2. The half sum of the distances taken between the suspension, and the upper and lower edges of the disk, gives the distance of the centre of the disk itself; without measuring its diameter with a compass, an operation exceedingly difficult to execute with the necessary precision. By this apparatus of microscopes the length may be measured at pleasure, even during the time of oscillation; and being attached to the wall, instead of supported by the floor, the risk of derangement by the tread of the observer is avoided.
3. The pendulum, and the clock by which its oscillations are measured, were not, as usually, near together and resting on the same base, but were perfectly separated. The coincidences of the oscillations were observed, by bringing the image of the pendulum of the clock, reflected by means of an oblique mirror, in contact with the image of the simple pendulum seen direct through a telescope. By this modification the risk of the mutual influence of the pendulum and the clock is avoided.
4. The disk was attached to the thread by means of knots in the thread itself; avoiding the correction for the small cup usually employed for that purpose.
5. An alteration was made in the weight and shape of the knife-edge suspension; reducing its weight to about 10 grains, and giving it the shape of a rotella, instead of that of a triangular prism.
The simple pendulum and microscopes were attached to a strong wall, in a room on the ground floor, contiguous to the temporary observatory, and well sheltered from the sun and weather. The clock with which the pendulum was compared, was supported by a pyramid of masonry resting on the ground, and occupying the middle of the room. The experimental length between the microscopes was referred to three standard metres, [p157] in perfect agreement with each other: one received from Paris by the Commission of Weights and Measures at Milan; a second brought more recently from Paris by Conte Moscati; and a third in the possession of the Royal Academy of Turin.
The experiments were commenced on the 3rd of September, and terminated on the 27th, being interrupted by M. Carlini’s absence at Chambery from the 7th to the 12th. The distance between the microscopes, and the oscillations and length of the pendulum, were measured alternately. Thirteen independent results were thus obtained, of which the greatest discordance from the mean was not more than 1310000ths of a British inch. The mean result was 39.0992 British inches, the length of the pendulum vibrating seconds in a vacuum, at the place of observation on Mont Cenis, 1943 metres, or 6374 feet above the sea, in the latitude of 45° 14′ 10″. To compare with this determination, we may obtain a tolerably fair approximation to the pendulum at the level of the sea in the latitude of 45° 14′ 10″, such as its length might have been found, if the mountain could have been removed and the pendulum placed on its site, by deduction from the lengths actually measured with a similar apparatus, on the arc between Formentera and Dunkirk, at stations not far removed from the level of the sea, in the adjacent parallels to Mont Cenis, and in the countries adjoining. Of these there are five, not including the station at Clermont, in consequence of its great elevation: they are as follows:—
| Dunkirk | 51° 02′ 10″; | its pendulum at the level of the sea = | 39.13771 |
| Paris | 48 50 14 ; | ditto | 39.12894 |
| Bordeau | 44 50 26 ; | ditto | 39.11295 |
| Figeac | 44 36 45 ; | ditto | 39.11212 |
| Formentera | 38 39 56 ; | ditto | 39.09176 |
The mean length of the seconds pendulum at the level of the sea, in the latitude of 45° 14′ 10″, deduced from these determinations, is 39.1154; and it is so equally, whether an ellipticity of 1288th, or of 1304th, or any intermediate ellipticity, be assumed in the reduction.
We have, then, 39.1154−39.0992 = ·0162 inch., as the [p158] measure of the difference in the intensity of gravitation at the place of observation elevated 1943 metres; and at the level of the sea. The radius of the earth, being 6,376,478 metres, this measure, according to the duplicate proportion of the distances from the earth’s centre, should be ·0238 inch. The attraction of the mountain is, then, equal to ·0238−·0162 = ·0076 inch. Whence it appears that, in this particular instance, the correction for the elevation is reduced, by the attraction of the interposed matter, 68100ths, or to about 710ths of the amount immediately deducible from the squares of the distances.
It is obvious that, if we possessed a correct knowledge of the density and arrangement of the materials of which Mont Cenis is composed, so as to enable a computation of the sum of all the attractions which they exercise on the place of observation, this result might furnish, as well as Dr. Maskelyne’s experiments on the deviation of the plumb-line produced by the attraction of Mount Schehallien, a certain determination of the mean density of the earth. Professor Carlini considers that the form of the eminence may be sufficiently represented by a segment of a sphere, a geographical mile in height, having as its base a circle of 11 miles diameter, the distance from Susa to Lansleburgo; the attractive force, on a point placed on the summit, would, in such case, be equal to 2 π δ (1−23 √111) or in numbers to 5·020 δ, δ being the density of the mountain, and 2 π the ratio of the circumference to radius. The attractive force of the earth, on a point at its surface, is 43 π r Δ, = 14394 Δ, r being the radius of the earth = 3437 geographical miles, and Δ its mean density. Now these two quantities, 14394 Δ and 5·020 δ, should be, to each other, in the proportion of 39.1154,—the pendulum at the level of the sea, representing gravitation at the surface of the earth,—to ·0076, the portion of gravitation at the summit of the mountain due to the attraction of the mountain. By the observations of M. de Saussure and other geologists, Mont Cenis is chiefly composed of schistus, marble, and gypsum; the specific gravities of which substances were ascertained, from numerous specimens in the possession of M. Carlini, to be respectively as follows:— [p159]