met. This difficulty is felt particularly in the Russian and Indian triangulations. While Colonel Chodsko found in the Caucasus a deflection of fifty-four seconds, and Schweitzer, in an open plain in the environs of Moscow, deflections of eight and nine seconds, the Himalayan chain appears to have had but an insignificant influence in place of the considerable one which the theory required-as if these mountains were composed of less dense rocks than the soil of the plain.

The operations referred to serve to indicate the form of the earth by the angles which the verticals of a series of stations-i. e., the direction of weight-make with the earth's axis. Another mode consists in measuring at numerous points the degree of the weight, and from this the distance to the center of the earth, the rate of oscillation of the pendulum being also noted. These oscillations are accelerated as the attractive power of the earth increases-that is, as the center is approached. We have seen that Richer remarked these variations of the pendulum in his voyage to Cayenne, and that Newton furnished the explanation of the phenomenon. At the commencement of the present century Biot, Sabine, Kater, Lütke, Foster, and others, made numerous experiments of this nature which have furnished a valuable verification of the results of geodesy, properly so called. But it must not be forgotten that the degree of weight may be changed by the same causes that change its direction. A local accumulation of very dense rocks may increase the terrestrial attraction, and light ones may diminish it. The de-leveling of the ocean of which we have spoken, by which the waters near continents are elevated while the mass of the ocean at large is lowered, results in making an ocean-valley, as it were, from which the islands, that are thus nearer the earth's center than the continents, project. This will explain the increased rate of oscillation of the pendulum observed in many islands, which is otherwise inexplicable.

The perturbations to which the direction as well as the degree of weight is subject have enabled us to determine the earth's mean density. The principle of the method is easily comprehended. Let us suppose that the deflection of the plummet has been measured near an isolated mountain whose volume and weight it is possible to estimate with some degree of precision. The amount of the deflection will furnish a means of calculating the relation of the mass of the mountain to that of the earth, and, the two masses being known, their relative densities can then be determined. The oscillations of the plummet at the summit and at the foot of the mountain afford the basis for a similar calculation. On carrying the plummet to the top some oscillations per day will be lost, the distance from the earth's center being increased; but the mountain's own attraction in part offsets the decrease in weight attributable to altitude, and herein we have the means of comparing its mass with that of the earth.

These methods were not neglected by Bouguer in his voyage to

Peru. Aided by La Condamine, he observed the variation in the plummet-line due to the influence of Chimborazo, and he noted the rate of the pendulum's movement on the volcanic mountain of Pichincha (which is equal in height to Mont Blanc), and at the sea-level. Unfortunately, the imperfection of his instruments, the rigor of the climate, and the violence of the winds, prevented the two French astronomers from attaining great precision in these observations. The effects they had expected to see confirmed were found to be much less marked than they had anticipated, and Bouguer therefore believed that the volcanic mountains of Peru were hollow and internally simply huge caverns. A repetition of his experiments, with the care required in researches of such a delicate nature, would determine the question whether the unsatisfactory character of his results was due to errors of observation, or if it was a case similar to that of the Himalayan chain.*

Bouguer's method was employed successfully in 1774 by the celebrated English astronomer Maskelyne. He chose for his experiments Mount Schiehallion in Scotland. This mountain is wholly isolated. Its geologic constitution is known, and its form is not very irregular; the calculations were thus simplified. By observations of the stars that passed near his zenith Maskelyne first determined the latitudes of two stations, one to the south and the other to the north of the mountainthe distance between them being 1,330 metres. The difference in the two astronomical latitudes was found to be 43" instead of 54′′.6, as shown by the measured distance. The excess of 11".6 represented the sum of the attractive force exerted by Schiehallion on its opposite sides. It then remained to ascertain the volume of the mountain, its exact configuration, density, and total weight, and by the aid of these factors to determine the theoretic sum of the attraction it exerted on the plummet of the two stations. The geologist Hutton was intrusted with this work, which occupied him three years. The result of his calculations was, that the deviation observed would be explained by supposing the mean density of the mountain to be to that of the earth as 5 is to 9. Hutton first adopted for the density of Schiehallion the number 2.5-about the density of quartzose sandstone; according to this the mean density of the globe was 45. He afterward modified these figures, taking 30 for the density of the mountain and 5:4 for that of the earth. The geological study of this mountain, undertaken subsequently by Playfair and Lord Webb-Seymour, showed the density of its component rocks to be intermediate between these two estimates, from which it would appear that the earth's density is 4.7.

