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TRACT XXVII.

SAlCULATIONS TO DETERMINE AT 'WHAT POINT IN TUBSIDE OF A HILL ITS ATTRACTION WILL BE THE GREATEST,&C. * READ AT THE ROYAL SOCIETY, NOV. 11, 1719.

Art. 1. The great success of the experiment, latelymade by the Royal Society, on the hill Shihallin, to deter-mine the universal attraction of matter, and the importantconsequences that have resulted from it, may probably giveoccasion to other experiments of the same kind to be madeelsewhere: and as all possible means of accuracy and faci-lity are to be desired, in so delicate and laborious an under-taking; it has occurred that it might not be unuseful toadd, by way of supplement to my paper of calculations re-lative to the above-mentioned experiment, an investigationof the height above the bottom of a hill, at which its hori-zontal attraction shall be the greatest; since that is theheight at which commonly the observations ought to bemade, and since this best point of observation has never beenany where determined, that I know of, but has been vari-ously spoken of or guessed at, being sometimes accountedat and sometimes at a of the height of the hill; whereas,from these investigations, it is found to be generally atabout only ^ of the altitude from the bottom.

2. Let abceda be part of a cuneusof matter, its sides or faces beingthe two similar right-angled trianglesarc, ade, meeting in the point a,and forming the indefinitely smallangle bad. Then, of any sectionbccd, perpendicular to the planesabd, ade, the attraction on a body at A, in the direction