GENERALIZATION. 273 



given in Erdmann's edition of Leibnitz' works, p. 104, 

 under the title ' Sur un Principe General utile a 1'expli- 

 cation des Lois de la Nature 1 *.' It has indeed been 

 asserted that the doctrine of the latens processus 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 Lav of Continuity. 



There are certain requisite cautions which must be 

 given as to the application of the principle of continuity. 

 In the first place, where this principle really holds true, 

 it may seem to fail owing to our imperfect means of 

 observation. Though a physical law may never 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 tem- 

 perature, 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 enor- 

 mous absorption of heat takes place without any rise of 

 temperature, and the volume of the ice decreases as it 

 changes into water. Unless most carefully investigated, 

 this change appears perfectly abrupt ; but accurate ob- 

 servation seems to show that there is a certain forewarn- 

 ing ; 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 exactlv, 

 would be represented not by angular lines, but con- 

 tinuous curves, undergoing rapid flexures ; and we may 



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



c Powell's ' History of Natural Philosophy,' p. 201. 'Novum Organum,' 

 bk. II. Aphorisms 5-7. 



VOL. II. T 



