But the visit of Lyell and Hall in 1841 led to the beginning of more accurate calculations. Professor Hall soon after had a trigonometrical survey of the falls made, from which a map was published in the State geological report. From this and from the monuments erected, we have had since that time a basis of comparison in which we could place absolute confidence. In recent years three surveys have been made: the first by the New York State Geologists, in 1875; and the third by Mr. R. S. Woodward, the mathematician of the United States Geological Survey, in 1886. The accompanying map shows the outlines of the falls at the time of these three measurements, from 1842 to 1886. According to Mr. Woodward, "the length of the front of the Horseshoe Fall is twenty-three hundred feet. Between 1842 and 1875 four and a quarter acres of rock were worn away by the recession of the falls. Between 1875 and 1886 a little over one acre and a third disappeared in a similar manner, making in all, from 1842 to 1886, about five and a half acres removed, and giving an annual rate of recession of about two feet and a half per year for the last forty-five years. But in the central parts of the curve, where the water is deepest, the Horseshoe Fall retreated between two hundred and two hundred and seventy-five feet in the eleven years between 1875 and 1886." [Illustration: Fig. 106.--Map showing the recession of the Horseshoe Falls since 1842, as by survey mentioned in the text (Pohlman). (by courtesy of the American Institute of Mining Engineers.)] It will be perceived that the recession in the centre of the Horseshoe is very much more rapid than that nearer the margin; yet this rate at the centre is more nearly the standard of calculation than is that near the margin, for the gorge constantly tends to enlarge itself below the falls, and so gradually to bring itself into line with the full-formed channel. Taking all things into account, Mr. Woodward and the other members of the Geological Survey thought it not improbable that the average rate of actual recession in the Horseshoe Fall was as great as five feet per annum; and that, if we can rely upon the uniformity of the conditions in the past, seven thousand years is as long a period as can be assigned to its commencement.