APPENDIX No. 6. List of Coast Survey discoveries and developments. The true object of the survey is to furnish charts of the coast for purposes of commerce, and making known what was previously unknown. In the course of preparing these, important discoveries are made. 1. Gedney's channel into New York bay, having two feet more water in it than the old channels. Had the true depth of this channel been known in 1778, the French flect under Count D'Estaing would have passed into the bay and taken the assembled British vessels. It is probable, from comparing the old and new charts, that this channel then existed. 2. Blake's channel into the Delaware; open when the eastern channel is filled with ice. This discovery has already developed the resources of that part of the State of Delaware in a remarkable way. 3. Davis' South shoal, discovered in 1846, six miles south of the old Nantucket South shoals. This shoal lies in the track of all vessels between New York and Europe, and between New England and the southern States, or New England and South America. 4. Davis' Bank. 5. Two feet more water in Mobile bay than existed six years age. Mobile entrance has near 203 feet at low water. 6. Horn Island channel, on the coast of Mississippi. 7. Blunt's channel, in Delaware bay. 8. Numerous rocks in Long Island sound and Martha's Vineyard sound, and the various bays and harbors connected with them. 9. Two shoals north and east of Nantucket, discovered in 1847. 10. Six shoals near Nantucket, the outermost one 14 miles from land and having but ten feet of water on it; not marked on any existing chart. 11. The remarkable increase of Sandy Hook, which has been traced from the surveys of the topographical engineers and coast survey. 12. The changes in the Delaware, near the Pea Patch. 13. A shoal at the mouth of the Great and Little Choptank, in the Chesapeake bay. 14. McBlair's shoals, off Nantucket, in 1849. 15. Deeper water found on Diamond shoal, and a dangerous ninefeet shoal off Cape Hatteras, 1850. 16. Hetzel shoal, off Cape Canaveral, 1850. 17. New channel into Key West. 18. New channel into Charleston, with same depth of water as the ship-channel, (Maffitt's channel,) 1850. 19. South channel of Columbia river, surveyed and rendered available to commerce. 20. A channel of 23 fathoms, upwards of a mile wide, distant 11 nautical miles from Bald Head light-house, across the Frying Pan shoals, Cape Fear, N. C., 1851. 21. A channel extending from 3 to 4 miles from the point of Cape Fear to 8 to 83 from it, with sufficient water at low tide to allow vessels drawing 9 to 10 feet water to cross with safety. 22. A channel at the distance of 14 nautical miles from Bald Head light-house, one mile wide, with 3 to 7 fathoms water on it. 23. The Frying Pan shoals extend to the distance of 20 nautical miles from Bald Head light-house. 24. Sixteen, 17, and 18 feet water found at the distance of 17 and 18 nautical miles from the Bald Head light-house. 25. Broad Sound channel into Boston harbor thoroughly surveyed, and marks recommended to facilitate passage through it, 1848. APPENDIX No. 7. Notes of a discussion of tidal observations, made in connexion with the Coast Survey, at Cut island, in the Gulf of Mexico, by Professor A. D. Bache, Superintendent of the Coast Survey. (See sketches H, Nos. 2 to 6 inclusive.) In executing the hydrography of the entrance of Mobile bay and of Mississippi sound, connected tidal observations were made under the immediate direction of Lieutenant Commanding C. P. Patterson, United States navy, assistant in the Coast Survey. The observations at Cat island, at the entrance to Lake Borgne, Louisiana, and at Fort Morgan, at the entrance to Mobile bay, have undergone more than one discussion, the peculiarities of the tides giving great interest to the observations. The results, as obtained from a year's hourly observations, day and night, at Cat island, will be given as far as obtained, the steps taken for further progress stated, and the information which has been obtained from other sources, bearing upon this most interesting problem of the tides in the Gulf of Mexico, will be briefly touched upon. I hope, in the progress of the survey along this part of our coast, to develop the subject of these tides, full of importance to the navigator, and of interest to the man of science. These tides, with special exceptions, ebb and flow but once in twenty-four hours. The tide-gauge was of the kind known as the box-gauge, with a float and staff, graduated into feet and decimals of a foot. It was placed in the harbor of Cat island, near the light-house, at the extremity of a temporary wharf. The harbor, as the Coast Survey chart which I now present to the meeting shows, turns its widest and deepest opening to the east. Apparent time was given by a mark, and the observations were made at mean solar time by applying the equations. The time was of less consequence than ordinary in these observations, from the small rise and fall of the tide, which prevented small differences of time from being noticeable by differences of rise and fall. Slight inequalities, caused chiefly by wind, were also found to