382 
PRESTON. 
of the sea, which is about as far below the surface as the top 
of Mauna Kea is above it. This view is entertained by Major 
Dutton and is borne out by soundings made around the 
island. The plumb line at K is principally influenced by 
the matter in the wedge, whose cross-section is M S D. Of 
this volume the effect of the parallopiped, whose cross-section 
is K X D Yj is neutral, since the matter is presumably uni¬ 
form throughout and is equally divided north and south of 
the station. There remains, then, the two wedges, M X K 
and K YS, each equal to the mountain, and the combined 
effect of these would be approximately that of a mountain 
whose density is equal to the difference of the densities of 
rock and sea water. 
It should be borne in mind that the relative dimensions of 
the mountain are considerably exaggerated in the diagram. 
The base is about fifteen times the altitude, so that the 
neglected matter is in reality much further from K than it 
appears to be in the figure. If it were possible to treat the 
problem in the most rigorous manner, by using more exact 
data, the result would probably undergo some modification. 
For instance, the matter beyond M and that not included 
in the figures already considered doubtless do both influence 
the plumb line at Kaupo to a certain extent; but when we 
remember that we are in total ignorance as to the exact 
density of this matter, and that with any plausible density 
its effect would be a very small fraction of that already con¬ 
sidered, the conclusion is that the use of our data has per¬ 
haps been carried far enough. Moreover, there is consider¬ 
able conjecture about the slope of the mountain below the 
sea-level, and it would seem hardly worth while to pursue 
further the evaluation of the effect of these volumes with 
our present knowledge of the subject. A better survey of 
the ocean bottom around the Hawaiian Islands is very much 
to be desired. With more trustworthy data in this direction, 
this group offers exceptional advantages for the study of 
geological and geodetic problems of the greatest impor¬ 
tance. 
