enlightened sphere. In an ellipse there
is less likelihood of his straying away from the course which the
directrix points out, on account of the two-fold guidance which he
receives from the two foci.

The following curious problem may be noticed. If a parabola roll on
another parabola, their vertices coinciding, the focus of the first
traces out the directrix of the second.

Here we come to the consideration of the international relationship of
States. Two nations have the same form of government (in this example
this form is Republican); their policies coincide: we may conclude from
this proposition that the course which the government of one nation will
pursue, will be that which is prescribed by the laws of the other.

The subject of the contact of curves presents many interesting problems
with reference to Polemical Science, and may be extended indefinitely.
It is well known that there are different orders of contact, which are
designated as the _first_, _second_, or _third_ order. This last order
may be termed the 'marriage of curves,' cemented by the osculating
circle, or 'wedding-ring;' and when two nations have contact of the
third order, they have formed a very close alliance, and by calculation
we can obtain the _radius of curvature_, or size of the wedding-ring, by
means of which they may be united.

The theory and nature of contact constitute a branch of our newly
discovered science which we commend to the careful consideration of
those who have undertaken the difficult and perplexing study of
international law. Alas! too many States refuse this friendly contact,
and, consequently, _cut_ each other, instead of blending in sweet
accord. Their peace is at best an armed neutrality; and if they have
contact of only the _first_ or _second_ order, we can prove
mathematically that they are sure to intersect in some other point or
points; and divergence of policy and disturbed relations are the
results. Contact of the _third, or highest, order_ is the only safe
position for two allied, or contiguous, States.

With your permission I will add a few words to those I have already
uttered with regard to the directrix. As necessary as the directrix is
to the curve, so are the corresponding laws to the State. I will prove
this fact by a few examples. English people have laws, and know how to
obey them; therefore their numbers increase; they thrive and are
prosperous. A friendly critic of another nation has said that