GEOLOGY: W. M. DAVIS 
469 
reef would have to grow outward in an overhanging, unsupported cor- 
nice. It is true that when upward growth becomes steep, the share of 
it that stands firm to build the reef upwards is smaller than before; 
thus the part that may be sacrificed for talus building is larger; but this 
will not make up for the increased demand due to increased talus 
length. A time must therefore come when upgrowth passes the ver- 
tical and thereafter inclines inward, as above K: then a decrease of 
perimeter sets in and the total volume of coral growth diminishes, while 
the demand for talus material still increases. Under these conditions, 
the angle of inward upgrowth must soon come to be but little steeper 
than the angle of talus slope. An atoll reef which has been reduced 
to a diameter of a mile when this condition is reached, will be reduced 
to a point when subsidence has progressed about 2000 feet farther. 
If subsidence then still continues the reef will be extinguished. Dana 
reached essentially the same conclusion, but without analysis; he 
briefly asserts that subsidence will gradually reduce the size of an atoll 
'until it finally becomes so small that the lagoon is obliterated;' then, 
if "subsidence continues its progress .... it finally sinks the coral 
island, which, therefore, disappears from the ocean" (Corals and Coral 
Islands, 1872, 322, 323). Thus a difference may be drawn between atolls 
that are 'extinguished' by the reduction of their diameter to zero dur- 
ing a uniform subsidence (or during an intermittent subsidence at a 
constant average rate), and atolls that are 'drowned,' as Moresby 
phrased it, by a too rapid subsidence, whatever their diameter may be. 
It is evident that many variable factors would enter the equation by 
which the ultimate extinction of a reef might be expressed; form of 
ocean floor, "rate of subsidence and length of intervening stationary 
periods" as Darwin phrased it, rate of coral growth, and strength of wave 
attack are the more important factors. The change in angle of upgrowth 
due to a change from slow to rapid subsidence is shown on the left side 
of figure 1. Further, an extinguished reef would be brought to light if 
subsidence were reversed into upheaval; such a reef might then in- 
crease in size if upheaval paused or halted; and thus increased, it might 
if subsidence were renewed again grow up for a while before being 
extinguished for a second time. Extinguished reefs thus brought to 
light may be called 'resurgent.' 
Many smaller reefs in Fiji appear to be resurgent, as thus defined. 
A good example is Frost reef, figure 2, a third way between Mango, 
M, 7 miles to the east, and Vatu Vara, F, 13 miles on the west. Mango 
appears to be a denuded caldera ring 3 miles in diameter, which has been 
submerged 450 feet or more and rimmed at that level with a fringing 
