Page:EB1911 - Volume 12.djvu/406

 observed. By taking the time of vibration of the pendulum first as used in the deflection experiment and then when a small weight was removed from the upper end a known distance from the knife edge, the restoring couple per radian defection could be found. The final result gave ＝5·579.

J. Joly’s suggested Experiment (Nature xli., 1890, p. 256).—Joly has suggested that G might be determined by hanging a simple pendulum in a vacuum, and vibrating outside the case two massive pendulums each with the same time of swing as the simple pendulum. The simple pendulum would be set swinging by the varying attraction and from its amplitude after a known number of swings of the outside pendulums G could be found.

The principle of the method is as follows:—Suppose a sphere of mass m and weight w to be hung by a wire from one arm of a balance. Let the mass of the earth be E and its radius be R. Then $$\textstyle w = \frac{\text{GE}m}{\text{R}^2}$$. Now introduce beneath m a sphere of mass M and let d be the distance of its centre from that of m. Its pull increases the apparent weight of m say by w. Then $$\textstyle \delta w = \frac{\text{GM}m}{d^2}$$. Dividing we obtain $$\textstyle \frac{\delta w}{w} - \frac{\text{MR}^2}{\text{E}d^2}$$, whence $$\textstyle\text{E} = \frac{\text{MR}^2w}{d^2\delta w}$$ and since $$\textstyle g = \frac{\text{GE}}{\text{R}^2}$$, G can be found when E is known.

Von Jolly’s Experiment (Abhand. der k. bayer. Akad. der Wiss. 2 Cl. xiii. Bd. 1 Abt. p. 157, and xiv. Bd. 2 Abt. p. 3).—In the first of these papers Ph. von Jolly described an experiment in which he sought to determine the decrease in weight with increase of height from the earth’s surface, an experiment suggested by Bacon (Nov. Org. Bk. 2, § 36), in the form of comparison of rates of two clocks at different levels, one driven by a spring, the other by weights. The experiment in the form carried out by von Jolly was attempted by H. Power, R. Hooke, and others in the early days of the Royal Society (Mackenzie, The Laws of Gravitation). Von Jolly fixed a balance at the top of his laboratory and from each pan depended a wire supporting another pan 5 metres below. Two 1-kgm. weights were first balanced in the upper pans and then one was moved from an upper to the lower pan on the same side. A gain of 1·5 mgm. was observed after correction for greater weight of air displaced at the lower level. The inverse square law would give a slightly greater gain and the deficiency was ascribed to the configuration of the land near the laboratory. In the second paper a second experiment was described in which a balance was fixed at the top of a tower and provided as before with one pair of pans just below the arms and a second pair hung from these by wires 21 metres below. Four glass globes were prepared equal in weight and volume. Two of these were filled each with 5 kgm. of mercury and then all were sealed up. The two heavy globes were then placed in the upper pans and the two light ones in the lower. The two on one side were now interchanged and a gain in weight of about 31·7 mgm. was observed. Air corrections were eliminated by the use of the globes of equal volume. Then a lead sphere about 1 metre radius was built up of blocks under one of the lower pans and the experiment was repeated. Through the attraction of the lead sphere on the mass of mercury when below the gain was greater by 0·589 mgm. This result gave ＝5·692.

Experiment of Richarz and Krigar-Menzel (Anhang zu den Abhand. der k. preuss. Akad. der Wiss. zu Berlin, 1898).—In 1884 A König and F. Richarz proposed a similar experiment which was ultimately carried out by Richarz and O. Krigar-Menzel. In this experiment a balance was supported somewhat more than 2 metres above the floor and with scale pans above and below as in von Jolly’s experiment. Weights each 1 kgm. were placed, say, in the top right pan and the bottom left pan. Then they were shifted to the bottom right and the top left, the result being, after corrections for change in density of air displaced through pressure and temperature changes, a gain in weight of 1·2453 mgm. on the right due to change in level of 2·2628 metres. Then a rectangular column of lead 210 cm. cross section and 200 cm. high was built up under the balance between the pairs of pans. The column was perforated with two vertical tunnels for the passage of the wires supporting the lower pans. On repeating the weightings there was now a decrease on the right when a kgm. was moved on that side from top to bottom while another was moved on the left from bottom to top. This decrease was 0·1211 mgm. showing a total change due to the lead mass of 1·2453 + 0·1211＝1·3664 mgm. and this is obviously four times the attraction of the lead mass on one kgm. The changes in the positions of the weights were made automatically. The results gave ＝5·05 and G＝6·685 × 10–8.

Poynting’s Experiment (Phil. Trans., vol. 182, A, 1891, p. 565).—In 1878 J. H. Poynting published an account of a preliminary experiment which he had made to show that the common balance was available for gravitational work. The experiment was on the same lines as that of von Jolly but on a much smaller scale. In 1891 he gave an account of the full experiment carried out with a larger balance and with much greater care. The balance had a 4-ft. beam. The scale pan were removed, and from the two arms were hung lead spheres each weighing about 20 kgm. at a level about 120 cm. below the beam. The balance was supported in a case above a horizontal turn-table with axis vertically below the central knife edge, and on this turn-table was a lead sphere weighing 150 kgm.—the attracting mass. The centre of this sphere was 30 cm. below the level of the centres of the hanging Weights. The turn-table could be rotated between stops so that the attracting mass was first immediately below the hanging weight on one side, and then immediately under that on the other side. On the same turntable but at double the distance from the centre was a second sphere of half the weight introduced merely to balance the larger sphere and keep the centre of gravity at the centre of the turn-table. Before the introduction of this sphere errors were introduced through the tilting of the floor of the balance room when the turn-table was rotated. Corrections of course had to be made for the attraction of this second sphere. The removal of the large mass from left to right made an increase in weight on that side of about 1 mgm. determined by riders in a special way described in the paper. To eliminate the attraction on the beam and the rods supporting the hanging weights another experiment was made in which these weights were moved up the rods through 30 cm. and on now moving the attracting sphere from left to right the gain on the right was only about mgm. The difference, mgm., was due entirely to change in distance of the attracted masses. After all corrections the results gave ＝5·493 and G＝6·698 × 10–8.

Final Remarks.—The earlier methods in which natural masses were used have disadvantages, as already pointed out, which render them now quite valueless. Of later methods the Cavendish appears to possess advantages over the common balance method in that it is more easy to ward off temperature variations, and so avoid convection currents, and probably more easy to determine the actual value of the attracting force. For the present the values determined by Boys and Braun may be accepted as having the greatest weight and we therefore take

Probably ＝5·53 and G＝6·66 × 10–8 are correct to 1 in 500.

 GRAVY, a word usually confined to the natural juices which come from meat during cooking. In early uses (in the New English Dictionary the quotations date from the end of the 14th to the beginning of the 16th centuries) it meant a sauce of broth favoured with spices and almonds. The more modern usage seems to date from the end of the 16th century. The word is obscure in origin. It has been connected with “graves” or “greaves,” the refuse of tallow in the manufacture of soap or candles. The more probable derivation is from the French. In Old French the word is almost certainly grané, and is derived