FIGURE. OF THE EARTH. 



325 



in theory, and to a certain point also by experiment, the hypothetical figure 

 most conformable to reality, the final problem, one of pure mathematical analysis, 

 and not certainly exempt from difficulties, will consist iu finding, by a collation 

 of the values of the several arcs of meridian and parallel already measured, 

 or hereafter to be measured, the curvature and dimensions of tjie ellipsoid of 

 the above species, which, without exactly satisfying one or two geodesical 

 operations, represents the results of all with the closest possible approximation. 

 In this difficult labor the Germans, Walbeck and Schmidt, by combining, re- 

 spectively, six and seven degrees of meridian, Bessel ten. Airy fourteen of 

 meridian and four of parallel, and, finally, the Englishman, Colonel II. James, 

 eight arcs of the former kind, which afforded the greatest assurance of exact- 

 ness, arrived independently at results closely coiuciding with one another, each 

 of which might serve, in the absence of the rest, for a definite solution of the 

 problem with which we are occupied. In the first of the two following tables, 

 taken, though not entire, nor in the form here presented, from the Annual 

 (Jahrbuch) of the Observatory of Berlin, for 1852, are .shown the principal 

 values given by the above mathematicians, together with the elements of the 

 ellipsoid, which served for the establishment of the decimal metric system, in 

 the calculation of which, as was before said, only the results obtained iu Peru, 

 France, and Lapland were taken into account, and that, too, before these were 

 competently known. In the second table are presented other values, relative 

 likewise to the form and volume of the earth, deduced from the fundamental 

 elements of the globe, calculated by Bessel, and not less worthy of attention 

 tlian those contained in the former table. The initials employed in both tables 

 signify as follows : 



In the first, R and r, the equatorial and polar radii ; D, their difference ; C, 

 the polar compression of the globe, or the difference of the radii referred to the 

 greater ; <? , the square of the eccentricity of any meridian ellipse, or, say, the 

 difference of the squares of the two principal radii, referred to the square of the 

 equatorial radius ; Q and q, the values of the equatorial and meridian quadrants; 

 and D and d, the values of a single degree of the equator and of a mean degree 

 of meridian, computed in metres like all the preceding which do not- express 

 abstract relations. 



In the second table the sign (p marks the latitude or distance from the equator 

 of the place or point to which the numbers on the right refer ; M expresses the 

 value of an arc of meridian of a single degree, comprised between the first and 

 the corresponding latitudes of the margin ; P, that of a degree of parallel ; R, 

 the terrestrial radius or distance of the surface from the centre of the earth 

 variable with the latitude ; and A, the area in square kilometres, comprised be- 

 tween two meridians separated by a degree of the equator and two parallels, 

 between which intervenes a degree of meridian for different latitudes. 



Elements of the terrestrial ellipsoid. 

 TABLE 1. 



