432 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



were themselves first produced by the depression. The diminution of 

 pressure at the earth's surface is increased when the air moves not in 

 rectilinear but in curvilinear paths, since then the ordinary centrifugal 

 force also comes into play. It is now customary, as is well known, to desig- 

 nate by the term " barometric gradient," or " the gradient," the differ- 

 ence of i^ressure for a given amount of distance, and in issuing " storm 

 warnings" one deduces the strength of the future wind from the magni- 

 tude of the gradient. We have just shown that the greatest part of an 

 observed gradient is not the cause but the result of the violence of the 

 wind. For practical storm predictions, however, this is, of course, im- 

 material. In general, the so-called " Buys Ballot's law " is only the 

 shortest expression for the facts graphically presented upon the synop- 

 tic charts, and it is therefore not aflected by the vagaries of the tljieories 

 of the origin of areas of low pressure. 



We believe we have now reached a point of view from which the labors 

 of Ferrel and Coldiug gain an increased interest; from which also, at 

 the same time, the limits of their applicability may be perceived, and we 

 can therefore proceed to their memoirs. 



The title of Ferrel's memoir reads: "Eelation between the Barometric 

 Gradient and the Velocity of the Wind" (Amer. Jour. Sci., vol. viii, 1874). 



The following is not a translation, but a sort of working over of Fer- 

 rel's text. Especially have we deduced equation (I) in a more elementary 

 way, and also given it a somewhat different form. 



When water has a motion of rotation in a stationary basin, the centri- 

 fugal force produced by the rotation causes the water to retreat from 

 the center, and to acquire a funnel-shaped surface ascending toward the 

 edge of the vessel. In consequence of this, the pressure on the bottom 

 of the basin increases from the center toward the circumference. If 

 r is the distance from the center of the basin, 

 M the angular velocity of the rotation, 

 then will 



/• \C^ express the magnitude of the centrifugal force. 

 But in case the basin itself has also a rotatory motion in the same direc- 

 tion, whose angular velocity we designate by w,then will the expression 

 for the magnitude of the centrifugal force be 



r (w + uY = r {lo'^ -j- 2 w « 4- n'-) = r lu^ -\- '2 w v -\- u i\ 

 because r u is the linear velocity of the movement of the water relative 

 to the basin. Now the increase of pressure or the gradient in the direc- 

 tion from the center toward the circumference depends on this quantity 

 [r u]. If, however, we refer the gradient to the surface of the water 

 when at rest with respect to the basin, which latter, however, itself has 

 an angular velocity w, then in the above expression we must omit the 

 term r io\ which depends simply upon w, and the expression for the 

 centrifugal force becomes 



2 w V -^ n V — {2 w -{- u) V. 



