THE PLAN OF THE EARTH AND ITS CAUSES. 379 



force of gravity throughout the globe. Figure 6 is a copy of Stein- 

 hauser's map, in which the variation of gravity is illustrated by showing 

 how many millimeters have to be added to the length of a pendulum 

 which beats seconds at the equator to make it vibrate at the same 

 rate elsewhere. In both Northern and Southern hemispheres the 

 second-beating pendulum has to be steadily lengthened as we approach 

 the poles, but the deviation is at a different rate for the two hemi- 

 spheres. The surface of the Southern Hemisphere does not approach 

 the earth's center of mass at the same rate as the Northern Hemisphere. 

 If the earth's center of mass is at its geometrical center, then the 

 earth's form is elongated southward like a peg top. It is often held 

 that the earth's center of mass is to the south of its center of form, 

 because of the accumulation of water in the Southern Hemisphere. It 

 is held that the water is piled up there owing to the greater density 

 of the Southern Hemisphere. If that be the case, then the peg-top 

 elongation is all the greater. 



Moreover, there is evidence to show that the earth's figure is still 

 more irregular than that of a peg top. 1 Sir John Herschel, although 

 taking the astronomical side in the controversy, aptly stated the facts in 

 the statement that "the earth is earth-shaped." Listing's name of 

 geoid, which expresses this view, has now supplanted the old oblate 

 spheroid from everything except the text-books. That there are local 

 deformations in the earth's shape is demonstrated by the differences 

 between the astronomical and trigonometrical determination of posi- 

 tions. Places have two different longitudes, the astronomical longitude 

 obtained by astronomical observations, and geodetic longitudes deter- 

 mined by terrestial measurements; the differences are often consider- 

 able. It was calculated, e. g., that the trigonometrical and astronomical 

 determination of the stations used in the delimitation of the Canadian 

 and United States frontier should have agreed within 40 feet, or 0.4 of a 

 second of arc; but the average error was more than five times as great, 

 and ran up to eighteen times as much as it should have been. 



Astronomical determinations, moreover, are often not only incon- 

 sistent with geographical measurements, but they are often inconsistent 

 with themselves. For example, one of the most refined estimations 

 of longitude that has yet been attempted, is the series undertaken 

 by the "K. K. topographische militiir Institut" of Vienna. To insure 

 accuracy during these observations the most elaborate precautions 

 were taken. Corrections were even made for the effect of the doses of 

 quinine whijh the astronomers took when working in malarial climates. 

 In one of the series of observations the difference in longitude between 

 Vienna and Milan was determined first directly, and then by determin- 

 ing the difference between Vienna and Brescia and that between 

 Brescia and Milan. But in spite of all the care the results did not 

 tally. The sum of the two differences was not the same as the single 



As Professor Darwin suggests, potato-shaped would be a more correct simile. 



