GLACIAL-CONTROL THEORY OF CORAL REEFS. 173 



ice-free earth by an amount lying between 60 m. and 140 m. The 

 larger limit is close to the estimate of von Drygalski and Penck, above 

 mentioned. 



The different estimates of the last two paragraphs imply that the 

 general sea-level has been raised by an amount ranging between 23 m. 

 and 129 m., since the assumed synchronous, maximum development 

 of the Pleistocene ice-caps. The extreme nature of that assumption 

 makes it improbable that the Recent rise of sea-level has been as much 

 as 129 m. On the other hand, the minimum estimate of the net 

 volume of ice melted since the Glacial climax is likely to be too small. 

 A revision of the evidence has led the writer to favor a rise of sea-level 

 of the order of 50 m. to 60 m. (27 to 33 fathoms). If the climax 

 occurred during the Kansan stage of the Glacial period, secondary 

 maxima in ice-formation and corresponding shifts of level occurred 

 during Wisconsin and other stages. In the 1910 paper an average 

 lowering of 25 fathoms (46 m.) was assumed for all the stages of heavy 

 glaciation. 



Gravitativc Influence of Ice-caps. Woodward's well known memoir 

 "On the Form and Position of the Sea Level" contains the formulas 

 necessary to compute the deformation of the sea surface due to attrac- 

 tion by an ice-sheet. Specially simple and convenient are the equa- 

 tions (67) on page 41 of his paper. The table and figure on page 70 

 are further aids to a quick understanding of the problem and its 

 solution. ^^ The figure clearly shows the strong uplift of the sea water 

 in the ^•icinity of the ice-cap and a maximum depression of the water 

 surface at the point antipodal to the center of the mass of ice. The 

 change from positive to negative values, for the case considered, occurs 

 in a zone situated more than 100 degrees of arc from the antipodal 

 point; and, for about 45 degrees from that point, the values for the 

 negative deformation are not far from the maximum. 



From Woodward's equation on page 41 it is easy to calculate ap- 

 proximately the antipodal sinking of level produced by an ice-cap 

 such as covered northern North America in the Glacial period, pro- 

 vided its thickness is known. If the average thickness was 1,000 m., 

 and if the sheet held that thickness nearly to its edge, the antipodal 

 sinking of level caused merely by attraction of the ice would be about 

 5 m., a value which is directly proportional to the thickness of the ice. 

 The antipodal point for this greatest of the vanished Pleistocene ice- 

 caps is in the Indian ocean, southwest of west Australia. That part 



22 R. S. Woodward, Bull. 48, U. S. Geol. Survey (1888). 



