78 CONSTRUCTION OF ISOBARIC CHARTS 



Significance of 'E^l^-maps. — The dynamic significance of the EP'-maps, Figs. 1 2-15, 

 results from a principle in hydrodynamics recently stated by Prof. V. Bjerknes,* and 

 I would first recall this principle. According to Lord Kelvin's definition, the circu- 

 lation of a closed curve made up of atmospheric particles, consists of the sum of the 

 tangential components of the velocity of every particle around the whole curve. If 

 the velocity of a particle of the curve be designated by u, and the tangential com- 

 ponent of this velocity along the curve by Ui, then the circulation "C" is expressed 

 by the integral 



where " 8s" is a longitudinal element of the curve and the integration is to be carried 

 out completely around the whole of the closed curve. This "circulation" is an 

 expression for the rotatory movement of the atmosphere, for wherever the velocity of 

 the air has a potential, there all closed curves have no "circulation "; and conversely, 

 the more intense is the rotatory movement of the air so much the greater is the " cir- 

 culation" of the closed curves. 



By means of the integral just cited, the "circulation" of a closed curve in the 

 atmosphere may be determined from simultaneous observations of the direction and 

 velocity of the wind at different points on the curve. Bjerknes has given a theorem 

 for calculating the increase or decrease of the " circulation " during a unit of time, by 

 using the observations of pressure, temperature and humidity at points along the 

 curve. If then we have the four elements — wind, pressure, temperature and rela- 

 tive humidity observed at any moment of time, for various points along a closed 

 curve in the atmosphere we may calculate the " circulation " of that curve not only 

 for the moment of observation, but also for a series of instants both preceding and fol- 

 lowing that moment. The theorem may be mathematically formulated as follows : 



dC 



= - j'vdp = A. (25) 



Here dC/dt is the increase of circulation C in a unit of time ; v is the specific volume of 

 a particle of air on the curve, and p is the pressure prevailing at this particle. The 

 integration is to be carried out around the whole closed curve and will give A = the 

 number of solenoids,! enclosed within the closed curve. The law may then be 

 stated as follows. 



*See V. Bjerknes. " The dynamic principle of circulatory movements in the atmosphere." — Monthly Weather Ke- 

 vie\D, Oct., 1900, p. 434. 



t A solenoid is a tnbalar figare in the atmosphere arising from the intersections of surfaces of equal pressure, or iso- 

 baric sorfaces, with surfaces of equal specific volume, or isosterio surfaces. The unit solenoid is found between two iso- 

 bario surfaces differing by the unit of pressure and two isosteric surfaces differing by the unit of specific volume. 



