= velocities of the superficial and lower strata when the effective surfaces are equal; and when these surfaces are unequal, the mean by weight. If x= velocity at surface, y velocity at lowest point; then with equal surfaces we obtain velocity of globes = (x + y.) If the effective surfaces opposed to the drifts (portions of great circles) are unequal, and their areas be represented by a and b, we have the velocity of globes 1 (ax+by.) This expression represents the immediate result or x a + b 1 obtained by the original manner of using the globes if the vessel be at anchor; but, in our modification, the result of our experiment is the difference between the motion of the free and that of the connected globes, (ax+by.) The extent of the wetted surface of the free globe will not affect the result, but it is convenient to have this globe of the same size as the others, so as not to be greatly affected by winds. If the paths of the surface and sub-currents do not lie in the same vertical plane, the connected globes take an intermediate course, with velo 1 a+b√ { (a x sin. §, + by sin. §,)2 + (a x cos. ß, + by cos. §2)2}, and tan (angle of direction): = 1 represent the respective angles of direction of the upper and lower drifts. When observations are to be made at sea, where there is a great depth of water, a further modification of the apparatus is necessary. In place of the two connected globes in the foregoing description, a hempen line is used, (perhaps two inches in diameter,) terminating in a wooden pole above and a leaden cylinder below, the former serving to float the shaft, while the latter sinks and straightens the line, and the reel is transferred to the free globe. The apparatus, thus modified, will serve to exhibit the difference between the surface drift and the mean velocity of a stratum of water whose depth equals the length of the shaft immersed. If we know the surface velocity we may readily obtain the velocity of the lowest point reached, if we suppose the change of velocity from point to point to be uniform, by subtracting the surface rate from twice the mean velocity. This supposition is not always correct, and must be tested by the following experiment: The log-line having been unfastened, the pole is passed through a copper globe, and the line drawn up until the globe can be secured at a point which will occupy a middle position of the wetted surface on again letting the shaft sink as far as it may. Upon a new trial, if the velocity observed is still the same, we may conclude that our supposition is correct; if not, we may, by shifting the position of the globe again and again, making at each remove an observation and record, or by using simultaneously several such shafts, calculate approximately the conditions of the sub-currents and the curve at which our deep shaft hangs. The globes which we have used measure two feet in diameter. Before closing this rapid sketch of our devices for obtaining the data required by your instructions, I would refer briefly to a new form given to a pile used in securing a tide-gauge at Fire Island, and which, I think, possesses some peculiar advantages for use upon sandy coasts where there is a heavy sea. This pile is of oak, or other heavy and strong wood, and is so cut that the lower portion of it, for a space of six or eight feet, pre sents the appearance of a number of inverted frustrums of cones, placed one above another-the series terminating in a sharp and heavy shoeing. As a whole, it is required to have a greater weight than the sand and water it is intended to displace. On working this pile into the sand, by swaying it to and fro, in the usual manner, each cone, as it sinks, acts upon the sand above and below, as at once a lever and a wedge, giving to the whole a continual downward thrust. In the same way the waves, instead of tearing it up, cause it to work deeper and deeper, and thus the lateral oscillation of the sea is converted into vertical motion, and brought to our aid. Of course this downward tendency of the pile can be easily checked if too great for our purposes. As my description of this pile is not altogether clear, I annex a diagram, which will require no explanation. Very respectfully, yours, HENRY MITCHELL, Assistant Coast Survey. Professor A. D. BACHE, Superintendent Coast Survey. TIDES AND CURRENTS IN NEW-YORK HARBOR AND ITS APPROACHES. This work, which has been going on under my immediate direction for several seasons past, was completed at the end of the summer by Assistant HENRY