252 



EXPLORATION GEOPHYSICS 



G = 



As r^ 



Cavendish's value for G = 66.579 



8DMml 

 10-". 



in terms of known quantities. (4) 



Use of the Gravitational Constant to Weigh the Earth. — The force 

 of gravity per unit mass (g) on the surface of the earth (neglecting for 

 the moment the effect of the earth's rotation) is merely a special case of 

 Newton's general law of gravitational attraction, as given by Equation 1. 

 If we substitute g = \F\ in that equation, mass of the earth (M) = mi; 1 

 gram at the earth's surface =^3/ and the radius of the earth R = r, \\. 

 follows that : 



g==G 



M* 1 



r M 



(5) 



In the above equation g is the magnitude of the pull or force exerted 

 by the earth on a gram of mass at its surface. As measured by means of 

 a pendulum (to be described later) the force g is approximately 980 dynes ; 

 the value of G is 66.7 • 10~^, and the radius of the earth is some 4,000 

 miles or (i.Z7 • 10^ cm. With this data the earth can be weighed, i.e., the 

 equation solved for its mass M, giving a value of 6.14 x 10"'^ grams. 



The mean density of the earth can also be derived from the above data, 

 since density equals mass divided by volume. If the earth is considered as 

 a sphere, its volume would be 4/3 tt R^. 



6.14 ■ 10^^ 

 Density = a 



■f • TT (6.37 • 108)^ 



= 5.32 = mean density. 



VALUE TENDING TO 

 DECREASE GRAVITY 

 EFFECT 



This value for mean density indicates a high density for the core of the 

 earth, as the density of rocks in general at the surface is about 2.7 to 2.8. 



The Effect of the Earth's Rota- 



ASTRONOMICAL ffow OH Gravitj. — The effective force 



of gravity at the earth's surface is the 

 resultant of the attractional effect of 

 the earth's mass less a component acting 

 in the opposite direction. This compo- 

 nent is due to the centrifugal force cre- 

 ated by the earth's rotation. Centrifugal 

 force is expressed by angular velocity 

 squared (symbol w^) times radius of 

 gyration x. The radius of gyration of a 

 point on the earth's surface is the per- 

 pendicular distance from the point to 

 ^ ,„, ^, . , , the axis of rotation of the earth (x of 



Pig. 124. — Showing the component of cen- i ^ ,1 \ t • 11 



trifugal force, due to the earth's rotation, FlgUre 124). It IS apparent that the 

 which acts in a direction opposite to gravi- ^ . . . . , mi 1 



tational attraction. = latitude; r = earth's Ceutnfugal forCC COmpOUCnt Will bC a 



[hfeaAhVsu^^1!c"e.°^^''"''°"°^'''°'"'°" maximum at the equator and zero at 



