THE

AMERICAN

JOURNAL OF SCIENCE AND ARTS.

[SECOND SERIES.]

ART. I.-On the Tides of the Western Coast of the United States. -Tides of San Francisco Bay, California; by A. D. BACHE, Superintendent U. S. Coast Survey.*

TIDAL observations have been made, in connexion with the hydrography of the Coast Survey, at several points on the Western coast, agreeing in showing the same interesting fact of the large diurnal inequality of the tides, already traced by Mr. Whewell in the observations at the Russian settlement of Sitka.

The diurnal inequality in height of the tides on the Atlantic coast is much more considerable than in Europe, and the diurnal inequality of interval is also well marked; but both require numerous, carefully made observations to establish their laws, in consequence of the particular relation between the semi-diurnal and diurnal waves. On the Gulf of Mexico west of St. George's Island, the semi-diurnal tide is almost merged in the diurnal, but the total rise and fall is quite small.

At Key West, and along the western coast of Florida, where the diurnal inequality is large, the whole rise and fall of the tides is small, rendering numerous observations necessary to obtain reliable numerical results. The same is not the case on the Western coast; observations made for a short period through the whole twenty-four hours showing a peculiarly large diurnal irregularity as the most remarkable phenomenon of the tides. It becomes * Report of the Superintendent of the Coast Survey, showing the progress of the Survey during the year 1853. Washington, 1854. p. *77—82*.

SECOND SERIES, Vol. XXI, No. 61.-Jan., 1856.

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one of great practical importance to the navigator; for, in San Francisco bay, a rock which has three and a half (3) feet of water upon it at the morning high water, may be awash at high water of the afternoon; and charts, of which the soundings are reduced to mean low water, will have no accurate significance, being liable to an average error of the soundings at either low water of the day, of 1.18 foot.

The results which I now present, and propose to discuss, are of two series of tides observed in connexion with the Coast Survey at Rincon Point, in the city of San Francisco, California. The observations were under the direction of Lieutenant Commanding James Alden, U. S. Navy, one of the assistants in the Coast Survey. They were made hourly, except about the time of high and low water, when the regular intervals were fifteen minutes, and the attempt was made to seize the precise time of high and low water.

The first series extended from January 17 to February 15, 1852, and the second from January 23 to February 17, 1853. Another set of similar observations was made at Saucelito, on the northern side of the Bay of San Francisco, but not with the same care which appears to characterize these. The results are in general accordant with those deduced from the Rincon Point series.

The reduction of the work of 1852 was made by Mr. W. W. Gordon, and that of 1853 by Messrs. Fairfield, Mitchell, and Heaton, of the tidal party of the Coast Survey office.

The results of 1852 are projected in the curves shown in diagram A, where the abcissæ represent the times from 0 hours midnight, and the ordinates represent the heights. The scale is such that the intervals between the vertical lines correspond to two hours, and between the horizontal lines to half a foot. The curve begins with midnight of the calendar day, January 16, 17, and ends with noon of February 15. The epochs of the moon's phases, and of zero, and of maximum declination of the moon, are marked at the head, and the times of transit at the foot of the diagram, the curves upon which, for convenience of the page, have been divided into two parts, so arranged with respect to each other that the days of corresponding declination fall nearly over and under each other. The curves of the series of 1853 present the same general results, with about the same extent of irregularities.

These tides obviously present a case of large diurnal inequality in height; the interference of the diurual and semi-diurnal waves going to produce one large and one small tide in the twenty-four

*The quantity given as the diurnal inequality in height, is the whole difference between the heights of two successive high waters or low waters and that for the interval, the whole difference between the lunitidal intervals of two successive high waters or low waters.

lunar hours. When the declination of the moon is at its maximum, the difference in the heights of consecutive high and low waters is nearly at its maximum; and when the declination is nearly zero, the difference is the smallest.

The diurnal inequality in the interval is also perfectly well marked in these tides, amounting when greatest, to about two hours for high water, and one hour and eleven minutes for low

water.

The usual discussions of the times and heights, corresponding to the same time of transit of the moon, were made from the two series of observations; a defect having been found in the operation of referring the level of one tide-gauge to the other, the two series of heights were combined, by assuming the mean height in each series to have been the same. The results were plotted on a diagram like B, but on a larger scale, for the purpose of graphical corrections in the mode used by Mr. Whewell.

