440 SCIENTIFIC THOUGHT. 



studying those properties of matter that are preserved 

 distinct in ever so large a number of individuals which 

 are characteristically and specifically alike : while physi- 

 cists had been mainly studying the properties of distance, 

 motion, velocity, and size, which, if added together, merge 

 themselves into a common sum, integral or average. It 

 does not follow that, even so far as these latter proper- 

 ties are concerned, the numberless individual particles of 

 matter behave alike ; their sizes, velocities, and move- 

 ments may be very different : indeed it is evident that, in 

 a large crowd of moving particles, they must be widely 

 different. 

 39. In assigning numbers to these data, it was therefore 



Doctrine of 



averages. clear that only average or mean values could be meant, 

 and that our actual physical knowledge of the individual 

 elements resembles that statistical information which we 

 possess, for instance, regarding the mortality, average 

 age, and general properties and ways of the members 

 of a great population. It is statistical knowledge, it is 

 not individual, historical, or biographical knowledge, that 

 we possess. 



The individual behaviour of the single molecules, their 

 sizes, their velocities, the length of their paths, their vibra- 

 tions, rotations, and internal motions, remain unknown. 

 What can be known is only the average magnitudes of 

 these quantities, and possibly the extreme limits within 

 which these individual magnitudes vary. The great dif- 

 ferences exhibited by larger portions of different kinds 

 of matter i.e., the chemical differences or qualities were 

 reduced to the actual composition and qualities of the 

 molecules and atoms themselves. Chemists and physi- 