These experiments were not supplemented by observations of the

*M. Saigey has shown that, by selecting from Bouguer's observations those which appear to have been made under favorable conditions, and by calculating the force of the attractions in a more exact manner, the density of the earth is found to accord with Maskelyne's estimate of it.

pendulum's oscillations; it is true the mountain's slight elevationone thousand metres-did not promise a very marked effect. An experiment of this kind was made in 1821 by the astronomer Carlini, on Mont Cenis, which showed the earth's density to be in the vicinity of the number given by Maskelyne. In 1854 Airy performed an analogous experiment at the bottom of the Harton coal-mine. At a depth of 1,220 feet it was demonstrated that the seconds pendulum advanced in speed two and a quarter seconds per day, and from this it was concluded that the mean density of the globe is to that of the surface as 2-63 to 1, and, taking the density at the surface to be 23, that of the globe is 6.1. M. Saigey endeavored to find the density of the globe by the deflection of the plummet-line due to a whole continent's attraction, calculating the theoretic deviation from the vertical at Evaux, a central point of France, and one of the stations of the meridian of Paris. According to Puissant's calculation, there exists between the astronomical and geodetical latitudes of Evaux a difference of about 7", which would indicate that the attraction of the southern part of France, i. e., to the south of the latitude of Evaux, exceeds that of the northern portion. Now, with a good orographic chart the average elevation of the ground from about Evaux to the Pyrenees, the Alps, and to the neighboring seas can be calculated, and with these data the effect of all the partial attractions that affect the plummet-line at Evaux. M. Saigey has shown that, to account for the discrepancy pointed out by Puissant (who supposes the attraction of the globe to be about 30,000 times greater than that of all France above Evaux), the mean density of the earth must be to that of France alone as 17 is to unity. Taking 2.5 for the density of the ground, as compared with water, it gives 4-25 as the density of the globe.

The researches of Maskelyne, above referred to, may be reduced to a closet experiment: one can weigh the earth in his own room! This was first done by the illustrious Cavendish. This, the youngest, son of the Duke of Devonshire, who sacrificed his hopes of fortune to his love of science, commenced his career in poverty. "His parents," M. Biot tells us, "seeing that he was good for nothing, treated him with indifference, and gradually became estranged from him. He made amends by becoming one of the first chemists of his time, and, when he had acquired celebrity, one of his uncles, who had been a general abroad, returned at a happy moment to leave him an inheritance of three hundred thousand francs rental. He also left him at his death a fortune of thirty million francs. Cavendish was thus the most wealthy of all the learned, and probably the most learned of all the wealthy."

Cavendish had received from Hyde-Wollaston an apparatus which he in turn had obtained as a bequest from John Michell, and which was designed to determine the weight of the earth by the attraction exerted by two large globes of lead on two small balls suspended from

the ends of a movable lever. There was certainly something novel and bizarre in this idea of attempting to observe the attraction of a ball of lead, which we are accustomed to consider an inert mass-in trying to demonstrate by sight its infinitesimal share in universal gravitation. It was accomplished, nevertheless. Cavendish improved Michell's apparatus by applying to it the principle of the famous torsion balance of Coulomb-the torsion of a wire opposed as a moderate force to the attraction exerted on a lever carried by the wire. His experiments were communicated to the Royal Society of London in 1798. The mode of making the observations is easily described. A horizontal lever of fir-wood was suspended to a metallic wire dependent from the ceiling of a closed chamber. At its two extremities were two small balls and two blades of ivory, marked with divisions. All the movements of the lever were observed from without through lunettes fixed in the walls of the chamber, and directed toward these divisions. Finally, two large globes of lead, each weighing 158 kilogrammes and sustained by a screw-gauge, could be moved toward or from the balls at will, by mechanism worked from the outside. Now, whenever they approached the small balls the latter were seen to obey the attraction of the globes of lead; they were displaced, and oscillated around a new point of equilibrium where the reaction of the torsion wire counterbalanced the attraction of the globes. From these experiments and the ascertained strength of the attraction of the globes in relation to their weight, it is easy to estimate the relation of the mass of the globes to that of the earth, and thence the density of the earth. Cavendish thus found the earth's density to be 5:48, that of water being unity.*

