(1) Imaginary, or false exceptions, that is, facts, objects, or events which are not really what they are supposed to be.
(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 supposed 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 hypothesis 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 principles, 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.”1 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 liquids expand by heat,” if I know that water below 4° C. does not; I ought to say, “All liquids, except water below 4° C., expand by heat;” and every new exception discovered will falsify the statement until inserted in it. To speak of some laws as being generally true, meaning not universally but in the majority of cases, is a hurtful abuse of the word, but is quite usual. General should mean that which is true of a whole genus or class, and every true statement must be true of some assigned or assignable class.
Imaginary or False Exceptions.
When a supposed exception to a law of nature is brought to our notice, the first inquiry ought properly to be—Is there any breach of the law at all? It may be that the supposed exceptional fact is not a fact at all, but a mere figment of the imagination. When King Charles requested the Royal Society to investigate the curious fact that a live fish put into a bucket of water does not increase the weight of the bucket and its contents, the Royal Society wisely commenced their deliberations by inquiring whether the fact was so or not. Every