cubic feet, is the contents of the tidal prism within the present mouth of the harbor discharged during an average ebb.

According to Professor Mitchell, the mean rise and fall at the mouth of the harbor is 3.07 feet, and at the head of the harbor 3.17 feet, and high and low water at the head of the harbor are 49 minutes, and 1 hour and 48 minutes after high and low water at the mouth of the harbor, respectively. Our observations very nearly agree with these statements.

THE PRESENT MOUTH OF THE HARBOR.

The present mouth of the harbor is between Brant and Coatue points, both of which are low and sandy. The distance between them is about 2,200 feet, and the area of the cross-section is about 24,500 square feet. The deepest water lies quite close under Brant Point, and has a maximum depth of about 25 feet, the distance between the 18-foot curves being about 350 feet. On the Coatue side there is a narrow channel, with about 10 feet of water, the distance between the 9-foot curves being about 200 feet. Between these channels the depth is shallow, and nearly one-half of the width has less than 6 (from 2 to 6) feet of water at mean low water. Estimating from the contents of the tidal prism above the mouth of the harbor, the sectional area of the latter, and the mean duration of the ebb as given by the Coast Survey (5 hours and 44 minutes), the mean velocity out of the harbor is about 1.04 feet per second. Were it not that this entrance is protected by the outlying flats (extending to a distance of about 1 miles with a depth of about 6 feet, mean low water, from the bar forming waves of Nantucket Sound, to which the mouth of the jetty channel will be subject, the velocity which maintains the deep part of the present entrance would furnish a measure by which we might roughly estimate the velocity we should provide for the jetty channel.

THE MATERIAL OF THE BOTTOM BETWEEN THE MOUTH OF THE HARBOR AND THE OUTSIDE OF THE BAR.

In the fall of 1883 the inspector of the construction of the western jetty made a series of borings on designated lines outside the mouth of the harbor in order to discover the nature of the material of the bottom. It was found to be sand, mostly very compact, covered in many places with seaweed, and mixed at different distances below the surface with gravel in varying proportions. It is anticipated that after the sand has been sorted out by the current and erosion to a certain depth has taken place there will remain a pavement of this gravel which none but quite high velocities will be able to remove, and which, in order to reach the full depth required, we may have to excavate by dredges. The locations of the borings will be found on the Plat B, herewith, and the results in the table of borings on the same plat.

THE CURRENTS OUTSIDE THE BAR.

The flood tide in Nantucket Sound, as a general rule, runs easterly and the ebb tide runs westerly; but at and near Nantucket Bar the currents are somewhat complicated, as will be seen in the tables of current observations, which are herewith. The observations were taken at the points marked F, G, and H on the Plat C. They have not been sufficiently extended in time to enable me to form any conclusions as to the direction of the prevailing littoral current, but from the great pre

ponderance of westerly winds in Nantucket Sound, this current might be supposed to come from the westward. I have no record of the winds at Nantucket, but the following table of winds observed at Block Island and Wood's Holl, compiled from the records of the Signal Office of the Army and kindly furnished at my request, enable us to form a pretty close estimate of them:

Statement showing the number of times the wind was observed blowing from the eight principal points of the compass at Block Island and Wood's Holl during the years specified.

These tables give the results of 3,414 observations of the winds at Block Island in the years 1881 to 1884, inclusive, and show that 2,204 times the wind was from a westerly direction and 1,210 times it was. from an easterly direction. At Wood's Holl it was from a westerly direction 631 times in the year 1881, and 280 times from an easterly direction.

If the prevailing littoral current at Nantucket be from the west, the direction both of the ebb current and of the channel which before the construction of the western jetty ran straight to the northwest and across the present site of the jetty, and the much greater extent of the shoals on the Coatue side of the channel than on its western side, might both be referred to the cause which I have found noted in "A Treatise on Rivers and Torrents, with a Method of Regulating their Courses and Channels," by Prof. Paul Frisi, F. R. S., translated by Maj. Gen. John Garstin of the Bengal Engineers. In applying the theory of Frisi to our case, however, it would be necessary to substitute the sand stirred up along the shore to the westward of the entrance of Nantucket by westerly wind-waves for the sedimentary matter contained in the river treated of by him, which enters the sea where the prevailing littoral current is from the left to the right, as, on account of the direction of the prevailing winds, it might be supposed to be at Nantucket. He says:

