254 EXPLORATION GEOPHYSICS 



Dividing both sides of the equation by gg gives 



ge Qe 



The above may be written 



ye 



g^ = geil+Bsm^<i>) (11) 



The quantity symbolized by B in formulae is known as the gravitational 

 flattening. It will be considered later in connection with gravity measure- 

 ments and geodesy. B is the difference between the polar and the equatorial 

 gravity, divided by the equatorial gravity. 



Helmert in 1884 published a formula for the go, or sea level, value of 

 gravity, as follows : 



go = 978.000 (1 + 0.005310 sin^ </>) (12) 



In 1901 he gave a more accurate form :f 



go = 978.046 (1 + 0.005320 sin^ cf> - 0.000007 sin^ 2<^) (13) 



From these formulae or others of similar type| the theoretical value of 

 gravity reduced to sea level may be calculated for a given latitude (<^). 



The variation in the force of gravity between the equator and the poles 

 is shown in the following table as determined from Berroth'sff formula 



of g = 978.046 (1 + 0.005296 sin2 «/, - 0.000007 sin^ 2<j>) : (14) 



t F. R. Helmert, "Die Schwerkraft und die Messenverteilung der Erde", Encyklopadie der 

 mathematischen Weissenschaften, Band VI, Teill, Heft 7, B. G. Taubner, Leipzig, 1906-1925, pp. 

 85-177. 



% G. L. Hosmer, Geodesy, 2nd Edition, Chapter on Gravity Measurements, John Wiley & Sons, 

 tt A. Berroth, Gerland's Beitrage sur Geophysik. Vol. 14, 215-57, 1916. 



§ This_ table of gravity values for different latitudes forms the basis for the latitude correction 

 necessary in gravity field work. This correction is analogous to the latitude and longitude correc- 

 tion in magnetic exploration. 



