346 W. Ferrel—Relation between the Barometric Gradient 
require too much mathematical analysis to be given here. It 
may, however, be important to give the following explanation, 
rather than a complete demonstration, of this law so far as it 
applies to ordinary cyclones of not very great extent, especially 
as the method of presenting the matter here is different from 
sure of the fluid upon the bottom of the vessel. If we let 7 
represent the distance from the center and wu the angular veloc- 
ity of gyration, the centrifugal force is expressed by rv? sim- 
ply. But if in addition to the gyratory motion of the water in 
the basin, the basin itself also has a gyration like a dish around 
its center, of which the angular velocity is represented by 7’, 
we then have for the whole centrifugal force 
r(n'+-u)?=r(n'?+2n'u+u?), 
+u)v for the centrifugal force upon which the gradient of the 
cyclone depends, for the term in this case depending upot 
n* sin? /, corresponding to n? in the case of the basin of water, 
must be neglected, as in that case, since the atmospheric gradi- 
ent is referred to the elliptic surface of the earth, and not to 
the surface in the case of no rotation around its axis. This 
