VERTICAL MOTION IN FREE SPACE COMPLETE KINEMATIC DIAGNOSIS. 145 



flow in virtue of the solenoidal condition. We thus have a method of drawing charts 

 of surfaces of flow in the atmosphere, giving the topography of these surfaces in 

 reference to the field of pressure. 



(C) Vertical component of specific momentum. When we make the change of 

 variables in the solenoidal condition in its differential form we shall come to the 

 equation 



m sV > a- 



(f) ^sp = ~ dlv * v 



or, solving with respect to the increase dV. of vertical specific momentum, we get 



(g) dV,= -(div,v) {-dp) 



By use of this equation we can find the increase d V z of vertical specific momentum 

 in a sheet the thickness of which is defined by the decrease of pressure dp. 



The practical work will begin by drawing a chart for the case in which the sheet 

 is defined by unit decrease of pressure, dp=i. The increase of vertical specific 

 momentum in this sheet will be 



(A) dV IlS = -div 2 v 



That is, it will be found if we draw the field of divergence of the given field of 

 horizontal velocity v, and then change the sign. 



From a sheet defined by unit decrease of pressure we can pass to one for any 

 decrease of pressure by multiplication by that pressure dp which defines the thick- 

 ness of the sheet. If dp is constant, the result will simply be a change of the 

 interval between the curves which represent dV s , z . If dp is variable from place 

 to place, it must be represented by a chart, which will then represent the topography 

 of the upper limiting surface of the sheet relatively to the lower one, topography 

 being expressed by decreases of pressure instead of by increases of height. By graph- 

 ical multiplication of the chart of dp hy that of dV ilZ we shall then arrive at the 

 chart of d V z , which represents the increase of vertical specific momentum in a sheet 

 of any variable thickness. 



188. Example. Cyclonic Center, United States of America, November 28, 

 1905. As the two sets of parallel methods which we have developed in the two 

 preceding sections lead to precisely the same formal constructions, it will be suffi- 

 cient to exemplify one of these sets. We shall take that of section 187, as we can 

 then apply directly the chart of observed horizontal velocity without changing it 

 first into a chart of specific momentum. 



In all cases we have to start with the chart of fig. 102, which represents the 

 observed horizontal velocity at 8 a. m., 75th meridian time. The fine lines are 

 curves for equal wind-velocity, expressed in meters per second. The thick lines with 

 arrow-heads are the lines of flow, which are seen to run into a marked center of 

 convergence. For further data regarding the meteorological conditions at the epoch 

 of observation see plates XXXV and XXXVI. 



