4gS Tables 167—168 



ACCELERATION OF GRAVITY 



Acceleration of gravity at sea level. — The International Association of Geodesy (Stock- 

 holm, 1930) adopted the International Gravity Formula * to represent the acceleration of 

 gravity at sea level. This formula assumes the figure of the earth to be that of the Inter- 

 national Ellipsoid of Reference a and the value of sea-level gravity at latitude 45° (g a ) to 

 be 980.629 cm. sec." 3 (Potsdam system). 3 Later summaries and investigations by Dryden* 

 and Jeffreys 4 have indicated that this value is too high by from 12 to 20 parts per million. 

 The best value of g K seems to be in the neighborhood of 980.616 cm. sec. -2 This latter 

 has been published by Birge 8 in 1929 and 1941, and has been generally accepted by 

 physicists and others. 



Resolution 77 of the I. M. O. Conference of Directors (Washington, 1947) states: 



The conference recommends that the International Meteorological Organization request 

 the International Geodetic Association to advise on the value that should be adopted for 

 gn> and on the form of the equation connecting g with latitude and height. 



In 1949, in response to this request, W. D. Lambert, President of the International As- 

 sociation of Geodesy, prepared a report on Gravity Formulas for Meteorological Purposes, 

 and made the following recommendations : 



(1) That meteorologists adopt either 980.616 or 980.62 cm. sec." 2 to represent gravity at 



sea level in geographic latitude 45°. 

 My own personal preference is for 980.616 cm. see." 3 and for two reasons : 



(a) It seems on the whole, as far as an outsider like myself can judge, to have been 



more frequently used than the round figure 980.62. 



(b) It represents a correction of — 0.013 cm. sec." 2 to the Potsdam system, which 



seems more in line with our present ideas as to the ultimate correction to the 

 Potsdam system than the correction of — 0.009 cm. sec."* implied by the 

 adoption of 980.62. 



(2) That meteorologists make every effort to obtain gravity observations at their 



weather stations, so as to rid themselves of the inevitable uncertainty of predicted 

 values. 



(3) That they apply the correction of —0.013 or —0.009 cm. sec." 1 to such observed 



values, since these latter will for the present be on the Potsdam system. 



(4) That it be made very plain in all meteorological publications, especially in those 



likely to be read by non-meteorologists, that all gravity values, observed or 

 theoretical, are on what might be called "The Meteorological Gravity System" 

 and therefore require corrections of + 0.013 or + 0.009 cm. sec."* to reduce them 

 back to the Potsdam system for comparison with other values in general use. 



(5) That the coefficients in the formulas for theoretical gravity at sea level and for the 



decrease of gravity with elevation and for geopotential be based with mathe- 

 matical rigor on whatever standard gravity may be adopted and on the dimen- 

 sions of the International Ellipsoid of Reference. 



(6) That, whenever an observed value of gravity is not available at the meteorological 



station, a value of gravity should be predicted by interpolation between other 

 gravity stations in the vicinity and computed according to equation (2). (See 

 below.) 



(7) That, whenever observed values of gravity are not available for either the meteoro- 



logical station or any other points within 25 to 50 miles from the meteorological 

 station, a value of gravity should be predicted by computation according to 

 equations (3) or (4). (See below.) 



Sea-level gravity formula. — In view of the above, a value of gu, = 980.616 cm. sec." 1 

 has been adopted for this volume. The equation recommended by Lambert for the varia- 

 tion of sea-level gravity with latitude in the "Meteorological Gravity System," based on 

 the International Ellipsoid of Reference, is 



g, = 978.0356 (1 + 0.0052885 sinV - 0.0000059 sin 2 2<t>) 



— 980.6160 (1 - 0.0026373 cos 2</> + 0.0000059 cos 2 2<f>) (1) 



1 Lambert, W. D., Amer. Journ. Sci., vol. 243-A, Daly volume, p. 360, 1945. 



1 Lambert, W. D., and Swick, C. H., Formulas and tables for the computation of geodetic positions 

 on the International Ellipsoid, Spec. Publ. 200, U. S. Coast and Geod. Surv., Washington, 1935. 

 8 Dryden, H. L., Nat. Bur. Stand. Journ. Res., vol. 29, p. 303, 1942. 



4 Jeffreys, H., Monthly Notices, Roy. Astron. Soc, Ceophys. Suppl., vol. 5, No. 7, July, 1948. 

 B Birge, R. T., Rev. Mod. Phys., vol. 13, p. 233, 1941, and Phys. Rev. Suppl., vol. 1, No. 1, 1929. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



