374 MOLECULES. 



which their previous character and their present circumstances, according to the 

 beat existing theory, would lead us to expect. Those who practise this method 

 endeavour to improve their knowledge of the elements of human nature in much 

 the same way as on astronomer corrects the elements of a planet by comparing 

 its actual position with that deduced from the received elements. The study 

 of human nature by parents and schoolmasters, by historians and statesmen, is 

 therefore to be distinguished from that carried on by registrars and tabulators, 

 and by those statesmen who put their faith in figures. The one may be called 

 the historical, and the other the statistical method. 



The equations of dynamics completely express the laws of the historical 

 method as applied to matter, but the application of these equations implies a 

 perfect knowledge of all the data. But the smallest portion of matter which 

 we can subject to experiment consists of millions of molecules, not one of which 

 ever becomes individually sensible to us. We cannot, therefore, ascertain the 

 actual motion of any one of these molecules ; so that we are obliged to abandon 

 the strict historical method, and to adopt the statistical method of dealing with 

 large groups of molecules. 



The data of the statistical method as applied to molecular science are the 

 sums of large numbers of molecular quantities. In studying the relations between 

 quantities of this kind, we meet with a new kind of regularity, the regularity 

 of averages, which we can depend upon quite sufficiently for all practical 

 purposes, but which can make no claim to that character of absolute precision 

 which belongs to the laws of abstract dynamics. 



Thus molecular science teaches us that our experiments can never give us 

 anything more than statistical information, and that no law deduced from them 

 can pretend to absolute precision. But when we pass from the contemplation 

 of our experiments to that of the molecules themselves, we leave the world of 

 chance and change, and enter a region where everything is certain and im- 

 mutable. 



The molecules are conformed to a constant type with a precision which is 

 not to be found in the sensible properties of the bodies which they constitute. 

 In the first place, the mass of each individual molecule, and all its other 

 properties, are absolutely unalterable. In the second place, the properties of 

 all molecules of the same kind are absolutely identical. 



Let us consider the properties of two kinds of molecules, those of oxygen 

 and those of hydrogen. 



