a new science, which
may be extended indefinitely, and applied to the various departments of
self-government and State control. This new science of polemical
mathematics is in itself an extension of the _principle of continuity_,
for the discovery of which Poncelet is so justly renowned. We can prove
by geometry that the properties of one figure may be derived from those
of another which corresponds to it; and the new science teaches us that
if we can represent, by projection or otherwise, a society of particles
or individuals on a plane surface, the properties of the State so
represented are analogous to the properties of the curve with which it
corresponds. It is only possible for me to touch upon the elements of
the science in these lectures, but I hope to arouse an interest in these
somewhat unusual complications and curious problems, that you may
hereafter make further discoveries in this unexplored region of
knowledge, and that the world may reap the benefit of your labours and
abstruse studies. I have already, in my previous lecture, touched upon
the social properties of the parabola, and examined the constitution of
erratic curves and eccentric nations. It is my intention to-day to speak
of similar problems which arise with reference to elliptical States.

But, first, let me answer an objection which may have occurred to your
minds. Am I wrong in my calculations in attributing too much to the
power and usefulness of forms of government? Does the well-being and
happiness of a nation depend on the government, or upon the individuals
who compose the nation? Most assuredly, I assert, they rest upon the
former. Men love their country when the good of every particular man is
comprehended in the public prosperity; they undertake hazard and labour
for the government when it is justly administered. When the welfare of
every citizen is the care of the ruling power, men do not spare their
persons or their purses for the sake of their country and the support of
their sovereign. But where selfish aims are manifest in Court or
Parliament, the people care not for State officials who are indifferent
to their country's weal; they become selfish too; Liberty hides her
head, and shakes off the dust of her feet ere she leaves that doomed
land, and the stability, welfare, and prosperity of that country cease.

I might refer you to many a stained page of national history in order to
prove this. Compare the closing chapters of the lif