690 THE PRINCIPLES OF SCIENCE. [CHAP. 



and it will even be impossible to lay down rules of pro- 

 cedure to assist those who are in search of a good arrange- 

 ment. The only logical rule would be as follows : Having 

 given certain objects, group them in every way in which 

 they can be grouped, and then observe in which method 

 of grouping the correlation of properties is most con- 

 spicuously manifested. But this method of exhaustive 

 classification will in almost every case be impracticable, 

 owing to the immensely great number of modes in which 

 a comparatively small number of objects may be grouped 

 together. About sixty-three elements have been classified 

 by chemists in six principal groups as monad, dyad, triad, 

 &c., elements, the numbers 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 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 should take 

 them out in a specified order, that for instance at present 

 adopted by chemists. 



The usual mode in which an investigator proceeds to 

 form a classification of a 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 resemblance, and the defi- 

 nition of a class will often have to be altered in order to 

 admit them. The early chemists 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, 



