TRANSACTIONS OF SECTION A. 381 
Maxwell terms. These equations must be of an atomic or discontinuous nature 
(e.g. they may be equations of finite differences instead of differential equations), 
both in order to satisfy the condition of Poincaré mentioned above, and to 
account for the atomicity of e. These equations will form the basis of the new 
dynamics. If in forming the equation of wave-propagation the new terms 
happen to be eliminated out, then the equation vy? ¢ = act will be true 
in the new dynamics as in the old, and there will be no discordance between the 
quantum theory and the undulatory theory. But the new terms will presum- 
ably stay in when the equations are applied to problems of interaction between 
matter and ether, so that A may be expected to play a part in all such phenomena. 
Professor Lorentz said tnat he agreed in the main with Mr. Jeans. It 
seems indeed that, in order to account for the facts of radiation, we must intro- 
duce a discontinuity of one kind or another, and that, at present, no hypothesis 
is more suitable than the assumption of definite quanta of energy. 
The theory may, however, be presented in different forms, which are best 
understood if, in the systems with which we are concerned, we distinguish three 
parts, viz., (1) molecules and atoms, between which and the ether there is no 
direct interaction, and which, for the sake of convenience, we may call 
‘matter’; (2) some kind of ‘ vibrators,’ each having a frequency of its own; 
and (3) the ‘ether.’ The vibrators must be considered as carrying electric 
charges, in virtue of which they can give rise to electro-magnetic vibrations 
Fropagated in the ether, and can, conversely, be set in motion by electro-mag- 
netic waves, the simplest type of vibrator being given by a single electron, 
moving about its position of equilibrium under the influence of a quasi-elastic 
force. On the other hand, the vibrators can exchange energy, by collisions or 
otherwise, with the material particles, so that they constitute a link between 
matter and ether. 
It need hardly be said that the distinction between the particles of matter 
and the vibrators is somewhat artificial; it may well be that in some cases the 
emission and absorption of heat is not due at all to vibrators having a definite 
period. It should also be remarked that, if we use the terms in the above 
sense, 2 mono-atomic gas consisting of uncharged molecules must be said to 
contain matter only, whereas a crystal composed of charged atoms arranged 
in definite positions of equilibrium would be entirely made up of vibrators. If, 
however, such a crystal were exposed to the bombardment of gaseous mole- 
cules, we should again have to deal with a system formed of the first two parts 
of which we have spoken. 
As to the third part, we may apply to it the time-honoured name of ‘ ether,’ 
without discussing the fitness, in the present state of science, of maintaining the 
ideas that were originally associated with the word. The principle of rela- 
tivity leads us to consider the question whether the ether has so much of 
substantiality that one can speak of the motion of a body relatively to it. For 
the present purpose this is irrelevant, and ‘ether’ is merely a word, for which 
we might as well substitute ‘ vacuum.’ 
Now it must, I think, be taken for granted, that the quanta can have no 
individual and permanent existence in the ether, that they cannot be regarded 
as accumulations of energy in certain minute spaces flying about with the speed 
of light. This would be in contradiction with many well-known phenomena of 
interference and diffraction. It is clear that, if a beam of light consisted of 
separate quanta, which, of course, ought to be considered as mutually indepen- 
dent ard unconnected, the bright and dark fringes to which it gives rise could 
never be sharper than those that would be produced by a single quantum. 
Hence, if by the use of a source of approximately monochromatic light, we 
succeed in obtaining distinct interference bands with a difference of phase of 
a great many, say, some millions, of wave-lengths, we may conclude that each 
quantum contains a regular succession of as many waves and that it extends 
therefore over a quite appreciable length in the direction of propagation. 
Similarly, the superiority of a telescope with wide aperture over a smaller 
instrument, in so far as it consists in a greater sharpness of the image, can only 
be understood if each individual quantum can fill the whole object-glass. 
These considerations show that a quantum ought at all events to have a size 
