ticularly near to Jersey City, pointing to the encroachments there as the cause of this change, and showing so clearly the connection of this line or border of the flats with the encroachments as to indicate for the future what must occur if they are extended. The material of these flats is of soft mud, supplied by the river from the upland and from the sewerage of the cities. There are rocky or stony patches scattered over the area, but these are exceptions. The mud extends to a considerable depth before firm bottom is reached. Between Ellis' Island and the canal basin, in Jersey City, the eighteen feet curve has advanced in twenty years some 230 yards. The computations of Mr. Boschke show that an average daily deposit of 1,550 cubic yards takes place on these flats. Gowanus Bay has in like manner shoaled from the same causes, increasing the area over which there is six feet and less of water by 177 acres. These spaces are, in fact, the expansions of the river bed, into which the waters, passing with diminished velocity, find places of deposit for the solid matter which the more rapid current above has carried off.

While these comparatively quiet spots have increased, the Middle Ground and the shoal south of Governor's Island have worn away. This is, in part, no doubt, due to the general increase of velocity in the currents by local encroachments, but, as the map shows, is also produced by the changes in the shore line below Castle Point, (Hoboken and Jersey City,) which have thrown the current more over on the eastern side of the bay.

This same increase of velocity in the tidal current has deepened the main ship channel generally, and especially at the mouth of Kill van Kull.

The small changes of velocity necessary to effect these and other similar changes could only be established by the most elaborate and refined observations on the tidal currents. Such results as are ample for purposes of navigation would fail to detect such small changes. The variations in the rate of the currents at different parts of the lunar month follow those of the tides from which they are derived, and must be connected with them by observation, or else marked out independently by such a long-continued series of observations as would deter the most indefatigable observer.

This entire matter would form part of the complete physical survey of the harbor, to which we have so often called your attention. The Coast Survey observations have shown, experimentally, the variation of the tidal currents with the well known tidal inequalities, called the halfmonthly and the daily inequalities. This whole field should be explored in a way to put upon permanent record the most minute information for future guidance in reference to encroachments and to improvements.

An examination of the tidal registers, in the archives of the Coast Survey, does not show any change in the tidal establishment at Sandy Hook or at Governor's Island of sufficient amount to be adopted as a certain conclusion. Had the observations of twenty years ago been continued over periods as long as those more recently made, we might have been able to decide this question definitely. In fact, in important harbors like New York, tidal observations should be constantly kept up, the time of high and low water, as well as the height, being carefully ascertained. The Coast Survey self-registering gauges give these elements, and, besides, the law of the rise and fall of the tide.

NEWARK BAY.

This tidal reservoir, containing an area, according to Mr. Boschke, of about 6,000 acres, is supplied and drained through Kill van Kull into New York Bay, and through Arthur's Kill and Staten Island Sound into Raritan Bay. It receives at its head the waters of the Hackensack and Passaic rivers. The bay is an extensive flat, with two channels, of which the principal one leads into Kill van Kull. The average depth of the bay is about six feet at mean low water, and the bottom generally of soft mud. The shortness, depth, and breadth of Kill van Kull render it the principal outlet and inlet for Newark Bay, notwithstanding the sharp turn which the water is obliged to make as it passes from the bay into the kill. Arthur's Kill is longer, narrower, shoaler, and more crooked than Kill van Kull, and the bottom is quite irregular, the profile of the channel presenting shoals and pools alternately. The minute tidal and current observations in the kills have shown that the tides meet somewhere between Fallen Beacon and Elizabethport, and that the tidal currents meet over an area south and west of Shooter's Island. The drainage channel from one kill to the other, across the mud flat, which is most clearly shown on the map, has really not less than seven feet in it at mean low water, but is so narrow that no vessel of any size can keep in it and carry this depth.

Newark Bay has not altered generally in depth since the first survey. Kill van Kull has deepened, and Arthur's Kill has undergone changes of different kinds in different localities. In our former report we strongly urged uniform shore lines for these passages. When they have been adopted, there will be a tendency to greater uniformity of depth in Arthur's Kill, and dredging will be very effective. This would even now be quite useful, and would produce favorable changes in the flow of the tides, and in the amount of rise and fall at the upper end of Arthur's Kill. Dredging is the best resource for making a deeper passage between the two kills, and would necessarily be resorted to at intervals. It is an easy operation in such a locality and with such a bottom as here.

HUDSON RIVER.

