290 
ME. GEOEGE H. DAEWIN ON THE INFLUENCE OF 
Then if we take £=’0033439, being the mean of the values given by Colonel A. R. 
Clakke, m= 9g g. 66 , and <?=20,899,917 feet*, M=|ttBc 3 , and y = 2 ’ we S’ et 
C- A=f 7T ? c 4 X -0010809 X 20,899,917 
and 
K=l-08986. 
3D 
If, in accordance with Thomson and Tait, y=2*l, K=l*0380, but I shall take K 
as 1’090. Then we have i" = KA\/ d 2 +e 2 , where K=T090, li being measured in feet, 
and i" being the angular change in the position of the principal axis of greatest moment 
of inertia of the earth, due to a deformation given by JiF(b, <p) all over the surface of 
the spheroid. 
^ j_ 2c • • • 
The angle — — — . t is clearly of the same order of magnitude as i, as it was assumed 
to be in Part I. 
III. FOEMS OF CONTINENTS AND SEAS WHICH PEODUCE THE MAXIMUM DEFLECTION OF 
THE POLAE AXIS. 
13. Conditions under which the Problem is treated. 
On the hypothesis of incompressibility, the effect of a deformation in deflecting the 
pole is exactly equivalent to the removal of a given quantity of matter from one part of 
the earth’s surface to another. But as no continent exceeds a few thousand feet in 
average height, the removal is restricted by the condition that the hollows excavated, 
and the continents formed, shall nowhere exceed a certain depth and height. The 
areas of present continents and seas, and their heights and depths, give some idea of the 
amount of matter at disposal, as will be shown hereafter. It is interesting, therefore, to 
determine what is the greatest possible deflection of the pole which can be caused by 
the removal of given quantities of matter from one part of the earth to another, subject 
to the above condition as to height and depth. 
14. Problem in Maxima and Minima. 
This involves the following problem : — To remove a given quantity of matter from 
one part of a sphere to another, the layers excavated or piled up not being greater than 
1c in thickness, so as to make V / D 2 +E 2 a maximum, the axes being so chosen as to make 
F=0. 
If D', E' be the products of inertia referred to other axes having the same origin 
and axis of z as before, it may easily be shown, from the fact that D 2 +E 2 =D' 2 -j-E' 2 , 
that D 2 +E 2 is greatest and equal to E' 2 for that distribution of matter which makes 
D'=0 and E' a maximum. 
* See Thomson and Tait, Nat. Phil. pp. 648, 651. 
