436 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



of 57 miles. We further learn from this example that iu whirlwinds of 

 smaller dimeusio/.s the influence of the centrifugal force many times 

 exceeds that of the earth's rotation, so that iu these cases the latter, iu 

 low latitudes, may be neglected without great error. 



Consequently, in our storms [latitude 50°] the barometric depressions 

 are principally a consequence of the influence of the earth's rotation upon 

 the moving masses of airj in the tropical cyclones, on the other hand, 

 the depressions are a consequence of the centrifugal force. 



Professor Loomis has endeavored to x>rove that the centrifugal force 

 can produce no sensible barometric depression. (See his memoir " On 

 Certain Storms, t&c," page 24, Smithsonian Contributions.) He computes 

 for the storm of the 25th December, 1839, in Central Europe, that at a 

 distance of 400 miles the centrifugal force was, in round numbers, only 

 ecHjo V^^^ ^^ gravity, and concludes thence, further, that therefore the 

 pressure could, on that account, only sink about the -^Iq = g.^^o ^^ ^^ 

 inch. That this conclusion is wholly erroneous need scarcely be re- 

 marked, had not the result been quoted in an excellent English hand- 

 book of meteorology. 



In nature, the conditions are not so simple as we have hitherto intro- 

 duced in our computations. The air does not move in a circular orbit 

 about the storm-center, but flows toward it in spiral paths. Ferrel 

 seeks to introduce this spiral movement, and also the frictional resist- 

 ance, into his computation. We give in the following his presentation 

 of the subject, but can, for several reasons, not consider it as correct. 



When the air flows in toward the center of the cyclone (or in the upper 

 strata flows away from it), we must in equation (I) introduce in the 

 right-hand member another term, F, which shall represent the resistance 

 to the movement. Similarly the entire centrifugal force of the curvilin- 

 ear movement is not now active, but a less force, whose amount we 

 find by dividing the actual velocity, ru, into two components, one in 

 the direction of the tangent and the other perpendicular thereto. 



If we indicate by i the angle between the actual direction of motion 

 and the tangent, then will the first of these components be represented 

 by r u cos i, or v cos f, and the centrifugal force depends only upon this. 

 We have therefore, now, as a new equation for spiral movements, the 

 following, iu which the value of F remains still to be determined : 



(I') ^B = r^ijn-i • y.- \ [2n sin <p + u) v cos i+ F > • 



According to the iirinciple of the conservation of areas in the case of 

 purely central forces, the following equations must obtain in all parts of 

 a cyclone: 



r^ (?^ sin <p -f «) = Constant; 

 and therefore 



— r chi = 2 {n sin ^ -\- u) dr. 



The second member of this last equation is the expression of the force 

 which would strive to preserve a rotatory motion about the center. In 



