THE GEOMETRICAL METHOD. 477 



Among the -differences "between geometry (a science of 

 coexistent facts, altogether independent of the laws of the 

 succession of phenomena), and those physical Sciences of 

 Causation which have been rendered deductive, the following 

 is one of the most conspicuous: That geometry affords no 

 room for what so constantly occurs in mechanics and its 

 applications, the case of conflicting forces ; of causes which 

 counteract or modify one another. In mechanics we conti- 

 nually find two or more moving forces producing, not motion, 

 but rest ; or motion in a different direction from that which 

 would have been produced by either of the generating forces. 

 It is true that the effect of the joint forces is the same 

 when they act simultaneously, as if they had acted one 

 after another, or by turns ; and it is in this that the difference 

 between mechanical and chemical laws consists. But still 

 the effects, whether produced by successive or by simulta- 

 neous action, do, wholly or in part, cancel one another : what 

 the one force does, the other, partly or altogether, undoes. 

 There is no similar state of things in geometry. The result 

 which follows from one geometrical principle has nothing that 

 conflicts with the result which follows from another. What is 

 proved true from one geometrical theorem, what would be 

 true if no other geometrical principles existed, cannot be 

 altered and made no longer true by reason of some other 

 geometrical principle. What is once proved true is true in 

 all cases, whatever supposition may be made in regard to any 

 other matter. 



Now a conception, similar to this last, would appear to 

 have been formed of the social science, in the minds of the 

 earlier of those who have attempted to cultivate it by a deduc- 

 tive method. Mechanics would be a science very similar to 

 geometry, if every motion resulted from one force alone, 

 and not from a conflict of forces. In the geometrical theory 

 of society, it seems to be supposed that this is really the 

 case with the social phenomena ; that each of them results 

 always from only one force, one single property of human 

 nature. 



At the point which we have now reached, it cannot be 



