124 
«¢ If the terms depending on 4? be neglected in equations 
(4), we obtain 
d2x x a dy dz 
qe tN 7 = 2h sim drs, + 2h cosd Fs 
d*y y ; dz 
ap t N7= 7 2hsmA a (5) 
dz z dx 
aa tN pag - hoor. 
Eliminating N between the first two equations, we find 
Gr. ae . dy _—_ dx dz 
BET Waar iS 2h sin X (vg +2 + 2h cosy 7. 
Integrating this equation, we obtain the following: 
y G2 Hm hin d (22 + y?) + 2h 008 A fyde. (6) 
Transforming (6) to polar co-ordinates, by the formule 
xz =Isin ¢ sin 8, 
y =lcos¢ sin 8, 
z=I1co30, 
in which ¢ denotes the azimuth measured from the north, and 
6 the deviation of the pendulum from the vertical, we find 
d. ; 2k cos X 
a eid Ne sin? 9 
This equation proves, that the azimuthal velocity consists of 
two parts; one uniform, and equal & sin X, directed from the 
north to the east; the other periodic, and passing through all 
its changes in the time of an oscillation of the pendulum, and 
depending on the amplitude of the vibration. As the azimuth 
@ may be considered constant during the time of an oscil- 
lation, the second term in equation (7) may be integrated. 
Hence we obtain, 
[cos @ sin? 6d0. (7) 
ob — h sin X ~ $k cos) cos 9 . 05 (8) 
