C—la

30

The intervals between high waters are: — Difference 10 times h. from M 2. Difference. M 2 12-42060122 h. h. N 2 12-6583482 +0-2377470 +2-37747 S 2 12-0000000 -0-4206012 -4-206012 &c. Hence, in forming the column for N 2 the initial value — 2-6272 is set on the calculating-machine and ten times the difference (= 2-37747) added continuously. When the values in the N 2 column exceed the interval between the N 2 high waters, an adjustment is made as shown at tide No. 70, where the interval 12-6583 is subtracted. This always keeps the intervals between the M 2 and N 2 high waters small, and is a convenience when adjusting the N 2 tide in place on the table as described below. In a similar way the other columns are filled up.

Schedule No. 2—Auckland, 1912.

On a table 12 ft. by 3 ft. a sheet of tracing-cloth is laid down, and on the cloth at intervals of 6-2103 in. lines are drawn across to represent, on a scale of 1 in. to 1 hour, the times of M 2 high and low waters. Parallel to and 1 in. distant from these lines other lines are drawn to represent the times 1 hour before and 1 hour after the M 2 high- and low-water times. (See Fig. 3.) On separate sheets of tracing-cloth 14 ft. long by 8 in. wide the N 2 , S 2 , K 1; M 4, K 2 , and. v 2 tides are drawn to a scale of 1 in. to 1 hour longitudinally and 5 in. to 1 ft. transversely. To set these curves in their correct relative positions reference must be made to Schedule No. 2. Thus, for N 2 it is seen that its H.W. takes place at - 2-63 L, that is, 2-63 hours before M 2 high water; accordingly the N 2 curve is placed so that its H.W. is 2-63 in. to the left of the M 2 H.W. At the other end of the table, at the 10th M 2 H.W., the N 2 H.W. is checked from Schedule No. 2, and is 0;25h. earlier than the M 2 H.W. In a similar manner the curves of the other tides are arranged and clamped to the table. The ordinates of the curves are next measured graphically on strips of paper, at — lh., Oh., and + lh. from each M 2 high and low water ; the transverse lines on the lowest sheet of tracing-cloth enable this to be readily done, and the resulting sum shows the correction to the M 2 curve. In Fig. 2 are shown portions of the M 2 curve drawn to scales of 2 in. to 1 hour and 5 in. to 1 ft.— i.e., the same scale for heights as the other curves. Thus, in the case of the 155 th low water, ACE represents part of the M 2 curve and AB, CD, and EF are the corrections due to the other tides obtained graphically from Fig. 3. The points B, D, and F then represent points on the curve of the tide, and it remains to determine the time and height of low water. For this purpose a series of template curves h = (H,,, + 0-2 k) cos i are drawn on separate pieces of tracing-cloth, his the ordinante of the curve ; H m is the semi-range of the M 2 tide ; A; is an integer from + 7to —7 ; iis the speed of the M 2 tide in degrees per mean solar hour. One of the templates is now selected, and, keeping the line G H parallel to the hour-lines, the curve is adjusted until it passes through the points B, D, and Fas shown in red on Fig. 3. The point G then represents the position of low water, and the correction to the M 2 low-water time is obtained

Tide No. N 2 s 2 Kj M 4 K 2 c s 0 10 20 h. -2-63 -0-25 + 213 h. + [4-73 + 0-52 -3-69 h. -5-40 -9-93 - 14-47) K, = 23-9:5 + 4-93 h. + 0-42 + 0-42 &c. h. -1-74 -6-27 - 10-80 h. -2-27 -0-22 + 1-83 30 + 4-51 -7-89 - 15-34) Kg = 11-97 [ - 3-37 j -7-90 + 3-89 40 + 6-88 - 12-10 S 2 = 12-00 —o-ioj -4-30 + 0-40 + 5-94 50 60 70 + 9-26 + 11-64 + 14-021 N 2 - l^66 + 1-36J + 3-73 -8-51 - 12-72) S 2 = I2-00 - 0 T 72J -4-92 -[413 -8-67 -13-20) K t = 23-93 + 10-73) + 6-20 - 12-44) K a = 11-97 - 047 ] -500 -9-54 + 8-00 + 10-05 + 12-10 80 - 14-071 11-971 - 2-10J -6-64 - 1117 + 14-16) v 2 = 25-26'- - 11-10) -9-04 -6-99 90 100 &c. + 6-11 + 8-49 -9-13 - 13-33) S 2 = 12-00 + 1-67 -2-87