SECT. 5] LONG-TERM VARIATIONS IN SEA-LEVEL 607 



C. Eustatic Changes, Tidal Friction and the Secular Acceleration of the Moon 

 A consequence of any variation in the angular speed, oj, of the earth is that 

 the moon's mean orbital speed, n, will be changed. It is known (Jeffreys, 1959, 

 §8.04) that an apparent secular acceleration, v,^ of the moon will result from a 

 deceleration in the earth's rotation according to the formula 



dn n do) 

 "" ^ ~di~ZW ^^^ 



Eustatic changes may be involved in this phenomenon in two ways, by altering 

 the earth's moment of inertia as discussed in A, and by altering the amount of 

 tidal friction. 



Consider the orders of magnitude involved. Combining equation (5) with his 

 results quoted in section A, Young (1953) suggests that a rise in sea-level of 

 1 cm/century would, if uncompensated, produce an average secular acceleration 

 of 2 in. /(century) 2 by changing the earth's moment of inertia. In consequence of 

 the classical paper by Taylor (1919), later amplified by Jeffreys (1920), numeri- 

 cal values have been given to the retardation of the earth's rotation by tidal 

 friction. The long-accepted conclusion is that nearly 70% of the friction arises 

 in the shallow Bering Sea. As its depth is some 50 m, and as the amount of 

 bottom friction generated by a tidal current, for a given velocity, is inversely 

 proportional to the depth, a mean rise in sea-level over the Bering Sea of 1 cm 

 would decrease the bottom friction by only 0.02%. The assumption that the 

 velocity of the tidal stream would itself be inversely proportional to the depth 

 would only double the above estimate ; nor would the increase in the frictional 

 area resulting from such a general rise in level make any appreciable change in 

 the energy dissipated. 



Estimates of that part of the moon's secular acceleration which cannot be 

 accounted for by gravitational theory, deduced from astronomical observations, 

 are most difficult to interpret ; especially is this so for ancient observations of 

 equinoxes and eclipses. Nevertheless, a secular acceleration of the order in 

 5 in./(century)2 can probably be accepted. 



Murray (1957) has succeeded in separating the tidal and non-tidal contribu- 

 tions to the acceleration from both ancient and more recent observations, and 

 his important results suggest that the rate of dissipation of energy through 

 tidal friction is nearly three times greater than Jeffreys proposed. He also 

 shows that the tidal contribution is now only half what it was 2000 years ago. 



The most recent review of these problems and the uncertainty surrounding 

 the various solutions proposed has been written by Munk and Macdonald 

 (1960). 



D. Oceanographic Levelling 



A revival of interest in the possibility of using the mean sea surface as a 

 levelling instrument, independently of the more orthodox methods of precise 



1 As observed from the earth, and relative to the stars. 



