Let us suppose the expansions to have taken place, and that the centre of gravity, remaining at the same distance from the point of suspension, the centre of oscillation is removed to a greater distance, as we have before explained. It is well known that the product obtained by multiplying the distance from the point of suspension to the centre of gravity, by the distance from the centre of gravity to the centre of oscillation, is a constant quantity; if, therefore, the distance from the centre of gravity to the point of suspension be lessened, the distance from the centre of gravity to the centre of oscillation will be proportionally, though not equally, increased, and the centre of oscillation will, therefore, be elevated. We see, then, if we elevate the centre of gravity precisely the requisite quantity, by employing a sufficient length of the compensating material, that although the distance from the centre of gravity to the point of suspension is lessened, yet the distance from the point of suspension to the centre of oscillation will suffer no change. The following rule for finding the length of the compensating material in a pendulum of the kind we have been considering will be found sufficiently accurate for all practical purposes:-- _Find in the manner before directed the length of the compensating material, the expansion of which will be equal to that of the rod of the pendulum. Double this length, and increase the product by its one-tenth part, which will give the total length required._ We shall give examples of this as we proceed. _Graham’s Mercurial Pendulum._ It was in the year 1721 that Graham first put up a pendulum of this description, and subjected it to the test of experiment; but it appears to have been afterwards set aside to make way for Harrison’s gridiron pendulum, or for others of a similar description. For some years past, however, its merits have been more generally known, and it is not surprising that it should be considered as preferable to others, both from the simplicity of its construction, and the perfect ease with which the compensation may be adjusted. We have already alluded to Mr. Baily’s very able paper on this pendulum, and we shall take the liberty of extracting from it the following description:-- At _fig. 223._ is a drawing of the mercurial pendulum, as constructed in the manner proposed by Mr. Baily.