From recent values of improved accuracy of the apparent secular accelerations
v
and
v'
of the Moon and Sun, the lunar and solar tidal couples
N
and
N'
can be found. The appropriate dynamical theory shows that the moment of inertia of the Earth,
C
, has been diminishing at an average rate of -1.67 x 10
27
cm
2
g s
-1
during the past 3300 years, giving rise to a non-tidal angular acceleration
ω
∙
i
= 1.52 x 10
-22
s
-2
in addition to the retardations of
ω
resulting from the lunar and solar couples. The intrinsic couple associated with
Ċ
, the time-rate of change of
C
, is considerably greater than the solar tidal couple on all values of
v
and
v'
so far determined. For an initially all-solid Earth, use of known seismic data shows that the moment of inertia has decreased during the past 3 Ga at an average rate of -1.72 x 10
27
cm
2
g s
-1
since a liquid core first began to form, a figure in close agreement with the value based on ancienteclipse data. On the time-honoured hypothesis that the core has resulted from iron separating downwards in an originally homogeneous Earth, the rate of decrease of
C
is -0.873 x 10
27
cm
2
g s
-1
, only about one-half of that based on ancient-eclipse data, while if applied to these data the ratio
N
/
N'
= 11.35, which is more than twice the theoretical ratio on any tidal hypothesis. These results show that the iron-core theory is physically unacceptable.
Modelling of spacecraft spin period during eclipse