Lettor of group. ward, re-appearing again north and east of Hatteras, and following the coast inwards towards Sandy Hook, and then towards Point Judith, and leaving the coast off the shoals of Nantucket and Cape Cod. The lines of 11h. and 11h. are approximately drawn outside of the line of 12h. which, in general, is quite near to the coast, and conforms to its sinuosities from Tybee to Narragansett entrance. TABLE No. 3. a... abis. The same uncorrected for 12 16 1-298 52 23 2.31 13 depth. b... Four stations from Old 12 18 0-411 2221 Point Comfort to Sandy 4.47 Hook. c... Four stations from Sandy 12 6 200 63 27 0.76 Hook to Quick's Hole. The co-tidal line of 15h. is the one which characterises the indentation between Cape Cod and Cape Sable, the probable connection of the depth of the sea there, and of the co-tidal lines, being traced on the chart. The lines connecting these two systems are uncertain. The tide-wave appears to move backward from the northern extremity of Cape Cod to the southern, or Monomoy Point; but this part of the subject requires further observations for its elucidation. I have tried, in discussing these observations, several other groups, but chiefly to learn whether stations must be multiplied or observations repeated; and it is not necessary to occupy the time of the association with a detail of these trials, or with their results. They will be used in the progress of the further observations. ART. IV.-Approximate Co-tidal lines of the Pacific Coast of the United States, from observations in the United States Coast Survey; by A. D. BACHE, Superintendent. Communicated by authority of the Treasury Department. THE Western coast of the United States, between San Diego, California, and Columbia river, extending through 13° 35′ of latitude, and 6° 43′ of longitude, is divided into three reaches, (see plate,) the first from San Diego to Point Conception, the second from this point to Cape Mendocino, and the third from that Cape to Cape Disappointment at the mouth of the Columbia. The first reach, about 220 miles in extent, is curved, the general trend being about N. 56° W. The second, about 430 miles in extent, is in general straight, with moderate indentations only, and its trend is about N. 27° W. The third, 370 miles in extent, is also nearly straight, trending nearly N. 5° E. The soundings on the coast generally, except in the harbors, have been for the purpose of general reconnoissance, and are not detailed enough to show the configuration of the bottom. Tidal Observations. Tidal stations for long series of observations have been established at San Diego, San Francisco, and Astoria, (Columbia river,) and between these, temporary stations at the points and for the periods stated in the annexed general table. Saxton's self-registering gauge has been employed at the permanent stations generally and at some of the temporary stations also. The observations are under the direction of Lieut. W. P. Trowbridge, U. S. Corps of Engineers, and Assistant in the Coast Survey. They were commenced in 1853, and are still in progress. The very intelligent and careful supervision of this officer is a guaranty for the character of the observations. The observers too were especially selected by him for their faithfulness and intelligence. The number of results collected is such as to warrant an approximate determination of the cotidal lines of this coast, to be checked when further results are obtained. This attempt has the advantage of pointing out deficiencies in the series, which otherwise would not so clearly appear. The following table shows the localities of observation and the duration of each series embraced in this discussion, the name of the observer, and the kind of gauge employed. TABLE I. Tide Stations on the Western Coast of the United States, the results of which are discussed in this paper. These results were in part tabulated by Lieut. Trowbridge, and in part in the Tidal Division of the Coast Survey office under the immediate direction of Assistant L. F. Pourtales. The discussions were made in general by Messrs. Heaton and Hawley of the same division. The times of high water are referred to the next preceding transit of the moon, transit F of Mr. Lubbock's nomenclature, the epoch having been found to correspond to that transit. mean interval between the time of high water, or the establishment corrected for half-monthly inequality for each station is given in the following table. A correction to carry the results to deep water is applied in the way described in my paper on the cotidal lines of the Atlantic coast of the United States,* giving the establishment used in obtaining the cotidal hour. The latitude and longitude from Greenwich of each tidal station is given in the table to the nearest minute. The cotidal hour found from the establishment corrected for depth and the longitude from Greenwich is in the last column of the table. It is not necessary to apply a correction for the different transits as the difference between the greatest and least corrections amounts to but five minutes. TABLE II. Data for the Co-tidal lines of the Pacific Coast of the United States. Proceedings of the Amer. Assoc. Adv. Science, Washington meeting, 1854. Co-tidal Hours. The cotidal hours thus far obtained between San Diego and Cape Disappointment, Columbia river, are contained between 17h 20m and 20h 10m, increasing as a general rule, but with striking exceptional cases, and not regularly in passing northward. The cotidal hour of 17h 20m characterizes the two stations in the southern reach referred to in the description of the coast; 18, 19, 20h are found on the middle reach, and 20h characterises the northern. Co-tidal Groups. In discussing these results I have followed the same course as in the paper on the cotidal lines of the Atlantic, dividing the stations into natural groups, and applying Lloyd's mode of discussion of magnetic lines to them. The northern group of stations, between Cape Disappointment and Cape Mendocino, (see plate) is composed of Cape Disappointment, Port Orford, and Humboldt. The mean cotidal hour is 19h 58m. The mean of the longitudes of the stations is 124° 12′; the mean of latitudes 42° 15'. Calling the differences between the mean longitude and the longitude of each station when reduced to nautical miles x, the differences between the latitude of each station and the mean y, the difference between the cotidal hour at each station and the mean cotidal hour z, and assuming as the sign of the algebraic sum of the numerical quantities obtained for the co-efficients of the equations furnished by each station, we form and solve the equations: In the case before us M gives for the co-efficient of the longitude 12 and N for that of latitude, 0·006. The tangent of the N angle which the cotidal line makes with the meridian =0.05 M and the angle is 2° 52'. The distance in nautical miles perpendicular to the cotidal line corresponding to one minute of establishment or M2+N2 is 1-2 miles, and therefore the progress of of the tide wave in one hour, 50 miles. This is a velocity less than the depth would indicate to be correct, and from the small differences in the establishments of the stations, this must be an uncertain datum. We shall see however that in the next group where the establishment varies more considerably this datum is still less probable than the one here obtained. The direction of the line is nearly coincident with that of the trend of the coast, the cotidal angle being 2° 52′ and the general trend of the coast differing but two degrees from it. The cotidal hours calculated from the separate equations are for Cape Disappointment 20h 00m, Port Orford 19h 44m, agreeing precisely with the observed, and for Humboldt 20h 09m, differing but one minute from the observed. The observations bearing upon this group are extending northward, but the difficulties in the way of maintaining the stations are such, on a coast inhabited by aborigines, that I do not venture to count upon speedy results. Lieut. Trowbridge is using his best efforts to establish the necessary stations. I precede the discussion of the Middle Group of stations by a table giving the results corresponding to several different hyturn be examined. potheses which will in TABLE III. Discussion of the Middle Group of Tidal Stations between Cape Mendocino and Point Conception. Mean Longitude. Mean Latitude. Mean co-tidal hour. Longitude. Latitude. angle geog. mile of Angle Co-tidal [tang.-N] hour for one Diff of cotidal hour correspond'g to one to cotidal line. Miles per h'r tid'l wave San Luis Obispo. San Francisco Taking the five stations between Cape Mendocino and Point Conception as one group, we find from the table the angle of the SECOND SERIES, Vol. XXI, No. 61.-Jan., 1856. 4 |