The ordinates of the diagrams Nos. 1 and 2, (diagram B,) correspond to the lunitidal intervals, and of Nos. 3 and 4 to the heights-the abcissæ, in each case, to the hours of the moon's transit. The scale is shown at the top and side of each diagram. No. 1, diagram B, shows the results for the half-monthly inequality of interval of high water, and the curves traced by them; No. 2 the same for low water; No. 3 shows the half-monthly inequality in the height of high water, and No. 4 in that of low water; the dots show where the observations fall. The comparison of the curves, with observations, is given in the annexed table:

TABLE No. 1.

Comparison of approximate curves of half-monthly inequality of the tides at Rincon Point, with observations.

The results, both for intervals and heights, are very good, considering the small number of observations (four,) of which each is the mean. The heights are, as usual, less regular than the

times, and the results for the inequality of the height of low water are the least regular of all.

The approximate mean lunitidal interval for high water, or corrected establishment of Rincon Point, is 12h. 03m. This corresponds to an epoch of 0 hours, showing that the tides belong to the next preceding transit (transit F) of the moon, and not to the fifth preceding, (transit B,) as was found by Mr. Lubbock for the tides of Great Britain. The epoch for low water corresponds also almost exactly to 0 hours. The same thing is shown, less forcibly, however, by the discussion of the observations before referred to at Saucelito.

From curve No. 1, it appears that the difference in the lunitidal intervals for 3h. and for 9h. is 1h. 20m., or (A) of Mr. Lubbock (tan 20°) is 0.342. The difference between the heights of high water, at spring and neap tides, is, from diagram No. 3, 1.12 foot, and E of Mr. Lubbock =1.66. The two series of observations, discussed separately, gave results which did not differ materially from these. These numbers will serve as a first approximation.

1.12 2(A)

TABLE No. 2.

Diurnal inequality of interval and height for high and low water, from observations in January, 1852 and 1853, at Rincon Point, San Francisco, California.

It should not be forgotten that, the observations having been made in successive years in the same month, the moon's age and declination, and the sun's declination are not very different, and the sun's declination is nearly the same on the corresponding days.

The diurnal inequality obtained by the usual method is given in the annexed table, No. 2. The two series are combined by taking the averages for the days on which the declinations correspond in the two series. Each average is thus the mean of four individual results.

These numbers are projected on diagram C, where the ordinates correspond to the intervals for one curve and to the heights for the other, and the abcissæ to the tidal days for both. Notwithstanding the small number of observations, the curves can be traced with tolerable certainty and follow the general law of the inequalities.

Each curve shows an inequality increasing and decreasing with the moon's declination nearly, crossing the zero line at or near the zero of declination, and reaching a maximum or minimum at the maximum of north or south declination. The observations do not furnish sufficient evidence to decide positively that the epochs of the several inequalities coincide with those of the declination or otherwise. On the average they are about half a day before the corresponding declinations.

The inequality in the height of high water and in the interval of low water increase and decrease together, and so of the inequality of high water and height of low water.

The declination of the moon and the inequality in interval of high water and in height of low water have the contrary sign; the reverse is the case with the other two inequalities.

The inequality in the height of low water is in general greater than that of high water, exceeding it when at the maximum in the proportion of two to one, (nearly 19 to 1). The same relation exists between the maximum inequality in interval of high water as compared with that of low, (17 to 1).

The maximum inequality in the height of low water is 3.60 feet, and of high water 1.85 foot. The maximum inequality of interval of high water, as shown by the curve, is 1h. 53m., and of low water 1h. 7m.

I am indebted to Mr. Heaton, of the tidal party, for the decomposition, under the direction of Mr. W. W. Gordon, of the curves of the daily observations in 1852, by the method adopted by me for the discussion of the tides of the Gulf of Mexico. Though, from some trials which I have made, these decompositions may be improved, they are, nevertheless, of great interest, and show well the causes of the forms assumed by the curves of diurnal inequality in height and interval, and for high and low water and their relations. When the observations now in progress on the Western coast shall have given additional results, I propose to take