ATTRACTION or MOUNTAINS. If every por tion of matter is attracted by every other portion of matter, with a force directly proportional to the number of gravitating particles, and inversely as the square of the distance, it might naturally be ex pected, that the attractive force of a large and solid mountain might be determined by direct experi ments. Though the clouds and vapoues which crown the summits of lofty mountains, or hover along their , sides, evidently indicate the exertion of an attractive. force, yet astronomers have sought for a more une quivocal proof of its existence, by measuring the de- . flection which it produced in attracting a plumb-line from its perpendicular position.
The earliest hint of this method was suggested by Sir Isaac Newton ; and it was first put in execution by the French academicians, who were sent to mea sure a degree of the meridian in Pcru. The celebra ted Bouguer selected the mountain Chin-,boraco as the most proper for this purpose ; and from a rough calcu- ' lation he concluded, that its attraction would be equal to the 1000th part of that of the whole earth, and might produce a deviation in of nearly ' 43 seconds. In order to determine this experimen , tally, Bouguer and Condamine observed the altitudes of several stars from two stations, one on the north, and the other on the south side of the mountain. The difference between the altitudes obtained on each side, diminished by the difference of latitude between the two stations, will be double of the angle of deviation produced by the action of the mountain. Thus, in Plate XLIX. Fig. 1. if the plummets are attracted into the positions AB, CD, deviating from the ver tical lines AP, CO, by the angles PAB, OCD, the difference of latitude between the stations 0, P, which is measured by the celestial arch MN, will, in consequence of the deviation of the plumbline, be measured by the arch Inn. But the arch MN is known from the distance between the stations 0, P ; therefore, by subtracting the arch MN from the arch sun, found by taking the altitudes of a star, we obtain the sum of the arches Mn, Nn, which measure the two angles of deviation PAB, OCD, produced by the attraction of the mountain. In the case of Chimboraco, the angle of deviation was 8 seconds.
This interesting experiment was repeated in this country by the learned Dr Maskelync, with the view not merely of ascertaining in general the attraction of mountains, but for the purpose of determining from the result the mean density of the earth. The hill
of Shehallien, in the county of Perth in Scotland, was reckoned the most convenient for this purpose, and preparations were made for executing this laborious undertaking in the summer of 1774. An observa tory was erected about half way up the north sine of the hill, and was afterwards removed to a similar po sition on the south side. No fewer than 337 obser vations were made with an excellent zenith sector of Sisson's upon 43 fixed stars ; and it appeared from these observations, that the difference of latitude be tween the two stations was 54P.6. By the trigono metrical survey it was found, that the distance be tween the stations was 4364.4 feet, which in the la titude of 56° 40' answers to a difference of latitude equal to 42".94. The difference between these re sults, viz. 11".6, is obviously the sum of the two de flections of the plumb-line, and therefore 5".8 is the measure of the attraction of Sheballien. A complete survey of the mountain was next made, in order to de termine its form and dimensions, for the purpose of calculating the attraction which it exerted upon the plumb-line of the In order to accomplish this, the hill was supposed to be divided into a number of vertical pillars, and the action of each pillar upon the plumb-line was computed from its altitude and its dis tance from the observatory. From these computa tions, which were made with great labour by the learned Dr Charles Hutton, it appeared, that the whole attraction of the earth was to the sum of the two contrary, attractions of the earth, as 9933 to 1, the density of the hill being supposed to be equal to the mean density of the earth. But the attraction of the earth is to the sum of the attractions of the hill nearly as radius is to the tangent of 11".6, that is, as 17804 to 1, consequently the mean density of the earth is to the mean density of the hill as 17804 to 9933, or nearly as 9 to 5. Dr Hutton supposes the 2 mean density of the hill to be nearly that of common . free stone, or 2.5, consequently the density of the mountain will he had from the following analogy : 5 : 9=2.5 : 4.5 the earth's density, that of water being 1.