188 ETHICAL ASPECTS OF EVOLUTION 



measurements, but, in part at least, discriminations by 

 comparison. Either the space element in the velocity, 

 or the time, or both, are guessed and not measured. 



In calculations of time and space, indirect measurements 

 are not indispensable, though they are commonly of the 

 highest convenience. In the case of other series, such, for 

 example, as those of sound, colour, or heat, which are not 

 obviously either temporal or spatial, they are the only 

 instrument we have for exact comparison. There are 

 apparent exceptions. It might be thought that the musical 

 scale, which admits of divisions into thirds, fifths, octaves, 

 &c., and subdivisions into simple fractions of tones, 

 was as truly an instrument for the measurement of pitch, 

 though it has no rhythmical basis, as the yard, with its divi 

 sion into inches, is an instrument for the measurement 

 of space. This, however, is not the case. The intervals 

 on the musical scale are not subdivisions of any objective 

 standard, like those of true measurement, but are based 

 on the subjective feeling for tone, which is not present in 

 all men alike. Again, they do not, like pure number, admit 

 of infinite subdivision. A half or a quarter of a tone may 

 be appreciated, but a hundredth part of a tone is a difference 

 which leaves no impression on the consciousness. If two 

 notes differed by as little as the hundredth part of a tone 

 we should say they were the same. And it is not necessary 

 to descend to such minute differences as this. The ordinary 

 intervals on the musical scale hold good only for those 

 whose sense is sufficiently acute to distinguish them. If 

 a man with an imperfect musical ear were to assert that 

 C and D were identical, there would be no means of con 

 vincing him of the contrary. The musical scale is merely 

 an example of discrimination by comparison, which with 

 many people has attained a high degree of fineness. It is 

 not measurement. Differences in pitch have always been 

 discriminated, but they were never measured before the 

 discovery of their correspondence with a numerical scale 

 of vibrations. Whether these vibrations are regarded as 

 external or internal, in the air or in the nerves, is im- 



