Owing to the difficulty of calculating the expansive ratios of metal which (particularly with brass and zinc) vary slightly with differences of manufacture, the manufacture of compensated pendulums from metal rods cannot be reduced to cutting up so many pieces and assembling them from calculations made previously, so that each must be separately built and tested. While this is not a great draw-back to the jeweler who wants to make himself a pendulum, it becomes a serious difficulty to a manufacturer, and hence a cheaper combination had to be devised to prevent the cost of compensated pendulums from seriously interfering with their use. The result was the pendulum composed of a steel rod and a quantity of mercury, the latter forming the principal weight for the bob and being contained in steel or glass jars, or jars of cast iron for the heavier pendulums. Other metals will not serve the purpose, as they are corroded by the mercury, become rotten and lose their contents.

Mercury has one deficiency which, however, is not serious, except for the severe conditions of astronomical observatories. It will oxidize after long exposure to the air, when it must be strained and a fresh quantity of metal added and the compensation freshly adjusted. To an astronomer this is a serious objection, as it may interfere with his work for a month, but to the jeweler this is of little moment as the rates he demands will not be seriously affected for about ten years, if the jars are tightly covered.

To construct a reliable gridiron pendulum would cost about fifty dollars while a mercurial pendulum can be well made and compensated for about twenty-five dollars, hence the popularity of the latter form.

Zinc will lengthen under severe variations of temperature as the following will show: Zinc has a decided objectionable quality in its crystalline structure that with temperature changes there is very unequal expansion and contraction, and furthermore, that these changes occur suddenly; this often results in the blending of the zinc rod, causing a binding to take place, which naturally enough prevents the correct working of the compensation.

It is probably not very well known that zinc can change its length at one and the same temperature, and that this peculiar quality must not be overlooked. The U. S. Lake Survey, which has under its charge the triangulation of the great lakes of the United States, has in its possession a steel meter measure, R, 1876; a metallic thermometer composed, of a steel and zinc rod, each being one meter in length, marked M. T., 1876s, and M. T. 1876z; and four metallic thermometers, used in connection with the base apparatus, which likewise are made of steel and zinc rods, each of these being four meters in length. All of these rods were made by Repsold, of Hamburg. Comparisons between these different rods show peculiar variations, and which point to the fact that their lengths at the same degree of temperature are not constant. For the purpose of determining these variations accurate investigations were undertaken. The metallic thermometer M. T. 1876 was removed from an observatory room having an equal temperature of about 2° C. and placed for one day in a temperature of +24° C., and also for the same period of time in one of -20° C; it was then replaced in the observatory room, where it remained for twenty-four hours, and comparisons were made during the following three days with the steel thermometer 1876, which had been left in the room. From these observations and comparisons the following results were tabulated, which give the mean lengths of the zinc rods of the metallic thermometer. The slight variations of temperature in the observatory room were also taken into consideration in the calculations:

These investigations clearly indicate, without doubt, that the zinc rod at one and the same temperature of about 2° C., is 0.018 mm. longer after having been previously heated to 24° C. than when cooled before to -20° C.

A similar but less complete examination was made with the metallic thermometer four meters in length. These trials were made by that efficient officer, General Comstock, gave the same results, and completely prove that in zinc there are considerable thermal after-effects at work.

To prove that zinc is not an efficient metal for compensation pendulums when employed for the exact measurement of time, a short calculation may be made—using the above conclusions—that a zinc rod one meter in length, after being subjected to a difference of temperature of 44° C. will alter its length 0.018 mm. after having been brought back to its initial degree. For a seconds pendulum with zinc compensation each of the zinc rods would require a length of 64.9 cm. With the above computations we get a difference in length of 0.0117 mm. at the same degree of temperature. Since a lengthening of the zinc rods without a suitable and contemporaneous expansion of the steel rods is synonymous with a shortening of the effectual pendulum length, we have, notwithstanding the compensation, a shortening of the pendulum length of 0.017 mm., which corresponds to a change in the daily rate of about 0.5 seconds.

This will sufficiently prove that zinc is unquestionably not suitable for extremely accurate compensation pendulums, and as neither is permanent under extremes of temperature the advantages of first cost and of correction of error appear to lie with the mercurial form.

