ATTRACTION. 



81 



Attraction turn round the pulley MM, and move the weights 

 of Moun- f rom one situation to the other. 



^ n " It is obvious that the weights W, W conspire, by 



' their action on the balls .r, x, to turn the arm kgh in 



Plate the same direction. Slips of ivory, divided into 20ths 

 XLIX. of an inch, are placed within the case at A, A, as near 

 *' * to the end of the arm as possible, for x the purpose of 

 determining its position. A small vernier scale, made 

 of ivory, is fixed at the end of each arm, by means of 

 which their motion may be estimated to less than the 

 100th of an inch. These divisions are viewed by 

 means of the short telescopes T and T, through slits 

 cut in the end of the case, and stopped with glass. 

 They are illuminated by the lamps L and L with con- 

 vex glasses, so placed as to throw their light on the 

 divisions, the room being in every other respect dark. 

 By means of the wooden rod FK, with an endless 

 screw at its extremity, the observer is enabled to turn 

 round the support J, to which the wire "7 is fasten- 

 ed, and then to move the wire till the arm settles in 

 the middle of the case. 



Let us now suppose that the arm hgh is at rest in 

 a known position ; then when the weights are moved, 

 the arm will instantly be drawn aside by their at- 

 traction, but it will be made to vibrate, and its vibra- 

 tion will continue a great while. By measuring the 

 length of these vibrations, and the time of their con- 

 tinuance, Cavendish found that the force which must 

 be applied to each ball j, in order to draw the arm 



one division out of its natural position, is , N 



being the time of a vibration in seconds ; and that the 

 attraction of the weight on the ball is to the attrac- 

 tion of the earth upon it as .9779 to 1, or as 1 to 

 8739000 D, D being the density of the earth, and 

 each of the weights weighing 2139000 grains, or be- 

 ing equal to 10.64 spherical feet of water. The at - 

 traction of the weight upon the ball will therefore be 



8739000 D ^ t ' le we 'S nt ^ l ^ at ball, and conse- 

 quently the attraction will be able to draw the arm 



out of its natural position bv .or 



p oy 8739000D' or 10683D 



divisions ; and therefore if, on moving the weights 

 from the midway to a new position, the arm is found 

 to move B divisions, or if it moves 2B divisions on 

 moving the weights from one near position to the 

 other, it follows that the density of the earth, or D. 



N 

 1S 10683B* ^ ter correcting this result as obtained 



from each experiment, Mr Cavendish obtained the 

 following Table of densities: 



From these results, it appears, that the mean density 

 VOL. III. PART I. 



of the earth is nearly 5.48, a result considerably AMractkw 

 greater than that which was deduced from the at- "' ^''de- 

 traction of Shehallien. /- -* 



Another method of ascertaining the attraction of 

 matter, has been suggested by the learned Dr Robi- 

 son. He supposes that a sensible effect mio-ht be 

 produced on a long plummet, or a nice spirit level, 

 by the immense quantity of water which is brought 

 to Annapolis Royal in Nova Scotia twice every day 

 by the tides, which rise above an hundred feet. " If 

 a leaden pipe," he observes, " a few hundred feet 

 long, were laid on the level beach at right angles with 

 the coast, and a glass pipe set upright at each end, 

 and the whole filled with water; the water will rise 

 at the outer end, and sink at the end next the land as 

 the tide rises." See Bouguer's Traitede la Figure de 

 Terre. Phil. Trans. 1775, vol. lxv. part ii. p. 495, 

 500. Id. 1 778, vol. lxviii. p. 689. Id. 1798, p. 469. 

 Pringle On the Attraction of Mountains, 9to, Losid. 

 1775; and Robison's Elements of Mechanical Phi- 

 losophy, vol. i. p. 339. (o) 



ATTRACTION of 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 propriety under 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- Atf . 

 tioned, that when the law of the force exerted by the of /phe're" 

 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 Prop. I. 

 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 PtATE 

 a particle attracted ; PASB the axis of the sphere XUX. 

 passing through the centre of the particle ; EF, ej, F'g- 3. 

 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 



