FOR HIGH LEVELS IN THE EARTh's ATMOSPHERE. 77 



particle, when it arrives at b, from the velocity r'o it had at a and the difference in 

 gravity-potential, ¥„ — F^, by the aid of the well known formula 



r2 — v'^ 



— o— = F - F. 



2 a i 



mile 

 Thus if it be assumed that the velocity Vq at the point a be 10 ^ — _ and that 



Va — Vf, = 1 000 r 2 then the velocity v^ of the particle on arriving at b is obtained 



by solving the equation 



vl = 10^ + 2 X 1 000 = 2 100 



mile 



■y, = l/2 100 = 45.8 



hour 



This method of using the map for calculating the acceleration of an air-particle 

 from the length of its path and the difference in gravity-potential, and for calculating 

 the velocity of the particle from the difference in gravity-potential and the initial 

 velocity, may also be used when we consider relative movements, since the component 

 of acceleration due to the Earth's rotation always acts in a direction at right angles to 

 the path of the particle and thus has no effect upon the acceleration along this path. 



The calculations have been carried out for a particle which always remains in the 

 same isobaric surface. They are, however, equally applicable to particles moving 

 within a slight distance from the given isobaric surface, because these surfaces, which 

 lie very close to one another, have almost mutually parallel directions, and thus inter- 

 sect very nearly the same number of level surfaces of gravity. 



Comparison of Vp- andpy-maps. — It seems to me that from a dynamic point of 

 view the Fj,-maps possess certain advantages over the j9,-maps. These advantages 

 arise, partly, from the fact that the acceleration and the square of the velocity of a 

 particle may be read directly from the 1^,-maps without taking into consideration the 

 density of the air, whereas the pressure-gradients obtained from the ^jj-maps must 

 first be divided by the density of the air in order to obtain these quantities. When 

 we limit ourselves to purely qualitative considerations these advantages appear yet 

 more striking ; for the accelerations are directly proportional to the number of lines 

 [between any two points] on the Vp charts and quite independent of altitude in the 

 atmosphere. On the other hand, if the ^^i^^^ps for two different levels show the same 

 number of lines [within the same distance], then the air-particles at the higher level 

 have the greater acceleration. It is thus seen that the I^-maps for different levels are 

 completely comparable with one another, while the pirmaps are not. 



