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Volume 45, 1912
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Art. III.—Harmonic Tidal Constants of New Zealand Ports—Wellington and Auckland.

[Read before the Wellington Philosophical Society, 23rd October, 1912.]

The harmonic tidal constants given in columns (1) and (4) of the attached schedule were obtained from an harmonic analysis of the hourly ordinates from the automatic tide-gauges at Wellington and Auckland. For each port the tidal abacus of Sir G. H. Darwin was used, and the whole of the calculation has been carried out in duplicate. For the additions the Mercedes adding-machine has been found to be of the greatest assistance, while the Brunsviga calculating-machine, with printing attachment, and the Millionaire calculating-machine have been invaluable in the numerous calculations. For the fine plotting of curves the Coradi co-ordinatograph has been very useful.

From the constants given in columns (1) and (4) the tides for Wellington and Auckland have been predicted, and are published in the “British Admiralty Tide-tables” and in the “New Zealand Nautical Almanac.” Comparisons between the predictions and actuality prove the correctness of the constants. For these comparisons see New Zealand Tidal Survey: Report of Department of Lands and Survey, Wellington, 1910–11 and 1911–12.

Other values of the tidal constants—(1) by the United States Coast and Geodetic Survey, and (2) by Mr. T. Wright—are given in columns (2) and (5) and (3) and (6) respectively.

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In the United States tide-tables, predictions for Wellington and Auckland are also given, but these do not agree so closely with actuality as those depending on the constants in columns (1) and (4).

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Tide. Wellington, N.Z. (Lat. 41° 17'S., Long. 174° 46' E.) Auckland, N.Z. (Lat. 36° 50'S., Long. 174° 49' E.)
H. in English Feet. k m. Degrees. H. in English Feet. k m Degrees.
(1.) (2.) (3.) (1.) (2.) (3.) (4.) (5.) (6.) (4.) (5.) (6.)
S1 0.005 151 0.006 50
S2 0.112 0.089 0.108 333 325 308 0.583 0.626 0.633 264 265 266
S4 0.005 181 0.018 341
S6 0005 299 0.002 27
M1 0.007 0.007 31 106 0.011 0.011 144 144
M2 1.594 1.598 1.702 134 137 123 3.814 3.782 3.826 204 205 205
M3 0.022 184 0.052 202
M4 0.030 0.045 276 332 0.113 0.200 127 74
M6 0013 0.015 77 135 0.026 0.100 283 67
O 0.110 0.099 0.121 34 36 194 0.059 0.071 149 121
K1 0078 0.085 0.071 78 81 275 0.233 0.241 0.265 169 167 169
K2 0042 0.060 0.029 312 339 308 0.145 0.171 0.172 255 265 266
P 0023 0.028 0023 53 67 275 0.068 0.079 0.088 166 169 169
J 0007 143 0.017 196
Q 0.036 0019 26 13 0008 0018 57 85
L 0093 0.034 142 71 0.221 0.144 0.164 210 209 196
N 0.431 0353 0.449 95 104 83 0.797 0.760 0.778 174 174 175
v 0.125 0.068 107 108 0.236 0.147 153 178
ü 0082 81 0.126 0091 178 144
R 0.024 170 0024 237
T 0.056 317 0058 0.037 103 265
MS 0039 138 0.169 195
2SM 0.039 20 0064 305
Mm 0.116 260 0.127 292
Mf 0048 172 0.072 205
MSf 0.161 61 0.075 123
Sa 0.049 0.241 0.073 202 54 295 0.091 0.357 0.354 63 88 139
Ssa 0073 0.035 0.204 166 240 212 0.028 0.185 0.224 57 266 242

(1.) New Zealand Tidal Survey: Report of Department of Lands and Survey, Wellington, for 1910–11.—Hourly ordinates for the calendar year 1909.

(2.) United States Coast and Geodetic Survey, Washington: Tide-tables for the Year 1911, p. 456.—Hourly ordinates for one calendar year, 1894.

(3.) Thomas Wright, Proc. Royal Soc., London, A. Vol. 83, p. 127: Harmonic Tidal Constants for certain Chinese and New Zealand Ports.—High and low waters for the year 1901.

(4.) New Zealand Tidal Survey: Report of Department of Lands and Survey, Wellington, for 1911–12.—Hourly ordinates for year beginning 1908, December 1.

(5.) United States Coast and Geodetic Survey, Washington: Tide-tables for Year 1912, p. 460.—High and low waters for two calendar years, 1896 (Service Hydrographique de la Marine, Paris) and 1900 (The Admiralty, London).

(6.) Thomas Wright, Proc. Royal Soc., London, A. Vol. 83, p. 127: Harmonic Tidal Constants for certain Chinese and New Zealand Ports.—High and low waters for one year beginning 1900, May 1.