GEOPOTENTIAL : DYNAMIC HEIGHTS Iv 



The factor — is substituted in eq. (i) to convert to units of dynamic 



height in dynamic meters (lo ywVsec"). 

 Integrating (3), we obtain 



(4) Hd= ^h-l.543XIO-'h- 



For a first approximation, we may neglect the term in h~ and take 

 g^ =9.8 ;n/sec-, 



whence 



(5) //d= 0.98 /z, approximately, 



and (6) h=i.02 Ha, approximately. 



Geometric heights (Ji) may be expressed in terms of dynamic heights 

 (Hd) by a convenient approximate relationship. 

 Substituting (6) in the h~ term of (4) we obtain 



(7) h= — H^+ — 1.543(1.02)- • 10- • Ha 



94> 9<P 



which is simplified for computation by taking 9.8062 as g^ in the second 

 term, this being the mean value at latitude 45° and sea level. 

 Thus (7) becomes 



(8) h= — H,i+ 1.637 X ^o-Urll approximately. 



We are indebted to Prof. V. Bjerknes and his collaborators for the above 

 formulation, and for tables 64, 65, 67 and 68, which are copied directly from 

 their " Dynamical Meteorology and Hydrography." ^ 



DESCRIPTION AND USE OF TABLES 64 TO 68 INCLUSIVE, 



The purpose of these tables is to convert from geometric heights to 

 dynamic heights and vice versa. Tables 64, 65, and 66 are used to convert 

 geometric meters to dynamic meters. Tables 66, 67, and 68 are used to convert 

 dynamic meters to geometric meters. 



Table 64. Heights reduced from meters to dynamic meters, the accelera- 

 tion of gravity at sea level being 9.80. 



This table, computed by means of equation (4) above, makes possible 

 the reduction of geometric heights to dynamic heights, the acceleration of 

 gravity at sea level being 9.80 m/sec^. In this table the side argument is geo- 

 metric height above sea level by intervals of 1000 m., and the top argument 

 is geometric height by intervals of 100 m. The proportionality table at the 

 foot of the main table makes it possible to obtain dynamic heights correspond- 

 ing to any integral number of geometric meters from o to 30,000. 



^ Bjerknes, V., and colleagues, Carnegie Inst, Washington, 1910. 



