MEAN DENSITY OF THE EARTH. 
387 
actly of this amount. The astronomic latitude determined 
at the base-line is of course influenced by the mountain, and 
the reference to this station simply gives a convenient means 
of comparison without implying any particular relation be¬ 
tween the individual attractions as a consequence thereof. 
In order to estimate how the discrepancy between the two 
amplitudes shall be divided between the two sides of the 
mountain and what part of it shall be attributed to each 
station we must consider the position of the center of gravity 
of the mass. The deflection will depend on its distance and 
azimuth from the points in question. To find the center of 
gravity a horizontal projection of Haleakala was divided 
into small squares and these were loaded by weights pro¬ 
portional to their respective heights. The position sought 
was then found experimentally to be near the line between 
sectors IV and V and not far from the 26th circle (11th in 
Plate 8). The azimuth from Haiku is 24° and from Kaupo 
38°. Considering the mass of the mountain concentrated 
at this point, which we may do in view of the approximate 
nature of our knowledge as to its uniform density, we find 
that the difference in the azimuths nearly compensates for 
the difference in distances. At equal distances these azi¬ 
muths would require about 32" of the deflection to be at 
Ilaiku and 27" at Kaupo, whereas with equal azimuths the 
difference in distance according to the law of inverse squares 
would demand about 26" at Haiku and 32" at Kaupo. The 
distances were taken from a large scale map (e-oiio o) an d are 
probably near the truth; so that with this nearly complete 
compensation before us we accept the value of 29".4 given 
by the triangulation and derive a from the equation 
A X 29".4 = 56".5 X d. 
The value of d is found to be 2.90 in the latter part of the 
paper, and we therefore have 
Mean Density of Earth from Haleakala = 5.57. 
