
Art. XLVII.— Harmonic Tidal Constants of New Zealand Ports—Dunedin and Port Chalmers.
[Read before the Wellington Philosophical Society, 22nd October, 1913.]
As in the case of Wellington and Auckland,* the harmonic tidal constants for Dunedin have been obtained from an harmonic analysis of the hourly ordinates from the automatic tide-gauge records at Dunedin. The tidal abacus of Sir G. H. Darwin was used, and the whole of the calculations have been carried out in duplicate, and with independent checks
[Footnote] * Trans. N.Z. Inst., vol. 45, 1912, p. 20.

where necessary. The constants resulting from this analysis are given in column (1), while those for Port Chalmers, which is eight miles lower down the harbour, are given in column (2).
The constants for Dunedin have been checked by computing from them the heights of the tide on different days, and comparing the values with the gauge-records. The results have shown that the constants have been determined correctly.
And in order to show the characteristic features of the New Zealand tides a comparative schedule is given—(I) comparing the various component tides with the chief lunar tide M2 = 1, and (II) comparing the diurnal tides with the K1 tide = 1; and for comparison with Australia the component tides for Adelaide, Melbourne, and Sydney are also shown.
In New Zealand the N2 tide ranks next the M2 in amplitude, with the S2 tide third both at Dunedin and Auckland; while at Wellington the S2 tide is sixth, being smaller than the long-period tides MSf and Mm, and the short-period tides M2, N2, and ν2.
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| Tide. | (1.) Dunedin, N Z. (Lat. 46°7′ S., Long. 170°30′ E.) | (2.) Port Chalmers, N.Z (Lat. 45°55′ S., Long. 170°32′ E) | ||
|---|---|---|---|---|
| H. in English Feet. | κ in Degrees. | H. in English Feet. | κ in Degrees. | |
| S1 | 0·016 | 294 | 0·074 | 90 |
| S2 | 0·251 | 125 | 0·239 | 107 |
| S4 | 0·006 | 318 | 0·007 | 335 |
| S6 | 0·005 | 61 | 0·003 | 334 |
| M1 | 0·004 | 178 | 0·009 | 165 |
| M2 | 2·535 | 121 | 2·358 | 104 |
| M3 | 0·019 | 277 | 0·018 | 142 |
| M4 | 0·255 | 174 | 0·036 | 316 |
| M6 | 0·082 | 356 | 0·047 | 340 |
| O | 0·088 | 302 | 0·087 | 54 |
| K1 | 0·062 | 90 | 0·089 | 79 |
| K2 | 0·086 | 130 | ||
| P | 0·030 | 34 | ||
| J | 0·004 | 129 | 0·005 | 163 |
| Q | 0·029 | 280 | 0·034 | 69 |
| L | 0·116 | 103 | 0·116 | 67 |
| N | 0·540 | 105 | 0·535 | 84 |
| ν | 0·043 | 167 | 0·175 | 50 |
| μ | 0·017 | 329 | 0·047 | 64 |
| R | 0·008 | 160 | 0·024 | 63 |
| T | 0·027 | 67 | 0·016 | 302 |
| MS | 0·113 | 141 | 0·075 | 92 |
| 2SM | 0·026 | 358 | 0·060 | 69 |
| Mm | 0·072 | 40 | 0·100 | 32 |
| Mf | 0·073 | 181 | 0·142 | 228 |
| MSf | 0·106 | 105 | 0·081 | 31 |
| Sa | 0·099 | 213 | 0·123 | 341 |
| Ssa | 0·046 | 77 | 0·157 | 117 |
(1.) New Zealand Tidal Survey: Report of Department of Lands and Survey, Wellington, for 1913–14.—Hourly ordinates for one year beginning 1911, July 1.
(2.) Thomas Wright, Proc. Roy. Soc., London, A. Vol. 83, p. 127: Harmonic Tidal Constants for certain Chinese and New Zealand Ports.—Hourly ordinates for the year 1901.

