G-EOLOGICAL CHANGES ON THE EAETH’S AXIS OF EOTATION. 
303 
On the whole, then, it appears that the deflection of the polar axis cannot exceed 
that which was found in the case of incompressibility, and it may possibly be consider- 
ably less. The complete want of knowledge of the internal movements only allows us 
to state a superior limit to the change which might be produced by any one upheaval 
or subsidence. 
YII. SUMMAEY AND CONCLUSION. 
24. Summary. 
For the sake of those who do not read mathematics, I will shortly recapitulate the 
chief results arrived at. 
The change in the obliquity of the ecliptic caused by any gradual deformation of the 
earth’s shape of small amount is very small. Even so great a redistribution of weights 
on the earth’s surface as is entailed by immense polar ice-caps during the Glacial Period, 
cannot have altered the obliquity by so much as 2 Too °f a second of arc ; and this is the 
most favourable redistribution of weights for producing this effect. Thus throughout 
geological history the obliquity of the ecliptic must have remained sensibly constant. 
And, further, when the earth undergoes any such deformation, the axis of rotation 
follows, and remains sensibly coincident with the principal axis of figure. 
It thus only remains to consider the change in the geographical position of the poles 
caused by the deformation. 
The principal axes at the centre of inertia of a body are three lines mutually perpen- 
dicular, and their position is entirely determined by the shape of the body. Hence if 
a nearly spherical body be slightly deformed, the extremities of these principal axes will 
move from their original positions and describe paths on the surface of the body, which 
may be shortly described as the paths of the principal axes. In the case of the earth, 
as geologically deformed, it is only of interest to consider the path of one of these axes, 
which is, in common parlance, the earth’s axis. 
If the earth be sensibly rigid, or should only readjust itself to an approximate form 
of equilibrium at long intervals (as maintained in Part I.), the geographical path of the 
axis is very nearly the same as is due merely to the geological deformation of the earth’s 
shape; but if the earth be more or less plastic, or should readjust itself frequently to an 
approximate form of equilibrium, the dynamical reactions introduced are such as more 
or less to modify the geographical path of the axis. In the case of great plasticity these 
reactions would suffice to entirely alter the character of the path. It seems probable 
that during the consolidation of the earth there was great instability in the geographical 
position of the poles. Throughout the rest of the investigation suppositions of plasticity 
are set aside, and the hypothesis of sensible rigidity is adhered to. 
Formulae for the change in the geographical position of the pole due to any small 
deformation are found in Part II. 
On the assumption that the internal density of the earth remains unchanged by the 
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