In the year 1869 Dr. E. Andrews, of Chicago, made an important series of calculations concerning the rate at which the waters of Lake Michigan are eating into the shores and washing the sediment into deeper water or towards the southern end of the lake. With reference to the erosion of the shores, it appears from the work of the United States Coast Survey that a shoulder, covered with sixty feet of water, representing the depth at which wave-action is efficient in erosion, extends outward from the west shore a distance of about three miles, where the sounding line reveals the shore of the deeper original lake as it appeared upon the first withdrawal of the ice. From a variety of observations the average rate at which the erosion of the bluffs is proceeding is found to be such that the post-glacial time cannot be more than ten thousand years, and probably not more than seven thousand. An independent mode of calculating this period is afforded by the accumulations of sand at the south end of the lake, to which it is constantly drifting by the currents of water propelled against the shores by the wind; for the body of water in the lake is moving southward along the shores towards the closed end in that direction, there being a returning current along the middle of the lake. All the railroads approaching Chicago from the east pass through these sand deposits, and few of the observant travellers passing over the routes can have failed to notice the dunes into which the sand has been drifted by the wind. Now, all the material of these dunes and sand-beaches has been washed out of the bluffs to the northward by the process already mentioned, and has been slowly transferred by wave-action to its present position. It is estimated that south of Chicago and Grand Haven, this wave-transported sand amounts to 3,407,451,000 cubic yards. This occupies a belt curving around the south end about ten miles wide and one hundred miles long. The rate at which the sand is moving southward along the shore is found by observing the amount annually arrested by the piers at Chicago, Grand Haven, and Michigan City. This equals 129,000 cubic yards for a year, which can scarcely be more than one quarter or one fifth of the total amount in motion. At this rate, the sand accumulations at the southern end of the lake would have been produced in a little less than seven thousand years. "If," says Dr. Andrews, "we estimate the total annual sand-drift at only twice the amount actually stopped by the very imperfect piers built--which, in the opinion of the engineers, is setting it far too low--and compare it with the capacity of the clay-basin of Lake Michigan, we shall find that, had this process continued one hundred thousand years the whole south end of Lake Michigan, up to the line connecting Chicago and Michigan City, would have been full and converted into dry land twenty-five thousand years ago, and the coast-line would now be found many miles north of Chicago."[EG]