In the twenty-fourth volume of the Society's Transactions, a very convenient formula is given for computing the time of oscillation in a circular arc; and the investigation of that formula is conducted by an appeal to the actual phenomena. It is defective in so far that it contemplates chiefly the time of oscillation over the whole arc, and does not enable us conveniently to compute the time in which a part of that arc is described.

The object of the present note is to supply that defect, and to present the whole subject in a new aspect remarkable alike for its generality and for its simplicity.