670 



NATURE 



\Oct. 24, 1878 



ON THE TIDES OF THE SOUTHERN HEMI- 

 SPHERE AND OF THE MEDITERRANEAN^ 

 ON the coasts of the British Islands and generally on 

 the European coasts of the North Atlantic and 

 throughout the North Sea, the tides present in their main 

 features an exceptional simplicity, two almost equally high 

 high-waters and two almost equally low low-waters in the 

 twenty-four hours, with the regular fortnightly inequality 

 of spring tides and neap tides due to the alternately con- 

 spiring and opposing actions of the moon and sun, and 

 with large irregular variations produced by wind. 

 Careful observation detects a small " diurnal " inequality, 

 (so called because it is due to tidal constituents having 

 periods approximately equal to twenty-four hours lunar 

 or solar) of which the most obvious manifestation is a 

 difference at certain times of the month and of the year 

 between the heights of the two high-waters of the twenty- 

 four hours, and at intermediate times a difference between 

 the heights of the two low-waters. 



In the western part of the North Atlantic and in the 

 North Sea, this diurnal inequality is so small in com- 

 parison with the familiar twelve-hourly or "semi-diurnal" 

 tides that it is practically disregarded, and its very exist- 

 ence is scarcely a part of practical knowledge of the 

 subject ; but it is not so in other seas. There is probably 

 no other greal area of sea throughout which the diurnal 

 tides are practically imperceptible and the semi-diurnal 

 tides alone practically perceptible. In some places in 

 the Pacific and in the China Sea it has long been 

 remarked that there is but one high water in the twenty- 

 four hours at certain times of the month, and in the 

 Pacific, the China Sea, the Indian Ocean, the West 

 Indies, and very generally wherever tides are known 

 at all practically, except on the ocean coasts of 

 Europe, they are known to be not "regular" accord- 

 ing to the simple European rule, but to be compli- 

 cated by large differences between the heights of conse- 

 cutive high-waters and of consecutive low-waters, and by 

 marked inequalities of the successive intervals of time 

 between high-water and low-water. 



On the coasts of the Mediterranean generally the tides 

 are so small as to be not perceptible to ordinary observa- 

 tion, and nothing therefore has been hitherto generally 

 krio^yn regarding their character. But a first case of 

 application of the harmonic analysis to the accurate 

 continuous register of a self-recording tide-gauge (pub- 

 lished in the 1876 Report of the B.A. Tidal Committee) has 

 shown for Toulon a diurnal tide amounting on an average 

 of ordinary midsummer and mid-winter full and new 



moons to nearly ^ of the semi-diurnal tides ; and the 



present communication contains the results of analysis 

 showing a similar result for Marseilles ; but on the other 

 hand for Malta, a diurnal tide (similarly reckoned), 



amounting to only ^o( the semi-diurnal tide. The 



semi-diurnal tide is nearly the same amount in the three 

 places, being at full and new moon, about seven inches 

 rise and fall. 



The present investigation commenced in the Tidal 

 Department of the Hydrographic Office, under the 

 charge of Staff-Commander Harris, R.N., with an 

 examination and careful practical analysis of a case 

 greatly complicated by the diurnal inequality pre- 

 sented by tidal observations which had been made 

 at Fremantle, Western Australia, in 1873-74, chiefly 

 by Staff-Commander Archdeacon, R.N., the officer in 

 charge of the Admiralty Survey of that Colony. The 

 results disclosed very remarkable complications, the 

 diurnal tides predominating over the semi-diurnal tides 

 at some seasons of month and year, and at others 



» Abstract of paper byCapt. Evans, R.N. , F.R.S., and Sir William Thom- 

 son, LL,.U., F.R.S., read in Section E of the Dublin meeting of the British 

 Association. 



almost disappearing and leaving only a small semi-diurnal 

 tide of less than a foot rise and fall. These observations 

 were also very interesting in respect to the great differ- 

 ences of mean level which they showed for different 

 times of year, so great that the low-waters in March and 

 April were generally higher than the high-waters in Sep- 

 tember and October. The observations were afterwards,, 

 under the direction of Capt. Evans and Sir William 

 Thomson, submitted to a complete harmonic analysis 

 worked out by Mr. E. Roberts. Not only on account of 

 the interesting features presented by this first case of 

 analysis of tides of the southern hemisphere, but because 

 the south circumpolar ocean has been looked to on theo- 

 retical grounds as the origin of the tides, or of a large 

 part of the tides, of the rest of the world, it seemed 

 desirable to extend the investigation to other places 

 of the southern hemisphere for which there are avail- 

 able data. Accordingly the records in the Hydrographic 

 Office of tidal observations from all parts of the world 

 were [searched, but besides those of Fremantle, nothing 

 from the southern hemisphere was found sufficiently 

 complete for the harmonic analysis except a year's 

 observations of self-registering tide-gauge at Port Louis, 

 Mauritius, and personal observations made at regular 

 hourly, and sometimes half-hourly, intervals for about 

 six months (May to December) of 1842, at Port Louis, 

 Berkeley Sound, East Falkland, under the direction of 

 Sir James Clark Ross. These have been subjected to 

 complete analysis. 



So also have twelve months' observations by a self- 

 registering tide-gauge during i87i-2at Malta, contributed 

 by Admiral Sir A. Cooper Key, K.C.B., F.R.S. 



Tide-curves for two more years of Toulon (1847 and 

 1848) in addition to the one (1853) previously analysed, 

 and for Marseilles for a twelvemonth of 1850-51, supplied 

 by the French Hydrographic Office, have also been sub- 

 jected to the harmonic analysis. 



These results, both for the southern hemishere and the 

 Mediterranean, will form the subject of a paper which 

 Capt. Evans and Sir William Thomson hope to communis 

 cate to the Royal Society in the course of the coming : 

 session. In the meantime the numbers resulting from 

 the harmonic analysis are submitted without further 

 comments to the British Association for comparison 

 with those for other places in previous Reports of the 

 Tidal Committee. Those of them which represent the 

 most important of the diurnal and semi-diurnal tides are 

 shown in the following table, which includes also for 

 immediate comparison the results for Toulon, 1853. 



R in every case denotes, as in previous tables of the 

 British Association Committee, the range of the particular 

 tidal constituent on either side of mean level; so that 

 2 /? is the whole rise /rom lowest to highest of the indi- 

 vidual constituent. (In comparing results with those- 

 shown in the Admiralty Tide Tables, it must be borne in 

 mind that in the latter it is the rise above the level of 

 ordinary low water spring tides that is given as 

 " heights." 



e (technically called the epoch) is the angle, reckoned 

 in degrees, through which an arm, revolving uniformly vet 

 the period of the particular tide, has to turn till high 

 water of this constituent, from a certain instant or era of 

 reckoning defined for each constituent as follows : — 



Definition of e. ' 



To explain the meaning of the values of f given in the 

 following table of results, it is convenient to use Laplace's 

 "astres fictifs," or ideal stars. Let them be as follows : — 



M the "mean moon." 



I This definition for the several cases of A'diurnal, and O, P, Q, and L differs 

 by 90*, or 180*, or 270' from the definition given in the British Association 1S7.6 

 Report for a reason obvious on inspection of Tables I. and II., pp. 304 and 

 305 of that report, which (except in respect to the longitudes of perigee and 

 perihelion) show e as previously reckoned for the several constituents. 



