MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
Table XIY. 
£ 
1- 
•96 
•92 
•88 
cl log tan JjJ /d£= 
cl log tan \\/d£=- 
+ -5547 
+ 1-0746 
+ •3915 
+ •8682 
+ •2088 
+ •6391 
+ •1925 
+ •3093 
Then integrating from £= 1 to '88 we have 
log e tan -|J=lo g e tan ^J 0 — - 0382 
log,, tan ^1 =log e tan ^I 0 — ‘0886 
Then putting I 0 =13° 13' and J LI =5° 44', from the previous integration, we have 
J — 5° 30', 1 = 12° 6'. 
These values of J and I give J =10° 49', ^=2° 40'. 
The physical meaning of the results of the whole integration is embodied in the 
followdng’ table. 
o 
Table XV.—Results of integration in the case of large viscosity. 
Day in m. s. 
Lours and 
minutes. 
Moon’s 
sidereal period 
in m. s. days. 
Inclination of 
earth’s 
proper plane 
to ecliptic. 
Inclination of 
equator 
to earth’s 
proper plane. 
Inclination of 
moon’s 
proper plane 
to ecliptic. 
Inclination of 
lunar orbit 
to moon’s 
proper plane. 
b. 
m. 
Days. 
O 
O 
O 1 
O 
i 
9 
55 
8-17 
17 
0 
0 
22 
0 57 
6 
0 
8 
45 
5'57 
15 
34 
1 
15 
3 37 
6 
9 
7 
49 
3-59 
13 
13 
2 
33 
8 46 
5 
44 
7 
15 
2-45 
12 
6 
2 
40 
10 49 
5 
30 
If we compare these results with those in Table VIII. for the case of small viscosity, 
we see that the inclinations of the two proper planes to one another and to the ecliptic 
are almost the same as before, but there is here this important distinction, viz. : that 
the inclinations of the two moving systems to their respective proper planes is less 
(compare 5° 30' with 6° 18', and 2° 40' with 3° 3'). 
And besides, if we had carried the integration, in the case of small viscosity, further 
back we should have found the inclination of the lunar orbit increasing. 
It will now be shown that, in the present case of large viscosity, the inclinations of 
