these ions, in different numbers and with different arrangements form 

 the atom; that the difference of number and arrangement of the ions 

 in the atom, conditions the difference of qualities expressed by the 

 Periodic Law. The mathematical reasonings involved in the theory 

 determining the number of ions in different atoms, and the causes of 

 instability of certain atoms are very difficult. Thus it is evident from 

 our examination that either method of procedure may give rise to 

 complex theories; complex 'from the point of view of structure and 

 difficulty of reasoning. 



So also the experimental method may give rise either to a simple 

 theory, simple meaning one whose materials can be directly pre- 

 sented in experience; or to a complex theory, a complex theory being 

 one whose materials cannot be presented in experience. Darwin's 

 theory we found to be simple in this respect; individual variations, 

 inheritance, and natural selection being processes subject to direct 

 observation: while the theory of ions, we found to be complex in this 

 respect; the ions and their combinations being inferred existences. 

 Both theories were derived by the experimental method. 



The method of assumption and deduction, however, will always 

 give rise to a theory complex in this respect; for the assumption is al- 

 ways of the existence or of the qualities of something out of experi- 

 ence. This is shown by both Hyslop's and Locke's theories. Hys- 

 lop's theory assumes spirits with certain powers to exist out of expe- 

 rience, and Locke's theory assumes minds, impressions upon minds, 

 and "real things" to exist, although never observed. Thus a theory 

 derived by experiment may be either simple or complex in this respect ; 

 that is, its materials may be either observed existences or inferred 

 existences; while a theory derived by the method of assumption, will 

 always be complex in this respect ; that is, its materials will always be 

 in whole or in part, existences beyond experience. 



It remains to consider the relation between method of procedure 

 and simplicity in the fourth sense, in which it was defined to mean free 

 from unintefligibilities. The theory of ions, we found to be a theory 

 based upon experimentation, while Hyslop's was found to be based 

 upon the method of assumption and deduction. Yet both theories 

 contain unintelligible elements. It is evident that a theory may be 

 complex, in the sense that it contains unintelligible elements, by which- 

 ever method it is derived. This will be obvious when we consider 

 the source of unintelligibilities. Things are unintelligible in the sense 

 of the word as here used, only because we do not know enough about 

 them. As knowledge is gained, primarily by observation and experi- 

 ment, it may be said that unintelligibilities arise when observation and 

 experiment are incomplete. In the theory of ions sufficient investigation 



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