h of the
satellite at any instant.)

Now if we consider all the possible elliptic orbits of a satellite about
its planet which have the same amount of "rotational momentum," we find
that the major axis of the ellipse described will be different according
to the amount of flattening (or the eccentricity) of the ellipse
described. A figure titled "A 'family' of elliptic orbits with constant
rotational momentum" (Fig. 1) illustrates for a given planet and
satellite all such orbits with constant rotational momentum, and with
all the major axes in the same direction. It will be observed that there
is a continuous transformation from one orbit to the next, and that the
whole forms a consecutive group, called by mathematicians "a family"
of orbits. In this case the rotational momentum is constant and the
position of any orbit in the family is determined by the length of the
major axis of the ellipse; the classification is according to the major
axis, but it might have been made according to anything else which would
cause the orbit to be exactly determinate.

I shall come later to the classification of all possible forms of ideal
liquid stars, which have the same amount of rotational momentum, and the
classification will then be made according to their densities, but the
idea of orderly arrangement in a "family" is just the same.

We thus arrive at the conception of a definite type of motion, with
a constant amount of rotational momentum, and a classification of all
members of the family, formed by all possible motions of that type,
according to the value of some measurable quantity (this will hereafter
be density) which determines the motion exactly. In the particular case
of the elliptic motion used for illustration the motion was stable,
but other cases of motion might be adduced in which the motion would
be unstable, and it would be found that classification in a family and
specification by some measurable quantity would be equally applicable.

A complex mechanical system may be capable of motion in several distinct
modes or types, and the motions corresponding to each such type may
be arranged as before in families. For the sake of simplicity I will
suppose that only two types are possible, so that there will only be two
families; and the rotational momentum is to be constant. The two types
of motion will have certain features in common which we denote in a sort
of shorthand by the letter A. Similarly the two types may