72 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



X ]>resupposes that the form of the rotating body is known [i. e. the 

 slope of the surface of revolution] therefore that r is given as a 

 definite function of the latitude or r = F. (<p) : for example, in the 

 case of a sphere r = R cos <p: in the case of a spheroid 



R cos <p 



VT= 



e- sin- o 



dX 



Since v sin d = r \ — ) , and v cos d = - 

 dt 



1 (*\ 



sin <p (1c ' 



d(f 

 dt 



therefore 



D 



r'co* - 



(? 



r 



(19) 



and from this by the elimination of dt is derived the definite inte- 

 gral: 



X = - 



r 



V'n 



) d<p 



r sm 



<p V Dr 1 - t 



O 



(20) 



in which the constants D and C from (16) can be expressed by the 

 values of v, 6, and r or from (14) and (15) by the values of V, S 

 and r for the initial circumstances of the motion as follows: 



D =v 2j r'2 r { ;or + 2 vr co sin 6 ( = V 2 + r Q 2 co 2 ) 

 C = ?- 2 a> + vr sin ( = V r sin d ) 



. (21) 



The solution of this problem leading to elliptic integrals does 

 not seem to be worth the while, because in the first place the func- 

 tion r = F. {(f) for the earth can not be given with entire certainty, 

 and in the second place the careful determination of the path has 

 only a subordinate interest in meteorology, since the notion, for- 

 merly entertained , that the particles of air act u ally follow the " inertia 

 path" has been completely refuted by the synoptic weather charts 

 that show the simultaneous conditions of the atmosphere over large 

 regions. It may even be asserted that in fact the direction of curv- 

 ature that pertains to the inertia path is not even the more frequent ; 



