438 SHOET MEMOIRS ON METEOROLOGICAL SUBJECTS. 



sents the influence of the centrifugal force appears to be iuclependent 



jf B v^ 



of i, since the development shows it to be equal to . _ . —(or, as 



' 287 T r 



given in the second page of the original, = j^ . .^ , which is 



the same, excepting, of course, the constant), but in our storms [latitude 

 50OJ almost the only term of influence is the first j therefore from Ferrel's 

 formula we should find too large a value for the gradients. 



In the latest number of Symon's Meteorological Magazine (March, 

 1875), Strachan has applied Ferrel's formula (II) to Toynbee's charts of 

 the 5th February, 1870. These latter give the gradients AB as = 0.114 

 English inch for each 100 miles; v was estimated as equal to 56 miles 

 per hour, and since <p = 45°, r = 350 miles, i = 45°, therefore the formula 

 gives AB = 0.320 which is nearly thrice too large. But if we compute 

 according to our formula (T), and neglect the centrifugal force, as is 

 allowable in this case, we find AB = 0.156 inch. Had we used the formula 

 (F), and neglected F, it would have given AB = 0.100 inch. Therefore, 

 in both cases, we obtain much more correct values than according to 

 Ferrel's formula (II). 



We give now in abstract Ferrel's discussion of formula (II). We have 

 designated by u the angular velocity of the rotating mass of air. Be- 

 sides this rotation, however, in general there Is also a movement either 

 toward or from the center of the cylone j the former occurs in the lower 

 portion, the latter in the upper portions of the cyclone. The value of i, 

 therefore, has opposite signs above and below, and somewhere in the 

 middle i must entirely disappear, the movement being assumed purely 

 circular. 



The value of * depends mostly upon the friction, but to a certain 

 extent also upon the inertia of the mass of air in those cases in which 

 the movement is increasing or diminishing, as in the beginning and end- 

 ing of the cyclone. It is therefore also greatest over the land and near 

 the earth's surface, and comparatively slight at sea, and especially so 

 in the upper strata of the atmosphere. It further depends on the geo- 

 graphical latitude, and at the equator we have i = 90°, for there can be 

 there no rotation, but the movements are directly toward or from the 

 center of a region of expansion or condensation. 



The greater the value of F' for the same value of v, so much the 

 greater will be dr, and therefore also *. When for different velocities 

 the friction increases in proportion to the velocity, then must dr increase 

 in the same proportion (since F' = 2 {n sin <p + u) dr) and i remains con- 

 stant for all velocities as long as « can be neglected in comparison with 

 n sin 0, that is to say, for large distances from the center. But nearer 

 to the center of a cyclone, where u is very large in comparison with 

 n sin ^, dr is very small, and, under the same circumstances, therefore 

 also the value of i. For all ordinary winds, the value of i is probably 

 nearly constant for all velocities, and therefore observations for a given 



