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The star S
The star M
The star K
The star o
It will be seen that the principal tides are first the quasi-semi-diurnal of M, and then the semi-diurnal of S and the quasi-diurnal of K, which range from one-third to one-fourth of the former. S and M being the principal stars, their sub-tides, down to the three-hourly tide of S and the corresponding tide of M, have been computed. For K the quasi-diurnal and semi-diurnal tides were computed ; for the stars 0 to Q only the primary tides. For the stars L to SM there are no primaries, and the tides of longest period are the quasi-semi-diurnal; for MS the longest tide is the quasi-demi-semi-diurnal ; these, being the principal ones for each star, have been computed.
Here it is necessary to observe that the number of sub-tides which have to be investigated in each instance, in order to evaluate the full influence of the star, is a matter which can only be decided after considerable experience of such investigations has been gained by the analysis of the tides at a great variety of stations. It was therefore left to Mr. Roberts, whose practical familiarity with the subject probably exceeds that of any other individual, to prescribe the number of terms to be computed for each star.
On inserting the numerical values of the constants R and e in the general expression, and substituting for nt its values in succession for every hour from the starting-point, the height (in feet) of each tide and sub-tide may be computed for every hour. The sum of these gives the portion of the height of the sea-level at that hour which is due to the influence of the short-period tides. This usually far exceeds the portion which is due to all other causes, and is thus frequently taken to represent the whole height.
Should it be desired to compute the hourly heights for any day of any year, without commencing at the starting-point of the observations, as may be necessary when tidal predictions are required, the values of y, n, o, and ô must be found, as stated on page 46, for mean noon of the day which may be adopted as the new starting-point ; the quasi-hour-angles of the several fictitious stars, other than S, at that moment must then be found, after which those for the succeeding hours may be obtained by successive additions of the respective hourly increments which are due to each star.
The values of the constants R and € having been determined for each of the three tidal stations, the next step taken was the calculation of the height of the sea-level at each hour, throughout the entire period of registration at each station. The differences between the observed and the computed values were then taken as the data for calculating the influence of variations in barometric pressure, and in the velocity and direction of the wind, on the sea-level. Equations were formed in which the unknown quantities were B, the effect of a barometric pressure of one inch, and N and E, the effects of the North and the East components respectively of winds blowing at the rate of 10 miles an hour. Of these equations there were as many as the number of days of observation; they were solved by the method
of minimum squares.
Corrections were then computed for the daily variations of the atmospheric influences on the sca-level, and were applied to the values of height resulting from the previous investigations of the short-period tides. Finally, the differences between the heights thus determined and those actually observed were taken as the data for calculating the influence of each of the long-period tides.
The evaluation of the atmospheric influences gave the following factors for changes of sea-level due to a barometric pressure of one inch, and to north and east winds travelling with a velocity of 10 miles per hour :
+0.356 feet - 0:438 feet.
0.262 East Wind
+ 0.087 These results are not satisfactory ; the height of the sea-level at Okha appears to increase with an increase of barometric pressure, which is scarcely possible. It happens that at this station the changes of pressure occurred, as a rule, simultaneously with the changes of wind; and thus it is impossible to determine the separate effect of each, otherwise than by some arbitrary method of treatment. The observations will therefore be again analyzed, with a view to ascertaining whether they may not be made to yield more consistent results. Meanwhile, the values of the atmospheric factors already obtained must be considered to be only approximate, giving fairly accurate results when employed collectively but not individually.
Of the constants for the long-period tides the following values have been computed for the stations of Okha and Hanstal, after the elimination of atmospheric influences, by employing the preliminary values of the factors which are given in the preceding paragraph. At Nawanár sufficient observations are not forthcoming for the evaluation of either the atmospheric or the long-period tides.
Long-period tides, and their Constants. (0 - 0) Lunar monthly elliptic tide,
20 Lunar fortnightly declinational tide, 2 (0 - m) Luni-solar synodic fortnightly tide,
n Solar annual elliptic tide,
Solar semi-annual declinational tide,
0.142, 45.74 0:136, 249.19 2 (0-n)
0.163, 11:76 0:162, 3:11
0.024, 195:32 144.75
Star S ...
