DtlE TO THE WEIGHT OF CONTINENTS. 
223 
A rough calculation* will show that if the planet Mars has ellipticity g- 0 - (about 
twice the ellipticity on the hypothesis of homogeneity) the central stress-difference 
must be 6 tons per square inch. It was formerly supposed that the ellipticity of the 
planet was even greater than - 8 - 0 -, and even if the latest telescopic evidence had not 
been adverse to such a conclusion, we should feel bound to regard such supposed 
ellipticity with the greatest suspicion, in the face of the result just stated. 
The state of internal stress of an elastic sphere under tide-generating forces is 
identical with that caused by ellipticity of figured Hence the investigation of § 5 
gives the distribution of stress-difference caused in the earth by the moon’s attraction. 
In Plate 19, fig. 1, the point called “ the pole” is the point where the moon is in the zenith. 
Computation shows that the stress-difference at the surface, due to the lunar tide¬ 
generating forces, is 16 grammes per square centimeter, and at the centre eight times 
as much. These stresses are considerable, although very small compared with those 
due to terrestrial inequalities, as will appear below. 
In § 6 the stresses produced by harmonic inequalities of high orders are considered. 
This is in effect the case of a series of parallel mountains and valleys, corrugating a 
mean ievel surface with an infinite series of parallel ridges and furrows. In this case 
compressibility makes absolutely no difference in the result, as shown in § 10. 
It is found that the stress-difference depends only on the depth below the mean 
surface, and is independent of the position of the point considered with regard to 
ridge and furrow; the direction of the stresses does however depend on this latter 
consideration. 
In Plate 19, fig. 2, is shown the law by which the stress-difference increases and then 
diminishes as we go below the surface. The vertical ordinates of the curve indicate the 
relative magnitude of the stress-difference, and the horizontal ones the depth below the 
surface. The depth OL on the figure is equal to the distance between contiguous 
ridges, and the figure shows that the stress-difference is greatest at a depth equal to 
wr of OL. 
The greatest stress-difference depends merely on the height and density of the 
mountains, and the depth at which it is reached merely on the distance from ridge to 
ridge. 
Numerical calculation shows that if we suppose a series of mountains, whose crests 
are 4000 meters or about 13,000 feet above the intermediate valley-bottoms, formed 
of rock of specific gravity 2'8, then the maximum stress-difference is 2*6 tons per 
square inch (about the tenacity of cast tin); also if the mountain chains are 314 miles 
apart the maximum stress-difference is reached at 50 miles below the mean surface. 
* The data for the calculation are: Ratio of terrestrial radius to Martian radius T878. Ratio of 
Martian mass to terrestrial mass T020. Whence ratio of Martian gravity to terrestrial gravity ‘3596. 
Central stress-difference, due to ellipticity e, 996e tons per square inch. “Homogeneous” ellipticity of 
Mars j™-; and -ff-f equal to 6. 
t This is subject to certain qualifications noticed in § 5. 
