METEOROLOGY AND ALLIED SUBJECTS. 295 



l^resent time applied to the explanation of the cyclonic movement of 

 the air consists especially in its great perspicuity, but also equally in 

 the difficulty of making a true law of deviation generally evident to read- 

 ers slightly acquainted with mathematics. It appears to me, however, 

 as though this difficulty could be overcome, and as though the correct 

 expression for the deviating force of rotation could be deduced in a 

 simple manner intelligible to all." Sprung then proceeds to consider the 

 case of a plain disk rotating with an angular velocity w, which is a 

 case precisely parallel to the condition of affairs on the earth's surface 

 in the neighborhood of the Xorth Pole. If the relative or absolute orbit 

 of any body jjasses through the center of rotation of the disk, then, in 

 the absence of all exterior forces, the body moves relatively to the earth 

 in an Archimedean spiral, in such a manner that its relative angular 

 velocity is equal to that of the disk itself, and perpetually moving 

 further and further from the center. 



This, therefore, is the inertia curve projected upon a rotating plane 

 disk. It is now evident that every relative movement on the disk that 

 differs from that of the inertia curve is also a departure from the absolute 

 rectilinear movement, and can therefore not take place except under the 

 influence of some exterior force. If, now, such exterior force be decom- 

 posed into components that are perpendicular and ijarallel to its orbit, 

 the study of the combined effects of these components and the cen- 

 trifugal force shows that on a i^arabolic surface rotating with the angular 



velocity w the inertia curve is a circle whose radius is ^o =— -— de- 



scribed with a constant relative velocity (v) which is entirely inde- 

 pendent of the distance from the center of rotation of the surface. 

 For movements upon the actual surface of the earth we have p = 



— - — —. — , The uniform motion in a straight line, or those forms of 

 2 to sin cp 



motion which, in absolute space, are the only ones that can exist in con- 

 sequence of the inertia, requires, on the rotating surface of the earth, the 

 action of an outer pressure from right to left capable of producing an ac- 

 celeration at the equator, whose value is expressed by 2 v ta sin <p. 



Sprungj by geometrical construction, makes it evident that under 

 otherwise similar circumstances in regard to the geographical latitude, 

 the velocity and ftiction, 1st, the cyclonal curvature of the wind orbit is 

 accompanied by a stronger gradient and greater angular deviation <p 

 than is the anti-cycloual curvature. 2d. For the same curvature of the 

 wind orbit and for equal velocity and increasing coefficient of friction 

 increases the gradient, but diminishes the angular deviation (p. 3d. For 

 equal curvature of the wind orbit, and equal coefficient of friction, and 

 equal velocity, both gradient and angle of deviation increase with the 

 approach to the equator, as was shown by Guldberg and Mohii. {Z. 0. 

 . 0. M., Vol. XV, 1880, pp. 1 to 21.) 



