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CALCULATIONS TO ASCERTAIN THE TRACT S*6.

to the great number of small pillars concerned in this busi-ness, let us suppose be and d to be constant or invariablequantities; and then it is evident that we shall have nothingmore to do, but to collect all the s’s, or sines of elevation, ofall the pillars, into one sum, and then multiply that sum bythe constant quantity be x d, by which there will be pro-duced the measure of the attraction of all the pillars, or of thewhole part of the ground on one side of we. Now be willbe made to become constant, by making the circles equi-distant from one another, or by taking the radii in arithmeti-cal progression. And d will be constant, by drawing the radiiso as to form, with an, angles whose sines shall be in arith-metical progression ; for then d is the common difference ofthe sines of those angles. Hence then we are easily led tothe best manner of dividing the plan into the small spaces,viz, from the centre A describe a sufficient number of con-centric and equi-distant circles ; divide the radius ai, of anyone of them, into a sufficient number of equal parts, and fromthe points of division erect perpendiculars to meet the circle ;then through the points of intersection draw radii, and theywill divide the circles in the manner required.

In a computation of this kind, we need only calculate theattraction of the matter which is above the plane or horizonof each observatory, and the attraction of so much matter asis wanting, to fill up the vacuity below that plane, lying be-tween it and the surface of the lower part of the hill. For theSouth observatory, the attraction of the Southern parts thatare above it, must be subtracted from that of the Northernparts, to obtain the attraction of the whole towards the North;that is, the Southern elevations are negative, and the North-ern ones affirmative. The contrary names take place withrespect to the depressions, or the vacuities below the planeof the observatory ; for if the whole space below this hori-zontal plane were full of matter, to an equal extent bothways, its attraction need not be computed, as those on thecontrary sides would mutually balance each other; but sincethere are unequal vacuities on each side, it is evident, that