The Tides in Relation to Geophysical and Cosmic Problems 515 



Therefore the ordinary friction of the tidal currents is not sufficient to account 

 for this secular acceleration. 



Taylor (1919, p. 1) showed that the loss of energy for the tides of the 

 Irish Sea (see p. 346) is largely of the order of 6x 10 17 erg/sec, which is in 

 itself alone already about 60 times larger than the value found from the open 

 ocean. Jeffreys (1920, p. 239) assumed therefore that the tidal friction in the 

 adjacent and boundary seas and on the vast coastal shelf could account for the 

 dissipation of energy required by the astronomers. In these shallow seas there 

 is mostly a considerable increase of the tidal ranges, to such an extent that 

 the tidal currents exceed by far 1 cm/sec. As a matter of fact, the area of 

 these seas is small in comparison to those of the ocean, but the dissipation 

 of energy per unit area is proportional to the third power of the velocity. 

 The fact that the small Irish Sea already furnishes one twentieth of the re- 

 quired amount suggests that the friction caused by tides in the adjacent seas 

 is the decisive factor in explaining this secular acceleration. 



Jeffreys has applied Taylor's method of evaluation of the dissipation of 

 energy to a large number of adjacent seas and straits in so far as the ob- 

 servations were available in order to obtain an estimate of the total value. 

 His computations refer to spring tides and thus give maximum values listed 

 in Table 87. 



Table 87. Average dissipation of frictional energy for the semi-diurnal tide 



(Unit 10 18 erg/sec) 



The total dissipation of energy for all parts of the oceans considered 

 amounts to 2-2 xlO 19 erg/sec. This is more than the amount required by the 

 theory. It should, however, be borne in mind that a reduction to average 

 conditions is necessary. 



The superposition of the tidal currents of the lunar tide expressed by Acosat and the solar 

 tide expressed by Avcos(l — r)ot in the same manner as was done with equation IX. 2, (p. 274) gives 

 a total current 



y4[coser/-H'COs(l-/-)ar] = A{\ +v 2 + 2v cos rat) 1,2 cos (o7-arctan 





1 + vcosrot) 



33* 



