THE THEORY OF CONTINUITY 139 



To this objection there are three supplementary 

 answers, physiological, psychological, and logical. We 

 will consider them successively. 



(1) The physiological answer merely shows that, if the 

 physical world is what the mathematician supposes, its 

 sensible appearance may nevertheless be expected to be 

 what it is. The aim of this answer is thus the modest 

 one of showing that the mathematical account is not im- 

 possible as applied to the physical world ; it does not 

 even attempt to show that this account is necessary, or 

 that an analogous account applies in psychology. 



When any nerve is stimulated, so as to cause a sensa- 

 tion, the sensation does not cease instantaneously with 

 the cessation of the stimulus, but dies away in a short 

 finite time. A flash of lightning, brief as it is to our 

 sight, is briefer still as a physical phenomenon : we 

 continue to see it for a few moments after the light-waves 

 have ceased to strike the eye. Thus in the case of a 

 physical motion, if it is sufficiently swift, we shall actually 

 at one instant see the moving body throughout a finite 

 portion of its course, and not only at the exact spot where 

 it is at that instant. Sensations, however, as they die 

 away, grow gradually fainter ; thus the sensation due to 

 a stimulus which is recently past is not exactly like the 

 sensation due to a present stimulus. It follows from 

 this that, when we see a rapid motion, we shall not only 

 see a number of positions of the moving body simultan- 

 eously, but we shall see them with different degrees of 

 intensity the present position most vividly, and the 

 others with diminishing vividness, until sensation fades 

 away into immediate memory. This state of things 

 accounts fully for the perception of motion. A motion 

 is perceived, not merely inferred, when it is sufficiently 

 swift for many positions to be sensible at one time ; and 



