1916] on Illusions of the Upper Air 617 



pressure, layer lies on lajer like a light iliquid on a heavy one — 

 temperatures are uniform, or very nearly so, in the vertical direction, 

 and therefore isotherms are also isobars, and winds are proportional 

 everywhere to pressure -differences, that is, to temperature-differences. 

 The rotation of the earth secures that air always moves along the 

 lines of pressure, keeping high pressure or low temperature on the 

 right. So the general idea is simple, but whether the streams of 

 air are long straight currents or local whirls we do not yet know. 



Numerical Calculations. 



Speculations of a qualitative character are apt to lead the 

 speculator into serious error ; the real test of any physical theory 

 is its quantitative application. 



It will be of great advantage to the further development of our 

 ideas if we can trust implicitly to the hypothesis of pressure balanced 

 by motion (let us call it the principle of strophic balance) as the 

 foundation of the structure of the atmosphere, and that hypothesis 

 will be confirmed in the orthodox scientific manner if the quantitative 

 conclusions to be drawn from it are verified by observation. I pro- 

 pose to ask your attention to some applications which can be tested 

 numerically. 



From this point of view the theory of strophic balance has the 

 great advantage of giving a definite relation between wind velocity, 

 pressure and temperature, and therefore brings the relations between 

 all these quantities within the region of arithmetical computation. 



Let us consider some of these relations. We require a number 

 of symbols for the meteorological quantities. 



p represents the atmospheric pressure. 

 $ „ the atmospheric temperature. 



p „ the atmospheric density. 



I „ horizontal distance. 



h „ vertical height. 



s i=^—E\ ,, the horizontal pressure gradient. 



q l=—-\ „ the horizontal temperature gradient. 



^. (11/ 



V „ the velocity of the wind. 



R = ]J I {pO) „ the constant of the gas equation. 



Certain geodesic quantities also come in, viz : — 

 E the radius of the earth. 

 g the acceleration of gravity. 



