so CONSTRUCTION OF ISOBARIC CHARTS 



By substituting these into (26) there results 



A = (EH^x - (E^?:D* (27) 



This formula holds true for any two points a and h on the Eo^.^-map and for the 

 corresponding closed curves in the atmosphere. For the points a and h shown on the 



\W 1 1 A 



E^^^j-map (Fig. 12) of page 71 we have (El5;°)„ = 40 200 j^^^^ and (E=?:«), = 40 100 



'12 '12 



^-Ai, so that by equation 27, A = 100 , 5. If now we move the points a and h 



hour^ •' ^ hour-" 



of this map at will along the curves 40 200 and 40 100 respectively, and imagine the 



closed curve consisting of the verticals a and h, and the connecting lines lying in the 



isobaric surfaces of p = 27.5 and yj = 25.0 as moving in a corresponding manner, then 



we see that during this movement the quantities (E|5;^)a and (E^,:^)^, always retain the 



values 40 200 and 40 100 just calculated for them. Therefore the closed curve, even 



during its movement, always encloses 100 solenoids. We therefore conclude that the 



tubular structure in the atmosphere, bounded by vertical walls through the curves 



40 200 and 40 100 and by the isobaric surfaces of p = 27.5 and p — 25.0, encloses 



exactly 100 unit solenoids whose courses must lie parallel to the curves 40 200 and 



40 100. By a series of analogous operations we are led to the conclusion that there 



are always 100 solenoids between each pair of adjacent curves on the E^5;^-map (Fig. 



12, page 71). 



According to Bjerknes' theory these solenoids tend to set up a rotational move- 

 ment in the atmosphere. The direction of this rotation is expressed by the rule that 

 the air tends to rise where Ej^i is large, and to sink where El';? is small. Thus the 

 movement resulting from the solenoid system of the chart of E,,;", page 71, Fig. 12, 

 is an ascending one in the vicinity of Pierre and Topeka, and a descending one in the 

 outer portions of the region shown on the map. 



Returning to the closed curve in the atmosphere indicated at ah in Fig. 12, we 

 know first of all that it embraces 100 solenoids. Therefore from the preceding theorem 

 we know that the increase of circulation along this closed curve is at the rate of 100 



"^^ ^ per hour, and that it is directed upward along the vertical a and downward 

 hour 



along the vertical h. If this increase in the circulation be divided by the length of the 

 line ah, which from measurement is seen to amount to 125 miles, then, according to the 



definition of circulation, we obtain a mean tangential acceleration of 0.8 j^^^^for the 



air-particles composing the curve. In other words, if we assume that the air was 

 originally at rest, and if we leave out of consideration the influences of friction and the 



