448 



SnORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



to lay before the society in the year 1869, and which may now be found 

 among the memoirs published by the Danish Society, 5th series, vol. 9, 

 part III. In that dissertation I showed that if a current of water moves 

 on a cylindrical surface perpendicular to its rectilinear elements, the 

 current of water having the depth n, and the surface of the current 

 moving with the velocity F, then the velocity of the current at the 

 depth X, beneath the free surface of the water, may be represented by 



(1) 



v=Y 



(1-0.433(1)^) 



when the resistance to the motion of the water is of the same magnitude 

 as that which would be offered by an underlying mass of water to the 

 current running above. 



In the present case, we will assume the cylindrical surface in ques- 

 tion to be a vertical surface of revolution, A X Y B, Fig. 1, within which 

 the current of water moves in the 

 direction indicated by the arrows. 

 Let C Z be the axis of the cylin- 

 der, and a «i hi b be the free sur- 

 face of the current, which is at 

 the distance a Z = OiC = a from 

 the axis, and at the distance 

 A a =X ((1= JI from the exte- 

 lior surface A X Y B, upon which 

 the current rotates. If it is now 

 assumed that the free surface 

 a a I hi h rotates with the velocity 

 V about the axis CZ, then any 

 element of the current which is at the distance wZ = »?i C = r from 

 the axis, and at the distance m a = Wicti = x from the free surface of the 

 current, as I have previously shown, will move with the velocity v, as 

 determined by formula (1), when the rotating current is surrounded by 

 an exterior mass of water which resists the rotation. It can then be 

 further shown that within this rotating volume of water there is a funnel- 

 shaped surface a ai hi j9, bounded within by the inner cylindrical surface 

 a Oi hi h, and without by the outer cylindrical surface A X Y B, in which 

 the pressure at all points is equal ; but, beside this level surface, there 

 is an endless number of other level surfaces in the fluid, both above and 

 below the surface a ai hi /9. All these surfaces are, meantime, so situ- 



States Coast Survey, 1877. For other papers on this subject by the same author see Am. 

 Jour. Sci., 18G1, 1874; Nature, 1871, iv, p. 22G ; 1872, v, p. 384; 1872, vi, p. 432. Of 

 additional recent literature relating to motions upon the earth we -will only mention 

 Hansen, Theorie der Tendelbewegung, 1856; E. Thomson, Rep. B. A. A. S., 1857; D. 

 Vaughan, Rep. B. A. A. S., 1859; Everett, L. D. E. Phil. Mag., 1871; also in his trans- 

 lation of Deschanel's Philosophy ; Colding, Danske Vid. Skab., 1863, 1871 ; Nature, 

 1871, V, pp. 71, 91, and 112; Schmidt, Vienna Mitt. Geog. Gesell., 1877; Finger, Vienna 

 Monatshefte, 1877 ; Guldberg and Mohu, Etudes sur les Mouvemens de TAtmosph^re, 

 Christiania, 1876; Zeit. Oest. Met. Gesell., 1876, 1877. 



