With regard to other advantages afforded by an elliptical social system, we will defer the consideration of this important subject until my next lecture. PAPER IV. THE SOCIAL PROPERTIES OF A CONIC SECTION, AND THE THEORY OF POLEMICAL MATHEMATICS--(_continued_). Most learned Professors and Students of this University,--You have already gathered from my preceding lecture my method of procedure in the investigation of the corresponding properties of curves and States. You have perceived that we have here the elements of 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.