ROTATION AND ATMOSPHERIC DISTURBANCES GORODENSKY III 



For these two cases there is a certain limit that the angle a can 

 only attain when / becomes infinitely large, which is determined 

 by the equation (10), 



K 



tang a = — (10) 



K as a function of a. — This function also has two branches. 



When a disturbance takes place in the equatorial regions the air 

 flows along the gradients, that is to say, towards the center (for 

 which a = o or away from the center in the opposite direction 

 (for which a = iz). The first case corresponds to an area of low 

 pressure and the second to an area of high pressure. If the center 

 of the disturbance moves towards the north, the currents of air will 

 deflect to the right (or a will increase with K). If the center moves 

 towards the south, the current will deviate towards the left and a 

 decreases with K. 



rj as a function of a. — It may be remarked that the analysis of this 

 function can only be of a general character because in the form 

 of equation (8) it occurs as a function of e of unknown form. If we 

 rely iipon equations (i), (2) and (7) we find without difficulty that. 

 e is infinitely large when r, = o; e is zero when rj is infinitely large; 

 finally the derivative of e with regard to rj is always very small or 

 nearly equal to zero. Moreover it is evident that if rj has positive 

 values, different from zero, then e also has values greater than zero. 



A discussion of equation (8) shows moreover that the product 

 erj is positive for rj = o and for rj = infinity. These peculiarities 



n 

 lead us to adopt e == - as the value of the function e, in which n is 



V 

 a constant. 



The vitality or duration of any atmospheric disturbance depends 

 directly on the magnitude of the angle a between the Avind and the 

 gradient; in proportion as a increases the duration increases also; 

 in proportion as the wind deviates from the gradient it is more ami 

 more difficult to reestablish static equilibrium. 



This being understood, let us examine some interesting me- 

 chanical phenomena that we may draw from the preceding analysis. 



(1) When an anticyclone continues to develop its vitality: 

 (a) increases steadily, whence it results that disturbances of this 

 character ought to have a very considerable stability not requiring 

 help from outside. 



(2) On the contrary, when a cyclone is developing, its vitality 

 is decreasing so that a fully formed cyclone carries within itself 

 the beginnings of its destruction, hence the extreme instability 



