818 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
The following table exhibits some of the stages of the computation. The results are 
given just as they were found, but it is probable that the last place of decimals, and 
perhaps the last but one, are of no value. As however we really only require a solution 
in round numbers, this is of no importance. 
Table II. 
b — 
1- 
•96 
•92 
•88 
■84 
•80 
•76 
V*o= 
1-00000 
1-04467 
1-08931 
1-13392 
1-17852 
1-22308 
1-26763 
log e + 10= 
8 40016 
8-43812 
8"47446 
8-50932 
8-54284 
8-57507 
8-60614 
log t'/t + 10= 
8-61867 
8-51230 
8-40140 
8-28557 
8-16435 
8-03721 
7-90356 
log \ +10= 
8-70384 
8’73805 
8-77533 
8-81581 
8-85966 
8-90712 
8-95841 
t'/2\Jt= 
16"3546 
10-8418 
7-0889 
4-5647 
2-8895 
1-7947 
1-0914 
m=a= 
■90035 
•97976 
1-06603 
1-16014 
1-26320 
1-37648 
1-50172 
log 7 + 10 = 
9-67591 
9-71452 
9-75343 
9-79287 
9-83307 
9-87430 
9-91693 
log 6 + 10= 
9 65551 
9-65745 
9-65824 
9-65788 
9-65631 
9-65341 
9-64900 
log (gb — ad) + 10 = 
8-83030 
8"86665 
8-91307 
8-96946 
9-03549 
9-11080 
9-19510 
CL — 
36-696 
23-186 
12-583 
4-144 
- 2-747 
- 8-605 
-13 873 
a'= 
- 7-4782 
- 8-6811 
-10-0883 
-11-7426 
-13-6966 
-16-0163 
-18-7899 
P' = 
— 6'4455 
- 6-9122 
- 7-4220 
— 7"9805 
- 8-5940 
- 9-2699 
-10 0184 
b' = 
- 6-4038 
- 6-8796 
- 7-3968 
- 7-9612 
— 8"5794 
- 9-2590 
-10-0104 
log —(Aj + a) + 10 = 
8-74306 
8-95453 
9-16587 
9-37077 
9-55751 
9-71146 
9-82404 
log (k 3 + <*) 
1-21135 
1-03659 
•86190 
■69374 
•54396 
•42731 
•35255 
lo g( K 2— K l) 
1-21283 
1-04017 
•87056 
•71393 
•58660 
•50372 
•46520 
The further stage in the computation, when these values are used to compute the 
several terms of the expressions to be integrated, are given in the following table. 
Table III. 
1- 
•96 
•92 
■88 
•84 
•80 
•76 
— (a —P')(k 1 + x)/lcn(K 2 — IC 1 )' 2 = 
•00995 
•02395 
•05424 
•10413 
•13350 
•03053 
- -26438 
a'b^ + *)/M> 2 + ^)(^2 — 
■00011 
•00064 
•00376 
•02041 
•08937 
"27505 
•57228 
&'h/lcn(>c 2 —K 1 f= 
-■03117 
-•07671 
—-18670 
-•42945 
-•86628 
-1-42975 
-1-93250 
b'a(/r 1 + op/lcn^tc^ + «)( k 2—= 
•00008 
•00049 
•00294 
•01606 
•07072 
•21887 
•45786 
b'a IJm(ic 2 — «r 1 ) 2 = 
--02403 
—-05970 
— T4593 
-•33778 
— "68546 
-1-13770 
-1-54610 
°/( + a)/kn( — — 
-•00179 
- -00452 
—-01141 
-•02759 
- -06001 
- -10969 
- -16534 
7( «r 2 + a.)lkn(K 2 — K 1 ) = 
•52483 
•54645 
•56651 
•58035 
■58167 
•57020 
•55832 
(- ~ )/ 'h)'l(lCo — 
-•00170 
— -00397 
- -00916 
- -02022 
- -03995 
- -06596 
- -08922 
"L a)/&ra(/c 2 — ' f i) — 
•50075 
•47916 
•45501 
•42530 
•38719 
•34288 
•30127 
(bg — ad )/Jcn( k 2 —^)= 
•00460 
•00713 
•01124 
•01764 
•02649 
•03675 
•04704 
