THE INFLUENCE OF DISTURBING ACCELERATIONS 131 



-.(l+f + ^)- (22) 



We transform the second factor of expression (21). Taking into account 

 (20), we obtain 



cos I 9? — arctan -tt-I ?«1 — — I99 I = 



= 1 - 2" U'o + 9^1 co^ {"'1^ + ^1) + ^2 cos (/jf + 62) - 



--^^-cos(;?i+(5;,)l . (23) 



Before proceeding to further transformations we wish to interpolate 

 the following comment which mil henceforward apply throughout. 



We assume that the amplitude of the accelerations does not exceed 20ga] 

 and that the dynamic coefficient is not greater than 0.01. In this case we 

 shall in future disregard all purely sinusoidal components of the second 



order of smallness by comparison with — 1- in our calculations since their 



g 

 registration will be reduced by the number of times by which the dynamic 



coefficient is less than unity. We shall only retain the systematic part of pe- 

 riodic components of the second order of smallness by comparison with — - , 



i.e. their mean value for a large time interval. 

 Thus we shall write for (21) 



8 



^(i+f+-25-)''-(''-f)- 



j 1 — Y U'o + 9^1 cos {n^t + dj) + (p2 cos (pt +62) cos (pt + dx) 



I a a ^ 1 



1 + -^ cos (pt + 6,) + j^cos^{pt+Sx)} X 



|l - y [9^0 + (Pi cos (n^t + d^) + aA. (24) 



