GENERALIZA TION. 269 



what is true of one case will be true of similar cases, and 

 probably true of what are probably similar. Whenever 

 we find that a law or similarity is rigorously fulfilled up 

 to a certain point in time or space, we expect with a very 

 high degree of probability that it will continue to be ful- 

 filled at least a little longer. If we see part of a circle, 

 we naturally expect that the form of the line will be 

 maintained in the part hidden from us. If a body has 

 moved uniformly over a certain space/we expect that it 

 will continue to move uniformly. The ground of such 

 inference is doubtless identical with that of all other in- 

 ductive inferences. In continuous motion every infinitely 

 small space passed over constitutes a separate constituent 

 fact, and had we perfect powers of observation the smallest 

 finite motion would include an infinity of information, which, 

 by the principles of the inverse method of probabilities, 

 would enable us to infer with actual certainty to the next 

 infinitely small portion of the path. But when we attempt 

 to infer from one finite portion of a path to another finite 

 part, the inference will be only more or less probable, 

 according to the comparative lengths of the parts and 

 the accuracy of the observations ; the longer our expe- 

 rience is, the more probable our inferences will be ; the 

 greater the length of time or space over which the in- 

 ference extends, the less probable. 



This principle of continuity presents itself in nature 

 in a great variety of forms and cases. It is familiarly 

 expressed in the dictum Natura non a git per saltum, in 

 other words, no change in a natural phenomenon comes 

 on with perfect suddenness or abruptness. There is always 

 some notice some forewarning of every phenomenon, and 

 every change begins by insensible degrees, could we observe 

 it with perfect accuracy. The cannon ball, indeed, is forced 

 from the cannon in an inappreciable portion of time ; the 

 trigger is pulled, the fuze fired, the powder inflamed, the 



