530 T. C. CHAMBERLIN 
one-fourth or some considerable fraction of the upper portion of the 
warped surface is above it and a still larger fraction, two-thirds or 
three-fourths or some such fraction, lies below it, the zone of shallow 
water will usually cut the warps at points where they have rela- 
tively high dips. The area between the water-surface and the shelf- 
limit in depth will therefore be proportionately small. For a rough 
illustration, if the average crests of the continental swells be taken 
at the modest figure of 6,000 feet above sea-level and the average 
bottoms of the oceanic sags at 18,000 feet below sea-level, the 
vertical depth of 600 feet spans only one-fortieth of the total range. 
The value of this fraction has yet to be reduced for the excess of 
slope of this portion over the mean slope to give the horizontal 
breadth of the belt really embraced within the shelf-depth. At the 
present time the extreme range of deformative heights and depths is 
more than twice that selected as the basis of this illustration. 
An inspection of present conditions seems to show that the sea 
surface so cuts the normal unmodified diastrophic surfaces that an 
area not more than half that of the present continental shelf would 
lie between the contours of zero and of 600 feet depth, or perhaps 
2.5 per cent of the earth’s surface. This differs radically from the 
broad areas of shallow water that obtained at the climax of the great 
sea-transgressions in Paleozoic times when from 40 per cent to 50 
per cent of the surface of the North American continent was covered, 
i.e., from 16 to 20 times as much, and more or less comparable por- 
tions of other continents were covered in a similar way and at the 
same time. That these transgressive seas were shallow is implied 
by the sediments and by the faunas alike. 
Various other modes of inspection lead to results of like order. 
The discrepancy is so great that the elements of the estimate may 
be liberally changed to cover all legitimate sources of doubt without 
affecting the general tenor of the results. 
If the borders of the continents be thought to be affected by 
faulting in some special degree, the incompetency of diastrophism to 
give these nicely adjusted shelves will be emphasized rather than 
mitigated, for the usual effect of faulting is an increase of the 
abruptness of the descent from the land to the deep sea. 
These facts seem, therefore, to force the serious consideration of the 
