o4 Scientific Proceedings, Royal Dublin Society. 
the various very complex and undescribed movements accompany- 
ing the spirality described, and the vector H to represent the still 
less clearly described movements accompanying the propagation of 
E. This may seem, at first sight, an unsatisfactory method, but 
it is really quite in accord with our methods of investigation — 
in other cases. Besides, the obvious case of temperature and 
entropy which measure properties of bodies whose dynamical 
character is only very vaguely known, I may take the example of 
pressure in a gas as very similar. ‘The pressure of a gas was for 
generations dealt with and most usefully employed long before 
the structure of a gas was understood. This state of affairs is 
‘quite analogous to the condition in which Maxwell left the ether 
theory of electro-magnetism. He postulated and discovered the 
properties of electric and magnetic force, without explaining them 
by any dynamical theory as to the structure of the ether. The 
analogies he put forward were just as vague and unsatisfactory, 
but certainly not more so than the gaseous theories that depended 
on explaining the elasticity of a gas by that of atmospheres of 
the hypothetical caloric. The kinetic theory of gases explaine 
their pressure and other properties upon dynamical principles, but 
when first propounded, and even still, the actual distribution of 
motion amongst the molecules, atoms, and within the atoms of 
gases are unknown, but that does not detract from the value 
of the dynamical theory, nor make us hesitate to use pressure as 
a function of the state of the gas, although we do not know 
exactly what that state is. 
I give these examples of pressure, temperature, and entropy 
to show that there is nothing abstruse or contrary to precedent 
in my assumption of H# and H as representing states which are: 
not, in their entirety, described or analysed. I might have in- 
stanced directed quantities as examples, such as the stress in a 
wire subjected to longitudinal pull. This is a very complicated 
state of stress which can be represented by a single vector, 
although in no single instance have we any except the very vaguest 
conception of what the actual state of affairs is inside the wire 
subject to this stress. 