affect the observations so materially that it was not deemed advisable to observe oftener than once the hour; and after attempting to determine the epoch of high and low water by more frequent observations, it was decided that errors would probably be introduced by aiming at a degree of precision which the phenomena themselves did not present. The observations were made day and night, hourly, for a year, with exceedingly rare omissions, and, as the discussion has shown, with a degree of faithfulness which merits very great praise. The observers were Messrs. Gustavus Würdeman and R. T. Bassett, attached to the coast survey. The general opinion of nautical men on the subject of these tides is, that they mainly depend upon the action of the wind; and the very regular effect which may be shown to result from a discussion of the tides, in reference to the local action by the wind, lends plausibility to this generalization, which nevertheless is unfounded. The causes are of a much more general character, and such as usually influence the tides, so modified as to be difficult to bring out; phenomena which are only accessory in the ordinary discussions assuming here the chief and overruling part. The regular tabulation of the observations was made by Lieut. Commanding C. P. Patterson, who did not fail to perceive that the ordinary methods of discussion of the tides were inapplicable. His removal from the survey on other professional service has devolved upon me the labor of discussing the results. Their importance, interest, and novelty, so far as our coast and their striking peculiarities are concerned, have justified me in giving much time to the discussion, which has been carried on, under my immediate direction, by Mr. G. W. Dean, sub-assistant in the coast survey, and by Messrs. R. M. Bache, A. S. Wadsworth, jr., and W. M. Johnson. I am indebted for the diagrams necessary to illustrate the conclusions already arrived at, to Messrs. Bache, Johnson, and Keyser. I present a part only of the labors of these gentlemen. The whole of the hourly observations for the year have been thrown into the form of curves, and numerous tables for examining and verifying the different hypotheses have been made by them. Though the subject was reached inductively, I do not propose to present it strictly in that form. The work even now is far from being complete: indeed, we have rather reached the true method of discussion, than have completed the discussion; and we may yet have to modify our hypothesis, though I think not materially. I present it to the association as a work in progress. When the investigation for this station is made complete, the application of the methods to the other stations on the Gulf of Mexico will be in a degree mechanical. It is curious that one among the earliest complete series of tidal observations on record, is of tides ebbing and flowing but once in twentyfour hours. The observations were made by Mr. Francis Davenport, at Batsha, of the tides on the bar of Tonquin, and communicated to Dr. Halley, who gave them, with a diagram connecting the phenomena with the moon's motion in the ecliptic, in the thirteenth volume of the Philosophical Transactions for the year 1683. Newton explained these tides by his lunar theory, but in a way, as appears to me, to leave it doubtful whether he supposed the interference of two ordinary or six-hour tides to produce the phenomena. These tides have been referred to since by almost every writer of note, who has given a general theory of the tides. The subject of the diurnal inequality of the tides has been so completely and ingeniously discussed by Mr. Whewell, Master of Trinity, that it may be said emphatically to be his own. He first pointed out the empirical law of variation of this inequality. The first distinct attempt to trace the cause of apparent ebb and flow once in twenty-four hours to the influence of the diurnal irregularity, is also, so far as I know, his. In discussing (Phil. Trans. for 1837, Part I) the tides at Singapore, where the diurnal inequality is very large, he was led to the conclusion, if carried a little further, "at a certain stage of it the alternate tides would vanish." To this effect he attributed the "singleday tides of King George's sound, on the coast of New Holland, as observed by Captain Fitz Roy," and gives the curves for a week's observations on the diagram accompanying his papers. The progress of the diurnal inequality wave along the coast of Europe forms an interesting part of Mr. Whewell's labors, the conclusions of which are given in the same volume of the Philosophical Transactions. In all these cases, however, there are two tides in the course of the day, so as to bring out the diurnal inequality by the comparison of the consecutive high or low water. The subject is followed up in the eleventh series of tidal researches by Mr. Whewell, and in the appendix, in which the diagram of the tides of Petropaulofsk, in the bay of Avatcha, Kamschatka, approaching very nearly, at certain parts of the lunar month, to the order of single-day tides, is given, to prove that the diurnal inequality may be so large "as to