234 INDUCTION. 



ting at all, is simply tlie sun; but the cause of lier gravitating with a 

 given intensity and in a given direction, is the existence of the sun in 

 a given direction and at a given distance. It is not strange that a modi- 

 fied cause, which is in truth a different cause, should produce a differ- 

 ent effect. But as the cause is only different in its quantity, or in some 

 of its relations, it usually haippens that the effect also is only changed 

 in its quantity or its relations. 



Although it is for the most part true that a modification of the cause 

 is followed by a modification of the effect, the Method of Concomitant 

 Variations does not, however, presuppose this as an axiom. It only 

 requires the converse proposition ; that anything upon whose modifica- 

 tions, modifications of an effect are invariably consequent, must be the 

 cause {or connected with the cause) of that effect; a proposition, the 

 truth of vvhich is evident; for if the thing itself had no influence on the 

 effect, neither could the modifications of the thing have any influence. 

 If the stars have no power over the fortunes of men, it is implied in the 

 very terms, that the conjunctions or oppositions of different stars can 

 have no such power. ' ■ 



Although the most striking applications of the Method of Concomi- 

 tant Variations take place in the cases in which the Method of Differ- 

 ence, strictly so called, is impossible, its use is not confined to those 

 cases ; it may often usefully follow after the Method of Diff'erenee, to 

 give additional precision to a solution which that has found. When 

 by the Method of Difference it has first been ascertained that a cer^ 

 tain object produces a certain effect, the Method of Concomitant Va- 

 riations may be usefully called in to determine according to what 

 law the quantity or the different relations of the effect follow those of 

 the cause. 



§ 7. The case in which this method admits of the most extensive 

 employment, is that in which the variations of the cause are variations 

 of quantity. Of such variations we may in general afiinn with safety, 

 that they will be attended not only with variations, but with similar 

 variations, of the effect: the proposition, that more of the -cause is 

 followed by more of the effect, being a coi-ollary from the principle of 

 the Composition of Causes, which, as we have seen, is the general 

 rule of causation; cases of the opposite descrijjtion, in which causes 

 change their properties on being conjoined with one another, being, on 

 the contrary, special and exceptional. Suppose, then, that when A 

 changes in quantity, a also changes in quantity, and in such a manner 

 that we can trace the numerical relation which the changes of the one 

 bear to such changes of the other as take place within our limits of 

 observation. We may then, with certain- precautions, safely conclude 

 that the same numerical relation will hold beyond those limits. If, for 

 instance, we find that when A is double, a is double ; that when A is 

 treble or quadruple, a is treble or quadruple ; we may conclude that 

 if A were a half or a third, a would be a half or a third, and finally, 

 that if A were annihilated, a would be annihilated, and that a is wholly 

 the effect of A, or wholly the effect of the same cause with A. And 

 so with any other numerical relation according to which A and a would 

 vanish simultaneously ; as for instance if a were j^roportional to the 

 square of A. If, on the other hand, a is not wholly the effect o^" A, 

 ■ but yet varies when A varies, it is probably (to use a mathematical 