The average mercurial compensation pendulums, on sale in the trade are often only partially compensated, as the mercury is nearly always deficient in quantity relatively, and not high enough in the jar to neutralize the action of the rigid metallic elements, composing the structure. The trouble generally is that the mercury forms too small a proportion of the total weight of the pendulum bob. There is a fundamental principle governing these compensating pendulums that has to be kept in mind, and that is that one of the compensating elements is expected to just undo what the other does and so establish through the medium of physical things the condition of the ideal pendulum, without weight or elements outside of the bob. As iron and mercury, for instance, have a pretty fixed relative expansive ratio, then whatever these ratios are after being found, must be maintained in the construction of the pendulum, or the results cannot be satisfactory.

First, there are 39.2 inches of rod of steel to hold the bob between the point of suspension and the center of oscillation, and it has been found that, constructively, in all the ordinary forms of these pendulums, the height of mercury in the bob cannot usually be less than 7.5 inches. Second, that in all seconds pendulums the length of the metal is fixed substantially, while the height of the mercury is a varying one, due to the differing weights of the jars, straps, etc.

Third, the mercury, at its minimum, cannot with jars of ordinary weight be less in height in the jar than 7.5 inches, to effectually counteract what the 39.2 inches of iron does in the way of expanding and contracting under the same exposure.

Whoever observes the great mass of pendulums of this description on sale and in use will find that the height of the mercury in the jar is not up to the amount given above for the least quantity that will serve under the most favorable circumstances of construction. The less weight there is in the rod, jar and frame, the less is the height of mercury which is required; but with most of the pendulums made in the present day for the market, the height given cannot be cut short without impairing the quality and efficiency of the compensation. Any amount less will have the effect of leaving the rigid metal in the ascendancy; or, in other words, the pendulum will be under compensated and leave the pendulum to feel heat and cold by raising and lowering the center of oscillation of the pendulum and hence only partly compensating. A jar with only six inches in height of mercury will in round numbers only correct the temperature error about six-sevenths.

Calculations of Weights.—As to how to calculate the amount of mercury required to compensate a seconds pendulum, the following explanation should make the matter clear to anyone having a fair knowledge of arithmetic only, though there are several points to be considered which render it a rather more complicated process than would appear at first sight.

1st. The expansion in length of steel and cast iron, as given in the tables (these tables differ somewhat in the various books), is respectively .0064 and .0066, while mercury expands .1 in bulk for the same increase of temperature. If the mercury were contained in a jar which itself had no expansion in diameter, then all its expansion would take place in height, and in round numbers it would expand sixteen times more than steel, and we should only require (neglecting at present the allowance to be explained under head 3) to make the height of the mercury—reckoned from the bottom of the jar (inside) to the middle of the column of mercury contained therein—one-sixteenth of the total length of the pendulum measured from the point of suspension to the bottom of the jar, assuming that the rod and the jar are both of steel, and that the center of oscillation is coincident with the center of the column of mercury. Practically in these pendulums, the center of oscillation is almost identical with the center of the bob.

2d. As we cannot obtain a jar having no expansion in diameter, we must allow for such expansion as follows, and as cast iron or steel jars of cylindrical shape are undoubtedly the best, we will consider that material and form only.

As above stated, cast iron expands .0066, so that if the original diameter of the jar be represented by 1, its expanded diameter will be 1.0066. Now the area of any circle varies as the square of its diameter, so that before and after its expansion the areas of the jar will be in the ratio of 1² to 1.0066²; that is, in the proportion of 1 to 1.013243; or in round numbers it will be one-seventy-sixth larger in area after expansion than before. It is evident that the mercury will then expand sideways, and that its vertical rise will be diminished to the same extent. Deduct, therefore, the one-seventy-sixth from its expansion in bulk (one-tenth) and we get one-eleventh (or more exactly .086757) remaining. This, then, is the actual vertical rise in the jar, and when compared with the expansion of steel in length it will be found to be about thirteen and a half times greater (more exactly 13.556).

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=8? 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.

To compensate a pendulum takes time and study of the clock, but if you follow out these instructions you will succeed in getting the clock to run regularly in both summer and winter.

Besides the oxidation, which is an admitted fault, there are two theoretical questions which have to do with construction in deciding between the metallic and mercurial forms of compensation. We will present the claims of each side, therefore, with the preliminary statement that (for all except the severest conditions of accuracy) either form, if well made will answer every purpose and that therefore, except in special circumstances, these objections are more theoretical than real.

