386 INDUCTION. 



been formed among simple substances, 

 (and the attempt has been often 

 made,) have, with the progress of 

 experience, either faded into inanity, 

 or been proved to be erroneous ; and 

 each Kind of simple substance re- 

 mains with its own collection of pro- 

 perties apart from the rest, saving a 

 certain parallelism with a few other 

 Kinds, the most similar to itself. In 

 organised beings, indeed, there are 

 abundance of propositions ascertained 

 to be universally true of superior 

 genera, to many of which the discovery 

 hereafter of any exceptions must be 

 regarded as extremely improbable. 

 But these, as already observed, are, 

 we have every reason to believe, pro- 

 perties dependent on causation.* 



* Professor Bain {Logic, ii. 13) mentions 

 two empirical laws, which he considers to 

 be, with the exception of the law connect- 

 ing Gravity with Resistance to motion, 

 ''the two most widely operating laws as 

 yet discovered whe>-eby two distinct pro- 

 perties are conjoined throughout sub- 

 stances generally." The first is "a law 

 connecting Atomic Weight and Specific 

 Heat by an inverse proportion. For equal 

 weights of the simple bodies, the atomic 

 weight multiplied by a number expressing 

 the specific heat gives a nearly uniform 

 product. The products, for all the ele- 

 ments, are near the constant number 6." 

 The other is a law which obtains "between 

 the specific gravity of substances In the 

 gaseous state and the atomic weights. 

 The relationship of the two numbers is 

 in some instances equality ; in other in- 

 stances the one is a multiple of the other." 



Neither of these generalisations has the 

 smallest appearance of being an ultimate 

 law. They point unmistakably to higher 

 laws. Since the heat necessary to raise to a 

 given temperature the same weight of diffe- 

 rent substances (called their specific heat) 

 is inversely as their atomic weight, that is, 

 directly as the number of atoms in a given 

 weight of the substance, it follows that a 

 s ngle atom of every substance requires 

 the same amount of heat to raise it to a 

 given temperature : a most interesting and 

 important law, but a law of causation. 

 The other law mentioned by Mr. Bain 

 points to the conclusion that in the 

 gaseous state all substances contain, in 

 the same space, the same number of 

 atoms ; which, as the gaseous state sns- 

 ]>end3 all cohesive force, might naturally 

 be expected, though it could not have 

 been positively assumed. This law may 

 a' an be a result of the mode of action of 

 c luses, namely, of molecular motions. Thp 



Uniformities of co-existence, then, 

 not only when they are consequences 

 of laws of succession, but also when 

 they are ultimate truths, must be 

 ranked, for the purposes of logic, 

 among empirical laws, and are amen- 

 able in every respect to the same 

 rules with those unresolved unifor- 

 mities which are known to be depen- 

 dent on caiisatioiu 



CHAPTER XXIII. 



OF APPROXIMATE GENERALISATIONS, 

 AND PROBABLE EVIDENCE. 



§ I. In our inquiries into the na- 

 ture of the inductive process, we must 



cases in which one of the numbers is not 

 identical with the other, but a multiple of 

 it, may be explained on the nowise un- 

 likely supposition that, in our present 

 estimate of the atomic weights of some 

 substances, we mistake two or three atoms 

 for one, or one for several. 



* Dr. M'Cosh (p. 324 of his book) con- 

 siders the laws of the chemical compo- 

 sition of bodies as not coming under the 

 principle of Causation, and thinks it an 

 omission in this work not to have provided 

 special canons for their investigation and 

 proof. But every case of chemical compo- 

 sition is, as I have explained, a case of 

 causation. When it is said that water is 

 composed of hydrogen and oxygen, the 

 affirmation is that hydrogen and oxygen, 

 by the action on one another which they 

 exert under certain conditions, generate 

 the properties of water. The Canons of 

 Induction, therefore, as laid down in this 

 treatise, ai-e applicable to the case. Such 

 special adaptations as the Inductive me- 

 tliods may re«[uire in their application 

 to chemistry, or any other science, are a 

 proper subject for any one who treats of 

 the logic of the special sciences, as Pro- 

 fessor Bain has done in the latter part of 

 his woik; but they do not appertain to 

 General Logic. 



Dr. M'Cosh also complains (p. 325) that I 

 have given no canons for those sciences in 

 which "the end sought is not the dis- 

 covery of Causes or of Composition, but of 

 Classes, that is, Natural Classes." Such 

 canons could be no other than the 

 principles and rules of Natural Classifi- 

 cation, which I certainly thought that I 

 had expounded at considerable length. 

 But this is far from the only instance 

 in which Dr. M'Cosh does not appear to bo 

 aware of tha contents of the books he i^ 

 criticising. 



