liv INTRODUCTION. 



are called " dynamic heights," after Prof. V. Bjerknes/ and indicate relative 

 potential energies of unit-mass. Thus, points of equal " dynamic height " lie 

 in horizontal or geopotential surfaces. 



The geopotential of a point, from the definition, is equal to the work 

 done in lifting a unit-mass from sea level to the point, and is defined precisely 

 by the expression : 



(I) T=-\\dh 



i o 



where 5r= acceleration of gravity 



and /z = geometric height of the point above sea level. 



The dimensions of geopotential in the absolute system are P/t-. Follow- 

 ing the proposal of Prof. Bjerknes,^ the unit of dynamic height is called the 

 " dynamic meter " and has the magnitude lO nf/s&c^ where g is measured in 

 w/sec-, and h in meters. 



The unit is chosen with this magnitude for convenience, since a change 

 in elevation of one meter geometric height produces a change in dynamic 

 height of approximately 98 per cent of one " dynamic meter," i. e., within the 

 range of the majority of present atmospheric observations. 



CALCULATION OF DYNAMIC HEIGHTS. 



Equation (i) may be solved by substituting in it Helmert's ^ equation 

 for the decrease of acceleration of gravity with height : 



(2) 9= — (5^0—0.000003086 h) 



where 



g,p = acceleration of gravity below given point at sea level, in 7n/sec-. 

 (7 = acceleration of gravity at point whose elevation is Ji above sea level. 

 /i= geometric height in meters, above sea level. 



The minus sign is used because gravity is directed downwards and heights 

 are measured upwards positively. 

 Equation ( i ) becomes : 



I f '' 



(3) Ha= — (^r,^, — 0.000003086/06^/1 



10 J O 



where //d = dynamic height, in dynamic meters. 



1 The claim for the use of geopotential in measuring heights was set forth by Prof. V. 

 Bjerknes and his collaborators in Vol. I of Dynamical Meteorology and Hydrography, 

 published in English in 1910 by the Carnegie Institution of Washington. The terms 

 " dynamic height " and " dynamic meter " were therein proposed. 



- Helmert : tjber die Reduction der auf der physischen Erdoberflache beobachteten 

 Schweerebeschleunigungen auf ein gemeinsames Niveau, Zweite Mitteilung. Sitzungsbe- 

 richte der Akademie der Wissenschaften, Berlin, 1903, p. 650. 



