DUB TO THE WEIGHT OE COUTIHEHTS. 
229 
The point at which this maximum is reached is given in each case, and Plate 20, fig. 4, 
illustrates graphically the law of variation of stress-difference. 
The second harmonic cannot be said to represent a continent, and the table shows 
that in each of the other cases the maximum stress-difference is very nearly 4 tons 
per square inch. The depths of the maximum point are of course very different in 
each case. 
We have concluded above that Africa and America are about equivalent to an 
harmonic of the fourth order, hence it may be concluded that the stress-difference 
under those continents is at a maximum at more than 1100 miles from the earth’s 
surface, and there amounts to about 4 tons per square inch. A comparison with 
Table VII. shows that marble would break under this stress, but that strong granite 
would stand. 
The case of the isolated continent investigated in § 8 appeared likely to prove the 
most interesting one, for the purpose of application to the case of the earth. But 
unfortunately I have found it difficult to arrive at a satisfactory conclusion as to the 
proper height to attribute to the continent. 
The average height of the American continent is about 1100 feet above the sea, and 
the average depth of the Pacific Ocean about 15,000 feet. If the water of the Pacific 
be congealed into rock, it will have an effective depth of 10,000 feet. The greatest 
height of the American continent above the bed of the dried Pacific when smoothed 
down must be fully 12,000 feet or 3700 meters. The height of the great central 
Asian plateau above the average bed of the southern ocean (after drying) must be 
considerably more than this. 
Now in the application to the homogeneous planet the heights are to be halved to 
allow for the smaller density of surface rock. 
I therefore take 2000 meters as the height of the top of the equatorial table-land 
above the remaining approximately spherical portion of the sphere. 
The investigation of § 8 then shows that the equatorial table-land will give rise to a 
stress-difference of 4*1 tons per square inch at a depth of 660 miles ; and that the 
equatorial table-land counterbalanced by the pair of polar continents (the second 
harmonic constituent being absent) gives a stress difference of about 3’8 tons per 
square inch at a depth of 590 miles. 
This estimate of stress-difference agrees in amount, with singular exactness, with 
that just found from the case of the 4th zonal harmonic, but the maximum is reached 
400 or 500 miles nearer to the earth’s surface. 
I think there can be no doubt but that there are terrestrial inequalities of much 
greater breadth than that of my isolated continent; thus this investigation for the 
isolated continent will give a position for the maximum stress-difference too near the 
surface to correspond with the largest continents. On the other hand, I do not feel 
at all sure that I have not considerably underestimated the height of such a compara¬ 
tively narrow plateau. 
