times a week throughout the year. Outside of the class-room, the study of Goethe's works continued from Course III.; special work assigned in some cases. Professor PUTZKER.

Elective, Junior and Senior years, to students in the Classical and Literary courses and the course in Letters and Political Science, who have completed Course I.

V. Composition and Conversation. Topics from History and German Literature. Twice a week throughout the year. Dr. SENGER.

This Course may be made elective in special cases. It is intended for students who speak German with some facility, and may be taken only after consultation with the instructor in charge.

VI. German Literature. Graduate Course. Twice a week throughout the year. Professor PUTZKER.

Gothic. See under English.

FRENCH.

In order to meet the wants of students who desire to obtain a reading knowledge only, the first two years are devoted mainly to translating French into English. An effort will be made, however, to give students some facility in understanding French when spoken, and some power of expressing themselves in French. Accordingly, occasional lectures in French, on the history of the language, will be given as soon as practicable; an endeavor will be made to use the language in conducting the recitations; translation of English into French will be begun.

The study of French, if begun, must be pursued for at least two years, except in the College of Chemistry. If Course I. is elected, it must be followed by Course II.

I. First Year. Keetels' Elementary French Grammar; Athalie. A part of Le Roi des Montagnes will be read in the class; the remainder will be read outside of the class, for examination. Four times a week throughout the year. Associate Professor PAGET.

Prescribed, Junior year, in the course in Chemistry; elective, alternatively with German, in the Freshman year, in the Classical course, the Literary course, and the courses in Letters and Political Science, Agriculture, Mechanics, Mining, and Civil Engineering; but students in the College of Civil Engineering are advised to elect French, those in the Colleges of Mechanics and Mining, German. Students in the Classical course who do not elect French or German in the Freshman year have an election, at the beginning of the Sophomore year, between this Course and German or studies in history and political science.

II. Second Year. Keetels' Elementary French Grammar; Polyeucte (Corneille); Britannicus (Racine); Hernani and Ruy Blas (V. Hugo); Grandeur et Décadence des Romains (Montesquieu); Le Misanthrope and Tartuffe (Molière). Histoire de Charles XII. (Voltaire) will be read outside of the class for examination. Further like work will be assigned as occasion requires. Three times a week throughout the year. Associate Professor PAGET.

Prescribed, Sophomore year, to students in the Classical course, the Literary course, and the courses in Letters and Political Science, Agriculture, Mechanics, Mining and Civil Engineering, who have completed Course I.

III. Third Year. Grammaire française (cours supérieur) by A. Chassang, as a book for reference. A course of lectures once a week will be given on La Chanson de Roland and other subjects of the French literature of the middle ages; and a study of the principal French writers will be begun. In this Course will come selections from Joinville (thirteenth century), Montaigne (sixteenth century), selections in prose from Pascal, Bossuet, Fénelon, La Bruyère, Descartes, and selections in poetry from Corneille, Boileau, Racine, Molière, La Fontaine (seventeenth century), and selections from Massillon, Voltaire, Buffon, Montesquieu (eighteenth century). Three times a week throughout the year. Associate Professor PAGET.

Elective, Junior year, to students in the Classical and Literary courses, and in the courses in Letters and Political Science, Agriculture and Mechanics, who have completed Course II.

IV. Fourth Year. The course of French literature will be continued with special study of the literature of the nineteenth century, and lectures in French on the same once a week during the second term. Twice a week throughout the year. Associate Professor PAGET.

Elective, Senior year, to students in the Classical and Literary courses, and in the course in Letters and Political Science, who have completed Course III.

SPANISH.

I. Monsanto and Languellier's Practical Course with the Spanish Language. Reading matter assigned as occasion requires. Three times a week throughout the year. Associate Professor PAGET.

Optional in all Courses.

MATHEMATICS.

I. Solid and Spherical Geometry, Algebra, Trigonometry, Analytic Geometry. The distribution of the work is as follows:

(1) Solid and Spherical Geometry, and Algebra. Four times a week throughout the Freshman year. Associate Professor EDWARDS, Assistant Professor HASKELL and Mr. LEUSCHNER.

