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Volume 46, 1913
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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.

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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°