440 JAMES CLERK MAXWELL. [CHAP. XIV- 



of human reason, and valid consequences may be deduced 

 from it by legitimate methods ; but there are certain peculi- 

 arities in the very form of the results which indicate that 

 they belong to a different department of knowledge from the 

 domain of exact science. They are not symmetrical func- 

 tions of the time. It makes all the difference in the world 

 whether we suppose the inquiry to be historical or prophet- 

 ical whether our object is to deduce the past state or the 

 future state of things from the known present state. In 

 astronomy, the two problems differ only in the sign of t, the 

 time ; in the theory of the diffusion of matter, heat, or 

 motion, the prophetical problem is always capable of solu- 

 tion ; but the historical one, except in singular cases, is in- 

 soluble. There may be other cases in which the past, but 

 not the future, may be deducible from the present. Perhaps 

 the process by which we remember past events, by submitting 

 our memory to analysis, may be a case of this kind. 



Much light may be thrown on some of these questions by 

 the consideration of stability and instability. When the state 

 of things is such that an infinitely small variation of the pre- 

 sent state will alter only by an infinitely small quantity the 

 state at some future time, the condition of the system, whether 

 at rest or in motion, is said to be stable ; but when an in- 

 finitely small variation in the present state may bring about 

 a finite difference in the state of the system in a finite time, 

 the condition of the system is said to be unstable. 



It is manifest that the existence of unstable conditions 

 renders impossible the prediction of future events, if our 

 knowledge of the present state is only approximate, and not 

 accurate. 



It has been well pointed out by Professor Balfour Stewart 

 that physical stability is the characteristic of those systems 

 from the contemplation of which determinists draw their 

 arguments, and physical stability that of those living bodies, 

 and moral instability that of those developable souls, which 

 furnish to consciousness the conviction of free will. 



Having thus pointed out some of the relations of physical 



