■■■VV'i*-«'^*'>^'s*'-«..Vw->i»«'.'>*-i-^'-^i,„v.>..v-.'^.--J"-'-' SITY Or CALtFORMIA AT LOS Af-IGELES 0mUI)0oiuan Contributions to linoiolcigc. TIDAL 0 B S R R V A ^^: 0 I S I.\ THE ARCTIC SEAS. BY ELISHAKENT KANE, M.D., U.S.N. MADE DURING THE SECOND GRINNELL EXPEDITION IN SEARCH OF SIR JOHN FRANKLIN, IN 1853, 1854, AND 1855, AT VAN RENSSELAER HARBOR. REDUCED AND DISCUSSED, BY CHARLES A. SCHOTT, ASSISTANT U. S. COAST SHRTEY. WASHINGTON CITY: PUBLISHED BY THE SMITHSONIAN INSTITUTION. OCTOBER, 186 0. K t\ i. " ■'* NEW YORK: D. APPLETON & CO. SMITHSONIAN CONTRlIiUTIONS TO KNOWLEDGE. TIDAL OBSERVATIONS ARCTIC SEAS. BY ELISHA KENT KANE, M.D., U.S.N. MADK DURING THE SECOND GRINNELL EXPEDITION IN SEARCH OF SIR JOHN FRANKLIN, IN 1853, 1854, AND 1855, AT VAN RENSSELAER HARBOR. REDUCED AND DISCUSSED, CHARLES A. SCHOTT, ASSISTANT U. S. COAi^T STTRVEV. [ACCEPTKI) for publication, JULY, 18G(i.] cni.LiKg, PRi.vmi. iMiii.AnKi.riiiA. K/3tr CONTENTS. CO en 3: =3 Introductory Letter ..... Explanatory and introductory remarks Record of tidal observations at Van Rensselaer Harbor, 1853-4 Discussion of half-monthly inequality in time and height . Effect of changes of the moon's declination and parallax . Discussion of the diurnal inequality in height and time . Investigation of the form of the tidal wave Note on the effect of wind on the tides Note on the progress of the tidal wave and depth of the sea Record of soundings ..... Appendix — containing a tidal record at "Wolstenholm Sound, Commander Saunders, 1849-50, with four iilatc.'! .......... PACE V 1 5 G7 72 74 78 81 81 82 8.3 304625 INTHODUCTORY LETTER. Washington, July 4th, 1860. Professor Joseph Henry, LL. D., Secretary of the Smithsonian Institution : Dear Sir: The records of the tidal observations made under the direction of Dr. Kane, in the second GrinncU Expedition to the Arctic Regions, were placed in my hands by his late lamented father. Judge Kane, in December, 185T. Dr. Kane had selected Assistant Charles A. Schott, of the U. S. Coast Survey, for the reduction of a considerable portion of the observations made on that expedi- tion; and I, therefore, placed them in Mr. Schott's possession for reduction, and recommend his paper for publication in the " Smithsonian Contributions to Knowledge." It is proper to state that the computations were at the expense of the Smithsonian Institution. This is the sixth and last paper of the series. Very respectfully, yours, A. D. BACHE, Superintendenl U. S. Coast Survey. RECORD AND REDUCTION OF THE TIDES. The observations and discussion of the tides at Van Rensselaer Harbor, tlie winter quarters of the Advance during 1853-54 and 1854-55, will form the last of the series of papers on the results of the expedition, prepared by me for publication. Occasional tidal observations were made after passing Smith Straits, when, owing to the peculiar navigation through the narrow openings between the coast and the bay ice, the vessel was much exposed to the tidal action, frequently grounding at low water, and otherwise, by taking advantage of high tides, slowly advancing to her winter quarters. The bay, near the head of which the Advance was laid up, and used as the winter quarters by Dr. Kane's party, is freely exposed to the north (true) and northwest; the indentation of the shore line is about five miles; some rocky islands are situated within the bay. Shortly after the vessel entered the harbor a tide staif was arranged, and a series of tidal observations was commenced on September 11, 1853, and continued, with occasional interruptions (partly owing to defects in the pulley-gauge, after- wards rigged up, and partly owing to other unavoidable accidents) till the 24th of January, 1855, on which date the regular log book appears to have been discon- tinued. The several series of observations during this period are of very unequal value, as will appear in the detailed examination and discussion of the results. The difficulties to be overcome in the attempt to secure a reliable set of observations were considerable, those of a physical nature being the greatest. The observations with the staff or sounding line are subject to irregularities from a slow movement of the vessel, which, though imbedded in ice during the greater part of the year, is yet not stationary; these observations may also be affected by the softness of the bottom; the observations by means of a pulley tide gauge may be defective, on account of a slow drift of the vessel and motion of the ice field, also in consequence of a lengthening or shortening of the rope, or it may be in consequence of slipping of the rope on the circumference of the wheel. The latter defect, or one similar in its nature, has been a source of much annoyance, requiring the application of corrections to the readings, in order to refer all observations to the same zero of the scale. There is another defect to which pulley-gauges are subject, namely, the gradual rise of the vessel, in consequence of the consumption of provisions and fuel. Notices of these defects will appear in the subsequent discussion. The pulley-gauge is described by Dr. Kane, in volume I of the Narrative, p. 117, as follows: " Our tide register was on board the vessel, a simple pulley-gauge, 1 2 RECORD AND REDUCTION OF THE TIDES. arranged with a wheel and index, and dependent on her rise and fall for its rotation."^ In order to ascertain the nature of the tides, as well as the degree of accuracy of the different observations, the readings were roughly plotted for a first examina- tion ; the following series were found suitable for discussion : — Series I. From October 10th, 1853, to December 2Sth, 1853. — This series, with the exception of three days, is complete ; the observations in the latter part of December appear to be of less reliable character. The observations between Sep- tember 11 and October 4, 1853, are too fragmentary to be used. The pulley-gauge observations between October 4 and October 9 seem to have been only experi- mental. The hourly readings are superseded by half-hourly readings on November 8, and continue half hourly, day and night, to the end of the series. After November 28, corrective soundings were taken at noon each day. In order to make use of these soundings, the mean depth of the water at the anchorage was deduced from them as follows : — Mean reading. December, 1S53. 43.8 feet, from 31 souiidiiigs (:il noon). January, 1854. 44.9 21 Fel)rnary, " 44 3 17 March, " 43.3 19 April, " 41.8 20 May, "43.5 9 The individual soundings will appear in the record following. Mean depth of water at anchorage, in winter, 1853-54, 43.6 feet, as obtained from 117 soundings. The monthly mean values for the tidal level accord well, and show that no lateral change took place in the position of the brig (or else that the bottom was level). It will be seen that for Series I the reading 7.0 was adopted to express the mean level, the zero of the scale was, therefore, at an eleva- tion of 36.6 feet from the bottom. The readings of the pulley guage are expressed in feet," as 1 have been informed by Mr. Sonntag. Series II. From January 28th, 1854, to April 1th, 1854. — The double half-hourly readings of the pulley-gauge are continued. The series is complete with the exception often days, which had to be omitted. The register broke January 22d; observations commenced January 24th, but were not sufficiently regular for use ' The following note is appended : One end of the cord represented a fixed point, by being anchored to the bottom; the free end, with an attached weight, rose and fell with the brig, and recorded its motion on the grooved circumference of a wheel. This method was liable to objections, but it was corrected by daily soundings. The movements of our vessel partook of those of the floe in which she was imbedded, and were unaccompanied by any lateral deviation. " Tiic following is an e.xtract from Mr. Sonntag's letter to me, dated New York, March 23, 1860: "The circumference of the wheel (of the pulley-gauge) was divided into feet and tenths of a foot, and the records by the sounding line are also expressed in feet and decimals. The records of the wheel arc very uncertain, as often the rope slid over the wheel without turning it, owing to the ice which surrounded the axis." RECORD AND REDUCTION OF THE TIDES. 3 until January 28th. The corrective soundings at noon are continued, with occa- sional omissions, throughout this scries. After April 7tli there is a break in the observations, those between the 14th and 2()th appear to be irregular. Series III. From April 20th, 1854, to August 3d, 1854.— The double half-hourly readings of the pulley-gauge continue to May 5th, after which date single half- hourly readings are recorded. The corrective soundings cease on the 12th of INfay. Interruptions occur between iSlay 4th and ]\[ay 7th, also on .July Sth, also between July 15th and 18th, and between July 20th and the 28th. Ou the 8th of August tho brig was released from her ice cradle, and rose two and a half feet; occasional warpings of tlie brig after this date render the observations woi'tlilcss. On tlic 2;3d of August the brig was in but seven feet of water, and grounded. Series IV. From September 1th, 1854, to October 22d, 1854. — The hourly obser- vations assume again a more regular appearance on the 7th of September; they were taken with the sounding line, and are expressed in fathoms and feet (as stated in a note, August 12th). The following note is of October 21st, 1854: "The tide register as yet not rigged, observations very faulty by sounding line." The irregu- larities increase after this date; on the 15th of November following, the tide register was arranged, and observations (hourly) commenced on the 17th; the slip- ping of the rope, however, was of so frequent occurrence and of so great an extent, that it was considered better to take no further notice of these observations ; the record continues to January 24th, 1855, wlien the strength of the jjarty no longer permitted due attention to the tidal phenomena. It was apparent that before any closer insight into the nature of these tides could be obtained, they must first be reduced to the same zero or mean level of the sea. To effect this in a manner apparently best suiting the case, and otherwise im objectionable, two curved lines were traced on the diagrams, the upper one enveloping the highest high water of each day, the other enveloping the lowest low water of each day ; in tracing these lines some allowance was made, when necessary, for disturbing causes, so as to obtain tolerably smooth curves ; cases of abrupt changes were, of course, treated accordingly. A line, equidistant from these curves, was assumed as representing the mean level, and when straightened out was adopted as axis of the mean level of the sea. The corrections to refer each observation to this adopted mean level; or, in other words, the corrections required to refer each observation to the same zero of the scale, so as to make them comparable with each other, were taken from the projection, and are given in the column headed " reduction," in the following record. This method of treatment excludes necessarily in Series I, II, and III, any dis- cussion of the variation in the mean level of the sea, the oscillations of which have been found small at other places. As an illustration of this, the tides at Singapore might be referred to ; the Rev. W. Whewell (7th series of researches on the tides, Phil. Trans, of the Roy. Soc, Part I, 1837), finds for these tides that, if a line is (h-awn representing the mean height (midway between high and low w'ater each day) it is very nearly constant, though the successive low waters often differ by six RECORD AND REDUCTION OF THE TIDES. feet (on account of the diurnal inequality), the mean level only oscillates through a few inches. It appears from Mr. Lloyd's paper {Phil. Trans, of 1831) that the mean level at Sheerness is higher in spring tides than in neap tides by seven inches nearly; also there seems to be no doubt (as shown by Mr. Whewell, Phil. Trans., 1839 and 1840) that the mean level increases as the moon's declination increases, amounting to three inclics at Plymouth, when the moon's declination is 25° ; at- Petropaulofsk and Novo-Arkhangelsk the mean level rises as the moon's declina- tion increases. The use of the soundings intended to furnish corrections to the readings of the pulley-gauge is in many cases a doubtful remedy, on account of the continued change in the zero of the wiieel's index; in fact, it would have required numerous soundings at other hours than noon. As it is, a combination of the corrections by enveloping curves and soundings had to be adopted. Thus, for December 5th, soundings at noon 43.0 feet (see record further on), mean level 36.6, hence reading of scale at noon 6.4; reading of pulley-gauge at that hour 19.0, correction by curve — 12.5, corrected reading 6.5, which agrees with the first number; this is, however, a very favorable case. For intermediate hours the correction as given by the curves serve as guides. The reduction to the same level afi'ects the times generally very little. The following table contains the soundings taken at noon between the interval of the first and second series, those taken during the series being given in the record. Soundings at Noon. 1853. r .nth. Feet. Inch. Register. 1854 Fath Feet. Inch. Kegister. December, 29. 7 3 0 January 13. ►7 1 3 6 30. 8 0 0 18.1 (chaugecl.) 14. 31. 8 2 0 15. 8 1 0 1854. Jan. 1. 8 1 6 16. 7 2 6 2. 8 1 6 17. . . - . - - 3. 7 .5 6 18. 7 8 9 4. 7 3 0 Changed to 16.0 19. 7 5 6 5. 7 1 G 20. 6 3 0 G. 6 4 G Changed to 10.5 21. 6 4 0 Changed to 1 0 7. G 3 0 22. Tide register broken. 8. ... 23. 11 1( It 9. C 4 2 24. 11 it 1( 10. 7 0 0 25. . - . 11. — 26. - - - 12. 7 4 0 27. 7 1 9 The following soundings were taken be tween the second and third series :-■ — 1854. Fath Feet. Inches. 18; 4. Fatl . Feet. Inches. April 8. 6 5 6 Apr 1116. 7 5 6 9. G 4 0 (Fall 15 feet 8 in 3hes.) ^ 10. 7 0 C (17. 6 5 0 11. 0 5 G at 20 minutes to 5.) 13. 7 4 0 (18. 6 0 0 14.' 7 b 0 at 8'' 15'" P. M.) 1.0. 8 0 0 19. 6 2 0 (Low water to bigh water 14 ft. 8 inch.) ' For the past ten days the tide register has not been reliable on account of the rope slipping. RECORD AND REDUCTION OF THE TIDES. 5 The note of February 3d, 1854, is very instructive in regard to the effect of the tides on the ice floe, viz: "The enormous elevation of the land ice by the tides has raised a barrier of broken tables seventy-two feet wide and twenty feet high between the brig and islands. This action has caused a recession of the main floe ; our vessel has changed her position twenty feet within the last two spring tides, and the hawser connected with Butler Island parted with the strain." The cutwater of the brig was then 280 feet from the margin of the ice. (Note of February 4th.) The mean of all the soundings taken during the fourth series is very nearly fifteen feet, hence the constant index error, to refer the observations to the level previously adopted, is eight feet, which correction was applied, converting at the same time the record of fathoms into feet. The following tidal record extends, therefore, over about nine and a half luna- tions between October 10, 1853, and October 22, 1854, during which interval the time and height of nearly five hundred high and as many low waters were secured. Record of the Observations of the Tides at Van Rensselaer Harbor, North Greenland, in 1853, 1854, and 1855. Position of the Winter Quarters, Latitude 78° 37' north, and longitude 70° 53', or 4" 43"'.5 west of Greenwich.' The first column for each day is copied from the original log-book, the second column contains the reduction to the adopted zero of scale found graphically as explained, and the third column contains the observations referred to the same mean level. ' See my discussion of the astronomical observations of the expedition in vol. XII of the Smilh- 6onian Contributions to Knowledge, 1860. RECORD AND REDUCTION OP THE TIDES. Series I.^Tidal Observations FROM October 10, 1853, to December 28, 1853. Hourly observations on the pulley-gauge. Adopted reading of mean level 7.0, expressed in units of the scale. Increasing numbers indicate rise of water. October, 1853. Mean 10th. Red. Ref. 11th. Red. Ref. 12th. Red. Ref. 13th. Red. Ref. Mth. Red. Ref. 17th. