Ixvi GEODESY. 



Assuming the mass of a cubic foot of water to be 62. 28 pounds (at 62° F.), 



Mass of earth* = 13 284 X lo"^ pounds. 



= 6 642 X 10^* tons (of 2000 lbs.). 

 = 60258 X 1 0-° kilogrammes. 



d. Principal moments of inertia and energy of rotation of earth. 



M =■ mass of earth, 



A = moment of inertia of earth about an axis in its equator, 



C = moment of inertia about axis of rotation, 



a = equatorial axis of earth, 



oj = angular velocity of earth, 



= (2 77/86164) for mean solar second as unit of time. 

 Thent 



A = 0.325 Ma'-, 

 C = 0.326 Jlfa'\ 



Energy of rotation of earth =z i- w^C. 



= 0.163 ^Ma^. 



:=504 X 10-* foot-poundals. 



= 217 X lo-*^ kilogramme-metres. 



= 212 X 10*^ ergs. 



References. 



The most exhaustive treatise on the theory of geodesy is found in " Die Mathe- 

 matischen und Physikalischen Theorieen der Hoheren Geodasie," von Dr. F. R. 

 Helmert. Leipzig : B. G. Teubner ; 8vo, 1880 (vol. i.), 1884 (vol. ii.). An excel- 

 lent work on the practical as well as theoretical features of the subject is '■ Die 

 geodatischen Hauptpunkte und ihre Co-ordinaten," von G. Zachariae ; autorisirte 

 deutsche Ausgabe, von E. Lamp. Berlin : Robert Oppenheim, 8vo, 1878. Of 

 works in English the most comprehensive is " Geodesy," by A. R. Clarke. Ox- 

 ford : The Clarendon Press, Svo, 1880. 



* The mass of the earth's atmosphere is about one-millionth part of the entire mass, or about 

 66 X iqI'* tons. 



t The values of A and Care those given by Harkness, loc. cit., but they are here abridged to 

 three places of decimals. 



