TRACT 26.

MEAN DENSITY OF THE EARTH.

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derably nearer than the other to the middle in a horizontaldirection; so that probably the one difference nearly balancesthe other; and accordingly we find that the sum of the affirm-ative altitudes for o is 44-587, and of those for p 45-339, whichdiffer by only a 60th part nearly.

It orly remains now to multiply the sum of the sines bythe common breadth of the rings, and by the common differ-ence of the sines of the angles made by the meridian and theseveral radii. It has already been observed, that the formeris 666-f, and the latter ; therefore x 666f. = 2 yg° = 5 v*is their product: consequently, 158-611 x 5 g.® =8811-f nearly,is the sum of the two opposite attractions, made by the hill&c, at the two observatories.

In order now to compare this attraction with that of the■whole earth ; this body may be considered as a sphere, andthe observatories as placed at its surface ; since the very smalldifferences of these suppositions from the truth, are of no con-sequence at all in this comparison. Now the attraction of asphere, on a body at its surface, is known to be = fed, whered is = the diameter of the sphere, and c ~ 3-1416 = the cir-^cumference of the circle to the diameter 1. But cd is = thecircumference of the circle to the diameter d ; and thereforethe attraction of a sphere will be expressed by barety -J of itscircumference ; which is a theorem well adapted to the pre-sent computation. The length of a degree in the mean lati-tude of 45°, is 57028 French toises (see p. 327, Phil. Trans.1768) : and the same result nearly is obtained, by taking amean among all the measures of degrees there set down, thatmean being 57038 toises. I shall therefore use the roundnumber 57030 as probably nearer the truth. This numberbeing multiplied by 6, the product 342ISO shows the number©f French feet in one degree; but, by p. 326 of the samevolume, the lengths of the Paris and London feet are as 76-734to 72, that is, as 4‘263to4; therefore, as 4 : 4-263 :: 342180:364678 = the English feet in one degree; and this being mul-tiplied by 360 the whole number of degrees, there res'ultsI312S4080 feet for the whole circumference, which arc equal

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