The Modern Clock / A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair

by Ward L. Goodrich

The mercury, therefore (still neglecting head No. 3), must be thirteen and a half times shorter than the length of the pendulum, both being measured as explained above. The pendulum will probably be 43.5 inches long to the bottom of the jar; but as about nine inches of it is cast iron, which has a slightly greater rate of expansion than steel, we will call the length 44 inches, as the half inch added will make it about equivalent to a pendulum entirely of steel. If the height of the mercury be obtained by dividing 44 by 13.5, it will be 3.25 inches high to its center, or 6.5 inches high altogether; and were it not for the following circumstance, the pendulum would be perfectly compensated.

3d. The mercury is the only part of the bob which expands upwards; the jar does not rise, its lower end being carried downward by the expansion of the rod, which supports it. In a well-designed pendulum, the jar, straps, etc., will be from one-fourth to one-third the weight of the mercury. Assume them to be seven pounds and twenty-eight pounds respectively; therefore, the total weight of the bob is thirty-five pounds; but as it is only the mercury (four-fifths) of this total that rises with an increase of temperature, we must increase the weight of the mercury in the proportion of five to four, thus 6.5 × 5 ÷ 4 = 8⅛ inches. Or, what is the same thing, we add one-fourth to the amount of mercury, because the weight of the jar is one-fourth of that of the mercury. Eight and one-eighth inches is, therefore, the ultimate height of the mercury required to compensate the pendulum with that weight of jar. If the jar had been heavier, say one-third the weight of the mercury, then the latter would have to be nearly 8.75 inches high.

If the jar be required to be of glass, then we substitute the expansion of that material in No. 2 and its weight in No. 3.

In the above method of calculating, there are two slight elements of uncertainty: 1st. In assuming that the center of oscillation is coincident with the center of the bob; however, I should suppose that they would never be more than .25 inch apart, and generally much nearer. 2d. The weight of the jar cannot well be exactly known until after it is finished (i. e., bored smooth and parallel inside, and turned outside true with the interior), so that the exact height of the mercury cannot be easily ascertained till then.

I may explain that the reason (in Nos. 1 and 2) we measure the mercury from the bottom to the center of the column, is that it is its center which we wish to raise when an increase of temperature occurs, so that the center may always be exactly the same distance from the point of suspension; and we have seen that 3.25 inches is the necessary quantity to raise it sufficiently. Now that center could not be the center without it had as much mercury over it as it has under it; hence we double the 3.25 and get the 6.5 inches stated.

From the foregoing it will be seen that the average mercury pendulums are better than a plain rod, from the fact that the mercury is free to obey the law of expansion, and so, to a certain degree, does counteract the action of the balance of the metal of the pendulum, and this with a degree of certainty that is not found in the gridiron form, provided always that the height and amount of the mercury are correctly proportional to the total weight of the pendulum.

Compensating Mercurial Pendulums.—To compensate a pendulum of this kind takes time and study. The first thing to do is to place maximum and minimum thermometers in the clock case, so that you can tell the temperature.

Then get the rate of the clock at a given temperature. For example, say the clock gains two seconds in twenty-four hours, the temperature being at 70°. Then see how much it gains when the temperature is at 80°. We will say it gains two seconds more at 80° than it does when the temperature is at 70°.

In that case we must remove some of the mercury in order to compensate the pendulum. To do this take a syringe and soak the cotton or whatever makes the suction in the syringe with vaseline. The reason for doing this is that mercury is very heavy and the syringe must be air-tight before you can take any of the mercury up into it.

You want to remove about two pennyweights of mercury to every second the clock gains in twenty-four hours. Now, after removing the mercury the clock will lose time, because the pendulum is lighter. You must then raise the ball to bring it to time. You then repeat the same operation by getting the rate at 70° and 80° again and see if it gains. When the temperature rises, if the pendulum still gains, you must remove more mercury; but if it should lose time when the temperature rises you have taken out too much mercury and you must replace some. Continue this operation until the pendulum has the same rate, whether the temperature is high or low, raising the bob when you take out mercury to bring it to time, and lowering the bob when you put mercury in to bring it to time.