Let us suppose the place of the centre of oscillation to be at O, about three or four tenths of an inch, in a pendulum of the usual construction, below the centre of gravity. Now, the object of the compensation is to preserve the distance from S to O invariable, and not the distance from S to C. The distance of the centre of oscillation varies with the length of the cylinder F B, and hence suffers an alteration in its distance from the point of suspension by the elongation of the cylinder, although the distance of the centre of gravity C from the point of suspension remains unaltered. We shall endeavour to render this perfectly familiar. Suppose a metallic cylinder, 6 inches long, to be suspended by a thread 36 inches long, thus forming a pendulum in which the distance of the centre of gravity from the point of suspension is 39 inches: the centre of oscillation in such a pendulum will be nearly one tenth of an inch below the centre of gravity. Now let us imagine cylindrical portions of equal lengths to be added to each end of the cylinder, until it reaches the point of suspension; we shall then have a cylinder of 78 inches in length, the centre of gravity of which will still be at the distance of 39 inches from the point of suspension. But it is well known that the centre of oscillation of such a cylinder is at the distance of about two thirds of its length from the point of suspension. The centre of oscillation, therefore, has been removed, by the elongation of the cylinder, about 13 inches below the centre of gravity, whilst the centre of gravity has remained stationary. Now the same thing as that which we have just described takes place, though in a very minor degree, with our former cylinder, employed as a compensating bob to a pendulum. The rod expands downwards, the centre of gravity remains at the same distance from the point of suspension, and the cylinder elongates both above and below this point; the consequence of which is, that though the centre of gravity has remained stationary, the distance of the centre of oscillation from the point of suspension has increased. It is, therefore, evident that the length of the compensation must be such as to carry the centre of gravity a little nearer to the point of suspension than it was before the expansion took place; by which means the centre of oscillation will be restored to its former distance from the point of suspension.