342 PLEISTOCENE OF INDIANA AND MICHIGAN. 



due to ice shoving, for in January, 1910, a gale from the west-southwest piled the ice of Saginaw 

 Bay on shore near Sebawaing into a ridge 10 miles long and in some places 70 feet high. The 

 floor of the shallows there is flat limestone. 



DEFORMATION OF WATER PLANE BY ICE ATTRACTION. 



THEORETICAL CONSIDERATIONS. 



It has been calculated theoretically by Woodward 1 that an ice sheet of a certain thickness, 

 configuration, and extent would draw up the water surface of a lake standing in contact with 

 it by a certain definable amount. Woodward's statements are often quoted, but a careful 

 examination of his paper makes it clear that the conclusions usually drawn from them are 

 unwarranted. 



Woodward adopts certain definite assumptions as the basis of his calculations. He assumes 

 an ice cap at its center 10,000 feet thick, covering the polar regions and extending symmetrically 

 to the thirty-eighth parallel. Then he gives a series of values for the deformation of the water 

 plane based on different assumptions as to the slope of the surface of the ice cap from its center 

 to its edge. One of these assumptions is that the ice cap is of uniform thickness throughout 

 (has no slope from center to edge) ; that is to say, that it is 10,000 feet thick at its edge on the 

 thirty-eighth parallel and that its front is a vertical cliff of ice 10,000 feet high. For this par- 

 ticular assumption Woodward finds that the water will be raised 573 feet at the edge of the ice 

 cliff and will slope away at an average rate of 1 foot to the mile for a distance of 1° from 

 the ice edge. This assumption, though very far from the conditions of the concrete case under 

 discussion, is invariably the one quoted, and this despite the fact that Woodward gives results 

 for several other assumptions which come much nearer actual conditions. No attempt is made 

 here to apply Woodward's analysis to the concrete cases found, but it seems worth while to 

 present certain facts bearing on the problem. 



AREA OF HORIZONTALITY. 



Several places within the Great Lakes region might be expected to afford a test of this theory, 

 and it is important to examine the data in these localities and to place the facts on record for the 

 use of any who may wish to pursue the inquiry further. If the old shore lines show the sup- 

 posed deformation by ice attraction, it is desirable to determine its amount and to recognize it 

 so that it can be eliminated from the estimates of the amount of deformation due to other causes, 

 where greater deformation occurs, and also in order that regions unaffected by other causes of 

 deformation may be recognized clearly and the slight deformations due solely to ice attraction 

 distinguished. The localities where the theory might be tested are not all in the area under 

 discussion, but they may be considered briefly. 



In discussing the deformation of the Great Lakes region it has for some years been regarded 

 as a fact that all the beaches south of a certain ill-defined line or narrow zone are horizontal. 

 The line runs from Ashtabula, Ohio, through the central part of Lake St. Clair, passes 4 or 5 

 miles north of Birmingham, Mich., and crosses Lake Michigan westward from a point a few 

 miles north of Grand Haven. South of this line the old water planes depart so little from hori- 

 zontality that the departures were regarded as possible errors of measurement, or as lying 

 within the limits of the natural range of altitude of normally developed shore formations, or as 

 due in part to ice attraction. This was more particularly the attitude of mind of students of 

 the subject before the publication of the more accurate topographic contour maps made in recent 

 years by the United States Geological Survey. In certain districts now covered by these maps 

 more refined studies can be made, but the maps now cover only a few limited areas. 



The line referred to above was taken to be the isobase of zero, or line of no deformation. 

 Apparently the land to the north of it has been uplifted and deformed, and the land to the south 

 of it has remained unaffected and in its original attitude of horizontality. In this sense the 

 isobase of zero has been called a " hinge line " and the region south of it is the so-called " area of 

 horizontality." 



i Woodward, R. S., On the form and position of the sea level: Bull. TJ. S. Geol. Survey No. 48, 18S8, pp. 13-85. 



