THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 23 



of consecutive terms. But a great many series which the 

 Objective presents to us have a structure which will not submit 

 to this simple operation. s Thus in the case of the series 

 composed of all sounds considered in respect of pitch it is 

 impossible even to conceive the series as divided into two parts 

 in such a way that one note is the highest of the first part, and 

 another the lowest of the other part. It is true that w^e may 

 determine that a given note say " middle C " shall be the 

 highest (or last) note of the former part ; but, whatever note is 

 now taken as the lowest (or first) of the latter part, it is always 

 possible to think of yet another note as intercalated between 

 this no.te and the middle C. In other words no note can claim 

 the title of the next note to C. 



It is clear that this statement^could never be directly 

 verified, but is rather of the nature of a postulate to which 

 common sense seems to have been led by considerations which 

 amount to the following.* It is possible to have a note B 

 which seems to 'be in unison both with A and with C when 

 tried separately, while, notwithstanding this, A and C are 

 perceptibly discordant. In order to avoid a contradiction 

 analogous to the supposition that things, which are equal to the 

 same, are not equal, to one another, it is concluded that the 

 note B is "really '^intermediate in pitch between A and C but 

 cannot be directly perceived to be so. There is no reason to 

 suppose that in the- same way other notes might not be 

 intercalated without limit" between A and B. Thus we reach 

 the notion that Poincare has called iliQ, physical continuum. 



It seems possible that this name is not the best that could 

 be chosen.' If the above analysis is correct the special charac- 

 teristic of these physical series as they are conceived is "that 

 it is always possible to find another term of the series between 

 any two. Thus starting with two terms TI and T 2 the inter- 

 mediate terms will be obtained by the constantly repeated 

 \1 : 



* Poincare, La Science et VBypotkese, p. 34. 



