Page:The American Cyclopædia (1879) Volume VI.djvu/365

 EAETH 357 of 5 '3 16 from observations made on Arthur's Seat, near Edinburgh. Another method of determining the earth's density is based on the circumstance that the earth's attraction is less on a body raised to a considerable height above its surface than on a body at the sea level. Hence a pendulum of given length swings more slowly the higher it is raised above the earth's surface. Now if such a pen- dulum be taken to the summit of a mountain, it is clear that the reduction of the rate of swing will not be so great as the estimated re- duction for the amount of elevation alone, sim- ply because the attraction of the mountain will have an appreciable effect on the pendu- lum's rate. Thus as in the former case it be- comes possible to compare the attraction ex- erted by the mountain with that exerted by the earth, and so to determine the density of the earth. From observations made on Mont Cenis by this method, Carlini and Plana de- duced for the earth's mean density the value 4'950. A third method may be described as the converse of that just mentioned. If a pen- dulum could be caused to swing at a great depth below the surface of the earth, it would swing more slowly than at the sea level. For, considering a spherical surface concentric with the earth's to pass through the place of the pendulum, the attraction of all the mass of the spherical shell outside that surface would pro- duce no effect on the pendulum; while the sphere within that surface would exert a less influence on the pendulum than is exerted by the earth's mass on a pendulum at the sea level ; for though the pendulum would be nearer to its centre, yet this cause could only be effective to increase attraction inversely as the squares of the radii of the two spheres, whereas the volume of the inner sphere would be less than the volume of the earth in the direct proportion of the cubes of the radii. But a pendulum placed at the bottom of a cavity, like a mine, would not have its rate reduced to the same extent, or might even have its rate increased. For, since the whole of the spher- ical shell just referred to exerts no attraction on the pendulum, the space dug out to form the mine should be occupied in order that the attraction of the shell should be nil; and when it is vacant there is wanting a portion of that matter whose attraction outward (or diminish- ing the earth's) is necessary to produce the equilibrium referred to. Failing, then, this at- traction outward, the remainder of the shell in question must exert a certain amount of at- traction inward, and according to the shape and extent of the cavity this attraction inward may cause the resultant attraction on the pen- dulum to be nearly or quite equal to, or even greater than, that at the sea level. And it is clear that if the geological structure of the re- gion surrounding the mine is known, as well as the exact shape and extent of the mine, this method, like the last, supplies a means of de- termining the mean density of the earth. Prof. Airy applied this method at the Harton col- liery in 1854 ; but it is to be noted that he first tried the experiment, though unsuccessfully, in 1826 and 1828. "The two stations selected were exactly in the same vertical, excellently walled, floored, and ceiled. Every care wa's taken to secure solidity of foundation and steadiness of temperature. At each station (upper and lower) was mounted an invariable brass pendulum, vibrating by means of a steel knife edge upon plates of agate, carried by a very firm iron stand. Close behind this was a clock, and before it a telescope mounted so that coincidences of the pendulum of the clock might be accurately observed through a slit in front of the telescope. By this means the pro- portion of invariable pendulum swings to clock pendulum swings was found; and then, as the clock pendulum swings in any required time are denoted by the clock dial, the correspond- ing numbers of invariable pendulum swings at the two stations were determined. In order, however, to do this, the clock rates had to be frequently compared ; this was done by means of an electrical apparatus. In this manner the pendulums were observed, with 104 hours of incessant observations, simultaneous at both stations, one pendulum (A) being above and the other (B) below ; then with 104 hours, B above and A below ; then with 60 hours, A above and B below ; then with 60 hours, B above and A below. No less than 2,454 effec- tive signals were observed at each station. The results showed that the pendulums suffer- ed no injury in their changes, and that the ac- celeration of- the pendulum on being carried down 1,260 feet was 214 seconds per day, or that gravity is increased by TS.TT<F part. It does not appear likely that this determina- tion can be sensibly in error." From it, taking into account the structure of the region and the figure of the mine, Prof. Airy deduced for the earth's density the value 6-565. The re- maining method of determining the earth's density is that of comparing the earth's attrac- tion directly with the attraction of large spheres of lead or other heavy metal. It was devised by Michell, who also prepared the appa- ratus by means of which it was first applied by Caven- dish in 1789. Two globes of lead, / and g in the engrav- ing, are attached to the extremities of a strong horizon- tal bar, movable in a horizontal plane around its centre. Above this centre a light horizontal rod, a 5, is supported by a fine wire. Two equal balls of lead, a and 5, about two inches in diameter, are attached to the ends of this rod ; and the proportions of the instrument are so adjusted Michell's Torsion Balance.