METEOROLOGY. 333 



formula for the change :n the velocity due to friction, in which respect 

 he agrees with Prof<'SSor Bruns, As has been before stated, tlie orbit 

 of a free particfe moving on a horizontal plane under the intiuence of 

 the earth's rotation and its own friction (.issumed to be directly propor- 

 tional to the velocity) will be a logarithmic spiral. If, however, the fric- 

 tion depends upon the square of the velocity, then the diflerential curve 

 is easily given, but the integrated equation involves a series of sines and 

 cosines. (Z. 0. G. M., xix, p. 523.) 



259. Prof. L. de Marchi, of Rome, has published in the Annals of the 

 Rome Meteorological Office an investigation into the mathematical 

 theory of the Avinds, in reference to which Dr. M, Margueles gives a 

 review with criticisms. Marchi aims to show that the quantity which 

 in hydrodynamics has been known as Wirbelgeschwindigkeit has an 

 imi)ortaut meaning in the mathematical theory of the winds. If we in- 

 dicate this quantity by C, then the total rotation of any parti'de of air 

 is equal to C ])lus the rotation of the earth, and the total rotation is 

 always positive or against the rotation of the sun; the lines of equal 

 total rotation are also curves of equal density; that any condition in 

 which the quantity C is zero cannot long exist over a large surface. If 

 we assume that the total rotation of a particle of air is constant for its 

 whole orbit, which Marchi thinks rendered probable by actual observa- 

 tions, but which Dr. Margueles thinks wholly arbitrary, then it follows 

 that the density is greater where C is greater. If a region where C is 

 zero divides two regions of positive and negative values of C, then the 

 density of the air will increase towards the positive and diminish 

 towards the negative C; he thus exi)lains the distribution of pressure in 

 cyclones and anti cyclones, and for the special case that the orbits of 

 the particles of air are logarithmic spirals the total rotation is con- 

 stant throughout the whole horizontal moven)ent. Assuming the Mohn 

 and Guldberg relation between density and temperature, Marchi finds 

 that when in the center of a cyclone C is negative, this is then a warm 

 center, but when C is positive it is a cold center, provided that in both 

 cases the curve of ^=0 completely incloses the center. After going 

 into many details in relation to individual simple cyclones, the author 

 remarks that by drawing lines for equal values of C, especially C=0, 

 we can easily study the ordinary complicated combinations of the daihy^ 

 weather map. He lays it down as a general rule that two lines of 

 equal values of C can never intersect each other, and that a line of 

 uniform C must either be con)[)letely inclosed or must extend to the 

 very limits of the liuid; he ])roves that if the line is closed, then tho 

 dilatation due to the motion will be greater on the north side than on 

 the south side, thus explaining the tendency of cyclones to move towards 

 the ])ole and of anti-cyclones towards the center in a diliereut manner 

 from that given by Ferrel. {Z. 0. 0. .¥., xix, p. 278.) 



260. In explanation of the above assumption to which Dr. Margueles 

 objects, Professor Marchi states that he did not enunciat<3 this as a 



