METEOROLOGY. 333 



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

 he agrees with Professor Bruus. As has been before stated, the orbit 

 of a free particle moving on a horizontal plane under the influence of 

 the earth's rotation and its own friction (assumed 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 differential 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 

 Eome Meteorological Office an investigation into the mathematical 

 theory of the winds, 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 

 important meaning in the mathematical theory of the winds. If we in- 

 dicate this quantity by ;', then the total rotation of any parti''le of air 

 is equal to C plus 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 explains 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 movement. Assuming the Mohn 

 and Guldberg relation between density and temperature, Marchi finds 

 that when in the center of a cyclone ^ 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 C=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 daily 

 weather ma\). 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 completely inclosed or must extend to the 

 very limits of the fluid; he proves that if the line is closed, then the 

 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 i)ole and of anti-cyclones towards the center in a different manner 

 from that given by Ferrel. {Z. O. G. il/., xix, p. 278.) 



260. In exi)lanation of the above assumption to which Dr. Margueles 

 objects^ Professor Marchi states that he did not enunciate this as a 



