cession, and assuming it to apply to the entire central tract of the Horseshoe, have drawn the system of parallel lines seen in fig. 4.

905

North

FIG. 4.- Outlines of Horseshoe Fall in 1842, 1875, and 1905, with lines used in computing the rate of recession. The line of crosses suggests a position of part of the crest in 1827.

There are six of these lines, each extending from the crest line of 1842 to that of 1905. Their interspaces, according to the scale of the map, are 100 feet wide. The average length of these lines represents approximately the average recession of the cataract in the part where the sheet of falling water is heaviest. Their lengths are, severally, 430, 292, 260, 276, 317, and 412 feet, giving an average length of 331 feet. This distance divided by the number of years, 63, gives

as the average annual recession 5.3 feet.

A somewhat allied method of estimate is concerned with areas. Still restricting attention to the central portion of the Horseshoe curve, I have drawn a line from A, the point at which the two crest lines begin to diverge, to the opposite shore at C, making its direction lie at right angles to the general direction of recession. The area contained between the two crest lines AZB and AEC, and limited downstream by the straight line AC, may be regarded as the area removed by the central portion of the fall between 1842 and 1905. The corresponding width of this part of the gorge in 1842 was AB, 570 feet; in 1905 AC, 760 feet. The mean of these, 665 feet, is assumed as the average width for the intervening period. The indicated area between the crest lines was found by measurement to be 223,000 square feet, and this quantity being divided by 665 feet, gives 335 feet as the average recession in a direction at right angles to AC. Dividing, as before, by 63, the number of years, I obtain again as an estimate of the average annual rate 5.3 feet,

The close coincidence of these two results is accidental, altho a general agreement was to be expected because the assumptions underlying the computations are harmonious. As already stated,

U. S. GEOLOGICAL SURVEY

BULLETIN NO. 306

HORSESHOE FALL IN 1895.
Photograph from same point as sketch, Pl. IV. The island at S is common to the two views. Their comparison shows the
recession of the fall and the change in its outline.

materially different results may be obtained with different assumptions.

Less harmonious results are obtained if the period from 1842 to 1905 is divided into parts and the parts are separately computed. Their discordance has two sources which can not be fully discriminated. From the nature of the case the rate of recession is not uniform. The distance to which the cornice of limestone comes to project before it is broken away depends not only on the strength of the rock, but on the local arrangement of vertical joints by which it is traversed, and also to some extent on the shape of the temporary outline of the crest. The fall of rock is therefore irregular and only obscurely rhythmic. In a period measured by centuries these irregularities would have little influence on the general average, but for short periods their influence may be great. A second source of discrepancy in the results lies in the inaccuracy of the surveys. Even where the sheet of water is so thin that the rock is visible through it there is some liability to error, and where the topographer could see only the curved and changing surface of the rushing water his observations were necessarily somewhat indefinite. Two observers might in fact differ by several feet in their estimate of the actual position of the rock crest over which the water pours. The only results for shorter periods. which it seems advantageous to place on record are those which use the map of 1875 in connection with the maps of 1842 and 1905. This approximately halves the whole period of sixty-three years, the earlier part being thirty-three years in length and the later part thirty years. By applying to these two divisions the methods already described for the whole period, and employing the same ordinates and the same limiting line, the following results were obtained:

Rates of recession computed for various periods and by different methods.

The indication is that during the thirty years following 1875 the lengthening of the gorge went on at a somewhat faster rate than during a similar period preceding that date. While it is quite possible that the apparent variation in the rate is sufficiently accounted for by the irregularity of the breaking away of the limestone sill, it is also possible that the rate has been influenced by a special condition affecting the mode of recession. A change in the outline of the fall which was mentioned nearly a century ago as diminishing its resemblance to a horseshoe consisted in the development of an angle near the head of the curve and on the side toward Goat Island (Z, fig. 4). Within the last thirty years the recession has been especially rapid in that angle, and there has developed a deep recess or notch. This appears to have been occasioned by a local weakness of the limestone, presumably its subdivision by a belt of vertical joints. Within the notch the mode of recession has been so far modified that the upper layers of limestone have been removed before the lower, so that at certain stages of the process the water after falling from the crest has been caught by a shelf. The configuration can be better understood by an examination of Pl. I (p. 41), which is based on a photograph made in or near the year 1886. Whatever the method of erosion in the notch, it appears to be superadded to the general erosion by undermining, and an acceleration of the rate may plausibly be ascribed to it.

If we regard the general method of recession by the process of sapping or undermining as normal, and the influence of joint systems as exceptional and temporary, the rate of recession computed for the period from 1842 to 1875 should be accepted as normal and the best available for use in geologic computations; but this involves the assumption that the limestone ledge was not affected in other parts of the gorge by belts of weakness similar to the one which has been exposed during the last few decades. It seems to me better, on the whole, to assume that the limestone eroded between 1842 and 1905 is fairly representative, so far as strength is concerned, of all that portion of the limestone ledge in which the cataract has done its work.

The maps of 1842 and 1905 represent the earliest and latest surveys, but do not include quite all the data worthy of consideration in this connection. A sketch by Basil Hall, made