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

I

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. 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 12 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

prevent sandy deposits, and that in case of a sandy bottom the mean velocity should not exceed 1.

Debauve states that sand is moved with a velocity of 1.

Other authors, instead of stating the bottom velocities required to "lift," "just lift," and "move" various substances on the beds of streams and canals, give what are termed "safe velocities," that is, velocities of the water under which different materials are not moved and the bed remains stable. In the hydraulic tables of Kutter we find that a sandy bottom is stable under a velocity of 1; that a gravelly bottom is stable under a velocity of 2, and that pebbles are not moved with a velocity of 3. Des Ingenieurs Taschenbuch (Hütte) states that 1 is a safe velocity for a sandy bottom and 2 for a gravelly bottom.

Morin gives 1 as a safe velocity in case of sand.

Mr. Login, after much experience in the construction of canals of India, states that deposits take place with velocities far in excess of those which we find in Dubuat's work.

At Oakland Harbor, California, Colonel Mendell at my request measured the velocity of the ebb in the deepest part of the channel between the jetties, where there were reported to be deposits of sand which the current failed to remove. The tide was about one-half ebb, and the depth of water was about 14 feet at mean low water. The surface velocity was 3.64 feet per second, and the mean velocity as found by a pole loaded so as to take an upright position was 2.92 feet. The bottom velocity was therefore about 2.20 feet per second. The sand, of which he sent me a sample, is very fine. It should be remarked in this case that the sand in the Oakland Channel is washed from the banks by the swash of passing steamers. It may be, therefore, that the daily supply is greater than the current can fairly be expected to remove.

At Nantucket, on a line parallel to and about 150 feet east of the western jetty, the ebb surface velocities from 1,000 to 3,500 feet out from shore are now from 1.33 to more than 2 feet per second, and yet no appreciable wear of the bottom takes place. I therefore assume that the bottom velocity required to scour the material at Nantucket is, at least, 1.25 feet per second, and in the calculations to be made for the width of the jetty channel I shall adopt this for the mean of the bottom velocities in the channel during each entire average ebb, under the supposition that the bottom velocities will be equal to and exceed this velocity during about two-thirds of the ebb, and that no scour is to be expected during the remainder of the ebb.

MAXIMUM VELOCITY OF THE CURRENT IN MIDCHANNEL.

Let 1.25 feet per second be the mean bottom velocity of the water passing through any section of the jetty channel during an entire tide, then 1.25.75 1.66 feet per second and 1.663 × 1.57 = 2.62 feet per second, will be approximatively the corresponding mean and maximum velocities of the whole section during an entire tide, respectively, and, denoting by x the greatest surface velocity in the middle of the channel at the time of this maximum velocity of the whole section, we have by Prony's formula:

or x=3.2 feet per second (about). This is at the rate of about 2 miles per hour, and it is not likely to prove at all inconvenient to navigation.

ALTERNATIVE LOCATIONS.

It is evident that in order to produce a deep channel by tidal forces alone the contraction of the water-way from one end to the other-that is, from the pocket of deep water before referred to, to the outside of the bar or shoal-must be such as to produce a scouring velocity throughout the entire length of the channel.

Assuming for the desired navigable depth of channel the same as the depth of the deeper part of the harbor inside, 15 feet at mean low water, the low-water mean depth of the channel will be about 15 × 2, or 11 feet, and the half-tide mean depth 123 feet. The average contents of the tidal prism above the mouth of the harbor is 529,050,157 cubic feet, and assuming that one-tenth, or 52,905,015 cubic feet, will be lost by leakage through the jetties, there would remain 476,145,142 cubic feet as the effective contents (effective for scour) of the tidal prism. (See note.)

