PATHS OF MOVING PARTICLES SPRUNG 5q 



ant of the attractive force of the earth and the centrifugal force 

 that is perpendicular to the earth's surface; the latter is moreover 

 a level surface only by virtue of its rotation. If the earth should 

 come to rest without a change of form, then the body would move 

 parallel to the surface under the influence of a horizontal force 

 directed towards the pole, which force is a component of the force 

 of attraction and whose magnitude can be easily given. If we 

 denote by <p the latitude of a point on the earth's surface (which 

 here and in what follows will be considered in an entirely general 

 manner as a body of revolution) by r the distance from the axis, 

 and by u>, the angular velocity of rotation of the earth, then the 

 acceleration 4 of the horizontal poleward directed component of the 

 force of attraction is equal to the expression 



r or sin <p 



which represents the horizontal component of the centrifugal force 

 directed toward the equator in the case of a point at relative rest 

 on the rotating surface of the earth; for in fact the condition that 

 these two horizontal forces are in equilibrium determines the form 

 of the surface of the rotating earth. 



At the pole and at the equator this force has the value zero, it 

 reaches its maximum at <p = 45 ; over the zone from the pole to 

 45 latitude it acts in a manner similar to the action of the com- 

 ponent of the force of gravity in the case of the spherical pendulum 

 under the influence of which for angles of elevation between o° and 

 90 the pendulum makes its vibrations. Hence in general the free 

 absolute motion of a body which does not take part in the rotation 

 of the earth's surface, but glides on it without friction will consist 

 of uninterrupted oscillations around the pole as a center; if the 

 original motion began in the direction of a meridian, then the body 

 would never leave it ; if the body be started in the direction of a 

 specific parallel of latitude (dependent on its velocity), then it would 

 forever keep moving along this parallel with constant velocity, etc. 



It cannot be doubted that it is allowable in our consideration of 

 the relative motion due to inertia on the rotating surface of the 

 earth to begin in the above indicated manner with the consideration 

 of the absolute motion; for since we do not consider the influence 

 of the rotating surface as any other than that of a rigid opposing 

 shell it can therefore be considered as infinitely thin and as closely 



4 In what follows, the expression "force" will for brevity always be used 

 for the accelerating force. 



