550 LOGIC OF THE MORAL SCIENCES, 



as the type of all deductive science; it is to geometry 

 rather than to astronomy and natural philosophy, that 

 they unconsciously assimilate the deductive science of 

 society. 



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 de- 

 ductive, 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 continually 

 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 mecha- 

 nical and chemical laws consists. jJBut still the effects, 

 whether produced by successive or by simultaneous 

 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 geo- 

 metry. The result which follows from one geome- 

 trical principle has nothing that contradicts 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 principle. What is once proved true must be 

 true in all cases, whatever supposition may be made 

 in regard to any other matter. 



Now a conception, similar to this last, would 



