718 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
C, A= the greatest and least moments of inertia of the earth ; if we neglect the 
ellipticity they will be equal to \Mcft ; n— angular velocity of diurnal rotation; 
xp= longitude of autumnal equinox measured along the ecliptic from a fixed point in 
the ecliptic—the ecliptic being here a name for a plane fixed in space; i— obliquity 
of ecliptic; y the angle between a point fixed on the equator and the autumnal 
equinox ; p the radius vector of any point measured from the earth’s centre. 
For Diana, let— 
c= mean distance; £=(c/c 0 ) 4 ; fl = mean motion; e= eccentricity of orbit; 77 = 
ellipticity of orbit; longitude of perigee ; j— inclination of orbit to ecliptic; N— 
longitude of node; e= longitude of epoch; m— mass; v— ratio of earth’s mass to 
Diana’s or Mjrn ; l— true longitude measured from the node; 6= true longitude 
measured from the autumnal equinox; r=|/xm/c 3 , so that t= 3/2 3 /2(1 -\-v), also 
r=r 0 /^ 6 ; r the radius vector measured from earth’s centre. 
Also \=S2/n; 111 the ratio of the earth’s moment of momentum of rotation to that of 
the orbital motion of Diana (or the moon) and the earth round their common centre of 
inertia. 
For the moon let all the same symbols apply when accents are added to them. 
Where occasion arises to refer merely to the elements of a satellite in general, the 
unaccented symbols will be employed. 
Let It be the disturbing function as ordinarily defined in works on physical 
astronomy. 
Other symbols will be defined as the necessity for them arises. 
Then the following are the well-known equations for the variation of the mean 
distance, eccentricity, inclination, and longitude of the node. 
clc 
dt 
2/2c 2 dR 
/x(M+m) de 
(1) 
de 
flc 
1 — e 2 dR y/l— e ; 
/dR 
dt 
e de e 
[de 
dR 
dor 
( 2 ) 
dj 
‘ dt 
flc 
) \/l — e 2 _sin j dN 
dR , . ./dR , dR 
+ tan D Te + ii 
■ (3) 
sm J 
dN 
flc 
dR 
dt ix{M+m) yl-e 2 dj 
• (4) 
The last of these equations will only be required in Part III. 
Now let Pc= \Y r C(d/+ ra)/Mm ; then if we substitute this value for P in each of the 
equations (1-4), it is clear that the right hand side of each will involve a factor 
flcC/pMm. 
