THE DISCOVERY OF LAWS 63 



false, for some swans in Australia are black. Instances 

 of the second kind are plentiful in actual science. When 

 a chemist makes a new compound, he often determines 

 its melting-point or density ; as a result of a single 

 measurement he will often be prepared to assert that 

 its melting-point or density is higher (say) than that of 

 water, and nobody will dream of doubting that the asso- 

 ciation he asserts is invariable or that subsequent measure- 

 ments will lead to the same result. 



These examples seem to prove that a^large number of 

 favourable instances, even if without exceptions, is nettjjiex: 

 suffioent_ jnorjwcessajy Jq^tablisl^ a, Jaw. But at the 

 same time they suggest what is the additional element re- 

 quired. V^e_haye_omitted to take into consideration other 

 laws^ closely .similar to those that are under discussion^ 

 The chemist is certain that, in measuring the melting- 

 point of a new compound, he is establishing an invariable 

 relation, because from the examination of a great number 

 of other compounds he has found that the density is an 

 invariable property. On the other hand seventeenth- 

 century naturalists ought to have regarded with suspicion 

 a law that all swans are white (and probably they did 

 actually so regard it) because the examination of other 

 animals would have shown them that colour is by no 

 means an invariable property, but is liable to vary very 

 widely even among closely related species. In putting 

 the matter as we did, the full evidence was not disclosed. 

 The evidence for the invariable density of a new compound H 

 is not the single measurement of it, but the general law 

 that all densities are invariable properties. This law is 

 established by the observation, not of a single instance 

 or of one or two, but of a very large number of instances, 

 in none of which the relation has been found to fail. 

 The evidence for the assertion of the law of the density 

 of the new substance is really of exactly the same nature \ 

 as that for the rising of the sun to-morrow. 



