where 12 is regarded as a function of r, v, y, or (as this may be expressed) where
fl=il(r, v, y).
If we neglect the disturbing forces, the planet moves in an ellipse; and taking
a to represent the semi-axis major, the mean motion will be n. The mean anomaly,
which I call g, will be a function of the form nt + c; but as c only enters through g,
it will be convenient to use the mean anomaly g (considered as implicitly involving
an arbitrary constant c) in the place of an element, and I write
а, the semi-axis major,
e, the eccentricity,
g, the mean anomaly,
б, the longitude of node,
(f), the inclination,
<D, the distance of pericentre from node.
f, the true anomaly,
z, the distance of planet from node,
x, the reduced distance from node.
We have then r and f given functions of t and the elements, viz. we may write
r = a elqr (e, g),
f= elta (e, g),
(read elqr. elliptic quotient radius, and elta. elliptic anomaly). These values
satisfy r = Moreover z, x, y, are the hypothenuse, base, and perpendicular
of a right-angled spherical triangle, the base angle whereof is cf>; the equations which
connect these quantities are therefore