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cotidal line with the meridian N. 35° 30' W. and the mean cotidal hour 18h 50m, the difference of establishment for one geographical mile perpendicular to the cotidal line 47 minutes. As the observations at Santa Cruz were comparatively few in number, it may be more proper to leave out that station, which will give for the corresponding results to those just stated N. 36° 43′ W., for the angle of the cotidal line, 18h 58m for the mean cotidal hour, and 3.9 minutes for the cotidal difference in one geographical mile.

Omitting Bodega from this group we obtain for the cotidal angle N. 37° 26' W., for the mean cotidal hour 18h 50m, and for the change of hour in one mile 3.9 minutes.

Omitting Bodega and San Francisco from the first group, the three southern stations, San Luis Obispo, Monterey and Santa Cruz, give for the same values N. 33° 06′ W., 18h 18m, and 4.9 minutes. The direction of the cotidal line being nearly the same, its denomination only is changed. The 18 hours would give nearly 18 if carried to the cotidal line of the first hypothesis, 18h 50m, which is a good agreement.

Omissions at the other end of the group produce the same result. Leaving out San Luis Obispo from 1, we obtain for the cotidal angle N. 36° 30′ W., cotidal hour 18h 47m, change per mile 4.4 minutes. The same result is obtained by other omissions in the series.

The introduction of Humboldt into a group with Bodega and San Francisco gives results materially different from those obtained, reducing the cotidal angle to 18° 05′, and increasing the velocity to 40 miles per hour.

The combination of San Pedro with southern stations also changes the results so rapidly as to prove that the group is limited to the south of Point Conception.

The proof seems complete that these five stations form a single group. Using the determination in which Santa Cruz is omitted for reasons already stated, we have for the cotidal angle N. 36° 43′ W., which gives an inclination to the general line of the coast of about ten degrees. The line of nineteen hours meets the coast north of Point Año Nuevo, and between it and Point San Pedro.

The comparison of the observed and computed establishments from either of these hypotheses, is very satisfactory, from that of the five stations. Santa Cruz alone stands out with a difference greater than fifteen minutes. For the second list of four stations the greatest difference is twelve minutes, and the mean without regard to signs is but six minutes.

The velocity of the tide wave is less satisfactory from the other data rising to but fifteen miles per hour. The depth should

give a greater velocity and the comparison with the northern group would indicate a much greater.

In drawing the chart of cotidal lines I have not followed the velocities strictly. This group however lies favorably for the determination of the rate of motion of the tide wave, and the results of the various hypotheses in the table are quite consistent with each other in giving a low velocity.

The southern group is imperfect as having but two stations in it. Further observations are required here and on the islands which separate Santa Barbara Sound from the great ocean. Combining San Luis Obispo with San Diego and San Pedro would require a retrograde wave, showing that they do not belong to the same group. The computations required in these discussions were generally made by Mr. Heaton of the Tidal Division under my immediate direction or that of Assistant Pourtales.

Chart of Co-tidal lines.

From this discussion I have drawn a chart of approximate cotidal lines for the coast of Oregon and California (see plate). The chart on a scale of senting the cotidal lines of the Atlantic coast of the United States, shows the general configuration of the coast.

,,, the same which was used in pre

The cotidal hours are marked near the several tidal stations. The straight lines resulting from the discussion of the northern and middle groups are delineated for the northern group the cotidal lines of xix and xx hours, and for the middle group of XVII, XVIII, XIX and xx hours.

The curves representing the approximate cotidal lines of 17, 18, 19 and 20 hours are drawn in dotted lines, the character of the dots differing for the several lines.

The line of 173 hours would follow the coast nearly from San Diego to Point Conception, then the line of 18 hours nearly to Point Pinos. North of this point the lines of eighteen and nineteen hours meet the coast obliquely at an angle of about ten degrees, the line of 20 hours appearing near Point Arena and following the coast generally to Cape Disappointment, the receding parts having a little later and the projecting parts a little earlier hour.

Throughout the extent of coast examined, the cotidal lines are either sensibly parallel to, or make a small angle with the general direction of the coast. The angle made with the coast between Point Conception and Cape Mendocino is greater than is general on the long reaches of Atlantic coast.

The successive charts of cotidal lines of the Pacific have been tending toward the representation now given as more reliable observations have been collected.

The last chart in 1848 of the Master of Trinity (Rev. Mr. Whewell*), to whom this subject owes so much of its progress, in comparison with that of Rear Admiral Lutke,t or with his own earlier map,‡ shows this tendency, the inclination of the lines to the coast being assured at each step.

ART. V.-Notice of the Tidal Observations made on the Coast of the United States, on the Gulf of Mexico, with type curves at the several Stations, and their decomposition into the curves of diurnal and semi-diurnal tides; by A. D. BACHE, Sup't. (Communicated to the American Association for the Advancement of Science under Authority of the Treasury Department.)

Abstract. The stations are eighteen in number. At four, hourly observations were made for one year or more, and at the remainder for not less than two lunations and generally for more. The stations at Cape Florida, Indian Key, Key West and Tortugas were intended to trace the tide wave through the Florida Channel; those at Egmont Key, Tampa, Cedar Keys, and St. Marks, to trace it along the Western Coast of Florida; at St. George's, Pensacola, Fort Morgan, Cat Island and E. Bayou, (entrance to the Mississippi,) to trace it along the south coast of Florida, Alabama, Mississippi and part of Louisiana, at E. Bayou, Dernière Isle, Calcasieu, Bolivar Point and Galveston, Aransas and Brazos Santiago for the coast of Louisiana and Texas.

