SKCT. 5 1 TIDES 779 



Co-tidal lines have been sketched for all oceans ; a general survey is given by 

 Doodson (1958). The most recent chart is given by Villain (1951). World charts 

 with co-range lines do not yet exist. The tides of the Atlantic are discussed in 

 many papers ; besides coastal observations there are some deep-sea current 

 measurements. Defant (1932) treated the Atlantic as a one-dimensional channel 

 and compares the results of his computations with observed data. Fig. 9 con- 

 tains co-tidal and co-range lines for the Atlantic. This has been the first attempt 



Fig. 10. Co-tidal and co-range lines for constituent K2. The numbers on the full lines give 

 the time of high water in hours, which are one twelfth of the period, the time origin 

 being on the standard meridian ^here the latitude is 32". The numbers on the broken 

 lines give the amplitude H in cm. (After Fairbairn, 1954, Fig. 6.) 



to determine the tides of the open ocean by help of difference methods using 

 the harmonic constants on the coast. Fairbairn (1954) has given co-range and 

 co-tidal lines for the Indian Ocean north of the equator (Fig. 10). 



5. Classical Theory 



Laplace extended Newton's theory of tides considering inertia as well as the 

 rotation of the earth and, by this, he developed a dynamical theory which 

 interprets the tides to be an oscillation of water-masses. Laplace considered 

 the diurnal tide Ki. Later Hough (1897) expanded Laplace's theory. Airy 

 (1842) treated the tides in zonal canals which go round the world or are of finite 

 length. Goldsbrough (1913, 1914) treated tides in oceans bounded by parallels : a 

 polar sea, zonal canals and a small canal, limited by parallels. When attempting 



