GRAVITATIONAL METHODS 255 



Units in Gravity Measurements. — Newton's second law of motion 

 states that F = ma, or force equals mass times acceleration. Acceleration 

 is the increase in velocity per unit of time, viz., cm./sec./sec. 



A force per unit mass, therefore, is equal to the acceleration. Hence, 

 the force of gravity may be expressed in units of force: dynes per unit 

 mass ; e.g., dynes/gram. It may likewise be stated in units of acceleration ; 

 e.g., cm./sec./sec. 



The force of gravity at a station may be, say, 980.112 dynes, or 980.112 

 dynes/gram. With equal accuracy it could be stated that the gravity at 

 the station was 980.112 cm./sec.^, which is in terms of acceleration. These 

 two forms of expression are numerically equal but convey a slightly dif- 

 ferent physical meaning. 



A special name gal has been given to the gravity units of acceleration, 

 (after Galileo). 1 gal = 1 cm./sec./sec. The 1/1000 part of a gal, or 

 milligal, (mg.) is commonly used in gravity prospecting. 1 mg. = 0.001 

 gal or 0.001 cm./sec.^ 



The previously considered Equation S, {g = G • M ' l/R^, symbols 

 as given) is based on the assumption that the earth is a homogeneous 

 stationary isolated sphere. Such a sphere would exert a radial ^ttractional 

 force on objects at its surface and the force per unit mass would be the 

 same at all points on the surface. Actually, the earth is neither homo- 

 geneous, stationary, isolated, nor spherical. The result is that the force 

 of gravity per unit mass varies, both in direction and in magnitude, from 

 place to place and from time to time. Furthermore, data on gravitational 

 anomalies furnish information about the deviation of the earth from a 

 homogeneous, stationary, isolated sphere. Interpretation of the field mea- 

 surements made in gravity surveying is based upon these variations or 

 gravitational anomalies.* 



Factors Causing Variations in Gravity. — The earth's deviation from 

 a sphere derives from two factors: (a) the topographical features, i.e., 

 the local phenomena of valleys, hills and mountains; and (b) the oblate 

 spheroid shape resulting from its rotation. This second factor introduces 

 a variation in the force of gravity which is a function of latitude. This 

 variation and the effect of the centrifugal force of rotation are usually 

 lumped together and called a "latitude, or north-south correction." From 

 a knowledge of the mean shape of the earth and its speed of rotation 

 about its axis, the latitude correction may be calculated mathematically; 

 the correction amounts to about 1/194 • sin^ (latitude). 



Another variation in gravity is caused by the differences in density 

 of the materials of the earth. This phenomenon furnishes the physical 

 basis of the gravitational methods of prospecting. Thus, a structure that 



* At present, as far as geophysical prospecting is concerned, the fact that the earth 

 is not isolated is of little importance. The attractions of the sun and the moon and the 

 effects of the tides caused by them introduce changes in gravity which are smaller than 

 the errors in observations. These latter are the time variations in gravity. 



