328 
MR. LUBBOCK’S RESEARCHES 
Let .r, y, z denote the rectangular co-ordinates 
r distance from the sun 
r' distance from the sun projected 
upon the plane x, y 
*X longitude reckoned upon the plane 
of its orbit 
X' longitude reckoned upon the plane 
xy 
s tangent of the latitude 
v .... a variable, which in the elliptic the- 
ory is the eccentric anomaly 
in .... the mass 
a semiaxis major 
e eccentricity 
7S longitude of the perihelion 
g longitude of the epoch 
v longitude of the ascending node 
i inclination of the orbit to the plane 
xy 
a .... a* constant quantity which accompa- 
nies v 
M ... . the mass of the sun. 
^of the planet 
m. 
M + m — p, — n. 
x = r cos X', y = r'sin X', z = r s, and in the elliptic motion r' 2 d X' = h d t. 
R = m l 
— m, 
{ 
{ 
xx i + yy\ + zz i l \ 
{ x ? +y? + s ? }* { (* — x if + (y - j//) 8 + (* - z,) 2 }* J 
r'{cos (A' — A',) -f ss,} 1 __ 
r * ( 1 + s i*)r |r' 2 (l +s 2 )— 2rV,{cos(A' — a',) + ss,} 
' Laplace uses the letter v to denote longitude, u the eccentric anomaly, and <p the inclination of 
the orhit to a fixed plane ; but as v is very frequently used to signify velocity, and <p geogra- 
phical latitude, and as the letters of the Greek alphabet arc generally used for angles, I have taken the 
letters A, u, and i for these quantities. 
