MECHANICAL ILLUSTRATION OF CRISES. 485 



hours, and then, receding from that luminary, takes a course not sensi- 

 bly differing from a straight line, and occupying perhaps centuries in its 

 accomplishment. The variations of direction and of velocity are, how- 

 ever, the necessary results of the conditions under which its movement 

 is taking place, and may be truly said to have been originally included 

 therein. 



This instantaneous or critical assumption of a new phase may also be 

 illustrated by the functions of organic beings. Thus the Illustratio n 

 foetal mammal, though provided with lungs, a mechanism in from the life 

 all respects ready for aerial respiration, does not pass by 

 graduated steps from placental, which is truly aquatic breathing, but the 

 change takes place on a sudden at the moment of birth. These and 

 other such instances may therefore satisfy us that what an imperfect in- 

 duction would lead us to look upon as a departure from the existing rule, 

 or as a breach of the law, may, in reality, be nothing more than the im- 

 mediate or legitimate consequence of it. They may teach us that, in 

 the natural progress of things, variations do not necessarily always take 

 place in so gradual a manner as to be un distinguishable from stage to 

 stage, but sometimes instantaneously, and, as it were, by a crisis. 



Again, this variation by crises may be illustrated by many familiar 

 mechanical contrivances. The case of the common seconds Mechanical ii- 

 striking clock may furnish an example. Let us trace the lustrations. 

 successive conclusions to which an ingenious man might have come at 

 the first introduction of this instrument, his investigation of it being sup- 

 posed to exclude an inspection of its parts. After listening for a length 

 of time to the beats of its pendulum, he would observe that these suc- 

 ceeded at precisely regular intervals, and after extending his examination 

 through two or three thousand of such occurrences, he would doubtless 

 feel justified in coming to the conclusion that the construction was of 

 such a nature that the passage of successive small intervals of time was 

 indicated by the occurrence of a brief, dull sound. His first conclusion, 

 therefore, would be, that the instrument would go on doing this continu- 

 ously. 



At the close of -3600 such observations, when the truth of his in- 

 duction appeared to have become irresistible, his attention would be ar- 

 rested, and his faith in the correctness and completeness of the extensive 

 inductive conclusion he had just drawn would be shaken by hearing one 

 loud stroke upon a bell. Now, probably, he would suspect that the struc- 

 ture of the instrument was such that it indicated the lapse of each 3600 

 minor beats by one louder stroke. This would be his second and more 

 improved induction. 



Setting himself to verify the truth of this hypothesis, he would watch 

 the instrument through 3600 beats more, confidently expecting that, at 



