264 G. II. iJartmi -Strrs*:* <-<iu.sr<l hi tin Earth b// 



The Burfai -moothed and dried in this man- 



ner, we require to find an ellipsoid of revolution which shall 

 intersect the corrugations in such a manner that the total 

 volume above it shall be equal to the total volume below it. 



Such a spheroid may be assumed to be the figure of equili- 

 brium appropriate to the earth's diurnal rotation ; if it departs 

 from the equilibrium form by even a little, then we shall much 

 underestimate the stress in the earth's interior by supposing it 

 i be a form of equilibrii 



~ " issor Bruns has in 

 any one of the "level" surfaces in the neighborhood 

 earth's surface, and he endeavors to form an estimate of the 

 departure of the continental masses and sea-bottoms from some 

 mean geoid.* From the geodesic point of view the conception 

 is valuable, but such ai sly what we require in 



the present case. The mean geoid itself will necessarily par- 

 take of the contortions of the solid earth's surface, even apart 

 from disturbances caused by local inequalities of density, and 

 thus it cannot be a figure of equilibrium. 



Thus, even if we were to suppose that the solid earth was 

 everywhere coincident with a geoid, which is far from being 

 the case, a state of stress would still be produced in the inte- 

 terior of the earth. 



An example of this sort of consideration is afforded by the 

 geodesic results arrived at by Colonel Clarke, R.E.,f who finds 

 that the ellipsoid which best satisfies geodesic measurement 

 has three unequal axes, and that one equatorial semi-axis is 

 1,524 feet longer than the other. Now, such an ellipsoid as 

 this, although not exactly one of Bruns' geoids, must be more 

 nearly so than any spheroid of revolution; and yet this 

 . (if really existent, and Colonel Clarke's own words 

 do not express any very great confidence) must produce stress 

 in the earth. Colonel Clarke's results show an ellipticity of 

 the equator equal to ttsist-. an ^ l ^ ]S i n ^ e homogeneous elas- 

 tic earth will be about equivalent to ellipticity ^y-^nn such 

 ellipticity would produce a central stress-difference of ^nnnr> or 

 nearly one-third of a. British ton per square inch. 



From this discussion it may, 1 think, be fairly concluded 

 that if we assume the sea-level as being the figure of equilib- 

 rium, and estimate the departures therefrom, we shall be well 

 within the mark. 



The average height of the continents is about 350 meters 

 (1150 feet), and the average depth of the great oceans is, in 

 round numbers, 5,000 meters (16,000 feet) ; but the latter data 



