826 
MR, G. H. DARWIN ON THE SECULAR CHANGES IN 
> . (263) 
All the other expressions in (251) remain as they were. 
Then the terms in F, A, G, D in (250) are the only ones which have to be recomputed. 
And all the other arithmetical work of the last section will be applicable here. Also 
all the materials for calculating these new terms are ready to hand. 
The results of the computation are embodied in the following tables. 
Table IX. 
1- 
•96 
•92 
•88 
•84 
•80 
"76 
log r + io= 
9-54901 
9-57529 
9-59914 
9-61994 
9-63663 
9-64791 
9-65092 
log A = 
•52876 
•55517 
•58023 
•60484 
•63005 
•65708 
•68739 
log (aD—bG) + 10= 
9-08381 
9-22356 
9-34416 
9-45433 
9-55931 
9-66259 
9-76574 
r=*m 
bG—aD= —m 
4X(1—\)' 
1 — 2 A, 
4A(1 
■ X) 
l-2\ 
.9 
Table X. 
1- 
•96 
•92 
•88 
•84 
•80 
•76 
r(/iT 1 + a)/t-n(/f 2 — K]) — 
--00133 
- -00328 
-•00800 
-•01853 
-•03818 
-•06513 
-•08961 
r(/c 2 +«)/^G 2 — k i ) = 
•39185 
-39657 
•39712 
•38973 
•37003 
•33856 
•30260 
A(k' 1 + a)/Z,-w(ff 3 — +) — 
-•00199 
--00485 
-•01168 
-•02688 
-•05553 
-•09627 
-•13761 
A(k 2 4~ A/t-wGa—^i) = 
•58529 
•58541 
•57994 
•56554 
•53826 
•50044 
•46468 
i (bG— aD)//«?(*: 2 — /Cj)= 
—-00825 
-•01622 
-•03034 
-•05388 
-•08850 
— T3092 
-•17504 
1 
Then combiniug these terms with those given in Table III., according to the 
formulas (250), (with T, &c., in place of y, &c.), we have the following equidistant 
values. 
Table XI. 
f 1- 
•96 
•92 
•88 
•84 
•80 
*76 
log tan 4J/4|;= —'3477 
-•2925 
-•1587 
+ -1125 
+ - 5036 
+ 
"+T 
00 
00 
+ -7195 
logtan^I/4^= +'6168 
+ •6661 
+ •7796 
+ 1-0107 
+ 1-3406 
+ 1-5458 
+ 1-4103 
By interpolation it appears that d3/d£ vanishes when £= - 8966. This value of £ 
corresponds with a period of 8 hrs. 54 m. for the earth’s rotation, and 5‘89 m. s. days 
for the moon’s revolution. 
