GLACIAL LAKE MAUMEE. 345 



In general the relation of the inclined part of the beach to the moraine and to the ice front 

 resting on it is what might be expected as a normal result of the attraction of the ice sheet, but in 

 detail some rather serious difficulties present themselves. As pointed out above, the inclined 

 part of the beach approaches the front of the moraine on an oblique line, rising 15 feet in 12 

 miles. But the true amount of deformation of the old water plane is found by measuring it on 

 the line of maximum deformation, which in this case would be on a line normal to the ice front. 



If the beach rises from Pandora 15 feet on an oblique line ending 3 miles south of the moraine, 

 the same amount of ascent would take place in a shorter distance on a line normal to the ice front. 

 Pandora is 8 miles south of the crest of the moraine. The altitude of the beach 3 miles south of 

 the moraine on this line ought to be the same as it is at the end of the oblique line the same 

 distance from the moraine, the two localities being so close together and there being no change 

 in the value of the larger factors of deformation. But if this be true the beach would rise the 

 observed 15 feet in going 5 miles north from Pandora, or at the rate of 3 feet per mile.' 



If the plane of the rising beach is carried up to a position in contact with the front of the 

 ice represented as resting on the crest of the moraine, the rising beach must be followed 3 miles 

 farther north, and even if its rate of rise is assumed to continue without increase it is necessary 

 to add 9 feet to the 15 feet of rise already found. But, theoretically, the rate of rise should 

 increase toward the ice. It seems certain, therefore, that this much additional rise must be 

 assumed on a line going north from Pandora, and this would lead one to expect the beach on the 

 crest of the moraine (supposing the moraine high enough to have the beach recorded upon it) to 

 have an altitude of at least 800 feet. But the end of the line running 8 miles north from Pandora 

 rests on the sandy belt at an altitude of 790 to 795 feet. Another difficulty arises from the fact 

 that the inclined part of the beach appears to come to a sudden end at Pandora, the beach being 

 horizontal beyond that point. It would seem as though deformation by such a cause would 

 give the water surface a gradual and progressive ffiminution of inclination in going away from 

 the ice front, one which would take the form either of a parabola or of a hyperbola when seen in 

 vertical section. The facts in this locality indicate that if ice attraction is the cause of the defor- 

 mation it chew the water surface up 25 or 30 feet in 8 miles from the edge of the ice, but had no 

 appreciable effect at a greater distance. In other parts of the area of horizontality, however, 

 there are facts which may be regarded as evidences of the attraction of the ice sheet at a distance. 

 (See pp. 346-348.) 



Application of theory. — On the assumption that the ice sheet maintains a thickness of 10,000 

 feet to its edge (p. 342) Woodward calculates that the water surface at the edge of the ice would 

 be drawn up 573 feet and would slope away at a rate of 1 foot to the mile. On the assumption 

 that the ice sheet slopes 18.34 feet per mile, which is in all probability less than its actual slope, 

 he calculates that the water surface at the edge of the ice would be drawn up 326 feet. The 

 observed effect, if rightly stated above, is less than one-tenth of this amount. 



When it is considered that the Maumee ice lobe protruded considerably forward from the 

 general front of the ice sheet, that it was in all probability a relatively thin body, and that by the 

 time the ice front had retreated to the Defiance moraine the thickness of the ice sheet at its center 

 was probably not over 5,000 feet, it is easily seen that the real values for the effects of ice attrac- 

 tion in the Great Lakes region are more hkely to be of the order of magnitude of the slight defor- 

 mation indicated by the features found west of Findlay than by the much larger values found 

 by Woodward. 



On a rough calculation, based on Woodward's assumption of an ice cap covering the north- 

 ern hemisphere completely down to the thirty-eighth parallel of latitude and having a uniform 

 thickness to its edge of 10,000 feet, it seems probable that the combined mass of all the actual 

 ice sheets in the northern hemisphere, even at their maximum extent, was not more than one- 

 fiftieth of the mass of Woodward's assumed ice cap. When the ice sheets had dwindled to 

 the stage marked by Lake Maumee, this combined mass was scarcely more than one seventy- 

 fifth or perhaps one one-hundredth. The. smallness of these values is due largely to the fact, 

 now well established, that there was no polar ice cap, like that assumed by Woodward, but 



