly from part to 

 part of the train within these limits, a difference exists between 

 the two cases. In the case of the white light the vibration- 

 curve of this approximately simple train is in appearance 

 steady : it is a curve of practically constant amplitude, but 

 of wave-length slightly erratic within the limits S\ and 

 therefore of phase at each point entirely erratic. In the 

 Fourier analysis of the Eontgen radiation the amplitude is 

 not regular, but on the contrary may be as erratic as the 

 phase. The origin of this difference is that the body radiating 

 the white light is presumably so far in a steady state that 

 each element of it has a definite temperature at each instant, 

 which implies a statistical uniformity in the vibratory dis- 

 turbance that is emitted. Or, approaching the subject from 

 the side of the thermodynamics of radiation, each elementary 

 constituent wave-train, say that corresponding to the interval 

 S\ above, has its own temperature which it carries permanently 

 along with it, the same as the temperature of its source 

 supposed a perfect radiator. This temperature is at each 

 point of it a function of the energy-density, and therefore of the 

 amplitude of the radiation. If the amplitude were different 

 along two reaches of the train, the reach of higher amplitude 

 could be in equilibrium of spontaneous exchanges of energy 

 with a perfect radiator of higher temperature than its own 

 source, and ideal automatic arrangements involving intensi- 

 fication of the energy would be possible, in opposition to Lord 

 Kelvin's fundamental principle of degradation. In the 

 internal equilibrium to which a material system nearly 

 instantaneously settles down, in acquiring a definite temper- 

 ature for each element of its mass, such differences of 

 amplitude must thus have disappeared : the state of uniform 

 amplitude is, in fact, the most probable one *. 



In the distinction which is here suggested, the average 

 degree of suddenness of the Rontgen pulses is not involved. 

 That would still be capable of estimation by experiments on 

 diffraction of rays travelling in free aether, in the manner of 

 Haga and Wind. But no physical rationale of prismatic 

 dispersion f except the influence of the vibrations excited in 

 the material system seems now to be entertained ; and this 



* It is hoped to pursue this idea in another connexion. 



t Propagation in limited systems such as bars is not to the point. 



