i8o 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



in order to be able to treat a problem of relative motion as if one 

 had to do with absolute motion. Denoting the angle between the 

 axis O X and the direction north by a and the components of the 

 deflecting force by X , Y and Z we have 



X = 2 io sin S v — 2 co cos 6 sin a w 



Y = 2 co sin u — 2co cos $ cos a w 



Z = 2 cu cos 6 sin a u + 2 co cos 6 cos a v 



(4) 



Here 6 denotes the latitude considered as positive in the northern 

 hemisphere and negative in the southern hemisphere and co denotes 

 the angular velocity of the earth per second of mean time. 



fig. 17 



The interior forces are the components of the internal friction 

 or viscosity produced by the difference between the velocities of the 

 different adjacent strata of air. The surface of the earth offers a 

 resistance to the currents of air, the effect of which, in diminishing 

 the velocity of the lower strata, is shown by the variation of velocity 

 between the different strata. The particles of air having a greater 

 velocity increase the motion of the particles having a less velocity 

 and, inversely, the particles having less velocity retard the motion 

 of the particles having greater velocity. The resistance of the sur- 

 face of the earth, therefore, transfers its influence through all the 

 Strata of air and influences both the direction and the velocity of 