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 1 ... 5.4 —1.0 4.4 5.0 —1.0 4.0 7.5 —1.3 6.2 7.0 —1.5 5.5 2 6.6 —1.0 5.6 5.4 It 4.4 5.0 It 4.0 6.4 (( 5.1 5.4 tl 3.9 3 7.6 tl 6.6 5.5 tt 4.5 5.2 tt 4.2 5.0 11 3.7 4.4 It 2.9 4 8.1 11 7.1 6.0 it 5.0 6.0 tl 5.0 5.5 It 4.2 4.2 tl 2.7 5 8.7 " 7.7 6.9 l( 5.9 7.0 tt 6.0 7.9 11 6.6 4.4 —1.6 2.8 6 8.7 (C 7.7 7.3 11 6.3 8.5 It 7.5 8.3 11 7.0 5.5 11 3.9 7 8.7 (( 7.7 7.7 11 6.7 8.9 tl 7.9 8.7 —1.4 7.3 7.5 li 5.9 8 9.0 tl 8.0 7.7 It 6.7 8.9 it 7.9 9.4 ft 8.0 9.6 11 8.0 9 6.4 11 5.4 7.6 il 6.6 10.5 t( 9.1 11.2 tt 9.6 10 5.9 it 4.9 6.6 tt 5.6 7.8 —1.1 6.7 10.5 11 9.1 11.4 It 9.8 11 5.7 11 4.7 6.1 tl 5.1 6.7 " 5.6 10.3 tl 8.9 11.3 11 9.7 Noon 5.8 tl 4.8 5.8 It 4.8 5.6 11 4.5 9.9 il 8.5 11.0 —1.7 9.3 1 6.7 it 5.7 5.8 tl 4.8 5.3 tt 4.2 7.6 tl 6.2 9.4 tl 7.7 2 7.3 11 6.3 5.8 li 4.8 5.3 11 4.2 6.7 tt 5.3 7.4 (t 5.7 3 8.9 11 7.9 6.3 It 5.3 5.3 11 4.2 5.6 —1.5 4.1 6.6 ti 4.9 ... 4 9.3 il 8.3 7.7 11 6.7 5.3 It 4.2 4.6 (( 3.1 4.4 It 2.7 5 10.2 tl 9.2 9.0 tt 8.0 6.4 —1.2 5.2 6.5 11 5.0 4.6 It 2.9 4.2 —2.7 1.5 6 10.2 11 9.2 10.1 It 9.1 7.8 tt 6.6 9.0 11 7.5 5.9 tt 4.2 4.5 tl 1.8 7 10.2 tl 9.2 10.5 tt 9.5 9.9 il 8.7 10.5 tl 9.0 9.2 It 7.5 8 9.9 il 8.9 10.5 tl 9.5 11.0 It 9.8 11.6 11 10.1 12.0 —1.8 10.2 9.5 li 6.8 9 8.8 11 7.8 9.8 ft 8.8 11.3 —1.3 10.0 12.4 11 10.9 12.4 tl 10.6 12.6 tl 9.9 10 7.5 It 6.5 9.0 l( 8.0 11.3 11 10.0 12.4 il 10.9 13.1 it 11.3 13.0 tl 10.3 11 6.3 it 5.3 7.2 li 6.2 9.7 it 8.4 12.4 11 10.9 13.1 11 11.3 13.4 il 10.7 Midn't 5.7 11 4.7 5.6 11 4.6 8.3 it 7.0 10.4 tt 8.9 13.0 —1.9 11.1 13.4 It 10.7 October, 1853. Mean :8th. Red. Ref. 19th. Red. Ref. 20th. Red. Ref. 2 1st. Red. Ref. 22d. Red. Ref. 23d. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 1 11.5 —2.7 8.8 13.6 —2.2 11.4 13.8 —2.3 11.5 11.6 —1.7 9.9 10.7 —0.2 10.5 7.0 + 0.8 7.8 2 8.9 (( 6.2 12.0 (( 9.8 12.6 a 10.3 " 10.2 It 10.0 8.0 " 8.8 3 6.8 (( 4.1 8.9 il 6.7 10.5 it 8.2 10.8 —1.6 9.2 10.0 — O.l 9.9 9.5 It 10.3 4 5.5 tl 2.8 6.6 11 4.4 8.0 It 5.7 9.6 -1.5 8.1 9.0 11 8.9 9.0 +0.9 9.9 5 4.4 —2.6 1.8 4.5 u 2.3 7.9 —2.2 5.7 6.7 —1.4 5.3 8.0 0.0 8.0 6.9 (1 7.8 G 4.4 it 1.8 3.8 It 1.6 7.9 (( 5.7 4.6 (( 3.2 7.0 u 7.0 4.5 II 5.4 7 6.5 11 3.9 3.8 It 1.6 7.9 11 5.7 4.1 —1.3 2.8 5.0 li 5.0 3.4 II 4.3 8 8.7 11 6.1 4.7 il 2.5 8.9 11 6.7 4.1 —1.2 2.9 5.0 +0.1 6.1 3.0 II 3.9 9 11.8 —2.5 9.3 5.3 a 3.1 8.7 11 6.5 6.7 ti 5.5 3.3 (( 3.4 3.1 tl 4.0 10 — 11.0 il 8.8 8.7 11 6.5 8.5 —1.1 7.4 4.5 +0.2 4.7 3.5 II 4.4 11 — 13.6 it 11.4 12.9 {( 10.7 lO.S (( 9.7 6.3 (( 6.5 3.7 II 4.6 Noon 14.4 tl 12.2 13.6 (( 11.4 11.7 —1.0 10.7 7.2 it 7.4 4.5 It 5.4 1 — ... 14.6 tl 12.4 14.0 —2.1 11.9 11.9 (( 10.9 7.0 +0.3 7.3 6.5 It 7.4 2 14.8 tl 12.3 12.6 u 10.4 14.0 tt 11.9 11.9 —0.9 11.0 7.5 il 7.8 7.0 II 7.9 3 10.6 —2.4 8.2 10.4 tl 8.2 11.9 —0.8 11.1 9.5 +0.4 9.9 8.5 It 9.4 4 8.6 (( 6.2 9.6 —2.3 7.3 11.8 •I 11.0 9.2 (( 9.6 9.5 It 10.4 5 6.6 11 4.2 6.6 II 4.^ 7.7 it 5.6 9.0 —0.7 8.3 9.2 tl 9.6 8.0 +0.8 8.8 6 4.4 (( 2.0 5.2 II 2.9 6.2 It 4.1 7.5 ti 6.8 6.7 +0.5 7.2 7.4 tl 8.2 7 4.4 -2.3 2.1 4.2 II 1.9 5.5 li 3.4 5.5 —0.6 4.9 5.2 (1 5.7 7.0 tl 7.8 8 5.5 u 3.2 4.8 II 2.5 5.2 —2.0 3.2 5.0 II 4.4 3.9 +0.6 4.5 6.1 It 6.9 9 8.3 II 6.0 6.8 11 4.5 4.7 (( 2.7 5.0 —0.5 4.5 3.9 4.5 5.5 It 6.3 10 10.4 II 8.1 9.4 II 7.1 6.8 —1.9 4.9 5.0 It 4.5 4.0 " 4.6 4.5 +0.'? 5.2 11 12.6 " 10.3 11.6 II 9.3 9.8 l( 7.9 5.0 —0.4 4.6 6.3 +0.7 j 7.0 5.0 " 5.7 Midn't 13.7 1 —2.2,11.5 13.4 (( 11.1 11.0 — l.S 9.2 5.0 —0.3 4.7 .... 5.5 " 6.2 EcRnlar ol iserrations commt nco October 10, 2 A. M. 0<;t. 1.0. 1 ide rope found In- oken at 10 A.M., md the load lo.st through the ice ho le. Oct. 17. T idcH irregular, ini: ox changed 12 un its ; honce most of the obsorvatioug on this day had to be omitted. Oct. 20. T he observation for 10 A. M. is incor rect, on account of obstruction by t le ice. Oct. 21. V lood [riHc] comini >nced at 8 P. M. Oct. 23. S lack wafiT [stand 1 at S o'clock, lion 1 commences. RECORD AND REDUCTION OF THE TIDES. SJilUES I. — 1 iDAL Observations from October 10, 1853, to December 28, 1853. n Hourly observations on the pulley-gauge. Adopted reading of mean level 7.0 , expressed in units | of the scale. Increasing numbers indicate rise of water. _ October, 1853. | Mean 24th. Red. Ref. 25th. Red. Ref. 26th. Red. Ref. 27th. Red. Ref. 28th. Red. Ref. 29th. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 1 6.5 +0.7 7.2 5.5 —0.1 5.4 5.0 +0.3 5.3 4.0 +0.8 4.8 4.5 +1.1 5.6 5.1 +0.9 6.0 2 7.0 (( 7.7 5.8 " 5.7 5.5 (( 5.8 4.0 tt 4.8 3.5 tt 4.6 4.4 (t 5.3 3 8.0 a 8.7 6.5 —0.2 6.3 5.5 +0.4 5.9 4.6 tt 5.3 3.4 (t 4.6 2.8 (t 3.7 4 8.0 + 0.6 8.6 7.2 " 7.0 5.8 (t 6.2 5.0 +0.9 5.9 4.3 It 6.4 2.5 li 3.4 5 7.3 (C 7.9 7.3 " 7.1 5.8 tt 6.2 6.0 tt 6.9 5.3 tl 6.4 3.0 ti 3.9 e ti.5 It 7.1 7.0 —0.3 6.7 6.2 +0.5 6.7 6.8 tt 7.7' 6.6 tl 6.7 5.5 ii 6.4 7 5.4 (C 6.0 6.4 {( 6.1 6.5 (( 7.0 7.1 +1.0 8.1 7.3 It 8.4 7.0 (f 7.9 8 4.0 +0.5 4.5 5.6 (( 5.3 6.6 (( 7.0 7.1 It 8.1 8.2 tt 9.3 7.8 (( 8.7 9 5.0 (( 5.5 5.6 —0.4 6.2 6.1 (( 6.6 7.1 (t 8.1 — 9.8 (t 10.7 10 5.0 It 5.5 5.6 it 5.2 5.6 1 " 6.1 6.0 (t 7.0 — 9.8 (t 10.7 11 5.0 (( 6.5 5.6 a 6.2 5.6 1 +0.6 6.1 5.6 tt 6.6 9.6 It 10.5 Noon 5.0 +0.4 5.4 6.6 it 5.2 6.5 1 " 6.1 4.6 tt 5.5 — 9.3 ii 10.2 1 7.7 tt 8.1 7.3 —0.3; 7.0 6.6 " 6.1 4.6 tl 5.5 4.8 tt 5.9 6.8 « 7.7 2 6.3 " ! 6.0 5.5 tt 6.1 5.0 tt 6.0 4.3 (t 5.4 4.8 (f 6.7 3 6.8 •—0.2 6.6 6.0 (( 6.6 5.3 tt 6.3 4.0 tt 5.1 4.0 tt 4.9 4 - * - 7.5 " 1 7.3 6.5 li 7.1 6.3 tl 7.3 4.0 (t 5.1 4.0 It 4.9 5 9.5 +0.2 9.7 7.3 — O.l' 7.2 7.5 +0.7 8.2 7.7 tt 8.7 6.0 ff 7.1 4.0 fC 4.9 (i 9.5 (( 9.7 7.6 " : 7.5 8.0 (( 8.7 7.3 +1.1 8.4 7.1 it 8.2 5.5 It 6.4 7 8.1 +0.1 8.2 8.3 " ! 8.2 8.2; " 8.9 8.6 tt 9.7 8.0 +1.0 9.0 6.7 fC 7.6 8 7.0 it 7.1 8.5 0.0 8.5 8.5 tt 9.2 8.7 tl 9.8 9.4 ! ti 10.4 9.0 tt 9.9 9 6.0 0.0 6.0 7.1 7.1 8.5 {( 9.2 8.7 tt 9.8 9.8 It 10.8 9.5 tl 10.4 10 5.8 « 5.8 6.1 +0.1 6.2 7.1 tt 7.8 7.1 +1.2 8.3 9.8 tt 10.8 10.6 tl 11.4 11 5.5 —0.1 5.4 5.4 11 5.5 6.1 +0.8 6.9 6.3 (( 7.5 9.0 +0.9 9.9 10.5 tl 11.4 Midu't 5.5 I " 5.4 5.0 +0.2 5.2 4.8 (( 5.6 5.9 " i^-^ 7.3 tt 8.2 8.5 li 9.4 ( Jctober, ] L853, November, 1853. Mean 30th. Red. Ref. 31st. Red. Ref. 1st. Red. Ref. 2d. Red. Ref. 3d. Red. Ref. 4th. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 1 4.5 +0.9 5.4 5.4 + 1.6 6.9 6.8 + 1.7 8.5 9.1 +1.4 10.5 13.5 —1.7 11.8 13.0 —1.4 11.6 2 3.5 " 4.4 3.8 It 5.3 4.0 (( 5.7 8.8 + 1.3 ,10.1 12.0 (( 10.3 12.5 tl 11.1 3 2.0 ti 2.9 3.0 +1.6 4.6 2.5 (( 4.2 7.1 +1.2 8.3 9.0 (( 7.3 11.2 tt 9.8 4 2.0 (( 2.9 0.0 It 1.6 1.0 ft 2.7 4.7 +1.0 5.7 6.7 —1.6 5.1 9.8 11 8.4 5 3.2 a 4.1 1.0 it 2.6 1.0 (C 2.7 1.5 + 0.7 2.2 3.7 (( 2.1 6.0 It 4.6 6 4.2 (1 5.1 1.2 11 2.8 2.2 t( 3.9 0.6 +0.5 1.0 1.8 tl 0.2 4.4 It 3.0 7 6.2 + 1.0 7.2 3.1 +1.7 4.8 3.2 tt 4.9 0.7 +0.2 ' 0.9 1.5 —1.6 0.0 2.0 tl 0.6 8 8.5 9.5 6.5 U 8.2 7.0 It 8.7 3.0 0.0 1 3.0 2.4 <( 0.9 1.7 tt 0.3 9 10.1 +1.1 11.2 8.5 « 10.2 9.5 +1.6 11.1 7.2 —0.2 1 7.0 3.4 (( 1.9 3.7 tt 2.3 10 10.4 " 11.5 9.3 It 11.0 10.5 " 12.1 9.8 —0.5 j 9.3 4.2 (( 2.7 7.3 It 6.9 11 10.4 (( 11.5 10.3 u 12.0 10.7 " 12.3 10.9 —0.7 110.2 6.0 « 4.5 10.5 tt 9.1 Noon 10.4 +1.2 11.6 10.0 it 11.7 10.7 " 12.3 15.3 —1.0 14.3 6.7 « 5.2 12.6 ii 11.2 1 8.2 (( 9.4 7.5 ft 9.2 10.2 " 111.8 15.2 -1.2 14.0 15.7 a 14.2 2 5.5 (( 6.7 5.2 (1 6.9 9.2 It 10.8 13.6 -1.5 12.1 15.2 tt 13.7 3 3.7 11 4.9 3.7 It 5.4 8.1 li 9.7 10.6 —1.6 8.9 12.5 " 11.0 12.0 It 10.6 4 3.4 tt 4.6 0.1 It 1.8 4.5 j +1.5 6.0 6.8 —1.7 5.1 10.1 a 8.6 11.5 it 10.1 5 2.6 +1.3 3.9 0.2 it 1.9 3.0 11 4.5 3.8 (t 2.1 6.5 a 5.0 9.0 tt 7.6 6 3.4 (t 4.7 1.2 it 2.9 2.3 (t 3.8 2.0 it 0.3 4.5 a 3.0 6.6 tl 4.1 7 5.1 it 6.4 3.0 it 4.7 2.1 (t 3.6 1.8 :t 0.1 3.5 c( 2.0 3.2 3.0 it tt 1.8 1.6 8 6.8 (( 8.1 5.2 " 6.9 4.0 t( 5.5 3.2 ii 1.5 3.6 3.0 It a 2.0 1.5 3.0 It 1.6 9 9.5 +1.4 10.9 8.1 It 9.8 9.0 <( 10.5 3.3 , " 1.6 4.5 (t 3.0 3.1 u 1.7 10 10.3 " 11.7 9.5 tt 11.2 10.1 " 11.6 3.3 j " 1.6 7.3 a 5.8 5.0 tl 3.6 11 10.3 " 11.7 9.5 t( 11.2 10.1 " ill. 6 3.3 : " 1.6 9.3 It 7.8 7.5 tt 6.1 Midn't 9.0 +1.5 10.5 10.6 tt 12.2 10.1 " 11.6 3.3 " 1.6 12.0 (( 10.5 9.8 it 8.4 Oct. 29. Slack water [stand] of ebb at 4" 30'" A. M. Oct. 31. Slack water [stand] of ebb at 5 A. M. Nov. 2 t a Nov. 6. Be tween these dates there are occasi onally half-hourly rea iings, I Hit unless ihey o ccur near high 3r low water they are omitted in the above. RECORD AXD REDUCTION OP THE TIDES. Series I.— Tidal Observations from October 10, 1853, to December 28, 1853. Hourly observations on the pulley-gauge . Adopted reading of mean level 7.0 , expressed in units of the scale. Increasing numbers indicate rise of water. November, 1853. Mean 5th. ' Red. Eef. 6 th. Red. Ref. 7th. Red. Ref. 8th. Red. Ref. 9th. Red. Ref. 10th. J Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 4.3 3.8 3.8 +0.2 4.0 4.5 —0.2 4.3 1 11.5 ^ —1.4 ,10.1 1 9.0 —1.0 8.0 6.6 —0.6 6.0 5.3 5.6 —0.5 4.8 5.1 3.9 4.2 (( 4.1 4.4 4.5 4.3 tl It 4.3 4.1 o 11.0 1 " 9.6 9.8 It ' 8.8 7.9 7.3 6.2 tl 5.7 4.0 (( 4.2 4.0 tl 3.8 j 9.9 tt 8.9 8.8 8.2 4.5 U 4.7 4.2 tt 4.0 3 10.0: " 8.6 10.0 tl 9.0 8.8 8.2 7.1 tt 6.6 5.0 " 5.2 4.5 —0.3 4.2 10.0 li 9.0 8.8 8.2 4.5 " 4.2 4 9.2 —1.3 7.9 10.0 —0.9 9.1 8.8 8-2 7.9 ,11 7.4 6.0 tl 6.2 4.1 (( 3.8 8.1 11 7.2 8.8 8.2 7.9 —0.4 7.5 5.8 « 5.5 5 5.7 11 4.4 7.7 (C 6.8 8.6 8.0 8.2 8.0 tt 7.8 7.6 7.5 11 7.7 6.5 tl 6.2 6 3.5 " ' 2.2 5.5 u 4.6 7.8 —0.5 7.3 7.8 tt 7.4 7.9 tl 8.1 8.5 11 8.2 7.9 It 8.1 9.9 11 9.6 t 2.3 ti 1.0 4.5 4.0 tt tt 3.6 3.1 6.5 (t 6.0 7.3 —0.3 7.0 8.0 8.0 +0.1 8.1 8.1 9.5 10.0 It tl 9.2 9.7 S 2.0 (( 0.7 3.6 —0.8 2.8 5.4 (C 4.9 6.3 (( 6.0 8.0 (( 8.1 10.2 -0.4 9.8 2.0 " i 0.7 3.1 (( 2.3 7.4 It 7.5 10.2 , tt 9.8 9 2.4 " 1.1 3.1 (( 2.3 4.0 ti 3.5 5.5 It 5.2 6.9 ti 7.0 10.2 tt 9.8 2.6 1 " 1.3 3.2 tt 2.4 4.0 (c 3.5 10.1 tt 9.7 10 2.7 —1.2 1.5 4.3 tt 3.5 3.7 3.9 (t tl 3.2 3.4 5.3 (t 5.0 6.0 tt 6.1 9.8 It 9.4 11 6.7 " ; 5.5 5.7 —0.7 5.0 4.4 ti 3.9 5.5 (( 5.2 4.8 tt 4.9 9.0 tl 8.6 5.5 (( 5.0 5.3 —0.2 5.1 Noon 11.1 9.9 8.3 tl 7.6 6.8 (( 6.3 5.1 5.3 tt tt 4.9 5.1 4.6 0.0 4.6 7.5 —0.5 7.0 1 13.1 13.6 11.9 12.4 ... 8.1 ti 7.6 5.6 It 5.4 4.4 4.5 tl tl 4.4 4.5 6.5 6.3 tt it 6.0 5.8 2 14.2 " 13.0 . - - 9.5 tl 9.0 7.1 It 6.9 4.5 11 4.5 6.0 It 5.5 14.2! " 13.0 5.1 tt 5.1 6.0 (( 5.5 3 14.1 i —1.1 13.0 13.0 " ,11.9 — 10.6 10.9 tt (t 10.1 10.4 8.3 It 8.1 5.5 It 5.5 6.5 —0.6 5.9 4 12.3 " 11.2 11.5 —0.6 10.9 11.2 11.2 t( 10.7 10.7 9.5 11 9.3 7.1 11 7.1 7.0 tt 6.4 5 10.8 " 9.7 11.0 tl 10.4 11.1 (( 10.6 10.1 —0.1 10.0 9.2 —0.1 9.1 7.9 C( 7.3 10.7 u 10.1 10.2 (( 9.7 10.5 (( 10.4 9.6 9.5 6 8.2 " 7.1 9.1 tl 8.5 10.2 tt 9.7 10.5 10.5 It It 10.4 10.4 10.1 9.5 " 10.0 9.4 9.5 cc 8.9 7 5.1! " 4.0 7.5 tl 6.9 8.5 tl 8.0 10.5 tl 10.4 11.1 11 11.0 10.9 it 10.3 ' 10.5 tt 10.4 11.1 11.0 11.4 tt 10.8 8 3.3 2.9 11 , 9 O T.8 5.4 it 4.8 7.5 (( 7.0 10.0 0.0 10.0 11.0 9.8 tl 10.9 9.7 11.0 11.0 tt tt 10.4 10.4 n 3.0 " ' 1.9 42 tt 3.6 5.6 (( 5.1 8.1 t: 8.1 8.9 It 8.8 11.0 11 10.4 S.5 ' " 2.4 4.0 It 3.4 11.3 tt 10.7 10 4.1!— 1.0 3.1 3.2 tt 2.6 4.4 ■ tt 3.9 7.0 +0.1 7.1 7.0 " 6.9 11.3 —0.7 10.6 ,3.2 " 2.6 4.3 tt 3.8 10.9 it 10.2 11 G.O " ' 5.0 4.0 (( 3.4 4.1 (( 3.6 4.9 tl 5.0 4.7 —0.2 4.5 9.5 (( 8.8 1 4.5 tt 3.9 4.1 tl 3.6 42 tl 4.3 4.7 4.5 Midn't 7.3 6.3 4.9 tt 4.3 4.0 ti 3.5 4.0 +0.2 4.2 4.5 It 4.3 8.5 It 7.8 Nov. 8. From this date the ohservations i irc half-hourly : in the iliOVO record, how ever, only those half- Itnnrly rf-nilini'w u' 5.0 " ' 5.0 8.5 (( 6.9 8.8 it 7.3 >'oon 16.5 " 13.5 11.9 tt 8.9 9.0 -4.0 5.0 8.0 —2.3! 5.7 8.0 —1.5 ti.5 8.5 —1.5 7.0 16.1 " 13.1 1 15.3 l( 12.3 14.7 " 11.7 9.7 (C 5.7 8.6 <( 6.3 7.5 11 6.0 7.0 (( 5.5 16.0 (( 13.0 7.0 »t 5.5 2 13.3 " 10.3 15.8 (( 12.8 11.0 —3.9 7.1 8.9 —2.2 6.7 7.5 11 6.0 7.0 (( 5.5 16.0 " 113.0 7.5 11 6.0 7.0 (( 5.5 3 12.3 it 9.3 15.2 " 12.2 11.3 a 7.4 8.9 —2.1 6.8 7.5 11 6.0 7.0 *' 5.5 12.3 —3.8 8.5 7.0 tt 5.5 4 S.l U 5.1 14.7 (t 11.7 13.1 12.9 —3.7 9.3 9.2 8.9 (t 6.8 7.5 11 6.0 7.0 11 5.5 .5 7.0 (C 4.0 12.9 (f 9.9 11.7 (( 8.0 8.6 8.9 —2.0 6.6 6.9 7.9 11 6.4 7.5 it 6.0 6 5.5 (( 2.5 10.8 (( 7.8 9.9 —3.6 6.3 8.9 (( 6.9 8.0 11 6.5 8.1 tt 6.6 8.7 —1.9 6.8 * 7 4.4 4.3 (I (1 1.4 1.3 11.5 (t 8.5 9.0 It 5.4 8.7 U 6.8 8.0 11 6.5 8.7 tt 7.2 8 4.3 (( 1.3 8.4 —2.9 5.5 8.0 —3.5 4.5 8.1 it 6.2 S.O 11 6.5 9.0 (t 7.5 4.4 1.4 7.0 I( 4.1 9 6.8 " 1 3.8 6.1 —2.8 3.3 8.2 -3.4 4.8 8.0 -1.8 6.2 8.2 (1 6.7 9.0 tt 7.5 7.6 (( 4.8 7.8 It 4.4 9.0 a 7.5 HI 10.3 " , 7.3 8.8 —2.7 6.1 7.5 —3.3 4.2 7.5 (I 5.7 7.8 11 « 6.3 9.0 tt 7.5 7.5 (( 4.2 7.5 (( 5.7 9.0 " 7.5 11 12.2 9.2 11.4 —2.6 8.8 7.5 —3.2 4.3 7.5 (( 5.7 7.3 11 6.8 9.0 '11 7.5 12.2 <( 9.6 7.7 (( 4.5 7.5 " 5.7 7.0 11 5.5 MidoM 13.1 " 10.1 13.0 —2.5 10.5 8.3 —3.1 5.2 7.5 —1.7 5.8 7.0 11 5.5 9.0 II 7.5 1 1 12.4 " 1 9.9 Filth. Teft. Inch. March 30 Sounding at noo n 7 4 6 Corr •etion l\v rurve.s preferred. " 31 No sounding, April 1-3 ti (t 4. Hounding at noo 1 i; ; (1 " r '' 6 2 0 Cor ret:lion.s derived frimi cur vcs, re-vlings (lu ;iglits) not '■ 6 2 6 re liable, see preceding note o; April 14. . " J . ': 1! 6 . RECORD AND REDUCTION OF THE TIDES. 27 Series III Tidal Observations from April 20 to August 3, 1854. Ho Ill- iy observations on the pul cy-Range. Adoptefl reading of mean level 7.0, e.vpress pd in units of the scak Increasing numbers indicate rise of water. April, 1854. Mean 20tli. Red. Ref. 2l8t. Red. Ref. 22d. Red. Ref. 23d. Red. Ref. 24th. Red. Ref 25th. Red. Ref snlar to obs. to obs. to obs. to ! obs. to obs. to obs. lidiir. level. level. level. level. level. level. 6.7 —2.2 4.5 7.8 —3.5 4.3 1 7.3 it 5.1 7.5 11 4.0 10.0 —4.2: 5.8 9.4 —4.0 5.4 11.1 —3.5 7.(i 7.5 tt 4.0 o 7.9 —2.3 5.6 7.7 —3.6 4.1 9.9 8.5 tt tt 5.7 4.3 7.5 (t 3.5 8.8 tt 5.3 3 9.0 —2.4 C>.6 7.9 tt 4.3 8.3 8.5 tl tt 4.1 4.3 G.7 6.5 (( 11 2.7 2.5 7.5 ft 4.0 4 .2 0 10.2 (; 7.8 8.9 —3.7 5.2 8.7 It 4.5 6.5 6.7 —3.9 2.6 2.8 6.4 5.8 —3.4 It 3.0 2.4 r, 11.4 —2.5 8.9 9.7 cc 6.0 10.2 (( 6.0 7.1 (( 3.2 5.0 6.0 1.6 2.6 G 12.1 (I 9.6 12.2 —3.8 8.4 11.8 ft 7.6 8.8 (C 4.9 7.0 U 3.6 7 12.5 12.6 —2.6 (t 9.9 10.0 13.3 13.7 tt tt 9.5 9.9 13.2 14.0 (t t( 9.0 9.8 10.5 (( 6.6 8.5 (( 5.1 8 12.5 —2.7 9.8 14.3 14.0 —3.9 10.4 10.1 14.9 14.9 t( It 10.7 10.7 12.9 15.0 9.0 11.1 10.9 —3.3 7.6 9 11.3 —1.0 10.3 11.0 —2.8 8.2 13.7 tt 9.8 13.0 tt 8.8 15.0 (( 11.1 13.4 tt 10.1 14.5 tt 11.2 10 8.3 —1.1 7.2 9.9 tl 7.1 12.3 il 8.4 ?8.1 ? --- 14.9 u 11.0 15.5 15.3 tl tl 12.2 12.0 11 6.7 —1.2 5.5 8.5 —2.9 5.6 11.3 ii 7.4 10.7 ft 14.6 u 10.7 14.1 tl 10.8 (5.4 " 5.2 Noon 6.4, —1.3 6.41 " 5.1 5.1 7.9 7.4 —3.0 4.9 4.4 10.7 —4.0 6.7 11.5 —4.3 7.2 12.9 —3.8 9.1 12.5 —3.2 9.3 1 6.7 11 5.4 7.0 7.0 CI 4.0 4.0 8.7 (( 4.7 ■ 9.5 It 5.2 10.6 (( 6.8 10.3 (( 7.1 •_; 7.1 —1.4 5.7 7.0 —3.1 3.9 8.3 tt 4.3 8.3 tt 4.0 9.0 (( 5.2 8.3 tl D.l 7.4 11 4.3 8.0 tl 4.0 3 7.9 " 6.5 8.0 It 4.9 8.0 8.0 It il 4.0 4.0 7.2 6.6 —4.2 3.0 2.4 7.4 tt 3.6 6.9 tt 3.7 4 9.0 —1.5 7.5 8.8 —3.2 5.6 8.0 (( 4.0 6.1 " 1.9 6.1 —3.7; 2.4 5.2 (( 2.0 8.3 it 4.3 6.0 " ' 1.8 5.4 " 1 1.7 5.0 " 1.8 5 9.5 9.7 8.0 8.2 8.5 (( 5.3 9.0 —4.1 4.9 6.5 —4.1 2.4 5.7 '* 2.0 5.0 5.0 1.8 1.8 0 9.7 9.7 —1.6 It 8.1 8.1 9.2 10.1 —3.3 5.9 6.8 10.8 tt 6.7 7.5 3.4 8.1 tt 4.4 5.2 tt 2.0 7 9.5 ti 7.9 10.5 10.5 7.2 7.2 11.5 it 7.4 9.3 (C 5.2 9.0 it 5.3 7.5 11 4.3 8 8.8 —1.7 7.1 10.5 10.5 ti 7.2 7.2 12.5 tl 8.4 10.8 It 6.7 10.4 —3.6 6.8 9.7 —3.1 6.6 9 7.9 —1.8 6.1 10.5 —3.4 7.1 13.0 tt 8.9 12.0 tl 7.9 13.5 (( 9.9 10.0 (( 6.6 13.9 It 9.8 12.8 it 8.7 13.5 t( 9.9 10 7.0 —1.9 5.1 9.1 IC 5.7 13.9 13.0 tt —4.2 9.8 8.8 13.6 13.6 —4.0 (i 9.6 9.6 13.5 12.5 it It 9.9 8.9 11 6.9 —2.0 4.9 8.4 ti 5.0 12.0 it 7.8 13.0 " 1 9.0 12.0 tl 8.4 ... Midu't 6.9 —2.1 4.8 7.9 —3.5 4.4 11.3 tt 7.1 9.0 5.0 11.5 —3.5 8.0 ... ... April 20. No sounding. Falli. Feet. luch. " 21. Sounding at nooi 6 1 0 \ (( OO (( (( 6 3 0 ) " 23. " " 6 3 6 \ Tlie corrections were deduced from tlie cu rve3. " 24. " " 6 4 5^ " 25. (( It 7 0 6 / 2S RECORD AND REDUCTION OP THE TIDES. Semes III.- —Tidal Observations from A PRiL 20 TO August 3, 1854. Ilourl}' observations on the pulley-gauge. Adopted reading of mean level 7.0, expressed in units 1 of the scale. Increasing numbers indicate rise of water. 1 April, 1854. May, 1854. Mean 26tfa. Red. Ref. 27tli. Red. Ref. 28tb. Red. Ref. 29th. Red. Ref. 30th. Red. Ref. 1st. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. 1 level. level. 