136 



K. YE. Veselov and V. L. Panteleyev 



Therefore the gyroscopic stabihzation decreases the correction for the 

 influence of accelerations on the pendulum of the instrument. 



All the previous conclusions have assumed a single degree of freedom 

 of the Cardan suspension and the presence of a single horizontal component. 

 In actual fact we have to deal with the two horizontal components and two 

 degrees of freedom of the Cardan suspension. Repeating an analogous 

 conclusion for the second degree of freedom we obtain thereby formulas 

 for long and short period Cardan suspensions analogous to formulas (34) 

 and (35) 



% 



+ f U'Ox + 



gTL 



2 



+ 



(pix+ 



kx 



bx 



+ 



-<■ , s 



+ 'w\rou+ 



+ cp\, , ^n^ol. , cLin\ 



+ 



gTh 



ny+ 



r^ n 



(36) 



g= G^- —\ 9?gx+ 2 ~ (p2x^o% {Oc^-Ox) + 



47r ^ I (pi -^ ^ "1 





Tl ' Tf 



2 



^2 I yfy+yiy 



- '^ 'P.; cos (3„„ - ^,) + ^ f„ (^ + f |\] . (37) 



The quantities denoted by subscript x relate to the degree of freedom of 

 movement of the instrument's pendulum in a plane; the quantities denoted 

 by subscripts relate to the degree of freedom perpendicular to the above. 



The principal correction term in formula (36) is the Brown term 



— 03.2+ a, it 



When the horizontal accelerations are small and the instrument is well 

 adjusted the remaining terms are negHgible. In such a case one can proceed 

 to calculate the accelerations without having recourse to accelerographic 

 devices. One can assume from the theory of trochoidal waves that 



/^ 2 , /Tl 2 I /-r 2 



given that there is a certain degree of approximation in the satisfaction 

 of this equation. 



