62

CALCULATIONS TO ASCERTAIN THE TRACT 26.

to 24864£ miles, making 69 t ' t to a degree in the mean lati-tude. Lastly, of 1312840S0 give 87522120 for the measureof the attraction of the whole earth.

Consequently, the whole attraction of the earth, is to thesum of the two contrary attractions of the hill, as the number87522720 to 8811^, that is, as 9933 to 1 very nearly, on sup-position that the density of the matter in the hill, is equal tothe mean density of that in the whole earth.

But the Astronomer Royal found, by his observations, thatthe sum of the deviations of the plumb line, produced by thetwo contrary attractions, was 11*6 seconds. Hence then itis to be inferred, that the attraction of the earth, is actuallyto the sum of the attractions of the hill, nearly as radius tothe tangent of 11*6 seconds, that is, as 1 to *000056239, oras 17781 to 1 ; or as 17804 to 1 nearly, after allowing for thecentrifugal force arising from the rotation of the earth aboutits axis.

Having now obtained the two results, namely, that whicharises from the actual observations, and that belonging to thecomputation on the supposition of an equal density in the twobodies, the two proportions compared must give the ratio oftheir densities, which accordingly is that of 17804 to 9933, or1434 to 800 nearly, or almost as 9 to 5. And so much doesthe mean density of the earth exceed that of the hill.

Thus then we have at length obtained the object which wehave been in quest of, through the very laborious calculationsthat have been described in this tract, and in the survey andmeasurements from which these computations were made;namely, the ratio of the mean density of all the matter in theearth, in comparison with the density of the matter of whichthe hill is composed ; which ratio we have found to be equalto that of 9 to 5. And, for the reasons before mentioned, Ithink we may rest satisfied, that this proportion is obtained toa considerable degree of proximity, probably to within the50th part, if not the 100th part of its true magnitude.

Another question however still arises, namely, what is thedensity of the matter in the hill ? Is its mean density equal