MEAN DENSITY OF THE EARTH. 
391 
3 
part of the actual plain effect being + j j an( ^ that °f the 
volume a P s d being 
3 d h 
4 A /TF+a* 
their difference gives the actual effect for the cone as ex¬ 
pressed in (16). For a mountain 2.5 miles high and having 
a radius of base equal to 30 miles, i nearly, so 
j/P -a 2 
that it makes an essential difference whether we treat the 
mountain as a cone or as a plain. 
The formula 
dg _ 2A/ 3 <5\ 
g r V 1 ~~4 AJ 
has long been known as Young’s rule, although it first ap¬ 
peared in 1749,in Bouguer’s work, “La Figure de la Terre.” 
He made the assumption that the surface density of the 
earth is equal to one-half the mean density— i. e., A = 2 
from which the total diminution of gravity on account of 
5 h 
distance and matter would be This correction has con- 
4 r 
tinually been applied in the treatment of mountains and 
table lands by most modern observers. Whether this form¬ 
ula is the proper one to use or whether, indeed, any correc¬ 
tion at all should be made for continental attraction is still 
an open question. It has been assumed that the whole cone 
of matter P s t might be brought down by compression to 
the line d c without materially altering the shape of the sea- 
level ; that is to say, that the vertical attraction at the point 
P before compression is approximately equal to that after 
compression. In other words, the intervening matter has no 
effect. This assumption has evidently been made in view 
of the earlier measurements of the force of gravity, which 
seemed to show a very small density for mountains. Two 
notable cases of this are the Andes, which appear to be not 
much heavier than ice,* and the island of Ascension, where 
the observed force of gravity at the sea-level was actually 
* Bouguer (Pierre). La figure de la terre. 4°. Paris, 1749, p. 362. 