The observations were chiefly made by Mr. Gustavus Würdemann with different assistants. At a few stations they were made by Corporal Thompson of the Engineers, Mr. Bassett, Mr. Tansill and Mr. Muhr. The reductions were made in the Tidal Division of the Coast Survey office by Assistant Pourtales, Mr. Gordon, Mr. Mitchell, Mr. Heaton and others. The methods used were those pointed out in my previous papers to the Association, the decomposition being in some cases made graphically, and at a part of the stations where the semi-diurnal wave is considerable, the ordinary method of working being used as well as those considered peculiarly applicable to these tides. As it would be tedious to present the results of these elaborate discussions in detail, when the co-tidal lines are introduced, I have thought it best briefly to refer now to the types of different tides, and to present to the Association the diagrams for the several stations showing upon a uniform scale the normal curves and their decompositions into the diurnal and semi-diurnal waves.

Royal Society's Transactions, vol. lxi, 1848.

Bulletin de la Classe Physico-Mathematique de l'Acad. Imp. des Sciences de Petersbourg, tome ii, No. 1. Royal Society's Transactions, vol. li, 1833.

ART. VI.-On the Distribution of Temperature in and near the Gulf Stream, off the Coast of the United States, from Observations made in the Coast Survey; by A. D. BACHE, Superintendent.*

(Communicated to the American Association for the Advancement of Science, by Authority of the Treasury Department.)

I PROPOSE to present to the Association a brief summary of the result of observations made in the progress of the Coast Survey, in exploring the Gulf Stream, so far as the distribution of temperature is developed by them. The entire observations have been reduced anew, under my immediate direction, by Professor Pendleton, U. S. N., assistant in the Coast Survey, who has also gone over with me, systematically, the discussion of the work, preparatory to its publication in detail, and whose care, assiduity, and intelligence in the matter I desire here to acknowledge.

At the Cambridge meeting of the Association, in 1849, I explained the general plan of the exploration of the Gulf Stream, and presented the results of the observations made up to that time by Lieutenants C. H. Davis, Geo. M. Bache, S. P. Lee, and Richard Bache of the U. S. Navy, in command of hydrographic parties in the survey.

Since then, the work has been continued by Lieutenants T. A. M. Craven and J. N. Maffitt, U. S. N., and has been extended south from Hatteras to Cape Canaveral. In addition to the sections across the stream, upon which the temperature had then been examined, between Cape Cod and Cape Hatteras, others have been since explored from Cape Fear, Charleston, St. Simon's, St. Augustine, and Cape Canaveral, and new and interesting results have been developed in relation to the distribution of temperature across the sections, and to the connection, at least in some of them, between the peculiar distribution and the form of the bottom of the sea.

The examination now made extends from about 42° north latitude to 2810, and from about 651° west longitude to 800. It authorizes the construction of a chart of the Gulf Stream, showing the distribution of temperature in and near it, not only at the surface but at various depths.

1. Distribution of temperature at different depths.

Having gone very fully into this subject, which was one of the first satisfactorily shown by the observations, I do not intend to repeat here what was then stated, except in a general way. The distribution of temperatures below a certain depth, in the cold current which exists between the shore and the Gulf Stream, and over which the warm waters of the Gulf flow, thinning out

* From Rep. Superintend. Coast Survey, for 1854, pp. 156*—*161.

as they approach the land, was shown to belong to a state of equilibrium of temperature which would be assumed by a mass of water having warm water above it and cold water below it, to be represented by a logarithmic curve, and therefore to be due to conduction. That in the Gulf Stream varied according to a different law, indicating a disturbance of equilibrium. Diagram No. 1 shows the distribution of temperature with depth, in the water between the shore and Gulf Stream, as deduced from the observations of Lieutenant G. M. Bache. The ordinates of the curve represent the depths, and the abcissæ the temperatures. The depths, in fathoms, are written at the side of the diagram, and the temperatures by Fahrenheit's scale, at the top. The position at which the temperatures at various depths, recorded in this diagram, were obtained, was in latitude 36° 15′ north, longitude 73° 52′ west, on the section intended to be made from Cape Henry perpendicular to the axis of the stream. This curve, and others of the same kind, were compared with the logarithmic curves which would best represent the observations, and their close coincidence with them shown. The curves were deduced by least squares, from an ingenious investigation by J. H. Lane, Esq., then of the Coast Survey, now one of the chief examiners, in the U. S. Patent Office.

Diagram No. 2, taken also from Lieut. G. M. Bache's observations, shows the character of the curve of distribution near the axis of the Gulf Stream. These particular results were obtained in one of the positions on the Cape Henry section, in latitude 35° 53′ N., and longitude 73° 34′ W.

The projecting form of the curve towards 300 fathoms, and the moderate change of temperature, ten degrees, from 150 to 400 fathoms, shown in that diagram, are characteristic features of the distribution in similar positions. The change from the surface to 150 fathoms was 170 Fahrenheit. Diagram No. 3 represents a corresponding curve to No. 2, from Lieut. Maffit's observations on the Charleston section, in latitude 33° 58′ N., longitude 73° 58′ W. In this the change between 100 and 400 fathoms is still less than in the former case, being but five degrees.

Diagram No. 3 bis shows the curve corresponding to that of diagram No. 1, but on the Charleston section nearer to the shore than the axis of the stream in latitude 31° 48′ N., longitude 78° 47' W.

2. Distribution of temperature at the same depth, on sections perpendicular to the axis of the Gulf Stream.

Diagram No. 4 contains the results of observations on the section perpendicular to the stream from Sandy Hook, and shows the mode in which the observations were discussed. The positions where the temperatures were observed are marked at the head of the diagram, and above them the distance from Sandy Hook in nautical miles. The temperatures are marked on the side of the

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