80 MODERN SEISMOLOGY 
calculations. The quantities 2 and & are not independent, 
but are related and dependent on the physical properties of 
the Earth as a whole. The simplest assumption that can be 
made is to regard the Earth as a uniform sphere which is in- 
compressible, but possesses rigidity mw, and further that the 
tides may be computed on an equilibrium theory. We then 
find that 
k= ph, and = $/(1+ 29H), 
2gpa 
Thus if we accept the experimental value 2- k= 1/3 we get 
h=5/6 and &=1/2 while ~=7°I x10" dynes per sq. em. 
This value of ~ which is nearly that of steel, formed the ground 
of Kelvin’s estimate of the Earth’s rigidity. Darwin, however, 
did not accept this, but regarded the observed reduction of 
the fortnightly tides as due to the difference between the 
dynamical and the equilibrium theory (cf. Lamb, “ Hydro- 
dynamics ”). 
The preceding result, however, conflicts with data derived 
from the free period of precessional nutation of the Earth as 
derived from astronomical observations. Larmor (‘“ Proc. 
R. S.,” Vol. 82, p. 89, 1909) shows that 
1-(\- PEE) 
where T, is the theoretical Eulerian period 306 days, 
T the observed Chandler’s period 428 days, 
w the angular velocity of rotation of the Earth. 
and is the ellipticity of the ocean surface. Thus since 
w’a]g=1/289 and e has practically the same value, we get 
k= 0°28, and this with 2 - k=0°33 gives =0'61 which does 
not satisfy the relation £= 3 and leads to a higher estimate 
of the Earth’s rigidity. 
Schweydar (“ Veroff. Kon. Preuss. Geod. Instit.,’ No. 54, 
1912) investigates the reason for the discrepancies. He takes 
account of the oceanic tides, and further introduces Wiechert’s 
assumption that the solid part of the Earth consists of a shell 
of density 3:2 and thickness 1500 km., and a nucleus of density 
8:2, It would perhaps have been an advantage to have 
