FIGUKK OF THE EAB PH. 165 



arements, made by the aid of new and more perfect analysis, 

 have, however, shown that the compression of the poles of the 

 terrestrial spheroid, when the density of the strata is regarded 

 as increasing toward the center, is very nearly g^oth. 



Three methods have been employed to investigate the curv- 

 ature of the Earth's surface, viz., measurements of degrees, 

 oscillations of the pendulum, and observations of the inequal- 

 ities in the Moon's orbit. The first is a direct geometrical 

 and astronomical method, while in the other two we determ- 

 ine from accurately observed movements the amount of the 

 tbrces which occasion those movements, and from these forces 

 we arrive at the cause from whence they have originated, viz., 

 the compression of our terrestrial spheroid. In this part of 

 my delineation of nature, contrary to my usual practice, I 

 have instanced methods because their accuracy affords a strik- 

 mg illustration of the intimate connection existing among 

 the forms and forces of natural phenomena, and also because 

 their application has given occasion to improvements in the 

 exactness of instruments (as those employed in the measure- 

 ments of space) in optical and chronological observations ; to 

 greater perfection in the fundamental branches of astronomy 

 and mechanics in respect to lunar motion and to the resistance 

 experienced by the oscillations of the pendulum; and to the 

 discovery of new and hitherto untrodden paths of analysis. 

 With the exception of the investigations of the parallax of 

 stars, which led to the discovery of aberration and nutation, 

 the history of science presents no problem in which the ob- 

 ject attained — the knowledge of the compression and of the 

 irregular form of our planet — is so far exceeded in importance 

 by the incidental gain which has accrued, through a long and 

 weary course of investigation, in the general furtherance and 

 improvement of the mathematical and astronomical sciences. 

 The comparison of eleven measurements of degrees (in which 

 are included three extra-European, namely, the old Peruvian 

 and two East Indian) gives, according to the most strictly 

 theoretical requirements allowed for by Bessel,=^ a compression 



* According to Bessel's examination of ten measurements of degrees, 

 in which the error discovered by Puissant in the calculation of the 

 French measurements is taken into consideration (Schumacher, Astron. 

 Nachr., 1841, No. 438, s. 116), the semi-axis major of the elliptical 

 spheroid of revolution to w^hich the irregular figure of the Earth most 

 closely approximates is 3,272,077-14 toises, or 20,924,774 feet ; the semi- 

 axis minor, 3,261,159-83 toises, or 20,854,821 feet; and the amount of 

 compression or eccentricity -^-^d ; the length of a mean degree of 

 the meridian, 57 013109 toi"ses, or 364,596 feet, with an error of -f 



