378 THE PLAN OF THE EARTH AND ITS CAUSES. 



tangential strains; for, while the sphere is of all geometrical bodies the 

 one with a minimum surface for a given capacity, the tetrahedron gives 

 a maximum surface for the same condition. Experiments on iron 

 tubes, on gas bubbles rising in water, and on rubber balloons all tend 

 to bear out the assumption that a homogeneous sphere tends to contract 

 into a tetrahedron." 



THE EARTH A GEOID. 



But it may be said this tetrahedral theory is impossible, because we 

 know from our elementary text-books that the earth is not tetrahedral, 

 but is an oblate- spheroid — that is to say, a sphere slightly flattened at 

 the poles. 



The oblate spheriod is no doubt the form that rotation would have 

 caused the earth to assume as it solidified if the earth were quite 

 homogeneous. But the earth is not homogeneous ; it varies in strength 

 and density, and an unequal load on the earth in any area leads 

 to a divergence there from the circular shape. It is, I believe, now 

 universally admitted that the earth is flattened laterally at the equator 

 as well as at the poles. The question was long disputed between the 

 astronomers, who, from theoretical considerations, declared what the 

 shape of the world ought to be, and the geographers, whose measure- 

 ments showed what the shape actually was. There is now a general 

 agreement that the geographers were right; that the equatorial section 

 of the earth is elliptical, similar to a section through the earth passing 

 across the poles. The earth is therefore not a true spheriod, and it 

 was accordingly regarded as an ellipsoid with three unequal axes. 

 But there is good reason to believe that the earth is not even an 

 ellipsoid, for the Northern and Southern hemispheres are unlike, and the 

 earth is therefore shaped like a peg top. This is shown in two ways. 

 It is a well-known property of the ellipse that degrees measured along 

 the flatter side are longer than degrees measured near the sharper end. 

 It was by proving that a degree of latitude in Lapland is longer than a 

 degree of latitude in Ecuador that the French astronomers in the seven- 

 teenth century definitely proved the earth's flattening at the poles. In 

 continuation of these observations La Oaille, in 1751, measured the 

 length of a degree at the Cape of Good Hope. His measurements 

 showed that the Southern Hemisphere was also flattened, but to a 

 different extent than the Northern Hemisphere. This anomalous result 

 of La Caille's was confirmed and extended by Maclear. 



The inequality of the two hemispheres has also been shown by the 

 variations of gravity in the two hemispheres, which, as it is more 

 easily tested, has been more widely applied. The principle is simple. 

 A pendulum swings more rapidly the nearer it is brought to the center 

 of the earth. A pendeluin swings more slowly on a mountain top than 

 at sea level. It was because Bicher, in 1C72, found that a clock which 

 kept correct time in Paris lost two minutes a day in French Guiana that 

 the polar flattening was first suspected. So many observations have 

 been made that maps havebeeu compiled showing the variation of the 



