602 
Proceedings of the Royal Society 
contemporaneous volcanic action has recently been observed in the 
Moray Firth area, the whole of the basin of Lake Orcadie being 
otherwise remarkably free from any trace of such action except 
on the northern margin in Shetland. The history of the area 
embraced by Lake Caledonia will form the subject of the next 
paper. 
3. On Beats of Imperfect Harmonies. By Sir 
William Thomson. 
According to a usage which has been adopted from the German 
of Helmholtz by the best English scientific writers on sound, a sound 
is called a “simple tone,”* or without qualification a “tone,” when 
the variation of pressure of the air in the neighbourhood of the ear 
which is the immediate excitant of the sense is according to a simple 
harmonic function of the time ; that is to say, when the whole 
pressure of the air varies in simple proportion to the distance, from 
a fixed plane, of a point moving uniformly in a circle. Consider- 
ing the actual sensibility of the human ear to musical sounds, we 
must introduce farther as a practical restriction that the period of 
the variation of the pressure must he less then ~ of a second, and 
greater than jo - J-yo - or t 0 cro"o °f a second. The vibrations of the air 
produced by a simple harmonic vibrator are either simple harmonic, 
or are in circular or elliptic orbits, resulting from the composition 
of two simple harmonic motions ; and the consequent change 
of air-pressure in the neighbourhood of the ear follows the simple 
harmonic law, provided the maximum velocity of the vibrator and 
of the air in its neighbourhood be infinitely small in comparison 
with the velocity of sound. Hence the more nearly this condition 
is fulfilled the more nearly a simple tone is the sound heard ; but 
it is far from being fulfilled when the vibrator, though itself per- 
forming simple harmonic motion, has sharp edges round which the 
* The old musical usage, according to which the word tone denotes an interval 
(the major tone or minor tone, or the mean tone of the tempered scale), though 
it unfortunately clashes with this recent scientific use of the word tone, can 
scarcely be abandoned. 
