VERTICAL MOTION IN FREE SPACE COMPLETE KINEMATIC DIAGNOSIS. 1 55 



In order to perform this diagnosis, we must first know the field of pressure, i. e., 

 we must have charts giving the topography of the standard isobaric surfaces and 

 of the pressure at the ground. From the latter we derive a special chart of the 

 difference of pressure between the ground and the lowest isobaric surface in free air. 

 Then we must have a chart of velocity at the ground, and charts of the average 

 horizontal velocity within each of the standard isobaric sheets, as well as of this 

 average velocity in the incomplete sheet between the ground and the lowest standard 

 surface in free air. The kinematic diagnosis will be accomplished as soon as we have 

 found the complete representation of the vertical motion. We shall arrive at this 

 representation by the following operations (compare the example, section 204, below) : 



(1) From the chart of velocity in connection with that of pressure at the ground 

 we derive the chart of the forced vertical specific momentum at the ground. 



(2) From the chart of the average horizontal velocity in the incomplete sheet 

 between the ground and the lowest standard isobaric surface in free air we derive 

 free vertical specific momentum through this surface. The construction is first 

 performed for a unit sheet, and then the result is obtained for a sheet of irregular 

 thickness by graphical multiplication by the decrease of pressure which defines the 

 sheet. 



(3) From the charts of average horizontal velocity in the different standard 

 isobaric sheets we derive the vertical specific momenta produced in each sheet. If 

 a sheet is partly incomplete, the limiting surfaces cutting the ground, we use the 

 method (2) for the incomplete parts of the sheet. 



By successive graphical additions of the charts (1), (2), (3), . . .we get the 

 charts of the absolute vertical specific momenta in the different standard isobaric 

 surfaces. If it be desired it will be easy afterwards to change them into charts of 

 vertical velocity. 



It will be understood at once how a perfectly similar kinematic diagnosis can 

 be carried out based upon the division of the atmosphere into level instead of into 

 isobaric sheets. 



