SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 469 



whence, substituting the value of M and dividing by S, 



We can also replace F by its value determined previously, and the 

 formula then becomes 



J » = — — • 2 F • Q sin A Jr. 

 ^ 9 



(4) Application to the Synoptical Charts. 



It is easy to applj- these theories to atmospheric currents, and to show 

 that they give the same laws that we have deduced from the examina- 

 tion of synoptic charts. 



The forces ni F have no components in the direction of the current; 



consequently, the pressure ought not to vary in this direction : in other 



words, the direction of the wind ought to be tangent to the curve of 



equal barometric pressure. The direction in which the pressure 



increases transversely to the current is opposite to that of the forces 



mF. It should change when the direction of the current changes ; and 



in our hemisphere, considering the direction of the terrestrial rotation, 



we recognize by the examination of the figure which gives the force F 



that the highest pressure should always, on the synoptic chart, be to 



An 

 the right of the current. Finallv, the coefficient -r- which measures the 



rapidity of the transverse variation of the pressure increases propor- 

 tionally to the force F; that is to say, increases on the one hand as the 

 velocity Fof the moving air, and, on the other hand, increases in pro- 

 portion to the sine of the latitude of the region under consideration. If 

 any region of the earth is traversed by a violent atmospheric current, 

 the curves of equal barometric pressure ought, in traversing this region, 

 to draw closely together, and so much the more for a given violence of 

 the wind in proportion as the region is further removed from the equa- 

 tor. 



(5) Extension to the Case of Rotatory Movements. 



These laws are those that relate to atmospheric currents of constant 

 direction and intensity ; when the movement of the air is not rectilinear, 

 these cease to be rigorously applicable. It is necessary then to com- 

 bine the composite centrifugal force with the forces which correspond 

 to the apparent movements of the particle of air. These forces are : 



dV V^ 



m -^ in the direction of the current, and *'^-t>~ in a direction normal to 



the current, H being the radius of the curvature of the apparent 

 trajectory. Consequently the formula? which give the variation of 

 barometric pressure become 



dp _ p dV^ 



'ds~ ~~(j ' dt^ 



-r=—'~'irr—2'-VQsinX. 

 dr g li fj 



