90 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



61. Consequences of the Principle of the Quasi Static State. In the pre- 

 ceding chapter we have shown how the results of meteorological ascents could be 

 worked out according to the principles of hydrostatics. 



In the case of true equilibrium, one ascent would be sufficient to give the state 

 of the whole atmosphere. For according to the principle of coincidence of surfaces, 

 the state will be the same at all points contained in the same level surface. There- 

 fore, if we know the state at the points of a curve cutting a set of level surfaces, we 

 also know the state at all points of these level surfaces. 



Now, the actual state of the atmosphere is not one of true equilibrium. But 

 owing to the principle of the quasi static state, the hydrostatic methods may still 

 be used to a certain extent. The curve along which the ascent of a kite or balloon 

 has taken place is always a quasi vertical curve. Along every curve of this kind 

 the conditions ot equilibrium are fulfilled with sufficient approximation to entitle us 

 to use the principles of hydrostatics. The states recorded by the instruments at 

 the different points of this curve maybe interpreted as if recorded at points of cor- 

 responding heights in a true vertical. By means of the developed hydrostatic 

 methods we therefore find the distribution of pressure and of mass along this 

 vertical. Although calculated upon a supposition not strictly fulfilled, the distribu- 

 tions of pressure and of mass found in this way will be very nearly the true ones. 



This does not, however, entitle us to draw any conclusion as to the distribution 

 of pressure and of mass along other verticals. For verticals of sufficient mutual 

 separation, the distributions will generally be distinctly different, and must be found 

 by independent observations. But this being done, we can easily calculate by inter- 

 polation the distribution of pressure and of mass also for all interjacent verticals, 

 and thus find this distribution in the whole atmosphere. 



Before concluding the consideration of atmospheric statics, we shall develop the 

 geometrical methods of representing synoptically the results obtained by this 

 method. 



62. Method of Drawing Charts Representing Scalar Fields. It will be use- 

 ful first to exemplify some practical methods of drawing charts representing scalar 

 fields in a plane. 



If the values of a scalar quantity be known at a number of points in a plane, we 

 always know how many equiscalar curves will pass between any two of these points, 

 the curves being drawn for fixed intervals, say for unit-differences of the scalar 

 quantity. By this condition the course of the equiscalar curves is determined to 

 some extent, the more accurately so the greater the number of points in which the 

 value of the scalar quantity is known. Therefore, knowing the value of such a 

 quantity at a sufficient number of points, we can draw the equiscalar curves with 

 sufficient accuracy, and thus arrive at the graphic representation of the scalar field 

 in the plane. 



This is the well-known method of drawing isothermic charts from the observa- 

 tions of temperature, isobaric charts from the observations of pressure, topographic 

 charts from measurements of heights, and so on. 



