468 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



(3) The Lato of Yar^aUon of Barometric Pressure within Atmosplieric 



Currents. 



We shall show that when any region of the earth is traversed by a 

 general atmospheric current which preserves its direction notwithstand- 

 ing the diurnal rotation, one can conclude with certainty as to the ex- 

 istence of horizontal forces perpendicular to the direction of the current 

 and affecting every particle that is in motion. 



The forces which can affect any particle of the earth's atmosphere may 

 be divided into two classes : First, the internal forces, or those exerted 

 by neighboring particles — in other words, the pressure; second, the ex- 

 ternal forces, or those exerted by exterior bodies. The external forces 

 can be reduced to, first, the attraction exerted by the earth, or the 

 weight of the particle ; and, second, the action of the solar heat. But 

 even this last is not a force, properly so-called, for it does not tend to 

 displace the particle of air or make it to move in one direction rather 

 than the opposite. Its only direct effect is a variation of the internal 

 living force, and consequently of the density. 



If, then, I neglect the problematic influence of the moon and of other 

 celestial bodies, and if, moreover, I expressly leave out of consideration 

 the forces due to atmospheric electricity, I shall find no exterior force 

 that has a horizontal component. There will remain then to me, in 

 order to take account of the forces m F which solicit the particles of the 

 current, only the variations of atmospheric pressure in a horizontal direc- 

 tion. 



Let us imagine a parallelopipedon cut from the mass of moving air, 

 and having a base whose surface is 8, in a vertical plane parallel to the 

 direction of the current, and a height equal to Ar. The volume of the 

 parallelopii)edon will be S Jr, and the total mass of particles of air 



which it contains If = — S Ar (where p is the density of the air, and 



g = 9™.8088 is the value of gravity. 



The forces exerted upon the mass M due to the particles of the sur- 

 rounding fluid have, for resultants, pressures upon the faces of the par- 

 allelopipedon. As these pressures are normal to the faces upon which 

 they act, the pressures upon the horizontal faces and upon the vertical 

 faces normal to the direction of the current give no components having 

 the direction of the forces m F. We have then to take account only of 

 the pressures j9 and j? ■{• Ap exerted upon the two vertical bases of the 

 surface S; and recollecting that the resultant of all the forces m ^ which 

 affect the particles contained in the parallelopipedon ought to be equi- 

 valent to the difference between these two pressures in opposite directions, 

 we shall have the equation* 



S^ — S (2^ + Jj9) = m F; 



* The theory that we shall here develop in order to obtain the law of pressures is 

 identically the same as that which, in mechanics, serves to establish the fundamental 

 equation of the motion of fluids. 



