327 
comparison with the quantities of which we have to take 
cognizance in this investigation. Its truth in no way depends 
upon the arrangement of the disturbed rocks, nor upon the 
time at which successive movements have taken place, nor 
upon the alternate elevations and depressions which have at 
different times affected any given region. It includes every 
effect of subsequent denudation, from whatever cause, and to 
whatever amount. In short, it is perfectly general, so long as 
it is strictly interpreted. But it does not take account of 
elevations or depressions of regions of the surface arising from 
unequal contraction in a radial direction, if their result should 
be to cause a defect of parallelism between the datum level and 
the surface of the ocean, to which all our measurements must 
be in practice referred. However, it does not necessarily follow 
that contractions in the radial direction will cause depressions 
sn the ocean-bed accompanied with a corresponding increased 
depth of water. For instance, the defect from a true circular: 
form in the equator affects the surface of the ocean, to which 
the measurements of geodesy are always referred, so that we do 
not get an additional mile depth of ocean at the extremity of 
the shorter radius. 
If the earth had cooled as a solid body, the outer layers at 
any epoch having attained their complete amount of contraction 
sooner than the interior, would have been too large to fit the 
snterior after the cooling had proceeded further. They would 
therefore have become corrugated. But in this case the corru- 
gation would have necessarily taken place wholly in an upward 
direction; and there could be no places where any portion of 
the surface could have become depressed below the datum 
level. Hence upon this hypothesis we may introduce into our 
datum-level equation the supposition that = (B)=0. And it 
becomes Area of the Globe x 2 ke = (A). 
A little consideration will give the following geometrical 
relation : 
