DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
517 
processes are reversible—are sufficient to account for any physical phenomenon, then 
we must show how to explain irreversible processes as the effect of changes all of 
which are reversible. It would not be sufficient to explain these irreversible effects by 
means of ordinary dynamical systems with friction, as friction itself ought on this 
view to be explained by means of the action of frictionless systems. 
If every physical phenomenon can be explained by means of frictionless dynamical 
systems, each of which is reversible, then it follows that, if we could only control the 
phenomenon in all its details, it would be reversible, so that the irreversibility of any 
system is due to the limitation of our powers of manipulation. It is because we only 
possess the pow~er of dealing with the molecules en masse and not individually, while 
the reversal of these processes would require us to be able to reverse the motion of 
each individual molecule. This was pointed out by Maxwell, who showed that an 
army of his “ demons ” would be able to prevent the dissipation of energy. 
Our want of power of dealing with very minute portions of matter imposes one 
kind of limitation on our control of physical processes ; another limitation to our power 
of interpreting them is caused by the time which our sensations last, causing any 
phenomenon which consists of events following one another with great rapidity to 
present a blurred appearance, so that what we perceive at any moment is not what is 
happening at that moment, but merely an average effect, which may be quite unlike 
the effect at any particular instant. In consequence of the finiteness of the time 
taken by our senses to act we are incapable of separating two events which happen 
within a very short interval of each other, just as the finiteness of the wave-length 
of light prevents us separating two points which are very close together. Thus, if 
we observe any effect, we cannot tell by our senses whether it represents a steady 
state of things or a state which is rapidly changing, and whose mean is what we 
actually observe. Thus we are at liberty, if it is more convenient for the purposes of 
explanation, to look upon any effect as the average of a series of other rapidly 
changing effects. 
Let us consider the case of a system whose motion is such that, in order to represent 
it, “ frictional terms ” have to be introduced. Let us first assume that the motion is 
represented at each instant by the equations with these terms in, and that these 
equations are not equations which are only true on the average. Let us assume that 
any phenomenon is capable of explanation by the principle of abstract dynamics. 
Then, from our point of view, we shall have explained the phenomenon when we have 
found a frictionless system whose motion would produce the phenomenon. 
It might at first sight appear as if we could explain the frictional terms in the 
equations of motion as arising from the connection of other subsidiary systems with 
the original system, just as in the first part of the Paper (‘ Phil. Trans./ 1885, p. 311) 
we explained the “ positional ” forces as due to changes in the motion of a system 
connected with the original system. Let us suppose for a moment that this is possible. 
Then, if T be the kinetic energy of the original system, and T' that of the subsidiary 