The advocates of metallic compensation claim that where there are great differences of temperature, the compensated rod, with its long bars will answer more quickly to temperature changes as follows:

The mercurial pendulum, when in an unheated room and not subjected to sudden temperature changes, gives very excellent results, but should the opposite case occur there will then be observed an irregularity in the rate of the clock. The causes which produce these effects are various. As a principal reason for such a condition it may be stated that the compensating mercury occupies only about one-fifth the pendulum length, and it inevitably follows that when the upper strata of the air is warmer than the lower, in which the mercury is placed, the steel pendulum rod will expand at a different ratio than the mercury, as the latter is influenced by a different degree of temperature than the upper part of the pendulum rod. The natural effect will be a lengthening of the pendulum rod, notwithstanding the compensation, and therefore, a loss of time by the clock.

Two thermometers, agreeing perfectly, were placed in the case of a clock, one near the point of suspension, and the other near the middle of the ball, and repeated experiments, showed a difference between these two thermometers of 7° to 10½° F., the lower one indicating less than the higher one. The thermometers were then hung in the room, one at twenty-two inches above the floor, and the other three feet higher, when they showed a difference of 7° between them. The difference of 2.5° more which was found inside the case proceeds from the heat striking the upper part of the case; and the wood, though a bad conductor, gradually increases in temperature, while, on the contrary, the cold rises from the floor and acts on the lower part of the case. The same thermometers at the same height and distance in an unused room, which was never warmed, showed no difference between them; and it would be the same, doubtless, in an observatory.

From the preceding it is very evident that the decrease of rate of the clock since December 13 proceeded from the rod of the pendulum experiencing 7° to 10.5° F. greater heat than the mercury in the bob, thus showing the impossibility of making a mercurial pendulum perfectly compensating in an artificially heated room which varies greatly in temperature. I should remark here that during the entire winter the temperature in the case is never more than 68° F., and during the summer, when the rate of the clock was regular, the thermometer in the case has often indicated 72° to 77° F.

The gridiron pendulum in this case would seem preferable, for if the temperature is higher at the top than at the lower part, the nine compensating rods are equally affected by it. But in its compensating action it is not nearly as regular, and it is very difficult to regulate it, for in any room (artificially heated) it is impossible to obtain a uniform temperature throughout its entire length, and without that all proofs are necessarily inexact.

These facts can also be applied to pendulums situated in heated rooms. In the case of a rapid change in temperature taking place in the observatory rooms, under the domes of observatories, especially during the winter months, and which are of frequent occurrence, a mercurial compensation pendulum, as generally made, is not apt to give a reliable rate. Let us accept the fact, as an example, of a considerable fall in the temperature of the surrounding air; the thin pendulum rod will quickly accept the same temperature, but with the great mass of mercury to be acted upon the responsive effects will only occur after a considerable lapse of time. The result will be a shortening of the pendulum length and a gain in the rate until the mercury has had time to respond, notwithstanding the compensation.

Others who have expressed their views in writing seem to favor the idea that this inequality in the temperature of the atmosphere is unfavorable to the accurate action of the mercurial form of compensation; and however plausible and reasonable this idea may seem at first notice, it will not take a great amount of investigation to show that, instead of being a disadvantage, its existence is beneficial, and an important element in the success of mercurial pendulums.

It appears that the majority of those who have proposed, or have tried to improve Graham’s pendulum have overlooked the fact that different substances require different quantities of heat to raise them to the same temperature. In order to warm a certain weight of water, for instance, to the same degree of heat as an equal weight of oil, or an equal weight of mercury, twice as much heat must be given to the water as to the oil, and thirty times as much as to the mercury; while in cooling down again to a given temperature, the oil will cool twice as quick as the water, and the mercury thirty times quicker than the water. This phenomenon is accounted for by the difference in the amount of latent heat that exists in various substances. On the authority of Sir Humphrey Davy, zinc is heated and cooled again ten and three-quarters times quicker than water, brass ten and a half times quicker, steel nine times, glass eight and a half times, and mercury is heated and cooled again thirty times quicker than water.

From the above it will be noticed that the difference in the time steel and mercury takes to rise and fall to a given temperature is as nine to thirty, and also that the difference in the quantity of heat that it takes to raise steel and mercury to a given temperature is in the ratio of nine to thirty.

Now, without entering into minute details on the properties which different substances possess for absorbing or reflecting heat, it is plain that mercury should move in a proportionally different atmosphere from steel in order to be expanded or contracted a given distance in the same length of time; and to obtain this result the amount of difference in the temperature of the atmosphere at the opposite ends of the pendulum must vary a little more or less according to the nature of the material the mercury jars are constructed from.

