CLA SSfFIf'A TIOX. 365 



in the classes varying from three to twenty elements. 

 Now if we were to calculate the whole number of ways 

 in which sixty-three objects can be arranged in six groups, 

 we should find the number to be so great that the life 

 of the longest lived man would be wholly inadequate 

 to enable him to go through these possible groupings. 

 The rule of exhaustive arrangement, then, is absolutely 

 impracticable. It follows also that mere haphazard trial 

 cannot as a general rule give any useful result. If we 

 were to write the names of the elements in succession 

 upon sixty-three cards, throw them into a ballot-box, and 

 draw them out haphazard in six handfuls time after 

 time, the probability is excessively small that we take 

 them out at any one trial in a specified order, for in- 

 stance that at present adopted by chemists. 



The usual mode in which an investigator proceeds to 

 form a classification of any new group of objects, seems to 

 consist in tentatively arranging them according to their 

 most obvious similarities. Any two objects which present 

 a close resemblance to each other will be joined and 

 formed into the rudiment of a class, the definition of 

 which will at first include all the apparent points of 

 resemblance. Other objects as they come to our notice 

 will be gradually assigned to those groups with which 

 they present the greatest number of points of resem- 

 blance, and the definition of a class will often have to 

 be altered in order to admit them. The early chemists, 

 for instance, could hardly avoid classing together the 

 common metals, gold, silver, copper, lead, and iron, which 

 present such conspicuous points of similarity as regards 

 density, metallic lustre, malleability, &c. With the pro- 

 gress of discovery, however, difficulties begin to present 

 themselves in such a grouping. Antimony, bismuth, and 

 arsenic are distinctly metallic as regards lustre, density, 

 and some chemical properties, but are wanting in ma lie- 



