THE OUTER AND INNER WORLDS 221 



arises when they reach a certain number, 

 and it changes as they increase. This, as 

 already pointed out, is well seen in a 

 spectrum. Proceeding from the low red 

 upwards we pass through the various colours, 

 red, orange, yellow, green, blue, indigo and 

 violet. The range is an octave, that is 

 to say, the number of vibrations producing 

 violet are about double the number required 

 for red. With the sense of hearing, the first 

 tone audible as a musical tone is produced by 

 about thirty-three vibrations per second, while 

 the highest audible tone corresponds to a little 

 over thirty thousand per second. Thus the 

 ear has in most individuals a range of about 

 eleven octaves. Beyond the highest audible 

 sound, there are however many vibrations 

 which make no impression on the human 

 ear, just as there are numerous vibrations 

 beyond the upper limit of the violet of the 

 spectrum, known to physicists, such as the 

 Rontgen rays. These have no effect on the 

 human retina, and yet their existence has 

 been proved by special methods of research. 

 It is possible, even probable, that some 



