GEOLOGY: W. M. DAVIS 
467 
ring diminished, but he did not explain the cause of the diminution. 
Dana used similar diagrams and insufficiently explained the diminution 
of diameter by saying: — ''a barrier, as subsidence goes on, gradually 
contracts its area, owing to the fact that the sea bears a great part of 
the material inward over the reef' (Corals and Coral Islands, 1872, 
263). Certain later diagrams, especially one by Lendenfeld (Wester- 
mann's Monatshefte, 1896, 499-519), represents a reef as growing up- 
wards and outwards, and hence of increasing diameter. Daly adopts 
essentially this view and adds: — ''When one remembers that most of 
the detritus abraded from the main reef goes to form talus on the 
outer submarine slope; and, secondly, that the growth of new coral is 
much faster on that side, we cannot fail to expect a centrifugal tendency 
for the encircling reef, as the island sinks" (Glacial-Control Theory of 
Coral Reef, Proc. Amer. Acad., li, 1915, 247). Both increase and de- 
FIG. 1. 
crease of reef diameter may take place, for both outward and inward 
upgrowths are possible, but in atolls that have grown upward during 
long continued subsidence in a deep ocean, diminution of diameter 
with inward growth is the more probable for the following reasons. 
Let a sea-level fringing reef be formed around a young volcanic cone 
at D, figure 1, and let the horizontal lines on the right side of the figure 
represent successive levels of the sea with respect to a uniformly sub- 
siding cone. Let the subsidence be so slow that the reef at first grows 
upward and outward, DE, on its own talus, which lengthens as subsid- 
ence progresses. The talus material consists chiefly of fragments 
broken by waves from the corals and other organisms which grow on 
the outer face of the reefs. In a given period of tim.e, a growing reef 
face of given perimeter and 20 fathoms deep cannot produce more 
than a certain maximum volume of new growth; and as some of the 
