THE DYXAJUCAL EVIDENCE OF THE 



The result which I published in 1860 has since been subjected to a more 

 trict investigation by Dr Ludwig Boltzmann, who has also applied his method 



the study of the motion of compound molecules. The mathematical investi- 

 gation, though, like all part* of the science of probabilities and statistics, it is 

 MBewhat difficult, does not appear faulty. On the physical side, however, it 

 leads to consequences, some of which, being manifestly true, seem to indicate 

 that the hypotheses are well chosen, while others seem to be so irreconcilable 

 with known experimental results, that we are compelled to admit that some- 

 thing essential to the complete statement of the physical theory of molecular 

 encounters must have hitherto escaped us. 



I must now attempt to give you some account of the present state of these 

 investigations, without, however, entering into their mathematical demonstration. 



I must begin by stating the general law of the distribution of velocity 

 among molecules of the same kind. 



If we take a fixed point in this diagram and draw from this point a line 

 representing in direction and magnitude the velocity of a molecule, and make 

 a dot at the end of the line, the position of the dot will indicate the state of 

 motion of the molecule. 



If we do the same for all the other molecules, the diagram will be dotted 

 all over, the dots being more numerous in certain places than in others. 



The law of distribution of the dots may be shewn to be the same as that 

 which prevails among errors of observation or of adjustment. 



The dots in the diagram before you may be taken to represent the velocities 

 of molecules, the different observations of the position of the same star, or the 

 bullet-holes round the bull's-eye of a target, all of which are distributed in the 

 same mariner. 



The velocities of the molecules have values ranging from zero to infinity, 

 so that in speaking of the average velocity of the molecules we must define 

 what we mean. 



The most useful quantity for purposes of comparison and calculation is called 

 the "velocity of mean square." It is that velocity whose square is the average 

 of the squares of the velocities of all the molecules. 



This is the velocity given above as calculated from the properties of different 

 gases. A molecule moving with the velocity of mean square has a kinetic 

 energy equal to the average kinetic energy of all the molecules in the medium, 

 and if a single mass equal to that of the whole quantity of gas were moving 



