SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 445 



H. 



EEPLY BY ME. FEREEL TO THE CEITICISMS OF ME. HA^^^^T. 



[Zeit. Oest. Met. Gesell., x, p. 254, August, 1875.] 



Ill the presentation of Ferrel's formula (vol. x, ITos. 6 and 7) we Lave 

 made certain objections to his method of introducing the friction therein, 

 to which Mr. Ferrel replies from Washington as follows, in a letter of 

 the 27th April : 



"The resistance of the earth's surface to the rotatory movement of 

 a cyclone can only be overcome by the force that according to the prin- 

 ciple of the conservation of areas results as soon as the air is constantly 

 drawn by a centripetal force toward a center. If at a distance of 400 

 miles from the center of a cyclone the air has no rotatory movement 

 relative to the earth's surface, nevertheless, it still has a rotatory move- 

 ment about the center of the cyclone in consequence of the earth's rota- 

 tion, the expression for which is r n sin (p ; or, at the parallel of 45°, a 

 linear velocity of about 74 miles per hour. Were there no friction, then 

 would the air when it arrives at a distance of 100 miles from the cen- 

 ter have a rotatory movement of 4 x 74 = 296 miles j and if we now 

 subtract the rotatory motion in this distance due to the earth's rotation, 

 that is to say, 15.8 miles, we obtain 277.5 miles for the velocity of rota- 

 tion relative to the earth's surface, and perpendicular to the radius. 

 The force which overcomes the inertia and produces this motion is ex- 

 pressed by 



du du 

 r ^ = — cos I. 

 dt dt 



Now, in the case of friction, we have, instead of a rotatory movement of 

 277.5, one, say, of 40 miles; so that in this case over ^ of this force is lost 

 in overcoming the friction, and this gives an approximate measure of 

 the amount of the frictional resistances. 



"The inertia, like the friction, opposes the force due to the centripetal 

 movement ; therefore, its expression is 



dt' 



and we thus obtain the expression for F' as it is given at the bottom of 

 p. 99, vol. X.* It must certainly be considered, however, that this is only 

 an approximate presentation of the frictional resistance, including the in- 

 ertia of the fluid, in case there occur changes in its velocity; but this latter 

 is in general only a very small part of the total resistance to movement. 

 "As the two components of the friction in the direction of the tangent 

 and of the radius, we now have 



F' : F =~ : V cos i, 

 dt 



and this gives F, as at the bottom of p. 99, vol. x,* as an approximate 



expression for the effect of friction in the direction of radius. In order 



* See page 62. 



