May 27, 1897] 



NATURE 



81 



In order to get a thorough check, the calculations are made 

 independent of each other for five series of observations as to 

 the height, and for three series as to the time of the tide. A 

 comparison of the results will show what degree of exactness 

 can be obtained, and how far the obtained results can be 

 trusted. 



The said series contain — 



(I) The height of high water at Ymuiden in 1895 



1896 

 1895 



and 

 II. 



(2) 



a' (3) 



(4) 



1(5) 



low 



high 



Hoek van Holland 



(i) The time of high water at Ymuiden in 

 (2) 



<3) 



Hoek van Holland 



1896 

 1896 



1895 

 [896 

 [896 



The importance of checking is further increased because of 

 the different methods of wind observation. 



At Hoek van Holland the indications of a self-registering 

 apparatus were used, which gave the force in kilogrammes (kg.) 

 per square metre, (i kg. per square metre) = 0-205 'b. per square 

 foot. ) 



At Ymuiden the direction and force were noted at 8 a.m. and 

 4 p.m. ; the force was estimated by a scale of 6 degrees, the 

 signification of these being as follows :— 



The tidal observation has in each case been combined with the 

 preceding meteorological observation ; thus the latter, on an 

 average, fell six hours before the moment of tida^^observation. 



This combination is not illogical. A special investigation at 

 Hoek van Holland, concerning the question how much time a 

 certain wind preceded its observed effect on the tide, in order to 

 find the limits of this precedence, showed that the average effect 

 on the height of tide followed the cause after a minimum of five 

 hours (out of 17 observations), and a maximum of 6 hours (60 

 observations) ; and on the time of high water alter a minimum 

 of 4 hours (13 observations) and a maximum of 7 hours (33 

 observations). 



The calculations for finding the efifect of wind and atmo- 

 spheric pressure have been made as follows. 



The variations between observation and prediction (those for 

 the height of tide after a proper correction concerning the annual 

 variation of the height of half-tide) were arranged in groups. 

 Each group contained the observations at a definite direction of 

 the wind and a definite force ,- e.g. all the observations during 



N. wind and a force =1° Ymuiden scale, were combined to a 

 group N I. 



Considering that each group corresponds to a definite influence 

 of wind, it is evident that the reciprocal differences of the varia- 

 tions, united in that one group, are caused by differences in 

 atmospheric pressure. 



A second supposition was, that the effect of atmospheric 

 pressure in every group was proportional to the difference of the 

 barometer from its normal value of 76 centimetres mercury. 



Let, therefore, the wind-effect for a certain wind-group and 

 normal barometer be jr . . . 



The rise of i centimetre barometric pressure corresponding 

 to a depression of the sea-level of y centimetres . . . 



The value of a variation =v . . . 



The observed barometric pressure = 76 -I- (5 centimetres, then we 

 have 



x^-by = v. 



We have, therefore, in one group containing n observations, n 

 equations with two unknown quantities x and y, out of which 

 the values of x and y can be solved. This method has beer» 

 applied to the groups containing ten or more variations. 



The values of y thus calculated, with consideration of the 

 number of the observations, served to deduce the effect of the 

 directions of the wind on the value of y ; this known, the 

 groups containing less than ten variations were submitted to a 

 correction according to the calculated value of _y, and so the 

 real value of x was obtained. 



These values of x now served to deduce the following quan- 

 tities : — 



(i) The effect of absolute calm. 



(2) ,, ,, the force of wind. 



(3) ,, ,, the direction of wind. 



As is known, the level of the sea at absolute calm differs 

 from the mean annual level, because the latter is influenced by 

 the prevailing winds. 



In calculating the effect of wind the supposition was made,, 

 that for every direction the effect of definite forces is always 

 expressed by the same proportion — e.g. the effect of a force 

 3 being double that of force 2 ; this proportion remaining the 

 same at all directions of the wind. 



The calculations made according to these principles showed 

 that the effect of wind and atmospheric pressure on the tides- 

 can be represented by the following formula : — 



C = (KR-«)-i-R»(B-76-o), 

 in which 



C is the correction in centimetres to be applied to the pre- 

 dicted height of high, as well as low water. 



K is a coefficient depending on the force of wind. 



R is a coefficient depending on the direction of wind. 



— a is the correction which should be applied in the case of 

 absolute calm (when K = o). 



Rj is a coefficient depending on the direction of wind,, 

 although relative to atmospheric pressure. 



B is the atmospheric pressure in centimetres mercury. 



In order to examine the results obtained by calculating the 

 independent series of observations, I give those in extenso. 

 They have reference to conditions which have, in general, 

 similarity enough to allow the comparison, as the following. 

 results will prove. 



/. Value of K. 



Calculated value- 

 of K at Hoek 

 van Holland, 

 high water 1896 



NO. 1439. VOL. 56] 



