VERTICAL MOTION IN FREE SPACE COMPLETE KINEMATIC DIAGNOSIS. 1 49 



mate height of 75 meters above the ground. If we multiply by 0.01 we get a sheet 

 of an approximate thickness of 7.5 meters; the tubes will have a transport of 

 5000 tons of air per second at the wall C , and the areas will represent a vertical 

 transport of 1000 tons of air per second through the surface which has the approxi- 

 mate height of 7.5 meters above the ground. Of course it will be legitimate to go 

 up to so great heights as 75 or 750 meters only on condition that the original chart, 

 fig. 102, represents the average horizontal motion between the ground and these 

 heights. 



A change in the interpretation of the charts, which will be useful for qualitative 

 purposes, can be obtained in this manner: we multiply the unit pressure which 



10" 

 defines the thickness of the sheet by - . We shall then obtain a sheet the thickness 



75o 



of which will be approximately 1, 10, 100, 1000, . . . meters, according 

 to the value given to n. In order to get the mass-transport in this sheet, we must 

 multiply the field of T l by the same number. But instead of that we can multiply 

 only by 10" on condition of interpreting T, as volume-transport instead of mass- 

 transport. For 750 is the approximate volume in cubic meters of a ton of air 

 in the lower strata of the atmosphere. In other words, for qualitative purposes 

 it will be permissible to give an interpretation like the following of the chart of 

 fig. 105. It represents a sheet of a thickness of 1000 meters. The tubes have a 

 horizontal transport of 500,000,000 cubic meters of air per second at the wall C, 

 and the areas represent a vertical transport of 100,000,000 cubic meters of air 

 through the surface of a height of 1000 meters. When we choose the thickness of 

 100 or 10 meters of the sheet, we get the proportional reduction of the numbers 

 representing the volume-transport. 



From the chart of fig. 105 we can see without difficulty how the tubes of flow 

 go up and down. Let us return to the original interpretation. The areas of 100,000 

 tons of vertical transport can then be conceived as the sections of the upper limiting 

 surface of the sheet with tubes of this transport. For each element of the curve C 

 five such tubes rest upon each other, giving the total horizontal transport of 500,000 

 tons. Each area shows one of these tubes coming up or going down through the 

 upper limiting surface of the sheet. (Compare the schematic examples of figs. 

 43 c and 45 c) 



(B) Topographic method. In order to follow not only qualitatively, but quanti- 

 tatively, the course of the tubes up and down, we can pass to the topographic method. 

 We then retain the curve C , its division into elements fulfilling the condition v'dn' = 5 

 and the corresponding division of the chart into bands of flow, fig. 103. Introducing 

 the value c' = 5 in formula (c) section 187, we get 



P' vdn 

 By use of the divided sheet for reciprocal length-measurements (fig. 81) we draw the 

 field . The curves representing this field will have the same course as those repre- 



