68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



well-known theorems of physics. For other geographical latitudes 

 the problem becomes considerably more difficult; however, even 

 here with the aid of our conception of the process we are enabled 

 to directly attain some results. 



The condition of relative rest of a body on a horizontal plane in 

 any latitude 0, consists, absolutely considered, of a circular oscilla- 

 tion (diurnal rotation about the axis of the earth) under the influ- 

 ence of a poleward-directed component no 2 sin of the force of 

 attraction of the earth which neutralizes the local equatorial tend- 

 ency. The forces required in the absolute motion are evidently the 

 same whether the circle of latitude is traversed from west to east or 

 east to west with the velocity rio. In the latter case, however, the 

 relative motion of the body is an east-west one with the relative 

 velocity v = 2rco; the latter motion is therefore, just as in the case 

 of relative rest, a special case of the relative inertia motion. Only 

 in two very special cases of the relative velocity is it possible for a 

 free body to remain on a circle of latitude, whilst it was formerly 

 assumed that the final results of every deviation due to the rotation 

 of the earth consists in a motion parallel to the circle of latitude. 



It can easily be seen that the horizontal radius of curvature of 

 the small circle of latitude (whose curvature must always be deter- 

 mined by comparison with the geodetic line which is a great circle 



f 



on the sphere) is equal to the slope - — of that cone which is tangent 



sine? 



to the earth's surface at the latitude 0. The "deflecting force of 



the earth's rotation" is therefore in this case (2rcu) 2 ( I and 



by using the above relation v = 2rco this can be written A = 2Vco 

 sin 0. The "deflecting force" at the latitude <p (at least for the 

 velocity v = 2roJ) is then smaller than at the pole, where the value 

 is 2Vco; its direction is the same as there, perpendicular to the path, 

 towards the right in the northern, towards the left in the southern 

 hemisphere, and the influence of the earth's rotation is thus repre- 

 sented perfectly, because the relative motion due to inertia here 

 under consideration is a uniform one. 



For the completion and generalization of this result the general 

 problem of absolute mi >ti< m under the influence of the force rco 2 sin 

 directed poleward will be here treated briefly. 



Denote by V the absolute velocity parallel to the surface of the 

 rotating body, by 6 the azimuth of the absolute motion (counted 

 positive from the north around by the east towards the south) and 



