152 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



We shall see that the law of inclination 'eq. 5) is quite conform- 

 able to the observations; however the observed velocities and grad- 

 ients do not follow our formulae always, which is very easily ex- 

 plained when we note that in nature the currents of air near the 

 equatorial calms have an ascending movement that diminishes the 

 horizontal velocity and the magnitude of the gradient. We could 

 easily introduce this influence into the formulas, but we shall not 

 profitably extend our researches any further since we shall treat 

 the problem in a more general manner in the second part of these 

 "Studies." 



§12. Horizontal currents of air with circular isobars around a 

 barometric minimum. 



We shall consider the latitude as constant 8 and the isobars as 

 concentric circles. The system being symmetrical with respect to 

 the center of the isobars therefore the quantity of air that enters 

 per unit of time must remain constant. Designating by^ the angle 

 between the direction of the wind and the radius, which latter 

 is the direction of the gradient, the component of the velocity in 

 the direction of the radius will be v cos <p. Let r be the radius and 

 h the altitude of the horizontal current, the section of the current 

 will be 27r r h, and remarking that h remains constant the equation 

 of continuity will give 



vr cos = constant (1) 



The acting forces are the same as in §10 and the equations 

 (2) and (^ hold good by substituting 



1 sin (f) d </> 



— = - - + cos 4> 

 R r dr 



cos <p d s = — dr 

 By the aid of equation (1) we shall find 



fx I v cos <j> v sin <j> d <J> 



- G COS d> = v \ k + — 



p \ r 



d r 



pt ' I v sin <l> v cos </> d <j) 



G sin d) = v I 2 to sin 6 + + 



p r d r 



8 That is, uniform over the whole barometric depression. — Editor 



