646 THE PRINCIPLES OF SCIENCE. [chap. 



(2) Apparent, but congruent exceptions, which, though 

 apparently in conflict with a law of nature, are really in 

 agreement with it. 



(3) Singular exceptions, which really agree with a law 

 of nature, but exhibit remarkable and unique results of it. 



(4) Divergent exceptions, which really proceed from the 

 ordinary action of known processes of nature, but which 

 are excessive in amount or monstrous in character. 



(5) Accidental exceptions, arising from the interference 

 of some entirely distinct but known law of nature. 



(6) Novel and unexplained exceptions, which lead to 

 the discovery of a new series of laws and phenomena, 

 modifying or disguising the effects of previously known 

 laws, without being inconsistent with them. 



(7) Limiting exceptions showing the falsity of a sup- 

 posed law in some cases to which it had been extended, 

 but not affecting its truth in other cases. 



(8) Contradictory or real exceptions which lead us to 

 the conclusion that a supposed h3^pothesis or theory is in 

 opposition to the phenomena of nature, and must therefore 

 be abandoned. 



It ought to be clearly understood that in no case is a 

 law of nature really thwarted or prevented from being 

 fulfilled. The effects of a law may be disguised and 

 hidden from our view in some instances : in others the 

 law itself may be rendered inapplicable altogether ; but 

 if a law is applicable it must be carried out. Every 

 law of nature must therefore be stated with the utmost 

 generality of all the instances really coming under it. 

 Babbage proposed to distinguish between universal jonVi- 

 ciplcs, which do not admit of a single exception, such 

 as that every number ending in 5 is divisible by five, 

 and general principles which are more frequently obeyed 

 than violated, as that " men will be governed by what 

 they believe to be their interest."^ But in a scientific 

 point of view general principles must be universal as 

 regards some distinct class of objects, or they are not 

 principles at all. If a law to which exceptions exist is 

 stated without allusion to those exceptions, the statement 

 is erroneous. I have no right to say that " All liquitls 



1 Babbage, The Exposition of 1851, p. i. 



