6 On the Mean Density of the Earth. 
the attraction of the earth, is actually to the sum of the attrac- 
tions of the hill, nearly as radius to the tangent of 11-6 seconds; 
that is, as 1 to 000056239, or as 17781 to 1; oras 17804 tol 
nearly, after allowing for the centrifugal force arising from the 
rotation of the earth about its axis. 
Having now obtained the two results, namely, that which arises 
from the actual observations, and that due to the computation 
on the suppostion of an equal density in the two bodies, the two 
ratios compared, must give the ratio of their densities, and which 
therefore is that of 17804 to 9933, or 1434 to 800 nearly, or al- 
most as 9 to 5; and so much does the mean density of the earth 
exceed that of the hill. Consequently, if we know the density 
of the latter, we shall thence obtain that of the former. 
At the time when this computation was first printed, in the year 
1778, the real density of the hill was unknown. It was only 
known that it consisted chiefly of very hard and dense rocks, 
much heavier than common stone, which is allowed to be 24 times 
the density of water. I then, by way of example in applying the 
density, multiplied 2 by 24, which produced or 44 for the den- 
sity of the earth, on the smallest assumption; ‘till such time as we 
should come to know more nearly what the real density of those 
rocks is: and therefore I must feel reason to complain, that this 
number (44) has often been stated, rather unfairly, as my final 
conclusion for the earth’s mean density; instead of being only 
the very lowest limit that might be used, till we could better 
learn something on that point with more certainty. But, a li- 
thological survey of the mountain being afterwards accurately 
made at my earnest request, by that excellest philosopher and 
geologist Mr. Playfair, the result of which was published in the 
Philos. Trans. for the year 1811 ; I then applied his mean state- 
ment of the rocks to my own calculations, which gave me the 
number 5 for the density of the earth; as I published in the 
14th volume of my edition of the Phil. Transactions, and in the 
2d volume of my Tracts. 
In Mr, Playfair’s account of the mountain, are given the names 
and nature of the several rocks that compose it, with tables or 
lists of their densities or specific gravities. In one table is a list 
of thirteen specimens of densities, contained between the numbers 
2°6109 and 2:6656, the medium of the whole being 2°639876. 
In another table, of fifteen specimens, the densities are limited be- 
tween 2°71845 and 3-0642, the medium of all which is 2°81039. 
And the mean between these two means, gives 2°7 25 for the medium 
density of the whole mountain, admitting it to be” quite solid, or 
without vacuities, as it appears to be on the exterior surface at 
least. But in the calculation in my Tracts, I went even a little 
higher, using the number 2°75 or 23, thus 2 x 23, which gives 
$6 