14.4 (( 11.4 16.4 —3.4 13.0 16.4 —3.6 12.8 16.2 tt 12.3 1 10.1 —3.0 7.1 14.5 —3.0 11.5 9.2 —3.0 6.2 16.0 t( 12.6 15.3 tt 11.7 16.5 tt 12.6 14.1 (C 11.1 16.5 tt 12.6 2 9.1 u 6.1 12.8 (( 9.8 7.8 11 4.8 14.9 (I 11.5 12.8 it 9.2 15.9 —4.0 11.9 3 7.1 G.3 (( 4.1 3.3 10.5 (f 7.5 7.0 tt 4.0 13.1 tt 9.7 10.3 u 6.7 14.7 ti 10.7 4 5.6 5.8 2.6 2.8 8.3 (( 5.3 G.O 5.3 tt il 3.0 2.3 11.7 It 8.3 7.6 it 4.0 13.4 ** 9.4 5 6.3 li 3.3 6.8 (( 3.8 5.0 5.1 it 2.0 2.1 9.8 It 6.4 6.2 5.5 it it 2.6 1.9 12.2 ft 8.2 G 7.3 4.3 4.7 4.0 u 1.7 1.0 5.7 11 2.7 8.0 il 4.6 6.2 tt 2.6 10.0 tt 6.0 7 8.5 tl 5.5 4.0 5.9 1.0 2.9 6.6 —3.1 3.5 5.9 5.5 il 2.5 2.1 7.7 tt 4.1 8.9 ft 4.9 8 9.4 t( 6.4 8.7 11 5.7 7.5 tt 4.4 6.2 it 2.8 9.1 tt 5.5 8.2 8.0 tt 4.2 4.0 9 10.6 (( 7.6 10.9 l( 7.9 8.R tl 5.7 8.3 U 4.9 10.1 tt 6.5 7.9 8.4 ft tt 3.9 4.4 10 11.4 It 8.4 12.7 tl 9.7 10.3 tt 7.2 10.9 tt 7.5 11.2 tl 7.6 9.7 tt 5.7 11 13.9 14.4 (( (( 10.9 14.4 11.4114.5 tl 11 11.4 11.5 11.7 tl 8.6 13.5 14.6 tt tl 10.1 11.2 13.0 tt 9.4 11.9 tl 7.9 Noon 15.0 (I 12.0 15.1 u 12.1 13.7 —3.2 10.5 15.5 —3.5 12.0 14.7 —3.7 11.0 13.1 —4.1 9.0 14.0 (( 11.0 15.2 (t 12.2 14.5 (( 11.3 14.5 tt 11.0 15.0 tt 11.3 13.5 *' 9.4 1 13.1 " 10.1 15.0 u 12.0 14.8 (( 11.6 13.2 It 9.7 14.4 " 10.7 13.0 If 8.9 • 14.4 " 11.2 9 10.7 (( 7.7 12.4 (( 9.4 14.3 " 11.1 10.9 1 1 " 7.4 12.6 ft 8.9 11.3 It 7.2 3 8.7 11 5.7^ 10.3 (( 7.3 12.4 t( 9.2 9.6 tt 6.1 10.2 t. 6.5 10.2 —4.2 6.0 4 G.l tt 3.1 7.3 6.2 tl tl 4.3 3.2 9.2 tt 6.0 7.1 ft 3.6 8.0 6.3 tt tt 4.3 2.6 9.8 tf 5.6 n 4.1 It 1.1 5.2 5.9 tl It 2 '* 2.9 6.0 t( 2.8 5.3 5.0 —3.5 1.8 1.5 5.5 5.5 -3.8 tt 1.7 1.7 9.1 8.6 ft ft 4.9 4.4 G 3.2 3.1 It tt 0.2 0.1 7.7 t( 4.7 5.5 5.3 It tl 2.3 2.1 5.1 *' * 1.6 6.2 tt 2.4 8.0 8.0 ft ft 3.S 3.8 7 4.6 tl 1.6 9.6 (( 6.6 5.3 —3.3; 2.0 7.1 C( 3.6 7.6 (1 3.8 8.0 —4.3 3.7 6.1 It 2.8 8.4 ft 4.1 8 7.2 tt 4.2 10.8 n 7.8 7.8 tt 4.5 8.6 (( 5.1 8.5 '• 4.7 8.8 ft 4.5 9 10.7 It 7.7 12.3 il 9.3 10.2 tl 6.9 10.4 tt 6.9 9.5 '• 5.7 10.2 tt 5.9 10 12.3 tl 9.3 14.0 " 11.0 12.8 11 9.5 13.4 tt 9.9 11.3 " 7.5 11.3 li 7.1' 11 14.2 tl 11.2 15.7 ? --- 14.8 tl 11.5 15.3 16.2 t( 11.8 12.7 13.9 —3.9 10.0 12.7 ft 8.4 Midn't 14.3 il 11.3 16.7 tc 15.5 —3.3 12.2 16.4 tt 12.9 15.4 tt 11.5 14.1 —4.4 9.7 - FhUi. I 'eet. Iiu'h. April 26. Souiidi ng at noon 7 3 0 Coire ctious deduced from the curves. K ' n. 7 3 2 It u tt tl 28-30. No sounding. May 1. Sound il ig at noon 7 4 0 RECORD AND REDUCTION OF THE TIDES. 29 Series III. — Tidal Observations from April 20 to August 3, 1854. Hourly observations on the pulley-gauge. Adopted reading of mean level 7.0, expressed in units | of the scale. Increasing numbers indicate rise of water. 1 May, 1854. Mean 2d. Ked. Ref. Sd. Red. Ref. 4th. Red. Ref. 7th. Red. Ref. 8th. Red. Ref. 9th. Red. Ref. solar to ob.s^. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 10.2 —4.2 6.0 10.5 —4.8 5.7 1 15.1 —4.4 10.7 13.2 (C 8.5 13.6 —5.2 8.4 10.2' " 6.0 10.0 5.2 10.7 -5.5 5.2 10.5 It 6.3 11.5 6.7 10.0 tt 4.5 2 10.7 10.8 il 11 12.3 12.4 14.0 (( 9.3 14.0 —5.3 8.7 10.8 tt 6.6 11.5 -4.9 6.6 10.0 10.5 —5.6 4.4 4.9 3 1(!.5 11 12.1 14.2 14.3 il 9.5 9.6 14.8 —5.4 9.4 11.3 It 7.1 11.8 6.9 11.3 (( 5.7 4 14.2 —4.5 9.7 14.3 14.2 9.6 9.5 10.1 —5.6 10.5 11.8 tt 7.6 12.4 7.5 12.6 -5.7 6.9 5 12.5 (( 8.0 14.1 li 9.4 10.2 -5.8 10.4 12.4 tt 8.2 13.0 8.1 14.3 tt 8.0 6 11.0 u 6.5 13.1 tl 8,4 16.2 15.7 —6.0 —6.1 10.2 9.6 13.2 —4.3 8.9 14.1 —5.0 9.1 15.6 It 9.9 7 S.4 (( 3.9 12.0 li 7.3 15.3 —0.3 9.0 13.2 (( S.9 16.2 11 11.2 16.4 16.9 —5.8 (t 10.6 11.1 8 ij.7 tl 2.2 10.9 It 6.2 13.0 It 8.7 16.0 " 11.0 17.2 —5.9 11.3 (;.4 It 1.9 10.2 tl 5.5 16.5 1 " 11.5 17.2 " 11.3 9 ii.4 —4.6 1.8 10.0 11 5.3 12.2 tl 7.9 16.5 —5.1 11.4 17.2 —6.0 11.2 10.3 tl 5.6 16.3 ■' 11.2 16.6 (( 10.6 10 7.4 U 2.8 10.5 tl 5.8 11.0 ti 6.7 16.0 " 10.9 16.0 —6.1 9.9 10.8 11 6.1 11 9.5 (( 4.9 11.0 It 6.3 10.2 li 5.9 15.1 (( 10.0 14.9 -6.2 8.7 Noon 11.3 —4.7 6.6 11.4 4.7 6.7 9.0 —4.4 4.6 14.1 —5.2 8.9 13.8 -6.3 7.5 1 13.1 (( 8.4 12.8 13.4 li 8.1 8.7 8.1 8.0 11 3.7 3.6 13.0 tl 7.S ? tt ... 2 14.9 li 10.2 13.8 It 9.1 a 8.0 ti 3.6 10.6 (( 5.7 11.2 It 4.9 15.0 tl 10.3 13.8 it 9.1 9 8.0 11 3.6 3 14.5 (( 9.8 13.8 13.8 It it 9.1 9.1 1 8.4 It 4.0 9.0 8.4 —5.3 (t 3.7 3.1 10.0 9.3 —6.2 tt 3.8 3.1 4 13.6 li 8.9 13.8 it 9.1 bo 9.0 —4.5 4.5 8.0 tl 2.7 8.0 tt 1.8 13.1 11 8.4 a 8.7 It 3.4 8.0 tt 1.8 5 12.(1 (( 7.9 12.7 11 8.0 '■5 9.S (( 5.3 9.0 -5.4 3.6 8.9 tt 2.7 6 10.1 tl 5.4 12.1 —4.8 7.3 « 10.3 (( 5.8 10.2 " 4.8 11.2 —6.1 5.1 7 9.5 It 4.8 11.8 11 7.0 11.0 —4.6 6.4 11.6 11 6.2 13.0 " 6.9 8 9.0 9.0 It 4.3 4.3 11.6 11.6 —4.9 6.7 6.7 11.3 (C 6.7 12.3 tl 6.9 14.2 (( 8.1 9 9.0 11 4.3 11.4 11 6.5 12.0 cc 7.4 12.9 It 7.5 15.5 « 9.4 9.1 11 4.4 11.6 It 6.7 12.5 11 7.9 1.3.3 1 « 7.9 10 9.5 (( 4.8 12.0 —5.0 7.0 12.5 12.5 —4.7 7.8 7.8 13.5 13.5 tt tt 8.1 8.1 14.6 tt 8.5 11 10.1 It 5.4 12.7 li 7.7 12.0 It 7.3 13.3 tl 7.9 14.0 tt 7.9 Midn't 11.1 tl 6.4 13.3 —5.1 8.2 10.5 —4.8 5.7 12.7 —5.5 7.2 13.5 —6.0 7.5 I ath. Feet. Inch. May 2. g onndiii g at iioou 7 10 Correction derived from s ounding and curves. " 3. (t " ■7 0 jl (( (' (' u (( " 4. (( (( 7 1 (1 " f). (( (( 6 5 0 From tliis d.\v there is bi it one reading at each half hour. " (J. ^ 0 souu ling. " 7. s ouudiu g at noon 6 3 0 " 8. " " 7 2 0 " 9. It tl 7 16 Correction from sounding and curves. 30 RECORD AND REDUCTION OF THE TIDES. Series III. — Tidal Observations from April 2 0 TO August 3, 1854. Hourly observations on the pulley-gauge. Adopted reading of mean level 7.0 , expressed in units | of the scale Increasing numbers indicate rise of water. May, 1854. Mean 10th. Red. iRef. 11th. Red. Ref. 12th. Red. Ref. 13th. Red. Ref. 14th. Red. Ref 15th. Red. Ref. solar to obs. to obs. to obs. to obs. to obs. to obs. hour. level. level. level. level. level. level. 17.0 tt 10.8 20.6 —6.7 13 9 1 12.5 —6.0 6.5 16.5 —6.3 10.2 17.4 —6.3 11.1 17.3 —6.5 10.8 18.3 —6.7 11.6 20.6 19.7 ii 13.9 13.0 2 9.8 (( 3.8 13.7 It 7.4 16.0 " 9.7 16.1 (( 9.6 16.2 tt 9.5 18.8 li 12.1 3 9.5 li 3.5 11.5 It 6.2 13.7 " 7.4 15.3 {( 8.8 12.3 tt 5.6 17.6 11 10.9 4 8.3 8.2 (C (( 2.3 2.2 9.6 8.2 tt 3.3 1.9 10.8 " 4.5 14.0 tt 7.5 9.9 It 3.2 16.5 it 9.8 5 8.0 8.0 2.0 2.0 8.3 7.7 16. 0 10.0 16.1 10.1 14.9 8.9 12.3 6.3 0) 21.3 7.0 20.0 5.4 22.2 7.3 14.0 8.2 16.1 10.1 16.0 10.0 15.9 9.9 .i: 20.2 5.9 1 14.2 8.4 16.0 10.0 16.0 10.0 16.0 10.0 14.1 8.1 b 19.1 4.8 19.6 5.0 20.1 5.2 13.1 7.3 16.0 10.0 14.4 8.4 19.1 4.8 19.0 4.4 2 12.1 6.3 15.2 9.2 15.3 9.3 16.0 15.1 10.0 9.1 15.2 15.2 9.2 9.2 (» s 19.1 19.3 4.8 5.0 19.3 4.7 19.4 19.7 4.5 4.8 b 10.2 4.4 13.2 7.2 13.2 7.2 14.2 8.2 15.2 14.4 9.2 8.4 O 20.2 5.9 19.3 4.7 20.4 5.5 4 8.0 7.8 2.2 2!o 10.0 4.0 11.0 5.0 13.3 7.3 14.3 8.3 a 21.3 7.0 20.0 5.4 21.2 6.3 5 7.11 7.0 1.2 1.2 8.7 7.8 2.7 l.S 10.0 4.0 — 13.0 7.0 22.1 7.7 21.1 6.5 (! 7.0 1.7 7.2 7.2 1.2 1 2 8.7 8.0 2.7 2.0 ... 12.8 6.8 23.2 23.4 8.8 9.0 22.4 7.8 7 10.1 4.2 7.5 1.5 7.2 7.2 1.2 1.2 9.0 8.7 3.0 2.7 23.6 23.6 9.2 9.2 23.6 9.0 3 S 13.1 7.2 9.0 3.0 7.6 1.6 8.4 2.4 23.6 23.3 9.2 8.9 23.9 24.0 9.2 9.3 1 y I.^kO 9.1 10.5 4.5 9.2 3.2 ... 8.5 8.9 2.5 2.9 22.9 8.5 24.0 23.4 9.3 8.7 en a 10 17.0 11.1 13.9 7.9 12.2 6.2 ... 9.0 3.0 22.1 7.? 23.4 8.7 OS 11 18.(i 19.0 12.7 13.1 16.8 10.8 16.8 10.8 --- ... 11.5 5.5 21.4 7.0 23.4 8.7 M Midn't 19.5 13.6 19.0 13.0 18.2 12.2 13.2 7.2 20.3 5.9 21.3 6.6 July 10. Correction — 5.8 July 11. Correction — 6.0 " 12. " — 6.0 " 13. '' — 6.0 " 14. " — 6.0 " 15. " ? " 18. " —14.3 " 19. " —14.6 " 20. " —14.9 304625 38 RECORD AND REDUCTION OF THE TIDES. Series III. — Tidal Observations from April 20 to August 3, 1854. Hourly observations on the pulley-gauge. Adopted reading of mean level 7.0, expressed in units of the scale. Increasing numbers indicate rise of water. July, 1854. Mean 2Sth. Kef. solar obs. hour. 1 2 o a 3 >f 4 "B a 5 G O a 7 8 o 9 a o 10 11 o Noon S.3 7.6 9.1 8.4 1 9.2 8.5 9.3 8.G 2 9.3 8.6 9.3 8.6 3 9.2 8.5 4 7.4 6.8 5 .5.5 4.0 G 3.7 3.1 7 2.0 2.3 2.7 2.1 8 2.G 2.0 3.0 2.4 9 3.2 2.7 10 5.4 4.0 11 G.4 5.9 Midn't 9.0 8.5 29th. Kef. obs. 10.6 11.3 12.3 12.5 11.3 10.2 8.4 6.1 3.0 2.3 2.0 2.0 2.2 3.5 4.8 7.2 9.2 10.2 11.3 11.4 11.5 11.0 10.0 7.8 4.2 3.4 3.3 4.0 4.9 6.0 8.0 10.1 10.8 11.8 12.0 10.8 9.7 8.0 5.7 2.6 1.9 1.7 1.7 1.9 3.2 4.5 G.9 8.9 9.9 10.0 11.2 11.3 10.8 9.8 7.6 4.1 3.3 3.2 3.9 .3.9 5.0 7.0 30th. Kef. obs. lO.G 11.2 11.2 11.2 11.2 11.0 10.8 10.2 6.4 5.1 3.2 3.2 3.2 3.3 3.4 4.2 6.1 7.0 8.3 8.5 9.2 9.0 8.3 6.0 5.1 4.3 4.1 4.1 4.1 5.0 5.2 6.4 10.5 11.1 11.1 11.1 11.1 11.0 10.8 10.2 8.5 6.4 5.1 3.2 3.2 3.2 3.3 3.4 4.2 6.1 7.0 8.3 8.5 9.2 9.0 8.3 6.0 5.1 4.3 4.1 4.1 4.1 5.0 5.2 C.4 31st. Kef. obs. 8.3 8.6 0.3 10.6 4.0 5.2 5.5 6.2 7.5 8.0 9.0 9.0 9.0 9.0 9.0 0.1 8.0 6.6 5.4 4.8 4.8 4.8 4.8 4.8 4.8 5.1 5.6 8.3 8.6 9.3 10.6 4.0 5.2 5.5 6.2 7.5 8.0 9.0 9.0 9.0 9.0 9.0 9.1 8.0 6.6 5.4 4.8 4.8 4.8 4.8 4.8 4.8 5.1 5.6 August, 1854. 1st. 8.0 8.4 9.1 9.3 9.3 9.2 9.0 0.0 9.0 7.5 5.5 4.6 4.4 4.4 4.4 4.4 4.4 4.4 5.0 5.7 7.0 S.7 9.5 10.4 10.4 10.4 10.4 10.2 9.0 6.2 6.0 6.0 6.0 6.2 6.5 Kef. obs. 8.0 8.4 9.1 9.3 9.3 9.2 9.0 9.0 9.0 7.5 5.5 4.6 4.4 4.4 4.4 4.4 4.4 4.4 5.0 5.7 7.0 8.7 9.5 10.5 10.5 10.5 10.5 10.3 9.1 7.5 G.3 6.1 G.l 6.1 6.4 6.7 2d. 6.8 8.0 8.7 9.0 10.2 9.1 7.4 6.4 5.0 4.2 4.1 4.1 4.1 4.1 4.3 4.8 5.9 6.4 6.8 7.0 8.2 9.1 9.0 0.0 0.0 7.4 G.2 5.8 5.6 Kef. obs. 7.0 8.2 8.9 9.3 10.5 9.4 7.8 6.8 5.4 4.6 4.5 4.5 4.5 4.5 4.7 5.2 6.3 C.8 7.2 7.4 8.6 9.5 9.4 9.4 9.4 7.8 6.6 6.2 6.0 3d. 5.3 5.5 6.0 G.5 7.3 8.2 8.4 8.4 8.4 8.4 8.4 7.7 6.0 4.4 3.4 3.4 3.4 3.2 3.2 3.2 3.2 4.0 4.5 6.2 7.4 8.2 8.8 9.0 9.0 9.0 9.0 9.0 8.2 7.3 6.0 Kef. obs. 5./ 5.9 G.4 GO 7.7 8.6 8.8 8.8 8.8 8.8 8.8 8.1 6.4 4.8 3.8 3.8 3.8 3.6 3.6 3.6 3.6 4.4 4.9 6.G 7.8 8.6 9.2 9.4 9.4 9.4 9.4 9.4 8.6 7.7 6.4 Between the 20th and 27th of .Tnly the observations do not appear sufficiently regular to promise any reliable results. .Inly 28. Correction —0.7 July 29. Correction —0.3 -Tuly 30. Correction 0.0 Aug. 2. +0.4 31. " 0.0 Aug. 1. " —0.0 Aug. 3. " +0.4 After this date tlie observations are irregular. On the 5th the rope slipped off the wheel. Aug. 8. The brig was released from the ice cr.adle at 10 A. M., rising suildmily '2\ feet position upon very slight disturbance of the external ice, and is now on an even koul for the first time in cloven months. The brig was frozen in .and fast since thci Olh of September, 1853. Aug. 10. Tint high-water mark was out on the island by Mr. McGary. Aug. 11. The warping of the ships was commenced. Tidal observations were resumed on the 12tli. register is kept in fathoms and feet. She resumed thi Tlio RECORD AND REDUCTION OE THE TIDES. 39 Series IV. — Tidal OisbEiivATiONs from Septemiser 1 to October 22, 1851. 1 Hourly observations on the pulley-gange. Adopted reading of mean level 7.0, expressed in units | of the scale. Increasing numbers indicate rise of water. i September, 1854. Mean solar hour. 7th. 8th. 9th. 10th. lltb. 12th, 13th. 14th. 16th. 17th. 18th. 19th. 20th. 21st. 22d. 23d. 24th. 25th. 26th. 27th. 1 10.0 13.5' 13.0 10.0:10.0 8.0 6.0 ... 5.0 7.0 9.0 9.0 10.0 11.2 12.0'll.O 13.0 13.0 10.0 2 5.0 13.5' 11.0 11.0 114.0 9.0 7.0 5.0 6.0 8.0 7.5 8.0 9.0 10.0 10.0 14.0 11.0 12.0 3 2.0 11. Oi 7.0 11.0 ll.OilO.O 4.0 6.0 6.0 7.0 5.0 6.0 4.0 7.0 8.0 10.0 10.0, 10.0 4 —1.0 7.0 4.7 9.0 9.0 9.0 3.0 7.0 5.0 5.0 3.0 5.0 3.0 3.0 6.0 7.0 8.0' 8.0 .5 —1.7 5.0 3.0 7.0 6.0 6.0 4.0 8.0 6.0 5.0 2.0 4.0 2.0 0.0 3.5 4.0 6.0 i 4.0 (i —1.7 3.0 1.0 5.0 4.0 4.0 5.0 9.0 7.0 7.0 4.0 5.0 3.0 —0.7 2.0 3.0 3.0 2.01 7 —1.0 2.2 —1.0 3.0 2.0 0.0 6.0 9.0 9.0 8.0 6.0 6.0 5.0 2.0 2.0 2.0 0.0 0.0 1 s 0.0 1.0—1.0 0.0 0.0 1.0 8.0 ... 9.0 8.5 10.0 7.0 7.0 6.0 4.0 2.0 0.0 1.0 —1.0 9 2.0 4.0 0.0 0.0 1.0 2.0 9.0 8.0 7.5 10.0 8.0 8.5 8.0 7.0 5.0 1.0 3.0-j 1.0 10 - - - 9.0 5.0 4.0 2.0 3.0; 3.0I10.0 6.0 9.0 9.5 9.0 10.0 10.0 lt1.0 10.0 3.0 4.0 3.0 11 14.0 6.5 4.0 4.0 i 5.0 4.0 4.0 5.0 7.0 8.5 9.5 11.5 12.5 11.012.0; 6.0 7.0 6.0 Noon 12.0 11.0 7.0 7.0! 6.0 4.0 5.0 6.5 8.0 10.0 13.0 13.0 13.0 I12.5 10.0] 9.0 1 11.0 13.0 9.0 9.0 3.0 8.0 5.0 5.0 6.0 7.5 9.0 10.0 11.0,12.0:13.0 12.0 10.0 14.0 c 1 '2 10.0 10.0 11.0 10.0 4.0 9.0 0 7.0 6.0 5.5 7.0 6.0 8.0 10.0 10.0112.0 13.0 12.0 3 ... 8.0 7.0 9.0 8.0 9.0 9.0 0 8.0 7.0 5.0 6.7 4.0 0.0 6.0 7.0 9.0 11.0 11.0, 13.0 4 6.0 4.0 6.0 9.0,10.0 9.0 & 9.0 8.0 7.0 6.5 2.0 1.0 3.0 5.0 6.0 7.0 9.0 10.0 5 4.0 2.0 .-- 10.0 8.0 9.0 CO 8.0 9.0 8.0 6.0 3.0 1.5 1.0 1.0 3.0 6.0 6.0 9.0 0 2.0 O.C ... 10.5 4.0 6.0 a 0 7.0 10.0 9.0 5.0 4.0 3.0 2.0 0.0 2.0 4.0 4.0 7.0 7 1.0 —0.5 9.0 1.0 4.0 o3 8.0 10.0 10.0 8.0 6.0 4.0 3.0 0.0 1.0 2.0 3.0 3.0 8 0.0 —0.5 5.0 0.0 3.0 > 9.0 10.4 10.5 11.0 8.0 7.0 5.0 4.0 2.0 0.0 0.0 0.0 0 11.0 5.0 4.9 2.0' 1.5 1.5 4.0 CD '2 10.0 10.0 10.5 11.5 10.0 9.5 7.5 5.0 5.0 1.0 1.0 10 13.0 8.0 6.C 1.0 3.0 3.0 5.0 § 9.0 10.0 12.0 12.0 12.0 12.0 11.5. 8.0 8.0 4.0 4.0 11 14.5 11.0 lO.C 7.0 7.0 5.6 54 8.0 10.4 11.0 12.6 13.0 14.0 10.0 9.0 11.0 7.0 6.0 Midn't 14.2 13.0 12.C 10.0 8.6 7.0 7.0 6.6 9.0 10.0 11.6 11.0 13.0 9.0 10.0 12.0 9.5 8.0 Se pt. 1854. October, 1854. Mean solar hour. 2Sth. 29th. 30th. 1st. 4th. 5th. 6th. 7th. 8th. 9th. 10th. nth. 12th. 15th. 17th. 18th. 19th. 20th. 21st. 22d. 1 <1.0 8.0 ... 9.0 6.0 10.0 12.0 14.0 8.0 13.0 10.0 8.5 6.0 5.0 --- 6.0 i 5.0 ... 2 12.0 10.0 8.0 4.0 7.0 10.0 12.2! 7.0 '12.0 14.5 7.0 4.0 4.0! 4.0 3 13.0 9.0 8.0 6.0 0.0 5.0 7.0 7.0; 4.0 10.0 9.0 10.0 8.0 3.0 3.0 1.0 3.0! 0.5 1.0 4 10.0 S.O 9.0 1.2 3.0: 4.0 5.0 2.0 7.0 8.0 7.0 10.0 4.0 4.0 0.0 2.0 1 0.0 0.0 5 9.0 8.0 8.0 1.0 -1.0, 2.0 2.0 1.0 4.0 4.0 5.01 9.0 5.0 6.0 2.0 1.0 1 1.0 0.5 G 5.5 7.0 7.0 0.0 0.4 1.0 1.0 0.0 0.0 2.0 4.0! 8.0 6.0 6.4 3.0 3.0 2.0 1.5 7 3.0 6.0 6.0 4.0 4.0 4.0 1.0 0.0 0.0 1.0 1 1.0 3.0 7.0 7.0: 7.0 6.0 5.0 3.0 1.0 8 1.0 4.0 5.0 c 5.0 7.0 7.0 5.0 —1.0 0.5 1.5; 0.0 2.0 6.0 8.0 I S.O 9.0 7.0! 6.0 3.0 9 2.0 3.0 5.0 3 10.0 10.0 10.0 8.5 7.01 7.0 2.5 2.0 3.5 5.0 9.0 11.0 12.0 10.0' 8.0 7.0 10 3.0 2.0 4.0 too 4) 10.0 11.0 11.5,11.5 9.0 10.0 5.0 5.5 5.0 4.0 10.0 10.0 11.5 ii.o;ii.o 10.0 11 7.0 4.0 3.0 9.0 12.0 12.0 13.0 11.210.0 7.0 11.0 6.0 3.0 8.0 8.0 10.0 12.0 12.0 13.0 Noon 9.0 6.0 4.0 Oi 8.0 13.0 12.0il4.0 13.012.0 10.0 13.0 8.0 4.0 6.0 7.0 8.0 10.0 12.0 13.0 1 12.0 7.0 6.0 a 6.0 7.0 12.0:13.0 13.0 13.0 il3.0 14.0 10.0 5.2 5.0 6.0 7.5 8.0 10.0 12.0 2 10.0 9.0 7.0 '•3 4.0 4.0 8.5 9.0 12.014.0 14.0 13.0 13.0 5.0 4.0 5.0 4.0 3.0 7.0 9.0 3 11.0 10.0 8.0 a 13 2.0 2.0 7.0; 5.0 8.0: 9.0 12.5 12.0 14.0 6.0 3.0 2.0 1.0 0.5 : 4.0 4.0 4 12.0 11.5 9.0 S 0.0 0.0 3.0 3.0 3.0 7.0 9.0 10.0 14.0 7.0 4.0 2.0 1.0 0.0 1 2.0 1.5 5 10.0 11.0 10.0 0.0 —2.0 1.0 0.0 2.0' 5.0 8.0 7.0 11.0 i 8.0 5.0 3.0 2.0 1.0! 0.0 0.0 6 S.O 11.0 10.0 5.0 3.0 0 0 0.0 1.0 3.0 4.0 4.0 9.0 9.0 7.01 4.0 6.0 3.0 1.0 1.0 7 CO 9.0 9.0 9.0 7.0 — O.5I 2.0 0.0 1.0 2.0 3.0 7.4 9.0 7.0! 7.0 7.0 4.0 1.0 3.0 s 4.0 6.0 8.0 10.0 9.0 0.0 5.0 1.0 0.0 0.5 2.0 6.0 10.0 7.0 9.5 8.0 7.0 3.0 7.0 ;i 2.0 3.0 7.0 12.0 13.0 9.0' 7.0 4.0 3.0 3.0 3.0 4.0 8.0 1 8.0!l2.0! 9.0 8.0 7.0 10.0 10 3.0 4.0 5.5 13.0 13.2 12.0 10.0 6.0 5.5 4.0 4.0 6.0! 6.011.0 10.0 10.0 9.0 10.0 12.0 11 5.0 5.5 5.0 14.0 14.0 14.0 13.6 9.0 8.0 7.0 7.0 8.0 5.0 8.0: 7.0,10.0 9.0 12.0 13.0 Midn't 6.0 5.5 4.5 13.0 14.0 13.6 14.0 10.011.0 1 10.0 10.0 10.0 7.0 7.0 6.0 11.0 11.0 11.0 1 11.0 Not [•E. — The above numbers were taken from the record, converting tlie fathoms into feet and deducting 8, in order to reduce tlie mean level of 15 feet to the adopted level of comparison of 7 feet. Tlie observations are takei with tlie sonnding line ; bottom weedy. Sei t. 8. Some doubt about tlie time between 1 and 5 P. M. Aft er October 22 the soundings are too irregular, and later observations with the pulley -gauge too much affect ed by changes of the index. Th s last series is considerably inferior in accuracy to the three preceding series. 