468 
GEOLOGY: W. M. DAVIS 
new growth stands firm to build the reef upward, while some is broken 
off and washed inward to form the flat reef and the lagoon shoals, only 
the remainder can be sacrificed for the talus. Let this remainder be 
represented in section by DEF. If equal remainders are applied to talus 
building in equal time intervals, they may be represented by the shaded 
and unshaded quadrilaterals, EFHG, GHLK, etc., in which the breadth 
diminishes as the length increases. 
So long as the reef growth is inclined outward, its increase in perim- 
eter will, by providing a larger volume of coral growth, aid in supply- 
ing the demand for more talus material due to increase of depth; it is 
indeed conceivable that, if a reef foundation subsides very slowly and 
of the talus slants down to a level ocean floor of moderate depth, increase 
of perimeter may more than compensate for increase of talus length 
in the deepening water. In this case, outgrowth will continue at a 
constant or a lessening instead of at a steepening angle, as on the 
left side of figure 1 . Especially favorable conditions for outward growth 
are provided when two islands stand so near each other that the sub- 
merged saddle between them is of moderate depth; for then the talus 
slopes on the line connecting the two island centers will be of decreas- 
ing length, if the rise of the talus intersection is faster than the sub- 
sidence of the islands. In such a case, reef cusps would tend to grow 
toward each other, and on uniting, the two concave reef faces would 
diminish their concavity by growing outward faster than the convex 
reef faces elsewhere, because the talus beneath a concave reef face is 
concentrated and thickened on converging lines of slope, while beneath 
a convex reef face it is distributed and thinned on diverging lines of 
slope. The double-looped barrier reef that encloses Makongai and 
Wakaya in central Fiji appears to be an example of this kind: on the 
other hand, four oval atolls north of the Exploring Isles in eastern 
Fiji, separated from each other by less distance than that which sepa- 
rates Makongai and Wakaya, show little tendency to develop ap- 
proaching cusps; hence subsidence there may have been relatively 
rapid; and this is made probable by the occurrence of several Mrowned 
atolls' not far to the northeast. 
But when the reef talus is built on the slope of a volcanic cone that 
rises from a deep ocean, the increase of coral growth on an enlarging 
reef perimeter may not fully compensate for increase of talus material 
demanded, especially if subsidence be relatively rapid; then the reef 
growth must be steeper in the second subsidence interval, EG, than in 
the first, DE; steeper in the third than in the second, and so on, in 
order that the thinner talus increments shall support it: otherwise the 
