But never pass my Little-go.

[1] We presume this is addressed to an imaginary brain wave.

[2] We observe here the dash of an indignant pen, and a substituted
for e. But now the rhyme is spoiled. Gentle Muse, thou art
sacrificed by the stern hand of Mathematical Truth!

[3] Query: Does the writer refer to the learned treatise on Finite
Differences by Professor Boole?

PAPER III.

LECTURE ON THE SOCIAL PROPERTIES OF A CONIC SECTION,
AND THE THEORY OF POLEMICAL MATHEMATICS.

Most Learned Professors and Students of this University,--From the
interest manifested in my first lecture, I conclude that my method of
investigation has not proved altogether unsatisfactory to you, and I
hope ere long to produce certain investigations which will probably
startle you, and revolutionize the current thought of the age. The
application of mathematics to the study of Social Science and Political
Government has curiously enough escaped the attention of those who ought
to be most conversant with these matters. I shall endeavour to prove in
the present lecture that the relations between individuals and the
Government are similar to those which mathematical knowledge would lead
us to postulate, and to explain on scientific principles the various
convulsions which sometimes agitate the social and political world.

Indeed, by this method we shall be able to prophesy the future of states
and nations, having given certain functions and peculiarities
appertaining to them, just as easily as we can foretell the exact day
and hour of an eclipse of the moon or sun. In order to do this, we must
first determine the _social properties of a conic section_.

For the benefit of the unlearned and ignorant, I will first state that a
cone is a solid figure described by the revolution of a right-angled
triangle about one of the sides containing the right angle, which
remains fixed. The fixed side is called the axis of the cone. Conic
sections are obtained by cutting the cone by planes. It may easily be
proved that if the angle between the cutting plane and the axis be equal
to the angle between the axis and the revolving side of the triangle
which generates the cone, the section described on the surface of the
cone is a parabola; if the former angle be greater than the latter, the
curve will be an ellipse; and if less, the section will be a hyperbola.

But the simplest conic section is, of course, a circle, whic