40 RECORD AND REDUCTION OF THE TIDES. Reduction of Tides, Van Rensselaer Harbor, 1853-'54. Having given the tidal record in a form ready for use, the observations next require to be properly tabulated for the pui-pose of deducing empirically their laws, and for comparison with theory. In the United States Coast Survey two blank forms are in use for this tabulation; they have in their essential part been adopted as suitable for the Van Rensselaer Harbor tides, and were used Avith permission of the Superintendent of the Survey. They are strictly applicable only for such cases where the diurnal inequality is comparatively small, or is at least not approximating to the production of single day tides. In order to show, at a glance, the general character of the tides under discussion, they were plotted a second time, and are given in Plates I, II, and III; the observations having previously been referred to the same mean level. From these diagrams it appears that the diurnal inequality is not of so great an effect as to render the use of the ordinary method of reduction unavailable ; on the other hand, it is sufficiently large to require a special discussion for time and height. The extension of the series of observations over a whole year must be considered as a fortunate circumstance, since the results thereby gain considerably in accuracy over others deduced only from a few disconnected lunations. The tidal record would not be complete without the observations for direction and force of the wind, and for atmospheric pressure ; the reader will find these records in ray discussion of the meteorological material of the expedition, in Vol. XI, Smithsonian Contributions to Knowledge, 1859. The following pages contain the first tabulation of the preceding record, viz: column 1 contains the date, civil reckoning, adopted for convenience sake. Co- lumn 2 gives the apparent time (civil reckoning) of the moon's superior and inferior transit over the Van Rensselaer meridian, obtained by adding nine minutes to the time of transit at Greenwich, allowing for a difference of longitude of 4'' 43*" W. The mean time was converted into apparent time by applying the equation of time. The time for the lower transit was obtained by taking the mean of the time of the preceding and following upper transit. Columns 3 and 4 contain the apparent time of high and low water, taken from the record; in some cases a graphical method was resorted to, to obtain the instant of these phases with greater precision. The equation of time has been applied to the mean time in which the observations are expressed. Columns 5 and 6 contain the lunitidal interval between the time of high water and low water, and the time of the transit of the moon immediately preceding, though in some cases, owing to the half-monthly inequality, it may be the second preceding, the establishment being about 11 1 hours. This transit of comparison has been called transit F by Mr. Lubbock,' The next columns, 7 and 8, give the height of high and low water, extracted from the preceding abstract. The remaining columns contain the moon's parallax and declination at noon. * Sec an Elementary Treatise ou the Tides, l)y J. W. Lubbock, Esq., London, 1839. RECORD AND REDUCTION OF THE TIDES. 41 Table for the Reduction of Tides. — No. 1. Showing the times of Ilifrli and TiOw "Water, and the Heights of High an d Low Tides; together with the time of the Moon's passing the Meridian of tiio place, and the Liinitidal Intervals, at 1 Van Rensselaer Harbor during the months of October 10, 1853, to October 22 , 1855. Series I. — From October 10 to December 28, 1853. Moon passes Apparent time of Lunititlal interval. Ileigllt of the meridian. Moon's parallax at noon. Moon's declination at noon. Date. 1853. Appar. time. H. water. L. water. H. water. L. water. H. water. L. water. H. M. H. M. H. M. H. M. H. 1 M. Ft. 1 Deo. Ft. Dee. Min. Dec. Degree.! Dec. Oct. 9 6 28 ... ... >•• ... ... " 10 6 7 57 26 8 G 13 13 ii 13 i's 11 45 16 16 45 8 9 6 2 4 7 58 4" —23 S " U 7 54 7 58 "i 43 12 32 18 46 6 7 "4 '4 57 8 —20 9 8 22 7 43 1 13 11 49 17 47 9 5 4 8 " 12 8 47 8 13 1 43 11 51 17 49 7 9 4 0 57 3 —17 0 9 12 9 29 2 43 12 42 18 21 10 0 4 2 " 13 9 37 9 59 3 14 12 47 18 27 9 1 3 7 56 7 —12 i 3 10 02 10 14 3 59 12 37 18 47 10 9 3 1 " 14 10 24 10 14 4 14 12 12 18 37 9 8 2 7 56 3 — 7 1 10 47 10 44 3 69 12 20 17 57 11 3 2 7 " 17 0 13 ... ... 54 9 + 8 9 0 35 11 45 5 15 11 i'o 17 02 i'o 7 i 5 " 18 0 57 6 00 17 25 ... 1 8 54 5 +13 7 1 18 6 30 17 33 12 3 2 0 " 19 1 40 0 30 6 45 ii 12 17 27 11 5 1 6 54 3 +17 9 2 02 1 15 7 15 11 35 17 35 12 4 1 9 " 20 2 25 1 15 5 45 11 13 15 43 11 5 5 7 54 2 +21 3 2 48 1 45 9 00 11 20 18 35 11 9 2 7 " 21 3 12 1 30 7 45 10 42 16 57 9 9 2 8 54 1 +23 8 3 36 3 15 8 30 12 03 17 IS 11 1 4 4 " 22 4 00 1 15 9 16 9 39 17 40 10 5 3 4 54 0 +25 2 4 25 3 16 8 46 11 16 16 46 9 9 4 5 " 23 4 51 3 16 8 31 10 51 16 06 10 3 3 9 54 4 +25 5 5 16 4 16 10 16 11 25 17 25 10 4 5 2 " 24 5 6 42 07 3 5 31 46 8 31 10 12 15 04 15 15 8 9 7 7 4 5 54 8 +24 7 » 25 6 32 5 01 "6 16 10 54 is 34 7 1 "5 "4 55 4 +22 1 6 6 57 8 16 10 46 13 44 16 39 8 5 5 2 " 26 7 22 7 46 0 31 12 49 17 59 7 0 5 1 2 56 1 + 19 5 7 46 8 46 0 46 13 24 17 49 9 2 6 1 " 27 8 11 8 16 1 46 12 30 18 24 8 1 4 8 67 0 +15 3 8 35 8 46 0 46 12 35 17 00 9 8 6 5 " 28 8 59 3 01 18 50 9 3 4 5 57 9 +10 3 9 23 9 46 3 46 12 ■47 19 11 10 8 5 1 " 29 9 47 9 46 4 01 12 23 19 02 10 7 3 4 58 8 + 4 6 10 11 10 46 4 16 12 59 18 53 11 4 4 9 " 30 10 36 12 01 3 46 13 50 17 59 11 6 2 9 59 7 — 1 5 11 01 10 46 5 16 12 10 19 05 11 7 3 9 " 31 11. 26 11 31 4 16 12 30 17 40 12 0 1 6 60 4 — 7 7 11 62 12 16 5 01 12 50 18 00 12 2 1 9 Nov. 1 11 46 4 46 11 54 17 20 12 3 2 7 60 8 —13 6 0 19 11 16 7 01 10 57 19 09 11 6 3 6 " 2 0 48 7 01 IS 42 0 9 61 0 —18 7 1 16 0 16 7 16 i'i 28 18 28 14 "3 0 1 " 3 1 46 1 16 7 16 12 00 18 00 11 8 ' 0 0 60 9 —22 7 2 16 1 31 8 46 11 45 19 00 14 2 i 1 5 " 4 2 3 47 19 1 16 8 8 01 01 11 00 17 17 45 14 11 6 0 1 3 6 60 5 —25 0 " 5 3 50 i 16 8 31 "9 57 17 12 16 i 0 7 59 9 —25 6 4 22 2 46 8 46 10 56 16 56 13 0 1 8 " 6 4 52 4 01 9 01 11 39 16 39 9 1 2 3 59 1 —24 5 5 23 4 46 10 31 11 54 17 39 10 9 2 6 " 7 5 6 52 21 3 4 46 31 10 16 10 10 23 39 16 53 8 10 2 7 3 2 58 4 —21 i 9 42 RECORD AND REDUCTION OF THE TIDES. Series I. — From October 10 TO December 28, 185S . Moon passes Apparent time of Lunitidal interval. Height of the meridian. Moo n's Moon's parallax at noon. declination at noon. Date 1S53. Appar . time. ,H. water. L. water. H. water. L. water. L. water. H. water. U. M. H. M. H. M. H. M. H. M. Ft. Dec. Ft. Dec. Min. Dec. Degree. Dee. Nov. S 6 48 5 16 0 16 10 55 18 24 7 8 3 5 57 6 —18 1 7 14 6 46 0 16 11 58 17 55 10 4 4 9 " 9 7 38 7 16 0 46 12 02 17 68 8 1 4 0 56 9 —13 5 8 02 7 31 1 16 11 53 18 02 11 0 4 4 " 10 8 25 8 46 0 46 12 44 17 08 9 8 4 3 56 3 — 8 4 8 48 9 46 2 31 13 21 18 29 10 7 5 5 " 11 9 09 10 01 2 46 13 13 18 21 9 5 2 3 55 7 — 3 1 9 31 9 31 3 31 12 22 18 43 11 8 4 2 " 12 9 52 10 01 4 16 12 30 19 07 11 2 2 8 55 2 + 2 3 10 13 9 46 3 31 11 54 18 00 11 5 3 8 " 13 10 34 10 16 4 46 12 03 18 54 11 5 2 6 54 8 + 7 5 10 54 11 15 6 15 12 41 20 02 11 0 2 5 " 14 11 15 10 45 5 0 11 51 18 26 12 7 2 1 54 5 +12 4 11 37 10 45 5 30 11 30 18 36 9 8 2 9 " 15 11 59 11 30 5 30 11 53 18 15 13 3 0 7 54 2 +16 8 12 00 6 30 12 01 18 53 13 0 3 5 " 16 0 21 12 30 5 0 12 09 17 01 13 6 0 4 54 1 +20 5 0 44 11 45 7 15 11 01 18 54 10 9 3 1 " 17 1 07 7 0 .., 18 16 1 3 54 0 +23 2 1 31 0 30 6 45 11 23 17 38 13 'o 3 1 » 18 1 55 0 45 7 15 11 14 17 44 13 7 — 0 1 54 0 +25 0 2 20 1 15 8 15 11 20 18 20 12 1 1 2 " 19 2 44 1 14 7 14 10 54 16 64 9 8 1 9 54 1 +25 7 3 09 1 44 8 14 11 00 17 30 13 0 2 3 " 20 3 34 1 44 8 14 10 35 17 06 9 1 2 6 54 4 +25 2 3 59 2 14 8 59 10 40 17 25 11 5 3 6 « 21 4 24 2 29 7 59 10 30 16 00 8 0 3 2 54 7 +23 5 4 49 2 44 11 14 10 20 18 50 10 7 3 6 " 22 5 14 2 49 8 44 10 (10 15 55 7 4 5 55 3 +20 7 5 37 3 43 11 13 10 29 17 59 10 1 3 " 23 6 6' 01 25 6 4 13 43 10 28 12 10 36 42 16 51 7 9 1 9 6 55 9 +16 9 " 24 6 48 8 13 0 43 13 48 i's 32 8 5 "3 56 8 +12 3 7 11 6 43 0 13 11 55 17 48 9 5 3 " 25 7 34 7 48 0 43 12 37 17 55 8 8 3 57 7 + 7 0 7 50 6 57 1 42 11 23 18 31 10 3 6 9 " 26 8 20 8 42 1 12 12 46 17 38 9 4 4 2 58 6 + 1 0 8 44 8 27 2 42 12 07 18 46 9 9 4 3 " 27 9 08 9 42 3 42 12 68 19 22 10 9 2 7 59 6 — 4 9 9 33 9 12 4 12 12 04 19 28 11 2 3 4 " 28 9 58 10 12 4 12 12 39 19 04 12 0 2 2 60 6 —10 9 10 24 11 11 4 41 13 13 19 08 12 S 2 6 " 29 10 51 11 41 4 41 13 17 18 43 13 8 0 7 61 0 —16 5 11 20 10 56 4 11 12 05 17 47 10 7 1 2 " 30 11 50 10 56 4 5 41 26 11 36 17 18 50 06 13 7 0 1 1 7 61 4 —21 1 D-c. ] 21 "o ii 5 41 12 21 17 51 10 "k — 1 2 61 4 —24 3 53 0 11 6 26 11 50 18 05 12 8 — 0 3 " 2 25 0 10 6 10 11 17 17 17 9 6 —2 1 61 0 —25 7 58 1 10 7 10 11 45 17 45 13 6 0 0 " 3 30 1 10 7 10 11 12 17 12 9 4 — 0 4 60 4 —25 2 03 1 55 8 40 11 25 18 10 12 8 — 0 1 " 4 32 1 54 6 39 10 51 15 36 8 3 0 1 59 6 —22 9 03 2 09 9 09 10 37 17 37 13 7 1 6 " 0 31 2 39 8 54 10 3G 16 51 9 1 1 3 58 7 —19 4 (III 3 39 9 39 11 08 17 08 11 1 1 0 " C 2t) 3 09 8 24 10 09 15 24 6 1 2 3 57 7 —14 9 :,i 4 24 11 39 10 58 18 13 10 3 1 0 " 7 11 0 :« 12 46 6 8 56 9 — 9 8 :;> T II OS 13 39 18 16 10 6 "3 "4 " 8 7 7 nil ' ■ - ' 1 0 118 38 11 45 18 18 54 00 7 6 3 2 5 9 56 1 — 4 4 • 9 7 42 "s 37 1 07 13 15 18 07 ii "2 3 I) 55 4 + 1 0 8 04 8 07 2 07 12 25 18 45 11 8 5 2 ' 10 8 25 9 37 2 07 13 33 18 25 11 1 5 3 54 9 + 6 3 8 46 9 07 2 07 12 42 18 03 9 2 5 3 RECORD AND REDUCTION OF THE TIDES. 43 Series I. — From October 1 0 TO December 28, 1853. Moon passes Apparent time of Lunitidal interval. Height of the meridian. Moon's pJira '" ^ Moon's 1 Bate. .... declinfl """ 1 Appar time. H. water. L. water. | H. water. L. water. H. water. L. water. at noon. at noon. 1 1853. H. M. H. M. H. M. II. M. H. M. Ft. Dec. Ft. , Dec. Min. Dec. Degree. Dec. Dec. 11 9 06 9 51 3 36 13 05 19 11 9 5 1 7 54 5 + 11 2 9 27 9 36 3 36 12 30 18 50 7 8 1 8 12 9 49 11 06 4 06 13 39 19 00 9 9 0 3 54 2 +15 7 10 10 11 06 4 36 13' 17 19 09 9 6 2 8 13 10 31 10 35 4 05 12 35 18 16 11 0 3 5 54 0 +19 6 10 54 10 20 4 35 11 49 18 25 8 6 2 8 14 11 17 11 05 4 35 12 11 18 04 12 5 2 3 53 9 +22 6 11 41 11 05 6 05 11 48 19 11 8 9 2 4 15 ... ... ... 5 05 ... ... 17 48 ... 2 4 53 9 + Zi 7 0 06 1 04 6 04 13 23 18 23 13 2 5 5 16 0 30 0 04 5 04 11 58 16 58 12 5 3 4 54 0 +25 6 0 65 0 19 7 19 11 49 18 49 12 8 1 6 17 1 1 20 44 0 34 6 5 03 18 11 39 17 15 08 58 7 5 2 0 7 6 54 2 +25 4 18 2 2 09 34 "i 03 7 03 i'i 19 17 19 ... 54 5 +24 0 19 2 58 "2 03 "7 32 i'i 29 17 58 ... 54 8 +21 5 3 22 1 32 8 02 10 34 17 04 ... ... 20 3 46 2 17 8 32 10 55 17 10 10 "9 "i 4 55 3 +18 0 4 09 2 47 6 02 11 01 14 16 10 4 ... 21 4 32 3 02 8 31 10 53 16 22 11 6 ■4 5 55 9 +13 7 4 54 3 46 9 31 11 14 16 59 11 5 4 4 22 5 17 4 31 9 16 11 37 16 22 9 1 5 1 56 5 + s 7 5 39 4 31 11 01 11 14 17 44 11 6 4 2 23 6 01 5 31 11 30 11 52 17 51 7 5 3 1 57 4 + 3 2 6 24 4 30 11 30 10 29 17 29 8 8 2 9 24 6 47 7 00 ... 12 36 7 8 58 3 — 2 6 7 10 6 30 0 00 11 43 17 36 9 3 "4 6 25 7 34 8 00 1 15 12 50 18 28 8 0 2 4 59 2 — 8 5 7 59 7 30 0 15 11 56 17 05 7 3 4 1 26 8 23 8 29 1 44 12 30 18 10 11 5 3 2 60 0 —14 1 8 50 8 14 2 44 11 51 18 45 9 2 4 8 27 9 18 9 28 1 59 12 38 17 36 11 2 1 8 60 7 —19 1 9 46 9 28 3 58 12 10 19 08 9 1 2 9 2S 10 16 10 13 3 28 12 27 18 10 11 6 1 9 61 2 —22 9 10 48 10 58 4 58 12 42 19 12 10 6 4 9 Series II. — Fi lOU Jani JARY 28 TO April 7, 1854. Jan. 27 10 11 58 30 ... ... ... ... ... ... 60 7 —25 0 (( 28 ... 0 17 5 17 13 19 18 i'9 10 "g "i 0 60 4 —22 5 0 01 0 17 6 17 12 47 18 47 12 4 2 6 (t 29 0 31 0 17 6 17 12 16 18 16 11 9 1 3 59 9 —18 6 1 01 0 2 8 02 11 31 19 31 13 3 — 1 8 (( 30 1 27 0 16 6 01 11 15 17 00 9 0 0 5 59 1 —13 7 1 55 1 16 7 46 11 49 18 19 13 9 — 0 4 (( 31 2 20 0 46 7 16 10 51 17 21 9 7 — 0 3 58 2 — 8 1 2 45 1 16 8 16 10 56 17 56 13 7 1 5 Feb. 1 3 08 f) 46 8 46 12 01 18 01 11 1 1 3 57 3 — 2 4 3 32 2 46 9 01 11 38 17 53 12 9 2 1 11 2 3 54 4 01 9 01 12 29 17 29 10 0 2 0 56 4 + 3 3 4 16 2 46 10 01 10 52 18 07 10 6 0 3 U 3 4 38 4 01 8 46 11 45 16 30 8 5 3 4 55 6 + 8 7 5 00 3 46 9 31 11 08 16 53 8 6 2 2 11 4 5 21 4 46 9 01 11 46 16 01 9 2 3 8 55 0 +13 6 5 43 5 16 12 16 11 55 18 55 8 9 3 8 11 5 6 06 6 16 12 16 12 33 18 33 10 5 5 0 54 5 +17 8 6 28 5 16 11 46 11 10 17 40 10 7 4 5 It 6 6 51 8 16 11 46 13 48 17 18 9 5 3 8 54 3 +21 3 7 14 8 01 11 16 13 10 16 25 7 2 3 7 It 7 7 38 7 46 ... 12 32 ... ... 9 4 ... 54 1 +23 9 8 02 7 31 "3 01 11 53 19 47 8 2 5 8 u RECORD AND REDUCTION OF THE TIDES. Series 11. — Fkom January 28 TO April 7, 1854. Moon passes Apparent time of Lunitidal interval. Height of the meridian. Moon's Moon's Date. parallax declination Appar. time. H. water. L. water. H. water. L. water. H. water. L. water. at noon. at noon. 1854. H. M. H. M. H. M. H. M. H. M. Ft. Deo. Ft. Dec. Min. Deo. Degree. Deo. Feb. 8 8 26 10 ! 01 2 46 13 59 19 OS 9 5 4 / 54 1 +25 4 8 50 9 15 3 15 12 49 19 13 6 7 3 3 9 9 15 10 15 3 15 13 25 18 49 9 7 3 S 54 3 +25 7 9 41 9 45 4 45 12 30 19 55- 7 2 3 3 " 10 10 06 10 15 6 15 12 34 21 00 9 2 3 7 54 6 +24 9 10 32 11 45 5 15 13 39 19 31 6 6 1 5 " 11 10 57 11 45 5 00 13 IS 18 54 10 5 1 3 54 9 +22 8 11 22 11 45 4 45 12 48 18 13 7 7 1 8 " 12 11 46 10 45 5 00 11 23 18 03 11 5 2 8 55 4 + 19 8 11 15 6 30 11 29 19 08 8 4 2 3 " 13 0 i'o 11 15 5 45 11 05 17 59 12 6 0 7 55 8 +15 6 0 33 10 45 5 15 10 12 17 05 10 6 4 1 '' 14 0 58 6 46 18 13 2 4 56 3 +10 7 1 21 0 46 7 16 11 48 18 18 13 • 6 2 6 " 15 1 44 0 31 6 46 11 10 17 25 11 8 3 2 56 8 + 5 3 2 06 1 16 7 46 11 32 18 02 12 9 4 1 1 " 16 2 29 0 16 7 46 10 10 17 40 13 1 2 2 57 3 — 0 3 2 51 2 01 8 16 11 32 17 47 13 1 2 3 „ 17 3 14 3 16 7 16 12 25 16 25 12 6 3 9 57 7 — 6 0 3 37 9 16 18 02 11 7 0 3 " IS 4 00 3 01 9 01 i'i 24 17 24 10 6 2 7 58 2 —11 7 4 24 2 16 9 16 10 16 17 16 10 2 3 0 " 19 4 49 3 16 10 46 10 52 IS 22 11 3 4 5 58 7 —16 8 5 16 3 16 10 16 10 27 17 27 10 7 3 0 " 20 5 6 42 10 3 3 46 46 9 16 10 10 30 04 16 00 10 10 8 7 5 5 59 1 —20 9 " 21 6 7 39 09 Hi 46 ... 17 36 '4 "3 59 5 -24 1 " 22 7 40 59 8 —25 7 8 10 "7 46 '4 16 12 06 21 07 "9 i "4 "7 " 23 8 41 10 16 2 46 14 06 19 06 10 7 4 1 59 9 —25 6 9 12 8 41 4 46 12 05 20 36 8 9 5 7 " 24 9 45 9 17 1 17 12 05 16 36 10 3 3 3 59 9 —23 7 10 15 10 17 3 47 12 32 18 35 9 7 2 8 " 25 10 45 10 17 3 47 12 02 17 52 11 2 2 8 59 6 —20 3 11 13 10 47 4 17 12 02 18 02 10 4 2 0 " 26 11 41 12 47 4 47 13 34 18 02 11 9 1 0 59 2 —15 7 11 47 6 02 12 06 18 49 11 3 3 0 " 27 0 07 11 47 5 02 11 40 17 21 12 7 — 0 4 58 6 .—10 3 0 33 11 47 6 02 11 14 17 55 10 3 — 0 9 " 28 0 57 12 32 6 17 11 35 17 44 13 0 0 1 57 9 — 4 5 1 22 11 47 7 02 10 25 18 05 12 4 1 1 March 1 1 45 7 02 17 40 0 5 57 1 + 1 4 2 09 "i 32 8 47 11 47 19 02 12 "9 1 3 " 2 2 31 1 18 7 48 11 09 17 39 12 0 2 5 56 4 + 7 0 2 53 1 33 9 18 11 02 18 47 13 0 1 9 3 3 15 2 03 8 18 11 10 17 25 10 6 2 5 55 7 +12 2 3 38 2 18 9 03 11 03 17 48 10 9 1 5 4 4 00 3 03 7 48 11 25 16 10 11 1 3 9 55 0 +16 7 4 23 2 48 8 48 10 48 16 48 11 1 1 0 5 4 46 3 48 8 48 11 25 16 25 9 2 3 1 54 6 +20 5 5 09 3 03 9 48 10 17 17 02 10 1 3 9 6 5 32 4 18 10 03 11 09 16 54 10 5 6 1 54 3 +23 4 5 56 5 19 10 34 11 47 17 02 9 6 4 1 7 6 6 22 47 4 49 10 49 10 53 16 53 8 8 5 8 54 2 +25 3 9 8 8 03 28 ... +25 5 " 10 8 53 "9 49 "4 21 13 21 20 18 "9 9 "3 y 54 9 +23 8 9 18 10 50 4 35 13 57 20 07 8 8 5 (1 " 11 9 10 42 08 10 50 4 35 13 32 19 42 10 6 5 4 55 4 +21 0 " 14 11 II 43 06 12 21 .A i'2 1 ir, ... 11 "2 + 7 1 RECORD AND REDUCTION OP TTIE TIDES. 45 Series II — From January 28 to April 7, 1854. Moon passes Apparent time of Lunitidal interval. Height of the meridian. Moon's Moon's 1 Date. parallax declin ition 1 1854. Appar . time. H. water. L. water. H. water. L. water. H. water. L. water. at noon. at noon. 1 H. M. H. M. H. M. H. M. H. M. Ft. Deo. Ft. Deo. Min. Dec. Degree. Deo. Mar. 1.5 0 0 29 52 11 21 6 8 21 06 10 52 18 19 15 37 12 7 2 2 3 7 57 6 + 1 2 " It; 1 15 "6 36 8 21 11 44 19 29 i'o 5 3 2 58 1 — 4 6 1 38 1 21 6 36 12 06 17 21 8 4 3 0 " 17 2 02 1 36 8 21 11 58 18 43 12 0 0 7 58 5 —10 5 2 26 8 21 ... 18 19 10 4 1 2 " 18 2 52 "i 52 9 22 n 26 18 56 12 1 1 6 58 8 —15 8 3 18 1 52 8 07 11 00 17 15 9 5 3 1 " 19 3 44 2 22 7 52 11 04 16 34 12 3 2 7 59 0 —20 4 4 12 2 37 8 37 10 53 16 53 10 7 2 6 " 20 4 40 4 22 12 10 ... 12 4 59 2 —23 8 ** 22 7 11 ... ... —26 0 " 23 7 42 7 23 12 12 ... 9 5 59 2 —24 6 8 12 8 23 "i 53 12 41 18 42 8 5 "5 3 " 24 8 42 7 64 2 09 11 42 18 27 10 2 4 8 59 0 —21 6 9 11 10 39 2 24 13 67 18 12 9 2 5 3 " 25 9 39 9 54 3 64 12 43 19 12 10 3 5 1 58 7 —17 5 10 05 9 54 3 54 12 15 18 43 9 6 4 3 " 26 10 31 9 24 4 24 11 19 18 45 11 7 3 8 58 3 —12 4 10 65 11 24 4 39 12 53 18 34 11 4 3 4 " 27 11 19 10 64 4 54 11 69 18 23 11 9 2 2 57 8 — 6 7 11 43 11 25 5 25 12 06 18 30 10 9 1 3 " 28 0 07 11 25 5 6 65 25 11 42 18 18 36 42 12 0 2 — 1 0 3 67 3 — 0 8 ** 29 0 29 0 40 6 26 12 33 18 18 12 "6 3 5 66 7 + -i 9 0 52 0 40 6 25 12 11 17 56 14 5 — 0 2 " 30 1 14 1 55 7 55 13 03 19 03 12 5 3 3 56 1 + 10 4 1 36 0 0 7 41 10 46 18 27 13 5 1 3 " 31 1 59 1 41 7 56 12 05 18 20 11 5 1 5 55 5 +15 3 2 22 1 56 8 56 11 67 18 67 13 0 3 3 April 4 5 11 54 3 +26 1 5 36 3 57 i'o 12 io 46 17 oi 9 "3 "4 "2 5 6 01 5 42 10 42 12 06 17 06 9 7 5 0 54 3 +26 1 6 27 5 42 10 42 11 41 16 41 6 9 5 7 6 6 52 6 28 12 01 8 8 54 6 +24 8 7 17 8 58 "i 28 14 06 20 01 6 7 "e 0 7 7 41 8 13 0 0 12 56 17 08 8 6 6 5 55 0 +22 3 8 07 9 58 2 28 14 17 19 11 7 5 5 5 Series II] ' From April 20 to August 3, 1854. April 19 6 17 " 20 () 45 ... ... 