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48 Illinois Industrial University. 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 Room, to which the Apparatus will be removed this summer, and where the expected additional instruments, necessary to fully illustrate the subject, can be accommodated. In connection with the lectures, Silliman's Physics is used as' a textbook; as many of the topics are more thoroughly discussed in other classes, special attention is paid to the portions remaining. The following are the main heads; Matter, Force, Motion. Properties and Laws of Solids, Fluids and Liquids. Acoustics and Optics, with mathematical discussions of the undulations and instruments, solar and stellar spectra, etc. Heat. Magnetism. Electricity. Chemical Physics is given in a special course of lectures. ASTRONOMY a n d GEODESY. Temporary arrangements have been made for Observatory Practice by the erection of a small observatory, and the mounting of instruments of convenient size for Students' use. DESCRIPTIVE A. isgiven by lectures, with Lockyer's Astronomy for a textbook. The Equatorial Telescope is in constant use during favorable weather. PRACTICAL A. is given by lectures, practical work with the Meridian Circle, Sextant, Theodolite, etc., and Astronomical Calculations. GEODESY is given by lectures, practice and calculations. Some first class instruments have been ordered and trigonometrical stations will be erected. DRAWING. Complete Courses in Geometrical and Projection, Architectural, Engineering, Mechanical and Freehand Drawing are given. FREEHAND D. is given by personal instruction in the execution, with pencil and crayon, of "studies" by celebrated French and German artists, and in drawing from plaster models and other objects. The selections are made from a large and valuable stock purchased in Europe. Painting in Oil and Watercolors will be provided for. MUSIC. Instruction is provided for on the Piano and Organ. This is charged for at the rate of $16 per term of 20 lessons, and if a University instrument is used for practicing, the charge per term for such use is $2 for each hour daily of practice. The class meets weekly for public practice, and at the end of the term they are examined in public and marked, as 'in the other classes.
 