570 Table 716 



MISCELLANEOUS GEOPHYSICAL DATA 



Equatorial radius of earth, a, 6,378,388 m ± 18. 

 Ellipticity, flattening, {a-b)/a, 1/297 or 0.003,367,003,4. 



(Adopted at International Geodetic and Geophysical Union, 1924.) 



Polar radius, b, 6,356,911.946 m. 



Square of the eccentricity, e 2 , or {a'-b 2 )/a 2 , 0.006,722,670,0. 



Quadrant of equator, 10,019,148.4 m; ditto of meridian, 10,002,288.3 m. 



Area of ellipsoid, 510,100,934 km 2 ; volume of ditto, 1,083,319,780,000 km 3 . 



Radius of sphere having same area, 6,371,227.7 m. 



Radius of sphere having same volume, 6,371,221.3 m. 



Difference between geographical latitude, 4>, and geocentric latitude : <£'. 

 <$ — $' = 695V6635 sin 2* — i'-'i73i sin 4* + o'-'oo26 sin 6<J> 

 = 695"6635 sin 2$' -f 1 '.' 1 73 1 sin 4*' + o'-'oo26 sin 6*' 



Newtonian constant of gravitation, G, (6.664 — 0.002) X io -8 dyne cirfg" 2 (Heyl). 



Mean density of the earth, 5.522 (Lambert). 



Continental surface density of the earth, 2.67. \ / darkness ) 



Mean density outer 10 miles of crust, 2.40. J *■ 



Rigidity, (i, 8.6 X 10" c.g.s. units. \ Michelson, Astrophys. Journ., 



Viscosity, 10.9 X io 16 c.g.s. units (comparable to steel). J 39, 105, 1914. 



Moments of inertia of the earth, the principal moments being taken as A, B, and C, and C 



the greatest (De Sitter, 1924) : 

 A = B = 0.33235 X Ea 2 C= 0.33344 X Ea 2 C — A = 0.0010921 X Ea 2 . 



(C — A)/C = 0.0032774, from precession. 

 Mass of the earth = E — 5.983 X io 24 kg ; a = equatorial semidiameter. 



Formulae for theoretical gravity at the surface of the ellipsoid (which is assumed to be an 

 equipotential surface) : 



7 = 7e ( 1 + 0.005288 sin 2 $ — 0.000006 sin 2 2*) cm/sec 2 . 

 = 7«(i + 0.002637 cos 2 * + 0.000006 cos 2 2$) cm/sec 2 . 

 7e = sea-level gravity at equator 745 = sea-level gravity at lat, 45 

 = 978.038 cm/sec 2 . Bowie = 980.621 cm/sec 2 . Bowie 



.052 Helmert .629 Helmert 



.052 Heiskanen .630 Heiskanen 



There is a systematic difference between gravity determinations over land or over sea, 

 the latter being greater ; this leads Bowie to favor a value of 078.5 2 — -°o8 for the value 

 above. 



This systematic difference has led to the formula : 



g = 978.052 ■{ 1 + 0.005288 sin 2 <£ — 0.000006 sin 2 20 -f- 0.000023 cos 2 «£ cos 2(\ + 5°) \ , 

 where X = east longitude. This longitude term has appeared to be indicated by the results 

 of several observers. — Clarke, 1878, Helmert, 1915, and Heiskanen, 1928. It could be taken 

 as indicating that the earth had three unequal axes. 



Mean linear velocity of the earth in its orbit, 29.77 km/sec. 

 Mean linear velocity of rotation of earth at equator, 0.465 km/sec. 

 Rotational energy lost by tidal friction, 1.1 X io 19 erg/sec. (Jeffreys). 

 Angular velocity of rotation, 72.921 X io" 6 radians/mean-solar-second. 

 Rotational energy, 2.160 X io 36 ergs/sec. 



(See Lambert, Science, 63, 242, Mar. 5, 1926; Journ. Wash. Acad. Sci., 18, 571, 1928.) 



Smithsonian Tables 



