ATTRACTION or SOLIDS. As this subject is so intimately connected with the important experi ments on the attraction of mountains and leaden balls, and with many other branches of physics, and as it cannot be introduced with proprietrunder any other head, we shall present the reader with some of the most important and useful propositions, referring to other works for the complete discussion of the sub ject.
In the chapter of Physical ASTRONOMY, entitled, On the Gravitation of a Sphere, we have already entered upon the subject as connected with astronomy ; we shall therefore resume the discussion where it was left in that article, following implicitly the steps of New ton, in so far as he has prosecuted the subject in the first book of his Principia. We shall then consider the subject of the solids of greatest attraction, which has been recently treated with such ability by Pro fessor Playfair, availing ourselves of the kind permis sion of that distinguished philosopher, to give an abridged view of his valuable paper.
We have already seen, in the article already men tioned, that when the law of the force exerted by the particles is inversely as the square of the distance, the centripetal forces of the spheres themselves, on rece ding from the centre, decrease or increase according to the same law. It will appear from the two follow ing propositions, that when the law of the force va ries in the simple inverse ratio of the distance, the centripetal forces of the spheres in receding from the centre will vary according to the same law as the forces of the particles.
If centripetal forces tend to the several points of spheres, proportional to the distances of those points from the attracted bodies ; the compounded force, with which two spheres will attract each other mu tually, is as the distance between the centres of the spheres.
Case 1. Let AEBF be a sphere ; S its centre • P a particle attracted ; PASB the axis of the sphere passing through the centre of the particle ; EF, cf, two planes, by which the sphere is cut, perpendicular to this axis, and equally distant on each side from the centre of the sphere ; G, g, the intersections of the L 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, onc 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. I. if the plummets arc 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 plumb-line, be measured by the arch mn. But the arch MN is
known from the distance between the stations 0, P ; therefore, by subtracting the arch MN from the arch mn, 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 Maskelyne, 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 side of the bill, 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 51".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° 4.0' answers to a difference of latitude equal to 42".91. 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 Shehallien. 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 sector. 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 bill 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 bill nearly as radius is to the tangent of 11".G, 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 be had from the following analogy : 5 : 9=2.5 : •.5 the earth's density, that of water being 1.