orte from F to F, say from 42 to 5,460
vibrations per second. But this high number is not anywhere near the
upper limit of audible sounds for man.

Very many of the familiar sounds of insects, such as crickets and
mosquitoes, have a much higher pitch. Helmholtz puts this upper limit at
38,000 vibrations per second, and Despraetz at 36,850. The discrepancy
of results is due solely to the marked difference in individuals as to
acoustic perception.

For the production of high musical tones, Koeenig of Paris makes a set of
steel rods. A steel rod of a certain length, diameter, and temper, will
give a musical sound which may be determined. The proper length for
other rods for giving higher tones may be determined by the rule that
the number of vibrations is inversely proportional to the square of the
length of the rod.

The dimensions of these rods when made 2 c. m. in diameter are as
follows:--

Length. Vibrations.

66.2 m. m. 20,000

59.1 " " 25,000

53.8 " " 30,000

50.1 " " 35,000

47.5 " " 40,000

These rods need to be suspended upon loops of silk, and they are struck
with a piece of steel so short as to be wholly beyond the ability of any
ear to hear its ring. Nothing but a short thud is to be heard from it
when it strikes, while from the others comes a distinct ringing sound.
In experimenting with such a set of steel rods I have not found any one
yet who could hear as many as 25,000 per second, my own limit being
about 21,000. But it has been experimentally found that children and
youth have a perceptive power for high sounds considerably above adults.
Dr. Clarence Blake of Boston reports a case in his aural practice, of a
woman whose hearing had been gradually diminishing for some years until
she could not hear at all with one ear, and the ticking of a watch could
only be heard with the other when the watch was held against the ear.
After treatment it was discovered that the sensibility to high sounds
was very great, and that she could hear the steel rod having a tone of
40,000 vibrations.

Last year Mr. F. Galton, F.R.S., exhibited before the Science Conference
an instrument in the shape of a very small whistle, which he had devised
for producing a very high sound. The whistle had a diameter less than
the one twenty-fifth of an inch. The length could be varied by moving a
plug at the end of the whistle.