ria, from July 11 to October 31, 1853; at San Francisco, from January 17 to February 15, 1852, and from January 5 to February 26, 1853; and at San Diego, from September 22 to November 31, 1853. All the observations were made with Saxton's self-registering gauge. I submit specimens of the actual curve traced by the gauge. The results have been computed, under the direction of L. F. Pourtales, Esq., assistant United States Coast Survey, by Messrs. H. Heaton and P. R. Hawley, and the diagrams were drawn by Mr. C. Fendall. Some of the curves of observation on a reduced scale are shown in diagram No. 1. The place of observation, and the dates for each series of curves, are stated on the diagram. The diagram represents the times from 0 hours to midnight, on a scale in which the distance between the vertical lines corresponds to two hours, and the heights on a scale of half a foot of rise or fall of the tide to each division between the horizontal lines. The phases and declinations of the moon are inserted at the top of the diagrams, and the times of the moon's transit at the foot. The curves have a striking similarity, and show a large diurnal inequality in both high and low water, in time and in height, at or near the greatest declination of the moon. The greatest inequality of the height is 2.76 feet at Astoria, 2:40 feet at San Francisco, and 2-77 feet at San Diego. The mean rise and fall, estimating the highest high and lowest low waters of each day only, is for the three places respectively, 7.86 feet, 5.92 feet, and 5:46 feet. Some of the daily curves of San Diego, near the period of greatest declination of the moon, approach in form to those at Fort Morgan, ou the Gulf of Mexico. The curves of half-monthly inequality of high and low water will be so much better determined hereafter, that I merely refer to them now in passing, to show their general resemblance to those formerly produced for San Francisco. The crude corrected establishment for the three places is— For Astoria, For San Francisco, For San Diego, 12h. 53m. 12 4 9 37 The value of A (the tangent of the difference of luni-tidal interval for three and for nine hours) and of E of Mr. Lubbock's notation, (half the difference in height of neap and spring tides divided by 2 A) are, for Diurnal inequality in intervals and heights of high and low water at San Francisco, San Diego, and Astoria. Inequality in interval Inequality in height Inequality in interval Inequality in height| of high water. of high water. of low water. of low water. 1.00 065-0.25 0 20 031 021-250-1·14-140 006-1·90-0·93-0·83 -1 09-0 46 -0 13 1 58 2 23 1 38-1-62-1·95-201-0 30-2 00 -1 20 2.99 2.79 3.85 .... .... 309 3.79 The foregoing table shows the diurnal inequality in time and height of high and low water at the three places before named. The whole difference in height and interval between the A. M. and P. M. tides is taken as representing the diurnal inequality, and no correction is made for the half-monthly inequality in preparing the tables. I may observe that upon trying the corrections with the half-monthly inequality, as at present determined, no special advantage resulted; and until the half-monthly inequality is determined by more numerous observations, I adhere to this form of discussion. The results are shown in diagram No. 2, in which the ordinates denote the inequality in interval and height on the days from zero of declination of the moon, denoted by the abscissæ. The dots show the actual observations, and the curves are drawn with a free hand among them. The results for the three places are distinguished as marked on the diagram. The following are the inferences from the discussion: 1. In every case, the inequalities increase and decrease with the moon's declination, reaching zero at or near the time of the moon's crossing the equator. The average epoch of the inequalities agrees almost exactly with the time of the zero of declination. 2. The inequality in height of high water, and in interval of low water, increase and decrease together, and so for the inequality in time of high water and in height of low water, as was remarked in the case of San Francisco. 3. The declination of the moon, and the inequality in interval of high water and in height of low water, have contrary signs at all three of the places: the reverse being true of the other two inequalities. 4. The inequality in the height of low water is, in general, greater than that of high water, as was before stated for San Francisco. The proportion of the average and maximum inequalities is nearly as follows: 5. The inequality in the interval of high water is, in general greater than that of low water, as follows: 6. The average and greatest inequalities in interval and height are shown in the following table: 7. The comparison of the values of the diurnal inequality in height with the theoretical expression m sin 2' is given in the annexed table and diagram, in which the value of m is taken at 2:35. The inequality results are grouped by the declinations. The observations of which these form a part are still in progress, under the direction of Lieutenant Trowbridge, whose assiduity and intelligence have already been rewarded by the success I had ventured to anticipate in my former reference to the tides. of the western coast. ART. III.-Preliminary determinations of Co-tidal lines on the Atlantic Coast of the United States, from the Coast Survey Tidal Observations; by A. D. BACHE, Superintendent.* (Communicated to the American Association for the Advancement of Science, by authority of the Treasury Department.) In the progress of the hydrography of the Atlantic coast of the United States, numerous tidal observations have necessarily been made for correcting the soundings and determining the establishments of the ports. With them I have connected observations of a more permanent character, intended to furnish the data for ascertaining the laws of the tides in important localities, and others for tracing the progress of the tide-wave along the coast generally, and in special cases in sounds, bays, and rivers. These observations are still in progress; indeed, those for developing the laws of the tides, and determining the constants of theory, depend for their value upon their long continuance. So many authentic results have now, however, been obtained, that it appears desirable to put them together, and to ascertain the conclusions towards which they tend as to the co-tidal lines, and by the agreement of the separate results with general laws, or their departure from them, to determine which of them require further observations to check their first results, and where new stations of observations are necessary for the purpose. My attention has been called, also, by the request of a valued friend, the Master of Trinity College, Cambridge, to some attempt of this sort, and his labors in connection with this subject on our own coast have entitled his request to the most respectful consideration. Report of the Superintendent of the Coast Survey showing the progress of the Survey during the year 1854, p. 147. Washington, 1855. I am indebted to L. F. Pourtales, Esq., in charge of the tidal party of the U. S. Coast Survey, for the revision of the computations given in this paper. The labor of reducing the observations themselves has fallen chiefly upon Messrs. Heaton, Fendall, and Hawley. The diagrams have been prepared by Mr. C. Fendall, under the direction of Mr. Pourtales. The stations at which observations of the tides have been made, of the more reliable class are thirty-three in number, extending |
