DUE TO THE WEIGHT OE CONTINENTS. 
221 
the same quantity from all three principal stresses, but leaves the difference between 
the greatest and least principal stresses the same as before. 
Difference of principal stresses may also be produced by crushing. 
In this paper I call the difference between the greatest and least principal stresses 
the “stress-difference/’ and I say that, if calculation shows that the weight of a certain 
inequality on the surface of the earth will produce such and such stress-difference at such 
and such a place, then the matter at that place must be at least as strong as matter 
which will break when an equal stress-difference is produced by traction or crushing. 
I shall usually estimate stress-difference by metric tonnes (a million grammes) per 
square centimeter, or by British tons per square inch. 
In Table VII., § 9, are given the experimentally determined values of the breaking 
stress-difference for various substances. The table is divided into two parts, in the 
former of which the stress-difference was produced by tension, and in the latter by 
crushing. It is not necessary here to advert to the difference in meaning of the 
numbers given in the first column and those given in the two latter columns in the 
first half of the table. 
The cases of wood and cast brass are the only ones where a comparison is possible 
between the two breaking stress-differences, as differently produced. It will be seen 
that the material is weaker for crushing than for tension. For the reasons given in 
that section, I am inclined to think that these tables rate the strength of the materials 
somewhat too highly for the purposes of this investigation. I conceive that the 
results derived from crushing are more appropriate for the present purpose than those 
derived from tension ; and fortunately the results for various kinds of rocks seem to 
have been principally derived from crushing stresses. 
This table will serve as a means of comparison with the numerical results derived 
below, so that we shall see, for example, whether or not at 500 miles from the surface 
the materials of the earth are as strong as granite. 
We may now pass to the mathematical investigation. It appears therefrom that 
the distribution of stress-difference is quite independent of the absolute heights and 
depths of the inequalities. Although the questions of distribution and magnitude of 
the stresses are thus independent, it will in general be convenient to discuss them 
more or less simultaneously. 
The problem has only been solved for the class of superficial inequalities called 
zonal harmonics, and their nature will now be explained. 
A zonal harmonic consists of a series of undulations corrugating the surface in 
parallels of latitude with reference to some equator on the globe; the number of the 
undulations is estimated by the order of the harmonic. The harmonic of the second 
order is the most fundamental kind, and consists of a single undulation forming an 
elevation round the equator, and a pair of depressions at the poles of that equator; it 
may also be defined as an elliptic spheroid of revolution, and the absolute magnitude 
is measured by the ellipticity of the spheroid. 