We quote from Mr. Boschke's report:-"The average width of the lower section of the Hudson River is 1,300 yards. Its average depth is from 30 to 50 feet, the channel being on the New York side, and the New Jersey shore being bordered by a flat of an average width of 400 yards, upon which there is at most eighteen feet of water.

"The construction of the Hudson River Railroad has closed up the various little bays, and has given a more uniform shore line to the river, which has caused a general deepening and more uniformity of depth. The considerable encroachments between Thirtieth-street and Hammondstreet have narrowed the river, and deepened it, on the average, six to ten feet in that locality, throwing, besides, the current over to the New Jersey shore. Below and above the projecting piers, and within the slips from about Thirtieth-street south, the ground shoals considerably, and, from the nature of things, dredging must necessarily be resorted to to give an increased depth. The extension of the piers on the New York side, and particularly near the Battery, has increased the eddy in front of the Battery, and therefore cause the extension of the shoal there."

These changes, which the map fully shows, enforce all that we have

heretofore said in regard to the danger of encroachments in this part of New York city front. We cannot too often repeat, that whatever changes the direction and velocity of the current, must change the regimen of the harbor for good or for evil.

EAST RIVER TO THROG'S NECK.

The value of Buttermilk Channel has been already referred to. Its eastern entrances are divided by a middle ground, one channel running close to Governor's Island, the other to the Brooklyn wharves. These channels should be most jealously guarded from obstruction. The middle ground has, according to the statement of Mr. Boschke, drawn from the map, increased in area within the eighteen feet curve by five-and-ahalf acres since 1836, and a spot of eleven-and-a-half feet at mean low water has formed since the first survey. A considerable deposit has occurred on the north shore of Governor's Island. While the eastern branch of Buttermilk Channel has somewhat deepened, there has been an accumulation on and south of the shoal in front of the Atlantic Dock. We agree with Mr. Boschke in the judgment, that while the encroachments on the East River, between Corlaer's Hook and Fulton Ferry, have increased the rapidity of the current so as to tear up the bottom in many places, they have also thrown the current of ebb more on the New York side, so that the Brooklyn side depends chiefly upon the flood current for keeping up the depth between the Atlantic Dock and Fulton Ferry. There is a general deepening of the river from the Navy Yard to the western side of Kip's Bay, caused by the contraction of the stream until the point is reached, where the influence of Lowber's Bulkhead, between Seventeenth and Fourteenth streets, is felt. The shoal between Fourth and Eighth streets has increased, and the channel has less water than before the construction of the bulkhead. This is caused by the deflection of the water from Kip's Bay more directly to the opposite, or Williamsburg shore, by Lowber's Bulkhead-an inference which the deepening in the new direction of the current towards the opposite shore fully sustains. The rocky character of the shore and bottom between the points just noticed and Hell Gate precludes much natural change. In the cove between 100th and 116th streets Mr. Boschke notices a slight deposit.

In

From Astoria to Throg's Neck great changes have been produced. the general there has been a deepening of the deeper water, but sometimes a mere transfer of shoal spots and deep ones to other localities, and sometimes a decrease of depth. Mr. Boschke computes that the area of this part of the river is 6,200 acres, and that 15,000,000 of cubic yards have been removed from its channels and shoals, giving an average deepening of between one and two feet.

The influence of the tide of Long Island Sound disappears almost entirely at Pot Cove, between which and Throg's Neck the tide wave is compounded of that of Long Island Sound and of the East River. The area over which the currents meet lies near to Throg's Neck and west of it.

Direct observations are wanting to establish definitely what changes have taken place in the rise and fall of the tides, and in the currents over this space; but we can hardly suppose that, with the great changes in the East River, some alteration has not occurred in the general phenomena of the tides and tidal currents. The changes shown by the map, like those in the upper and lower bays of New York, correspond on the

average to an increased velocity of current, which is thus, as before, fully established by the indirect observations, and is in accordance with what the encroachments of the kind and degree already made upon the waterspace would necessarily produce.

Some of the changes in this part of the river require especial notice; such, for example, as the decrease of the shoal on the eastern side of Riker's Island, where the six-feet shoal has, according to Mr. Boschke, lost 130 acres in area; the decrease of the eighteen-feet shoal of Flushing Bay by 35 acres; the deepening of the passages between Port Morris and North Brother Island, and between North and South Brother islands.

The shoals having six feet and less than six feet upon them, in the bays and coves, have generally increased in extent since 1836.

