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ME. GEOBGE H. DAEWIN ON THE INELUENCE OE 
23. Changes of Internal Density producing Elevation. 
In discussing the above hypothesis, I shall confine myself to the case of the upheaval 
or subsidence being of uniform height over given areas, and shall make certain other 
special assumptions. This will considerably facilitate the analysis, and will give suffi- 
cient insight into the extent to which previous results will be modified. 
I assume, then, that the elevation of the surface is produced by a swelling of the 
strata contained between distances r l and r 2 from the centre of the globe and imme- 
diately under the area of elevation, and that the coefficient of cubical expansion a is 
constant throughout the intumescent portion. 
This will cause a fracture of the strata of equal density, and will produce a discon- 
tinuity such as that shown in figure 7, where the dotted circle of radius r 2 indicates the 
upper boundary of the swelling strata before their intumescence. 
But the shift of the earth’s axis, caused by this kind of Fig. 7 . 
deformation, will differ insensibly from what would obtain 
if there were a more or less abrupt flexure of the strata of 
equal density at the boundaries of the intumescent volume 
and of the area of elevation. 
Suppose, as before, that h is the height to which the con- 
tinent is raised above the surface; then we require to know 
a in terms of h. 
Before intumescence, let r, 9, <p be the coordinates of any 
point within the intumescent volume ; and suppose that r 
becomes r-\-u , whilst 9 and <p, of course, remain constant. 
The equation of continuity is easily found to be 
du 2 u 
d?+T =a ’ 
of which the integral is wr 2 =^r 3 -fi/3. 
If j3 be determined, so that when r=r 15 u= 0, 
But when r =r 2 , u=h, the elevation of the surface ; therefore 
3 h 1 
the required expression for a in terms of h. 
Also, before intumescence, Laplace’s law of internal density held good, viz. Q^r^, 
therefore afterwards the density of the stratum distant r-j-u from the centre is 
