MEAN DENSITY OF THE EARTH. 
381 
been used in a few rings where its omission would have been 
immaterial. The space between Kaupo and the 25th circle 
was also considered in circles with radii in an arithmetical 
progression giving 10 rings. The attraction was calculated 
for these by formula (10). The result for the attraction 
agreed satisfactorily with that from the regular geometric 
division and showed that no sensible error had occurred in 
the computations. 
It may be worth while to add a word concerning the land 
lying to the southwest of Kaupo. This has not been con¬ 
sidered in the computation, both on account of its position 
and insignificant volume. If we apply equation (7) to this 
matter, it is easily shown that its effect on the resulting 
mean density of the earth may well be neglected. In the 
first place, its center of gravity lies so nearly in the same 
latitude as Kaupo that the component of attraction in the 
direction of the meridian is probably not one tenth of the 
total attraction of this mass; besides, the mass itself is com¬ 
paratively small, having on the average an elevation of about 
500 feet. In fact, if we had this height of matter spread over 
a space equal to sector I between the 10th and 20th circles, 
which would augment the attraction on account of the in¬ 
creased difference in latitude, even then we should only 
have approximately 
Nap. log 2 or h $ X 0.007, 
which would be of no importance in the final result. This 
disposes of all the matter lying above the sea level. 
Sea level —-- —^K _ S 
Fig. 16. 
The influence of the matter below the sea level is perhaps 
best understood by reference to Fig. 16. 
The latitude station is at K. We assume that the slope of 
the mountain is continuous from the summit to the bottom 