58 8 —22 6 7 13 6 01 0 16 11 16 17 69 "s 1 5 1 " 21 7 41 7 31 0 31 12 18 17 46 10 0 4 5 58 4 —18 7 8 07 7 46 1 31 12 05 18 18 7 2 4 0 " 22 8 35 8 02 1 17 11 55 17 36 10 4 4 0 57 9 —13 8 8 69 9 47 3 17 13 12 19 10 9 8 4 0 " 23 9 24 8 17 3 02 11 18 18 27 10 7 4 1 57 4 — 8 5 9 47 19 17 4 32 12 53 19 33 9 6 1 8 " 24 10 10 9 02 3 32 11 15 18 08 11 1 2 5 57 0 2 6 10 32 9 32 4 32 11 22 18 45 9 9 1 7 " 25 10 11 54 16 02 5 5 32 04 11 30 19 18 22 32 12 2 1 1 6 8 56 4 + 3 1 " 2fi 11 38 4 02 ... 17 OS ... 2 6 56 0 + s 7 12 00 0 02 6 32 12 46 19 16 12 0 0 1 " 27 1 02 6 47 13 24 19 09 11 5 1 0 55 5 +13 8 0 22 0 32 5 02 12 32 17 02 12 2 2 2 " 28 0 45 ... 5 03 ... 16 41 2 0 65 0 +18 3 1 09 "i 03 7 03 12 18 18 18 li "e 2 0 " 29 1 33 0 33 7 33 11 24 18 24 13 0 2 1 64 7 +21 9 1 56 0 03 5 33 10 30 16 00 12 0 1 5 J 46 RECORD AND REDUCTION OF THE TIDES. Series III . — From April 20 to August 3, 1854. Moon passes Apparent time of Lunitidal interval. Heiglit of the meridian. Moon s parallax at noon. Moon s declination Date. 1854. Appar time. H. wat«r. L. water. H. water. L. water. H. water. L. water. at noon. H. M. H. M. H. M. H. M. H. M. Ft. Dec. Ft. Dec. Min. Dec. Degree. Dec. April 30 2 20 0 03 5 33 10 07 15 37 12 9 1 9 54 4 +24 5 2 45 0 33 5 17 10 13 14 57 11 3 1 7 May 1 3 09 1 18 9 03 10 33 18 18 12 6 3 9 54 2 + 26 0 3 34 0 33 7 03 9 24 15 54 9 4 3 7 2 3 59 2 33 9 03 10 59 17 29 12 4 1 8 54 2 +26 3 4 25 2 33 8 33 10 34 16 34 10 3 4 3 3 4 50 3 48 9 03 11 23 16 38 9 6 5 3 54 3 +25 4 5 15 3 03 9 03 10 13 16 13 9 1 6 5 4 6 5 6 7 7 39 04 14 38 4 33 ... 11 18 ... 10 5 ... ... 64 55 6 6 +23 +16 4 3 1 8 02 "e 34 0 49 io 56 17 35 8 9 "e 0 56 4 +11 4 8 25 9 34 2 04 13 32 18' 26 7 9 3 6 8 8 48 8 34 1 04 12 09 17 02 11 5 5 2 57 3 + 6 0 9 10 10 19 4 04 13 31 19 39 8 1 2 7 9 9 33 8 34 2 04 11 24 17 16 11 3 4 4 58 1 0 0 9 56 9 04 3 19 11 31 18 09 9 4 1 8 10 10 19 10 49 5 34 12 53 20 01 8 9 2 0 58 5 — 6 0 10 43 12 04 3 34 13 45 17 38 11 8 2 2 11 11 09 11 04 4 34 12 21 18 15 10 5 1 9 59 7 —12 0 11 35 10 49 5 04 11 40 18 21 13 7 1 3 12 12 02 12 04 5 49 12 29 18 40 11 0 1 0 60 2 —17 4 ... 11 34 4 34 11 32 16 59 13 1 0 9 13 "6 30 10 49 ... 10 19 ... 12 4 ... 60 5 —22 0 1 00 11 04 5 19 10 04 ie 49 13 6 i "3 14 1 30 ... ... 60 6 —25 0 2 01 "6 4 "e 19 io 34 16 49 11 "3 0 "s 15 2 33 0 49 7 34 10 48 17 33 13 9 1 7 60 4 —26 3 3 05 1 49 8 19 11 16 17 46 12 3 6 5 16 3 38 0 49 8 04 9 44 16 59 12 4 1 8 60 0 —25 8 4 09 2 34 7 19 10 56 15 41 10 4 2 3 17 4 41 2 49 9 04 10 40 16 i 55 12 8 1 8 59 4 —23 5 5 10 2 49 8 19 10 08 15 38 10 6 2 0 18 5 40 3 49 10 49 10 39 17 39 12 5 1 8 58 8 —19 8 6 07 3 49 9 19 10 09 15 39 9 6 4 2 19 6 34 5 19 11 12 ... 11 7 58 1 —15 0 6 59 6 19 0 04 11 45 17 57 10 2 "3 0 20 7 24 7 19 0 34 12 20 18 00 9 8 5 2 57 5 — 9 7 7 47 8 34 3 04 13 10 20 05 8 7 3 8 21 8 10 7 34 2 19 11 47 18 55 11 1 4 4 56 9 — 4 0 8 32 8 34 2 34 12 24 18 47 8 6 3 7 22 8 55 8 04 1 34 11 32 17 24 10 6 3 4 56 3 + 1 6 9 16 9 04 3 19 12 09 18 47 9 3 2 5 23 9 38 8 04 3 04 10 48 18 09 11 3 3 5 55 8 + 7 3 9 59 10 19 4 19 12 41 19 03 11 4 3 3 24 10 21 8 48 4 48 10 49 19 10 9 9 4 0 55 3 +12 4 10 43 11 48 4 18 13 27 18 19 12 9 2 0 25 11 05 10 18 5 03 11 35 18 42 10 0 2 0 54 9 +17 1 11 28 11 03 5 33 11 58 IS 60 10 8 2 0 26 11 51 12 45 5 03 13 17 17 58 9 7 2 7 54 6 +20 9 12 45 6 33 12 54 19 05 12 5 3 4 27 0 0 15 39 1.0 48 6 4 18 18 10 33 18 16 27 03 9 7 2 0 4 5 54 3 +23 9 28 1 04 "6 33 6 48 i'i 54 18 09 io 7 1 6 54 1 +25 7 1 29 0 03 4 48 10 59 15 44 8 7 2 3 29 1 54 0 03 7 03 10 34 17 34 10 9 1 5 64 0 +26 3 2 19 0 48 7 18 10 64 17 24 8 5 1 6 30 2 44 1 03 8 18 10 44 17 59 12 0 2 5 54 0 +25 8 3 09 2 18 6 48 11 34 16 04 8 5 2 5 31 3 34 3 18 9 18 12 09 18 09 11 5 2 5 54 2 +24 1 3 59 2 33 8 33 10 59 16 59 8 5 3 5 Juuo 1 4 22 2 18 9 47 10 19 17 48 11 0 4 0 54 6 +21 4 4 47 4 17 10 02 11 65 17 40 8 0 3 6 RECORD AND REDUCTION OP THE TIDES. 47 Series III. — I 'ROM April 20 to August 3, 1854. Moon passes Apparent time of Lunitidal interval. Height of the meridian. Moon's parallax Moon's 1 declina* Date. I'lUU 1 185-^ Appar time. H. water. L. water. H. water. L. water. H. water. L. water. at noon. at noon. | U. M. H. M. H. M. H. M. H. M. Ft. Dec. Ft. Deo. -Min. Dec. Degree. Deo. June 2 5 09 4 02 10 32 11 15 17 45 9 8 3 7 54 9 +17 6 5 32 4 47 10 17 11 38 17 08 7 8 4 8 3 5 54 ... ... ... 9 6 4 5 55 5 +13 1 () 16 "i 02 10 02 io 08 16 08 8 1 5 2 4 () 38 ... ... ... 9 4 ... 56 3 + 8 0 7 00 7 32 12 02 12 54 17 24 8 6 "5 6 5 7 22 8 02 13 02 9 7 ... 57 2 + 2 3 7 44 9 02 0 32 13 40 17 32 9 2 4 7 6 8 07 9 02 1 32 13 18 18 10 10 1 6 1 58 2 — 3 6 8 30 8 02 2 32 11 55 18 48 10 4 4 0 7 8 54 9 02 4 02 12 32 19 55 10 2 4 3 59 0 — 9 5 9 18 9 02 3 02 12 08 18 32 11 1 3 4 8 9 44 8 01 2 47 10 43 17 53 9 3 4 0 59 9 —15 2 10 10 10 01 2 31 12 17 17 13 11 6 1 8 9 10 38 ... ... 60 6 —20 1 11 07 9 01 3 01 10 23 16 51 12 9 1 4 10 11 38 10 01 5 01 10 54 18 23 11 7 2 1 61 1 —23 9 13 31 6 01 13 53 18 54 11 4 0 6 11 0 io 10 31 6 01 10 21 18 23 9 4 1 8 61 2 —26 0 0 43 13 01 6 31 12 18 18 21 13 2 2 0 12 1 16 11 31 6 31 10 15 17 48 10 4 1 6 61 1 —26 2 1 49 6 31 17 15 12 2 0 4 13 2 21 8 30 18 41 0 2 60 6 —24 5 2 52 1 00 8 00 10 39 17 39 10 3 1 1 14 3 24 1 30 7 30 10 38 16 38 12 1 1 6 GO 0 —21 0 3 53 0 30 8 00 9 06 16 36 10 3 1 3 15 4 23 2 30 9 00 10 37 17 07 12 3 1 3 59 2 —16 5 4 49 1 30 8 00 9 07 15 37 8 5 2 3 IG 5 16 4 0 9 45 11 11 16 56 11 7 2 5 58 3 —11 2 5 40 2 0 9 00 8 44 15 44 8 9 3 7 17 U 04 3 0 9 00 9 20 15 20 11 4 2 8 57 4 — 5 4 6 27 2 30 11 29 8 26 17 25 9 3 4 6 18 6 49 4. 59 11 29 10 32 17 02 10 2 3 2 56 7 + 0 4 7 11 4 59 11 59 10 10 17 10 10 5 5 6 19 7 33 5 59 10 48 10 5 ... 56 0 + 6 0 7 54 7 29 "i 29 11 56 is 18 10 0 4 0 20 8 16 7 59, 2 14 12 05 18 41 9 9 5 2 55 4 +11 3 8 37 9 29 3 29 13 13 19 35 10 5 4 4 21 8 59 8 59 2 44 13 22 18 28 9 4 5 8 54 9 +16 0 9 22 9 29 2 59 12 30 18 22 13 0 3 0 22 9 44 9 28 2 58 12 06 17 59 9 9 2 9 54 5 +20 1 10 07 10 13 4 58 12 29 19 36 10 6 3 3 23 10 31 9 28 3 58 11 21 18 14 8 5 3 6 54 3 +23 2 10 55 11 28 5 43 12 57 19 36 11 0 2 9 24 11 19 12 13 4 28 13 18 17 57 8 1 3 6 54 1 +25 4 11 44 10 58 5 28 11 39 18 33 11 3 2 0 25 0 io 11 58 4 6 58 58 12 14 17 19 39 14 8 3 2 3 4 1 54 0 +26 3 2(5 0 35 1 13 4 58 13 03 16 48 12 "i 2 0 53 9 +26 0 0 59 0 57 6 27 12 22 17 52 9 9 2 4 27 1 24 4 57 15 58 12 3 1 9 54 0 +24 6 1 49 0 27 7 27 11 03 18 03 9 8 3 0 28 2 13 0 57 7 57 11 08 18 08 11 4 3 2 64 2 +22 1 2 37 0 57 7 27 10 44 17 14 9 2 2 5 29 3 00 1 12 7 57 10 35 17 20 11 4 3 6 54 5 41s 6 3 24 1 42 6 27 10 42 15 27 9 1 2 0 30 3 46 3 27 8 57 12 03 17 33 12 3 3 9 54 9 +14 3 4 08 0 12 7 27 8 26 15 41 9 4 3 8 July 1 4 30 4 42 9 57 12 34 17 49 11 6 2 6 55 5 + 9 4 4 52 4 57 8 57 12 27 le. 27 9 3 5 0 O 5 12 3 26 10 41 10 34 17 49 11 7 2 2 56 2 + 4 0 5 33 5 26 11 26 12 14 1 18 14 7 3 3 8 3 5 55 4 11 10 26 10 38 1 16 53 9 1 4 8 57 0 — 1 7 6 17 5 26 10 56 11 21 i 17 01 9 8 6 9 4 U 39 6 41 11 11 12 24 1 16 54 10 2 4 4 57 9 — 7 5 _ 7 02 6 56 ... 12 17 ... ... 9 8 ... 48 RECORD AND REDUCTION OF THE TIDES. Sekies III Fkom April 20 to August 3, 1854. Moon passes Apparent time of Lunitidal interval. Height of the m jridian. Moon's Moon's Date. 1854. parallax at noon. declination at noon. Appai . time. H. water. L. water. H. water. L. water. H. water. L. water. H. M. H. M. H. M. H. M. H. M. Ft. Dec. Ft. Dec. Min. Dec. Degree. Dec. July 5 7 26 6 56 0 26 11 54 17 47 10 1 6 5 58 8 —13 1 7 51 7 56 1 26 12 30 18 24 10 6 4 3 " 6 8 18 7 41 1 66 11 50 18 30 9 4 6 0 59 7 —18 3 8 45 8 56 1 26 12 38 17 35 11 2 3 9 7 9 9 14 43 7 55 2 3 55 10 11 10 18 18 37 25 9 2 5 3 6 0 60 5 —22 5 8 10 10 15 47 ... 61 1 —25 3 9 11 20 io 40 "4 40 11 53 is 25 "s "5 2 "4 61 4 —26 3 11 54 11 40 4 25 12 20 17 38 12 5 1 2 " 10 ... 12 55 5 25 12 51 18 05 8 4 2 2 61 4 —25 4 0 27 11 65 5 10 11 28 17 26 13 6 1 2 " 11 1 00 12 25 6 25 11 25 17 58 10 1 1 5 61 0 —22 5 1 31 12 55 6 10 11 24 17 10 13 3 1 2 " 12 2 2 02 31 11 40 6 7 55 10 9 38 17 17 24 08 10 1 1 1 0 2 60 3 —IS 3 " 13 3 00 i 10 7 40 io 39 17 09 13 "e 1 0 59 5 —12 9 3 26 1 25 7 55 10 25 16 55 10 0 2 4 " 14 3 52 1 55 9 10 10 29 17 44 12 6 1 8 58 5 — 7 2 4 15 2 24 8 54 10 32 17 02 9 2 2 5 " l.'i 4 39 ... 57 6 — 1 2 " 17 6 31 +10 2 " 18 6 53 ... ... 65 3 +16 1 7 16 "7 24 i 24 12 31 is 53 "9 2 4 8 " 19 7 38 8 54 13 38 • •• 7 6 4 6 54 7 +19 3 8 01 8 39 i 24 13 01 18 08 9 3 4 4 " 20 8 24 9 54 2 1 39 54 13 63 19 17 01 53 8 7 5 4 6 5 54 4 +22 6 " 27 2 04 • •• ... ... ... +15 3 " 28 2 26 ... *.. ... ... 55 2 +10 4 2 48 i 64 7 54 11 28 17 28 8 "e "2 "6 " 29 3 09 2 54 8 09 12 06 17 21 12 0 1 7 55 7 + 5 2 3 30 3 54 8 64 12 45 17 45 11 3 3 2 " 30 3 51 2 09 8 24 10 39 16 54 11 1 3 2 56 3 — 0 4 4 13 2 54 8 24 11 03 16 33 9 2 4 1 " 31 4 34 ... 10 6 4 0 56 9 — 6 1 4 56 "2 39 9 39 io 05 17 05 9 0 4 8 Aug. 1 5 19 3 24 10 39 10 28 17 43 9 3 4 ' 4 67 7 —11 6 5 43 4 39 9 54 11 20 16 35 10 5 6 ' 1 " 2 6 07 32 4 5 54 54 11 09 11 11 11 47 17 26 10 9 5 5 4 5 58 5 —16 8 3 6 59 5 54 0 54 11 22 18 47 8 8 "5 7 59 3 —21 3 7 27 8 24 1 09 13 25 18 37 9 4 3 6 Series IV -From September 1 to October 22, 185 4. Sept. 7 0 0 23 47 ii "2 ... 10 15 14 "5 ... 69 3 — 5 7 " S 1 1 12 36 11 2 5 8 32 02 9 60 16 18 45 50 14 0 — 1 0 "7 0 58 5 + 0 5 9 >) 01 "i 32 8 02 i'i 56 18 26 13 "5 1 0 57 7 + 6 6 2 24 1 32 7 32 11 31 17 31 14 0 — 0 5 " 10 2 47 1 03 7 33 10 39 17 09 13 0 — 1 0 56 9 +12 3 3 10 2 03 10 03 11 16 19 16 11 0 1 0 " 11 3 33 2 33 8 33 11 23 17 23 11 0 0 0 56 1 +17 2 3 57 9 03 17 30 10 5 1 5 " 12 4 22 "2 04 8 03 16 07 16 06 14 0 0 0 55 4 +21 2 4 46 4 03 8 03 11 41 15 41 10 0 0 0 ):; 5 11 3 04 7 04 10 18 14 18 10 0 0 0 54 8 +24 2 0 35 3 34 8 04 10 23 14 63 9 0 3 0 • 14 G (J 00 25 52 17 2 04 8 29 ... 7 0 54 5 +26 1 " ir. 7 ... ... ... ... ... +26 7 Ri:c()Hr> AN1> i; E DUCTIO X OF T II K TIDHS. 49 Series IV.— From September 7 to October 22, 185 4. Moon pn.ttses Apparent time of Lunitidal interval. Height of the meridian. 1 Moon's 1 Moon (leclinji tion Bate. 1 pariil iJl.V 1 S 'H ■§■§ Moon's transit. Lunitidal interval. H. water. Height of H. water. $■1 o c Cm a O rn Moon's transit. Lunitidal interval. H. water. Height of H. water. ii App. time. H. water. App. time. App. time. H. M. H. 1 M. Ft. Dee. H. M. H. M. Ft. '■ Dec. H. M. H. M. Ft. Dec. 0 0 0 0 0 57 19 21 5i 30 io 12 n 11 57 09 17 49 12 11 13 9 12 3 6 6 5 8 I. 40 16 07 55 58 11 12 11 11 11 35 00 23 20 12 12 11 13 12 9 4 8 0 1 4. I. 2 2 2 2 25 16 44 58 11 11 11 10 20 00 00 34 11 11 13 9 6 0 I. 2 2 2 2 2 2 45 29 09 53 02 52 12 11 11 11 ii 01 32 09 10 00 11 13 12 10 10 9 1 1 0 6 4 5 II. 0 0 0 0 0 0 0 01 10 58 33 29 07 52 12 11 11 11 10 12 13 IG 05 48 14 52 33 03 11 12 13 10 12 12 12 9 6 6 3 7 0 5 11. 01 55 44 22 15 36 11 10 11 10 12 12 15 51 32 25 06 05 9 9 12 12 8 0 7 9 4 4 II. 11 . , 2 45 2 .^3 10 11 10 10 10 9 12 33 16 44 39 35 38 06. 12 12 12 10 11 10 12 6 3 0 3 4 1 0 III. -, 09 56 30 29 16 49 00 11 10 10 10 10 11 11 24 07 34 34 15 08 25 13 12 11 10 10 11 10 0 9 3 9 4 4 1 III. 0 0 0 0 0 30 39 10 10 59 10 11 10 13 19 54 21 03 12 10 9 12 12 4 7 4 1 3 III. 2 2 2 2 2 19 21 37 02 48 0 0 0 22 46 41 12 11 11 46 26 04 12 14 13 0 0 0 IV. 2 1 01 2 47 2 39 2 21 11 11 10 11 31 16 30 52 14 11 13 14 0 0 0 0 IV. 12 07 52 33 9 12 12 11 50 01 16 10 14 11 14 13 0 0 0 0 IV. MEANS. 0 0 29 31 11 40 12 1 18 20 1 1 29 29 11 12 ii 6 22 22 2 2 32 29 11 04 ... ... 11 "s 20 20 • 52 RECORD AND REDUCTION OF THE TIDES. Table for the Reduction of Tides — No. 2. Slioning tlie Interval between the App. Time of tbe Moon's Superior Transit and the Time of Iligli Water, and also the Heights of High Water, at Van Rensselaer Harbor, from Fonr Series of Observations made between October 10, 1853, and October 22, 1854. 3" to i\ Moon's Lunitidal transit. , interval. App. time. H. water. H. I M. ! H. I M. 12 12 1 03 19 ' 9 ! 57 34 I 10 i 40 03 10 51 46 11 01 Height of H. water. Ft. 'Dec ■^ ■a !5-c: 11 '■ 1 10 I 1 11 5 8 10 32 12 14 38 11 44 10 29 25 53 10 11 11 10 I 7 34 38 09 59 24 24 00 52 30 59 56 09 19 06 03 25 32 39 12 4 10 4 11 5 11 0 10 3 12 3 10 0 9 O 11 1 III. 4'' to 5\ Moon's transit. App. time. Lunitidal interval. H. water. H. I M. M. 00 11 51 11 22 11 24 10 03 10 32 11 16 11 00 10 49 10 23 11 16 25 39 20 36 14 25 41 47 23 08 52 13 56 11 10 11 9 12 10 10 Height of H. water. Ft. Dec. App. time. H. water. II. III. s"- to e*". Moon's Lunitidal i j transit. interval. Height of H. water. H. M. H. M. Ft. Dec. >£ 42 23 14 00 12 10 10 10 52 [ 12 17 11 00 43 42 09 56 36 11 12 10 11 10 12 5 15 11 18 10 5 40 10 09 9 5 32 9 5 16 8 U 8 5 33 10 38 9 5 43 11 11 10 II. III. 3 33 3 32 io 3 10 11 10 5 12 0 14 0 IV. 22 11 27 10 00 9 51 10 IV. 11 25 10 8 23 45 9 10 0 0 IV. ME.4NS. 30 29 10 10 19 21 The highest and lowest value of tlie interval balance nearly. 4 27 10 52 4 27 io 5 21 22 27 27 10 53 19 20 The criterion rejects no value of the interval, the two high and two low values balance nearly. ■ ^*F% l»l IIWII IIWI RECORD AND REDUCTION OF THE TIDES. 53 Table FOR THE Reduction of Tides.— So. 2. Showing llic Interval between the App. Time of the Moon's Super or Trans t and the Time of High 1 Water, and also tiie Heights of High 'Water, at Van Rensselaer Harbor, from Four Scries of 1 Observations made between October 10 , 1853, and October 22, 1854. C' to 7". •7'' to S\ S"- to 9". Moon's Lunitidal ki Moon's Lunitidal a £ Moon's Lunitidal iS transit. interval. 1 Height of ^s transit. interval. Height of h^ transit. interval. Height of fe S -o'? ■il App. time. H. water. O ^ App. time. H. water. A ° App. time. H. water. A ° . H. M. H. M, Ft. Dec. >«•:: H. 1 M. H. M. Ft. i Dec. £ = H. ; M. H. M. Ft. Deo. !?.- G 28 13 45 8 0 7 j 26 12 32 6 1 7 8 ! 22 11 51 7 9 G 32 13 44 8 5 7 1 22 13 24 9 2 8 11 12 35 9 8 6 21 10 55 7 8 7 ! 14 12 02 8 1 I. 8 59 12 47 10 8 H 01- 10 42 9 9 I. 7 ' 34 11 23 10 3 8 02 12 44 9 8 G 48 11 55 9 5 7 22 13 15 11 ! 2 8 ■ 48 13 13 9 5 I. C 38 11 45 7 6 7 34 11 56 7 ; 3 8 20 12 07 9 9 6 01 10 29 43 S 9 8 3 8 8 04 46 13 13 33 05 11 9 1 5 ti 47 11 7 '14 12 32 9 i 4 7 40 7 42 7 1 17 12 12 12 06 41 56 9 i 1 8 5 8 5 8 23 11 51 9 2 G , 28 6 ' 27 13 12 48 9 01 8 5 8 11. n. 8 02 13 59 9 5 8 8 50 41 13 12 or: 9 8 »7 6 4.5 11 16 8 1 7 41 12 05 7 ; 2 05 9 II. G 34 11 45 10 2 7 38 10 56 8 1 9 8 28 13 21 9 9 G 16 • •• 9 4 7 24 13 10 8 7 8 42 13 57 9 2 i; 04 G 49 8 10 9ft a 3 5 7 i 00 7 i 44 13 13 02 18 9 10 7 1 10 I 10 III. III. 8 35 13 12 9 6 G 17 r-i 24 1 10 2 7 , 33 11 56 10 ;' 0 8 25 12 09 11 5 6 53 12 31 1 9 2 7 02 11 54 10 i 1 8 10 12 24 8 6 6 32 11 22 ; 8 8 7 51 11 50 9 i 4 8 55 12 09 9 3 III. 7 ' 38 13 01 9 3 g 5n 12 13 12 32 13 30 10 10 13 2 5 0 »; *^^ 9 42 9 0 IV. 8 ! 16 8 1 59 7 i 43 10 1 0 IV. 7 23 12 51 10 0 8 ' 45 11 10 9 2 i 8 34 11 , 32 10 4 IV. 8 57 13 18 11 0 MEANS. 6 30 11 35 IS 7 28 12 26 20 8 ' 32 12 42 24 6 29 9 i 19 7 i 29 ... ... 9 i 21 8 32 9 ! 9 24 Peirce's criterion rejects the value S"" 26"', new mean — 6 31 11 45 17 • 54 RECORD AND REDUCTION OF THE TIDES. Table for the Reduction of Tides. — Xo. 2. Showing the Interval between the App. Time of the Moon's Superior Transit and the Time of High Water, and also the Heights of High Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. 9" to 10^ 10" to ll". 11" to 12". Moon's transit. Lunitidal interval. H. water. Height of H. water. 0 a <*-. si 0 ^ 6 g Moon's transit. Lunitidal interval. H. water. Height of H. water. > -r •§1 0 yj Moon's transit. Lunitidal interval. Height of H. water. d 0 App. time. App. time. App. time. H. water. H. 1 M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. 9 9 9 9 9 9 9 12 47 31 08 58 27 18 12 12 12 12 13 13 12 47 59 30 04 13 39 10 9 11 11 11 12 9 9 1 4 2 2 5 9 1 I. 10 10 10 10 10 10 10 10 02 36 13 54 51 10 54 16 12 12 12 11 12 12 12 12 12 10 03 51 05 25 11 42 9 11 11 12 10 11 12 10 8 7 5 7 7 0 5 6 I. 26 37 50 41 12 11 12 13 50 53 21 23 12 13 10 13 2 3 8 2 I. 32 41 19 11 12 12 23 06 06 11 11 10 5 3 9 II. 9 9 10 9 2 7 6 6 II. 9 9 9 45 18 39 12 13 12 32 32 15 10 10 1(1 10 58 32 45 31 13 13 12 12 19 13 02 53 10 10 10 11 6 5 4 4 II. 38 35 05 51 07 19 54 13 12 11 12 10 11 24 29 58 54 54 39 51 11 11 10 12 11 11 8 5 0 8 5 7 3 4 III. 9 9 9 9 9 9 24 10 56 38 18 44 12 11 12 12 10 12 53 24 53 41 43 29 9 11 8 11 9 10 6 3 9 4 3 6 III. 10 10 10 43 10 ''1 11 12 13 12 11 22 21 27 57 53 9 10 12 11 8 9 5 9 0 5 III. 10 10 31 47 39 10 59 08 53 11 13 12 13 11 28 02 13 07 22 14 13' 12 11 12 0 0 0 0 0 IV. 9 9 22 41 12 11 44 34 12 12 0 0 IV. 10 10 10 10 09 55 20 24 12 12 11 57 12 21 12 13 10 11 6 0 0 0 IV. MEANS. 9 31 9 31 12 30 io "4 in 19 10 10 32 31 12 23 li "i 20 21 11 11 32 32 12 17 ... 