of experiments on the pendulum. 93. 
through all its steps with precision. It would indeed be so 
much the more superfluous to insist on this minute accuracy, 
as variations so much more considerable in the form of the 
earth's surface are commonly neglected : for example, in the 
allowance made for the reduction of different heights to the 
level of the sea, which has usually been done without any 
consideration of the attraction of the elevated parts, interposed 
between the general surface and the place of observation. It 
is however obvious, that if we were raised on a sphere of 
earth a mile in diameter, its attraction would be about ^ Q l Q Q 
of that of the whole globe, and instead of a reduction of ~ q Q - 
in the force of gravity, we should obtain only or three 
fourths as much : nor is it at all probable that the attraction 
of any hill a mile in height would be so little as this, even 
supposing its density to be only two thirds of the mean density, 
of the earth : that of a hemispherical hill would be more than 
half as much more, or in the proportion of 1.586 to 1 ; and it 
may easily be shown, that the attraction of a large tract of table 
land considered as an extensive flat surface, a mile in thickness, 
would be three times as great as that of a sphere a mile in 
diameter: or about twice as great as that of such a sphere of 
the mean density of the earth : so that, for a place so situated, 
the allowance for elevation would be reduced to one half : 
and in almost any country that could be chosen for the expe- 
riment, it must remain less than three fourths of the whole 
correction, deduced immediately from the duplicate proportion 
of the distances from the earth's centre. Supposing the mean 
density of the earth 5.5, and that of the surface 2.5 only, the 
correction, for a tract of table land, will be reduced to 1-—^. 
— or of the whole. 
5.5 44 100 
