224 
MR. G. H. DARWIN ON THE STRESSES 
It may be necessary to warn the geologist that this investigation is approximate in a 
certain sense, lor the results do not give the state of stress actually within the mountain 
prominences or near the surface in the valley-bottoms. The solution will however be 
very nearly accurate at some five or six miles below the valley-bottoms. The solution 
shows that the stress-difference is nil at the mean surface, but it is obvious that both 
the mountain masses and the valley-bottoms are in some state of stress. 
The mathematician will easily see that this imperfection arises, because the problem 
really treated is that of an infinite elastic plane, subjected to simple harmonic tractions 
and pressures. 
To find the state of stress actually within the mountain masses would probably be 
difficult. 
The maximum stress-difference just found for the mountains and valleys obviously 
cannot be so great as that at the base of a vertical column of this rock, which has a 
section of a square inch and is 4000 meters high. The weight of such a column is 7'I 
tons, and therefore the stress-difference at the base would be 7'1 tons per square inch. 
The maximum stress-difference computed above is 2 - 6, which is about three-eighths 
of 7T tons per square inch. Thus the support of the contiguous masses of rock, in the 
case just considered, serves as a relief to the rock to the extent of about five-eighths 
of the greatest possible stress-difference. This computation also gives a rough estimate 
of the stress-differences which must exist if the crust of the earth be thin. It is 
shown below that there is reason to suppose that the height from the crest to the bottom 
of the depression in such large undulations as those formed by Africa and America is about 
6000 meters. The weight of a similar column 6000 meters high is nearly 11 tons. 
In § 7 I take the cases of the even zonal harmonics from the 2nd to the 12th, but 
for all except the 2nd harmonic only the equatorial region of the sphere is considered. 
Plate 19, fig. 3, shows an exaggerated outline of the equatorial portion of the inequali¬ 
ties ; it only extends far enough to show half of the most southerly depression, even for 
the 12th harmonic. It did not seem worth while to trace the surfaces of equal stress- 
difference throughout the spheroid, but the laborious computations are carried far 
enough to show that these surfaces must be approximately parallel to the surface of 
the mean sphere. It is accordingly sufficient to find the law for the variation of stress- 
difference immediately underneath the equatorial belt of elevation. It requires com¬ 
paratively little computation to obtain the results numerically, and the results of the 
computation are exhibited graphically in Plate 20, fig. 4. 
Table V. (b), § 7, gives the maximum stress-differences, resulting from these several 
inequalities, computed under conditions adequately noted in the table itself. It will 
be convenient to postpone the discussion of the results. 
In § 8 I build up out of these six harmonics an isolated equatorial continent. The 
nature of the elevation is exhibited in Plate 20, fig. 5, in the curve marked “ represen¬ 
tation;” no notice need be now taken of the dotted curve. This curve exhibits a belt 
of elevation of about 15° of latitude in semi-breadth, and the rest of the spheroid is 
