138 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



In all cases when the density-chart is found, we have simply to perform the 

 graphical multiplication of the charts of vertical velocity by that of density in order 

 to get the chart of vertical specific momentum. 



184. Direct Method of Determining Vertical Specific Momentum from Hori- 

 zontal Velocity at the Ground. If the chart of vertical velocity is drawn already, 

 the method given in the preceding section will give the easiest construction of the 

 chart of vertical specific momentum. But we can also use a direct method without 

 passing through the vertical velocity. As the contour-lines of our charts can be 

 interpreted as lines of equal dynamic height H, we can write equation 181 (b) 



1 \ dH 



(a) v, = v-g 



Now, according to the fundamental equation of hydrostatics, we have dH = adp, 

 where pressure p is measured in decibars when dynamic height H is measured in 

 dynamic meters. When we introduce this and divide by the specific volume a, i. e., 

 multiply by the density p, we get on the left side the vertical component V v of 

 specific momentum, 



(b) V v = -vf 



as 



This equation gives the following rule for drawing the chart of vertical specific 

 momentum at the ground : We first draw the chart which represents the field of 

 pressure at the ground; then we perform the graphical differentiation of this field 

 with respect to the length of arc along the lines of flow ; finally we perform graphical 

 multiplication of the field thus obtained by the field of the scalar value v of velocity. 



This method is precisely like that which we have developed for the velocity 

 except that we use the chart of pressure at the ground instead of the topographic 

 chart. But it will give more work, inasmuch as the topographic map always remains 

 the same, while that of pressure changes and must be drawn again in each case. 

 If we ignore, however, the variations in time of the pressure, we can draw a chart 

 representing the average pressure at the ground and use this chart consistently for 

 the determination of vertical specific momentum, precisely as the topographic map 

 for the determination of the vertical velocity. Then it will be as easy to draw charts 

 of vertical specific momentum as of vertical velocity. The errors in the determina- 

 tion of vertical specific momentum caused by the use of the average pressure will 

 amount to a small percentage and thus always be small compared to those which 

 arise from the imperfectness of the observations of the wind. Therefore in general 

 there will be no objection to using this simplified method. 



We have therefore drawn the charts of plates XXVII and XXX, which give the 

 average pressure at the ground in the United States and in Europe. As to the degree 

 of idealization, they correspond to the strongly idealized topographic maps of plates 

 XXVI and XXIX. The coast-line is to be considered as an isobaric line of pressure 

 about 1013 m-bar. Then the curves for 1000, 900, 800, . . . m-bar have been 

 drawn as continuous lines, while a curve for the pressure of 980 m-bar is dotted and 

 a curve for 950 m-bar is stippled. 



