EXPLANATION OF LAWS. 523 



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 sub- 

 ject 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 differing only in the propor- 

 tions in which they are combined, often produce effects 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 altered, it is demon- 

 strated 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 motion 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 rectilineal 

 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 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 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 



