CHAPTER XIX. 



OF THE EXTENSION OF DERIVATIVE LAWS TO 

 ADJACENT CASES. 



1. WE have had frequent occasion to notice the inferior 

 generality of derivative laws, compared with the ultimate laws 

 from which they are derived. This inferiority, which affects 

 not only the extent of the propositions themselves, hut their 

 degree of certainty within that extent, is most conspicuous in 

 the uniformities of coexistence and sequence obtaining between 

 effects which depend ultimately on different primeval causes. 

 Such uniformities will only obtain where there exists the same 

 collocation of those primeval causes. If the collocation varies, 

 though the laws themselves remain the same, a totally different 

 set of derivative uniformities may, and generally will, be the 

 result. 



Even where the derivative uniformity is between different 

 effects of the same cause, it will by no means obtain as uni- 

 versally as the law of the cause itself. If a and b accompany 

 or succeed one another as effects of the cause A, it by no 

 means follows that A is the only cause which can produce 

 them, or that if there be another cause, as B, capable of pro- 

 ducing a, it must produce b likewise. The conjunction there- 

 fore of a and b perhaps does not hold universally, but only in 

 the instances in which a arises from A. When it is produced 

 by a cause other than A, a and b may be dissevered. Day 

 (for example) is always in our experience followed by night ; 

 but day is not the cause of night; both are successive effects 

 of a common cause, the periodical passage of the spectator 

 into and out of the earth's shadow, consequent on the earth's 

 rotation, and on the illuminating property of the sun. If, 

 therefore, day is ever produced by a different cause or set of 

 causes from this, day will not, or at least may not, be followed 



