86 THE CREATION OF MATTER 



are due to accurately numbered vibrations, so it is in the 

 case of sounds. Begin where we please with any num- 

 ber of vibrations, by doubling them a musical and prac- 

 tised ear recognises the sound as the octave of the first. 

 Thus, from 40, the lowest, to 4000, the highest, the 

 sounds ascend, step by step, with a regularity which 

 commands our admiration, even as the music which 

 they make. 



The length of the waves. As the motion is uniform 

 throughout, it is evident that the time required by any 

 particle to execute a complete vibration is also the time 

 in which a wave moves forward a distance equal to its 

 own length. A particle rushes forward and a condensa- 

 tion is produced, it stops, it rushes backward to the point 

 whence it came, and while it is doing so, the motion 

 which it has created, advancing with the same velocity, 

 darts forward the same distance as it does backward. In 

 the time in which a complete oscillation is thus performed 

 by the first particle, the motion has advanced by one wave 

 length ; when it has made two oscillations, by two wave 

 lengths ; when it has made 200 oscillations, by 200 wave 

 lengths. When a tuning-fork vibrates 250 times in a 

 second, it also in the same time forms 250 waves, and 

 advances 1120 feet. The length of 250 waves is there- 

 fore 1120 feet, and so dividing, we get the length of one 

 as 4 feet 5 inches. Three tuning-forks, vibrating 320, 

 384, and 512 times per second, create waves 3 feet 

 6 inches, 2 feet 11 inches, and 2 feet 2 inches in length. 

 In hydrogen, waves of a certain length yield a note two 

 octaves higher than if formed in air, because, in conse- 

 quence of the velocity of advance, the ear receives four 

 times the number of impulses. Each substance has its 

 own measure of wave for each note, and always and every- 

 where for that substance in the same circumstances it is 



