NOTE.-The means, given at the bottom of the tables, are from the sums of all the observations in the 9 months, and not from the sums of the means of the several months given in the tables. It will be seen from the above, which I regret are not complete for 12 months, that the average rise and fall, as well as zero, vary considerably in different months. This is due mainly to prevailing winds. Thus far it seems that at Dutch Gap zero, according to the levels of 1852, is more nearly true than that found by Mr. Popp in the survey of 1874. He reports "that low-water is now (1874) apparently 0.63 foot lower than it was in 1872." ANALYSIS OF THE SURVEY OF 1874. Some of the characteristics of James River were given in the last annual report, and during the winter I have made an analysis of the survey of 1874, made by Mr. William Popp, under your direction, which is submitted. This survey gave the widths and depths at mean low-tide from the ship-lock in Richmond to the lower end of Dutch Gap Canal by way of the bend at Osborne's, a distance of 19.3 miles, the canal saving 5 miles of navigation. The lines of soundings were generally at right angles with the direction of the current, and were taken at intervals of 20, 50, 100, and 200 feet in the length of the river, as the condition of its bed required. The soundings across the river were from 10 to 15 feet apart. The survey included the leveling to ascertain the low-water slope and observations on the tides. In making the analysis, I have taken from the map the cross-section at average distances of 500 feet, and ascertained the width, channel, and mean depth, and sectional area at each point. From the areas was ascertained the position of a vertical line dividing the mass in 2 equal parts on each line; the points marking the position of these lines were located on the maps, and curves made to pass through them. Tables 1, 2, 3, 4, and 5 give the widths, depths, and areas, and the radii and direction of curves, and the number of degrees in each. I have divided the river within the limits of this survey into 5 sections, 4 of these reaching in the aggregate to the entrance of Dutch Gap Canal, and the fifth covering the bend cut-off. The curvature in the fifth section is not given. Table No. 6 gives the mean, and the greatest and least widths, depths, and areas on each of the 5 sections, and table No. 7 the mean depths and areas corresponding to various surface-widths. The first section is from Richmond to Randolph Flats The third section ends at end of Kingsland's Reach. Feet. 19,500 18,500 18,500 18,500 26,500 With the exception of Kingsland, sometimes called Grave-yard Reach, which is at the end of third section, all the difficulties to navigation at high-tide between Richmond and Dutch Gap, for vessels drawing 18 feet and under, are confined to the first 2 sections, and end with Warwick Bar, 5 miles below the city. The least midchannel depth in Kingsland's Reach is 134 feet at low-tide, and there are 1,100 feet with less than 15 feet; elsewhere below Warwick Bar there are 15 feet and over; the mean rise and fall of tides being about 34 feet. Low-water. Least. Greatest. Highest. Lowest. Highest. Lowest. Scale. Staff. The river varies considerably in width above Warwick Bar, and is more uniform below, (excepting Kingsland's Reach,) at least to the entrance of the Dutch Gap Canal. Table No. 6 shows that the widths diminish and the depths and areas increase from Richmond down, the only exception being the width of section 5, on which the shoal in Trent's Reach is a leading feature. As the river has few and inconsiderable affluents in the distance covered by this survey, and these could not account for the increased sections, I was interested to know whether the lower sections, i. e., those below Richmond Bar, were to be considered an estuary, as was assumed by me in the last annual report, and by Mr. Popp, in his report on the survey; or if the decrease in the slope of the river at low-tide on the lower sections required the larger area observed, Mr. Popp ascertained the slope by leveling at extreme low-tide, on a favorable day, at 4 points, and made the fall as follows: From Rockett's Reef ( mile below dock) to Richmond Bar.. From Richmond Bar to Drury's Bluff From Drury's Bluff to entrance of Dutch Gap Canal.... Totals...... These points do not correspond with the divisions I have mentioned, and in order to discuss the effects of the slopes, corresponding to these levels, another division into 3 sections has been made. On these 3 sections the mean widths, depths, and areas were ascertained, as well as the aggregate curvature, and are given below: 2.4 (1) for IX P The mean velocity corresponding to these elements was then ascertained by the Humphreys and Abbot formulæ as given in their work on the Physics and Hydraulics of the Mississippi, viz: v = √0.00816+ (225 r1 §) 1⁄2 — 0.09 (b 1⁄2 )2 sections 1 and 2, where the mean radius is less than 12, and = ([225 r. S] for section 3. The correction for curvature was made from their formula p: v2 N. Sin 30° where N represents and p the fall equivalent to the re134 curvature -0.0388) = sistance. The calculation for velocity and discharge, neglecting the influence of bends, resulted as follows: |