274 INDUCTION. 



first of the three modes of resolution. When the law <yf an effect of 

 comMned causes is resolved into the separate laws of the- causes, the 

 natm-e 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 com- 

 bined ; 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 manifest 

 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 

 dejjends upon it, and thereby de-feats the complex law. The mere 

 msting, " for examjile, 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 a still stronger reason why the law of a complex 

 effect must be less general than the laws of the causes which conspire 

 to produce it. The same causies, acting according to the same laws, 

 and differing only in-the proportions in which they ai"e combined, often 

 produce effects which differ not merely in quantity, but in kind. The 

 combination of a tangential with a centripetal force, in the proportions 

 which obtain in all the planets and satellites 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 demonstrable that the motion produced 

 would be in a circle,- or a, parabola, or an hyperbola: and it has been 

 supposed that in the case of some comets one of these is really the 

 fact. Yet the law of the parabolic motion would be resolvable into 

 the- very same- simple laws into which that of the elliptical motion is 

 resolved, namely, th"e law of the permanence of rectilineal motion, 

 and the law of an unifomi centripetal force. If, therefbre, in the 

 course of ages, some .cii-cumstance were, to manifest itself which, 

 without defeating the law of eitber of those forces, should merely 

 alter their proportion to one another, (such as the shock of a comet, 

 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 j^lace;) the_ellij3tical motion might be changed 

 into a motion in some other curve ; and the complex law of the heav- 

 enly motions, as at present -understood, would be depri-^ed of its 

 universality, although the discovery would not at all detract from the 

 universality of the simpler laws intq which that complex law is resolved. 

 The law, in short, of each of th6 concurrent causes remains the same, 

 however their collocations may vary ; but the law of their joint effect 

 varies with every difference in the coltocations. There needs no more 

 to show how mueh more general th6 elementai-y laws must be, than 

 any of the cornplex laws which are derived from them. 



§ 5. Besides the two "modes which have been". treated of, there is a 

 third mode in which laVvs. are resolved into one another; and in this it 

 is self-evident that they are resolved into laws more general tlrah them- 

 selves. This third rriode is the subsumftion (as it has been called) of 

 one law under another; or (what Comes to the same tiling) the gatlier- 

 •ing up of several laws into one more general law -which includes them 

 all. The most splendid example of this operation was,- when tejres- 



