362 Scientific Proceedings, Royal Dublin Society. 
Before this change the internal events were Ba and Be events, 
but, owing to the introduction of the slight roughness, the Be 
events have become Bd events; 7. e. they have acquired the power 
of very slowly, and through a great number of collisions, affecting 
uw, v, and w, which are the A events. But even if the roughness 
be so slight that they require a million of collisions to impart a 
sensible proportion of their energy to the A events, they will 
accomplish a protracted task of this kind in about the seventh part 
of the thousandth of one second, if, as we have supposed, the 
rapidity of events in our model is as great as it is in gases at 
atmospheric pressures and temperatures. Now, observations with 
the phosphoroscope indicate that the persistence of Bd events, 
when once excited, is in all the observed cases much greater ; so 
that the outer surfaces of our model molecules should be very 
nearly, though not quite, smooth. Other experiments which are in 
progress seem to show that, in some instances at least, the energy 
radiated away from phosphorescent events is much less than that 
which they lose by conduction, 7. e. by imparting energy to A or 
Ba events. Now an excessively small defect in smoothness, such 
as we have supposed, would not prevent the Boltzmann-Maxwell 
distribution of energy from being nearly the actual distribution 
among A and Ba events, wherever the other conditions of the 
theorem are, or are nearly, fulfilled ; while side by side with them 
any amount of energy may be maintained in Bd events by the 
electro-magnetic waves which unremittingly traverse the surround- 
ing ether, or may be set up by chemical reaction.* 
Another important matter to be referred to is that in the cases 
in which the theorem holds good, y, the ratio of the two specific 
1 It is easy to contrive other useful models, and to treat them like those in the text. 
Of this kind are models with spherical, spheroidal, or ellipsoidal outer surfaces, but 
with centres of inertia, either displaced from the centre of figure, or moving about it 
under definable conditions; or with more than one body inside the outer surface, and 
either concentric or not concentric withit, and with viscous or other connexions which 
would provide for various kinds of interaction ; or with the rigid outer surface discarded, 
and central forces put in its place—a substitution which either need not, or need not 
more than a little, alter the condition that the average energy shall be a sum of squares; 
and many others. Each may be in its way instructive if we use it to enable us to 
picture modes of action that occur in gases, and if we are careful not to be misled into 
fancying that any of our models can be accepted as even in a remote degree resembling 
the state of things that does prevail within the molecules of matter. 
