Tables 167—168 (continued) 439 



ACCELERATION OF GRAVITY 



where g* is the sea-level acceleration of gravity in cm. sec." a , at latitude <p. Tables 167 and 

 168 have been computed from equation (1). 



It is emphasized that all values of g* in this system are 0.013 cm. sec." a lower than 

 those given by the Potsdam System (g t s = 980.629 cm. sec." 2 ) which is now in universal 

 use by geodesists. 



A discussion of the value of standard gravity to be used in reducing meteorological 

 observations appears in the Introduction, page 3. 



Local acceleration of gravity. — Three methods, in order of preference, for obtaining the 

 local value of gravity gi at a given station are : 



1. Observe gravity with a gravimeter or any other type of gravity apparatus. 



2. Compute gravity by interpolation of Bouguer anomalies. (Equation (2).) 



3. Compute theoretical gravity using a combination of the free-air and Bouguer re- 



ductions. (Equations (3) or (4).) 



Use of gravimeters. — The rapid development of gravimeters in recent years has com- 

 pletely changed the problem of values of gravity at meteorological stations. Over large 

 parts of the land area of the globe it is no longer necessary to depend on theoretical values 

 of gravity, with all their uncertainties. Nets of gravity stations are so widespread that 

 existing meteorological stations can be readily tied into them. The determination of 

 gravity differences by means of gravimeters is very rapid. (From the report to the 

 I. M. O., by W. D. Lambert.) 



It is again to be emphasized that allowance must be made for the difference between 

 the Potsdam system, the basis for the gravity station network, and the gravity system 

 adopted by the meteorologist. In accordance with the system adopted in this volume, the 

 correction to be applied to the Potsdam system is — 0.013 cm. sec." a 



Interpolation methods. 9 — For interpolation from known gravity values, the methods 

 of using free-air anomalies, Bouguer anomalies, and isostatic anomalies will be the only 

 ones considered here. Gravity anomaly data can be secured from the various national 

 geodetic surveys. The free-air and the Bouguer anomalies are simple to compute : the 

 gravity data furnished for any gravimetric survey includes either one of these two types 

 of anomalies or both. The free-air anomaly is obtained by reducing the theoretical value 

 of gravity at sea level for the latitude of the station to the elevation of the station, and 

 then taking the difference between the observed and the theoretical values. The Bouguer 

 anomaly is obtained by applying an additional correction for the horizontal slab of 

 topography above sea level. Either the actual density of the terrain or some assumed 

 average density is used to compute the effect of the topography. The isostatic anomaly 

 includes, besides the correction for the elevation of station, the effect of the topography 

 and some assumed distribution of compensating mass over the entire earth. 



Using either the interpolated isostatic anomalies or the interpolated Bouguer anomalies 

 leads to gravity values which agree much better with the observed gravity values than 

 using the interpolated free-air anomalies. There does not seem to be much choice between 

 using the isostatic or the Bouguer anomalies. However since the Bouguer anomalies are 

 much more generally available and since they are simpler to compute than the isostatic, 

 the Bouguer interpolation method of obtaining gravity may be considered as the most 

 satisfactory. 



Computation by interpolated Bouguer anomalies. — The expression for local gravity, 

 <7i, using interpolated Bouguer anomalies is 



^ = ^ — 0.0001968/1 + ^8 (2) 



where g* is the sea-level value of gravity at the latitude of the station, h is the elevation 

 of the station above sea level in meters, and Ab is the interpolated Bouguer anomaly. 



If the gravity stations are spaced at a density greater than one station per 2,500 square 

 miles, interpolation is usually fairly satisfactory. For a lower density of stations, theoreti- 

 cal values of gravity are probably as good as or better than values of gravity derived 

 from interpolation. 



8 Duerksen, J. A., U. S. Coast and Geodetic Survey, private communication, 1948. 

 See also Swick, C. H., Pendulum gravity measurement and isostatic reductions. Sopc. Publ. 232. 

 U. S. Coast and Geod. Surv., Washington, 1942. 



{continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



