754 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Sidereal diurnal term. 
_1 
n dt : g s ~~2PQ _ 
cTW dW ' 
/ -p o ’’ 2 | “ '* 2 
= — 2G sin g(-|F) and ^^=4pY2(jirG sin g 
dg 
Therefore 
di t 2 . 
n— -i-—=2G sm sr 
dN' 
P 2 -Q 2 2f,f 
(Tx 
4P0 1 PQ 
On substitution from (53) and (84) for r and (fa and simplification, we find that if 
G=i{(i >3 -^ ! ) 3 [(p s -2 2 ) !! -2y 2 2 J*-2(P*-e 2 )[(l >3 -Q 2 ) 3 -12F ! C 8 ]pV(l> 2 -2 2 ) J 
-4(P 2 -C 2 )(P‘+4P 2 C 2 +W5 4 } (95) 
Then 
Fast diurnal term. 
di r- _ ~ . . 
n-- — = -2Gh sm g sm % 
dt g & 
(96) 
di 
dt ’ g 2PQ 
3P 2 -f Q~ dW 3 dW 3 
2 de' dN' 
As the fast semi-diurnal is derived from the slow, so here also ; and if 
G s =i{c 1 (3P'+ev+2<?-(3P 3 -'?' ! )T 6 r+9(P 3 -C 2 )W-2P 2 (P !! -3<? a )¥ 2 ,i 
-P 3 (P 3 + 3C S ) 2 8 } (97) 
Then 
Fortnightly term. 
d/i t 2 ^ ~ . 
n—-p = — 2C3 9 vjto sm g. ? sm % 
dt g ■" 2 62 
di m t 2 _ 1 / dW 0 dW 0 \ 
dt~ g — 2PQ \ de 7 '~dJF) 
(98) 
If we take the term in W 0 which has 2h positive in the exponential, we have 
„2h 
dWp _ 3 c ~ r 
dN'—'' 3 2y/- i L 
dW, 
8P 2 q\f z - g 2 )W4- 4[(P 2 - o 3 ) 2 -2P 2 o 3 ] W. 
+ 24P 2 ^ 2 (P 2 -0 3 ) 3 pY 5 + 8P 4 0V] 
^r°=-f 2 -^[4P^y+16P 2 Q 2 (P 2 -0 2 )W+4[(P“~^)'-2P 2 (> 2 ]W 
+16P 2 g 2 (P 2 -Q 2 )yg 6 +4PY¥] 
