388 
PliESTON. 
Determination of the Mean Density of the Earth from Pendulum 
Observations on Mauna Kea. 
The method used involved a study of the rocks compos¬ 
ing the mountain and a determination of the decrease of the 
force of gravity in passing from the sea level to the summit. 
The formula employed is based on the assumption that the 
shape of the mountain is intermediate between that of a 
truncated cone and an extended plain. This estimate results 
from a comparison of photographs taken on different sides 
of the mountain. The gravity observations were made with 
Dr. Mendenhall’s new half second pendulums, which attain 
an accuracy in the periods of oscillation of one part in two 
millions. The density of the mountain depends on a study 
of more than 40 rock specimens. 
The formula usually employed in the treatment of the 
change of the force of gravity with elevation is : 
where g = the force of gravity at the sea level, 
h = the elevation, 
r — the radius of the earth, 
d = the density of the mountain, and 
A — the mean density of the earth. 
This formula is derived by combining the earth attrac¬ 
tion, varying inversely as the square of the distance, with 
the attraction of the matter lying between the sea level and 
the upper station. Certain suppositions are made in regard 
to the form of this exterior matter, and it has been gener¬ 
ally considered a sufficient approximation to regard all the 
matter as equivalent to that contained in a plain of infinite 
extent and of a thickness equal to the elevation (7i). Whether 
this view be admissible depends, of course, on the relation 
between the vertical and horizontal dimensions of the inter¬ 
vening mass. If we suppose this to be of a conical form, 
