302 
ME. GEORGE H. DARWIN ON THE INFLUENCE OF 
Substituting 
in the expression i— 
Vd 2 +e 2 
C-A ’ 
and using the coefficient K, we get 
a"=2KU 7iv/d 2 +e 2 . 
It must be noticed that this investigation is applicable as much to subsidence caused 
by internal compression as it is to elevation ; and the word intumescence is used to cover 
both phenomena. In the case of subsidence h is negative. 
Now on the hypothesis of incompressibility it was shown that i"=T&.h\ / d 2 +e 2 . Hence, 
on the present hypotheses, the estimated deflection of the pole must be diminished in 
the proportion of 2U : 1. 
• 2D 
Taking qc— 141° (which makes y=2, very nearly), I have calculated the values of 
2U, when^=ff§, and -f, i, 0. If the earth’s radius be taken as 4000 miles, 
this gives, that the superficial strata for 10 miles in thickness do not swell, but are 
merely heaved up, and that the lower surface of the intumescent volume is at the 
various distances from the earth’s surface given in the first column of the following 
Table. The second column gives 2U, or the factor by which previous results would 
have to be diminished on the present hypothesis. The third column gives the so dimi- 
nished value of 1° of deflection of the pole. 
Depth below surface 
of bottom of 
intumescent volume, 
in miles, 
(c~r 2 ). 
Factor of 
diminution of 
former results, 
(2E). 
A deflection of 
1° would be 
reduced to 
(2Uxl°). 
50 
•0126 
46” 
400 
•1011 
6' 4" 
1000 
•2731 
16' 23” 
2000 
•5171 
31' 2" 
4000 
•6721 
© 
K) 
© 
The last row, of course, indicates that the intumescence extends quite down to the 
centre of the earth. 
This Table shows that if elevation is due to the swelling of strata at all near the sur- 
face, the alteration in the position of the polar axis would be reduced to quite an insig- 
nificant amount. The alleged deficiency of density under the Himalayas affords some 
slight evidence that it is so, at least occasionally. I believe, also, that Mr. Mallet is 
of opinion that the centre of disturbance of earthquake-shocks is not at a greater distance 
than 30 miles below the surface*. It does not, of course, follow from this evidence that 
there may not be elevations of both kinds going on, some being approximately super- 
ficial phenomena, and others probably due to unequal shrinking of the earth as a whole. 
The latter kind would be likely to produce more extensive deviations from the external 
form of equilibrium than the former. 
* Referred to at second hand by Mr. Caeetjthees. Trans. New-Zeal. Inst. vol. viii. p. 363. 
