80 



ATTRACTION. 



l'l.ATl 



XL1X. 



rig. i. 



Maske- 

 lyne's ex- 

 periments 

 on Shehal- 

 lien. 



might produce a deviation in the'plumh-line of nearly 

 48 seconds. In order to determine this experimen- 

 tally, Bong u er and Condai red tho altitudes 



of several stars from two station;, on. 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 O, 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 O, 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 M, Nn, which measure 

 the two angles of deviation PAB, OCD, produced 

 by the attraction of the mountain. In tKe 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 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 ,54".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. 1 1".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 tc 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 



mean density of the hill to be nearly that of common 

 free stone, or '_'..">, consequently the density of the 

 mountain will be had from the following anal< 

 5 : 9=2.5 : 4.5 the earth's density, that of water 

 being 1. 



It is obvious, that the accuracy of this result de- 

 pends on the correctness of the number 2.."i, which is 

 assumed as the average density of the hill. With the 

 view of ascertaining the real density of Shehallien, a 

 complete mineralogical survey of it has been recently 

 made by Professor Playfair. He found that it con- 

 sisted of granular quartz, whose average density was 

 2.61, and of mica slate, whose average density was 

 2.81 ; and that the density of a homogeneous moun- 

 tain, that would have produced the same effect upon 

 the plumb-line, was 2.716. Mr Playfair has, with 

 great labour, computed the correction that must be 

 made on the attraction of the mountain, in conse- 

 quence of the variation in the specific gravity of its 

 parts ; and it would appear from these calculations, 

 that the earth's density is about 4.867, a result which 

 approaches nearer than the former to the result of Mr 

 Cavendish's experiments on the attraction of leaden 

 balls. A detailed account of Mr Playfair's survey and 

 calculations will, we trust, be soon given to the pub- 

 lic. To the kindness of that celebrated philosopher, 

 the editor has been indebted for the preceding inter- 

 esting facts. 



The experiments made by Mr Cavendish on the 

 attraction of leaden balls, in order to determine the 

 density of the earth, are so intimately connected with 

 the attraction of mountains, that we cannot omit the 

 present opportunity of presenting our readers with an 

 account of the apparatus which he employed, and of 

 the results to which he was conducted. 



This ingenious and simple machine was invented 

 for the purpose of measuring the earth's density, by 

 the Rev. John Michell, a young and accomplished 

 philosopher, who was carried off in early life from 

 the scientific labours which he had so successfully be- 

 gun. It afterwards came into the hands of Mr Ca- 

 vendish, who made a few improvements on its con- 

 struction, and conducted the experiment to a succes- 

 ful issue. 



A longitudinal vertical section of the instrument is 

 represented in Plate XLIX. Fig. 2. where GGHH 

 is the building in which it was placed, and ABCDD 

 CBAEFFE its case; x and .rare the two balls which 

 are suspended by the wires h-x from the arm ghmh, 

 which is itself suspended by the slender wire gl. This 

 arm consists of a slender deal rod hmh, strengthened 

 by a silver wire hrh, which renders it sufficiently 

 strong to support the balls. 



The case, which rests on posts /3, /3 firmly fix- 

 ed into the ground, is supported and set horizontal 

 by four screws, two of which are seeTi at S, S. W 

 and W are the leaden weights or balls, which are sus- 

 pended from the centre-pin Pp by the copper rods 

 Rr, PrR, and the wooden box rr. This centre pin 

 passes through a hole in the beam HH, perpendicular- 

 ly over the centre of the instrument, and turns round 

 in it, being prevented from falling by the plate p. 

 MM is a pulley fastened to this pin, and M)M a cord 

 coiled round the pulley, and passing through the end 

 wall GG. By means of this cord the observer may 



Professor 

 Play lair's 



mtver uf 



Shchullieii. 



Caven- 

 dish's ex- 

 periments 

 on the at- 

 traction of 

 leaden 

 balls. 



Plate 



XLIX. 

 Fig. 2. 



