MEAN DENSITY OF THE EARTH. 
379 
each ring counted from the parallel of latitude through 
Kaupo on the left around toward the right until the shore¬ 
line is reached. Some of these are fractional compartments, 
but where they fall short or overlap a compensation is made 
in estimating the number. The last column shows the 
numerical part of equation (8) as far as it depends on the 
length of the radii, the heights of the land and the azimuths 
of the angles forming the sides of the compartments. The 
sum of this column multiplied by k d gives the total attrac¬ 
tion of the mountain in the direction of the meridian at 
Kaupo; so that finally we have 
F=kdx 2.723. 
( 12 ) 
If we take into account West Maui by the application of 
formula (7) we have for the 
Leeward side- k d X 0.473 X TO - X Nap. log 5 
Windward side. .Hx 0.284.X to X Nap. log > 
giving a total attraction of 0.020 X k 8. So that the entire 
influence of the island of Maui on the plumb-line at Kaupo 
in the direction of the meridian is 
F ?=k d X 2.743. 
(13) 
The attraction of the earth on a point at its surface is f 
k 7T A F, where A is the mean density, R the radius, and k , 
as before, is the constant of gravitation. Assuming R to be 
3,960 miles, the earth’s attraction is 16,588 k A. The an¬ 
gular deflection of the plumb line at Kaupo will be equal 
to the attraction of the mountain divided by the attraction 
of the earth, and we shall have * 
2.743 d 
D = 16588 a = 2 ’ 743 
X 12" .44 = 34". 12 t' 
(14) 
