I36 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



with care for the details, it will prove to be the most laborious operation of kinematic 

 diagnosis. The reason is that in spite of all idealizations, the topographic chart 

 will remain more complicated than the charts which represent the field of the 

 meteorological quantities observed. 



In order to simplify the work another way may be suggested : From the topo- 

 graphical map we could derive a chart representing the ascendant of the ground, 

 and print it as a blank. The process of differentiation would then be performed once 

 for all ; for it is easily seen that the vertical velocity may be expressed as the scalar 

 product of this ascendant and the horizontal velocity. Each chart of vertical 

 velocity could then be derived by a simple algebraic process (section 156). But 

 when this method does not work as well as might be expected, it is due to the great 

 complexity of the isogons and the intensity-curves representing the ascendant. The 

 control due to direct intuition is lost, and keen attention will be required to avoid 

 mistakes ; but this method may be considered if extensive detailed investigations on 

 the vertical motion at the ground are to be performed. 



A method which also might be considered in such a case would be the consist- 

 ent use of rectangular components. If the W.-E. and the S.-N. components of the 

 wind were observed, we might draw and print as blanks two special auxiliary charts, 

 one of the W.-E. component and one of the S.-N. component of the ascendant. 

 By a simple graphical multiplication we should then be able to derive a chart of the 

 vertical velocity due to each component of the wind, and afterwards a chart of the 

 total vertical velocity by graphical addition. 



183. Change of Velocity into Specific Momentum. Charts of Density at the 

 Ground. If we have a chart which represents the density of the air at the ground, 

 we can at once by graphical multiplication change a chart of velocity into one of 

 specific momentum. It will be sufficient if the chart of density has an accuracy 

 corresponding to that of the wind-observations. We can then ignore the influence 

 of humidity on density and consider density as a function only of pressure and 

 temperature. When we know the topography of the isobaric surfaces in free space, 

 we can draw their curves of intersection with the ground. These curves will give 

 a chart of the pressure at the ground. By this chart, together with a corresponding 

 chart of temperature at the ground, we can draw a chart of the density at the ground, 

 using one of the two auxiliary tables N. 



Table N, a, contains density and pressure as argument, and temperature as 

 the tabulated quantity. It gives the temperature of the point where the equiscalar 

 curves for the required field of density cut the given isobaric curves. Table N, b, 

 contains density and temperature as arguments and gives the pressure of the points 

 where the required curves for equal density cut the given isothermal curves. 



A density-chart drawn by one of these tables will possess an accuracy far 

 exceeding that of the observations of velocity. In most cases we can therefore still 

 further simplify the method, treating pressure at the ground as if it depended only 

 upon the height above sea-level and ignoring its variations from day to day. We 

 can then get the density of the air as function of height and temperature. 



