354 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. $1 



where G is the gradient, i.e., the difference of barometric pressure 

 between two points distant from each other by one degree of the 

 meridian, or iii,in meters on the spherical surface of the earth, 

 and in the direction of the maximum change of pressure. 

 But we also have 



h 



r = i g = s tan « ( 8 ) 



where h is the altitude by which the surface of equal pressure (iso- 

 baric surface) drawn through the point under consideration, rises 

 or falls in the course of the horizontal distance /, and where a is 

 the angle that the surface of equal pressure at this point makes with 

 the horizon. 



Therefore the acceleration that is given to the air by the gradient 

 force is equal to that which a heavy point experiences when it glides 

 without friction along an imaginary rigid isobaric surface, at least 

 in so far as a is small enough to allow us to consider sine a as equal 

 to tangent a, which is always the case in our problem." The acceler- 

 ation due to gliding down such a surface is g sin <t, whereas the force 

 g tan a acting on the point horizontally, is required to prevent the 

 gliding downward. 



If we substitute in (7) and (8) the value of 7- given in equation 

 (6) and write r instead of r c since the quantity r i no longer occurs 

 in the problem, then the equation of condition for the centered whirl 

 finally assumes the form 



0.000 122 37 g- = - + wfcsin <p (9a) 



p r 



or if /? is the barometric pressure 



13.6 d(S v> , . , Q7 , 



g — — = — + v k sin <p (9o) 



p dr r 



or finally 



g tan a = - + v k sin <p (9c) 



r 



11 In my original memoir the first deduction and formulation of this theorem 

 was attributed to Moeller, but it is due to Hann, who first gave it in his mem- 

 oir "On the relations between wind velocity and differences of pressure 

 according to the theories of Ferrel and Colding, " Zeit. d. Oest. Gcsell. f. Met. 

 1875, X, pp. 81-88, 97-106. Compare also my memoir of 1901, XVIII of 

 this collection of translations. (Note added 1906. W. v. B.) [My transla- 

 tion of I hum's memoir will be found in my "Short Memoirs," Smith. Rept. 

 1877.— C. A.] 



