508 The Tides in Relation to Geophysical and Cosmic Problems 



through numerical integration, the tidal range t] — r) except for one unknown 

 constant; it therefore only gives a relative tide of the solid earth, i.e. the 

 difference between the elevation of the crust r\ related to the elevation caused 

 by the attraction of the protuberance. 



The second method is less dependent upon the accuracy of the observations. 

 If we replace u and r\ by ue iat and Fe iat and if we take 



V — yVi + ^2 and u = yuj_ + lu 2 

 then equations (XV. 3) and (XV. 4) become 



toh+g'to 







(XV. 5) 



The two expressions between brackets, put equal to zero, give with the 

 boundary conditions rj x = and Su x = for x = 0, a forced oscillation 

 caused by the force grj. The two expressions between parentheses with the 

 boundary condition r) 2 = 1 cm, Su 2 = for x = give a free oscillation 

 with boundary conditions which are at first arbitrary. A general solution 

 of the equations is then 



u = {{\-h + k)u x +lu 2 )e^\ K " ' 



A comparison with the observations on at least one station (section) allows 

 one to compute both the unknown y = 1 — h + k and /, while it is also possible 

 to determine differences in phase (4 unknown). 



Grace (1930, p. 273; 1931, p. 301) has applied this method to Lake Baikal 

 and the Red Sea. He used the second method for Lake Baikal. Neglecting 

 the tides of the solid earth, he repeated, first, the computation of Sterneck 

 (see p. 454), and he obtained the same results. The amplitudes at the ends 

 of the lake were 15-7 and 12-3 mm (see Fig. 192). Taking into consideration 

 the tides of the solid earth, and basing himself on the observations made in 

 the Petschannoja Bay, he found y = l — h + k = 0-54 for M 2 and 0-73 for K x 

 and at the same time a reduction of the amplitudes to the observed values. 

 The average of the two y values happens to agree with Jeffreys's value. It can 

 be taken for granted that the tides of the solid earth eliminate the contra- 

 diction which existed between the observations, and the results of the theory 

 which, owing to the smallness, narrowness, and great depth of the oscilla- 

 ting water-masses, had to follow the simple equilibrium theory. It is not 

 necessary to attribute these differences to the friction as Sterneck did. 



Proudman proposed the Red Sea as especially suitable for the computation 

 of the tides of the solid earth, Grace has made such survey for the M 2 tide 

 for this sea, using both methods. In following the second method there he 



