KINEMATIC PROGNOSIS. l6l 



Here we can first perform the integration with respect to p, denoting by v the 

 average value of v n along a vertical line of the cylindrical surface, and by p p' the 

 difference of pressure between bottom and top of the cylinder. Then 



jv n da =0.1 {p-p') jv n ds 



Finally we can by v denote the average value of v when we integrate with respect 

 to s, i. e., around the base of the cylinder. The circumference being s, we get 



/ 



v n da = o.i {p p') sv n 



Equation (6) thus takes the form 



i dp s = 



p-p'St <r a 



If the cylinder is circular, the ratio of its circumference to the area <r of its base 

 will be^ , D being the diameter of the base. As p' is the pressure in very great 



height, and thus very small, we can leave it out without essentially changing the 

 formula. Thus we get for a circular cylinder of sufficient height 



i?p g = 



- pft =0 *D V " 



In order to estimate the exactitude required in the observations of velocity if 

 it should be possible to forecast pressure at the ground by this formula, we solve 

 with respect to v 



\Sp D 

 V "~ p?to. 4 g 



In this formula we can express pressure in any unit. We shall then use m-bars. 

 Passing at the same time from second to hour as unit of time, calling m the change 

 of pressure in m-bars per hour, setting g = 9 . 8, and calling d the diameter of the cylin- 

 der expressed in kilometers, d = 0.001 D, we get 



v n = 0.00007 md 



For the change of pressure of 1 m-bar per hour, m = i,we shall then have 



d = 1000 km. v = 7 cm. per second. 



d = 100 km. v n = 7 mm. per second. 



d = 10 km. v= 0.7 mm. per second. 



Thus, even if we take areas of a diameter of 1000 km., the observations of the 

 wind-velocity would have to be correct to a centimeter over the whole area of a cylin- 

 der having this diameter and extending up to heights where pressure is imperceptible. 

 Of course observations of wind-velocity of this exactitude and completeness can not 

 be thought of in the present state of development of meteorological observations. 



Kinematic prognosis could therefore hitherto only give the displacements of 

 the masses of air as developed in sections 190 and 191. 



