ISAAC NEWTON 95 



in U-tubes, propagation of waves, internal friction or 

 viscosity, the resistance to projectiles, damped oscillations, 

 and many similar matters. He thus became the founder of 

 the science of sound (acoustics). He developed, as the 

 result of a profound insight into the phenomena of waves, 

 the method of calculating the velocity of sound, finding it 

 to be equal to the square root of the ratio between elastic 

 force (pressure of the air) and density (specific gravity), 

 and concludes from this that the velocity of sound must 

 increase with increase of temperature. The calculation 

 agreed with that already found since Leonardo's time by 

 observation of echoes. It was a hundred and thirty years 

 later that something new was added to this by Laplace, 

 whereby agreement with later and more refined measure- 

 ments of the velocity of sound was arrived at. Newton 

 also developed the fundamental and simple relationships, 

 holding for all wave processes, between velocity of propaga- 

 tion, wave-length, and period of vibration, or frequency. He 

 then calculated the wave-length of a note of known frequency, 

 and found it to be double the length of the open pipe 

 producing the note.^ 



The velocity of water waves, and its dependence upon the 

 wave-length, was also calculated by Newton directly (for 

 small amplitudes), with the assumption of rectilinear motion 

 of the particles of water; but he also remarks that the motion 

 really takes place in circles, which fact was further developed 



^ As regards the determination <)f the frequency, Newton refers to 

 Sauveur in Paris, who was the first to determine absolute frequencies of 

 musical notes. This was done by counting the beats - which Sauveur 

 also interpreted for the first time correctly — between two deep notes, 

 which were related to one another as fundamental and second, whereupon 

 the two unknown frequencies could be calculated from the difference and 

 the ratio. All other sounds could then be given in absolute terms by 

 ear, making use of Galileo's proof of the fixed relationship between the 

 frequencies of the musical intervals. Sauveur (1653-1716) was also 

 the first to investigate thoroughly the different forms of oscillation of 

 stretched strings, which are responsible for the harmonic overtones. For 

 this purpose he used paper riders, and gentle contact, in the same manner 

 as to-day, and he invented the terms 'loop,' 'node,' and 'stationary wave.' 



