308 



INDUCTION. 



there be oases in which the sequence 

 of A and C does not bold, these are 

 most likely to be found by studying 

 the effects or the conditions of the 

 phenomenon B. 



It appears, then, that in the second 

 of the three modes in which a law 

 may be resolved into other laws, the 

 latter are more general, that is, ex- 

 tend to more cases, and are also less 

 likely to require limitation from sub- 

 sequent experience, than the law 

 which they serve to explain. They 

 are more nearly unconditional ; thoy 

 are defeated by fewer contingencies ; 

 they are a nearer approach to the 

 universal truth of nature. The same 

 observations are still more evidently 

 true with regard to the first of the 

 three modes of resolution. When 

 the law of an effect of combined 

 forces is resolved into the separate 

 laws of the causes, the nature of the 

 case implies that the law of the effect 

 is less general than the law of any of 

 the causes, since it only holds when 

 they are combined ; while the law of 

 any one of the causes holds good both 

 then, and also when that cause acts 

 apart from the rest. It is also mani- 

 fest that the complex law is liable to 

 be oftener unfulfilled than any one 

 of the simpler laws of which it is the 

 result, since every contingency which 

 defeats any of the laws prevents so 

 much of the effect as depends on it, 

 and thereby defeats the complex law. 

 The mere rusting, for example, of some 

 small part of a great machine, often 

 suffices entirely to prevent the effect 

 which ought to result from the joint 

 action of all the parts. The law of 

 the effect of a combination of causes 

 is always subject to the whole of the 

 negative conditions which attach to 

 the action of all the causes severally. 



There is another and an equally 

 strong reason why the law of a com- 

 plex effect must be less general than 

 the laws of the causes which conspire 

 to produce it. The same causes, act- 

 ing according to the same laws, and 

 differing only in the proportions in 

 which they are combined, often pro- 



duce effects which differ not merely 

 in quantity, but in kind. The com- 

 bination of a centripetal with a pro- 

 jectile force, in the proportions which 

 obtain in all the planets and satel- 

 lites of our solar system, gives rise to 

 an elliptical motion ; but if the ratio 

 of the two forces to each other were 

 slightly altered, it is demonstrated 

 that the motion produced would be 

 in a circle, or a parabola, or an hyper- 

 bola ; and it is thought that in the 

 case of some comets one of these is 

 probably the fact. Yet the law of 

 the parabolic motion would be re- 

 solvable into the very same simple 

 laws into which that of the elliptical 

 motion is resolved, namely, the law 

 of the permanence of rectilineal mo- 

 tion and the law of gravitation. If, 

 therefore, in the course of ages, some 

 circumstance were to manifest itself 

 which, without defeating the law of 

 either of those forces, should merely 

 alter their proportion to one another, 

 (such as the shock of some solid body, 

 or even the accumulating effect of 

 the resistance of the medium in which 

 astronomers have been led to surmise 

 that the motions of the heavenly 

 bodies take place,) the elliptical mo- 

 tion might be changed into a motion 

 in some other conic section ; and the 

 complex law that the planetary mo- 

 tions take place in ellipses would be 

 deprived of its universality, though 

 the discovery would not at all detract 

 from the universality of the simpler 

 laws into which that complex law is 

 resolved. The law, in short, of each 

 of the concurrent causes remains the 

 same, however their collocations may 

 vary ; but the law of their joint effect 

 varies with every difference in the 

 collocations. There needs no more 

 to show how much more general the 

 elementary laws must be than any of 

 the complex laws which are derived 

 from them. 



§ 5. Besides the two modes which 

 have been treated of, there is a third 

 mode in which laws are resolved into 

 one another ; and in thi* it is self-evi- 