Cavendish's experiments were repeated by F. Reich, at Freiberg, in two trials in 1837 and 1849, and also at London in 1842, by Francis Baily, under the auspices of the Astronomical Society. Reich's figures differed but little from Maskelyne's (5:44 to 5:58). Baily's experiment gave a little larger figure (567). Baily improved upon the apparatus of Cavendish in several ways: he changed the size and material of the small balls, using balls of platinum, lead, brass, zinc, glass, and ivory. The figure he settled upon was the average of over two thousand tests; still, it is not wholly reliable, his results being affected by certain errors the cause of which was for a long time unknown. The question was of an importance that warranted a reexamination of the data with all the resources of modern science. Two French physicists, A. Cornu and J. Baille, have recently accom

* The considerable difference between this number and that furnished by Maskelyne's observations induced Hutton, then advanced in age, to examine anew Cavendish's experiments. "I could not," he says, "rely on these results without repeating the entire computation. Still, after a long life spent in abstract researches, being now eighty, and overwhelmed with infirmities, I feel that I may be pardoned for shrinking from the task. But I should have no rest were I not myself to undertake the work." Hutton discovered many small errors in calculation, and he found 5:31 to be the measure of the earth's density.

plished this work. Their experiments, commenced in 1870, have been the subject of various interesting communications to the Academy of Sciences. Their apparatus are deposited in the vaults of the Polytechnic School. They are much smaller than those of Cavendish and Baily, for, as Messrs. Cornu and Baille have remarked, there is an advantage gained in these experiments by reducing the dimensions of the apparatus. The attracting mass, formed of mercury contained in two hollow spheres of bronze, 0·12 metre in diameter, weigh twelve kilogrammes. By transpiration the mercury can be made to pass from one sphere to the other, thus doubling the effect of the attraction, and this change is effected without shock or disturbance.* The lever of the torsion-balance is a little tube of aluminium, 0·50 metre in length, carrying at each end a ball of copper weighing one hundred and nine grammes. A flat mirror fixed in the middle reflects the divisions of a horizontal scale five or six metres distant, and the slightest movement of the lever is thus revealed by a displacement of the scale divisions. The time of a double oscillation of the lever is about seven minutes. The phases of these oscillations are registered by electricity. A great merit of these researches consists in the opportunity they afford for a thorough study of all the causes of perturbation that can introduce error into such experiments. The definite result can be accepted with confidence. The figure thus far obtained is 5.56. It may be added that Messrs. Cornu and Baille have discovered the cause of the too large number given by Baily. In correcting the errors of system in his experiments, it is probable that a slightly different number will be obtained—5.55. To sum up, the earth's mean density thus appears to be five and a half times that of water, and the density at the surface is less than half that of the interior, or about 2.5. Consequently there must be in the interior heavy masses whose excess of density compensates for the lack thereof in the rocks at the surface. This need not be surprising, for the heavy pressure sustained by the deeper strata must naturally increase the density. But what is the law governing this increase of density from surface to center? Legendre formulated a simple law, adopted also by Laplace, according to which the surface density is 2.5, at the middle of the radius 8.5, and at the center 11.3, the mean being taken as 5·5. A different law, to which M. Edouard Roche arrived by theoretic considerations, gives a surface density of 21, a mid-radius density of 8.5, and 10.6 at the center. This agreement of results deduced from three different hypotheses shows that the decision of the question is narrowed to small dimensions. Adopting M. Roche's conclusions as the most probable, it can be said that the mean density of the earth is about double that of its surface, and that the density of the center is double that of its mid-radius. The central strata or masses have a density approximating to that of lead.

* In the later experiments the number of the spheres was doubled.