The main channel through this part of the river, from Throg's Point to Hell Gate, has nowhere less than thirty-seven feet of water at mean low water, affording the greatest encouragement to the removal of the dangers of Hell Gate from this eastern entrance to New York harbor.

The general changes in New York harbor, within the last twenty years, are thus shown to have been beneficial, while in special cases encroachments are found, conclusively, to have acted most injuriously upon particular localities, turning the channel away from the New York city side of the river, where natural causes had made it flow, increasing the velocity so as to wear the river-bed into hollows and contribute materials to shoals, and even, in some cases, to be injurious to navigation. While thus the general result is a favorable one, so many of the particular local results have been bad as to make it plain that a very different system should have been pursued in furnishing the facilities required by commerce on the water and on the laud. The same good result, and a much better one, could have been obtained without such instances of evil had the shore-line been regulated years ago according to a systematic plan. The advisory council has not been opposed to such additions to the land as were required for present or future accommodation by wharves and docks; on the contrary, they have everywhere endeavored to provide such, where encroachments had not already been carried to the verge of imprudence, or beyond it, or had not been guided by erroneous principles, tending to produce injury to many while seeking individual benefit.

We have endeavored to trace such lines as would produce regular shores without abrupt changes of direction and width, to alter the proper directions of currents, or to increase or check their regular movement. The large traced map furnished to the commissioners, when spread upon a level surface, shows admirably the general harmony of the harbor lines which we have proposed. That we have not been unmindful of the wants of future commerce is proved by the fact that we have provided 1,840 acres of area for dock accommodation, according to the calculations of Mr. Boschke, made in reference to this matter. That we have not feared to recommend proper facilities for the riparian owners, within just limits, is proved by the fact that our lines contemplate the filling in of 2,480 acres of land now under water, amounting to some thirty-four millions of cubic yards. But this is done according to a systematic plan, which will avoid the dangers we have observed or have been able to foresee, and which will, as far as they have effect, favor those changes for the better which are now going on, and avoid injurious ones.

Art. III.-VALUATION OF LIFE INSURANCE POLI CIES.

NUMBER VI.

FOR the true valuation of a life policy, a correct table of mortality is necessary. For this purpose we have in former articles brought together the rate of mortality in Sweden for 81 years, in Norway for ten, in the city of Carlisle for ten, in Northampton for seven, and in the Tontines and Annuities of Great Britain for more than fifty years. We propose now to add to these the results in England, Prussia, Saxony, and Hanover, reserving the experience of life insurance companies for a subsequent article.

The first table of Dr. Farr is founded on the mortality in England and Wales during the year 1841. The census of the living having been taken in that year, and the registered deaths being nearly an average for several years before and afterwards, the numbers are worthy of much confidence. The population amounted to 15,927,847, and the deaths to 343,847.

In constructing his table, Dr. Farr adjusted the irregularities in his observations, and corrected the "inaccuracies in his returns," by treating "the two series of numbers representing the mortality from 15 to 55 and 55 to 95, as geometrical progressions." In this way the decennial mortalities were made regular. The logarithms of the probabilities of living a year for each intermediate age were then interpolated by the method of differences.

These two mathematical artifices are very ingenious, and no doubt give close approximations to the true mortality at every period of life. They are not precisely in accordance with the laws of Mr. Gomperz or of Mr. Edwards, to which laws the Doctor refers with approbation in his report, but are more nearly correct than either of those laws would give. Since, however, they modify the observations considerably, (as much as ten to fifteen per cent in some of the quinquennial periods,) and are founded on an assumed law extending over forty years of life, we have thought it best to reconstruct the table, and give one corresponding exactly to the observations. For this purpose we have taken the living and the dying for each decade, and interpolated them by the method of differences, and thence obtained the ratio, and then the mortality for every age from 15 to 100. So far the results will agree precisely with the observations. We have then adjusted the rates of mortality, by supposing the law of geometrical progression to extend for each five years, from 15 to 20, from 16 to 21, from 17 to 22, &c., to the end of the table-this being the same law which Dr. Farr extended to forty years. For the short periods proposed, it is entirely free from objection.

In column second, at the end of this article, is inserted the rate of mortality from Dr. Farr's table, the rates being adjusted by the method of geometrical averages. This produces no effect scarcely, except near the age of 55, which was the dividing point with Dr. Farr of two separate laws of mortality above and below that age. The adjustment, therefore, merely smooths over the breach of continuity at that period, and harmonizes the whole table.

In column third is to be found Dr. Farr's rates for males only, adjusted