476 Tides of the Oceans 



make the velocity of propagation of the waves computed from the establish- 

 ments agree with the known depths. In order to explain many discrepancies 

 KrUmmel assumed interferences of waves travelling in opposite directions 

 which are very improbable. 



Harris (1904, Part IV B, p. 315) in his general treatment of the oceanic 

 tides started from a different viewpoint. He used for the first time the harmonic 

 constants of a large number of coastal stations. He followed a thought expres- 

 sed by Ferrel that the ocean tides are not progressive waves, but standing waves. 

 These theoretical assumptions were, in many instances, based on not sufficiently 

 secured fundamentals, so very soon the reliability of his results was questioned. 

 Harris divides arbitrarily the oceans into areas of oscillation, adapting their 

 dimensions to the period of oscillation and the depth of the area. Each area 

 oscillates then independently. Darwin (1902, p. 145) has rejected these 

 assumptions, pointing out that the complicated co-tidal maps of Harris is 

 inducive to find a simpler solution which will be representative of all the facts. 

 Harris should be given credit for having been the first to include the diurnal 

 tides in his considerations. Sterneck (1920, 1921, 1922) has given a different 

 presentation of the co-tidal lines of the oceans. He had at his disposal a greater 

 number of harmonic constants; furthermore, he referred his maps of the 

 semi-diurnal tides to the high water at spring and he used numerous data 

 of the establishments found in the tide tables of the various countries His 

 method is based upon the simple principle of splitting the tidal motion ob- 

 served in each locality into two orthogonal oscillations, whose phases thus 

 differ by a quarter period. Each of the oscillations is a standing wave in itself. 

 For the semi-diurnal tides he chose as basic phases and 3 h in such a way that 



i] = Hcosa(t—E) = // 1 cos(7/+i/2COSo'(f— 3h) , 

 H x = Hcosae , H 2 = Hcoso(e—3h) . 



The first term of the decomposition with the amplitude H x represents a system 

 of synchronous oscillations covering the entire ocean and which is nothing 

 else than a standing wave with the phase and 6 h respectively. The points 

 H x = will fall on certain lines which are to be considered as nodal lines 

 of this standing oscillation. Along these lines we will observe exclusively 

 establishments of 3 or 9 h because only the second term of the equation will 

 then be instrumental in determining the establishments in these points. 

 Similarly, the second term represents a system of synchronous oscillations 

 covering also the entire ocean and whose phase is 3 and 9 h respectively. 

 At points where H 2 = we will have the nodal lines of this system and here 

 the establishments will be and 6 h. Establishing these nodal lines is most 

 important, because these nodal lines form the frame of the whole system 

 of co-tidal lines. The establishments of the coastal localities give the position 

 of the nodal points on the coasts, and their connection across the oceans 

 from coast to coast gives the position of the nodal lines on the open ocean. 



