ig8 SMITHSONIAN' MISCELLANEOUS COLLECTIONS VOL 51 



From this table one can construct the curves of velocity, gradient, 

 and pressure, and the system of isobars and we shall find a system 

 of curves analogous to those of fig. 23. 



We can compare this last wind system with the lower half of a 

 system of parallels of the first order in nature and we can make the 

 same remarks as on the first example. 



§ 2 5. System of parallel winds of the second order 



Mathematically speaking the systems of parallels have an infinite 

 length. In nature the length is limited, but we can neglect the 

 disturbances produced by the lateral limits. Along the surface of 



the earth the system of parallel as- 

 cending winds presents two horizontal 

 currents, which flow from both sides 

 toward the barometric minimum or 

 trough situated along a straight line. 

 We distinguish two halves on each 

 side of the barometric minimum and 

 /J" 1 7 each half has its internal part whose 



-* — j /- me ! breadth may be r , and its exterior 

 \ »»;wmw»,///w//w///////.'/?/, part. The horizontal current moves 



fig. 24 in the exterior part approximately at 



a constant altitude, and in the lower 

 part at an increasing altitude. Consequently the horizontal veloc- 

 ity has its maximum value £/„ at the distance r from the barom- 

 etric minimum. 



Denoting the height of the external current by h (see fig. 24) and 

 the angle between the maximum velocity and the gradient by <p , 

 the quantity of air which enters per unit of length is represented 

 by U cos (p h. In the interior the current changes little by little 

 into a vertical current whose velocity we may indicate by w and 

 consequently we have the condition 



u> r = U cos (p h (1) 



It is probable that in nature the ratio h / r is so small that we can 

 neglect the vertical velocity and the vertical barometric depression 

 that results from it. We shall therefore consider only the horizon- 

 tal currents with either constant or variable velocity. 



