412 INDUCTION. 



3. That effects are proportional to their causes is laid 

 down by some writers as an axiom in the theory of causation ; 

 and great use is sometimes made of this principle in reason- 

 ings respecting the laws of nature, though it is incumhered 

 with many difficulties and apparent exceptions, which much 

 ingenuity has been expended in showing not to be real ones. 

 This proposition, in so far as it is true, enters as a particular 

 case into the general principle of the Composition of Causes ; 

 the causes compounded being, in this instance, homogeneous ; 

 in which case, if in any, their joint effect might be expected 

 to be identical with the sum of their separate effects. If a 

 force equal to one hundred weight will raise a certain body 

 along an inclined plane, a force equal to two hundred weight 

 will raise two bodies exactly similar, and thus the effect is 

 proportional to the cause. But does not a force equal to two 

 hundred weight actually contain in itself two forces each 

 equal to one hundred weight, which, if employed apart, 

 would separately raise the two bodies in question ? The fact, 

 therefore, that when exerted jointly they raise both bodies at 

 once, results from the Composition of Causes, and is a mere 

 instance of the general fact that mechanical forces are subject 

 to the law of Composition. And so in every other case which 

 can be supposed. For the doctrine of the proportionality of 

 effects to their causes cannot of course be applicable to cases 

 in which the augmentation of the cause alters the kind of 

 effect ; that is, in which the surplus quantity superadded to 

 the cause does not become compounded with it, but the two 

 together generate an altogether new phenomenon. Suppose 

 that the application of a certain quantity of heat to a body 

 merely increases its bulk, that a double quantity melts it, and 

 a triple quantity decomposes it : these three effects being 

 heterogeneous, no ratio, whether corresponding or not to that 

 of the quantities of heat applied, can be established between 

 them. Thus the supposed axiom of the proportionality of 

 effects to their causes fails at the precise point where the prin- 

 ciple of the Composition of Causes also fails ; viz., where the 

 concurrence of causes is such as to determine a change in the 

 properties of the body generally, and render it subject to new 