(2) Plane and Spherical Trigonometry, and Analytic Geometry. Three times a week during the first term of the Sophomore year. Professor STRINGHAM, Associate Professor EDWARDS and Mr. LEUSCHNER.

Prescribed in the Classical and Literary courses, and the course in Letters and Political Science. But to Freshmen in the courses named, who have completed in a satisfactory manner the subject of solid and spherical geometry as a preparation for the University, is assigned in its place some other equivalent subject.

II. Geometry, Algebra, Trigonometry, Prolegomena to the Calculus. Six (recitation) hours a week during the first term; five (recitation) hours a week during the second term. The several subjects are treated according to the following scheme:

NOTE.-Section A comprises all Freshmen in Scientific courses who have the subject of solid and spherical geometry to their credit on entering the University, and maintain creditable scholarship afterwards; section B, all other Freshmen in Scientific courses.

(1) Solid and Spherical Geometry (B). The fundamental propositions of the Euclidean geometry of space. Three recitations a week during the first term, with section B. Mr. LEUSCHNER.

(2) Projective Geometry (A and B). A brief discussion of the projective properties of geometrical figures in the plane and in space. This subject forms a part of Course (1) during the first term with section B, and of Course (6) during the second term with section A. Professor STRINGHAM and Mr. LEUSCHNER.

(3) Algebra (A and B). The later chapters in elementary algebra, the general theory of equations, elements of the theory of determinants, discussion of series. With sections A and B three recitations a week during the first term, and with section A two additional hours of impromptu exercises for which no preparatory study is required. Associate Professor EDWARDS and Mr. LEUSCHNER.

(4) Trigonometry and Hyperbolic Functions (A and B). The development of the general formulæ of plane and spherical trigonometry; solution of plane and spherical triangles; practice in the use of logarithmic tables; algebraic trigonometry and hyperbolic functions. Two recitations, and one hour of impromptu exercises requiring no preparatory study, each week during one term; with section A the first term, with section B the second term. Assistant Professor HASKELL and Mr. LEUSCHNER.

(5) Analytic Geometry (A and B). The analytic geometry of the straight line, the circle and the conic sections, including a discussion of the general equation of the second degree and some special examples of transcendental and higher plane curves. Two recitations, and two hours of impromptu exercises requiring no preparatory study, each week during the second term, with sections A and B. Associate Professor EDWARDS and Mr. LEUSCHNER.

(6) Prolegomena to the Differential and Integral Calculus (A). A discussion of first principles and the development of the earlier fundamental formulæ of the differential and integral calculus. Two recitations, or lectures, and one hour of impromptu exercises each week during the second term, with section 4. Professor STRINGHAM.

The rir subjects in this group are prescribed, Freshman year, in all the Scientific courses, in accordance with the foregoing scheme.

III. Analytic Geometry. Supplementary to Course I. (2). The straight line, the circle and the conic sections; discussion of the general equation of the second degree. Twice a week during the second term. Assistant Professor HASKELL.

E'ective, Sophomore year, in the Classical and Literary courses and the course in Letters and Political Science; required of Sophomores in the courses named who intend to elect mathematics in the Junior year.

IV. Theory of Equations. The general theory of algebraic equations, including the elements of determinants. Twice a week during the first term. Assistant Professor HASKELL.

Open to students who have completed Course I. or Course II.

V. Projective Geometry. Twice a week during the second term. Assistant Professor HASKELL.

Open to students who have completed Course I. or Course II.

VI. Analytic Geometry of Space. The elementary analytic geometry of the straight line in space, the plane, the sphere and the conicoids, and a discussion of the theory of higher curves and surfaces, including the determination of curvatures by the methods of the differential calculus. Three recitations, and three hours of impromptu exercises requiring no preparatory study, each week during one term; with section A the first term, with section B the second term. Professor STRINGHAM, Assistant Professor HASKELL, and Mr. LEUSchner. Prescribed, Sophomore year, to students in the College of Mechanics, Mining and Civil Engineering; elective to Juniors in the Classical and Literary courses. Admission to this Course is conditioned upon the successful completion of the prescribed work in trigonometry and conic sections.

