Connected with the Earth's Field of Force. 135 



only forces and therefore there is no equilibrium but a 

 tendency to move towards the equator. To avoid some of 

 the difficulties suggested at the beginning of this paper 

 that arise in problems of motion relative to axes that are 

 themselves moving, we suppose a constraint applied in the 

 form of a track along the meridian to which the sphere is 

 thus confined. The resultant force along the meridian 

 is indeed small — of the order of magnitude of one one- 



FiG. 3. 



Fig. 3. — Showing the difference in direction between the force of gravity 

 acting on a sphere and the reaction of the level surface on which the sphere 

 rests. 



millionth of the force of gravity — but a few figures on the 

 effects produced may seem somewhat surprising until we 

 remember that even a small force can accomplish much by 

 long-continued action.^ ^ Suppose the radius of the 

 sphere to be one kilometer and that the latitudes from 

 which it starts are successively 30°, 45° and 60°. The 

 little table shows the journey to the equator divided into 

 thirds and gives the time (in days and hours) taken to 

 cover one, two and three-thirds of the journey and the 

 velocity attained in meters per second. 





Initial latitude 30° 





Eeaches 







Velocity 



lat. 



aJ 



?ter 



m. per sec. 



20° 



9^ 



11^ 



3.1 



10 



11 



9 



4.0 







14 



11 



4.3 



See Appendix A to this paper for the mathematical developments. 



