62 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Eliminating the specific volume by the equation of state 



we get 



dp 



1 



or 



(d) H b -H a =-R r dd nat. log. p 



Considering henceforth nat. log. p as the independent variable, and taking out- 

 side the integral sign the average value t?^ of the virtual temperature, we get the 

 simple formula 



(e) // t -//=^nat.log.^ 



giving the dynamic height from the isobaric surface p a to the isobaric surtace p b . 



The defined average value # a6 of the variable virtual temperature & r has a simple 

 meaning: It is that constant temperature which, substituted for the variable tem- 

 perature & r gives the sheet between the two isobaric surfaces p a and p b its true 

 thickness. This average value is easily found by the virtual-temperature diagram, 

 this diagram being drawn with logarithmic scale for the pressure, as in fig. 5, 

 example 1 below. Here the horizontal lines correspond to constant pressures and 

 the vertical lines to constant temperatures. Three curves running close together 

 are seen in the diagram. The middlemost is that representing the virtual tem- 

 peratures derived from the observations. The vertical segments of line give the 

 required average values of the virtual temperature of each of the standard isobaric 

 sheets. Each segment is drawn so that the two triangular areas limited by the 

 urve, the segment, and the two standard isobaric lines are equal. These vertical 

 segments may generally be drawn free-hand with a precision exceeding that of the 

 observations from which the curve of virtual temperature has been derived. Of 

 course greater precision, if required, may be obtained by use of a planimeter. 



51. Fundamental Tables. The sheet between the isobaric surfaces p a and p b 

 will generally contain a set of isobaric standard sheets. The height H h H a can 

 therefore be calculated as the sum of three terms: (1) the height from the isobaric 

 surface p a to the nearest standard surface; (2) the height from this standard sur- 

 face to a certain higher standard surface; (3) the height from the last standard 

 surface to the isobaric surface p b . 



To find height (2), we determine the thickness of any standard sheet. Let n be 

 the pressure in any standard surface. The pressure being measured in decibars, n 

 will have one of the values 1, 2, 3, . . . 10. The thickness H n , ll _ x of the standard 

 sheet between the surfaces n and n 1 is obtained if in the fundamental formula 

 section 50 (e) we introduce p a n, p b n 1. Substituting further fori? its 

 numerical value when the pressure is expressed in decibars, R = 28.7, and writing 



