up this branch of the subject again. In the mean time, it appears to me, the results now obtained are of sufficient interest to be presented to the Association. I have taken, as an example of the decomposition, the curve from the observations of January 21, 1852, the results corresponding nearly to the maximum of the moon's declination and to full moon. The diurnal curve, the interference of which with the semidiurnal produces the form shown in diagram A, and also on a larger scale in diagram D, is given on the diagram. Its maximum ordinate, as found by summing the two series of heights from the hourly observations in which the same values of the ordinate of the diurnal curve occur with opposite signs, and referring to the curve of sines for their relation to the maximum ordinate, is 2.20 feet. The sum of the squares of the differences between observation and computation is the least when the interference takes place, as shown in diagram D, the maximum ordinate of the diurnal curve being seven hours and a half from the maximum ordinate of the semi-diurnal curve. Subtracting the ordinates of the diurnal curve, assumed as a curve of sines, from the heights given by the hourly observations, we have a residual curve, which is traced on the diagram. The average of the four loops of this curve is almost precisely a curve of sines, of which the maximum ordinate is 2.30 feet. The tidal curves near the maximum of declination, and for several days each side of it, result from the interference of a semi-diurnal and diurnal wave, which at the maximum of each are nearly equal in magnitude, the crest of the diurnal wave being at that period about eight hours in advance of that of the semi-diurnal wave. The following table gives the comparison made in the diagram. The first column contains the ordinates of the curve of observation; the second, those of the diurnal curve of sines; the third, those of the residual curve; the fourth, the ordinates of the semidiurnal curve, which most nearly satisfy the residual; and the fifth, the small remaining differences-on the average, being about 0.14 foot. The crest of the diurnal curve is seven and a half hours from the semi-diurnal, and its maximum ordinate is 2.2 feet. For equal maximum ordinates of the diurnal curve and semidiurnal curve, 21 feet, we have for E=8 hours the diurnal inequality in height of high water 2.03 feet, or 18 foot greater than the mean found by the curve of diurnal inequality, and of low water, 3.57, or 0.3 foot less than the value given by the curve. So, also, for the inequality in the intervals of high and low water, we have, respectively, 105 and 61 minutes, instead or 113 and 66 given by the diagram, differing but 8 and 5 minutes, respectively, and having the same ratio to each other as the latter numbers. The mode of interference thus explains satisfactorily the curious relations of the inequality of both time and height of high and low water. TABLE No. 3. Analysis of curve of observation for January 21, 1852. Rincon Point. Ordinates, curve Ordinates, diurnal Ordinates, residu of observations, Feet. -0-23 curve of sines. al curve. Feet. +0.05 Ordinates, semi diurnal curve of Differences. Feet. -0.28 Taking the values of the maximum ordinate of the diurnal curve (D) as deduced by Mr. Heaton, tracing a curve for them and folding this over on its greatest ordinate, as a hinge, we bring five values of D to the determination of each point in the curve from the observations of 1852. Treating the curve of twice the sine of the moon's declination in the same way we obtain a curve for comparison with the former. Neglecting the sun's action, we have from theory m sin. 28' D. Taking the mean of the values of D, which nearly correspond to each other in the half declination, and the mean of the corresponding values of the sine of twice the declination, we obtain m=29 nearly. The following table, No. 4, gives a comparison of the values of the semi-diurnal ordinates, and of m sin. 28'. I have also deduced the diurnal inequality, from Mr. Heaton's compound or interference curves, and have compared it in the same way with m sin. 28'. The value of m found from these, was m=28. The last column of Table No. 4 refers to this com parison. TABLE No. 4, Showing the values of the maximum ordinate of the diurnal curve (D) deduced from analyzing the curves of observation and comparison with theory; also the value of comparison of the diurnal inequalities measured on the compound curves. The changes in the value of E have been distinctly traced by Mr. Heaton from the observations; but before presenting the conclusion on this subject, I desire to subject them to the test of further computations, which are now in progress. In order not to interfere with the regular work of the hydrographic party, a separate tidal party has been organized under the direction of Lieutenant Trowbridge of the corps of engineers, assistant in the Coast Survey, and supplied with the necessary means for a full investigation of the tides of our Western coast. It is proposed to establish three permanent relf-registering tidegauges, under intelligent supervision, at San Diego, San Francisco, and Columbia river entrance, and to connect them by observations at suitable intermediate points. There are difficulties to be overcome in the character of the coast itself, and of the aborigines who still inhabit portions of it, but I expect, nevertheless, entire success from the zeal and ability of Lieutenant Trowbridge. The following tide table