28 THE TIDAL PROBLEM. 



larger circular element of the Chandlerian nutation of the pole, and this 

 period of Kimura is perhaps to be regarded as a closer approximation 

 than the earher estimates of 427 to 430 days. As the sums of the tides 

 formed when the moon is on the equator, is north of the equator, and is 

 south of the equator, respectively, are different from one another, partly 

 because of the differences in the moon's position and partly because of 

 differences in the configurations of the lands and seas on the two sides of 

 the equator, there seems to be a fair presumption that there would be a 

 periodic difference in the tidal influences on the rotation of the earth 

 about its axis corresponding to the fortnightly excursions, which would 

 express itself in a nutation. Now if this period of forced nutation happens 

 to be commensurate with the free period of the earth as a rotating body, 

 the effect would be cumulative. Euler long ago computed that the period 

 of free nutation of the axis of the earth, if it were an absolutely rigid body, 

 would be 305 days. Newcomb, on the assumption that the earth has the 

 rigidity of steel, found that the period would be increased to 447 days. 

 This seems to imply that the earth is somewhat more rigid than steel 

 and has a free nutation period somewhere about 427 to 436 days. As the 

 fortnightly group of tides have a cumulative period commensurate with 

 the latter, the nutation of 436 days may perhaps be due to the agency 

 of this tidal group. 



In addition to this larger circular nutation, whose radius is about 15 

 feet, there is a smaller elliptical nutation, of about 4 feet by 14 feet, with 

 an annual period. This is assignable to the annual migration of the sun 

 north and south of the equator, which gives rise to a variety of dynamic 

 effects in the form of changes in the circulation of the atmosphere and of 

 the ocean, in the accumulation and melting of snow and of ice, etc. This 

 is in line with the common explanation of this minor nutation. 



It is an established principle that when the normal period of oscilla- 

 tion of a body is less than the period of the periodic force acting on it, 

 the oscillations of the body will agree in phase with those of the force. 

 On this principle the oscillations of the lithosphere should agree in phase 

 with the period of the tidal forces. There should therefore be direct co- 

 operation between the waves of the lithosphere and the forced water-waves. 

 On account of this close coincidence there is an obvious difficulty in dis- 

 tinguishing the contributions of the lithosphere to the water-tides from 

 those tides which spring directly from the attraction of the tide-producing 

 bodies. The two should merge into a common tide, but, if the view here 

 entertained relative to the development of water-tides through oscillations 

 of the lithosphere be valid, the actual tides are to be regarded as composite. 



If the tides of the lithosphere were of the fluidal type and acted in strict 

 coincidence with the water-tides, they would reduce the latter to the extent 

 of their own magnitude, as urged by Kelvin and Darwin;^ but in so far as 

 the pulsations of the lithosphere have the effect of a series of tiltings of the 

 basins on the lithospheric surface, they must impart oscillatory movements 

 to the water held in the basins. It is safe, on observational grounds, to 



Thomson and Tait, Natural Philosophy, Pt. II, p. 439. 



