318 Scientific Intelligence. 
of ssh the earth is made must be strong enough to bear this 
stre 
We are thus led to enquire how the stresses are distributed in 
the earth’s mass, and what are magnitudes of the stresses 
In this paper I have solved a a problem of the kind indicated for 
the case of a homogeneous incompressible elastic sphere, and have 
applied the results to the case of the eart 
the earth be formed of a crust with a semi-fluid interior, the 
stresses in that crust must be greater than if the whole mass be 
solid, very far greater if the crust be thin. As regards the con- 
ition of incompressibility attributed to the materials of the earth, 
it is proved in this paper that the er ey of the solid 
nh a harmonic class, when large compressibility would con- 
cerned modify the results, 
The strength of an elastic solid is here estimated by the differ- 
ence honwaee the greatest and least principal stresses, when it is 
on the point of breaking, or, according to si phraseology adopted, 
by the breaking stress-difference . The most familiar examples of 
of the mat ie Sisen-diGeeonie. is thus to be measured by tons 
per square 
Tables of aan stress-differences for various materials are 
given in the paper. 
he problem is only solved for the class oa ee ee called 
onal harmonics; these consist of a num ng 
fobed the globe in parallels of latitude. The. sashes of waves is 
determined by the order of the harmonic, In the application to 
the earth the equator here referred to may be any great carole, 
and is not necessarily the terrestrial equator. The second hat 
monic has only a single wave, and consists of an elevation at an 
equator and depression at the pole; this constitutes Sige ga! of 
~ ae An wegen of a hi zh ae may be rope as 
es of mountain chains, with i ening valle ey ee 
pond the globe in parallel of | poctiach eeininied with te ste 
to the pigs equato 
ase of the end harmonic is considered in detail, and it 
is mowed that the stress-difference rises to a maximum ’at the 
center of the globe, and is constant all over the surface. The 
central stress-difference is eight oie as great as the superficial. 
On evaluating the — arising from given ellipticity 
in a rotating spheroid of the size and density of the earth, it 
appears that if the excess or detest of ellipticity above or below 
the equilibrium value were z;4;5, then the stress-difference at the 
centre would be 8 tons per square inch; and that, if the sphere 
were made of material as strong as brass, it would be just on the 
point of rupture, Again, if the homogeneous earth, with minyery 
ztz, were to stop rotating, the central stress-difference would b 
