200 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The normal angle of inclination being expressed by the formula 



2 co sin 6 



tang a = 



k 



we shall have 



and 



2 co sin 8 tang a 

 tang * = *_ (7) 



k + c c 



k 



U p. cos <J> p sin (p 



G p k + c p 2 co sin 6 



(8) 



From these equations we conclude: That the angle of inclination 

 ,W is constant for a wind of variable velocity and rectilinear isobars, 

 but that it differs from the normal angle ex. The ratio between the 

 velocity and the gradient remains constant and is expressed by 

 the same function of the latitude and of the angle of inclination 

 as for winds of constant velocity. 



The gradient increases proportionally to the velocity and con- 

 sequently to the distance x. It follows that the depression between 

 two isobars is found by multiplying the distance by the mean of 

 the corresponding gradient. 



When c > o the wind blows with increasing velocity and the angle 

 of inclination is less than the normal angle. When c < o the wind 

 blows with decreasing velocity and the angle of inclination is greater 

 than the normal angle. 



If we consider a station situated on the seashore and note that 

 the coefficient of friction is greater on the land than on the ocean, 

 we must expect that the ocean winds at such a station will have 

 an angle of inclination greater than the inclination for the land 

 winds. 



Let us consider a system of par- 

 allels in which we can represent 

 the curve of velocities approxi- 

 mately by two straight lines (see 

 fig. 25). The curve of the gradient 

 will be also represented by two 

 straight lines and placing the maximum gradient equal to G we 

 shall have 



D = G r (9) 



