266 



DEPARTMENT OF THE NAVAL SERTICE 



If we divide the circulation thus arrived at by the length of the curve, we obtain 

 the mean tangential velocity along the closed curve. By marking this off on the dia- 

 gram, we obtain in the horizontal line there dividing the same into two parts, so that 

 the area above the line is equal to that below. 



This mean tangential velocity may now be again applied to the original closed 

 curve. Circle No. 2 in fig. A8 shows what is then arrived at, viz., the rotary movement 

 of the water. 



The circulation of closed curves in the sea thus affords a measurement of the rota- 

 tion of the water. Tlie translatory movement in the water is not discernible in the 

 circulation. A closed curve in a current, where all the particles have the same velocity 

 will always have a circulation = 0. By calculating the circulation, we thus obtain the 

 pure rotary movement of the water, vide fig. 48. 



Fig. 49. — Relation between solenoidti 

 ;uid circulation. 



It now only remains to find the relation between the circulation C, and the number 

 of solenoids A. To arrive at this, we lay out a closed curve in the section, fig. 46 

 (vide fig. 49), and calculate the circulation in the manner shown in fig. 48. This 

 gives a certain value, C. This value is, however, not invariable, but is continually 

 augmented by the rotary tendency of the solenoids. According to Bjerknes, the increase 

 of circulation per second is equal to the number of solenoids within the closed curve. 

 After the lapse of t seconds, therefore, the circulation of the curve will be 



C = Co + At 



By derivation we then obtain, 



d C 



dt 



A 



(5) 



indicating that the increment of circulation per second is equal to the number of 

 solenoids. By means of Bjerknes formula for the relation between distribution of 

 density in the sea and movement of the water, we can thus in the easiest possible 

 manner calculate the latter from the former. 



Obviously, the circulation is affected, not only by the distribution of density, but 

 also to a very high degree by the earth's rotation. Each latitude circle of the globe 

 has a considerable circulation owing to the earth's rotation. By a simple calculation, 

 this will be found to be C = 2oj*S' where to is the angular velocity of the earth, and 8 

 the area of the latitude circle. Bjerknes has shown, however, that this formula applies 

 equally to any closed curve on the globe, if we take 8 as indicating the area given by 



