r to you, most noble professors,
somewhat novel and imaginary, remember the maxim of the sage, that in
the infancy of science there is no speculation which does not merit
careful examination; and the most remote and fanciful explanations of
facts have often been found the true ones. Perhaps some
'self-opinionated particle' (I speak mathematically) may have been
inclined to laugh at our theories and discoveries, as the wise fools of
the day laughed at Kepler and his laws; but time has changed the world's
laughter into praise, and a century hence our discoveries may rank among
the achievements of modern science. As Cicero says, 'Time obliterates
the fictions of opinions, but confirms the decisions of nature.'

I have not shunned, most noble professors, to enlist Imagination under
the banner of Geometry; for I am fully persuaded that it is a powerful
organ of knowledge, and is as much needed by the mathematician as by the
poet or novelist. It is, I fear, often banished with too much haste from
the fields of intellectual research by those who take upon themselves to
give laws to philosophy. We need imagination to form an hypothesis; and
without hypotheses science would soon become a lifeless and barren
study, a horse-in-the-mill affair ever strolling round and round,
unconscious of the grinding corn. In my previous investigations my
imagination pictured the symmetry of curves and States; the hypothesis
followed that the laws which regulated them were identical, and you have
observed how the supposition was confirmed by our subsequent
calculations.

In this lecture I propose to examine some of the forces which exist in
our social system, and shall endeavour to estimate them by methods of
mathematical procedure and analogical reasoning. We will begin with the
old definition of Force as _that which puts matter into motion, or which
stops, or changes, a motion once commenced_. When a mass is in motion,
it has a capacity for doing work, which is called _Energy_; and when
this energy is caused by the motion of a body it is called Kinetic
Energy (in mathematical language KE = 1/2 MV^2). Another form of kinetic
energy is called Potential Energy, which is in reality the capacity of a
body for doing work _owing to its position_. For example we may take an
ordinary eight-day clock. When the weights are wound up, they have a
certain amount of potential energy stored up, which will counteract the
friction of the wheels and the resistan