August 4, 19 10] 



NATURE 



145 



vides just what is wanted to meet this requirement 

 with all needful accuracy. He has computed a set of 

 auxiliary tables from which the required results may 

 be extracted with a fair degree of rapidity. It is in 

 the explanation of the use of these tables that I fear 

 the Dutch language may prove a difficulty to some 

 would-be users of the method.' 



I shall not try to explain the process in detail, but 

 will only sketch the ideas on which it is founded. It 

 is assumed that sufficient accuracy will be obtained 

 if the phase of each of the constituent tides is speci- 

 fied to the nearest exact hour of mean solar time. 

 It is easy to compute the fall and rise of any con- 

 stituent tide for successive hours. For example, sup- 

 pose that we consider the tide M,, that its amplitude 

 is, sav, 174 (expressed in cm. or any other unit), and 

 that we designate the hour of its high water as on.; 

 then its march would run thus : — 

 h. h 



... 174 I 3 ••■ 9 



1 ... 152 4 ■•• -70 



2 ... 92 I &c. cVc. 



Now if at any given place, and on any given day, we 

 find the incidence of the high water of M, to the 

 nearest clock hour, it is easy to write down the suc- 

 cessive heights from the table in a schedule numbered 

 from oh. to 23 h. If, for example, high water of M„ 

 is found to occur at 13 h. of clock time on the day in 

 question, we should write 174 opposite 13 h., 152 oppo- 

 site 14 h., and so on. The same process may be car- 

 ried out for each of the principal component tides, 

 and the sum may be obtained for each hour of the 

 twenty-four, thus furnishing the resultant height of 

 water! Auxiliary tables are furnished by Dr. van der 

 Stok from which it is easy to determine the incidence 

 of each partial high water in clock time, and tables 

 of fall and rise are given for any reouircd amplitude. 



I should guess that it would take from twenty 

 minutes to half an hour to compute and draw a fairly 

 .-iccurate tide-curve for any given day. If this estimate 

 is correct, it would take a computer a month to draw 

 a tide-curve for a whole year. Probably the work 

 would be quicker when the tide is to be found for a 

 succession of davs, and in any case the task would 

 not seem to be prohibitive to compute a year's tide- 

 lable with accuracv sufficient for practical purposes. 



The paper also gives an example of the synthesis 

 from harmonic constants of the tidal currents at a 

 place called .Sembilangan. This last statement may 

 well prove almost unintelligible even to a man versed 

 in tidal work. For a full explanation I must refer 

 the reader to Dr. van der Stok's " litudes des 

 Phenomenes de Maree sur les Cotes N^erlandaises." ^ 

 Four of this series of papers have been already pub- 

 lished bv the Xederlandsch Meteorologisch Instituut. 

 I have not seen the first, but the second and third 

 are dated igOj, while the last is of later date than the 

 paper which we are now reviewing. I gather_ that 

 the first of the series gives a method of obtaining 

 tidal constants from observations taken every six 

 hours, and the subject is resumed in the last paper, 

 which contains an immense mass of information about 

 the constants along the whole length of the Dutch 

 coast. But I must revert to the subject of tidal cur- 

 rents discussed in the second and third of the series, 

 and explain in outline what is meant by the harmonic 

 analysis of tidal currents. 



1 Something of tl'e kind has been done bv Harris in his "Manual of Tides," 

 part iii.. p. 183. His procedure seems 10 be more ela*iorate, and probably 

 more accurate, but also less rapid than that devised by Dr. van der Stok. 



1 These papers ought to have been noticed in the article " Bewegung der 

 Hvdrosphiire " of the German Encyclopedia of Mathematics. Mv article was 

 really written before the publication of Pr. van der Stok's first three papers, 

 but in the subsequent and final revision for the press I carelessly look these 

 papers merely to relate to local hvdrographv. References are given in them 

 10 other papers by MM. Phaff, Petit, van Hcerdt, &c., on the hydrography 

 of the Dutch coast. 



NO. 2127, VOL. 84] 



The author caused a large number of observations 

 to be made from light-ships off the Dutch coast, and 

 then undertook to make an elaborate studv of the 

 tidal currents which had been noted. He found it 

 possible to define the velocities and phases of the com- 

 ponents of current by means of a notation analogous 

 to that used in defining the rise and fall of the tide. 

 Thus the velocities for the several kinds of tide were 

 specified in centimetres per second, and the phases by 

 angles analogous to the it's in use in the more or- 

 dinary harmonic analysis. A similar investigation 

 had been carried out at Sembilangan, in the Dutch 

 Indies, and it is the result for that place which is 

 given in the paper under review. 



It is clear that the harmonic constants which define 

 the horizontal motion of the water cannot claim a 

 high degree of accuracy, but it affords a conspicuous 

 advance that the attempt should have been made and 

 crowned with a certain amount of success. 



The vortices off the Dutch coast are very compli- 

 cated, and the author refers to .Airy's theory ("Tides 

 and Waves," §§ 358-63) as affording in some measure 

 an explanation of the facts, although he does not find 

 the explanation by any means complete. 



In No. ii. of the papers to which I now refer. Dr. 

 van der Stok integrates, for the light-ship station of 

 Schouwenbank, the expressions for the components 

 of velocity, and thus finds the trajectories of a particle 

 of water under the influences of the tides M,, S„, and 

 Mj ; he also determines the general drift of the water. 

 The figures illustrative of his conclusions are very 

 interesting, and I commend these papers to the notice 

 of all who are interested in tidal theorv.' 



G.'H. D.ARWiN. 



THE LEANING TOWER OF PISA. 



THE first stone of the campanile of Pisa was laid 

 in August, 1174, by Bonanno of Pisa and 

 William of Innsbruck, but accounts given us by 

 various authors are very conflicting and uncertain in 

 regard to the construction of this splendid work of art, 

 which, after being interrupted several times, was com- 

 pleted nearly two centuries later. 



The tower, which is entirely of white marble, is of 

 cylindrical shape, hollow in the centre, with a spiral 

 staircase constructed in the thickness of the outer 

 wall which leads up to the belfry floor. The first tier 

 is surrounded bv fifteen large columns, with vaulted 

 arches half-encased in the wall, and the six upper 

 tiers are each decorated by an equal number of peri- 

 styles with arches, supported by altogether 192 isolated 

 columns. The eighth and "last tier, of smaller 

 diaineter, on which are placed the bells, was con- 

 structed, according to tradition, by one Tommaso, 

 architect and sculptor, a pupil of .\ndrea Pisano. 



.\s is commonly known, the tower, the height of 

 which is about 56 metres, has a noticeable leaning 

 on its axis, and the cause of this leaning gave rise to 

 bitter controversy among the Pisan writers in past 

 centuries, some of whom attributed the strange_ piece 

 of architecture to the high ingenuity of the builders, 

 while others more reasonably maintainetl that the 

 explanation was to be sought 'in the instability of the 

 Pisa subsoil. 



The recent investigations of a competent Govern- 

 ment Commission, composed of Profs. :Mario Cana- 

 vari, Paolo Pizzetti, and Agenore Socini, and Drs. 

 Giovanni Cupoari and Francesco Bernieri, have not 

 only confirmed that the leaning of the tower is cer- 

 tainly due to a subsidence of the ground, but that this 



1 Similar results will be found in Helland-Hansen and Nansen's " Nor- 

 wegian Sea. Report on Norwegian Fishery," vol. ii , 1909, No. 2, p. 107 ; 

 and Miss Kirstine Smith's " Gezeitenstroemern, " Havenundersogelser, vol. 

 ii., No. 13, igio. 