results from the observations already discussed. Corrected establishment at Rincon Point: High water, 12 hours 3 minutes; low water, 17 hours 51 minutes. Mean rise and fall of tides, 3 feet 11 inches; of spring tides, 4 feet 11.8 inches; of neap tides, 2 feet 11 inches. Mean duration of rise 6 hours 30 minutes, including half the stand; fall 5 hours 52 minutes, including half the stand; stand, 30 minutes. Difference in height of highest tide and lowest tide in day: average, 5 feet 11 inches; greatest, 7 feet 7 inches. When the moon's declination is north, the highest of the two high tides of the day is the one which occurs about twelve hours after upper culmination. I have given elsewhere, for the use of navigators, a set of rules founded on these observations, and containing no technical term unfamiliar to them. Notes on the Tides at San Francisco, California. Besides the ordinary changes in the time and height of the tides known to all navigators, it is important to note the following, generally applicable to the Western coast, and particularly to San Francisco bay. They relate to peculiarities in the tides which occur on the same day, the necessity for knowing which is shown by the fact that a rock having three feet and a half of water upon it at low tide, may, at the succeeding low water, on the same day, be awash: 1. The tides at Rincon Point, in San Francisco bay, consist generally of a large and small tide on the same day; so that of two successive high waters in the twenty-four hours one is much higher than the other, and of two successive low waters one is much lower than the other. 2. The difference in height of two successive tides (either high or low waters) varies with the moon's declination. When the declination is nothing, the difference is nothing, or very small. When the declination is greatest, whether south or north, the difference is greatest. When the moon's declination is nearly nothing, the intervals between two successive high or two successive low waters are nearly twelve hours, and twenty-five minutes, and differ most from this when the moon's declination is greatest. 3. The inequalities in the heights of successive low waters are more considerable than those of successive high waters; while, on the contrary, the inequalities in the times of high water are more marked than those of low. 4. The average difference between the heights of two successive high waters is one foot three inches; and of two successive low waters, two feet and four inches. The average difference of these same heights, when the moon's declination is greatest, is for the successive high waters two feet, and for the low waters three feet six inches. 5. The average variation from twelve hours and twenty-five minutes in the interval between two successive high waters is one hour and twelve minutes, and between two successive low waters fifty-three minutes. The average variations of the same interval when the moon is farthest from the equator are, respectively, two hours and one hour and a quarter. SECOND SERIES, Vol. XXI, No. 61.-Jan., 1836. 2 6. When the moon's declination is north, the higher of the two high tides of the twenty-four hours is the one which occurs about eleven and a half hours after the moon crosses the meridian, (souths) and when the moon's declination is south, the one which occurs about twenty minutes after the moon's meridian passage, (southing). 6 bis. Or the following rule may be used, which applies when the moon crosses the meridian between midnight and 11 A. M., or between noon and 111⁄2 P. M.: If the moon is south of the equator, and passes the meridian (souths) in the morning, the morning high water will be higher than the afternoon high water, if, in the afternoon, the afternoon high water will be the higher. If the moon is north of the equator, and passes the meridian (souths) in the morning, the afternoon high water will be the higher; if in the afternoon the morning high water will be the higher. 7. The lowest of the two successive low waters of the twentyfour hours occurs about seven hours after the highest of the two high waters. 8. The average difference between the height of the highest high water and of the lowest low water is five feet eleven, and the greatest difference is seven feet seven. ART. II. Comparison of the diurnal inequality of the tides at San Diego, San Francisco, and Astoria, on the Pacific Coast of the United States, from observations in connection with the Coast Survey; by A. D. BACHE, Superintendent.* (Communicated to the American Association for the Advancement of Science, by authority of the Treasury Department.) Ar a meeting of the American Association in August, 1853, I submitted some remarks on the diurnal inequality of the tides as observed at San Francisco. I propose now to compare this important inequality at the three ports of San Diego in California, San Francisco in California, and Astoria in Oregon. The results are the first fruits of the tidal observations under the immediate charge of Lieut. Trowbridge, of the Corps of Engineers, to which I referred at the same meeting, as in progress. The series is intended to develop the tidal phenomena of that coast, and the three stations referred to are those for permanent reference, at which self-registering tide-gauges have been put up. The results now communicated are derived from observations at Asto From Report of the Superintendent of the Coast Survey, showing the Progress of the Survey during the year 1854, p. 152. Washington: 1855. |