VERTICAL MOTION IN FREE SPACE COMPLETE KINEMATIC DIAGNOSIS. 1 43 



Instead of expressing the vertical dimension in the direct way by the length 

 dz measured along a vertical line, we can express it indirectly by the decrease of 

 pressure dp along this line. For when the field of pressure is known, the indication 

 of a pressure will be equivalent to that of a height. In order to bring in pressure we 

 can first substitute dynamic height H for geometric height z. This can be done 

 with sufficient accuracy by the relation 



dz = 1.02 dH 



dz being expressed in meters and dH in dynamic meters. Then we can pass from 

 dynamic height to pressure by the equation of hydrostatics 



dH = adp 



where pressure p is to be expressed in decibars and // in dynamic meters. When 

 we introduce this in the expression of T and remember 



v = aV 



we shall get as a new expression of the horizontal mass-transport 



(a) T = (1.02 v) dn { dp) 



or, when we leave out the practically insignificant factor 1.02 



(a') T = vdn (-dp) 



When we compare this expression with the original, T= Vdndz, we conclude 

 that in the formula? of the preceding section we are entitled to introduce the decrease 

 of pressure dp instead of the increase of height dz on condition of introducing at 

 the same time horizontal velocity v instead of horizontal specific momentum V. 

 This change of the formulae leads at once to the following general rule : 



The constructions described in the preceding section may be performed upon charts 

 of horizontal velocity v instead of upon charts of horizontal specific momentum 

 V. The charts resulting will then describe the vertical motion in reference to the 

 pressure decreasing upward instead of in reference to the height increasing 

 upward. 



Thus to mention the special cases : 



(A) Areas for equal vertical mass-transport. We start with a chart representing 

 horizontal velocity, and propose to draw a chart representing the transport (a 1 ) . 

 For this we first draw a chart of the expression 



(b) T, = vdn 



which represents the horizontal mass-transport in a sheet of a thickness defined by 

 unit decrease of pressure from bottom to top, dp=i. In order to get this chart 

 we first draw an initial curve C and divide it into elements which give 



(c) v'dn' = c' 



where dn' denotes the projection of the element of the curve C on the normal to the 

 lines of flow, and c' is a constant chosen so as to get proper breadths of the bands of 

 flow. Through the points of division we draw lines of flow dividing the field into 

 the bands of flow to which the transport T 1 is to be referred. Then we draw curves 



