122 Mr. H. Jeffreys on Periodic 



It remains to determine L from the condition that 



~du ~dw _ <yv 



On collecting the terms with the same exponent in this 

 equation, we find that the terms involving e~ vz , e"**/ 1 , and 

 ze~ mz vanish. The coefficient of e~ mz sm (jrxjly^ remaining 

 gives 



bgair 2 {y — m) boay(mvl 2 — ir 2 ) 



{ cr y-k(v 2 -7r' 2 /l 2 )}{v 2 r 2 -7r- 2 ) ~ v 2 1 2 -tt 2 



OLqir 2 C JjCtTT I tt\ r. /1 _. 



-^Ky-^ C+ ^\ m -V = °- (1?) 



Up to this point the solution is exact, whatever be the 

 values of the quantities concerned. Our object being to 

 apply the results to the variation of atmospheric mass 

 distribution and pressure in the interior of the continents, 

 we proceed to consider the order of magnitude of the 

 quantities involved. 



For Asia I is about 6000 kilometres ; for Australia it would 

 be of the order of 2000 kilometres. 



Taking fc = 3 x 10 3 and 7 = 2tt/(1 year) = 1*99 x 10" 7 /1 sec, 

 we have 



^_ 0-816xlQ - 5 

 k ~ 1 cm. 



so that the annual variations depending on the e~ mz term 

 will extend upwards for several kilometres. Nevertheless, 

 7r/l may be taken as small in comparison with \Z{^jk). 



Again, it is stated that § of the insolation received by the 

 earth is absorbed in the atmosphere. Thus Ijv must be of 

 the order of the height of the atmosphere. Hence v and m 

 are of the same order, and both are large compared with 

 it II. Applying these approximations to the last equation, it 

 reduces to 



lybgwiv — m) by 2 l giro <y 2 cl ■ t _ p 

 (cy — kv 2 )v 2 lm vl 2 ir 2m 2 l mir 



Then the value of p' at the surface is given by 



— r>'£-*T'cosec-7- = — : — I b— — — — c 



p * I V 2 ITi 



iybgir{v — 7)\) by 2 girck _ y 2 d 

 (iy — kv 2 )v 2 hn"~'vlTr 2hy mir 

 _ gv+tkiyv 2 + y 2 (pnk y 2 l\ 



v 2 \ iy mir) " • \ ' 



