TRACT 26. MEAN DENSITY Or THE EARTH.

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taken, from them are then determined, in this plan, the placesof all the other points in the sections, whether vertical, hori-zontal, or inclined. These places or points were determined,by drawing lines from each extremity of the base, so as toform with it angles equal to those which were observed onthe ground, for each corresponding pole: the intersectionsof these lines are the places of the poles, which having markedwith a fine dot or point of ink, and written close to each pointthe proper number expressing its relative altitude, and clean-ed the paper by rubbing out tbe lines forming the angles, bywhich the points were determined, there remained only thepoints, with the figures expressing their altitudes, distinctlyexhibited in the plan. See plate 2.

It remains now to apply all the foregoing calculations, andconstructions, to determine the effect of the attraction, in thedirection of the meridian. And here it soon occurs, that thebest method is, to divide the plan into a great number ofsmall parts, which may be considered as the bases of as manyvertical columns, or pillars of matter, into which the hill, andthe adjacent ground, may be supposed to be divided, by ver-tical planes, forming an imaginary group of vertical columns,something like a set of basaltine pillars, or like the cells in apiece of honeycomb ; then to compute the attraction of eachpillar separately, in the direction of the meridian; and lastly,to take the sum of all these computed effects, for the wholeattraction of the matter in the hill, &c. Now the attractionof any one of these pillars, on a body in a given place, maybe easily determined, and that in any direction, to a sufficientdegree of accuracy, because of the smallness and given posi-tion of the base: for, on account of its smallness, all the mat-ter in the pillar may be supposed to be collected into its axis,or vertical line erected on the middle of the base ; the lengthof which axis, as the mean altitude of the pillar, is to be esti-mated from the altitudes of the points in the plan which fallwithin, and near, the base of the pillar: then, having obtainedthe altitude of this axis, with the position of its base, and thematter supposed to be collected into it, a theorem can easily