﻿Effects of Diurnal Rotation on tlie Upper Atmosphere. G65 



Let N be the molecular density at the pole at height r . 

 If co is the earth's angular velocity the density at a point of 

 latitude X will then be N exp. hmr^co 2 sin 2 \ (Ji being in- 

 versely proportional to the absolute temperature of the 

 isothermal region). Since the mass velocity of the air is 

 r co sinX eastwards, the molecule we have considered above 

 has, as components of molecular velocity, 



V sin O cos cp , Y sin O sin <f> — r &) sin X , Y cos O , 



southwards, eastwards, and upwards. 



The number of molecules which have position and velocity 

 in the element 



r 2 sin \ o dr o d\ dl . V 2 sin o dY o d0 Q d^> o 



is 



N I — I exp — hm[Y 2 — 2Y sin O sin <j> r co sin X ) 



X r 2 sm\ dr dk dl Y 2 sin o dY o d0 o dcp Q . 



These molecules will all pass into the corresponding region 

 at r, X, I with the corresponding velocity V in direction 6 y cp ; 

 so that they will be in the element 



t 2 sin XdrdXdl Y 2 sin 0dYd0dcj>. 



Thus the number in this element is 



N / — J exp - lvm{Y^ 2 — 2Y r sin O . sin X sin <£ ) 



x r 2 sin XdrdXdlY 2 sin 0dYdOdcf> 

 = K e- 2hwffa2 (k ~ I) (^J exp - km (V 2 - 2Yr sin . sin X sin cb) 



X r 2 sm\drd\dlT 2 sm 0dYd0dcf>. 



Put 



AT -2hm 3 cfi(L- 1 :) __ 



N 



the polar density proper to the height r on the ordinary 

 kinetic theory. The distribution of velocities in unit 

 volume at r then is 



( -~ Jexp-/<m(Y 2 -2Y sin (9 sin . rco sin X)V 2 dY sin OdddQ. (A) 



If we suppose this expression true for all values of Y,0.<£, it 

 at once follows by integration that the density isN6> Wiw8sin5J \ 

 the mass velocity is rco sin X eastwards, and ihe temperature 



is ^.p (U being here the gas constant); and this is true 



for all regions above the adiabaticno matter what the height. 



