SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 467 



Comparing these values, and passing to the limit by making t dimin- 

 ish to zero, we shall obtain, for the value of the force F^ 



F=2 FQ sin /I. 



As to the direction of the force, it is that of the deviation P M per- 

 pendicular to the line bisecting the angle P A M, and passing to the 

 limit we obtain a direction A F perpendicular to A P, or the direction 

 of the current at the point A. 



The force m F, whose direction and value we have determined, is that 

 known in mechanics as a composite centrifugal force. We will now 

 apply to our special case the general theory, by means of which we pass 

 from forces of apparent movement to real forces. 



We will now determine the effect of rotation about the terrestrial 

 radius passing through the point A. The second rotation, that which 

 takes place about the radius perpendicular thereto, will give to the real 

 trajectory a new curvature, and consequently we should have to con- 

 clude the existence of a new corresponding force; but this second com- 

 posite centrifugal force is feeble relatively to the first, and does not 

 seem to manifest itself in existing meteorological observations. In order 

 to simplify our formulas, we shall, in what follows, neglect it as being 

 insensible. 



A calculation analogous to that which precedes shows that if the air 

 moves parallel to the terrestrial surface, or if the level of the particle of 

 the air m does not vary, the second composite centrifugal force is ver- 

 tical and has for its value 



2 m 7 sin ^ Q, cos X 



{<P being the angle that the velocity V makes with the meridian). 



This force having the same direction as the force of gravity, and ex- 

 tremely feeble in comparison with it, should exert an influence propor- 

 tional to its value. We do not think its effects can be clearly distin- 

 guished from those of the weight of the air. When the air is animated 

 by au ascending or descending movement, such that the velocity V of 



the particle m has a vertical component tt) the composite centrifugal 



force that we are studying has a second component 



dv 

 2m-j- Q cos X , 



which is horizontal and perpendicular to the meridian. It is possible 

 that this second component produces some appreciable effects in meteor- 

 ological phenomena when the vertical movements of the air become im- 

 portant, as, for example, in storms and hurricanes.* 



* Note by the Translator. — It will be perceived that in these foruiulse Peslin treats 

 of the rotation of the earth to the neglect of the rotation of storm-winds a^out their 

 centers. 



