103, 104] EFFECT OF EARTH'S ROTATION. 321 



The equations of motion of a body acted on by forces X } F, Z are 

 m 



dt 



241) 



the terms in & having the usual property of gyroscopic forces. For 

 a falling body we have, if the plane XZ is the vertical plane at the 

 place of observation, 



X = mg cos qp, Z = mg sin <p, Y = 0. 

 Then the equations are 



< * 



242) 



Let us now introduce a set of axes |, ??, g, with g vertical, 

 | from north to south, 9? from west to east (Fig. 112). The direc- 

 tion cosines of the new axes are given by 

 the table 



from which we have for the equations for 

 the transformation of coordinates 



x = I sin y + g cos <p 



= ff sin 9? cos 9, 



243) 2/ = i? , n = y , 



= I cos 9? 4- g sin 9, g = x cos <p + sin (p. 

 Inserting in the differential equations 242), 



s 



Dynamics. 



21 



