4 3o THE POPULAR SCIENCE MONTHLY. 



another, when sensible motion is not produced nor destroyed, is always 

 accompanied by the evolution of heat, is little more than an induction. 

 Now, it has been shown by experiment that, when a gas is allowed to 

 expand without doing work, a very small amount of heat disappears. 

 This proves that the particles of the gas attract one another slightly, 

 and but very slightly. It follows that, when a gas is under pressure, 

 what prevents it from collapsing is not any repulsion between the parti- 

 cles, since there is none. Now, there are only two modes of force 

 known to us, force of position or attractions and repulsions, and force of 

 motion. Since, therefore, it is not the force of position which gives a 

 gas its expansive force, it must be the force of motion. In this point 

 of view, the kinetical theory of gases appears as a deduction from the 

 mechanical theory of heat. It is to be observed, how T ever, that it sup- 

 poses the same law of mechanics (that there are only those two modes 

 of force) which holds in regard to bodies such as we can see and exam- 

 ine, to hold also for what are very different, the molecules of bodies. 

 Such a supposition has but a slender support from induction. Our be- 

 lief in it is greatly strengthened by its connection with the law of 

 Boyle, and it is, therefore, to be considered as an hypothetical inference. 

 Yet it must be admitted that the kinetical theory of gases would de- 

 serve little credence if it had not been connected with the principles of 

 mechanics. 



The great difference between induction and hypothesis is, that the 

 former infers the existence of phenomena such as we have observed 

 in cases which are similar, while hypothesis supposes something of a 

 different kind from what we have directly observed, and frequently 

 something which it would be impossible for us to observe directly. Ac- 

 cordingly, when we stretch an induction quite beyond the limits of our 

 observation, the inference partakes of the nature of hypothesis. It 

 would be absurd to say that we have no inductive warrant for a gen- 

 eralization extending a little beyond the limits of experience, and there 

 is no line to be drawn beyond which we cannot push our inference ; 

 only it becomes weaker the further it is pushed. Yet, if an induction 

 be pushed very far, we cannot give it much credence unless we find that 

 such an extension explains some fact which we can and do observe. 

 Here, then, we have a kind of mixture of induction and hypothesis sup- 

 porting one another ; and of this kind are most of the theories of 

 physics. 



v. 



That synthetic inferences may be divided into induction and hypoth- 

 esis in the manner here proposed, 1 admits of no question. The utility 

 and value of the distinction are to be tested by their applications. 



1 This division was first made in a course of lectures by the author before the Low- 

 ell Institute, Boston, in 1866, and was printed in the " Proceedings of the American Acad- 

 emy of Arts and Sciences," for April 9, 1867. 



