DUE TO THE WEIGHT OE CONTINENTS. 
213 
The maxima in the two curves are merely found graphically, and the distances where 
the maxima are reached (viz. : 660 and 590 miles from the surface) are written down 
on the supposition that the radius of the sphere is 4000 miles. 
In the discussion in the second part of this paper, I have endeavoured to make an 
estimate of the proper elevation to attribute to these isolated continents ; so as to make 
the case, as nearly as may be, analogous to the earth. 
Although it appears impossible to make an accurate estimate, I conclude that it will 
not be excessive if we assume that the greatest difference of height, between the 
highest point in the equatorial elevation and the approximately spherical remainder of 
the globe, is 2000 meters. 
Accordingly for the representation I put 1*58^=2000, and for the second curve 
l*4/t=2000 ; these give h=l’27 X 10 5 c.m. and A=l*4x 10 5 am. respectively. 
Taking w=5*66, then for the representation we have wh— *72 tonnes per square 
centimeter, and for the other curve wh —'79 of the same units. The maximum stress- 
differences are '§lwh and ’76wh respectively. 
Therefore for the equatorial table-land (called above the representation) we have a 
maximum stress-difference of *66 metric tonnes per square c.m. or 4*1 British tons per 
square inch; and for the equatorial table-land balanced by a pair of polar continents 
(2nd harmonic omitted) we have a maximum stress-difference of *60 tonne per square 
c.m. or 3*8 tons per square inch. 
I therefore conclude that our great continental plateaus produce a stress-difference of 
about 4 tons per square inch at a depth of 600 or 700 miles from the earth's surface. 
§ .9. On the strength of various substances , 
In order to have a proper comprehension of the strength which the earths mass 
must possess in order to resist the tendency to rupture, produced by the unequal 
distribution of weights on the surface, it is necessary to consider the results of 
experiments. 
Bankine* gives a large number of results obtained by various experimenters, and 
Sir William Thomson also gives similar tables in his article on ‘ Elasticity.'! 
Amongst other constants Sir William gives Young’s modulus and the greatest 
elastic extension. If the materials of a wire remain perfectly elastic when the wire is 
just on the point of breaking under tension, then the product of Young’s modulus 
into the greatest elastic extension should be equal to what is called the tenacity, 
which is defined as the breaking tension per square centimeter of the area of the wire. 
* ‘ Useful Rules and Tables:’ Griffin, London, 1873, p. 191, et seq. 
f 4 Elasticity:’ Black, Edinburgh, 1878. This is the article from the ‘ Encyclopedia Britannica,’ but 
it is also published as a separate work. 