In combining the motion of the sea along the coast with the motion of any river at its mouth, it is evident [since the motion of the sea at the mouths of the rivers in question is from left to right] that the waters of the river ought to take an intermediate direction and turn their course more or less towards the right, as Guglielmini has remarked in the seventh corollary to the fourth proposition of his seventh book. Thus the current and the river being both turned from their first direction, and the current being more so than the river, since the velocity of the river is about twentyfour times greater than that of the current, the sea, lying on the right hand between the line in which all the blended waters are now directed and the shore, will no longer be assisted by the coast current already broken and turned aside. The sediment incorporated with its waters will consequently begin to settle along that part of the shore and form diverse sand banks, which will go on gradually and continually increas

ing, and hence the river, finding always greater impediments on its right, will turn by degrees towards the spot where its course is more free, and in time will at last establish its course in a direction quite opposite to that in which it at first set out; that is, by tending constantly to the left of its opening. Montanari observes that this is precisely the manner in which the mouths of the Tagliamento, the Piave, and other rivers in the Venetian States maintain their outlets. Zendrini, in the report before quoted, adds also the example of the rivers in Romagna; and in the first chapter of another report on the harbor of Viareggio, he has applied the same principles to the rivers of the Mediterranean, with this difference only, that the tides being weaker in the Mediterranean, the motion along the shore is there more perceptible, and the deposits are formed to greater distances and in much greater abundance on the right, while none are ever seen on the left.

Against this view of the subject, however, are the facts that the angle west of the western jetty has not filled as rapidly as might have been expected, and that the deposits on Coatue Flats continue in spite of the western jetty, which has now been carried 4,000 feet out from the shore. If these latter deposits come from the westward, they must be carried around the end of the jetty where the water is from 6 to 7 feet at low water, and from 9 to 10 feet deep at high water, which does not appear probable. The question of the littoral current outside of Nantucket Bar does not now affect the question of the position of the mouth of the jetty channel. This has been determined by the location of the western jetty; but it may affect the question of the relative lengths of the two jetties. It will probably be found desirable, as we approach the outside of the bar, that one of them shall overlap the other, and the experience gained after the two jetties get far enough out to become parallel, will best determine this latter question.

THE EASTERN JETTY.

A single jetty having failed to procure the desired depth of water into the harbor, another jetty is required, and it becomes necessary to determine its location and height. The only expression of judgment on these questions, on which the success of the improvement so much depends, that I have been able to find, is the following remark of the Board of Engineers in its report of August 23, 1880, which is contained in the Report of the Chief of Engineers for 1881, Part I, pp. 542–545 :

"Should the deep water not be reached thereby," (that is, by means of the western jetty,) "an eastern jetty, starting from Coatue Beach would be necessary, having its inner portion, say to the 6-foot curve of the flats, held at a very low level, and its outer portion parallel to the direction of the western jetty."

In my last annual report, I stated as follows in regard to the harbor of refuge at Nantucket :

Since writing the above I have devoted much thought and study to the subject and I intended to submit the results at an early day, but have been prevented until now by other unforeseen duties, in making plans and arrangements for the completion of emplacements for 15-inch guns at the fortifications in my charge, before the end of the fiscal year.

GENERAL CONSIDERATIONS.

Whatever width of jetty channel may be decided on, there will be a portion of time during each ebb and each flood when the bottom velocities will not be sufficient to move the material of the bed and of the bar, and prevent deposits. During the remainder of each tide (unless the width of channel be excessive) this material and these deposits wil be in motion, outward on the ebb, inward on the flood. If the outward and inward movements of the material should be equal, not only would

there be no deepening of the channel, but it might become shoaler than it now is, by means of new deposits. If they should be unequal the channel would be deepened provided the resultant of the movements should be outward, but the harbor might be shoaled if the resultant should be inward. The times of ebb and flow at Nantucket being essentially equal, and unlike the mouth of the Mississippi and all the harbors on the Atlantic and Gulf coasts, at which the jetty system has been applied, there being no outflow of fresh water to strengthen the ebb, the mean velocity through the jetty channel during the entire flood will generally be the same as during the entire ebb, whatever the width of jetty channel.

The success of the application of the jetty system at Nantucket would seem, therefore, to be doubtful, but it is universally conceded that the scouring effect of the ebb is superior to that of the flood tide (although the cause of it is only surmised), and even in such an unpromising case as Nantucket may appear to be, the resultant of the outward or forward movement of the material of the bed of the channel during the ebb, and the inward or backward movement during the flood (whether by reason of the inclination of the bed or the carrying in of water by on-shore wind-waves of translation, or otherwise) may be assumed to be outward. Although it will require more force to erode the contracted bed of the proposed channel than to maintain it afterward, the velocities before and during erosion will be greater than when the channel will have been established. I therefore assume that if the velocity required to maintain the desired channel be properly determined, the antecedent higher velocities will excavate the channel.

