C—la

28

marks are shown in the figure. Consequently it is now no longer necessary to interpolate between the starting anc , ending times on the record-sheet. The scales on the diagram are- —vertical, 1 in. to 6 in. ; horizontal, 6 in. to 1 day. The ordinates were measured twice independently at every mean solar hour, and the measurements called over and checked. The additions on the abacus were done by means of the Mercedes adding-machine, which has been of invaluable assistance in this work, and in every set of additions the gross totals were checked for each tide before the abacus was arranged for the next tide. The whole of the analysis has been done in duplicate, and independent checks have been applied wherever possible. It is hoped, therefore, that no serious errors remain undetected. As the Millionaire and the Brunviga printing calculating-machines were largely used in the analysis, a number of abbreviations were introduced on the printed computation forms : thus, it was found to be unnecessary to enter the individual products in columns vi, vii, ix, x, xvi, xviii, in the analysis of M, for it was easy with the machine to obtain the final sum without recording the intermediate results ; and similarly for the other tides; and in the S series the constant divisions by 12 and 30 were postponed until the final result was reached. On sheets 11 and 12, the natural tangents of £ were obtained on the machines, and then the valuable tables of Professor 0. Lohse (Tafeln fiir numerisches Rechnen mit maschinen, Leipzig, Verlag yon Wilhelm Engelmann, 1909) were used to obtain £ in degrees and decimals. These tables give the trigonometrical functions (sin, esc, tan, cot, sec, and cos) for each hundredth of the degree to five decimals, and are invaluable for this work ; they also contain tables of reciprocals of numbers, squares, and square roots, &c. The table of square roots is most conveniently arranged, and gives opposite the argument a both yi and v 10a- The first differences are given both in the trig, functions and in the square-root table. In calculating H, it was found most convenient to square A and B and sum the results on the machine, and then to use the square-root table. An independent analysis for the S series was carried out, using the gross totals from sheet 1, and adding in the values of the omitted days, the results compared as under : — Abacus, Independent Tide. Sheet 11. Analysis. Differences. Ft. Ft. Ft. Sj B, +-0026 +-0020 + -0008 A 1 - -0048 - -0048 0-0000 S 2 B 2 --0506 --0575 + -0069 A 2 +-0994 +-1018 --0024 S 4 B 4 +-0001 +-0001 0-0000 A 4 --0051 --0051 0-0000 S 6 B e --0043 --0044 +-0001 A c +-0023 +-0022 +-0001 Harmonic Tidal Constants for Wellington, New Zealand, 1909. Latitude, 41° 17' S.; longitude, 174° 46' E. A o 37-931 ft. I O ' H 0-036 ft. c, (H 0-005 v Ik 26-35 Ol \k 151-36 T iH 0093 <, IH 0-112 Ik 141-99 2 Ik 332-98 N <H 0-431 „ IH 0-005 Ik 95-47 ° 4 l« 181-34 'H 0-125 „ IH 0-005 v Ik 107-37 ° c U 298-67 |H 0-082 M IH 0-007 U 81-28 1 U 30-85 P |H 0-024 M <H 1-594 U 169-69 2 U 133-65 T iH 0-056 M (H 0-022 Ik 317-20 ivl3 Ik 184-01 „„ IH 0-039 M (H 0-030 U 137-58 M * U 275-89 9S , M <H 0-039 M (H 0-013 /Oil Ik 19-73 ivl " \k 76-55 M iH 0-116 o iH 0110 Mm v 260-23 • Ik 33-66 Mf <H 0-048 X iH 0-078 MI Ik 172-03 1 U 77-59 M . iH 0-161 X [H 0-042 iIM Ik 60-87 - U 312-25 „ 'H 0-049 p iH 0-023 oa v- 201-65 Ik 53-04 a iH 0-073 T iH 0-007 om Ik 165-59 d [k 143-21 Values of H are in English feet, k in degrees. These values are corrected for the errors made in the printed computation forms supplied by the Cambridge Scientific Instrument Company (see Proc. Roy. Soc, Series A., Vol. 84, No. A 572, " On a Mi take in the Instructions for the Use of Certain Apparatus in Tidal Reductions," by Sir G. H. Darwin, X.C.8., F.R.S.).