234 
THE EFFECT OF THE ROTATION OF THE EARTH 
To commence with we will take the centre of the earth as the 
origin of a system of rectangular axes, that of z being in the direction 
of the north pole, that of x in the meridian plane of the station from 
which the gun is fired. 
Let mf be the attraction of the earth on the projectile (m being its 
mass); which, be it observed, is not the same as the ‘ force of gravity ’ 
at the station; for the latter includes the effect of ‘ centrifugal force,’ 
due to the rotation of the earth. 
Let a , o, c be the coordinates of the station, u, v , w, the components 
of the initial velocity parallel to the axes, and 6 the geocentric NP.D. of 
the station. Then the equations of motion of the projectile, co being 
the angular velocity of the earth about the axis of z, are 
x — 2 <ay - a> 2 x = - /sin 0) . 
.(1), 
y + 2(ox-a) 2 y=0 > . 
.(2), 
z — -/cos 6) . 
...(3). 
From (1) 
x - 2ooj/ - (o 2 x— 0, 
••• (2) 
x + 3a 2 x - 2a?y = 0. 
From (2) 
y + 2axr- co 2 y = 0. 