Differences in the temperature of the atmosphere of a room will generally vary according to its size, the height of the ceiling, and the ventilation of the apartment; and if the difference must continue to exist, it is of importance that the difference should be uniformly regular. We must not lose sight of the fact, however, that clocks having these pendulums, and placed in apartments every way favorable to an equal temperature, and in some instances, the clocks and their pendulums encased in double casing in order to more effectually obtain this result, still the rates of the clock show the same eccentricities as those placed in less favorable position. This clearly shows that many changes in the rates of fine clocks are due to other causes than a change in the temperature of the surrounding atmosphere. Still it must be admitted that any change in the condition of the atmosphere that surrounds a pendulum is a most formidable obstacle to be overcome by those who seek to improve compensated pendulums, and it would be of service to them to know all that can possibly be known on the subject.

The differences spoken of above have resulted in some practical improvements, which are: 1st, the division of the mercury into two, three or four jars in order to expose as much surface as possible to the action of the air, so that the expansion of the mercury should not lag behind that of the rod, which it will do if too large amounts of it are kept in one jar. 2nd, the use of very thin steel jars made from tubing, so that the transmission of heat from the air to the mercury may be hastened as much as possible. 3rd, the increase in the number of jars makes a thinner bob than a single jar of the same total weight and hence gives an advantage in decreasing the resistant effect of air friction in dense air, thereby decreasing somewhat the barometric error of the pendulum.

The original form of mercurial pendulums, as made by Graham, and still used in tower and other clocks where extraordinary accuracy is not required, was a single jar which formed the bob and had the pendulum rod extending into the mercury to assist in conducting heat to the variable element of the pendulum. It is shown in section in Fig. 13, which is taken from a working drawing for a tower clock.

The pendulum, Fig. 13, is suspended from the head or cock shown in the figure, and supported by the clock frame itself, instead of being hung on a wall, since the intention is to set the clock in the center of the clockroom, and also because the weight, forty pounds, is not too much for the clock frame to carry. The head, A, forms a revolving thumb-nut, which is divided into sixty parts around the circumference of its lower edge, and the regulating screw, B, is threaded ten to the inch. A very fine adjustment is thus obtained for regulating the time of the pendulum. The lower end of the regulating screw, B, holds the end of the pendulum spring, E, which is riveted between two pieces of steel, C, and a pin, C', is put through them and the end of the regulating screw, by which to suspend the pendulum.

The cheeks or chops are the pieces D, the lower edges of which form the theoretical point of suspension of the pendulum. These pieces must be perfectly square at their lower edges, otherwise the center of gravity would describe a cylindrical curve. The chops are clamped tightly in place by the setscrews, D', after the pendulum has been hung.

The lower end of the regulating screw is squared to fit the ways and slotted on one side, sliding on a pin to prevent its turning and therefore twisting the suspension spring when it is raised or lowered.

The spring is three inches long between its points of suspension, one and three-eighths inches wide, and one-sixtieth of an inch thick. Its lower end is riveted between two small blocks of steel, F, and suspended from a pin, F', in the upper end of the cap, G, of the pendulum rod.

The tubular steel portion of the pendulum rod is seven-eighths of an inch in diameter and one-thirty-second of an inch thickness of the wall. It is enclosed at each end by the solid ends, G and L, and is made as nearly air-tight as possible.

The compensation is by mercury inclosed in a cast iron bob. The mercury, the bob and the rod together weigh forty pounds. The bob of the pendulum is a cast iron jar, K, three inches in diameter inside, one-quarter inch thick at the sides, and five-sixteenths thick at the bottom, with the cap, J, screwed into its upper end. The cap, J, forms also the socket for the lower end of the pendulum rod, H. The rod, L, one-quarter inch in diameter, screws into the cap, J, and its large end at the same time forms a plug for the lower end of the pendulum tube, H. The pin, J', holds all these parts together. The rod, L, extends nearly to the bottom of the jar, and forms a medium for the transmission of the changes in temperature from the pendulum tube to the mercury. The screw in the cap, J, is for filling or emptying the jar. The jar is finished as smoothly as possible, outside and inside, and should be coated with at least three coats of shellac inside. Of course if one was building an astronomical clock, it would be necessary to boil the mercury in the jar in order to drive off the layer of air between the mercury and the walls of the jar, but with the smooth finish the shellac will give, in addition to the good work of the machinist, the amount of air held by the jar can be ignored.

