26 MAGNITUDE, FIGURE, AND 



exact knowledge of particular dates has a great interest in 

 the history of the establishment of physical astronomy on 

 mathematical foundations. 



If the direct measurements of arcs of meridians and pa- 

 rallels (particularly the Erench arc ( 15 ) of the meridian 

 between lat. 44 42' and 47 30', and the parallel arc 

 between points situated east and west of the Graian, Cot- 

 tian, and Maritime Alps), ( 16 ) show great deviations 

 from the mean ellipsoidal figure of the Earth, the irregu- 

 larities in the measure of the ellipticity given by pendulum 

 stations differently distributed or grouped as respects 

 geographical relations, are much more striking. The de- 

 termination of the figure of the Earth by the increase or 

 decrease of gravity (intensity of attraction at the respec- 

 tive places) supposes that the intensity of the force at the 

 surface of the terrestrial rotating spheroid has remained the 

 same as at the period of solidification from a fluid state, 

 and that no subsequent changes of density have taken place 

 init.( 17 ) Notwithstanding the great improvement of instru- 

 ments and methods by Borda, Kater, and Bessel, there are at 

 present in both hemispheres, from South Shetland to Spitz- 

 bergen therefore from 62 56' S. to 79 50' N. latitude- 

 only between 65 and 70 points very irregularly distributed 

 over the earth's surface, ( ls ) at which the length of the 

 simple pendulum has been determined with the same exact- 

 ness as the position of the place in latitude, longitude, and 

 height above the sea. 



The pendulum experiments made on the part of an arc of 

 the meridian measured by the Erench astronomers, as well as 

 the observations made by Captain Kater in connection with 

 the Trigonometrical Survey of Great Britain, showed that the 



