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.

CONTENTS

To extract any Root whatever

Table of Squares, Cubes, Square-Roots and Cube-Roots

Ratios, Proportions, and Progressions

Of the Conic Sections as expressed by Algebraic equations, called the