The present appears to be a good opportunity for giving the tidal constituents which were calculated by Mr. Roberts for the Port of Tuticorin, from observations taken there in the year 1871-72, by Captain Branfill, with a self-registering tide-gauge similar to those employed in the Gulf of Cutch.
Short period Tides at Tuticorin, and their Constants.
Star P R,=0:061, €,=281.78 R,=0:429, 62
R;=0·011, ez 181.70 R=0:073, 6 =282165
R,=0:274, € €,=132.80
R=0;143, 6 g
=116.25 R:=0.007, 68 = =262:75
Q R,=0.032, 6,=359:08 PR=0.006, €,=234.64
L R,=0.030, €2
-242:50 | R,=0:596, €, 55.81
N R,=0.072, e,= 38.69 Rg=0:015, 63 =182 86
R,=0.019, €,=248-415 Star M... Re= 0.022, € -192:76
R;=0.022, 6,= 35.58 R=0:010, 6s = = 45.91
R,=0:016, 6,=183.83 R=0.004, Es=319.74 2SM... R,
R,=0.011, 6=246:37 Star 0 ...R,=0:112, €,=314.25 MS ... R.=0.018, €4
=018=282.99 Long-period Tides at Tuticorin, and their Constants.
69.54 Luni-solar fortnightly
307.85 Solar annual
313.35 Solar semi-annual
87.50 Here there were no data for evaluating the atmospheric tides separately, and it is probable that the magnitude of the amplitude of the solar annual tide is in great measure due to atmospheric influences.
PROGRAMME OF FUTURE OPERATIONS.
The following important orders on the systematic record of tidal observations at selected points on the Coasts of India, were issued by the Government of India in the Department of Revenue, Agriculture, and Commerce, under date 4th July, 1877 :
“The Governor General in Council observes that the great scientific advantages of a systematic record of tidal observations on Indian coasts have frequently been urged upon, and admitted by, the Government of India. Hitherto the efforts in the direction of such a record have been desultory, and in many cases wanting in intelligent guidance and careful selection of the points where the observations should be recorded. Additional importance has recently been given to the subject by the institution of a Marine Survey Department, for whose operations accurate tidal observations are a
necessity, without which no permanent record of the changes of ground in the different harbours of the coast can be kept up.
- 2. The advantages to be expected from well-considered and carefully conducted observations of the tides are mainly the following:
(1) They enable standards to be fixed for the purposes of survey.
tides, and thus subserve the purposes of navigation.
ness as stated above. “ The first two of these advantages are of strictly local bearing : an accurate survey of a port is essential to the safety of the shipping frequenting it, and correct tide-tables are necessary for the convenience of navigators and for engineering purposes within the port itself.
“3. The Governor General in Council is of opinion that, in view of these considerations, every port where a tide-gauge is set up should pay for its establishment and maintenance from port funds. The third object, the scientific results to be expected from the record, will be sufficiently provided for by the appointment by the Government of India of one of its own officers to supervise and control the local observations, and to arrange for their utilization to the utinost extent possible. The charges will thus be divided in a manner appropriate to the advantages to be secured.
“4. His Excellency in Council accordingly resolves to entrust the general superintendence and control of tidal observations upon Indian coasts to Captain Baird, R. E., Deputy Superintendent in the Great Trigonometrical Survey Department, who will be guided in his operations by the orders and advice of the head of that Department. This will involve no new charge upon Imperial Funds, for Captain Baird has for some years past been engaged upon observations of this nature in the Gulf of Cutch and in reduction of the observations in England : the work is of a nature which properly falls within the scope of the operations of the Great Trigonometrical Survey; and the object of the present change is merely to provide for its extension and systematization under an undivided control. Captain Baird will thus remain a member of the Department, and his operations will form one of the subjects to be treated by the Superintendent, in his annual report.
“5. The first duty of the Superintendent will be to instruct Captain Baird to determine, in communication with the Governments of the maritime provinces, the points where .observations should be carried out. The necessary gauges (where these do not already exist) will then have to be provided from port funds, and the establishments entertained under the sanction of the Local Governments. It will probably be most convenient that all Captain Baird's communications with the establishments in charge