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II. Discussion of the Preceding Eesults. 



The tides seem to be normal for a place in the Southern Ocean. The semi-diurnal tides are considerable, 

 but the solar tide is unusually large compared with the lunar tide, the ratio being f, or 0-6, as compared 

 with ■ 465 of the equilibrium theory. The semi-diurnal tides are almost exactly " inverted," so that low 

 water occurs very nearly when the moon is on the meridian. 



The "age of the tide," or the mean interval from full and change of moon to springs, is (197°'8 - 172°'3) 

 -^1°-016 hours, or 2.5 hours. This is a normal result, for the ages at Madras, Bombay, and Karachi are 

 29 hours, 32 hours, and 27J hours, respectively. 



The diurnal tides are well marked, as might be expected ; and it is interesting to note that they 

 are " direct " and almost exactly in the phase indicated by the equilibrium theory. The age of the 

 diurnal inequality may be defined as the mean interval which occurs after the moon has attained her 

 maximum declination before the diurnal tide reaches its maximum. This is given by the excess of k 

 for K] over k for 0, divided by twice the moon's mean motion. Thus, in the present case, the age is 

 { 14'-6 - ( - T'O)} -^ 1°'098 hours, or 14^ hours. There does not seem to be any prevalent rule as to 

 this "age" in India, for whereas at Madras the corresponding period is 14 hours, at Bomliay and Karachi 

 this retardation is replaced by a small acceleration. 



These results are very valuable, as relating to the only ocean uninterrupted by land throughout the 

 whole circumference of the globe, yet in themselves they do not seem to present any features of special 

 interest. But they do acquire much importance when considered in connection with the very abnormal 

 results obtained by the " Discovery," which I hope to discuss in the volumes to be devoted to the 

 scientific work of that expedition. 



I wish to use the present opportunity of drawing attention to a mistake which was made in the article 

 on Tides in the ' Admiralty Scientific Manual.' It was discovered by Mr. Selby when he came to apply 

 the methods of that article to these reductions. The mistake occurs in the ' British Association Report ' 

 for 1886, referred to above by Mr. Selby, and was carried on into the Manual. The principle of the 

 method was given correctly in my paper in the ' Proceedings of the Eoyal Society ' for 1893, vol. 52, p. 365, 

 but certain small changes are needed for applying the method to the case in point. 



I hope to correct the mistake in vol. 1 of my Collected Papers, which are to be puljlished by the 

 Cambridge University Press, but it may suffice here merely to correct the errata in the Manual as 

 follows : — 



At p. 63, — Far the tides Ko and S. In the formula for tan i/-, in the denominator, for 3 • 67 p, read 

 3 '71 p, for a fortnight's observation, and 3 '84 p^ for a month's observation. In the formula for H,,, 

 wherever 3 '67 occurs, read 3-71 for a fortnight, and 3 '84 for a month's observation. The formula 



H" = — ^ H. remains coirect. 

 3-67 



For the tides Ki and P. In the formula for H' the 3 in the numerator (but not that in the denominator) 



should be replaced by 3-007 for a fortnight's observation, or by 3-027 for a month's observation. The 



formula Hp = ^H' remains correct. 



For k' = Kp = f ' + V + <^ read 



k' = K-p = f'-|-V' + <^ + 6°-88 for a fortnight, and k = k^ = f + V'-|-<^+ 13° -29 for a month. 



The succeeding numerical example must be corrected accordingly. The only sensible change is that 



k' = Kp = 334° in place of 327°. 



G. H. Darwin. 



December, 1906. 



