130 K. YE. Veselov and V. L. Panteleyev 



of a point on a moving body onto a co-ordinate consists of the corresponding 

 components of translated, tangential and centrifugal accelerations, i.e. 



r=Co"-lo'?"-Co(9'r. (18) 



In order to evaluate the influence on the readings given by the gravi- 

 meter, we need to know the equation of the motion of the instrument 

 itself or the equation of the motion of the Cardan suspension. 



The Cardan suspension is a damped or undamped pendulum subjected 

 to the disturbing influence of accelerations. 



The Cardan suspension will have natural and induced oscillations, the 

 period of which will equal that of the horizontal accelerations. 



Thus, if 



X = a^ cos (pt^d^), (19) 



it follows that 



(p = (Po+ fi cos (%« + dj) + 9?2 cos {pt + ^2)5 (20) 



where cpQ is the constant component of the angle of inchnation of the 

 instrument's pendulum; 9?^^ is the amphtude of the natural oscillations of 

 the Cardan suspension; re^ is the frequency of the natural oscillations of the 

 Cardan suspension ; 953 is the amphtude of the induced oscillations ; a^ is 

 the amphtude of the horizontal acceleration components ; p is the oscillatory 

 frequency of the horizontal component. 



Let us now find the values entering equation (18). 



The influence of the translated acceleration can be written in accordance 

 with (17) as 



Cq = :tsin 9? + zcos (p = ]/ x^ + z^ cos I 9?— arctan .. | . (21) 



Taking into account that 



where 



^1 = a, cos (pt + d^), 



X 



and also that — is small, we obtain 

 g 



l/.-^+(., + ^)-^-|/(| + l)Vj=^(l+|^ 



2 x^M 



g g^ g^ 



2 _ 



