434 ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1908. 



poles. One kilogram at the pole exerts the same force as 1 kilogram 

 5 grams at the equator. A pendulum clock set correctly at the 

 equator would gain 3| minutes every day at the pole, by reason of 

 increased gravitation, though the length of the pendulum remains 

 the same. The observation of these variations in gravitation is also 

 one of the methods by which we may infer the flattening of the 

 earth. It would even seem as if this method were at present the 

 best. This is all the more the case because an enormous number of 

 observations have been made in the study of variations of gravitation 

 on the globe, for the purpose of determining the flattening and for 

 other geophysical purposes, some of which I will mention later on. 

 On mountains, in valleys, in plains, in the interior of continents, on 

 coasts, on islands, on the open sea, measurements of gravitation have 

 been made. The Geophysical Institute on Hainberg possesses a 

 special treasure in an apparatus for the measurement of gravitation, 

 which some years ago was carried by the German South Polar Expe- 

 dition on the ship named after our great mathematician, astronomer, 

 and geophysicist, Gauss, of Gottingen, in order to make gravitation 

 measurements in the South Polar Sea, so rarely visited by human 

 beings. As the shape of the earth is influenced by tlie distribution 

 of gravitation, it also shows itself in the effect exerted by the earth 

 on the moon. By reason of the flattening of the earth, the moon 

 revolves somewhat differently from what would be the case if the 

 earth were a perfect sphere. Here is a third way of determining 

 the flattening of the earth. It is practicable, too, for the movements 

 of the moon must be determined with extreme care, on the one hand 

 for scientific reasons, and on the other because the movement of the 

 moon in the sky supplies an important means for determining geo- 

 grajDhic position, which is of importance, especially for the navi- 

 gator. Now the final result of thousands of observations and of the 

 extensive mathematical investigations to which I alluded culminates 

 in the statement that the flattening of the earth amounts to about 

 one two-hundred-and-ninety-eighth — that is to say, that the radius 

 of the earth at the pole is about one two-hundred-and-ninety-eighth 

 shorter than the radius at the equator. You will notice that, as in 

 the case of the measurement of gravitation, the final result of an 

 immense amount of labor is a simple numerical figure ; but you will 

 understand that to the investigator this one figure recalls the strug- 

 gles, the toil, the success of a whole science. 



I will mention that the figure one two-hundred-and-ninety-eighth 

 is not yet quite accurately determined; it is possible that the value 

 one two-hundred- and-ninety-seventh or even one differing still more 

 may prove to be the true value. 



Now, what significance has the flattening for our speculations on 

 the interior of the earth? For an answer w^e must apply to the 



