508 PLEISTOCENE OF INDIANA AND MICHIGAN. 



and correlative ice fronts and beaches in the marine region, but data for doing so are not yet 

 available. 



In the Great Lakes region the first period of uplift raised the Warren beach at Bad Axe, 

 Mich., about 100 feet above the level of that beach in the area of horizontality. Bad Axe 

 was not far outside the front of the ice as it then stood, and it seems certain that the uplift 

 involved much land that was still under the ice sheet. No correlative beaches and moraines 

 found in the deformed area show diminution of uplift on approaching the front of the ice and 

 some of them show increased northward rise, even after allowing for ice attraction. Indeed, 

 it seems probable that the whole area of Lake Algonquin and perhaps much more was uplifted 

 at least 100 to 150 feet by the first movement while still covered by the ice sheet. This occurred 

 before the beginning of Lake Algonquin and requires the addition of some such amount to the 

 total uplift recorded in the Algonquin beach in the northern part of the Great Lakes region. 



THEORETICAL PRINCIPLES. 



On its theoretical side the relations of ice weight to land depression and resilience present 

 many difficult problems. Some of the most important elements that must enter into any 

 attempt at numerical evaluation have not yet been satisfactorily determined. One such 

 element is the thickness of the ice over a given locality or area at a given time. It seems certain 

 that it will be possible some day to determine this with a close degree of accuracy, but at present 

 all estimates are uncertain. 



According to Lane the weight of the ice sheet might depress the land in two ways — by elas- 

 tic compression and by actual transfer of fluid or plastic molten magma in relatively large 

 quantities from one place to another beneath the earth's crust. 



Woodward 1 has shown that one atmosphere of pressure on the earth's surface tends to 

 shorten the earth's radius about 2 meters. This furnishes the required datum for estimating 

 the amount of depression due to elastic compression under the weight of the ice. 



On the basis of this hypothesis Lane 2 estimated the proportion of the total depression that 

 might be ascribed to each of these two modes of adjustment on the assumption of certain con- 

 ditions of ice thickness which he thought applicable to a particular area in Michigan. He 

 points out that 2 meters of compression by one atmosphere of pressure means that an ice or 

 water load on the surface woidd tend to compress the earth underneath by about one-fifth 

 as much as the thickness of the water or ice. 



On the assumption that the earth's crust is a somewhat flexible sheet resting on a more 

 or less fluid interior, Lane shows that the weight of the ice or water would bend the crust down 

 into this fluid interior and that, neglecting for the time the lateral or shearing stresses, the 

 depression would be accomplished by the displacement of an equal weight of the magma or 

 fluid rock beneath the crust. The density of the rock below being approximately three times 

 that of water, the amount of depression would be about one-third of the thickness of water 

 or ice. The use of this ratio without qualification implies the assumption that the relation is 

 truly and simply hydrostatic, that the interior fluid has no physical quality which prevents 

 it from obeying hydrostatic laws with substantially complete fidelity, and therefore that vis- 

 cosity in such degree as is allowed for the interior fluid of the earth is no bar to interior read- 

 justments of mass in strict accordance with hydrostatic laws. 



Lane's assumption that resilience may be caused by the hydrostatic inflow of a fluid molten 

 ■ magma previously displaced by depression of the earth's crust seems to the present writer out 

 of accord with the best modern conclusions regarding the conditions of the earth's interior. 

 Years ago the physicists gave the geologists reason enough for believing the earth to be solid 

 to its center and to have there its greatest density and a rigidity greater than that of steel; 

 and the more recent records of the propagation of earthquake waves through the deeper parts 

 of the earth seem, through many repetitions, to have fully established its essentially solid, 

 rigid character. Again, though some physical phenomena affecting the earth find no bar to 



1 Bull. U. S. Geol. Survey No. 48, 1888, p. 66; Sixth Ann. Eept. U. S. Geol. Survey, 18S5, pp. 295-296. 

 - Personal communication, Nov. 9, 1907. 



