Repository: UIHistories Project: Board of Trustees Minutes - 1873 [PAGE 58]

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54 and Sciences, and of Civilization, the principles of civil polity and law, the philosophy of history, and the principles of political economy and constitutional law. The instruction is given chiefly by lectures, with readings of specified authors, and the study of historical geography and chronology. The course occupies two terms in the first, and three each in the third and fourth years of the University Courses.

1.—Discovery, settlement and colonial history of the United States, with notices of other American States; American Geography; History of the United States from the time of the Revolution—two lectures, or lessons, a week. 3.—Ancient history of Greece and Rome, with notices of other ancient nations; Ancient Geography ; Medieval History; Modern History; general European History; European Geography. 4.—Constitutional History of England, and of the United States—four lectures a week. History of Civilization; analysis of historical forces and phenomena; notices of the arts and of the inductive sciences. Constitutional and international law. Political economy.

PHILOSOPHY AND LOGIC.

The studies of this department are taught chiefly by lectures, with readings of specified authors and written essays.

4.—First Term—Mental Philosophy. Analysis and classification of mental phenomena; theories of perception, imagination, memory, judgment, reason, intuition. The aesthetic. Phenomena of dreaming, clairvoyance, and insanity. Doctrines of the absolute and the unconditioned. Philosophy of education. Second Term—Moral Philosophy—three lectures a week. Theory of conscience ; Nature of * moral obligation; Moral Feeling; The Right; The Good. Practical ethics; Duties. Formation of character. Logic, formal and inductive—two lectures a week. Third Term—History of Philosophy. Ancient schools of philosophy; Scholasticism ; Modern schools of philosophy; Influence of philosophy on. the progress of civilization, and on modern sciences and arts. Inductive logic.

P U R E MATHEMATICS.

1.—Geometry—Facts and principles, demonstrated, illustrated, and applied, with reference to right lines, circles, angles, triangles, polygons, planes, solid angles, prisms, pyramids, cylinders, cones and spherical surfaces, and the measurement of their lengths, areas or volumes. Algebra—Powers, roots and radicals of any degree; binomial Theorem; Properties and summation of series; Exponential quantities; Logarithms ; General theory and methods of solving equations. Trigonometry—Analytical, Plane and Spherical. Relations between the functions of an arc; Formation and use of tables; Solution of plane and spherical triangles. 2.—Analytical Geometry—Construction of equations by means of co-ordinates; Discussion in a plane of the point, right line, circle, ellipses, parabola, and hyperbolas; Higher plane curves ; cycloid, cissoid of Diocles, etc. Differential Calculus—Differentials of algebraic and transcendental functions; Maclaurin's Theorem; Maxima and minima of functions; Equations of tangents, normals, sub-tangents, sub-normals, etc.; Differentials of lines, surfaces, and volumes. Integral Calculus—Integration of known forms, and of rational fractions; Rectification of curves, quadrature of plane areas and surfaces of revolution, and cubature of solids of revolution. 3,—Analytical Geometry—Loci in space ; Surfaces of the second order. Differential Calculus—Differentials, and maxima and minima of functions of two or more variables; Taylor's Theorem; Osculatory curves, radius of curvature; Evolutes. involutes, envelopes; Discussion of algebraic and transcendental curves and surfaces. Tangent plane and normal; Partial differentials of surfaces and volumes, Integral Calculus—Integration of transcendental and irrational differentials; Differentials of higher orders; Differential equations; Rectification, quadrature and cubature in general; Calculus of Variations.

PHYSICS.

This subject has been amply provided for in the new building by the appointment of a Physical Laboratory and a Lecture Booin, to which the apparatus will be removed this summer, and where the expected