MITCHELL, so far as the principal field labors are concerned. It was commenced with the view of ascertaining the causes of certain important changes in the hydrography of the harbor as developed by the comparison of charts of different dates. All the natural forces, such as tides, currents, winds and waves, which might be supposed to concur in producing the physical effects noticed, were included in the series of observations, and the large amount of information thus obtained will, no doubt, when fully discussed, determine the conditions under which the harbor exists. In my last report reference was made to the discovery of a class of sub-currents, the motions of which were found to be quite at variance with those of the surface currents. The observations made during the present season connect these sub-currents with the path of the Hudson in its course through the waters of New-York bay, and for their full development it was found necessary to extend the current stations about sixty miles outside of the bar, and also along the coast of Long Island. In the latter vicinity the effect of the land waters was traced quite beyond the reach of the tidal drifts. Observations were made in the same quarter with a view of developing the conditions under which the inlets on the south shore of Long Island are maintained and for ascertaining the causes of their change in position. Thirty-seven current stations were occupied, the records from which contain over eight thousand observations. More than three thousand of the entries are for points below the surface. Appendix No. 26 contains the report of Assistant MITCHELL on the season's labors. His report contains remarks on improvements in the apparatus for observing currents at great depths below the surface, and refers also to an improved form of pile for securing tidegauges on the sea-coast. HARBORS AND RIVERS OF THE UNITED STATES. TABLE SHOWING THE LEAST WATER IN THE CHANNELS OF CERTAIN HARBORS, RIVERS AND ANCHORAGES ON THE COASTS OF THE UNITED STATES, REPRINTED Salem, Mass.,. Northern ship channel, between Baker's and Misery Islands,. Inside of Salem Neck,, 19 28.2 18.3 28.9 Main channel, between Governor's Island and Castle Island,. 18 28 17.3 28.6 Up to anchorage inside the pier-head on Long Beach,.. At anchorage inside the pier-head,... Anchorage in the Cow Yard,... Narragansett bay to Pru- Entering with Boston Neck on port hand, Beavertail and Dutch Island dence Island,.. lights on starboard hand,. Entering with Beavertail light on the port and Castle Hill on starboard hand, up to Goat Island,... .. Anchorage southward and westward of Goat Island,.. Abreast of wharves inside of Goat Island,.. From Newport harbor, inside of Gull Rocks to Prudence Island,.. 31 To Mount Hope bay,.. 63.9 59.6 64.2 ::::: 36.9 82.6 37.2 To Mount Hope bay, with Cormorant Rock, Sachuest Point on port, and Saughkonnet Point on starboard hand,.,. 20 23.9 19.6 24.2 ::::: Main ship channel, after passing SW. Spit buoy on NE. course, one mile up the bay for New-York,. From Bergen Point lighthouse to the mouth of Hackensack River, 7 11.6 6.5 12.2 C. S., 1855. 82 86.0 81.6 36.8 do. From Manhattanville to Yonkers,.. 27 30.8 26.7 81.8 do. HARBORS AND RIVERS OF THE U. S.-(Continued.) Off Brandywine lighthouse,... 43 46.5 42.4 46.9 Main ship channel, passing False Liston's tree to abreast of Bombay C. S., from 1840 to Hook light,.. 27.5 33.4 27.3 34.2 1844, inclusive. Blake's Channel, along Flogger Shoal,.. 13.5 19.4 13.3 20.2 Blake's Channel, passing Mahon River light,. 13.5 19.4 13.3 20.2 Main ship channel approaching Liston's Point,. 20 25.9 19.8 26.7 Delaware River, Main ship channel up to Reedy Island,. 20 26 19.6 26.3 Main ship channel, opposite Reedy Island lighthouse,. Opposite Delaware City,. Up to Christiana Creek light,. 20.5 27 20.3 27.2 C. S., from 1840 to Up to Marcus Hook,.. 20.5 27 20.3 27.2 Opposite Chester,. 24.5 30.7 24.4 31.2 1844, inclusive. Bar off Hog Island,. 18.5 24.7 18.4 25.2 Between Greenwich Point and Gloucester Point,. 31.5 37.5 31.4 38.2 From Greenwich Point up to Philadelphia,. 21.5 27.5 21.4 28.2 Chesapeake Bay, From capes at entrance to Hampton Roads,. 30 82.5 29.8 82.8 Anchorage in Hampton Roads,.. 59 61.5 58.8 61.8 From Hampton Roads to Sewall's Point,.. 25 27.5 24.8 27.8 South of Sewall's Point, (one mile and a half,). 21 23.5 20.8 23.8 Up to Norfolk,. 28 25.5 22.8 25.8 From Hampton Roads to James River, entering to the northward of New 1852, 1858 and 1854. From Hampton Roads to James River, entering to the southward of New |