lead to the appearance of only one tide in twenty-four (lunar) hours." The equations of the diurnal and semi-diurnal tide-waves are given in this paper, and the wave produced by certain cases of their interference is discussed. (Phil. Trans. for 1840.) I do not pretend to give such notice of these important papers as would be necessary in a formal communication. Unquestionably the observations now under examination would have furnished to Mr. Whewell only the means of trying ideas and consequences flowing from those which have been already discussed by him; yet the forms of discussion are original, and perhaps new, and the conclusions present so much of novelty, that they remain to be fully put to the test by more elaborate discussion, and by bringing the results at other places to bear upon the same question. I am forced, by the necessity for brevity, to omit a reference to the learned, ingenious, and elaborate paper of Mr. Airy, in the Philosophical Transactions for 1848. The small rise and fall of the tides, amounting on the average to but one foot, would seem to make it difficult to obtain the law of the phenomena, even with the aid of the most careful and truthful observations-the class to which those under discussion have proved to belong. In regard both to time and height, we may expect to be baffled by small irregularities, requiring long continuance of observations and comparisons of means to get rid of. Thus far few cases have occurred which do not exhibit more striking coincidences than differences. 1. To show the time of high or low water in such a way that the dis cussion might be readily generalized, the diagrams, of which a specimen is before the association, were made, (Pl. 3, or H No. 2.) The hours of the day are the ordinates, and the days of the month the abscissa. The signs H and L show in their proper place the hour of occurrence of high and low water for each day. The time of the moon's superior transit is marked, and the periods of greatest declination, and of crossing the equator. The result is easily generalized, that there is ordinarily but one high and one low water at Cat island in twenty-four (lunar) hours, and that when there are two tides they occur about the time of the moon's crossing the equator, and are usually most regular and strongly marked when in syzigies, with declination nearly zero. Following one set of high and low waters, it will be found that they occur later and later as the lunar day gains on the solar, with very remarkable differences, of which the explanation will be given towards the period of small declinations. The interval from high to low water is generally less by some hours than that from low to high. That as the moon approaches the equator, there are a few days of singular double tides, or of single tides, in which the times from low to high water are very much increased. That when the declination changes its name, a high tide takes nearly the place of a low in time, and vice versa, with an interval of irregularity; or, in other words, the tides are displaced by nearly twelve hours. 2. There is, as Mr. Whewell has remarked, no proper establishment to be derived from such tides; yet, we may obtain a desirable datum by throwing the results into the form of tables, in which the luni-tidal intervals are arranged according to the days from the zero of declination and the corresponding superior and inferior transits, and for north and south declinations. This will be made more clear by subsequent explanation. These afford a test of the theory of these tides by showing the displacement of the ordinate of high and low water, and might be used for the inverse purpose of forming prediction tables. Such tables of luni-tidal intervals for three months I now submit. They show considerable steadiness and similarity of intervals towards the maximum of declinations and great variations near the zero, and greater discrepancies than is usual in ordinary tides. These are from a series of tables computed by Mr. R. M. Bache for the year, and containing the times of high and low water, deduced from the daily curves, the readings of the gauge, the rise and fall of the tides, the times of the moon's superior and inferior transit, and the moon's declination. The intervals serve to show that the high water belongs alternately to the superior and inferior transits of the moon, according as the moon's declination is north or south, with a few cases only which admit of doubt. Two sets of luni-tidal intervals were computed (see tables) for three months, to ascertain the proper epoch of reduction, or age of the tide. In one case, the intervals were referred to the superior transit of one day before; and in the other, to the superior transit of two days before. The square of the discrepancy of the mean in the latter case was greater than in the former. An establishment deduced from these numbers for high-water, without correction, would have a probable error, as tried by discrepancy from the mean, of nearly eightyfour minutes. I have little doubt of being able to reduce this error, by computation, much within the limits of observation, so as to give useful |