THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



infinite or closed like the series of palings round a field. 

 In addition, it may happen that two or more terms are identical 

 in respect of the terms that they lie between which implies, 

 that none of thes particular terms is between another of them 

 and any one of the other terms. In this case the terms in 

 question occupy the same place in the series it being carefully 

 noted that no- spatial ideas are intended by this or by similar 

 expressions. In the case we have considered two notes which 

 are "equally squeaky " occupy the same place in the series. 



If we consider two terms a\ y a 2 of any of the above series 

 there will in general be a number of terms between them : 

 these terms, together with one of the two a\, a 2 , constitute 

 what may be called the 'stretch from &i to a 2 . To be distin- 

 guished from .this notion is that of the distance of a 2 from i, 

 an idea which must be kept free from spatial associations, 

 although, of course, it takes its name from its analogy with 

 distance in space. Thus in the case of two notes in a scale 

 the distance would be in the " interval " between them while the 

 stretch would consist of all the notes that could be intercalated. 

 Distances, then, are asymmetrical quantitative relations between 

 the terms of a series such that one and only one belongs to 

 any given pair. In all the series suggested above there are 

 distances as well as stretches. There are, similarly, distances 

 between shades of colour, degrees of hotness, &c., but it is 

 curious that, if after the consideration of such cases one 

 returns to the series of positions in space or time, it is doubtful 

 whether distance can still be detected in them !* 



Again, it is possible to divide each' of the suggested series 

 into two parts so that one of the original terms becomes the 

 " last " term of the first part, and another (the " next " term) 

 becomes the "first" term of the second part; for between these 

 two terms no further terms of the series occur. Series which 

 can be treated in this way are discrete, and consist of a succession 



* Kussell, op, cit. y p. 255. 



