in the length of the pendulum vibrating seconds. 353 
number of vibrations of the pendulum represents the force of 
gravity, we have this simple rule : convert the height of the 
station into the decimal of a mile, and divide it by the radius 
of the earth (3954,583) the quotient is the factor by which 
the number of vibrations in 24 hours being multiplied, the 
product will be the correction required. 
But the quantity thus obtained is evidently erroneous, being 
founded on the supposition that the experiments are made on 
an elevation having no attractive matter surrounding it; and 
it is observed by Dr. Young, in a letter which that eminent 
mathematician addressed to me, and which is published in the 
Phil. Trans, for 1819, entitled “ Remarks on the probabilities 
“ of error in physical observations, and on the density of the 
“ earth, considered especially with regard to the reduction 
“ of experiments on the pendulum that “ if we were raised 
“ on a sphere of earth a mile in diameter, its attraction would 
“ be about of that of the whole globe, and instead of a 
“ reduction of i n f° rce of gravity, we should obtain 
“ only -g^ 0 , or 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 of the same height would be more than half as much 
“ more ( than the sphere ) or in the proportion of 1,586 to 1. 
“ And it may be easily 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 
MDCCCXIX. 3 A 