11 7 19 19 The value lO"- 43"' i.s rejected by Peirce's criterion, and there is no corresponding high value to balance it ; the new mean becomes — ^ 9 32 12 36 ... ... 18 RECORD AXD REDUCTION OF THE TIDES. 55 Table for the Reduction of Tides No. 2. Showing tlic Interval between the App. Time of the Moon's Inferior Transit and the Time of High ■Water, and also the lleights of Iligh Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. 0" to 1\ 1" to 2\ 2'' to S\ Moon's transit. Lunitidal interval. Height of H. water. is 0 a Moon's transit. Lunitidal interval. Ileight of 1 £ 'd U. water S S Moon's transit. Lunitidal interval. Height of H. water. i s 0 0 0 „ ii App. time. H. water. App. time. H. water. = 0 App. time. H. water. H. M. H. M. Ft. Dec. n. M. H. M. Ft. Dec. n. M. H. M. Ft. Dec. 0 0 0 0 0 0 35 48 44 21 06 55 11 11 11 11 11 11 10 28 01 50 58 39 10 14 10 12 12 7 7 3 9 8 5 5 I. 18 46 31 25 44 11 11 11 11 11 12 45 14 45 19 11 14 13 13 5 2 7 6 I. 2 2 2 2 2 02 48 20 30 34 11 10 10 11 11 13 42 54 25 29 11 9 9 12 5 9 8 8 I. 1 27 21 45 38 14 59 11 11 11 11 10 11 49 10 47 58 46 57 13 11 12 12 13 13 9 8 9 0 5 0 II. 2 2 2 2 2 20 06 51 31 26 10 10 12 11 11 56 10 25 02 26 13 13 12 13 12 7 1 6 0 1 II. 0 0 0 0 0 0 0 33 07 57 06 S2 29 11 10 11 11 12 11 12 31 12 40 35 15 44 11 13 10 12 13 11 10 14 3 6 7 0 2 5 5 ir. 2 2 2 2 2 2 2 20 01 44 52 13 31 26 10 10 11 10 10 10 11 13 48 34 38 44 39 28 11 13 8 12 9 13 8 3 9 5 1 2 6 6 III. 33 00 04 54 49 24 31 10 10 10 10 i'i 11 30 04 59 54 03 24 12 13 8 8 12 9 13 0 6 7 5 2 8 3 III. 0 0 0 0 0 0 0 00 45 02 15 43 35 27 12 12 11 ro 12 12 11 32 18 32 33 18 22 28 12 11 13 9 13 9 13 2 6 1 7 2 9 6 III. 2 2 2 24 15 45 10 10 10 0 0 0 IV. 36 29 09 57 11 10 11 10 56 39 03 16 13 13 14 10 5 0 0 0 IV. 63 28 13 13 0 0 0 0 0 47 00 45 22 17 10 12 11 10 11 15 07 23 50 28 14 13 13 14 13 5 0 0 0 0 IV. MEANS. 0 0 29 29 11 34 12 "2 25 25 1 1 31 31 11 13 ... ... 12 "3 21 21 2 2 27 10 27 ... 59 ... ... 11 8 20 19 • oG R E C 0 R P AND REDUCTION OF Til E T I D E S. Table for the Reduction of Tides. — No. 2. Showing the Interval between the Ajip. Time of the Moon's Inferior Transit and the Time of High "Water, and also the Heights of High Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. 3'' to 4\ Moon's I Lunitidal transit, i interval. App. time. : H. water. 11. M M. Height of H. water. Ft. Dec. c c 4'' to 5". Moon's j Lunitidal transit. interval. I App. time, II. M. H. water. H. M. Height of H. water. Ft Deo. c o to 6\ Moon's transit. App. time. Lunitidal interval. H. water. M. H. M. Ft. Height of H. water. Dec. a 36 9 50 10 09 10 59 10 32 10 22 10 23 07 03 10 38 9 4 10 3 12 4 8 5 12 3 9 1 9 4 12 6 11 3 9 2 III. 11 0 14 0 13 0 13 0 10 0 IV. 10 11 10 11 10 11 3S 24 00 4S 12 16 10 15 52 10 39 37 12 36 26 10 58 39 11 52 III. IV. 21 11 16 10 32 11 11 10 10 10 09 11 54 10 40 9 12 12 55 11 19 11 35 8 57 10 II. III. IV. MEANS. 3 31 10 40 3 31 ... ... 11 1 26 26 The two greatest deviations from the mean, viz., 8'' 26"" and 12'' 45"', nearly balance in the mean, hence no value was rejected. 33 33 II 01 10 20 20 5 30 10 56 5 30 9 4 18 18 The criterion rejects no value of the interval ; the low value 8'' 29'" is so near the limit of rejection and not balanced in the mean that I prefer to reject It. 5 30 11 04 17 RECORD AND REDUCTION OF THE TIDES. 57 Table FOR THE Reduction of Tides. — No. 2. Showing the Iiik'i'vul IkjIwoth the A))]). I'imc of the Moon's Inferior Trnnsit and the Time of Iligli | Water, and also the Heights of High Water, at Van Rensseh er Harbor, from Four Series of 1 Observations made between October 10, 1853, and October 22, 1854. 6" to 1\ T" to 8^ S*- to S\ Moon's Lunitidal , ^ Moon's Lunitidal Moon's Lunitidal * n transit. interval. Heipht of ffe transit. interval. Heipht of transit. interval. Height of >'Z TI w»t»r j=.a 11. water. •^-^ H. water. %l App. time. H. water. c „ App. time. H. water. App. time. H. water. H. M. n. M. Ft. Dec. H. M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. 6 .'57 n 16 9 2 7 54 11 49 9 5 8 47 12 42 10 0 6 07 10 54 7 1 7 46 12 30 8 1 • 8 35 ... 9 3 6 f>7 12 49 7 0 7 38 11 53 11 0 8 25 i3 21 10 7 I. C 48 11 58 10 4 I. 7 11 12 37 8 8 1. 8 44 12 58 10 9 (i 2.5 13 48 8 5 7 56 12 46 9 4 8 25 12 42 9 2 « 14 13 39 10 6 7 42 12 25 11 8 8 50 12 38 11 2 6 24 12 3B 7 8 7 10 12 50 8 0 7 59 12 30 IX 5 s ''6 T>, 44 G 7 ft nd 11 13 10 10 10 7 7 2 g 10 14 06 10 7 6 .51 II. 7 38 11 53 8 2 8 53 13 57 8 8 II. (5 01 11 41 fi 9 7 11 12 12 9 5 II. 8 12 11 42 10 2 G .52 14 0« fi 7 7 41 14 17 7 5 8 07 11 55 10 4 fi 07 11 12 11 7 7 13 12 18 10 0 8 59 11 18 10 7 fi 59 12 20 9 8 7 47 11 47 U 1 8 02 13 32 7 9 6 .S8 12 54 8 « 7 22 13 40 9 2 8 48 13 31 8 1 C, 27 10 32 10 2 III. 7 11 10 48 10 5 III. 8 32 11 32 10 6 III. fi 39 12 17 9 8 7 54 12 05 9 9 8 07 11 55 10 4 6 07 11 47 9 5 7 26 12 30 10 6 8 54 12 OS 11 1 6 59 13 25 9 4 7 16 13 38 7 6 S S 37 IS 12 22 38 9 11 4 6 50 10 41 10 0 IV. • •• • •• IV. 8 01 13 53 8 7 6 5S 10 0 8 08 11 58 9 0 8 58 9 0 IV. 8 34 13 41 10 0 MEANS. 6 33 12 13 19 7 33 12 28 18 8 29 12 44 21 6 34 ... ... 9 1 20 7 33 ... 9 6 18 8 30 ... ... 9 7 23 There are two high and two low The high and low values in the values, viz., 14i> 00'", 13" 48'", aud interval balance. 10" 32", lOi" 41"', noarly balancing each other; tliero wa,s, thorefore, no rejection required. 58 RECORD AND REDUCTION OF THE TIDES. Table for the Reduction of Tides. — No. 2. Showing the Interval between th B App. Time of the Moon's Inferior Transit and the Time of High 1 Water, and also the Heights of High Water, at Van Rensselaer Harbor, fr ora Four Ser es of Observations made between 0 etober 10, 1853, and October 22, 1854. 9" to 10\ 10'' to 11''. 11 '■ to la"". Moon's , Lunitidal t CO Moon's Lunitirlal i i Moon's Luni tidal « i transit. 1 interval. Height of transit. interval. Height of > X transit. interval. Height of > 'z H. water. S. "' H. water. •I'S H. water. .OT3 A pp. time. H. water. "s^ App. time. H. water. <„ 3 ii App. time. H. water. ^1 H. M. H. M. Ft. Dec. II H. M. H. M. Ft. Dec. H. M. H. M. Ft. Deo. 9 37 12 37 10 9 10 24 12 20 11 3 01 12 30 12 0 9 23 12 23 10 7 10 11 13 50 11 6 52 11 54 12 3 9 09 12 22 11 8 10 34 12 41 11 0 I. 15 11 30 9 8 I. 9 S2 11 54 11 5 I. 10 24 13 17 13 8 59 12 01 13 0 9 33 12 39 12 0 10 31 11 49 8 6 20 11 36 13 7 9 9 06 49 12 13 30 17 7 9 8 6 17 n 48 8 9 10 06 13 39 6 6 9 1 46 12 27 11 6 10 57 12 48 7 7 30 12 47 12 4 10 15 !•?, 0-^ 11 9. II. 46 11 ;w K 4 9 15 12 30 •7 2 10 05 11 19 11 7 13 13 34 11 9 II. 9 9 12 11 12 05 12 43 10 10 3 3 II. 10 55 11 59 11 9 43 11 42 12 0 10 10 32 19 11 13 30 45 12 11 2 8 16 09 12 11 46 40 12 13 0 7 9 47 11 1 15 11 1 9 33 11 31 9 4 10 43 11 35 10 0 HI. 28 13 17 9 7 III. 9 16 10 , 48 11 3 III. 10 38 10 23 12 9 38 13 53 11 4 9 59 10 , 49 9 9 10 07 11 21 8 5 44 12 14 8 3 9 44 12 17 11 6 10 55 13 18 8 1 11 1 20 12 20 12 5 9 22 12 06 9 9 • 10 45 T?, 96 14 0 11 17 11 50 11 5 9 47 10 49 10 0 IV. 10 02 11 13 12 0 IV. 36 1 12 06 14 0 IV. 9 19 11 56 11 0 10 46 12 29 12 0 30 1 12 15 12 0 MEANS. 9 30 12 03 19 10 29 12 18 19 11 28 12 16 ... 19 9 30 10 4 19 10 29 10 9 19 11 28 ... ... 11 5 19 '1 liere being tlirce low and but one liigli value in the interval, it seemed preferable to adopt a mean re.sulting after the rejection of 10'' ■48™, viz:— 9 30 12 07 ... ... 18 RECORD AND REDUCTION OF THE TIDES. 59 TAnr.E FOR THE Reduction of Tides. — No. 2. Showing Uic Interval belweeii the A pp. Time of the Moon',s Superior Transit and the Time of Low Water, and also the Heights of Low Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. O"- to 1". 1" to 2^ 2" to 3\ Moon's transit. Lunitidal interval. Height of L. water. i ,2 a. 0 a 0 ^ Moon's transit. Lunitidal interval. Height of L. water. 0 a Moon's transit. Lunitidal interval. Height of L. water. si n App. time. L. water. App. time. L. water. App. time. L. water. H. M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. H. M. H. M. Ft. De«. 0 1 13 0 57 0 19 0 21 0 53 (1 30 17 17 18 18 17 18 02 33 42 54 1 2 0 3 0 5 0 9 1 1 6 I. 40 16 07 55 58 20 17 18 17 18 17 15 35 00 38 20 12 58 1 0 3 1 — 0 0 9 0 1 2 4 6 I. 2 2 2 2 25 16 44 58 18 17 17 17 35 45 30 04 2 0 2 7 3 3 I. 49 i 1 2 2 2 2 2 2 45 29 09 53 02 52 18 17 17 17 18 17 01 47 39 25 19 15 1 2 2 2 1 3 3 3 5 5 2 1 II. 0 0 0 0 0 0 0 01 10 58 33 29 07 52 18 17 18 17 19 18 19 16 05 18 44 37 18 03 1 4 2 0 2 3 3 3 1 B 1 7 5 3 n. 01 55 44 22 15 36 17 17 18 17 17 18 00 21 02 40 21 20 0 — 0 4 0 3 1 5 3 1 5 0 5 II. 2 2 2 2 2 2 2 45 33 19 21 37 02 48 18 17 17 17 17 17 17 18 46 59 39 20 08 21 3 0 2 1 3 1 1 9 5 5 1 6 2 7 III. 09 56 30 29 16 49 00 18 15 16 17 17 18 17 24 37 49 34 15 08 10 2 1 0 1 0 3 1 1 9 8 5 4 2 2 III. 0 0 0 0 0 0 22 30 39 10 10 59 1(! 16 IS 18 16 15 41 49 09 21 48 58 2 1 1 I 1 0 3 6 0 0 9 111. 2 2 2 2 01 47 39 21 17 19 16 17 31 16 30 52 — 0 1 0 0 5 0 0 0 IV. 0 11 22 4« 17 16 46 56 — 0 0 7 0 IV. i 12 07 52 33 18 18 18 17 50 01 16 40 0 2 0 0 0 0 0 0 IV. MEANS. ' 1 0 0 30 30 17 49 ... 1 "7 21 21 1 1 29 29 17 34 "i 3 23 23 2 2 31 30 17 43 i "7 21 20 The highest and lowest valae of the Intervals balance In the mean, hence no value is rejected. 1 The low value 15" 37'" is rejected, hence new mean — 1 28 17 39 22 60 RECOKD AND REDUCTION OF THE TinES. Table for the Reduction of Tides. — No. 2. Showing the Interval between the App. Time of the Moon's Superior Transit and the Time of Low Water, and also the Heights of Low Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. S*- to 4". 4" to 5". s"- to 6^ Mood's transit. Lunitidal interval. Height of L. water- ^1 Moon's transit. Lunitidal interval. Height of L. water. 0 a 0 ^ Moon's transit. Lun]ti<]»! interval. Height of L. water. li It 0 ~ App. time. L. water. App. time. L. water. App. time. L. water. H. M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. H. M. H. M. Ft. Dec. 3 3 3 3 3 .12 19 34 03 46 17 17 17 15 14 18 12 25 36 16 4 0 3 0 4 7 6 1 I. 4 4 4 4 4 4 00 51 22 24 03 32 16 17 16 18 16 16 46 25 39 50 51 59 4 5 2 3 1 4 5 2 3 6 3 4 I. 5 5 5 5 5 5 42 23 14 00 52 17 18 16 17 15 18 17 17 ., 34 53 59 24 16 5 3 3 2 3 4 4 2 7 3 4 2 I. 3 3 3 3 32 14 38 44 17 18 16 16 29 02 10 53 2 0 3 2 0 3 9 6 11. 4 4 4 4 4 4 4 4 4 4 4 4 16 00 49 23 25 41 47 23 08 52 13 56 16 17 17 16 16 15 17 15 17 17 i'7 30 16 27 25 3 3 3 3 4 0 0 1 11. 5 5 5 5 5 5 5 5 5 5 00 43 09 56 36 40 32 16 33 43 16 18 16 16 17 15 15 16 17 01 33 54 53 06 39 44 53 26 3 5 6 5 5 8 0 1 8 0 11. 3 3 3 3 3 3 3 3 3 *4 38 09 59 24 24 00 52 30 17 15 18 17 16 17 16 17 16 29 41 09 48 36 33 55 02 54 1 2 2 4 1 3 2 2 3 8 3 5 0 3 9 4 5 2 III. 38 38 45 37 49 49 43 5 2 3 2 2 2 4 4 3 0 7 3 6 2 0 4 III. 4 4 3 4 4 2 5 7 8 5 III. 5 5 11 25 14 16 53 45 3 2 0 0 IV. 3 3 3 33 32 10 17 16 17 30 37 03 1 — 1 0 5 0 5 IV. 4 4 4 4 22 27 00 51 15 15 16 16 41 42 13 23 0 1 2 4 0 0 0 0 IV. MEANS. 3 3 28 16 27 ... 56 "2 "i 21 20 4 4 27 27 16 52 "3 "i 21 22 5 5 27 27 16 65 "4 "i 17 18 The low values Wi" IC"' is reject- ed, hence new mean — The high value IS" 50" is in a measure balanced by two low va- lues, 15" 37"' and 15'' 37™. The low value 14" 53'" is rejected, hence new mean — 3 28 17 04 ... ... 20 5 27 17 02 ... ... ,. RECORD AND REDUCTION OP THE TIDES. 01 Table for the Reduction of Tides. — No. 2. Showing; the Interval between tlie App. Time of the Moon's Superior Transit and the Time of Low Water, and also the Heights of I.10W Water, at Van Rensselaer Harbor, from Fonr ^criea of Observations made between October 10, 1853, and October 22, 1854. e"- to 7". 7'' to S\ S*- to 9". Moon's transit. Lunitidal interval. Height of L. Water. 0 c 0 ^ Moon's transit. Lunitidal interval. Height of L. water. Moon's transit. Lunitidal interval. L. water. Height of L. water. 41 App. time. L. water. App. time. L. water. App. time. H. M. H. M. Ft. Deo. H. M. H. M. Ft. Deo. H. M. H. M. Ft. Dec. 6 6 6 6 6 6 6 6 28 32 21 01 48 38 01 47 16 17 17 18 17 18 17 18 45 59 55 32 55 00 29 28 4 5 4 3. 3 2 2 2 7 2 9 7 7 9 9 4 I. 7 7 7 7 7 7 26 22 14 34 22 34 17 18 18 17 18 18 47 24 02 38 45 10 4 4 4 t 3 8 8 4 2 2 2 I. 8 8 8 8 8 8 8 8 8 22 11 59 02 48 20 04 46 23 18 18 19 18 18 19 18 18 17 21 50 02 29 43 22 03 50 36 4 4 3 5 4 2 5 1 1 2 5 4 5 2 7 3 8 8 I. 7 7 7 7 14 40 42 17 19 19 18 19 47 06 27 11 5 4 4 5 8 1 8 5 II. 6 6 28 27 17 20 18 01 3 6 8 0 II. 8 8 8 8 8 02 50 41 28 42 19 19 16 20 19 13 55 36 07 12 3 3 3 5 5 3 3 3 0 1 H. 6 6 6 6 6 6 6 45 34 04 49 17 53 32 17 18 17 17 16 18 46 00 25 10 54 37 4 5 4 5 4 4 3 5 2 6 6 4 6 6 III. 7 7 7 7 7 7 7 7 7 41 38 24 00 44 33 02 51 38 17 18 18 17 18 18 18 17 19 36 26 55 32 48 41 24 35 01 4 3 4 4 4 5 4 3 5 0 6 4 7 0 2 3 9 6 III. 8 8 8 8 8 8 8 8 35 25 10 55 30 16 59 45 18 19 17 18 18 18 17 18 27 39 24 09 32 28 59 25 4 I 3 3 5 I 1 7 4 5 4 8 9 0 III. 6 28 16 42 3 0 IV. 7 7 43 23 17 15 53 51 5 5 0 0 IV. 8 8 8 34 01 57 19 19 18 32 14 18 5 3 3 0 0 0 IV. MEANS. 6 6 28 17 29 ... 49 "4 "2 j 17 18 7 29 7 29 18 17 4 "e 21 21 8 8 30 30 18 15 "3 '7 25 25 The liigh value 20'' 01™ is reject- ed, hence new mean — The low value 15'' 51'" is rejected, hence new mean — 6 28 17 42 ... 16 7 29 18 24 ... ... 20 62 RECORD AND REDUCTION OF THE TIDES. Table for the Reduction of Tides. — No. 2. Showing the Interval between the App. Time of the Moon's Superior Transit and the Time of Low Water, and also the Heights of Low Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, and October 22, 1854. 9" to 10\ 10" to IP. IP to 12\ Moon's transit. Lunitidal interval. Height of L. water. (3 « Cm *n transit. interval. Height of fc i L. water. I'H L. water. •1'^ L. water. 1 App. time. L. water. 11 App. time. L. water. ii App. time. L. water. H. 0 M. 35 H. M. Ft. Dec. H. M. H. M. Ft. Dec. H. 1 M. H. M. Ft. Dec. 17 25 1 8 18 17 27 1 6 2 ; 02 15 43 5 7 0 48 18 28 0 1 46 19 00 1 5 2 48 16 57 2 8 0 44 18 16 1 3 I. 31 17 44 — 0 1 I. 2 1 47 17 14 1 6 I. 0 21 18 05 — 0 3 25 17 45 0 0 2 20 16 54 1 9 0 00 16 58 3 4 44 17 19 ... 2 30 18 10 — 0 1 0 55 17 08 2 l-r 2 34 17 58 27 21 18 17 19 25 — 0 3 4 2 0 31 19 31 — 1 8 2 20 17 56 1 5 0 33 18 13 2 4 45 19 02 1 3 II. 2 06 17 40 2 2 0 07 17 55 — 0 9 38 18 43 0 7 2 51 16 25 3 9 II. 0 57 18 05 1 1 II. 14 18 27 1 3 2 31 18 47 1 9 0 Oti 18 15 2 3 59 18 57 3 3 2 26 18 56 1 6 0 52 19 29 3 2 0 29 17 56 — 0 2 33 16 00 1 5 2 i 20 14 57 1 7 04 54 15 17 44 24 2 1 3 6 2 ' 01 2 44 17 16 33 04 1 2 7 5 0 00 17 02 2 2 III. 0 45 18 18 o 0 49 18 41 0 2 2 j 52 16 38 1 6 111. 0 15 16 03 0 5 III. 24 18 03 3 0 2 1 13 17 14 2 5 0 43 17 48 1 6 31 17 24 1 0 2 1 31 17 09 1 0 Q 35 17 17 52 2 4 5 1 2 t 26 17 28 2 0 u 27 58 1 36 29 09 18 17 19 26 39 03 1 1 — 1 0 0 0 2 1 24 2 ' 15 17 17 09 53 — 1 0 0 0 0 47 16 45 — 1 7 IV. IV. 0 00 17 07 1 0 57 16 46 0 0 2 ; 45 15 28 0 0 0 45 17 53 0 0 IV. 0 22 18 20 1 0 0 17 16 58 0 0 MEANS. 0 30 17 50 24 1 33 17 52 21 2 28 17 09 21 0 30 ... i i 24 1 33 ... 1 1 20 2 28 1 i 20 The two higli and two low values The value IS^ 44"" is rejected. The lowest value 14" SS" is re- of the intervals nearly balance in the mean. hence new mean— jected, hence — 1 34 17 1 58 20 2 28 17 15 ... ... 20 64 RECORD AND REDUCTION OP THE TIDES. Table for the Reduction of Tides. — No. -2. Showing the [iiterval between the A pp. Time of the Moon's Inferior Transit and the Time of Low "Water, and aI.so tlie Heights of Low AVater, at Van Rensselaer Harbor, from Four .Series of Observations made between October 10, 1853, and October 22, 1854. 3'' to 4^ 4" to 5\ 5" to G\ Moon's transit. Lunitidal interval. Height of L. water. ii Moon's transit. Lunitidal interval. Height of L. water. t '^ Moon's transit. Lunitidal interval. Height of <— si o ,„ t5- App time. L. water. App. time. L. water. App. time. L. water. H. I'm. H. M. Ft. Dec. H. M. H. M. Ft. |Dec. H. M. H. M. Ft. Dec. 3 3 3 3 3 3 36 50 09 59 32 22 17 16 17 16 17 17 40 56 05 00 37 10 3 1 2 3 1 1 4 8 6 2 6 4 I. 4 4 4 4 4 4 25 52 49 31 09 54 16 17 15 17 16 16 06 39 55 08 22 22 3 2 5 1 4 5 9 6 1 0 5 1 I. 5 5 5 5 5 16 52 37 26 39 15 18 16 18 17 15 24 51 13 51 4 3 6 1 3 5 5 6 0 1 I. 5 5 5 5 21 16 32 11 18 16 17 17 55 00 02 01 3 5 4 4 8 ' i 3 3 3 3 3 OS 54 37 15 18 17 18 17 17 16 53 07 24 48 34 2 0 2 1 2 1 3 7 5 7 II. 4 4 4 4 38 24 00 46 16 18 16 17 53 22 48 02 2 4 1 3 2 5 0 9 II. 5 1 2 II. 5 5 5 5 5 5 5 10 09 54 40 12 55 19 17 17 16 15 18 17 16 39 08 OS 20 14 01 35 1 4 5 2 3 6 6 8 1 ^ 4 4 4 4 4 4 50 09 22 49 30 34 16 16 17 16 16 17 13 55 40 5G 27 05 III. 8 2 8 8 9 1 III. 3 3 3 3 3 3 3 3 3 3 09 59 05 34 53 00 46 26 09 51 15 IG 16 16 17 15 15 17 17 16 54 34 59 59 07 27 41 44 45 33 3 4 1 3 1 2 3 1 3 4 7 3 8 5 3 0 8 8 2 1 III. 1 3 2 5 4 8 6 5 0 8 4 4 4 46 56 25 14 16 15 18 13 48 0 2 2 0 0 0 IV. 5 57 15 13 3 0 IV. 3 3 3 3 3 10 17 57 i 16 06 ' 17 59 16 35 16 23 Ob- OS 10 38 0 0 0 0 0 0 0 0 0 0 IV. MEANS. 