HELMHOLTZ IN BONN 



subject. The mere enumeration of the subjects 

 discussed will give one a faint idea of the breadth and 

 fulness of this magnificent work. And yet even all 

 this was only a part of the labours of Helmholtz in 

 acoustics. As already mentioned, there is scattered 

 throughout the volume, and in appendices, numerous 

 examples of a mathematical treatment of the subject 

 under discussion. In addition, we have papers on the 

 motion of the strings of a violin, communicated, 

 during one of Helmholtz's visits to his friend Lord 

 Kelvin, then Professor William Thomson, to the 

 Philosophical Society of Glasgow, on igth December 

 1860. In this paper he fully discussed and repre- 

 sented graphically the course of the vibration. 1 As 

 already mentioned, he investigated mathematically 

 the theory of damping, and calculated, for various 

 intervals, the number of vibrations, after which the 

 intensity of a free vibration is reduced to one-tenth. 

 He estimated also the pitch of the partials produced 

 immediately after a tuning-fork has been struck. He 

 invented an electric interrupter, so as to produce an 

 intermittent current in the best way and without 

 making a noise by the production of sparks. He 

 discussed the reciprocal relations of sounds, showing 

 that a sound originating at one point is perceived at 

 another point, even if there are obstacles between the 

 two points, with the same intensity as if it originated 

 at the last point and was perceived at the first ; just as 



1 See also Rayleigh's Theory of Sound t op. cit^ vol. i., p. 231. 

 I6 5 



