31

C—la

by scaling the distance of G from the Oh. line. The datum for heights is the Admiralty one, and is 4-5 ft.J? below mean sea-level for Auckland. The height is scaled from the diagram. The following template curves are shown on the diagram in red : — Tide. Template, Value of k. Tide. Template, Value of k. 153 L. - 1 .. 154 H. +7 154 L. +1 .. 155 H. +7 155 L. +1 .. 156 H. +7 In practical work an excellent check is afforded by noting the value of k in the templates used. Any sudden variation in kis at once investigated and traced to its source In this way errors are easily detected. Check of Predictions. To check the Wellington predictions, the tide-record for 1911, March 25 to 31, has plotted on it in red the results obtained from a diagram similar to Pig. 2. It will be noted how well the times of high and low water agree with actuality, while the heights also agree very fairly. As so much plotting from co-ordinates is required a co-ordinatograph is being obtained, and when that instrument is available a number of improvements will be effected. Thus the X curves will be associated together and the combined curve drawn, and similarly in other cases, and, instead of the M 2 curve only being used on the diagram, all the M curves will be used. But for the present it has been found simpler to keep the curves separate. Datum Levels. In the report on Datum Levels drawn up by Sir G. H. Darwin (British Association Report for 1886, pp. 40-58, reprinted in Scientific Papers Vol. 1, p. 97, by Sir G. H. Darwin), a description of a datum to be called the " Indian spring low-water mark," is given. And in the Tide Tables for 1911, published by order of the Lords Commissioners of the Admiralty, p. vi, this datum has been adopted for places where there is a large diurnal inequality. The datum suggested is to be below mean sea-level a distance equal to the sum of the mean semi-ranges of the tides M 3, S 2 , and 0. Thus for Wellington — Tide. Semi-range. M, 1-594 S a 0-112 XtK t 0078 O 0110 the suggested datum is 1-894 ft. below mean sea-level. But this takes no account of the relatively large N tide (H = 0-431 ft.) ; nor of L(H = 0-093 ft.); v(H = 0-125 ft.); /* (H = 0-082 ft.); which are all larger than the XtK t tide (H = 0-078 ft.). Perhaps it might be well to define the datum as being below mean sea-level a distance equal to the sum of the mean semi-ranges of all the short-period tides. Or, for practical purposes, it might be sufficient to include only those short-period tides whose semiranges are greater than one-tenth of the M 2 semi-range. List op Automatic Tide-gauges in New Zealand. Tide-gauges from which continuous records are obtained are established at Auckland, Wellington, Lyttelton, Port Chalmers, Dunedin, Bluff, Westport, and Greymouth ; while at Napier and Wanganui the records are irregular, owing to the exposed positions of the gauges. Level Bench-marks. A start has been made with a precise levelling survey, and over twenty bench-marks established between the Wellington Harbour Board tide-gauge on Jervois Quay, Wellington, and the Public Works Department tide-gauge at Seatoiin. (See Pig. 4 for the situation of the bench-marks and their heights, which are in terms of the Wellington City datum.) The mean sea-level as determined from hourly ordinates of the Wellington tide-gauge for 1909 was 37-931 ft. in terms of the same datum. Mr. Frank C. Hay, Assoc. M.lnst.C.E., Assistant Engineer of the Public Works Department, carried out the levelling with a high degree of precision. Other Methods op Harmonic Analysis of Tidal Observations. As opportunity offers other methods of harmonic analysis are investigated. Among them Dr. Borgen's* method has been tried, and a complete example of the analysis of the K 2 tide is given. The observations submitted to analysis are those given in the Great Trigonometrical Survey of India, Vol. xvi, and are hourly observations for Bombay for the year 1884. The hourly observations were first summed continuously throughout the year, and were cut down to one decimal of a foot and written out in a list of sums as under : — h. h. h. h. h. Day. 0 12 22 23 0 155 130 91 .. 142 161 1 322 284 213 .. 260 308 2 488 454 365 .. 349 429 367 43697 43809 41081 .. 40413 42754 368 43834 43194 41160 .. 40544 42896

* Ueber cine neve Methode, die harmonischen Konstanten der Gezeiten abzuleiten, Yon Admiralitatsrath Prof. Dr. Borgen, Anualen der Hydrographie und Maritimen Meteorologie, Juni, Juli, August, 1894.