EXPLANATION OF LAWS. 335 



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 con- 

 tingency 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 complex 

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

 produce it. The same causes, acting according to the same laws, and differ- 

 ing only in the proportions in which they are combined, often produce ef- 

 fects which differ not merely in quantity, but in kind. The combination 

 of a centripetal with a projectile 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 al- 

 tered, it is demonstrated that the motion produced would be in a circle, or 

 a parabola, or an hyperbola ; and it is thought that in the case of some 

 comets one of these is probably the fact. Yet the law of the parabolic mo- 

 tion would be resolvable into the very same simple laws into which that of 

 the elliptical motion is resolved, namely, the law of the permanence of rec- 

 tilineal motion, 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 accumula- 

 ting 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 el- 

 liptical motion might be changed into a motion in some other conic section ; 

 and the complex law, that the planetary motions take place in ellipses, would 

 be deprived of its universality, though the discovery would not at all de- 

 tract 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 this it is self-ev- 

 ident that they are resolved into laws more general than themselves. This 

 third mode is the siihsumption (as it has been called) of one law under an- 

 other ; or (what comes to the same thing) the gathering up of several laws 

 into one more general law which includes them all. The most splendid ex- 

 ample of this operation was when terrestrial gravity and the central force 

 of the solar system were brought together under the general law of gravi- 

 tation. It had been proved antecedently that the earth and the other plan- 

 ets tend to the sun ; and it had been known from the earliest times that 

 terrestrial bodies tend toward the earth. These were similar phenomena; 

 and to enable them both to be subsumed under one law, it was only neces- 

 sary to prove that, as the effects were similar in quality so also they, as to 

 quantity, conform to the same rules. This was first shown to be true of 

 the moon, which agreed with terrestrial objects not only in tending to a 



