NEWTON S FRINCIPIA. 283 



and therefore the time of oscillation is 



where A is the length of a wave, measuring either from 

 top to top or hollow to hollow. This expression for the 

 time is the same as that for the oscillation of a simple 

 pendulum whose length is A. Hence a wave whose length 

 is equal to the length of a simple pendulum should advance 

 a space equal to that length in the time of one vibration 

 of that pendulum. The velocity of the wave will therefore 

 be 



1 



Thus the velocity is independent of the magnitude of the 

 waves, or the density of the fluid. It is greater for long 

 waves than short ones. The waves of sound in air travel 

 with equal velocity, whatever be their length. The undu- 

 latory theory of light requires us to believe that, except 

 when light goes through a vacuum, the waves of different 

 length travel with different velocities. 



Newton does not propose this as more than a first 

 attempt. He says, &quot; These things are true on the suppo 

 sition that the particles of water ascend and descend in a 

 right line. But, in truth, that ascent and descent is per 

 formed in a circle, and therefore I propose the time defined 

 by this proposition as only near the truth.&quot; In modern 

 times the motions of waves have been more accurately 

 investigated. If h be the uniform depth, A the length of 

 the waves, v the velocity of propagation, 



- 



_45rA 



/ 1-e ~ 

 / ~EI*v 



\f 1 + CX 