NECESSITY FOR HIGH VELOCITIES.

Dubuat observed that sand dragged by currents down the beds of streams moves in the form of waves, and in the case of a stream flowing with a bottom velocity of from sixty-seven hundredths to 1 foot per second, he found that the sand moved at the rate of about 3 miles in two years, or about 21 feet per day. The observations of General Comstock on the Mississippi River (Report of the Chief of Engineers, 1879, Vol. III, p. 1892), and of the late General Warren on the Wisconsin and Mississippi rivers (Report of the Chief of Engineers, 1876, Vol. II, page 25), appear to confirm Dubuat's statement, as do also the reports of the Mississippi River Commission. General Comstock reported the rate of motion of the sand waves (which is equal to the average rate of motion of the grains of sand which form the wave) at about 18 feet a day. General Warren estimated the rate of motion of the sand waves observed by him, to be about 800 feet a year. In one case of observation under the Mississippi River Commission, the mean velocity of the water being 3.5 feet per second, and the depth from 20 feet to 30 feet, the av. erage daily motion of the sand was 13 feet, and the maximum daily motion was 20 feet. At another place where the mean velocity was 5.8 feet per second, and the depth of water from 45 to 60 feet, the average daily motion of the sand was 35 feet. The length of that part of the jetty channel at Nantucket which requires to be excavated is about 8,000 feet, and at the rates just noted, it would be more than a year before the sand at the upper end of this space would begin to reach the outer side of the bar. This is under the supposition that the sand would be always moving in the same direction, as in the case of a non-tidal stream. But our case is different. In the first place, during the times of slack water, and for some time before and after slack water, there

will be no motion of the material of the bottom; and in the second place, the outward resultant of the inward and outward movements of this material during the remainder of the time (that is, during the time when the bottom velocities will be effective as regards scour), will be but a small fraction of the movement that would obtain were the current always running in the same direction. In other words, instead of motion always outward, each successive thin layer of sand on the surface of the bottom of the jetty channel will be at rest a considerable portion of the time, and during the remainder each flood will carry it nearly as far backward as the preceding ebb has carried it forward, and the motions of the sand will be similar to those of sewage held in suspension, which in the Clyde and Thames were found to have a resultant motion towards the sea of about 5 miles in a fortnight. I should suppose, however, that the difference between the alternate motions of sand on an inclined bed of a tidal stream, the velocity of the current being the same, would be greater than those of sewage in suspension. It is for these reasons, it appears to me, that the deepening of the entrance to all tidal harbors by means of jetties is a very slow process, and especially must this be the case when, as at the entrance to Nantucket Harbor, the ebb and flow, both in respect of time and of the quantity of water in motion, are essentially equal; and if this view be correct, it is not strange that in all of our jetty channels erosion has been so tedious, and resort is often had to dredging. Even at the South Pass of the Mississippi, with outgoing velocities of 3, 4, 5, and 6 feet per second, the scour of the sand on the crest of the bar was exceedingly slow, and at Dublin Harbor a case of successful application of the jetty system (and very much like ours at Nantucket), where the surface velocities at spring tides are 3 miles per hour (or more than 4 feet per second), the scour which has deepened the water on the bar from 6 to 16 or 17 feet at low water, has had only an average yearly rate of about 13 inches.

It seems to me, therefore, of very great importance since the outward resultant, or the difference between the inward and outward movements of the material of the bed of the channel will be the greater, the greater the velocity of the water, that we provide for as high a velocity as the conditions governing the case will allow.

EFFECTIVE BOTTOM VELOCITIES.

I assume that to scour such material as composes the bed of the proposed channel and of the bar, sea-sand mixed with gravel, there is required a velocity of the water in the channel close to the bed (the bottom velocity) of at least 1.25 feet per second. The authorities differ in respect of the velocity required in a case like the present, as will be seen from the following statements, in which the velocities are in feet per second, and, unless otherwise stated, bottom velocities.

Dubuve is variously quoted by different authors, but in his table of experiments he gives the following velocities as required to move various substances: Sand of the size of anise seed, .5; coarse yellow sand, 1; Seine gravel of the size of peas and little beans, .67 and 1.46, respect ively; rounded pebbles, 1 inch in diameter, 3; and angular gravel, the size of hens' eggs, 3.75.

Mr. Login (quoted by David Stevenson) gives for sand as coarse as linseed, .67; fine gravel, 1; and rounded pebbles 1 inch in diameter, 2. Weisbach says that in canals a mean velocity of 1.25 is required to