85. It will be seen, on comparing the results contained in the previous Report with the above, that the chief tides (the lunar and solar semidiurnal) are now more retarded by about 4° than during the years previously analyzed. The calculated heights in the comparison should therefore more nearly represent the heights about eight minutes after the hours assigned to them. An examination of the differences will show this to be the case. A fresh calculation and due allowance made for atmospheric pressure would doubtless very considerably reduce the discrepancies.

86. The gradual increase in the height of the mean level of the water (A.), probably arising from the filling in of the bed of the river and consequent increase of friction, will account for some portion of this increased retardation. There was a very violent rise in the mean level for the year 1868-69, amounting to four tenths of a foot; it, however, in the following year had again subsided to about its anticipated height. The uncertainty in the mean level of the water is an element which must at times seriously affect the differences between calculated and recorded heights in any method of computation of heights from a fixed datum. With respect to these changes now taking place in Liverpool Bay, the following extract contains the substance of the Marine Surveyor's report, dated October 2nd, 1871, and confirms the results determined by the preceding reductions :

“ The result of the survey of the channels of the river for the current year shows that the changes rendered necessary in the arrangements of the lighting and buoyage are more important in their immediate effect on the course of navigation than any which have occurred for some years. The present Queen Channel was opened in 1854, but was not buoyed for navigation purposes until two years afterwards. Since that time the process of advance from southward to northward of the Great Burbo Bank had been very gradual for the first ten years, but more rapid recently, so that the advance had extended to about half a mile. At the same time the North Channel had widened in the same proportion, and there was no appreciable narrowing of the channel in that direction. On the north side, however, during the last four years, the changes had been more rapid, and the buoys had been altered twice within that period. It was now necessary that the Bell Beacon should be removed northward one third of a mile, and also that the Formby light-ship should be removed one third of a mile westward. Thus the Bell Beacon buoy would be brought into a direct line with the Crosby light-ship. The bar was in a satisfactory state, and the whole of the channels were in as safe a condition as they had been for many years, being deeper as well as more straight and not narrower than formerly.”

87. It is very much to be regretted that the authorities at Liverpool have chosen the George's landing-stage for a tide-float, affected as it must be (sometimes to a considerable extent) by the ever-varying weight it has to bear. This will affect the whole of the tide-components evaluated, but more especially the solar components, and will account for the different values of the solar semidiurnal tide, which, judging from the corresponding lunar component, should agree within much narrower limits. It is therefore thought that, should it be determined to again discuss the Liverpool tides, it will be better to take the tide-curves as self-registered at Helbre Island at the mouth of the Dee, in preference to those of George's Pier. The Helbre Island tide-curves it is considered will give much superior results.

88. Through the kindness of the United States' Coast Survey Office, two years' tide observations, taken at Fort Point, San Francisco Bay, California, being a continuation of the observations already analyzed (8 66), have been

received. The results of the analysis of these observations (those contained in $ 66 being also included for the sake of comparison) are as follow :

Series A.
1859-60. 1860-61.

66

89. Here again we have an abrupt diminution in the height of mean level for the first two years, which the following extract from a letter received from J. E. Hilgard, Esq., fully explains:

“ The change in the mean-level reading at Fort Point is a matter of much annoyance to us. The tide-gauge was put up in a small building near the “ end of a wharf, and the tide-staff used for comparison was close to it. Now “it was observed after the observations had continued some time that the “wharf was settling,—at least the part where the gauge stood. Then the

gauge was moved to a point a little nearer to the shore believed to be firm, “but we think the whole wharf settled and continued to do so for years. “ There seems to be a bog formation underlying the surface deposit at that “place. There is probably no way of ascertaining the amount of settling

except from the observations themselves. We are now having frequent “levellings made, referring the tide-staff to a rocky ledge further inland.”

It is contemplated including the new tide-components now evaluated in the calculation of the tide-heights shown in $ 69, doubtless to their improvement.

90. It having come to the knowledge of the Tide Committee that the United States' Coast Survey Office was in possession of a series of hourly tide observations taken at Cat Island in the Gulf of Mexico, and which were of a very remarkable and interesting character, it was thought a favourable opportunity of testing the value of the harmonic analysis for the evaluation of the components of the tides of this place, which appeared very complicated and peculiar. Application having been made, a series of about thirteen months were received through the kindness of J. E. Hilgard, Esq. These are now in course of reduction.

The following results represent the tide-components as far as they have at present been evaluated. Datum 10 feet below datum of United States' Coast Survey :

Year 1848. A.=4.8574 ft. I=180.45

Series S. Series M. Series L. Series N.
R

0'0442
10°.04

950-21
R, O'0677 Oʻ1195 O'0118 O‘0269
€2 239.80
10°:75 2220:40

......

а

91. It is extremely interesting to find that, although the lunar and solar semidiurnal tides are very small in value. the series of means from which they were obtained were extremely regular and good, and the consequent determination of the phase of spring-tides from their respective epochs is probably correct within a few minutes. The proportion between the amplitudes of the lunar and solar semidiurnal tides is the nearest to equality yet obtained, being in the ratio of 11 to 6. The comparatively large value of R, of Series S is undoubtedly a genuine tide, but the smallness of the corresponding value of Series M must forbid the conclusion of its being purely astronomical. It is perhaps produced by temperature or wind, its time of maximum being about 40 minutes after noon. There are also indications of a similar and large annual tide of 0.3 foot amplitude, and maximum about July, which is also probably meteorological in its origin. The proportion between the lunar and solar diurnal (Declinational) tides (R, of Series 0 and P) will be, on the assumption of the variation of R, of Series O being as the square of the sine of the declination, about 4 to 1.

92. The following are the values of the long-period tides which have been obtained since the Edinburgh Meeting :

R

ft.
Solar annual tide (elliptic and meteorological) 0'274 144:50
Solar semiannual tide (declinational and meteoro-
logical)..........

O‘128

35'02 Lunar monthly tide (elliptic)

0'106

304'17
Lunar fortnightly tido (declinational)

O'043 136.69
Luni-solar fortnightly tide (synodic)

336-26 The above epoch for the solar annual tide would place the maximum about August 16.