THE THEORY OF CONTINUITY 141 



dictionary, into propositions about the kinds of objects 

 which are given in sensation. 



Applying these general considerations to the case of 

 motion, we find that, even within the sphere of immediate 

 sense-data, it is necessary, or at any rate more consonant 

 with the facts than any other equally simple view, to 

 distinguish instantaneous states of objects, and to regard 

 such states as forming a compact series. Let us consider 

 a body which is moving swiftly enough for its motion to 

 be perceptible, and long enough for its motion to be not 

 wholly comprised in one sensation. Then, in spite of the 

 fact that we see a finite extent of the motion at one 

 instant, the extent which we see at one instant is different 

 from that which we see at another. Thus we are brought 

 back, after all, to a series of momentary views of the 

 moving body, and this series will be compact, like the 

 former physical series of points. In fact, though the 

 terms of the series seem different, the mathematical char- 

 acter of the series is unchanged, and the whole mathe- 

 matical theory of motion will apply to it verbatim. 



When we are considering the actual data of sensation 

 in this connection, it is important to realise that two 

 sense-data may be, and must sometimes be, really different 

 when we cannot perceive any difference between them. 

 An old but conclusive reason for believing this was 

 emphasised by Poincare. 1 In all cases of sense-data 

 capable of gradual change, we may find one sense-datum 

 indistinguishable from another, and that other indis- 

 tinguishable from a third, while yet the first and third 

 are quite easily distinguishable. Suppose, for example, a 

 person with his eyes shut is holding a weight in his hand, 

 and someone noiselessly adds a small extra weight. If 



1 " Le continu mathematique," Revue de Metaphysique et de Morale, 

 vol. i. p. 29. 



