May 7'], 1897] 



NATURE 



The given data may serve to show the value of the results. 



We see that the correction for the height of high water, as 

 well as of low water, at Ymuiden and Hoek van Holland, can 

 be expressed by one formula with a sufficient degree of exactitude 

 for practical use. 



Heresvith the proof is given that the wind and atmospheric 

 pressure do not considerably change the range of tide, but affect 

 the high and the low water in the same way, both being raised 

 or depressed. 



The value of a at low water seems rather larger than at high 

 water ; thus on an average the absolute calm-level at low water 

 is 5 centimetres lower than the mean low water, and at high 

 water 2 centimetres lower than the normal. In practice this 

 difference of 3 centimetres may fairly be neglected ; for the study 

 of the phenomena, however, they are important, because they 

 show that the raising of the level, caused on the Holland coast 

 by the prevailing western winds, is rather more considerable at 

 low water than at high water. The reason of this is the greater 

 depth of water at high water-level. 



The tables show very clearly that the influence of atmospheric 

 pressure on the height of the tides is not the same for the 

 different directions of the wind, but is the greatest during 

 northern winds, the feeblest during southern winds ; the propor- 

 tion often being much more considerable than we might expect 

 from the proportion of the densities of mercury and sea-water. 



I think it probable that in this proportional factor, the char- 

 acter of wind is comprehended — that is to say, that at a certain 

 atmospheric pressure the same observed wind may be more 

 local than at another barometric pressure ; in the latter case the 

 wind, for instance, reigning over a more considerable part of 

 the North Sea, and thus having a greater effect on the height of 

 the sea- level. 



Very remarkable is the evident and regular influence of atmo- 

 spheric pressure on the time of high water, which at first con- 

 sideration one would not expect. High barometer retards the 

 time of high water. 



The values of R show clearly that the sea winds raise the 

 level of the sea, and off-shore winds cause a depression. NoVth 

 and south winds act as sea winds ; the neutral line lies N.N.E. 

 and S.S.E. The greatest rise is more considerable than the 

 greatest depression, the former being caused by W.-W.N.W. 

 wind, the latter by E.-E.S.E. wind. 



The effect of wind on the time of high water is not in phase 

 with that on height, but differs about 90° with it. 



The tables indicate that southern winds, which have the same 



direction as the tidal wave, advance the moment of high water, 

 whilst northern winds retard this moment. The most im- 

 portant retardation is observed during N.N.E.-N.E. wind ; the 

 most important advance during southern winds ; the neutral line 

 is between E.N.E. and E. and between W. and W.N.W. 



The most remarkable result, brought out with surprising 

 clearness, seems to have the character of a general law of nature 

 (which, however, should be affirmed with perfect evidence by 

 comparing the obtained results with those on other points 

 observation), and is the following : — 



That the raising or depressing is proportional to the pressure 

 of wind, and that the advance or retardation in time is propor- 

 tional to the velocity of wind. 



It would be highly interesting if the same kind of investi- 

 gation could be applied to the English North Sea coast, in 

 order to see whether the influence of wind, as found for the 

 Holland coast, is local, and therefore opposite to the results to 

 be obtained at the English side ; or if the results are the same, 

 thereby indicating the influence to dominate the whole North 

 Sea. 



A special investigation as to whether a wind, continually blow- 

 ing, increases or decreases the effect on the high water-level, did 

 not give a definite rule. In general there seemed little difference 

 in height between the first and the second high water for the 

 same conditions of wind. 



Strong off-shore winds seem to influence the second, and, 

 principally the third and following high water-tide less than the 

 first ; so that the long duration seems to weaken the effect of off- 

 shore winds. 



Preceding formulae now permit us to give a formula for practical 

 use. This formula is : 



( 1 ) For the height of high water and low water at Ymuiden 

 and Hoek van Holland, 



C = KR-3-R6(B-76-o), 



expressed in centimetres. 



(2) For the time of high water at Ymuiden and Hoek van 

 Holland, 



a = K,R,-<-RaB-76-o), 



expressed in minutes. 



These formulae give, as for the sign, the correction to be 

 applied to the height, and the time predicted in the tide-tables. 



The value of the coefficients are given in the following 

 tables : — 



The way in which the values of K and K, are to be chosen, 

 depend on the way of observing the force of the wind. The 

 mentioned relation between pressure, velocity of the wind, and 

 the value of K and K, permits the choice of the proper value of 

 the latter, pressure or velocity of wind being given. 



If the force is estimated in degrees of the Beaufort scale, as is 

 usual among mariners, we may choose K and K^ according to 

 the following table : — 



1-5 

 3 



4-5 

 6-5 



8 



15 

 18 

 21 

 25 



The mean age of the effect of wind and atmospheric pressure 

 in the calculation being considered as six hours, which is not 

 far from the truth, we may consider that the prediction of 



the next high water in general ought to be corrected with the 

 observation of wind and barometer at about the precedmg low 

 water ; a case which will often occur in practice, when vessels 

 wait for the rising water to enter into the harbour. 



Suppose a sea captain approaches a harbour entrance, and 

 wishes to determine the correction for the next high water, ia 

 order to apply it to the predicted height of the tide-table. 

 He therefore observes direction and force of the wind, and 

 also the state of the barometer, and finds, for instance :— 



Direction N. 



Force 7 Beaufort. 



Barometer 77-5 centimetres. 



The values to be found in the given tables are :— 

 K = 50 R=o-6 R6=I2. 



The correction C = (SOxo-6) -3- 12(77-5 - 76-o) = 30- 3 - 

 18 = 9 centimetres. 



Thus the high water-level will be raised by 9 centimetres 

 above the predicted height of the tide-table. 



It will be easy for English mariners to change these formulse 

 into others, expressed in feet and inches instead of in 

 centimetres. 



At the end of these deductions it will, perhaps, not be out 



NO. 1439, VOL. 56] 



