Particle on the Surface of a Smooth Rotating Globe. 459 



Hence the \, <f> equation of the track is 



_/sinA,\ ,/tan\\ 



4> = secX cos i^J-cos" ^— ). 



Other tracks on the rotating sphere corresponding with 

 other initial conditions will have similar features, though 

 the cusps will not usually occur. In every case the track 

 crosses the equator, and the velocity of the particle relative 

 to the sphere reaches a value of the same order of magni- 

 tude as the velocity with which the surface of the sphere is 

 moving itself *. 



Fig.l.- 

 'FIG. I 



' -PARTICLE ON SMOOTH SPHERICAL GLOBE 

 •!5- %i. STARTING FROM RELATIVE REST IN LATITUDE I3i°N. 

 'W® PERIOD l\ HOURS 41 MINI. 

 WAVE LENGTH 137 KM. 

 •.EQUIVALENT TO 1023° OF LONG, 

 - fo; MAXIMUM VELOCITY 177 m/s 



$' 500 



. nv -. / \ il77M/s 



*. 500 



<5 



1000 



do" 



.1500/ 



3. Turning to the problem of the motion of a particle on 

 a smooth rotating globe bounded by a " level " surface, we 

 notice in the first place that every point on the globe is a 

 position of equilibrium. As the particle moves on the sur- 

 face the relative velocity V remains constant. Owing to 

 the rotation of the globe, the track of the particle is curved. 



* The diagram (fig. 1) illustrates motion on a sphere with circumference 



ours. 



2K2 



40,000 km. rotating once in 24 hours. 



