OF SOCIETY. 



435 



natural cannot be understood by separating, dissecting, 

 or arranging them in artificial order, that they exist 

 only in company with others of similar or different 

 nature, and that their reality is complex and manifold, 

 and not simple or detached ; that this applies to their 

 together in space as much as to their succession in time. 

 The scientific movement which has given the greatest 

 impetus to this tendency is that which centres in 

 Darwin. From this centre it has spread not only 

 into all the natural sciences, but likewise into those 

 regions of thought which profess to deal with the 

 phenomena of mind. Here a great array of novel terms 



provinces of thought is shown by 

 the fact that it took a long time 

 before thej^ were understood and 

 recognised in their importance and 

 fruitf ulness. Both sprang up about 

 the same time. One of these is the 

 synthetic geometry which started 

 with geometrical, i.e., visible struc- 

 tures, such as lines and planes, and 

 did not generate them tlu-ough 

 points and equations in the anal- 

 ytical fashion, but operated with 

 them as wholes, moving them 

 about, projecting them, and bring- 

 ing them into various relations. 

 Allied to this was the study of the 

 mathematics of Order which may 

 be termed "tactics" in conti'a- 

 distinctiou from "quautics." The 

 enormous development of mathe- 

 matical science through the later 

 combination of the analytical and 

 what was termed "synthetical" 

 methods has been dwelt on at 

 length in the last chapter of the 

 first section of this History (not- 

 ably pp. 441 sqq.) The second 

 instance I single out is that of 

 Faraday's method of observation 

 and experimenting, resting on the 

 conviction that electrical and mag- 

 netic phenomena cannot be studied 



exclusivelj' by the point method 

 adopted by Continental mathe- 

 maticians, but that the whole of 

 space must be considered as being 

 filled with lines and tubes of force. 

 How this introduction of the field 

 instead of the point of action was 

 slowly appreciated and led to the 

 great modern development of elec- 

 trical science, has been shown in 

 chapters ii. and iii. (notably pp. 

 201, 266) of the first section. "That 

 the ".synoptic" view leads to the 

 discovery of new relations which 

 can again be studied in their isola- 

 tion, and, in consequence, always 

 stimulates the analytical inethods, 

 making them more fruitful by 

 leading them into new channels 

 of research, is shown clearly every- 

 where, notably also in the influ- 

 ence of the Darwinian conception 

 of the continuity of organic forms. 

 The more we study Continuity in 

 nature the more the existence of 

 Discontinuities is forced upon us. 

 The discontinuous may disappear 

 and be smoothed down at one 

 point, but only to reappear again 

 in a more mysterious manner at 

 other points. 