The cast iron jar was decided upon because it was safer to handle, can be attached more firmly to the rod with less multiplication of parts, and also on account of the weight as compared with glass, which is the only other thing that should be used, the glass requiring a greater height of jar for equal weight. In making cast iron jars, they should always be carefully turned inside and out in order that the walls of the jar may be of equal thickness throughout; then they will not throw the pendulum out of balance when they are screwed up or down on the pendulum rod in making the coarse regulation before timing by the upper screw. The thread on the rod should have the cover of the jar at about the center of the thread when nearly to time and that portion which extends into the jar should be short enough to permit this.

Ignoring the rod and its parts for the present, and calling the jar one-third of the weight of the mercury, we shall find that thirty pounds of mercury, at .49 pounds per cubic inch, will fill a cylinder which is three inches inside diameter to a height of 8.816 inches, after deducting for the mass of the rod L, when the temperature of the mercury is 60 degrees F. Mercury expands one-tenth in bulk, while cast iron expands .0066 in diameter: so the sectional area increases as 1.0066² or 1.0132 to 1, therefore the mercury will rise .1-.013243, or .086757; then the mercury in our jar will rise .767 of an inch in the ordinary changes of temperature, making a total height of 9.58 inches to provide for; so the jar was made ten inches long.

Pendulums of this pattern as used in the high grade English clocks, are substantially as follows: Rod of steel 5/16inch diameter jar about 2.1 inches diameter inside and 8¾ inches deep inside. The jar may be wrought or cast iron and about ? of an inch thick with the cover to screw on with fine thread, making a tight joint. The cover of the jar is to act as a nut to turn on the rod for regulation. The thread cut on the rod should be thirty-six to the inch, and fit into the jar cover easily, so that it may turn without binding. With a thirty-six thread one turn of the jar on the rod changes the rate thirty seconds per day and by laying off on the edge of the cover 30 divisions, a scale is made by which movements for one second per day are obtained.

We will now describe (Fig. 14) the method of making a mercurial pendulum to replace an imitation gridiron pendulum for a Swiss, pin escapement regulator, such as is commonly found in the jewelry stores of the United States, that is, a clock in which the pendulum is supported by the plates of the movement and swings between the front plate and the dial of the movement. In thus changing our pendulum, we shall desire to retain the upper portion of the old rod, as the fittings are already in place and we shall save considerable time and labor by this course. As the pendulum is suspended from the movement, it must be lighter in weight than if it were independently supported by a cast iron bracket, as shown in Fig. 6, so we will make the weight about that of the one we have removed, or about twelve pounds. If it is desired to make the pendulum heavier, four jars of the dimensions given would make it weigh about twenty pounds, or four jars of one inch diameter would make a thinner bob and one weighing about fourteen pounds. As the substitution of a different number or different sizes of jars merely involves changing the lengths of the upper and lower bars of the frame, further drawings will be unnecessary, the jeweler having sufficient mechanical capacity to be able to make them for himself. I might add, however, that the late Edward Howard, in building his astronomical clocks, used four jars containing twenty-eight pounds of mercury for such movements, and the perfection of his trains was such that a seven-ounce driving weight was sufficient to propel the thirty pound pendulum.

The two jars are filled with mercury to a height of 7? inches, are 1? inches in diameter outside and 8? inches in height outside. The caps and foot pieces are screwed on and when the foot pieces are screwed on for the last time the screw threads should be covered with a thick shellac varnish which, when dry, makes the joint perfectly air-tight. The jars are best made of the fine, thin tubing, used in bicycles, which can be purchased from any factory, of various sizes and thickness. In the pendulum shown in the illustration, the jar stock is close to 14 wire gauge, or about 2 mm. in thickness. In cutting the threads at the ends of the jars they should be about 36 threads to the inch, the same number as the threads on the lower end of the rod used to carry the regulating nut. A fine thread makes the best job and the tightest joints. The caps to the jars are turned up from cold rolled shafting, it being generally good stock and finishes well. The threads need not be over ³/16 inch, which is ample. Cut the square shoulder so the caps and foot pieces come full up and do not show any thread when screwed home. These jars will hold ten pounds of mercury and this weight is about right for this particular style of pendulum. The jars complete will weigh about seven ounces each.

