Stargazing: Past and Present

by Sir Norman Lockyer

The latter point is provided for in the dead beat arrangement of Graham, and in the “gravity” and other forms of escapement, about which more presently. At present we have been dealing with pendulums as if they were simple pendulums, which are almost mathematical abstractions.

Everything that we have said assumes that there is a mass depending from such a fine line that the mass of the line shall not be considered; but if we examine the pendulum of some clocks we see that the rod is of steel, and that its weight or bob is elongated, and consists of a long cylinder of glass filled with mercury, and carried in a sort of stirrup of steel; this is very different from our simple pendulum—it is a compound pendulum. In a compound pendulum we have first of all the axis of suspension, which is the axis where the pendulum is supported on the top, and below that, near the centre of gravity of the pendulum, we have what is called the centre of oscillation. It will at once be perceived that as the rate of the pendulum depends upon its length, the particles in the upper part of the pendulum will be trying to go more rapidly than they can go, seeing that they are connected in one series of particles, and that the particles at the lowest portion are carried with greater velocity than they would be if they were left to themselves, because they are connected rigidly with the upper ones. Therefore we have to find a point, which oscillates at the same rate as it would if all the other particles were absent.

This is called the centre of oscillation, and it is on the distance of this from the point of suspension that the rate depends.

What is the use of the mercury? It is to compensate for the expansion of the rod by temperature. We shall at once see the reason of this from the fact that the pendulum gets longer by being heated, and the rate of the pendulum depends on the square root of its length; that is, if we multiply the length by four, the square root of which is two, we shall only multiply the rate by two, or double the time of oscillation. Therefore, since temperature causes all metals to vary in length, and metals are the most useful things we can employ for the support of the weights, we find that we have to consider further the alteration of the length of the pendulum due to the variation of the length of the metal we employ. Hence, in addition to the necessity of an arrangement which gives the shortest possible swing, we require also a method for compensating for changes of temperature.

Fig. 90.—Graham’s, Harrison’s, and Greenwich Pendulums.

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.

This is Graham’s mercurial pendulum, invented by him in 1715. There is another compensating pendulum, called Harrison’s gridiron pendulum, from the bars of metal sustaining the pendulum being arranged gridiron fashion, Fig. [90]. At the top is a knife edge or spring for the centre of suspension, and the pendulum bob is suspended by a system of rods, the five black ones being made of a less expansible metal than the other four; consequently, as the five black ones expand and tend to lower the bob, the intermediate ones expand also and tend to raise it; the length of the black rods exceeding that of the others, these latter must be made of a more expansible metal to make up for their smaller length. Thus the acting length of the shaded rods is two-thirds of the acting length of the black ones (each pair is considered as one rod because they act as such), so that a metal is used for the former which expands more than that used for the latter in the proportion of about three to two, and brass is found to answer for the most expansible metal, and steel for the less. These rods are packed side by side, and look very ornamental. If l be the length of the brass rods, and l´ that of the steel rods, and e the coefficient of expansion of the brass, and e´ that of the steel, then l: l´:: e´: e. The pendulum is then compensated, and the bob remains at the same distance from the centre of suspension at all temperatures.

For the pendulum of the clock at the Royal Observatory a modification of the gridiron form has been adopted; for it was found on trial with a mercurial pendulum that the steel rod gained in temperature more rapidly than the mercury, and lost heat quicker, so that the pendulum did not compensate immediately on a change of temperature. The form adopted is as follows (Fig. [90]):—A steel rod is suspended as usual, and is encircled by a zinc tube resting on the nut for rating the pendulum; the zinc tube is again encircled by a steel tube resting on the top of the zinc tube and carrying at its lower end a cylindrical leaden bob attached at its centre to the steel tube; slots and holes are cut in the tubes to expose the inner parts to the air, so that each will experience the change of temperature at the same time. It is of course possible that the tubes forming the pendulum rod are not of exactly the right length to perfectly compensate; a final delicate adjustment is therefore added. On the crutch axis, and held by a collar to it, are two compound bars of brass and steel, h and i, Fig. [96]. The collar fits loosely on the axis, so that the rods, which carry small weights at their extremities, can be easily shifted to make any angle with the horizontal; then, since brass expands more than steel for the same degree of heat, the bars will bend on being heated or cooled, and if the brass be uppermost the weights at the ends of the rods will be lowered with an increase of temperature, and will tend to increase the rate of the pendulum, and vice versâ. So long as the rods are horizontal and in the same straight line their centre of gravity is in the crutch axis, and they are therefore balanced in every position; they therefore only retard the pendulum by their inertia; but when the ends are bent down the centre of gravity is lowered, and they have a tendency to come to a horizontal position and to balance each other like a scale beam, and so swing with the pendulum and overcome its retardation.