I will not trouble you with the proof of this proposition, as it is evident to all mathematicians, and can easily be demonstrated. But mark well the deductions, when we interpret this mathematical language in correct polemical terms. A State, through various convulsions of its own, has merged into a condition represented by a straight line, having lost its symmetry, its beauty, its curvilinear proportion. An individual unhappily situated in this unfortunate community regards with longing eyes the prosperous condition of those who enjoy the social advantages of a settled form of government, and other blessings which accompany elliptical jurisdiction and laws. [Two tangents are drawn to an ellipse.] No matter where the individual may be in the unhappy envious straight line, the result of his reflection will be the same. Sympathetic chords are drawn, joining the points of contact of the tangents with the curve; they all pass through a fixed point. All these conclusions of the various individuals on the straight line will be the same. All are of opinion that the elliptical form is the best; and they mourn in secret over the sad events which have occurred in their own national life, their eccentricity, their lawlessness, when they see the advantages which their more staid and sober-minded neighbours so freely enjoy. 2. The normal at any point of an ellipse bisects the angle between the focal distances of that point. The normal is the perpendicular from the point on the major axis; it is the line of thought directed by the observance of just laws and rules. Hence this proposition shows that the individual citizen, when guided by sound judgment, regards with equal favour and entire approval the existence of both foci, or Houses of Legislature. He considers that both are necessary to his comfort, and the right regulation of the State's welfare. He cares not for the _abnormal_ condition of those who talk as if the existence of either House were unnecessary to his country's weal, and bestows a pitying glance on those wandering lights, or disturbed erratic governments, which do not possess the advantages which from experience he has learned to love and to respect. No matter what his condition may be, the same opinions are held by all classes, all ranks and degrees; and if a self-opinionated particle think otherwise, he ought to be transferred to a less enlightened sphere, and migrate to a parabolic state, or uninteresting straight line. And when he has changed his location, he will look back on his old home and old surroundings with longing eyes and an aching heart, thinking of the blessings he has lost by his own rash act. This can be proved mathematically. He looks for an ideal state of society, leaps after the shadow his fancy has depicted; and when he finds himself outside his former state, he looks back with longing eyes at the once-scorned focus. What is the focus of a perpendicular on the tangent of an ellipse from any external point? Can