The mean duration of the ebb-tide is five hours and forty-four minutes, or 20,640 seconds. As before stated, the mean velocity of the tidal current through any cross-section of the jetty channel during an average tide is to be 13 feet per second. Representing by Vm this mean velocity in feet per second, Q the contents of the effective tidal prism in cubic feet, t the duration of the average tide in seconds, d the depth, and W the width of the jetty channel in feet, we have

corresponding to a width of 1,092 feet between interior crests of the jetties, in case the entire channel from the pocket of deep water outside the present mouth of the harbor to the outside of the bar is to be excavated by tidal scour alone. The eastern jetty in this case, I would propose to start from the southernmost of the three short spurs which are on the extreme western point of Coatue, and carry it thence on a line running south westerly until it would intersect a line parallel to and about 1,500 feet from the beach west of Brant Point; thence along this line and a tangent curve drawn with a radius of 1,500 feet connecting this portion of the jetty with the main portion, which would be parallel to and 1,092 feet from the western jetty. This position of the jetty and the corresponding position of the channel are shown on the accompanying drawing, marked A, which also shows the position of a half-tide training-wall, by means of which, the eastern jetty being in this posi

NOTE. In regard to the allowance for loss of water by leakage through the jetties, it will have been observed in the description of the western jetty that the width of its inner portion at the mean low-water line is only 10 feet, and of its outer portion only 14 feet. On account of the size of the riprap stones it is found difficult to build with a less width at top than 4 feet, and I propose that the eastern jetty shall have a width at the low-water line of 14 feet throughout. The widths of the jetties being so small and the interstices large, a large amount of water will pass through them, and there will be a corresponding loss of head of the water inside, which will reduce the velocities of the currents through the mouth of the jetty channel. At the mouth of the Mississippi it was estimated that from 30 to 40 per cent. of the water passing through South Pass was lost by leakage through and over the jetties.

tion, I would propose to regulate the channel in the angle between the western jetty and the shore east of the western jetty.

The alternative and in my judgment the better location of the eastern jetty which I propose for adoption, is shown on the accompanying drawing marked B. The entire tidal prism in this case contains 592,150,657 cubic feet or 63,100,500 cubic feet more than the other, and it is considered that this increase of tidal prism is of especial importance, in view of the anticipated loss of water through the jetties, which loss would have to be borne by the tidal prism above the mouth of the harbor alone, in case the jetty should be built on the inner location. Allowing 10 per cent. loss by leakage, as before, we have for the effective contents of the tidal prism above the outer location of the jetty 532,935,592 cubic feet, and assuming the same formula and the other quantities as before, we have

W =

532,935,592

20,640 × 13 × 123

= 1,215 feet at half-tide,

corresponding to a width of 1,222 feet between the interior crests of the jetties. The eastern jetty in this case I propose to start at a point on the beach of Coatue, about 750 feet southwesterly from Triangulation Station No.35, and to carry it thence in a northwesterly direction on a line which, if prolonged, would intersect the line of the western jetty about 5,780 feet from its extreme inner end, and on a tangent curve drawn with a radius of 1,000 feet, connecting this portion of the jetty with the portion which will be parallel to the western jetty, and 1,222 feet from it. I give the parallel portions of the jetties a length of 1,500 feet in order to provide that the ebb shall issue square out from the mouth of the jetty channel, and not obliquely. In case the eastern jetty is built on the outer location, resort must be had to dredging between the deep water at the mouth of the harbor and the inner end of that part of the length of the channel which will be excavated by scour. This point will probably be not far inside the inner ends of the parallel parts of the jetties. It is proposed to make the width of the dredged channel in the first instance 300 feet, and the depth 12 feet at mean low water, and to increase the width and depth as necessity requires.

HEIGHT OF THE EASTERN JETTY.

I submit the following considerations concerning the height of the eastern jetty:

(1) If the inner part of the jetty be built only to a low level, say to half-tide, it is almost certain that in a very short time, probably within a few months, the sand would bank up on the outside to the top, and would then commence to be carried over the jetty at half-tide of every flood. This sand would soon encroach upon the channel and crowd it over toward the shore at and to the westward of Brant Point, as is now the case, and it would be likely to form shoals in the channel farther down, making it tortuous and difficult of navigation. It is proper here to note the fact that, standing after a storm on the end of one of the short spurs which run out from Coatue, the water there being 3 or 4 feet deep and otherwise clear, and not agitated by waves at that place, I have seen it literally "alive" with sand nearly to the surface during the higher velocities of the flood, which are there about 3 feet per second. (2) Outgoing currents neither containing nor dragging along solid matter from above would have much greater scouring power, and would