1 3 3 31 31 16 1 56 ... 1 ... 1 2 0 26 26 4 4 34 34 16 38 3 3 19 19 5 5 30 30 16 59 4 2 17 17 The value 14'' 18™ is rejected, hence new mean — The three highest anil three low- est values of tlio intervals balance in the mean. 4 34 16 45 18 J RECORD AND REDUCTION OF THE TIDES. 65 Table for the Reduction of Tides No. 2. Showing the Interval between tl e App. Time of the Moon' 3 Inferior Transit and the Time of Low 1 Water, and also the Heights of Low Water, at Van Rensselaer Harbor, from Four Series of 1 Observations made between October 10, 1853, and October 22, 1854. G" to v. 1" to 8". 8" to S". Moon's Lunitidal i • Moon's Lunitidal | Moon's Lunitidal a S transit. interval. Height of > 'u. transit. interval. Height of n transit. interval. Height of £-C S " T. „..(„■ S " JU'TS ■ •S'^ "ttivi. App. time. L. water. O ^ App. time. L. water. App. time. L. water. ° a ll H. M. H. M. Ft. Deo. H. M. H. M. Ft. Dec. H. M. H. 1 M. Ft. Dec. 6 57 18 46 4 4 7 54 17 49 4 0 8 47 18 27 3 7 6 07 16 39 5 2 7 46 17 00 5 5 8 35 19 11 5 1 6 57 17 49 6 1 7 38 17 08 4 3 8 25 IS 21 2 3 6 48 17 58 4 0 I. i 11 18 31 6 9 8 44 19 28 3 4 I. 6 25 17 48 3 4 7 56 18 46 4 3 r. 8 25 19 11 1 7 6 14 18 54 3 5 7 00 18 07 3 e 8 50 19 08 2 9 6 94 17 3ii 4 fi 7 4'', 18 ?,5 5 s 7 7 10 59 17 18 05 45 4 4 1 8 8 i 26 8 ; 10 18 20 49 36 3 5 8 7 6 06 17 40 4 5 g 51 16 25 3 7 3 8 8 03 53 20 19 18 42 3 5 9 4 II. 6 10 17 36 4 II. 7 38 19 08 4 7 6 01 16 41 5 7 7 09 21 07 4 7 II. 8 12 18 12 5 3 6 ft?. 17 08 5 5 7 n 18 49, 5 3 8 8 07 59 19 19 10 33 4 1 0 8 6 17 17 59 5 1 7 13 18 18 4 0 6 07 17 57 3 0 7 14 17 35 6 0 8 02 17 02 5 2 6 59 20 05 8 8 7 47 18 47 3 7 8 48 17 16 4 4 6 38 17 24 5 6 III. 7 22 18 10 6 1 III. 8 32 18 47 2 5 6 27 17 02 3 2 7 11 18 18 4 0 8 07 19 55 4 3 III. 6 39 17 47 6 5 / 54 19 35 4 4 8 54 17 53 4 0 6 31 18 53 4 8 7 26 18 30 6 0 8 37 18 22 3 0 6 : 07 18 47 5 7 7 16 18 08 4 4 8 18 IS 37 5 6 8 01 17 53 4 5 6 ."ifl 17 11 4 5 7 17 16 18 5 0 IV. 6 58 16 16 3 0 IV. 8 08 15 58 5 0 8 58 18 08 5 0 IV. 8 34 18 41 3 0 MEANS. 6 31 17 45 22 7 28 18 18 21 8 29 18 41 24 6 31 4 6 22 7 28 ... i 8 21 8 29 ... ... 4 6 24 The high value 20" 05"' is re- The high value 21" 07" is re- The low value 15" 58'" is rej ected. jected, hence new mean — jected, hence new mean — hence new mean — 6 30 17 39 21 7 29 18 10 20 8 30 18 48 23 66 RECORD AND REDUCTION OF THE TIDES. Table foe the Reduction of Tides. — No. 2. Showing the Interval between the App. Time of the Moon's Inferior Transit and the Time of Low Water, and also the Heights of Low Water, at Van Rensselaer Harbor, from Four Series of Observations made between October 10, 1853, to October 22, 1855. 9" to 10". Moon's transit. App. time. M. tunitidal interval. L. water. Height of L. water. H. M. Ft. Dec. 18 18 19 18 19 19 18 19 37 63 07 54 08 00 16 12 20 18 00 3 35 2 43 4 45 01 03 19 36 19 26 ^•1 II. III. IV. 10" to 11". Moon's transit. App. time. M. 11 34 24 31 33 45 02 46 Lunitidal interval. L. water. 18 18 18 18 IS 18 18 18 18 19 18 18 M. Height of L. water. Ft. Dec. II. III. IV. 11" to 12". Moon's transit. App. time. Lunitidal interval. L. water. M. 30 4G 13 43 H. M. Height of L. water. Ft. Dec. 01 18 00 52 19 09 15 18 15 59 17 01 20 18 06 17 17 48 18 17 18 18 47 59 49 42 2 0 3 — 1 16 19 IB 09 18 40 28 19 05 38 18 23 44 19 14 20 18 05 17 15 50 1 36 17 36 30 17 45 fS II. in. IV. MEANS. 30 30 19 06 3 "o 18 18 The highest value 211" 00"" is re- jected, hence new mean — 9 30 19 00 17 10 29 18 19 10 29 i 9 20 20 11 28 18 14 11 28 ... ... 1 4 19 19 The low value 15'' 50°" is rejected, hence new mean — 11 28 18 21 18 i RECORD AND REDUCTION OF THE TIDES. 67 The preceding tables (No. 2) contain the individual and mean values for interval and height, for high and lovp vv^ater, and the moon's upper and lower transit. The mean, in some cases, was improved by the application of Peirce's criterion for the rejection of doubtful observations ; a few other rejections were made, as stated, in order to obtain a well-balanced mean; of 982 observations of the interval, but 17 were thus rejected. Half -mo7ithly Inequality . — For the comparison of the observed with the theoretical values, it is customary to use the forms of the equilibrium theory or of the wave theory,' certain modifications being necessary to produce an agreement between these theories with observation. According to the equilibrium theory the formula for the position of the pole of the tidal spheroid is : tan.2e' = - J''^''-^^ , h' + h COS. 2

— 5° IgO " ^ ^ l + 0.4649co5.2((?)— 5°15') » « u 1 4- * r,,n> crionn,\ 0.4771 sm. 2 (d) — 12° 30') " " " low waters tan. 2 (6 — 26 i° 00')= — i-l ^ ^ ^ 1+0.4771 COS. 2 ( s 1 \ / \ 1 \ V \ 1 \ * on . \ ' \, \ \ n s \ \. \ \ \ \ \ \ 'N 1 /*o \ \ y V k ^ . l\lO "' V i 0" 1 2 3 4 5 6 7 8 9 10 11 12'' 0" 1 2 3 4 5 6 7 8 9 10 11 121' 30"' 30'" 30"' H l( tt tl (( (( (( (( (( It 30"' 70 RECORD AND REDUCTION OF THE TIDES. In the above diagram, the observed values are indicated by dots ; the computed values are represented by curves. From the times we have seen the mean value ^ (or ^ of the wave theory and (A) of Lubbock's) = 0.471, and a = 0*^ 36" ; hence, h' \ 31" J \ ^ the age of the tide, or the time requisite for the moon to increase its right ascen- sion by that amount, becomes ff days, or 18 hours. Half-mottfhij/ Inequalify in Height. — The theoretical expression for the half monthly inequality in height of high water is: ,7 = ^/ J/t'2 + A^ + 2 h'hcos. 2 cp\' where y; expresses the height of the \)o\e of the equilibrium spheroid above the mean level of the surface ; for its application, and according to the wave theory, it must be changed to: ,7 = v/ \h'' + h"+ 2h'h COS. 2 (^— a) p The foUowingi table contains the results of the observations from the high and low waters, and the moon's superior and inferior transit: From superior transits. From inferior transits. Means. Moon's Height of Number. Moon's Height of Number. Height of Number. transit. high water. transit. high water. high water. Feet. Feet. Feet. 0'' SI-" 12.1 20 0i> 29" 12.2 25 12.1 45 1 29 11.6 22 1 31 12.3 21 11.9 43 2 29 11.8 20 2 27 11.8 19 11.8 39 3 29 10.9 21 3 31 11.1 26 11.0 47 4 27 10.5 22 4 33 10.5 20 10.5 42 5 27 9.5 20 5 30 9.4 18 9.5 38 6 29 9.1 19 6 34 9.1 20 9.1 39 7 29 9.1 21 7 33 9.6 18 9.3 39 8 32 9.9 24 8 30 9.7 23 9.8 47 9 31 10.4 19 9 30 10.4 19 10.4 38 10 31 n.i 21 10 29 10.9 19 11.0 40 11 32 11.7 19 11 28 11.5 19 11.6 38 248 247 10.67 495 From superior transi ts. From inferior transits. Means. Moon's Height of Number. Moon's Height of Number. Height of Number. transit. low water. transit. low water. low water. Feet. Feet. Feet. C .30°' 1.7 21 0" 30"' 1.1 24 1.4 45 1 29 1.3 23 1 33 1.1 20 1.2 43 2 311 1.7 20 2 28 1.7 20 1.7 40 3 27 2.1 20 3 31 2.0 26 2.0 46 4 27 3.1 22 4 34 3.3 19 3.2 41 r, 27 4.1 18 !") 30 4.2 17 4.1 35 G 29 4.2 18 C, 31 4.6 22 4.4 40 7 29 4.6 21 7 28 4.8 21 4.7 42 s 30 .3.7 2.0 8 29 4.0 24 3.8 49 :• 32 2.6 18 9 30 3.0 18 2.8 36 10 32 1.9 22 1(1 29 1.9 20 1.9 42 11 32 1.3 19 11 28 1.4 19 1.4 38 247 250 2.72 497 ' Sue I'liil. Trans. Ruyul Soc, 1«.'J4 tuid 1830. » EncyclopiEtlia Metropolitaiia, Tides and Waves, Art. (535). The expression given by Mr. Lub- bock is : l,==r>+ (E) .[ (] _,. 1) (A)ro..: (24 — 2t) + (1 + 5-')fo.«. 24]- ; '■ c ) for wliiuii see liis treatiw. RECORD AND REDUCTION OF THE TIDES. 71 The values for h', h and a were found from the maxima and minima values of the inequality, viz., for the high water: y = V \ lO.G- + 1.5' + 31.8 COS. 2 ( _ 7m + 5" — 12ra +14- — 7™ 1 30 +15 — 5 —18 —17 +17 + s 2 30 + 21 — 7 —12 —11 +12 — 2 3 30 + 23 —11 — 1) — 1 +20 —10 4 30 + 9 0 — 13 — 1 + 1 — 3 5 30 + 14 + 4 —1.5 +16 + 19 — 3(; H 30 — 9 J-IS — 3 + 7 — 3 — 2 7 30 + 1 —13 + 9 + 5 — 3 — 6 8 30 .> + 9 + 15 +26 —10 + 8 9 30 — 6 + 1 +22 + 9 —11 10 30 + 1 — U --10 + 10 — n — 7 11 30 »7 + 3 — 4 + i + ■i Mean + 5"' — 1°' — l'» + 2"' + 4"' — .'j"| No. of observ. 373 2G2 34-- 3s7 244 333 Mean declination 10°. n. Mean parallax 57'.0. The above table of declination corrections exhibits systematic values for the periodical part of the lunar effect, or for the term D sin. 2 (<^ — y). Between 0° and 13° of declination, the correction is positive for transits between l*" and 1^, for other hours negative; for declinations between 13° and 21° it is positive, between the hours of 4 and 10 ; for remaining hours it is negative, and for declinations 21° to 27°. 5, the correction is positive, for hours 7 to 1, and negative for remainino- hours of transit. The quantity D is accordingly about 14 minutes, and y equals 15°, 60°, and 105° respectively. The variation in the inequality due to the changes of the moon's declination appears large when comparetl with its value at other places, but is in conformity with the large value of the half-monthly inequality itself. The periodical part of the parallax correction is of the same form as given above. 10 74 RECORD AND REDUCTION OT THE TIDES. The empirical values for the groups of small and middle values of parallax appear sj'stematic ; the values in the last column for large parallax are less regular. The maximum correction on the average is somewhat greater than one-fourth of an hour. The corrections to the mean establishment for changes of the sun's declination and parallax may be taken as one-third of the corresponding lunar values, and in the present case will probably not exceed five minutes of time. The means of each column, containing the non-periodical part, are small, and appear rather irregular; they are variable with the transit or the moon's age adopted in the discussion.^ Diurnal Inequality. — We now proceed to the examination of a prominent feature in the Kensselaer Harbor tides, namely, the diurnal inequality. This inequality is well marked in the diagrams, Plates I, II, and III. Although the existence of this inequality, in height and times, has long been known to practical men, it was not until about twenty-five years ago that its laws were understood and reduced to computation by Mr. Whewell.^ The subject has since been taken up by the present superintendent of the U. S. Coast Survey, Prof ]5ache ;'' his researches commenced about nine years ago, and resulted in a further extension of the method of discussion as well as in the recognition of the geographical limits of the pheno- mena on our own coast ; further, tlie discussion of single day tides, produced by this inequality in extreme cases, and here complicated by an extremely small rise and fall of the tides, was now successfully accomplished. According to the equi- librium theory, the diurnal tide ought to be very small in latitude 79° ; but viewing the Rensselaer Harbor tide as a wave, produced principally in the Atlantic, and propagated through Davis's and Smith's Straits, the existence of the diurnal inequality in so high a northern latitude cannot surprise us. The following notes were extracted from Captain ]McClintock's narrative of the voyage of the " Fox," • On tbis point the reader may consult Wbeweirs 9tb series of tidal researcbes : "Laws of the Tides from a Short Series of Observations," Pbil. Trans. 1838; also Airy, "Tides and Waves," articles 552 and following. ' Researches on the Tides, sixth series. On the Results of an Extensive System of Tide Observations made on the Coasts of Europe and America in June, 1835. By the Rev. W. Wbevvell. Fhil. Trans. Roy. Soc. 1836. Researches on the Tides, seventh series. On the Diurnal Inequality of the Height of the Tide, espe- cially at Plymouth and Singapore. By the same author. Phil. Trans. 1837. Researches on the Tides, eighth series. On the Progress of the Diurnal Itieqnality Wave along the Coasts of Europe. By the same author. Phil. Trans. Roy. Soc. 1831. " Note on a Discussion of Tidal Observations at Cat Island in the Gulf of Mexico, by Prof A. D. Bache. Coast Survey Report for 1851, App. No. 7 ; Additional Notes thereto, Coast Survey Re|)ort for 1852, App. No. 22. On the Tides at Key West and of the Western Coast of the United States. Coast Survey Report for 1853, App. Nos. 27 and 28. By Prof A. D. Bache. Comparison of the Diurnal Inequality of the Tides at San Diego, San Francisco, and Astoria, on tlie Pacific Coast of the United States. Coast Survey Report for IS;")!, App. No. 2G. By Prof. A. D. BacJie. Approximate Co-Ti 29 18 1'' 3" May 9 24 9 0 1 0 tl V 12 10 1 11 13 1 7 " 23 14 June 7 9 21 17 5 10 1 21 1 23 li a 27 22 26 4 1 IS " 10 9 17 22 1 11 ii Dec. 9 9 8 19 0 14 July 5 4 2 17 2 11 11 " 25 12 23 13 1 23 " 31 22 29 22 2 0 1854 Jan. not observecl. 5 2 Sept. 9 3 7 22 1 5 t( (( t( (( 19 18 Remaining observa- 22 9 t( Feb. 3 4 " l(i 18 1 15 10 23 1 IS 0 10 tions of S, ries IV not suificiently re- 11 Mean. 1'' 15" (C Mar. 3 12 j 28 19 1 17 liable. t( " IH 0 15 5 0 19 it Mar. obs'n incompl. 28 4 The results for the epoch are very regular, and with the exception of part of the last series, which is of inferior accuracy, no observation has been omitted. The inequality vanishes at the distance of 1.62 days' motion of the moon from her nodes. The magnitude of the diurnal inequality, and its variation depending on twice the moon's declination, was made out by dividing the inequality curves in six parts between the times of disappearance, and by tabulating the ordinatcs as well as the corresponding declination of the moon, the following results were obtained from 12 complete cycles, omitting no value, viz : — AMOUNT OF DIURNAL INEQUALITY IN THE HEIGHT OP HIGH WATER. Ordinate. {In feet.) Mean Mean II dh. declination. 1 \ II II 11 11 0 0 0 0 0 0 0 0.0 0° 1 1.1 2.1 li.-S 2.7 l.u 0.3 0.2 1.4 2.7 1.5 1.5 1.0 1.4 12 2 (1.5 2.9 2.3 4.0 4.2 2.5 1.0 1.5 2.2 2.0 2.1 3.0 2.3 21 3 1.5 2.2 3.0 4.« 4.0 2.8 1.1 1.6 2.2 3.1 2.0 2.0 2.5 25 4 I. (3 2.3 3.0 4.6 0.2 3.C 1.5 1.4 1.8 1.9 3.3 2.7 2.3 22 5 0.8 1.1 11 3.0 2.4 1.2 0.7 3.5 2.2 1.0 2.0 2.0 1.7 13 i; II II II 0 I) (1 0 0 0 II 0 0 0.0 (1 RECORD AND REDUCTION OF THE TIDES. 77 The mean declination corresponds to an epoch 1.6 days anterior, which remark apphes also to the formula dh = C sin. 2 h', representing the diurnal inequality dh in two successive high or low waters, h' being the moon's declination. For the value of C we obtain 3.3, which gives us the following comparison : — DIURNAL INEQUALITY IN HEIGHT. (Epoch 1.6 (lays.) Moon's declination. Observed dh. Computed dh. Difference. Feet. Feet. Feet. 0° 0.0 0.0 0.0 12 1.4 1.4 0.0 21 2.3 2.2 0.1 25 2.5 2.5 0.0 22 2.3 2.3 0.0 13 1.7 1.5 0.2 0 0.0 0.0 0.0 The diurnal inequality in time I have tried to exhibit by numbers as well as by diagrams; it seems, however, that the incidental irregularities in the observations themselves, coupled with the fact that the observations generally were only made half-hourly and at other times hourly — so far exceed in magnitude the inequality itself as to make the effect of the changes of the moon's declination exceedingly obscure. The lunitidal intervals (for high and low water) between Oct. 17 and Dec. 28, 1853, between Jan. 28 and March 7, 1854, and between June 1 and July 7, 1854, were tabulated in vertical columns; the means of the alternate values were tabulated in the 2d column, and placed in the horizontal line opposite the intermediate value of column one. The numbers in the first column were next subtracted from the corresponding numbers in the second column, if the interval belonged to the inferior transit ; if belonging to the superior, the values in the second column were subtracted from those in the first. The moon's declination, for noon each day, was also set down. The 276 values for diurnal inequality in time, thus obtained, were plotted. After attempting to deduce an epoch and arranging the values for different assumptions for epoch, no satisfactory result could be obtained in any way according with the expression ^^ ^ 9 fn»- ^' (spe Lubbock, Phil. Trans. 