On the Mean Density of the Earth. 5 
of the plumb line, on both sides of the mountain; and that in 
all probability within much less than half a second of the truth. 
Other instruments used, were the Royal Society’s: transit instru- 
ment made by Bird, and an astronomical clock by Shelton, which 
had both been provided on occasion of the observations on the 
transit of Venus, in 1761 or 1769. Besides these and several 
other instruments, one of Ramsden’s best theodolites was used, 
im measuring the figure and dimensions of the mountain, which 
was performed in the most correct manner by skilful surveyors ; 
so as that thence an exact model of it might ‘be made, or all its 
dimensions accurately taken, for computing the attraction. 
By only reading over the accounts of these operations (in the 
places before mentioned) made by means of such instruments, 
and im-such hands, every person must be convinced of the im- 
possibility almost that any error could have been committed, ca- 
pable of causing any scnsible inaccuracy in the conclusion of the 
work. 
‘It remains now to deseribe the share which I bore in this im- 
portant business ; which consisted in taking all the measurements 
as above described, and from those data, calculating what must 
have been the exact magnitude of the mountain, what its attrac- 
tion on the plummet, relatively to that of the globe of the earth 
on the same, and what must be the mean density of the earth. 
These computations, which employed my daily and assiduous la- 
bours during the greater part of two years, are recorded in the 
Philosophi cal Transactions of the year 1778, and also in the 2d 
volume of my Mathematical Tracts. It may therebe seen that, 
after computing trigonometrically the bearing and distance of 
every point in the numerous sections of the mountain, from the 
two observatories, I conceived it to be divided into nearly one 
thousand vertical columns, of given bases and altitudes. I then 
computed the quantity of the attraction of all these columns, on 
the plummet, in the direction of the meridian, when placed at 
the two observatories, on both sides of the hill, where the whole 
effect had been observed, which attraction was thus found to be 
expressed by the number 88112. I then computed, from the 
magnitude of the earth, what must be its attraction on the same 
plummet, and found it expressed by the number87522720. Con- 
sequently, the whole attraction of the earth, is to the sum of the 
two contrary attractions of the mountain, as the number 87522720 
to 88114, that is, as 9933 to | very nearly ; on supposition that 
the density of the matter in the hill, is equal to the mean density 
of that in the earth, 
But Dr. Maskelyne found by his observations, that the sum of 
the deviations of the plumb line, produced by the two contrary 
attractions, was 11°6 seconds. Hence then it is inferred, that 
the 
