Tides in the Mediterranean and Adjacent Seas 



411 



of small bodies of water like canals, and he has also given methods to com- 

 pute numerically this influence. We will discuss this problem of the ocean and 

 earth tides later on more thoroughly (p. 506). Here we will mention only the 

 results obtained by Grace (1930, p. 274) who was the first to apply Proudman 

 methods to the A/ 2 tide of the Red Sea. For this purpose, it is necessary to 

 have tidal data as accurate as possible along the central axis of the sea, for 

 which reason a reduction of the harmonic constants of the coastal localities 

 to the centre line of the Red Sea should be made. Under certain conditions, 

 such a reduction is feasible and Grace obtained for certain points on the centre 

 line the constants of the M, tide listed in Table 55 (see "corrected" values). 

 With these values one obtains, by numerical integration of the hydrodynamical 

 equations, provided appropriate factors are selected to satisfy the boundary 

 conditions, the theoretical M 2 tide. Then, from the factors one obtains also the 

 proportionality factor of the motion of the earth to the tide generating force 

 (seep. 508). The comparison between the theoretical tides and the observations 

 shows that in the Gulf of Suez the agreement is not good, perhaps for the rea- 

 son that transverse motions and friction are more disturbing here. In the Red 



1000 



2000 



Fig. 173. Distribution of amplitude along the Gulf of Suez and the Red Sea. — 

 puted by Grace; x: observed values, reduced to the centre axis. 



-, com- 



Sea the values for Massaua, which are locally disturbed, do not agree; other- 

 wise, the agreement is in general somewhat better than by Defant's method. 

 In Fig. 173 the theoretical distribution of the amplitudes of the longitudinal 

 oscillation is represented by the full-drawn curve, whereas the observed values 

 are indicated by dots. 



For determining the ratio of the co-oscillating tide to the independent 

 tide, the theoretical and the observed values of Table 55 can be divided into 

 two parts, one of which will have the phase of the tide-generating potential 

 on the central axis of the sea in its principal direction (Phase: 44° or 224° 

 from Greenwich), the other one the phase of M 2 in Aden 136° from Green- 

 wich. We, therefore, put Hcos(at—y) = H t cos(ot—44°)+H 2 cos(at—\36) in 

 which 



