CHAPTER VII. 



SYNOPTIC REPRESENTATION OF THE FIELDS OF PRESSURE AND 

 OF MASS IN THE ATMOSPHERE. 



60. Quasi Static State. Setting aside extraordinary phenomena, as, for 

 instance, waterspouts, we may characterize atmospheric motions as slow motions 

 going on near a state of equilibrium. Comparing simultaneous barometric records 

 taken from two different places, we find the conditions of equilibrium apparently ful- 

 filled, if the two places are at small or moderate distances from each other. Only 

 as the distance increases do we find a gradual departure from the fulfillment of these 

 conditions. As long, therefore, as the distance is small, the correct result will be 

 produced if we use the barometric records for calculating the difference of height 

 between the two barometers. The instruments will especially show the same pres- 

 sure if they are placed on the same level. But if we sufficiently increase the dis- 

 tance between them, they must finally be placed on distinctly different levels in 

 order to show the same pressure. 



Thus, in reality, there is a deviation from the principle of the coincidence of sur- 

 faces (sections 35, 38). But the angle of intersection is so small that we must fol- 

 low the surfaces over great distances in order to find an appreciable separation. 

 On the other hand, proceeding along the plumb-line, we can not attain distances 

 sufficiently great in order to prove an unquestionable deviation from the principle of 

 the unit-sheets (sections 35, 38). Owing to the great lateral and small vertical 

 extent of the atmosphere, we have therefore this peculiar relation, characterizing 

 what we may call the quasi static state of the atmosphere : 



The conditioti of equilibrium is apparently fulfilled along every vertical 

 line. But as we proceed in a horizontal direction, there is a gradual change 

 from vertical to vertical in this apparent state of equilibrium. 



This important principle forms the basis of all practical investigations in atmos- 

 pheric dynamics. In making use of it, it is important to remark that we need not 

 take the expression "vertical" in the narrow sense of the word. We can consider 

 the greatest angle of inclination of the isobaric surfaces as a kind of critical angle. 

 Every curve whose angle of inclination is everywhere great in comparison with this 

 critical angle will be called a quasi vertical curve, while curves whose angle 

 of inclination is of the same order of magnitude or smaller than this critical angle 

 will be called a quasi horizontal curve. The latter curves may attain lengths 

 comparable to the lateral extent of the atmosphere, while the first remain short in 

 the same sense as the true vertical curves are short. Following a quasi vertical 

 curve, we can not therefore attain sufficient distances to be able to observe any 

 appreciable departure from the hydrostatic conditions, and the principle stated 

 above can therefore at once be extended from true vertical to quasi vertical curves. 



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