The frame is also made of steel and square finished stock is used as far as possible and of the quality used in the caps. The lower bar of the frame is six inches long and ? inch square at the center and tapered, as shown in the illustration. It is made light by being planed away on the under side, an end view being shown at 3. The top bar of the frame, shown at 4, is planed away also and is one-half inch square the whole length and is six inches long. The two side rods are to bind the two bars together, and with the four thumb nuts at the top and bottom make a strong light frame.

The pendulum described is nickel plated and polished, except the jars, which are left half dead; that is, they are frosted with a sand blast and scratch brushed a little. The effect is good and makes a good contrast to the polished parts. The side rods are five inches apart, which leaves one-half inch at the ends outside.

The rod is 5/16 of an inch in diameter and 33 inches long from the bottom of the frame at a point where the regulating nut rests against it to the lower end of the piece of the usual gridiron pendulum shown in Fig. 14 at 10. This piece shown is the usual style and size of those in the majority of these clocks and is the standard adopted by the makers. This piece is 11? inches long from the upper leaf of the suspension spring, which is shown at 12, to the lower end marked 10. By cutting out the lower end of this piece, as shown at 10, and squaring the upper end of the rod, pinning it into the piece as shown, the union can be made easily and any little adjustments for length can be made by drilling another set of holes in the rod and raising the pendulum by so doing to the correct point. A rod whose total length is 37 inches will leave 2 inches for the prolongation below the frame carrying the regulating nut, 9, and for the portion squared at the top, and will then be so long that the rate of the clock will be slow and leave a surplus to be cut off either at the top or bottom, as may seem best.

The screw at the lower end carrying the nut should have 36 threads to the inch and the nut graduated to 30 divisions, each of which is equal in turning the nut to one minute in 24 hours, fast or slow, as the case may be.

The rod should pass through the frame bars snugly and not rattle or bind. It also should have a slot cut so that a pin can be put through the upper bar of the frame to keep the frame from turning on the rod and yet allow it to move up and down about an inch. The thread at the lower end of the rod should be cut about two inches in length and when cutting off the rod for a final length, put the nut in the middle of the run of the thread and shorten the rod at the top. This will be found the most satisfactory method, for when all is adjusted the nut will stand in the middle of its scope and have an equal run for fast or slow adjustment. With the rod of the full length as given, this pendulum had to be cut at the top about one inch to bring to a minute or two in twenty-four hours, and this left all other points below corrected. The pin in the rod should be adjusted the last thing, as this allows the rod to slide on the pin equal distances each way. One inch in the raising or lowering of the frame on the rod will alter the rate for twenty-four hours about eighteen minutes.

Many attempts have been made to combine the good qualities of the various forms of pendulums and thus produce an instrument which would do better work under the severe exactions of astronomical observatories and master clocks controlling large systems. The reader should understand that, just as in watch work, the difficulties increase enormously the nearer we get towards absolute accuracy, and while anybody can make a pendulum which will stay within a minute a month, it takes a very good one to stay within five seconds per month, under the conditions usually found in a store, and such a performance makes it totally unfit for astronomical work, where variations of not over five-thousandths of a second per day are demanded. In order to secure such accuracy every possible aid is given to the pendulum. Barometric errors are avoided by enclosing it in an air-tight case, provided with an air pump; the temperature is carefully maintained as nearly constant as possible and its performance is carefully checked against the revolutions of the fixed stars, while various astronomers check their observations against each other by correspondence, so that each can get the rate of his clock by calculations of observations and the law of averages, eliminating personal errors.

One of the successful attempts at such a combination of mercury and metallic pendulums is that of Riefler, as shown in Fig. 15, which illustrates a seconds pendulum one-thirtieth of the actual size.

It consists of a Mannesmann steel tube (rod), bore 16 mm., thickness of metal 1 mm., filled with mercury to about two-thirds of its length, the expansion of the mercury in the tube changing the center of weight an amount sufficient to compensate for the lengthening of the tube by heat, or vice versa. The pendulum, has further, a metal bob weighing several kilograms, and shaped to cut the air. Below the bob are disc shaped weights, attached by screw threads, for correcting the compensation, the number of which may be increased or diminished as appears necessary.

Whereas in the Graham pendulum regulation for temperature is effected by altering the height of the column of mercury, in this pendulum it is effected by changing the position of the center of weight of the pendulum by moving the regulating weights referred to, and thus the height of the column of mercury always remains the same, except as it is influenced by the temperature.