1S37), 1 + ^ COS. -A ^ ^' and the results of the investigation must be confined to the following general remark. The diurnal inequality in time is in maxima probably not exceeding two hours ; it seems to be less in amount for the times of high water than for the times of low water, a result the reverse of that belonging to the inequality in height. A similar conclusion was arrived at in the discussion of the tides at San Francisco, Cal. (Prof A. D. Bache in Coast Survey Report for 1853, p. *81), when the smaller inequality in height of high water (when compared with that for low water) cor- responded to the greater inequality in time of high water (when compared with the inequality for low water). "NMiether the inequality of the height for high or low water is the greater or smaller depends only on the epoch of the diurnal wave compared with the epoch of the semi-diurnal wave. There is no regular increase 78 RECORD AND REDUCTION OF THE TIDES. of the inequality corresponding to an increasing (irrespective of sign) declination of the moon, but the curve appears double-crested about the time of maximum declination, there being a sudden diminution in the inequality, preceded and fol- lowed by high values; about the time of the moon's crossing the equator the inequality is very irregular. On Plate IV, the actual separation of the semi-diurnal and the diurnal wave has been effected graphically, for which purpose a part of the best observations was selected; these observations extend over the period from Oct. 30 to Nov. 22, 1853. The process of decomposition in use in the U. S. Coast Survey Avas at first an analytical one, by computing sine curves ; since 1855, however, a graphical process, equivalent thereto, was substituted ; this latter method, as introduced by assistant L. F. Pourtales, may be briefly explained as follows : After the observations are plotted and a tracing is taken, the traced curves are shifted in epoch 12 (lunar) hours forward, when a mean curve is pricked off between the observed and traced curves; this process is repeated after the tracing paper has been shifted 12 hours backAvard ; the average or mean pricked curve thus obtained represents the semi- diurnal wave. On an axis parallel with that on which the time is counted, the differences between the originally observed and the constructed semi-diurnal wave were laid off; this constitutes the diurnal curve. In the case in hand I have simplified the process of separation by blackening the under surface of the tracing paper with a lead pencil, and running in with a free hand ; the intermediate curves by the pressure of a style, an average of the two traces thus left on the lower paper, gave the semi-diurnal wave in quite an expeditious manner. On the diagram, the diurnal curve with its epoch of high water nearly coinciding with that of the semi- diurnal wave, appears plainly with its variation in size depending on the moon's declination. Investigation of the Form of the Tide Wave. — The shape of the tide wave has been ascertained in the manner described in art. (479) Tides and Waves, and depends on the hourly observations of 60 tides, 30 during spring tides and an equal number during neap tides, that is, the observed heights on the day of the syzygies and quadratures and on the first and second day after, were tabulated, forming ten groups of three columns each, from low water to low water. The columns of an equal number of hours (they vary from 1 6 hours to 1 1 hours) were united in a mean. In order to combine these it was assumed that the interval from the observed low water to the next following low water corresponds to 360° of phase, and tlic time of every intermediate observation was converted into phase by that proportion. In order to render the observed heights comparable, the range from high to low water in evcM-y half tide (the reading of low water for phase 0 generally not being identical witli the reading of the succeeding low water or phase 360°) was supposed to correspond to 2.00, and the elevation above the low water was converted into number by that proportion, thus furnishing a series of ordinates for equidistant abscissae. Tlie means of all the phases and corresponding converted depressions within every 30th degree of phase were then taken with proper regard to the weights, depending on the number of columns, of equal hours, united at tlic commencement of the reduction. By observation of the progress of the numbers. RECORD AND REDUCTION OF THE TIDES. 79 it was easy to alter the latter so as to make them exactly correspond to the phases 30°, G0°, 90°, 120°, etc. In this manner the following numbers have been obtained : — FOR THE SPRING-TIDE WAVE OCCURRING ONE AND A QUARTER DAY AFTER FULL AND NEW MOON. Phase of grou IIS. Prni nrtional '. leight above low water. Mean. Mean. 0° 0° 0° 0° 0° 0° 0.00 0.00 0.00 0.00 0.00 0.00 26 28 30 33 36 30 0.06 0.23 0.24 0.27 0.10 0.21 51 55 60 65 72 69 0.32 0.68 0.90 0.70 0.46 0.71 77 83 90 98 108 89 0.91 1.13 1.36 1.32 1.17 1.24 103 111 120 131 144 120 1.39 1.68 1.73 1.76 1.52 1.70 129 138 150 164 180 156 1.84 2.04 1.98 1.93 2.00 1.95 154 166 180 196 216 180 1.94 1.98 2.00 2.00 1.88 2.00 180 194 210 229 252 208 2.00 2.00 1.84 1.56 1.23 1.88 206 222 240 262 288 237 1.84 1.84 1.45 1.15 0.70 1.46 231 249 270 294 324 270 1.58 1.23 1.00 0.65 0.41 0.97 257 277 300 327 360 300 1.14 0.79 0.27 0.25 0.00 0.37 283 305 330 360 330 0.60 0.40 0.17 0.00 0.17 309 332 360 360 0.15 0.16 0,00 0.00 334 360 0.02 0.00 360 0.00 Weight 5 4 13 7 1 Weight 5 4 13 7 1 The columns headed " mean" show the ordinates of the waves for (nearly) equidistant intervals of time. The following table contains the corresponding numbers for tlie ucnip tide wave occurring 11 day after the first and last quarter, and as derived from 30 tides observed hourly from low to low water : — Phase of groups. Proportional height above low water. Mean. 'Mean.l 0° 0.00 24 0" 0.07 0.00 48 26 0° 0.26 0.17 0.00 ' 72 51 28 0° 0"= 0.49 0.55 0.24 0.00 ; 0.00 96 77 55 30 0° 29 0.89 1.11 0.59 0.20 0.00 i 0.20 120 103 83 60 33 0" 58 1.19 1.53 0.93 0.50 0.60 0.00 0.52 144 129 111 90 65 36 89 1.55 1.83 1.35 1.05 1.02 0.00 1.08 168 154 138 120 98 72 119 0.82 2.00 1.73 1.60 1.44 0.35 1.51 192 180 166 150 131 108 147 2.00 1.95 2.00 1.85 1.81 1.06 1.82 216 206 194 180 164 144 180 1.92 1.62 1.96 2.00 2.00 1.88 1.97 240 231 222 210 196 180 213 1.64 1.43 1.72 2.00 1.72 2.00 1.84 264 257 249 240 229 216 241 1.25 1.09 1.32 1.84 1.43 1.63 1.58 288 283 277 270 262 252 271 0.94 0.67 0.80 1.37 0.79 0.99 , 1.08 312 309 305 300 294 288 301 0.51 0.24 0.,32 0.79 0.15 0.10 0.56 336 334 332 330 327 324 331 0.23 0.05 0.04 0.42 0.00 0.00 0.22 260 360 360 360 360 360 360 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weight 3 4 8 13 1 1 Weight 3 4 8 13 : 1 1 The results are represented in the annexed diagram. The result for the neap tide curve has also been multiplied by y^xa' ^^^ ratio of neap and spring tide range as found on a preceding page, and was increased by 0.5 to refer it to the same level. 80 RECORD AND REDUCTION OF THE TIDES. - / ■^ - -!; k ', \ N / . \ / / i / / A / , \ ^ 1, ^ ' N, 1 l\ ■ 1 1 A S V L y > \ ft / L / / \ - fi \ \ 7 1 y s ^ h ^ - / '/ / /- \ f/ s4 1 1 1' s^i •*, / isl 2.00 .80 .CO .40 .20 1.00 .80 .60 .40 .20 O.OO 0° 30 GO 90 120 150 ISO 210 240 270 300 330 360' The full curves in the diagram show the form of the spring and neap tide wave (the scales being arbitrary), to Avhich has been added for convenient comparison the dotted curve representing the neap tide wave on the same relative scale as the spring tide wave. It is apparent that the spring tide wave is slightly steeper between low and high water than between high and low water, and that the neap tide wave is very nearly symmetrical in respect to rise and fall. We have seen that the duration of rise is 6** 04". 7, hence the duration of fall will be G"" 19.^7 ; or in making ebb the time is 15 minutes greater than in making flood, a circumstance in conformity with the shape of the curves of rise and fall. This holds good for an average tide; according to art. (510) Tides and Waves, if the place of observation is not for from the sea, or, as in our case, in a bay, the water will occupy a shorter time to rise than to fall, and the inequality will be greater at spring tides than at neap tides ; this is fully illustrated in the preceding diagram, the spring tide wave being the steeper of the two. The form of the tide waves will be found closely represented by the following expressions: — For the spring tide wave — 5.83 + 5.58 sin. {6 + 278°) + 0.20 sin. (2 0 + 281°) ; For the neap tide wave — 2.42 + 2.25 sin. {0 + 269°) + 0.09 sin. (2 0 + 290°) ; in which expressions the angle 6 counts from low water to low water, from 0 to 360°, and the height of the wave is expressed in feet. The relative numbers, given above, as the ordinates, have been changed in the proportion of 2 to 11.1 for the higher and of 2 to 4.7 for the lower wave. The following table shows the agreement between observation and tlie numerical expressions, in wliich tlie 3d and higher terms are zero : — RECORD AND REDUCTION OF THE TIDES. 81 FORM OF THE TIDE WAVE AT VAN RENSSELAER HARBOR. Phase. Height of Spring tide, in feet. Height of nea p tide, in feet. Observed. Computed. Observed. Computed. 0 0.0 0.1 O.ll 0.1 3(1 1.2 1.4 0.5 0.4 60 3.9 3.9 1.3 1.3 90 6.9 6.8 2.5 2.5 120 9.4 9.3 3.5 3.0 150 10.7 10.9 4.3 4.3 180 11.1 11.1 4.6 4.6 210 10.4 10.2 4.3 4.4 240 7.9 8.0 3.7 3.7 270 r,A .5.3 3.5 2.5 300 2.1 2.4 1.3 1.3 330 0.9 0.5 0.5 0.4 360 0.0 0.1 0.0 0.1 Respecting the effect of the wind and ice on the tides, it may be remarked that the former can only be slight, since the sea is protected from the direct action of the wind by its icy cover for the greater part of the year. When the sea is par- tially open, the effect becomes sensible, as may be seen by the following note extracted from the log-book : — "August 17, 1853. The above records show a heavy gale from the southward gradually hauling to the eastward ; the eifect of this gale on the tides was very marked ; our flood rose two feet above any previous register, overflowing the ground ice, and our last ebb or outgoing tide was hardly perceptible." The ice crust can- not sensibly aff"ect (by friction on its lower surface) the progress of the tide wave, and will certainly not sensibly interfere (by friction on the ice foot and breakage of the ice fields) with the rise and fall of the tide. Prop-ess of the Tide Wave. — The tide at Van Rensselaer Harbor may be taken as a derived tide, and transmitted to it from the Atlantic Ocean, and in part modi- fied by the small tide originating in the waters of Baffin's Bay ; Avhich latter tide, however, must necessarily be small, particularly on account of the general direction of the bay, which is very unfavorable for the production of a tide wave. That the tide wave is travelling up along the western coast of Greenland, or, in other words, reaches Van Rensselaer Harbor from the southward, may be seen from the follow- ing observed establishments : — Holsteinhorg Harbor, latitude 66° 56', longitude 53° 42'. High water at F. & C. 6'^ 30'". Spring tides rise 10 feet. — Capt. Inglefield, 1853. Whalefish Islands (near Disco), latitude 68° 59', longitude 53° 13'. Time of high water F. & C. 8'' 15'". Highest tide Ih feet. — Parry's 3d Voyage of Discovery. Godham (Disco), latitude 69° 12', longitude 53° 28'. Tidal hour 9". Rise and fall "th feet. — See Map in Narrative of Kane's First Voyage. Vpernavik, latitude 72° 47', longitude 56° 03'. High water at F. & C. 11". Rise 8 feet.— Capt. Inglefield, 1854. Wolstenholm Sound, latitude 76° 33', longitude 68° 56.' High water at F. & C. 11'' 8'". Rise, both at sprhig and neaps, 7 to 7i feet. — (See Admiralty Chart of Baffin's Bay, sheet 1, 1853, corrected to 1859.) The observations themselves, taken by Captain Saunders of H. M. S. North Star, in 1849 and 1850, were kindly fur- 11 82 RECORD AND REDUCTION OF THE TIDES. nished to Prof. Bache by the Hydrographer to the Admiralty, Captain J. "Wash- ington, E,. X., and are given in the appendix to this paper. And finally, Van Rensselaer Harbor, latitude 78° 37', longitude 70° 53'. High water at F. & C. 11'" 50", as derived from the preceding analytical expression. Rise and fall at spring tide 11.1 feet, at neap tide 4.7 feet, average range 7.9 feet. By means of the difference in the establishments of Holsteinborg and Van Rensselaer, we ran obtain an approximation to the depth of Baffin's Bay and Smith's Straits, viz: — Tidiil hour. Longitude. Sum. . Difference. Holsteinborpr 6" 30'" S"" 35° lO"" 05"" , I Difference corrected for the Vau Rensselaer 11 50 4 43 16 3?, { moon's motion 6" 26°. Assuming the distance along the channel to be 770 nautical miles, we have a velocity of the tide wave of about 202 feet in a second, which, according to Airy's table (174), Tides and Waves, would correspond to a depth of nearly 1300 feet, or about 220 fathoms — a result probably smaller than the true value, since the other observations indicate a greater depth, it may be taken as an inferior limit ; in the same manner we find from the co tidal hours of Upernavik and Van Rensselaer a depth of near 800 fethoms, and a similar result from the Wolstenholm observa- tions ; this last result may perhaps he taken as an upper limit. Soundings. — The following soundings have been copied from the log-book: — Jime 19, 1853. I-at. 51^ 12', long. 52^^ 8' (government sounding twine and .32-pound shot). Chronometer time. Mark. 8" 4T" 0' Red, started. 49 10 Wliite. 52 10 IJottom, with 118 fathoms; shot brought up with graj' mnd and fine sand. The line was afterwards measured. June 26, 1853. Lat. 59° 48', long. 50° 3' (government sounding twine and 32-pound shot). Mark. Clironometer time Started 15 fathoms from tlie ne.xt mark. 4'' 21'" 25' Red. 25 Wliite. 29 Red. 33 Blaclc. 31 White. 42 Red. 46 White. 51 Red. 56 Missed tlie mark. 58 August 1, 1838. Melville Ba_v, lat. 15° 40', long. 62° 12' (government sounding twine and 32 shot). Chronometer time S*" 56"' ■3S' 51 25 58 50 4 00 31 •2 48 5 16 8 n 11 0 14 5 time. Mark. 25' White. 10 Red. 15 White. 25 Red. 30 Black. 0 White. 30 Red. 15 White. 0 Red. 0 Bottom with 1811 fa thoms. line cut. Chronometer time. Mark. r,l, 4^m 6" Started. 48 8 Red. 49 40 White. 51 40 Red. 54 0 Black. 54 45 Bottom with 429 fathoms ; shot brought up with green sand (specimen preserved). dar APPENDIX. Tidal Observations made on boaed IT. M. S. North Star, Commander Saunders, at the WiN'TEi! (Quarters in Wolstenholm Sound. (From the Ship's Loo.) Date. 1849. High water. Low water. Date. 1850. High w.iter. Low water. Time. Height. Time. Height. Time. Height. Time. Height. Ft. In. Ft. In. Ft. In. Ft. In. Nov. 10, A. M. 12" 0'" 78 0 4'' 0'" 69 4 Mar. 13, P. M. (jh o- 69 0 " 17, A. M. 5 30 70 11 " 19, A. M. 3" O- 75 6 " 17, P. M. 0 30 78 6 " 19, P. M. 11 0 70 10 " 29, A. M. 11 0 7(i 5 5 0 71 4 " 27, P. M. 11 0 76 2 5 30 67 9 " 30, A. M. 10 0 79 1 4 30 70 0 April 4, A. M. 12 0 69 9 Dec. 14, P. M. 11 0 ()9 6 6 0 65 2 " 4, P. M. 4 0 72 2 " 22, P. M. 4 0 70 9 10 30 65 4 « 12, A. M. 11 30 70 1 5 0 69 2 " 29, A.M. 11 0 73 10 3 30 64 0 " 26, A. M. 11 0 70 3 5 0 69 2 1850. May 4, P. M. 5 0 75 0 Jan. 13, A.M. 12 0 71 6 5 30 64 2 " 19, A. M. 5 30 77 2 " 21, P.M. 4 0 70 4 10 30 65 1 " 19, P. M. 11 30 72 6 " 27, A. M. 11 0 72 4 5 30 64 2 " 26, A. M. r-l 75 10 6 0 69 0 Feb. 3, P. M. 3 30 70 0 9 0 63 10 June 2, P. M. 1 0 68 11 " 19, P. M. 4 0 70 3 9 30 66 S " 23, P. M. 11 0 74 4 March 5, P. M. 4 30 70 0 10 0 66 10 July 9, P. M. 11 0 74 10 3 0 66 1 " 13, A. M. 11 30 76 0 From the rough manner with niiicli the above observations appear to liave been made, an appro.xi- mate establisliraent and rise of tide only can be deduced from them. H. W. F. and C. appears to take place between XI'" 0™ and XI'' 1.3", say XI'' 8"', and the rise both at springs and neaps from 7 to 7t feet. (Signed) JNO. BURWOOP, Master R. X., ( Tide Computer). Admiralty, Sd July, I860. PUBLISUED BY THE SMITHSONIAN INSTITUTION, WASHINGTON CITY, OCTOBER, 1860. o o hi- ISecond Series concJuded Third Se-ies ^ I UNIVERSITY OF CALIFORNIA, LOS ANGELES THE UNIVERSITY LIBRARY This book is DUE on the last date stamped below University of Caiitornia SOUTHERN REGIONAL LIBRARY FACILITY 405 Hilgard Avenue, Los Angeles, CA 90024-1388 Return this material to the library Irom which it was borrowed. m T-i CO cn o ^-( u en in ^ u UJ ^. £> L^ o „ o 0 cn * UJ * UJ CO cn UJ Ba ■ a n r-i ^ UJ CJ z ^5 ^5 C'i T3 u o a: a. 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