128 THE PRINCIPLES OF SCIENCE. [CHAP. 



property appears, the other likewise appears. All crystals 

 of the cubical system, are all the crystals which do not 

 doubly refract light. All exogenous plants are, with some 

 exceptions, those which have two cotyledons or seed-leaves. 



A little reflection will show that there is no direct and 

 infallible process by which such complete coincidences 

 may be discovered. Natural objects are aggregates of 

 many qualities, and any one of those qualities may prove 

 to be in close connection with some others. If each of a 

 numerous group of objects is endowed with a hundred 

 distinct physical or chemical qualities, there will be no 

 less than \ (100 X 99) or 4950 pairs of qualities, which 

 may be connected, and it will evidently be a matter of 

 great intricacy and labour to ascertain exactly which 

 qualities are connected by any simple law. 



One principal source of difficulty is that the finite powers 

 of the human mind are not sufficient to compare by a 

 single act any large group of objects with another large 

 group. We cannot hold in the conscious possession of the 

 mind at any one moment more than five or six different 

 ideas. Hence we must treat any more complex group by 

 successive acts of attention. The reader will perceive by 

 an almost individual act of comparison that the words 

 Roma and Mora contain the same letters. He may 

 perhaps see at a glance whether the same is true of 

 Causal and Casual, and of Logica and Caligo. To assure 

 himself that the letters in Astronomers make No more 

 stars, that Serpens in akuleo is an anagram of Joannes 

 Keplerus, or Great gun do us a sum an anagram of Au- 

 gustus de Morgan, it will certainly be necessary to break 

 up the act of comparison into several successive acts. The 

 process will acquire a double character, and will consist in 

 ascertaining that each letter of the first group is among 

 the letters of the second group, and vice versa, that each 

 letter of the second is among those of the first group. 

 In the same way we can only prove that two long lists of 

 names are identical, by showing that each name in one 

 list occurs in the other, and vice versa. 



This process of comparison really consists in establishing 

 two partial identities, which are, as already shown (p. 58), 

 equivalent in conjunction to one simple identity. We 

 first ascertain the truth of the two propositions A = AB, 



