We have not space to go through the history of compensating pendulums, but we may direct attention to some of the best results which have been obtained in this matter. We will first examine the mercurial pendulum, Fig. 90, which we have referred to. In this case the compensation is accomplished as follows: Mercury is inclosed in a glass cylinder M M; shown in the left hand side of the figure; and as the mercury expands more than the glass, it will rise to a higher level on being heated; and the lengthening of the steel rod R R will be counteracted by a similar lengthening due to the expansion of mercury, so that the centre of oscillation is carried down by the steel rod, and up by the mercury, and it is therefore not displaced if the proper ratio is maintained between the length of the steel rod and the column of mercury in the glass vessel. The mercury in the glass will lengthen fifteen times as much as the steel rod, if we have equal lengths of each, so that in order that they may expand equally the rod must be fifteen times as long as the mercury column. This would keep the top of the mercury at the same distance from the point of suspension, but we want to keep the centre of oscillation, which is about half way down the column, at the same distance, so we double the height of the mercury, making it two-fifteenths of the length of the steel rod, so that the surface is over-compensated, but the centre of oscillation is exactly corrected. An astronomer can alter the amount of mercury as he pleases, making it now more, now less, till the stars tell him he has done the right thing, and the pendulum is compensated, and the clock keeps correct time at all temperatures. The little sliding cup C is to carry small weights for final delicate adjustment, the addition of a weight thus obviously tending to increase the rate of the pendulum.