FIGURE OP THE EAETH. 157 



is so far surpassed in importance by the incidental gain 

 which, in the course of its long and arduous pursuit, has 

 accrued in the general cultivation and advancement of 

 mathematical and astronomical knowledge. The compari- 

 son of eleven measurements of degrees (including three 

 extra European, the old Peruvian and two East Indian 

 arcs), discussed by Bessel in a memoir in which due regard 

 is paid to the most modern refinements, gives an ellipticity 

 of -2-fg-, ( 13 ) being a difference between the polar and equa- 

 torial semi -diameters, of 10938 toises (69648 English feet), 

 or about 11-6 geographical miles. The excess of the 

 equatorial radius resulting from the curvature of the surface 

 of the spheroid amounts, therefore, in the direction of gra- 

 vity, to more than 4-f- times the height of Mont Blanc, or 

 twice and a half the probable height of the summit of the 

 Dhawalagiri in the Himalaya Chain. The lunar inequalities 

 (perturbations of the Moon's motion in longitude and 

 latitude), give, according to Laplace's most recent investi- 

 gations, almost the same result for the Earth's ellipticity 

 as the measurements of degrees, viz. ?%-. The experiments 

 with the pendulum give a much greater compression, viz. 

 -2Tr( 131 )' It i s related that Galileo, when a boy, observed, 

 during the performance of divine service, that the height of 

 the vaulted roof of a church might be measured by means of 

 the time of vibration of chandeliers suspended at different 

 heights ; but he could scarcely have anticipated that pendu- 

 lums would one day be carried from pole to pole to determine 

 the figure of the earth. In this research it has been found 

 that the length of the seconds pendulum is aflected by the 

 unequal density of the superficial strata of the earth. This 

 geological influence on an instrument by wlich time is 



