xxvii.] GENERALISATION. 6l9 



title "Sur un Principe General utile h rexplication des 

 Lois de la Nature." ^ It has indeed been asserted that the 

 doctrine of the latens jJ^'occsms of Francis Bacon involves 

 the principle of continuity,- but I think that this doctrine, 

 like that of the natures of substances, is merely a vague 

 statement of the principle of causation. 



Failure of the Law of Continuity. 



There are certain cautions ■which must be e-iven as to the 

 a]>plication of the principle of continuity. In the iirst 

 }»lace, where this principle really holds true, it may seem to 

 fail owing to our imperfect means of observation. Though 

 a physical law may not admit of perfectly abrupt change, 

 there is no limit to the approach which it may make to 

 abruptness. When we warm a piece of very cold ice, the 

 absorption of heat, the temperature, and the dilatation of 

 the ice vary according to apparently simple laws until we 

 come to the zero of the Centigrade scale. Everything is 

 then changed; an enormous absorption of heat takes place 

 witiiout any rise of temperature, and the volume of the ice 

 decreases as it changes into water. Unless carefully in- 

 ■vestigated, this change appears to be perfectly abrupt ; but 

 accurate observation seems to show that there is a certain 

 forewarning; the ice does not turn into water all at once, 

 but through a small fraction of a degree the change is 

 gradual. All the phenomena concerned, if measured very 

 exactly, would be represented not by angular lines, but 

 continuous curves, undergoing rapid llexures ; and we may 

 probably assert with safety that between whatever points 

 of temperature we examine ice, there would be found some 

 indication, though almost infinitesimally small, of the 

 apparently abrupt change which was to occur at a higher 

 temperature. It might also be pointed out that the im- 

 portant and apparently simple physical laws, such as those 

 of lioyle and Mari'iotte, Dalton and Gay-Lussac, &c., are 

 oidy approximately true, and the divergences from the 

 simple laws are forevvarnings of abrupt changes, which 

 would otherwise break the law of continuity. 



' Life of Sir W, Hamilton, p. 439. 



^ Powell's History of Natural riiilosopliy, p. 201. Novum 

 Organumy bk ii. Aphoiisms 5 — 7. 



