IbC) THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



uuiform gradieuts, theu the angle between the direction of the wind and 

 the gradient is smaller in the variable system than in the invariable 

 when the intensities increase, and, inversely, larger when the intensities 

 are diminishing. 



(b) If in one and the same system of winds having a progressive 

 movement we compare two points that have equal velocities and equal 

 gradients then the deviation of the wind direction from the gradient is 

 smaller at the point where the wind velocity is increased than where it 

 is diminished. Therefore in general the departures from the gradient 

 will be smaller throughout the advancing half or front of a moving- 

 cyclone than within the rear half. 



((') For steady motions of moderate intensity, where therefore 



dt 



the velocity is proportional to the projection of the gradient on the 

 direction of movement. Furthermore for equal gradients and equal 

 velocity the deviation of the direction of the wind is greater in propor- 

 tion as the friction is less. 



Some of these theorems have been proven already for special casea 

 by Guldberg and Mohn. The theorem expressed in paragraph (c) has 

 also been attained in an entirely different way by A. Sprung.* 



I pass now to the investigation of the invariable systems of wind, 

 and therefore assume that 



If further we put 



P=|4-i^,(u^ + r-') 



(9) 



then the equations (5) give 



^+^.= _(A+r).; 1 



If in these we introduce for u and v expressions of the form ordina- 

 rily used in hydro-dynamics, namely : 



s 



* See Wiede.mauu, Beiblatier, 1881, vol. v, page 240 : and Sprung Meteorologie, Ham- 

 burff, 1835. 



