TRACT 26.

MEAN DENSITY OF THE EARTH.

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the attraction of the matter that might be contained in them,must be deducted from the other two equal quantities, toleave the real attraction of those two sides; then subtractingthe remainder on the South side, from that of the Northernside, there will at last remain the joint effect of all the matterbelow the plane, in the Northern direction : but as the oneremainder is to be subtracted from the other, the two equalquantities may be omitted in both, and only the effects of thevacuities brought into the account, which being twice sub-tracted, their signs become contrary to those of the partsabove the horizontal plane; that is, the effect of the Southernvacuity is affirmative, and that of the Northern one negative.But for the Northern observatory, when the attraction towardsthe South is to be found, the contrary names take place; thatis, in the elevations the Southern parts are affirmative, and theNorthern parts negative; but in the vacuities or depressions,the Northern parts are affirmative, and the Southern onesnegative.

According to the foregoing method the plan of the groundwas divided into 20 rings, by equidistant concentric circles,described about each observatory as a centre ; and each qua-drant was divided into 12 parts, or sectors, by lines forming,with the meridian, angles whose sines were in arithmeticalprogression ; by which means, the space in each quadrantwas divided into 240 small parts, making almost a thousandof such parts in the whole round, for each observatory, ornear 2000 for the two observatories. This was judged to bea sufficiently great number of parts, to afford a very consi-derable degree of accuracy ; or at least that number was asgreat, and the parts as small, as was well consistent with thedegree of accuracy afforded bjr the number of points, whoserelative altitudes had been determined.

In this division, the common breadth of the rings, or thecommon difference of the radii, is 666f- feet; and the commondifference of the sines of the angles, formed by the radii andthe meridian, is T Vth of the radius; and consequently, thoseangles are expressed, in degrees and minutes, as here below,