352 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



(D) Anticyclonic rotation with gradients directed inward, viz: 

 with cyclonal distribution of pressure. In this case the condition 

 as to centering is 



Pe-Pi~r = Q (5) 



As to this equation also it is doubtful whether it has any practical 

 importance. In general, in the lower strata of the atmosphere we 

 meet only with the above-mentioned cases (A) and (C). 



We usually assume that in the upper portion of the anticyclone 

 there is a cyclonal distribution of pressure, that is to say, a gradient 

 directed inward, 9 since we consider this necessary in order to explain 

 the" inflow of air from above. But the presence of such a distribu- 

 tion of pressure in the upper half of an anticyclone has, sofaras 

 known to me, never been shown by any facts; on the contrary, 

 thermodynamic considerations make it in the highest degree improb- 

 able that the low temperatures observed at the lower surface of the 

 so-called cyclones with cold centers extend to any considerable 

 altitudes. But if this latter is not the case then also the assumed 

 change in the curvature of the surface of equal pressure (which 

 should generally pass from convex above, at great altitudes, to 

 concave above, at lower altiudes) will not exist. Consequently the 

 flow in the upper regions toward the anticyclone is not to be 

 explained as the result of a gradient directed inward, but rather 

 dynamically as a heaping up phenomenon due to obstruction. 



However, if in individual cases the assumption of a cyclonal 

 distribution of pressure in the highest part of an anticyclone should 

 be correct, as has hitherto ordinarily been assumed, still by reason 

 of the slight moment of inertia that is ordinarily present in an 

 anticyclonic whirl there is no reason why the direction of the rota- 

 tion should remain the same over extensive regions, as in the case 

 of cyclones where the pressure distribution is of the opposite type. 



These considerations show that of the four cases of centered whirls 

 that can be imagined, only the first mentioned has any practical 

 importance in meteorology and the following lines are therefore 

 devoted to its consideration. 



Therefore we consider here only a-]whirl with barometric gradients 

 directed inward, circular isobars, and cyclonal motion of the air, 

 under the special assumption that the directions of the wind agree 

 everywhere with those of the tangents of the isobars. 



Under these conditions the equation 



p e + -Pi - r - , 



* Sprung: Lehrbuch, p. 211, fig. 39. 



