There are three methods of adjusting this compensation: the first, by increasing or diminishing the weights W and W; the second, by varying the distance of the weights W and W from the middle of the bar; and the third, by varying the distance of the bar from the bob of the pendulum, taking care not to pass the middle of the rod. The effect of the compensation is greater as the weights W and W are greater or more distant from the centre of the bar, and also as the bar is nearer to the bob of the pendulum. M. Biot says that he and M. Matthieu employed a pendulum of this kind for a long time in making astronomical observations in which they were desirous of attaining an extreme degree of precision, and that they found its rate to be always perfectly regular. In all the pendulums which we have described, the bob is supposed to be fixed to the rod by a pin passing through its centre, and the adjustment for time is to be made by means of a small weight sliding upon the rod. _Of the Mercurial Pendulum._ We have been guided, in our arrangement of the pendulums which we have described, by the similarity in the mode of compensation employed; and we have now to treat of that method of compensation which is effected by the expansion of the material of which the bob itself of the pendulum is composed. On this subject, as we have before observed, an admirable paper, from the pen of Mr. Francis Baily, may be found in the Memoirs of the Astronomical Society of London, which leaves nothing to be desired by the mathematical reader. But as our object is to simplify, and to render our subjects as popular as may be, we must endeavour to substitute for the perfect accuracy which Mr. Baily’s paper presents, such rules as may be found not only readily intelligible, but practically applicable, within the limits of those inevitable errors which arise from a want of knowledge of the exact expansion of the materials employed. At _fig. 222._, let S B represent the rod of a pendulum, and F C B a metallic tube or cylinder, supported by a nut at the extremity of the pendulum rod, in the usual manner, and having a greater expansibility than that of the rod. Now C, the centre of gravity, supposing the rod to be without weight, will be in the middle of the cylinder; and if C B, or half the cylinder, be of such a length as to expand upwards as much as the pendulum rod S B expands downwards, it is evident that the centre of gravity C will remain, under any change of temperature, at the same distance from the point of suspension S. M. Biot imagined that, in effecting this, a compensation sufficiently accurate would be obtained; but Mr. Baily has shown that this is by no means the fact.