310 



THE MECHANICS OF THE EARTH's ATMOSPHERE. 



When T=A (co) sin (wf+A), then £, b, c, are to be sought in expres- 

 sions of the following form : 



€=E (&)) sin (Hf-f A), 

 b = q) (gj) cos (?if+A), 

 c'=:?/- {oj) sm (wf + A), 



wherefore the last of equations {ha) becomes 



nS{E-A)-{- 

 whilst the first two give 



1 ) rf(^ sin Cfj] 



sin oa 



doo 



+ ^ 



f 1=0, 



(pz 



dE p2 cos oj 



RTq doo sin cd 



V-: 



/i/i!»' 1 — 4 COS^ 00 



dE ^ ^ E 



jyrr J — 2COSOJ+^ 



MTo doo sin 00 



nS 



1—4 cos^ 00 



These latter values substituted in the preceding equation lead to a 

 relation between U and A only, or between e and t. It will be con- 

 venient for the further computation to introduce an auxiliarv function, 



nS 

 ^{oo)=j^(pM sin {(^) 



(1 — 4 COS^ OO) 4>00:= 



1 ^(^sin^Gjl 



sin 00 



doo 





Ez=i-^~T, — f 4> io^j) sin 00 (4 sin^ oo—d>) doo 

 sin^ 00-^ 



2 ^ 1 I d4> ,2 cos &? E \ ,^ 



u^ ' ^moo\ doo sin ck; sin a? > 



(11.) 



then 



00 sin Ce? 



If we assume <I> to have the following form : 



$ (gl))=cos cj(fl, sin &9-|-ff3sin^ oj-f assin^cj-f- . . . ) 

 ^ ((i9)=6] sin (i9-|-/>3sin^cj4-for, sin^ fy+ . . . 



, , 4ai— 3^3 - 4^3— Stts 



/>i=o„ lh= =^ — -, h= ^ , . . • 



Let the temperature amplitude diminish from the equator to the pole 

 according to the cosine of the latitude or 



and for brevity put 



A {oo) = C sin {&)) 



k=n^ 



RL\ 



