PATHS OF MOVING PARTICLES SPRUNG 75 



the expression for the vertical acceleration, The entire system 

 of vertical forces must be considered as a modified force of gravity 

 g, and therefore it must be introduced, instead of g alone, in the 

 differential equation dp = —agdhoi the barohypsometric formula 

 if it is desired to take the state of motion of the atmosphere into 

 account in the derivation of the hypsometric formula. According 

 to the equation for the gaseous condition the density a is dependent 

 on the pressure p and the absolute temperature T in the following 

 manner : 



p =oKT 



where K is the gas constant for atmospheric air. 



If the change with altitude in the composition of the air is left 

 out of account and the decrease of the temperature upwards, in 

 accordance with the usual custom, is assumed to be constant so 

 that T = T — eh then there results finally the following equation 



p T -eh\^ * R' df/ 



(Strictly speaking g is also a function of the height h and the 

 geographical latitude (p.) This equation is of great importance in 

 meteorology inasmuch as it gives us the means of determining the 

 horizontal distribution of pressure at any altitude h, in case this 

 distribution is known for any other altitude (for example, at the 

 mean level of the ocean where h = o), and provided sufficient 

 initial points are given for the estimation of the condition of the 

 atmosphere as to temperature. and motion. 



For the purpose of illustration and investigating briefly the mag- 

 nitude of the influence of the horizontal motion of the air on the 

 vertical distribution of pressure, it will be assumed that the tem- 



d% 

 perature everywhere = T , therefore £ = o; since also — =o, there- 

 fore by integration there results: 



T Q Kl P ° = (h - h \ ( g - 2 z/wcospsin - — f V 



For an atmosphere at rest we should have 



T Kl*> = (h -h )g (27) 



P 