VII. Differential and Integral Calculus. Development of the later fundamental formulæ of the differential and integral calculus. Applications to various problems in geometry and analysis, such as indeterminate forms, maxima and minima values, expansion of functions, lengths of curves, areas of surfaces, volumes of solids, centers of gravity, curve tracing, etc. Three recitations and three hours of impromptu exercises requiring no preparatory study, each week during one term; with section B the first term, with section A the second term. Professor STRINGHAM, Assistant Professor HASKELL and Mr. LEUSCHNER.

Prescribed, Sophomore year, to students in the Colleges of Mechanics, Mining and Civil Engineering; elective to Juniors in the Classical and Literary courses. Admission to this Course is conditioned upon the successful completion of the prescribed work in trigonometry and conic sections.

VIII. Differential and Integral Calculus. Advanced Course; a continuation of Course VII. Twice a week throughout the year. Associate Professor EDWARDS.

Open to students who have completed Course VII.

IX. Conic Sections. Continuation of advanced Course; involving modern algebraical methods. Salmon's Conic Sections. Twice a week during the first term. Professor STRINGHAM.

Open only to students who have read the first ten chapters of Salmon's Conic Sections, or an equivalent.

*X. Higher Plane Curves. Continuation of Course IX. Salmon's Higher Plane Curves. Twice a week during the second term. Professor STRINGHAM. Open to students who have completed Course IX.

XI. Differential Equations. Theory and methods of solution of total differential equations. Forsyth's Differential Equations. Twice a week throughout the year. Professor STRINGHAM.

Prescribed, Junior year, in the College of Mechanics.

XII. Method of Least Squares. The fundamental principles and processes of the method of least squares, and their application to the problems involved in the reduction of astronomical and physical observations. Twice a week during the first term. Professor STRINGHAM and MR. LEUSCHNER.

Prescribed, Junior year, in the Colleges of Mechanics and Civil Engineering. *Not given in 1890-91.

XIII. Quaternions. An elementary presentation of the principles of the subject, with illustrations of its applications to geometry and mechanics. Twice a week throughout the year. Associate Professor EDWARDS.

Involves an elementary knowledge of the differential and integral calculus.

XIV. Higher Analysis.

Seminary study of selected topics in the higher analysis in the light of recent investigation. Once a week, in sessions of two hours each, throughout the year. Professor STRINGHAM and Assistant Professor HASKELL.

Open to graduates and to such Seniors as are qualified for entering upon the work of the Course.

XV. Hyper Space. Lectures on the generalized notions of space and on the geometry of space of four dimensions. Once a week during the second term. Professor STRINGHAM.

An elementary knowledge of the differential and integral calculus and of quaternions is prerequisite for this Course.

XVI. Teachers' Course.

Seminary study of special topics in elementary mathematics, including criticisms of text-books and methods of teaching. Once a week, in sessions of two hours each, throughout the year, on Saturdays. Professor STRINGHAM and Associate Professor EDWARDS.

Arranged especially for those who are either already engaged in teaching or are preparing themselves as teachers of mathematics.

Descriptive Geometry. See Course II. under Drawing.

Analytic Mechanics. See Course I. under Mechanical Engineering.

Hydrodynamics. See Course II. under Mechanical Engineering.

Kinematics. See Course IV. under Mechanical Engineering.

Thermodynamics. See Course V. under Mechanical Engineering.

PHYSICS.

I. General Physics. (a) Lectures on the following topics, illustrated by experiments: Mechanics. Properties of matter; measure of force; motion and laws of motion; composition and resolution of forces; centrifugal force; laws of gravity and falling bodies; center of gravity; elementary machines; laws of friction; motion on inclined planes; theory of the pendulum; impact of bodies; projectiles. Mechanics of Liquids: Transmission of pressure; buoyancy; specific gravity; motion of liquids; spouting liquids; motion of water in pipes, canals and rivers; theory of water motors; hydraulic ram. Mechanies of Gases: Laws of compressibility and elasticity; atmospheric pressure; theory of pumps; siphons. Mechanics of Capillarity. Statical Electricity: Electrical action; electrical forces; Leyden jar; mechanical and chemical effects; atmospheric electricity. Heat. Thermometry; laws of expansion of solids,