be easily removed when it is required to detach the pendulum from the clock, in order that the stirrup might then stand securely on its base. One of the screw holes should be rather larger than the body of the screw, in order to admit of a small adjustment, in case the steel wire should not stand exactly perpendicular to the axis of motion. The scale should be divided into _degrees_, and not _inches_, observing that with a radius of 44 inches (the estimated distance from the bend of the spring to the end of the steel wire) the length of each degree on the scale must be 0·768 inch.” [7] The variation produced in the height of the column of mercury (supposed to be 6-1/2 inches high) by an alteration of ± 16° in the temperature will be only ± 1/100 of an inch, or in other words, 1/100 of an inch will be the total variation from its _mean_ state, by an alteration of 32° in the temperature. It is therefore probable that, in most cases of moderate alteration in the temperature, the _centre_ only of the column of mercury is subject to elevation and depression, whilst the exterior parts remain attached to the sides of the glass vessel. It was with a view to obviate this inconvenience that Henry Browne, Esq. of Portland Place (I believe) first suggested the piece of floating glass. In order to determine the length of the mercurial column necessary to form the compensation for this pendulum, we must proceed in the following manner:-- Let us suppose the length of the steel rod and stirrup together to be 42 inches. The absolute expansion of the mercury is ·00010010; but it is not the absolute expansion, but the vertical expansion in a glass cylinder, which is required, and this will evidently be influenced by the expansion of the base of this cylinder. It is easily demonstrable that, if we multiply the linear expansion of any substance (always supposed to be a very small part of its length) by 3, we may in all cases take the result for the cubical or absolute expansion of such substance. In like manner, if we multiply the linear expansion by 2, we shall have the superficial expansion. If we want the apparent expansion of mercury, the absolute or cubical expansion of the glass vessel must be deducted from the absolute expansion of the mercury, which will leave its excess or apparent expansion. In like manner, deducting the superficial expansion of glass from the absolute expansion of mercury, we shall have its relative vertical expansion. Now, taking the rate of expansion of glass to be ·00000479, and multiplying it by 2, the relative vertical expansion of the mercury in the glass cylinder will be ·00010010 - ·00000958 = ·00009052. The expansion of a steel rod, according to our table, is ·0000063596; which, divided by ·00009052, gives ·0703 for the length of a column of mercury, the expansion of which is equal to that of a steel rod whose length is unity.