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| Port. | New Zealand. | Australia | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dunedin. | Wellington. | Auckland. | Adelaide. | Melbourne | Sydney | |||||||
| Longitude from Greenwich | 170° 30′ E. | 174° 46′ E. | 174° 49′ E. | 138° 35′ E. | 144° 59′ E. | 151° 13′ E. | ||||||
| Latitude | 46° 7′ S. | 41° 17′ S. | 36° 50′ S. | 34° 56′ S. | 37° 50′ S. | 33° 52′ S. | ||||||
| Period of observation | 1 year | 1 year | 1 year | 2 years | 1 month | 1 year | ||||||
| Beginning | 1911, July 1 | 1909, Jan. 1 | 1908, Dec. 1 | 1889, Feb. 28 1893, Jan. 1 | 1894, May 1 | 1888, Jan. 1 | ||||||
| Observations used | Hourly ordinates | Hourly ordinates | Hourly ordinates | Hourly ordinates | High & low waters | High & low waters | ||||||
| M2 tide in feet | 2·535 | 1·594 | 3·814 | 1·700 | 0·806 | 1·636 | ||||||
| Tide | H. | κ | H | κ | H. | κ | H | κ | H. | κ | H. | κ |
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| I. Component Tides compared with M2 = 1. | ||||||||||||
| M2 | 1·00 | 121° | 1·00 | 134° | 1·00 | 204° | 1·00 | 120° | 1·00 | 69° | 1·00 | 254° |
| S2 | 0·10 | 125° | 0·07 | 333° | 0·15 | 264° | 0·99 | 181° | 0·13 | 164° | 0·23 | 268° |
| N2 | 0·21 | 105° | 0·27 | 95° | 0·21 | 174° | 0·05 | 246° | 0·12 | 65° | 0·20 | 250° |
| L2 | 0·05 | 103° | 0·06 | 142° | 0·06 | 210° | 0·07 | 140° | 0·02 | 74° | 0·04 | 237° |
| ν2 | 0·02 | 167° | 0·08 | 107° | 0·06 | 153° | 0·04 | 76° | 0·02 | 66° | ||
| K2 | 0·03 | 130° | 0·03 | 312° | 0·04 | 255° | 0·27 | 178° | 0·03 | 172° | 0·06 | 268° |
| K1 | 0·02 | 90° | 0·05 | 78° | 0·06 | 169° | 0·49 | 53° | 0·36 | 132° | 0·26 | 129° |
| O1 | 0·03 | 302° | 0·07 | 34° | 0·02 | 149° | 0·31 | 32° | 0·27 | 95° | 0·21 | 86° |
| MS4 | 0·04 | 141° | 0·02 | 138° | 0·04 | 195° | 0·05 | 99° | ||||
| M4 | 0·10 | 174° | 0·02 | 276° | 0·03 | 127° | 0·01 | 173° | 0·03 | 49° | ||
| Mf | 0·03 | 181° | 0·03 | 172° | 0·02 | 205° | 0·04 | 181° | ||||
| MSf | 0·04 | 105° | 0·10 | 61° | 0·02 | 123° | 0·07 | 255° | ||||
| Mm | 0·03 | 40° | 0·07 | 260° | 0·03 | 292° | 0·04 | 200° | ||||
| Ssa | 0·02 | 77° | 0·05 | 166° | 0·01 | 57° | 0·13 | 88° | 0·01 | 97° | ||
| Sa | 0·04 | 213° | 0·03 | 202° | 0·02 | 63° | 0·18 | 126° | 0·06 | 16° | ||
| II. Diurnal Tides compared with K1 = 1. | ||||||||||||
| K1 | 1·00 | 90° | 1·00 | 78° | 1·00 | 169° | 1·00 | 53° | 1·00 | 132° | 1·00 | 129° |
| O1 | 1·42 | 302° | 1·41 | 34° | 0·25 | 149° | 0·63 | 32° | 0·73 | 95° | 0·80 | 86° |
| Q1 | 0·47 | 280° | 0·46 | 26° | 0·03 | 57° | 0·08 | 31° | 0·14 | 77° | ||
| P1 | 0·48 | 34° | 0·29 | 53° | 0·29 | 166° | 0·26 | 57° | 0·33 | 129° | 0·33 | 129° |
