36 Mr. E. Gold : Relation between Periodic Variations of 



on the rotating Earth, expressed in polar coordinates,, are, 

 neglecting terms o£ the second order in u, r, iv *, 



-7- + Zmy sin <f> 4- 2nv cos <p = = — 7 =^r , 



dt r r r sin <p 0\ 



-77 —Anu cos cd = ^-7 , 



dt ' r 09 



die . 7T Be 



dt r * 1 ^r J 



where the Earth's axis is the axis o£ reference, 



<£> is polar distance, 



A is E. longitude, 



u, Vj w are velocities in the direction of increasing X, c/>, r, 



p L e is the pressure variation, 



T l r „ temperature „ 



p 1 and T 1 are the pressure and temperature in the 



undisturbed state, 

 n is the angular velocity o£ the earth about its axis, 

 k is the constant in the gas equation p = kpT. 



With these equations must be taken the equation of con- 

 tinuity 



dt + Vr"*T 1 ""T 1 -drr + lr 



_l 1 r 3 / • jL\ , 9 W 1 v X ^ T i n 



+ — ? — j <7 i'sm0)+-^7 — - m ^TT~ = U. 



The observed value of e for the semi-diurnal wave may be 

 represented with fair accuracy by 



e = E sin 3 c/> sin (2nt + 2\ +c^~^) = E sin 3 c/> sin x, say. 



Here z is height above M.S.L. and the term ce~^: r is 

 introduced to represent the diminution f of phase with height. 



* It is fair to neglect pure viscosity terms of the form - \r 2 u because 

 (see infra) the greatest of these would be - c 2 fi 2 u, which bears to the 

 terms retained the ratio lO -7 -" nearly. The" value of Jc/p found by 

 experiment is 0*1 3 for air at 0° C. 



