66 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



becomes negative, that is to say, when the original relative velocity 

 is directed from east to west. 



For v = o, we have t] m = b, p = o and a = b, that is to say, 

 the point remains at rest relatively while its absolute path is a circle. 



For v = — bco, we have t] m = + \b and a = o; the absolute 

 path consists of a pendulous oscillation in a straight line. When 

 a changes sign, that is to say, for still smaller values of the 

 velocity v , the ellipses are described in the opposite direction. 



For v = —2baj, we have T) m = o, p = b, and a = —b; the center 

 m of the relative inertia circle coincides with the center of rotation 

 M, the absolute path is again a circle as for v Q = o, but the direction 

 of the rotation is opposite to what it was before. 



The angular velocity 2co of the relative inertia motion is twice as 

 great as that of the rotation of the system, the relative path will 

 therefore be traversed twice during the time T of one revolution 

 of the system. The figures i and 2 also show directly, as has 

 already been indicated above, a time of rotation of 12 seconds, when 

 24 seconds is assumed for the whole system. As now our investi- 

 gation may be applied with a high degree of approximation to the 

 region surrounding the north pole we attain at once the interesting 

 result that a body confined to the earth's surface, but otherwise free 

 to move, will deviate from its original direction twice as much as 

 does the plane of the Foucault pendulum. 



The value of oj is 0.00007992 m, so that the length of the radius 

 p becomes about 69 km. when the velocity is v = 10 m. or that of a 

 fresh breeze; at this velocity therefore the. body only passes a little 

 way beyond the space between two successive parallels of latitude. 8 



Now on a plane that is not in rotation a path can be produced, 



similar to the path of inertia found for the relative motion, by intro- 



v- 

 ducmg a physical force A = - always acting from left to right, per- 



P 



pellicular to the momentary direction of motion, But if the value 



of p given by (n') is substituted in this expression, then we have 



A = 2Vco (12) 



The motion on the rotating region near the pole can therefore be 

 treated as an absolute one, if in addition to all the forces customarily 

 taken into consideration there is introduced this other force -A, which 

 in modern meteorology is called the "deflecting force of the earth's 

 rotation. " 



Namely, the difference between 1 38 and 1 r 1 km. 



