466 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



conditions that the constitution of the atmosphere imposes in order 

 that this current may be maintained for an indefinite length of time, 

 and in order that the diurnal rotation of the earth shall not modify the 

 direction which the current has at the surface of the globe. Let A be 

 one of the points of the region over which the atmospheric current pre- 

 vails. Let B A be the direction of the current, V the velocity with 

 which the air moves. Let A ?/ be the meridian of the point A; A a? the 

 perpendicular to A ?/, or the tangent to the parallel through the point A. 



Let us represent by X the latitude of the point A, and by Q = J^ 



the angular velocity of the diurnal rotation of the earth. The curve 

 really described in space by a particle of air is obtained by compound- 

 ing the apparent movement of this particle on the surface of the earth ; 

 that is to say, the translation corresponding to the velocity of the cur- 

 rent, with the movement of the terrestrial surface, or the translation 

 corresponding to the diurnal rotation. 



I decompose the diurnal rotation into two component rotations, the 

 first having for its axis that radius of the earth which passes through 

 the point A, the second having for its axis the terrestrial radius perpen- 

 dicular thereto and in the plane of the meridian of the point A. The 

 angular velocities of these component rotations will be, for the first, 

 Q, sin A, and for the second Q cos X. 



Let us first consider the effect of the first rotation. The apparent 

 trajectory of the particle of air which passes by A being the line A P, 

 the real trajectory will be a curve AM, determined in polar coordinates 

 by the equations A M = A P = V ^. Angle F AM = Q t sin X, where t is 

 the time employed by the particle of air in describing the arc A M. 



The trajectory described is a curve. Consequently the particle of air 

 is subject to the action of a force whose value depends upon the curva- 

 ture of the trajectory, and is easy to calculate according to the princi- 

 ples of mechanics. 



The tangent to the trajectory at A is A P, for the limit of the angle 

 P A M is for i = 0. The velocity at A is V, for this velocity is the 

 limit of the ratio of the arc A M, or of the chord A M = Y ^, to the time 

 t required to describe it. Consequently, the effect of the force that ^e 

 desire to calculate, acting through the time t upon the particle of air, 

 is to produce a deviation, represented in our figure by the line P M. 

 Let m be the mass of the particle of air and m F the force that acts 

 upon it. We shall, according to mechanical principles, have 



Ihe figure gives us the geometrical relation 



PM = AM.2.sin(L|l^), 



^^ PM = 2y-^sini^^^iHi. 



