294 THE PRINCIPLES OF SCIENCE. 



movement we pass by analogy to waves of sound, varying 

 in length from about 32 feet to a small fraction of an inch. 

 We have but to imagine, if we can, the fortieth octave of 

 the middle C of a piano, and we reach the undulations of 

 yellow light, the ultra-violet being about the forty-first 

 octave. Thus we pass gradually from the palpable and evi- 

 dent to that which is obscure, if not incomprehensible. Yet 

 the very same phenomena of reflection, interference, and 

 refraction, which we find in the one case, may be expected 

 to occur mutatis mutandis in the other cases. 



From the great to the small, from the evident to the 

 obscure, is not only the natural order in which inference 

 proceeds, but it is the historical order of discovery. The 

 physical science of the Greek philosophers must have re- 

 mained incomplete, and their theories groundless, because 

 they do not seem ever to have understood the nature and 

 importance of undulations. All their systems were there- 

 fore based upon the entirely different notion of continuous 

 movement of translation from place to place. Modern 

 Science tends more and more to the opposite conclusion 

 that all motion is alternating or rhythmical, energy 

 flowing onwards but matter remaining comparatively 

 fixed in position. Diogenes Laertius indeed correctly 

 compared the propagation of sound with the spreading of 

 waves on the surface of water when disturbed by a stone, 

 and Vitruvius displayed a more complete comprehension 

 of the same analogy. It remained for Newton to create 

 the theory of undulatory motion in showing by mathe- 

 matical deductive reasoning that the particles of an elastic 

 fluid, by vibrating backwards and forwards, might carry- 

 forward a pulse or wave moving onwards from the source 

 of disturbance, while the disturbed particles return to their 

 place of rest. He was even able to make a first approxi- 

 mation by theoretical calculation to the velocitv of sound- 

 waves in the atmosphere. His theory of sound formed a 



