604 SCIENTIFIC THOUGHT. 



sideration, which is interesting inasmuch as it shows 

 that that which I called above the inverse method of 

 statistics does not involve ideas identical with those 

 which the direct method — as applied in ordinary 

 economic and social statistics — involves. In the direct 

 processes of statistics, which we may class under the 

 all-case or enumerative method, we rise, from a large 

 number of individual facts and data which are all 

 different, to the conception of certain uniform averages, 

 to recurring, or continuously and slowly changing, totals, 

 such as we handle daily in sciences like meteorology, 

 in moral, economic, and industrial statistics. The 

 averages are nowhere represented by the individuals, 

 and the regularity of the totals does not appear in 

 dealing with single instances, or with such restricted 

 numbers as come under the personal control of any 

 of us ; hence the general uselessness of statistics in 

 handling individual cases or predicting special occur- 

 rences. But the statistical view of natural phenomena, 

 as applied to the atomic constitution of bodies, leads 

 us ultimately to the conception that the smallest con- 

 stituents of matter, the atoms, exhibit a regularity and 

 recurrent uniformity of structure which reminded Sir 

 John Herschel of manufactured articles. The attempt 

 to reduce the somewhat numerous types of these ulti- 

 mate elements to purely geometrical configurations of 

 the homogeneous elements of one substance has indeed 

 failed, though it is being continually revived. But 

 allowing that there exist some sixty or seventy distinct 

 forms of matter or atomic structures, these structures 

 seem to be alike and stable wherever we meet with 



