CANADIAN FISHERIES EXPEDITION, WUf-lo 



265 



be located, vide fig. 47. It is easy to find the number of solenoids in this case. If the 

 specific volume of the upper layer be vi, and that of the lower vo, there will then be 

 vi — Vo isosteral surfaces in the boundary surface. And if the pressure at the lowest 

 point of the boundary surface be pi, that at its uppermost point po, then these isos- 

 terical surfaces will be intersected by pi — po isobaric surfaces. The number of solenoids 

 A will thus he A = (pi — po) (vi — vo) where pi — po indicates the slope of the isosteric 

 surfaces, and v\ — vo the stability of the water layers. The number of solenoids is the 

 product of these two factors. 



In order to ascertain the effect of the solenoids upon the movement of the water, 

 Bjerknes takes a closed curve composed of water particles in the sea, and calculates the 

 product of the curve's length and the mean velocity of the water along its r^ov.vse. This 

 product is called the circulation of the curve. Where the velocity oi the water is not 

 uniform at all parts of the curve, the circulation may be most easily urrivcd at by 

 integrating the tangential velocity of the water along the curve for the whole length of 

 the same. 



-j"' 



ds. 



(4) 



This integration may best be represented graphically by setting out the length of the 

 curve, reckoned from any point, in a rectangular co-ordinate system, as abscissa, with 

 the tangential velocity of the water as ordinates, and then, by means of a planimeter, 

 measuring the extent of the surface between the curve thus produced and the 

 abscissal axis. Fig. 48 shows the application of this method for calculating the cir- 

 culation of a circular curve situated in a current. The current is here taken as flowing 



Fig. 48. —Method of calculating the circulation in a closed circulation curve in a sea current. 



horizontally, at the velocities shown in the diagram on either side of the figure. The 

 curve is first divided up into a suitable number of parts. At each point of division, 

 the velocity of the water is marked oif, and its tangential component along the curve 

 constructed. In the diagram at the bottom of the figure, the length of the curve 

 reckoned from the point is set oif as abscissa. At the points 0, 1, 2 of the abscissa, 

 corresponding to the similarly designated point on the closed curve, the tangential 

 velocities are thereafter marked off as ordinates. The area of the diagram is then 

 measured with the planimeter, the part below the abscissa being of course taken as 

 negative, and subtracted, accordingly ; this gives the circulation of the closed curve. 



6553— 4e 



