DR S. CHAPMAN ON THE DIURNAL VARIATIONS OF THE 



Considering the diurnal variation first, the terras (a) are found, from the formulas 

 at the foot of p. 296, to be 



)<W [W-13Q, 1 ) cos 2 S sin (X'- 1 )-(12Q4 1 + 16Q a ') sin 2 S sin (x'-a,) 



-{(4Q 4 '+3Q 3 3 ) sin (2X'-a 1 )-(48Q 1 -6Q 2 ) sin (-a,)} sin S cos S 

 -Q< 3 cos" Jain (3X'-a,) + 3 (Q^-Qa 1 ) cos 2 i sin (-X'-a,)], 



and the terms (l>) are 



MCMHQ/- W) sil1 (2X'-a,) + ( W-Q,) si" (-i)l cos i 



-(*W+ Q. 1 ) sin <* sin (x'-0], 



sin (2X'- ai ) + Q 2 sin (-"')} cos ^-Qs 1 sin <S sin (x'-a,)], 



'-aOl cos J 

 Q 2 2 ) sin S sin (2X'-a 1 )], 



2 1 ) {sin (X ; -a,) + sin (-X'-a,)} cos S 



2) sin 5 sin (-a,)], 



i^i[{-W sin (X'-a^-iQ, 1 sin (-X'-a,)} cos ^-2Q 2 sin S sin (-a,)]. 



The sum of the coefficients of any particular term Q/ sin (o-X'-a^ in the above, 

 must be equated with p n 'n (n + 1 ) Q." sin (o-X' - a,). The values of p.' thus calculated 

 are given in Table I. It should be remarked that Q^ 1 has been replaced by 

 -Qn/n(n + l), and the coefficient of Q, 1 sin (X' + a,) will be denoted by q n \ 



20. The second order terms arising from the semi-diurnal atmospheric oscillation 

 are similarly written down as follows : 



() P.M[{(W-4Q/) cos 2 <HQ 5 2 + 4Q 3 2 ) sin 2 S} sin (2X'-a 3 ) 



+ {(- W-Q/) sin (3X / -a 2 ) + (Y-Q5 1 -6Q 3 1 ) sin (x'-a a )} sin S cos S 

 - iW cos 3 S sin (4X'-a i! ) + (l2Q 3 -A r QQ 5 -^Q 1 u ) cos 2 S sin (-0,)], 



(l>) p a 'di[{-W sin (2X'-a 8 ) + (VQ 3 u -SQi u ) sin (-a s )} cos S 



-(- 1 5 <i Q 3 1 + IQi 1 ) sin S sin (X'-a,)], 

 in (2X'- 2 ) + (-m u -Q 3 ) sin (-a,)} cos 3 



-(Q B 1 + Q 8 1 ) sin S sin (x'-a a )], 

 sin (3X'-o a ) + (gQ 3 1 - VQ, 1 ) sin (x'-a,)} cos S 



i[{(-5Qo 3 +tQ 3 3 ) sin (3X'-a 2 ) + (lGQ 5 1 -25Q 3 1 ) sin (X'-a,)} cos S 



-(8Q B 3 + 10Q 3 a ) sin S sin (2X'-a 3 )], 



+P<*di [{~^Q 8 4 sin (4X'-a 2 ) + (8Q 5 2 -35Q 3 3 ) sin (2X'-a a )} cos S 



-(Q 5 3 +-m 3 )smr]. 



The values of p.* calculated from the above expressions are given in Table II. 





