ADDRESS TO THE MAimniATICAL AND PHYSICAL SECTIONS 



state. Thus, if two gasea be put into the same vessel, they become mixed, 

 and the mixture tends continually to become more uniform. If two unequally 

 heated portions of the same gas are put into the vessel, something of the 

 kind takes place, and the whole tends to become of the same temperature. 

 If two unequally heated solid bodies be placed in contact, a continual approxi- 

 mation of both to an intermediate temperature takes place. 



In the case of the two gases, a separation may be effected by chemical means ; 

 l>ut in the other two cases the former state of things cannot be restored by 

 :iny natural process. 



In the case of the conduction or diffusion of heat the process is not only 

 irreversible, but it involves the irreversible diminution of that part of the whole 

 stock of thermal energy which is capable of being converted into mechanical work. 



This is Thomson's theory of the irreversible dissipation of energy, and it is 

 equivalent to the doctrine of Clausius concerning the growth of what he calk 

 Entropy. 



The irreversible character of this process is strikingly embodied in Fourier's 

 theory of the conduction of heat, where the formulae themselves indicate, for 

 all positive values of the time, a possible solution which continually tends to 

 the form of a uniform diffusion of heat. 



But if we attempt to ascend the stream of time by giving to its symbol 

 continually diminishing values, we are led up to a state of things in which 

 the formula has what is called a critical value ; and if we inquire into the 

 state of things the instant before, we find that the formula becomes absurd. 



We thus arrive at the conception of a state of things which, cannot be 

 conceived as the physical result of a previous state of things, and we find 

 that this critical condition actually existed at an epoch not in the utmost 

 depths of a past eternity, but separated from the present time by a finite interval. 



This idea of a beginning is one which the physical researches of recent 

 times have brought home to us, more than any observer of the course of 

 scientific thought in former times would have had reason to expect. 



But the mind of man is not, like Fourier's heated body, continually settling 

 down into an ultimate state of quiet uniformity, the character of which we 

 can already predict; it is rather like a tree, shooting out branches which adapt 

 themselves to the new aspects of the sky towards which they climb, and roots 

 which contort themselves among the strange strata of the earth into which they 

 delve. To us who breathe only the spirit of our own age, and know only the 



