not shew the relation between the time and any number of

vibrations actually performed; but merely gives the limit to

which this relation approaches, when the horizontal velocity

is indefinitely diminished. If therefore we would use the

new formula as an approximation in very small finite vibra-

tious, the times must not be extended without limitation.

ROBERT ADRAIN.

New-Brunswick, New-Jersey,

July 31, 1812.