a—ia.

32

The figures in the list are given in tenths of a foot. The method consists in selecting from the list the particular days that will give the best values of the tide sought, at the same time eliminating the effect of the S tides and reducing the effect of the other tides as much as possible. Example for K 2 tide : — If the following lines are used from the list — (185-97)-(96-8), i.e., equal intervals of 88 days —then the S tides are completely eliminated and the maximum value is obtained for the K 2 tide. If the following lines are used when the observations extend over a year, a further value is obtained :— (362-274) - (273-185). The selection of these lines and the sums from the list is shown in detail on the schedule, giving the twenty-four values of D, which are subjected to analysis. S L and S (i h+ t are next formed, and then A t . 5 5 The calculation of the values of F 2 =SA, sin (9+t)i and G 1 = 2A t cos (9+t)i is most readily o o done on the calculating-machine, and the printed record obtained on the arithmotype is very useful for checking from. The corrections due to the tides M 2, N, L, v, T, and R are calculated and applied to F and G. The rest of the calculation is shown on the schedule, where comparisons with the results in Vol. xvi of the Indian Survey, p. 296, are also given, the differences in the values of k and R being 4°-745 and 0-0020 ft. Reference must be mado to Dr. Borgen's paper for details of the method. The whole of the calculation is, however, given in full, and the brevity of the method will be appreciated by those who have had experience in the analysis of tidal observations. For the other tides more lines from the list of sums are used ; but even then the labour of analysing a year's observations is estimated by Dr. Borgen to be about one-tenth of the labour of the method proposed by Sir W. Thomson and Mr. Roberts, and to be about one-third or half of that of Darwin's abacus. X,. (1.) + - j (3.) ix,y Kx,y. T " 1- 8 185 96 1 ForK * +231-31 5-6748 9 S6O 273 274 M * ~ 020619 1572318 2 185 362 273 274 N + 253 . 6761 (2 ° & sm( UA CO I { UAo * I OS4 2SOSJ ! IS US I I + JO-696 177-1626 •2 - 0-48628 + 0-87380 E " 10 695 182-8374 3 + 0-01720 + 0-99985 4 + 0-51605 + 0-85656 5 + 0-87589 + 0-48252 (4.) Correction for F l . Correction for G l . For M 2 - 11-471A m - 2-475B m + 2-732A m - 11-770B m N - 10-939 A n - 3588B n + 4043A n - 11-364B n L - 11-832 A! - 1-2818, + 1-374 A, - 11-9678, v - 11033Ai> - 3-4488,/ + 8-876Av - 11-4438 v T - 12-004 A, - 0-3018, + 0-292A t - 119898, R - 12022A r - 0-1118, + 0-087A r - 11-977 \i T or approximately, Correction = - 115505 A, - l-86758 y + 20672 Ay - 11-75258 y . (5 ) A = + 0083127 F - 000011230 G B = - 000011230 F + 0083549 G. R and £ are determined from the equations— R sin (£ - N) = £ R cos (C - N) = j while H and k are determined from — H =^R