A correction of the compensation should be effected, however, only in case the pendulum is to show sidereal time, instead of mean solar time, for which latter it is calculated. In this case a weight of 110 to 120 grams should be screwed on to correct the compensation.

In order to calculate the effect of the compensation, it is necessary to know precisely the coefficients of the expansion by heat of the steel rod, the mercury, and the material of which the bob is made.

The last two of these coefficients of expansion are of subordinate importance, the two adjusting screws for shifting the bob up and down being fixed in the middle of the latter. A slight deviation is, therefore, of no consequence. In the calculation for all these pendulums the co-efficient for the bob is, therefore, fixed at 0.000018, and for the mercury at 0.00018136, being the closest approximation hitherto found for chemically pure mercury, such as that used in these pendulums.

The co-efficient of the expansion of the steel rod is, however, of greater importance. It is therefore, ascertained for every pendulum constructed in Mr. Riefler’s factory, by the physikalisch-technische Reichsanstalt at Charlottenburg, examinations showing, in the case of a large number of similar steel rods, that the co-efficient of expansion lies between 0.00001034 and 0.00001162.

The precision with which the measurements are carried out is so great that the error in compensation resulting from a possible deviation from the true value of the co-efficient of expansion, as ascertained by the Reichsanstalt, does not amount to over ± 0.0017; and, as the precision with which the compensation for each pendulum may be calculated absolutely precludes any error of consequence, Mr. Riefler is in a position to guarantee that the probable error of compensation in these pendulums will not exceed ± 0.005 seconds per diem and ± 1° variation in temperature.

A subsequent correction of the compensation is, therefore, superfluous, whereas, with all other pendulums it is necessary, partly because the coefficients of expansion of the materials used are arbitrarily assumed; and partly because none of the formulÆ hitherto employed for calculating the compensation can yield an exact result, for the reason that they neglect to notice certain important influences, in particular that of the weight of the several parts of the pendulum. Such formulÆ are based on the assumption that this problem can be solved by simple geometrical calculation, whereas, its exact solution can be arrived at only with the aid of physics.

This is hardly the proper place for details concerning the lengthy and rather complicated calculations required by the method employed. It is intended to publish them later, either in some mathematical journal or in a separate pamphlet. Here I will only say that the object of the whole calculation is to find the allowable or requisite weight of the bob, i. e., the weight proportionate to the coefficients of expansion of the steel rod, dimensions and weight of the rod and the column of mercury being given in each separate case. To this end the relations of all the parts of the pendulum, both in regard to statics and inertia, have to be ascertained, and for various temperatures.

A considerable number of these pendulums have already been constructed, and are now running in astronomical observatories. One of them is in the observatory of the University of Chicago, and others are in Europe. The precision of this compensation which was discovered by purely theoretical computations, has been thoroughly established by the ascertained records of their running at different temperatures.

The adjustment of the pendulums, which is, of course, almost wholly without influence on the compensation, can be effected in three different ways;

These weights are to be placed on a cup attached to a special part of the rod of the pendulum. Their shape and size is such that they can be readily put on or taken off while the pendulum is swinging. Their weight bears a fixed proportion to the static momentum of the pendulum, so that each additional weight imparts to the pendulum, for twenty-four hours, an acceleration expressed in even seconds and parts of seconds, and marked on each weight.

Each pendulum is accompanied with additional weights of German silver, for a daily acceleration of 1 second each, and ditto of aluminum for an acceleration of 0.5 and 0.1 second respectively.

A metal clasp attached on the rear side of the clock case, may be pushed up to hold the pendulum in such a way that it can receive no twisting motion during adjustment.

Further, a pointer is attached to the lower end of the pendulum, for reading off the arc of oscillation.

The essential advantages of this pendulum over the mercurial compensation pendulums are the following:

(1.) It follows the changes of temperature more rapidly, because a small amount of mercury is divided over a greater length of pendulum, whereas, in the older ones the entire (and decidedly larger) mass of mercury is situated in a vessel at the lower end of the pendulum rod.

(2.) For this reason differences in the temperature of the air at different levels have no such disturbing influence on this pendulum as on the others.

(3.) This pendulum is not so strongly influenced as the others by changes in the atmospheric pressure, because the principal mass of the pendulum has the shape of a lens, and therefore cuts the air easily.