I Quite agree with Mr. Hardy (Gazette, vol. 3, p. 284) in his contention that the real basis of the power-series for sin x; and cos x is given by the two equations

But I am inclined to doubt whether at present the difficulties of exposition will not outweigh the advantages of his method (iii); and for this reason the following method may be worth considering, although it is a fairly obvious modification of my previous note (Gazette, vol. 3, p. 85). The only preliminary knowledge implied is that of the elementary differential calculus, and of Argand’s diagram.

The measurement of the acceleration due to gravity by means of the compound pendulum is a very common laboratory experiment; but there are certain simple principles involved in the theory of it which are not, as it seems to me, sufficiently emphasized by teachers, and which are not stated (at all events explicitly) in any text-book known to me. It may be of use to some to enunciate them here, and to shew their importance both to the instrument-maker and the student.