HO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The values of K and rj being absolutely independent of v, as also 

 are the values of J and a, for the given disturbance, as has been 

 demonstrated in our study, therefore the coefficient e is also inde- 

 pendent of v. But equation (7) expresses a certain property of the 

 atmosphere, whatever may be the special phenomena by means 

 of which it has been determined. It results from this that the value 

 s in formula (8) is absolutely constant for any physical state of the 

 atmosphere and that it cannot vary with a nor with /, but only 

 with the coefficient 77; the values of e and rj characterize the friction, 

 both of them, but in different directions only. 



This argumentation may seem to be erroneous, as I have already 

 had occasion to convince myself on hearing the opinions of several 

 experts to the effect that any such process of investigation seems 

 to them doubtful and untrustworthy. 



In place of defending my logic or my honest)^ against the incredu- 

 lous, I allow myself here to show in brief some properties of equation 

 (8) which result from the assumption as to the invariability of the 

 coefficient e. 



We can consider equation (8) as the expression of the connection 

 that must exist between the angle a on the one hand and the values 

 J K and rj on the other. Let us examine each of these connections 

 separately by means of the special partial derivatives: 



a considered as a function of J. — This function has two different 

 branches: 



(1) At the moment when a disturbance originates / = o, the 



air is put into gyratory motion in the direction of the hands of a 



3^ 

 watch in the southern hemisphere, for which a = ~ and in the 



inverse direction in the northern hemisphere for which a = \ n. In 

 proportion as the velocity of rotation increases the current of air 

 deviates towards the center, that is to say, to the right hand in the 

 southern hemisphere (and / a l so increases as a increases), but to 

 the left-hand in the northern hemisphere, where / increases as a 

 decreases. We thus have a cyclone properly so-called, and par- 

 ticularly so far as regards its lower portion. 



(2) At the commencement of the phenomenon the air expands 

 outward from the center along the radius for which a = x. Then 

 as the disturbance develops the currents of air commence to deflect 

 in the direction of the movement of the hands of a watch in the 

 northern hemisphere, where a increases, and in the inverse direc- 

 tion in the southern hemisphere, where a decreases. This is the 

 lower portion of the anticyclone. 



