TRANSACTIONS OF THE SECTIONS. 7 



This subject is one in whicli we, as a scientific body, take a warm interest; and 

 you are all aware of the vast amount of scientific work which has been expended, 

 and profitably expended, in providing weights and measures for commercial and 

 scientific purposes. 



The eai'th has been measured as a basis for a permanent standard of length, and 

 every property of metals has been investigated to guard against any alteration of 

 the material standai'ds when made. To weigh or measure any thing with modern 

 accuracy, requires a course of experiment and calculation in which almost every 

 branch of physics and mathematics is brought into requisition. 



Yet, after all, the dimensions of om- earth and its time of rotation, though, rela- 

 tively to our present means of comparison, very permanent, are not so by any phy- 

 sical necessity. The earth might contract by cooling, or it might be enlai-ged by 

 a layer of meteorites falling on it, or its rate of revolution might slowly slacken, 

 and yet it would continue to be as much a planet as before. 



But a molecule, say of hydrogen, if either its mass or its time of vibration were 

 to be altered in the least, would no longer be a molecule of hydrogen. 



If, then, we wish to obtain standards of length, time, and mass which shall be 

 absolutely permanent, we must seek them not in the dimensions, or the motion, or 

 the mass of our planet, but in the wave-lengih, the period of vibration, and the 

 absolute mass of these imperishable and unalterable and perfectly similar molecides. 



\Mien we find that here, and in the stan-y heavens, there are innumerable mul- 

 titudes of little bodies of exactly the same mass, so many, and no more, to the 

 grain, and vibrating in exactly the same time, so many times, and no more, in a 

 second, and when we reflect that no power in nature can now alter in the least 

 either the mass or the period of any one of them, we seem to have advanced along 

 the path of natural knowledge to one of those points at which we must accept the 

 guidance of that faith by which we understand that " that which is seen was not 

 made of things which do appear." 



One of the most remarkable results of the progress of molecular science is the 

 light it has thro^vn on the nature of in-eversible processes — processes, that is, which 

 always tend towards and never away from a certain limiting state. Thus, if two 

 gases be put into the same vessel, they become mixed, and the mixture tends con- 

 tinually 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 temperatui-e. If two unequally heated solid bodies be 

 placed in contact, a continual approximation of both to an intermediate temperature 

 takes place. 



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

 but in the other two cases the former state of things cannot be restored by any 

 natural process. 



In the case of the conduction or diff"usion of heat the process is not only u-rever- 

 sible, but it involves the in-eversible 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 equi- 

 valent to the doctrine of Clausius concerning the gTOwth of what he calls Entropy. 



The iri'eversible 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 diiRision of heat. 



But if we attempt to ascend the stream of time by giviug to its symbol conti- 

 nually 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 absiu'd. 



We thus anive 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. 



