PATHS OF MOVING PARTICLES SPRUNG 



65 



that v is perpendicular to the radius vector b, and that v is reck- 

 oned positive in the direction of rotation of the system (from west 

 to east). Hence v + bco is the absolute west-easterly velocity of 

 the body at the time / = o, for which according to (3) we have the 

 expression (U x ) f= aw; we have therefore the relation: 



CUD 



v n + be 



or 



a-b = 12 



CO 



(10) 



by using which relations the equations (9) finally pass into the fol- 

 lowing form: 



£ = -12- sin 2 cot, 

 2 co 



- V ° cos 2cot + (b + ^- 

 2 co \ 2 co 



(11) 



Therefore we have: 

 v, 



the radius of the circle of inertia, 

 2co 



b + - the n-coordinate of its center 

 2co 



.(11') 



These equations give us all desired information concerning the 

 relative motion due to the inertia of the body. We first derive 



dt 



= v cos 2 cot; 



—L=v n sin 2 cot. 

 dt 



But from these we have 



•-■J 3; 



+ 



drj 

 dt 



= v„ 



that is to say, the relative motion due to inertia is a uniform one 

 and only distinguishable from the absolute motion due to inertia 

 in free space, by this, that its path is not a straight line but curved. 

 For the direction of rotation of the system assumed in our figure, 

 which agrees with that of the northern hemisphere, the center of 

 curvature always lies on the right-hand side of the path, since the 

 co6rdinate i} m of the center of the circle will be < b as soon as v 



