123 
Pe. gx (2'- 2x). 
"Hele 5 halter keke 
ay 7 Cag). 
oy RY cea i a @) 
@z . gz (2'- z) 
we eae 
‘¢ In these equations the origin is the centre of the earth, 
the positive axis of z is the axis of rotation of the earth di- 
rected upwards; the positive axis of y is directed towards the 
spectator, and the positive axis of z to the right hand; z, y, z 
denote the co-ordinates of the centre of oscillation of the pen- 
dulum; 2’, 7’, 2’ the co-ordinates of the point of suspension ; 
g is the attraction of the earth; 7 the length of the pendulum, 
and N is the tension of the string. 
‘< If equations (2) be transformed to the point of suspen- 
sion as origin, the positive axis of z being vertically down- 
wards, the positive axes of x and y being in the horizon, and 
directed towards the east and north respectively, we shall ob- 
tain the following : 
eS 2k sin + 28 cosd & + ite (3) 
muy =~ h®rcos\ sin A- Qh sind + Bsind(y sind+-2008); 
il = =g —h®rcos®\— ~2 eos) + cos) (ysin A+2008)). 
« Or supposing the axes of co-ordinates transformed to the 
vertical and horizon of the actual spheroid, and supposing g to 
denote gravity, we find 
2 
C2 NZ =2h sin) + Dh cos AT + x 
2, NY - hsin dS + # sind (y sind + 2008); (4) 
2 
=e, +Ni=g- 2h cos NX + A cos A (y sin d +z cos d). 
