372 EXPLORATION GEOPHYSICS 



the astatizing force is C.v. Hence, the resulting force on the mass when 

 it is in equihbrium is : 



A{g-g,)-{B-C)x^Q 



The displacement is : 



•^' = ^ _ (^ (9~9o) 



It is evident from the last relation that if C can be made approximately 

 equal to B, the sensitivity, A/[B — C), can be increased to any desired value. 

 Naturally, this involves many instrumental difficulties. 



It is interesting to notice that if D(Px/dt'^ is the force required to pro- 

 duce an acceleration of d'^x/dt^, the equation for small motions, neglecting 

 the effect of damping, is 



D^ = A{g-g,)-{B-C)x 

 which has the solution 



X = ^_^ {g - go) + Aq sin {2ir t/T) 



where 



Aq^ 2i constant which depends on initial conditions 

 and 



T = 27r \ T3 _ r ~ P^'^^o^ o^ oscillation about the 

 new equilibrium position. 



The last relation shows that the sensitivity is proportional to the square of 

 the period; that is, 1/(5 — C), and hence A/(B — C), is proportional to T^. 

 A second classification of gravimeter types depends upon the method 

 of reading the change in gravity. In scale reading instruments, an indi- 

 cator of some kind moves across a graduated scale. In null reading in- 

 struments, an opposing force is applied to return the mass to a standard 

 reference position and the amount of this force is measured on a scale 

 based on prior calibration of the instrument. 



Operating Principles of Various Gravimeters 



The particular instruments described in the following pages illustrate 

 representative types. The list is not intended to be exhaustive, but merely 

 illustrative of the general trend of design. 



Hartley Gravimeter. — The Hartley instrument, illustrated in Figure 

 218, is one of the simplest types of gravimeters. f In this instrument, dis- 

 placements of the mass M due to variations in gravity are compensated by 

 changing the pull of the spring So so that the mirror D will show the 



t A. B. Bryan, "Gravimeter Design and Operation," Geophysics, Vol. II, No. 4, pp. 302-308. 



