372 Tides in the Mediterranean and Adjacent Seas 



individual waves can be shifted with respect to each other. Hansen (1938, 

 p. 429) has given detailed explanations regarding the ratio of the amplitude 

 and the difference in phase of the harmonic components in the North Sea. 

 For details of the tides in the Deutsche Bucht see also the paper of Moller 

 (1933). Table 42 gives a compilation of the harmonic constants for a series 

 of coastal localities of the North Sea (north of 53° N. lat.). 



In all following tables, unless indicated otherwise, the amplitudes are expressed in cm, the 

 phases x in degrees. The origin of time is local time of the maximum value of the corresponding 

 term of the tide-generating potential (referred to the upper transit of the tide generating "Active" 

 moon through the meridian). 



A comparison between the phases and a presentation of the tides by co-tidal lines, require 

 a reduction of the phases to a reference meridian. It is useful to give the equations necessary for 

 this reduction, because often in the literature we find that incorrect equations have been applied. Let 

 in a locality (geographical longitude X, positive towards the east) the considered partial tides have 

 the form Hcos(ot —x), t is the local time in hours, x the phase referred to local time. According 

 to equation (VIII. 13), this same partial tide, in Greenwich time, has the form H cos(otQR+pA.— x), 

 in which Iqr is the Greenwich time in hours and p is 1 or 2, according to whether the tides are 

 diurnal or semidiurnal. If we designate the phase referred to the meridian of Greenwich by g , 

 then we have g n = x—pX (A positive towards the east). 



If we select as reference meridian the meridian of S°, Greenwich time must still be changed into 

 ts time. As tQR = ts—S°l\5 (S positive towards the east), then H cos(ots +pX — o(S°ll5) — x) 

 and the phase of the tide referred to the meridian of S° will be #5 = x— pA + oS°ll5 (A and S 

 positive towards the east). The last equation is particularly used to reduce x values of a small 

 area of an ocean to a central meridian; like, for instance, the x values of the Mediterranean to the 

 meridian of 15°E., which divides this sea nearly in half. 



A reduction of the phase to mean solar hours is obtained by dividing the phase values by the 

 angular velocities (per hour) of the respective tide (for instance, M 2 = 28-984°, S 2 = 30°, K x = 

 = 15-041°, O x = 13-943°, for further partial tides see Table 28a, p. 267). 



2. The Tides of the Kattegat and the Baltic Sea 



The narrow and shallow communication between the North Sea and the 

 Baltic through the Kattegat and the Sound does not allow a good trans- 

 mission of tidal energy into the Baltic, the more so as the tides in the Ska- 

 gerrak are not very developed. The Kattegat has the form of a narrow, shallow 

 canal opening at its northern end into the Skagerrak and the North Sea, and 

 at its southern end there are three openings (Lillebelt, Storebelt and Oresund) 

 into the Baltic. The tide wave penetrates into this channel from the north, 

 is reflected partly in the south, and a part of the tidal energy penetrates into 

 the Baltic. Thus the tide wave in the Kattegat takes the form of a progressive 

 wave travelling southwards with somewhat larger amplitudes at the east coast 

 of Jutland (12-30 cm) and smaller amplitudes at the Swedish coast (4 cm). 

 Defant (1934) has given an accurate analysis of the M 2 wave, using the obser- 

 vations gained during the international Kattegat expedition of 1931. He was 

 able to show that the observations (tides and corresponding currents) can be 

 represented, according to the theory previously developed (p. 345), as the 

 superposition of two standing waves which are shifted against each other. The 



