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2.284 m. effective length and 15.2 cm. apart. Each pendulum rod, except for a few cm. at each end, is of mild steel, perfectly straight and 1.6 mm. diam. Both rods were cut from the same specimen, so as to have the same temperature coefficient. The upper 20 cm. of each rod is 0.4 cm. diam. round steel with fine screw thread and thumb nut on its upper part. The thumb nut has eight radial holes for a long brass pin, the whole adapted to effect very fine adjustment of pendulum length. The thumb-nut rests on the horizontal face of a 60° triangular "knife-edge" of hardened steel through which the rod passes. The upper part of the rod is slightly flattened on one side by grinding, and a thumb-screw in one end of the knife-edge block bears against the flattened side of the rod and clamps it firmly in the block after each length adjustment is made. The knife-edge, ground true and sharp, rests in the plate groove above described, while the rod passes downward through an opening in the side of the plate.
Each pendulum rod terminates at its lower end in a straight brass rod 13 cm. long and 0.4 cm. diam. A perfectly straight horizontal steel pin passes loosely through the brass rod near its lower end, and on this pin the cylindrical bob, or weight as I shall hereafter call it, rests.
Fig. 2 shows the upper and lower parts of one pendulum in detail, with the bismuth weight in place.
The brass rod at the lower end passes just freely through the weight, and accurately in its axis. A weight is easily removed from either pendulum by lowering it after the pin is withdrawn, and another weight may be substituted by reversing the procedure. While this is being done the pendulum rod is kept taut by another temporary, radially slotted, lead weight applied just above, and resting on the upper end of the brass rod. Thus the weights forming the bobs of the two pendulums may readily be exchanged without disturbing anything else.
The weights to be compared, bismuth and zinc in the first instance, were made very accurately the same in height, and with upper and lower ends as nearly plane and parallel as possible, by careful grinding on a perfectly flat surface.
It is essential that the centers of gravity of the weights be exactly the same distance above their supporting pins. To assure this, each weight was adjusted to have its center of gravity exactly midway between its upper and lower ends by the following procedure: The pendulums having been started swinging with a definite amplitude
and brought to synchronism by length adjustment, one of the weights was turned over; this at first resulted in loss of synchronism at the same amplitude. Then, as indicated, the upper or lower cylindrical portion was slightly reduced in diameter by turning off or sandpapering in the lathe. Again the pendulums were synchronized, and again the same weight was turned over and synchronism tested. This process was repeated again and again with each weight until either could be turned over without affecting synchronism in the slightest observable degree. In making these adjustments very minute departure from synchronism could be detected in half an
hour at the turning points of the swing. For certain reasons all tests were made with the same initial amplitude.
Instead of making the cylinders the same in diameter, they were made approximately the same in weight, about 1.377 kg., so that when they were exchanged the length of the pendulum rods would not be affected. Otherwise it would have been necessary to apply corrections for the elastic modulus of the rods and for their weight with every exchange. The latter correction would have been very important, but liable to error.
Finally, the zinc and bismuth pendulums were adjusted to synchronism as perfectly as possible in 40-minute runs with initial amplitude of 35 cm. As it turned out, the bismuth pendulum was then materially longer than the zinc one. It was the whole aim of the pendulum experiments to detect and measure this difference if it existed.
Next the weights were exchanged, so that, in effect, the bismuth pendulum was now the shorter one by double the former difference. On again starting the pendulums, at the former amplitude, loss of synchronism was easily observable in 2 minutes-the bismuth gaining. In 40 minutes the bismuth gain was very large. In the same and other forms this experiment was repeated many times, and always with the same unequivocal result.
Equality of air resistance was effected by attaching small paper projections to opposite sides of the bismuth normal to the line of swing, of such size as to produce air damping equal to that of the zinc as shown by equal time loss of amplitude.
It appears from this experiment that the earth's gravitation field, which is here the accelerating force, grips the bismuth more strongly per unit of mass than it grips the zinc per unit of mass; in other words, a given mass of bismuth appears to weigh more than the same mass of zinc. Apparently the length of a seconds pendulum depends on the material of which it is made.
The greater diameter of the zinc cylinder slightly lowers its center of oscillation, and this accounts for about 10 per cent. of the effect above described, as determined by elaborate experimentation which need not be detailed here, and which was verified by computation.
A pair of high-grade, weight-driven clock movements were next added to the apparatus, as shown in the upper part of Plate VI., and adapted to drive the pendulums continuously at an amplitude of 13 cm.
After synchronizing the zinc and bismuth pendulums at this amplitude, the zinc and bismuth weights were exchanged as heretofore described. Then they were started exactly together and allowed to run until they were again exactly together, the bismuth having thus gained two full beats. Half the elapsed time was taken as the value of one beat gain.
Again the pendulums were synchronized, the zinc weight now being on the pendulum formerly occupied by the bismuth weight; then the weights were exchanged as before, the pendulums started together, and allowed to run until the bismuth had gained two beats as formerly. This procedure was for the purpose of verifying the first finding and to expose any considerable difference there might be in the performance of the driving clocks. No such difference was found; yet for verification the same procedure was followed in the next experiments.
A cylinder of very pure iron was next prepared, of exactly the same height, and approximately the same weight as the zinc and bismuth cylinders, and adjusted for center of gravity with the same
The iron weight or cylinder was then compared with the zinc weight and with the bismuth weight, with the same care used in comparing the zinc and bismuth as above described. The iron gave results intermediate between those of zinc and bismuth, rather nearer the zinc.
Table II. shows the performance of the zinc-iron, the iron-bismuth and the zinc-bismuth combinations. The measurements of time required to gain one beat check and confirm each other remarkably well.
As the pendulums make about 2,388 oscillations per hour, the bismuth gains one beat, or oscillation, in about 17.432; but as before pointed out, the real zinc-bismuth effect is only half of this, say one part in 35.000. This weight-mass difference effect, though not large, appears fairly well established and is impressive.
Various further pendulum experiments are contemplated; and an apparatus adapted to compare the velocities of freely falling masses of zinc and bismuth, and perhaps even measure their difference, if any, has been designed.
In the foregoing pendulum experiments the only force involved for both weight and acceleration was gravity. In the following experiments the accelerating force of a flexed spring was substituted for that of gravity.
Everybody is familiar with the so-called "anniversary" clock, a slow motion, torsion-pendulum clock adapted to run at least a year without rewinding. One of these clock movements of the best quality was used, and its regular disc pendulum was replaced by the arrangement shown in Fig. 3.
a is a very narrow ribbon of tempered steel about 11 cm. long, from which depends the brass member b. Rigidly clamped into the lower end of b is the horizontal brass rod c, carrying at its ends two bismuth cylinders Bi. e e are brass sleeves of equal length, just loosely fitting the rod c, to aid in the first rough adjustment of the cylinders.
The bismuth cylinders, and a similar pair of zinc cylinders, one of which is shown at the upper left, are all accurately cylindrical,