MODERN PROBLEMS IN ACOUSTICS. 131 
the sound. The velocity in solids has been much studied, 
and measured even in soft bodies like paraffin and rubber. 
The Frequency of Vibration, in specially favorable cases, 
can now be measured to within a few parts in a million ; so 
the writing tuning-fork is now the usual means of dividing 
a second, say into 100 parts; but in ordinary cases, especially 
where the pitch is high, or the sound weak or short of dura¬ 
tion, as in musical performances, errors of some per cent are 
frequent. Quite recently the sets of high forks made by 
Appunn for physiologists have been found to be extrava¬ 
gantly in error; but as partial compensation for the disap¬ 
pointment the science has been enriched by new experi¬ 
mental methods. * 
Of extreme importance to the modern physicist is the 
question of the energy involved in any movement. The 
experimental study of the Energy of Vibration began, I be¬ 
lieve, with the ingenious optical determination by Toepler 
and Boltzman, in 1870, of the actual variations in density in 
the air of a sounding organ pipe and the distance at which 
it could be heard, and so of the amount of energy per second 
required at the limit of hearing. More recently a Swedish 
experimenter found by thrusting periodically a thermopile 
mounted on a tuning-fork prong into a sounding pipe at the 
node a rise of 0°.l C., due to the adiabatic compression of 
the air. Since 1870 experiments on the energy of organ pipes 
have been multiplied and refined. Similarly determina¬ 
tions on the intensity of telephone currents and the move¬ 
ment of its disc have testified to the incredible sensitiveness 
of the ear (A. G. Bell). An amplitude of vibration of air par¬ 
ticles of only one-fifteen-millionth of a millimeter in the 
region of 440 d. v. produces sensation. 
Other investigators have traced the expenditure of the 
energy stored in a vibrating mass; so the rate of damping 
of forks under various conditions has been observed (Wead); 
also the dissipation of energy in a resonator and the decay 
of sound in free air. It has been noted that a sound reflected 
repeatedly through a tunnel changes in quality, owing to the 
more rapid absorption of the overtones of high pitch. A con- 
