(E) TRIGONOMETRY. One-half unit. Definitions and relations of the six trigonometric functions as ratios; circular measurement of angles. Proofs of principal formulas, in particular for the sine, cosine, and tangent of the sum and the difference of two angles, of the double angle and the half angle, the product expressions for the sum or the difference of two sines or of two cosines, etc.; the transformation of trigonometric expressions by means of these formulas. Solution of trigonometric equations of a simple character. Theory and use of logarithms (without the introduction of work involving infinite series). The solution of right and oblique triangles and practical applications, including the solution of right spherical triangles. (F) PLANE TRIGONOMETRY. One-half unit. This subject is the same as the preceding except that no topics from spherical trigonometry are included. PHYSICS. The present definition of the requirement in physics was framed by a commission appointed for the purpose by the College Entrance Examination Board in cooperation with other associations.1 GENERAL STATEMENT. 1. The course of instruction in physics should include: (a) The study of one standard textbook, for the purpose of obtaining a connected and comprehensive view of the subject. The student should be given opportunity and encouragement to consult other scientific literature. (b) Instruction by lecture table demonstrations, to be used mainly for illustration of the facts and phenomena of physics in their qualitative aspects and in their practical applications. (c) Individual laboratory work consisting of experiments requiring at least the time of 30 double periods, two hours in the laboratory to be counted as equivalent to one hour of classroom work. The experiments performed by each student should number at least 30. Those named in the appended list are suggested as suitable. The work should be so distributed as to give a wide range of observation and practice. The aim of laboratory work should be to supplement the pupil's fund of concrete knowledge and to cultivate his power of accurate observation and clearness of thought and expression. The exercises should be chosen with a view to furnishing forceful illustrations of fundamental principles and their practical applications. They should be such as yield results capable of ready interpretation, obviously in conformity with theory, and free from the disguise of unintelligible units. Slovenly work should not be tolerated, but the effort for precision should not lead to the use of apparatus or processes so complicated as to obscure the principle involved. 2. Throughout the whole course special attention should be paid to the common illustrations of physical laws and to their industrial applications. 3. In the solution of numerical problems, the student should be encouraged to make use of the simple principles of algebra and geometry to reduce the difficulties of solution. Unnecessary mathematical difficulties should be avoided and care should be exercised to prevent the student from losing sight of the concrete facts in the manipulation of symbols. 1 The commission and its work are described in the ninth annual report of the secretary of the College Entrance Examination Board, pp. 4-12. SYLLABUS. The following is a list of topics which are deemed fundamental and which should therefore be included in every well planned course of elementary physics. Only a few of the most important applications of these topics have been mentioned; teachers should add liberally to them. It is expected that the teacher will arrange these topics in such order as will suit his individual needs. I. INTRODUCTION: a. Metric system. Linear measure, units-meter, centimeter, millimeter. Cubic measure-cubic centimeter, liter. b. Volume, weight, density. c. States of matter: Solids, liquids, gases. II. MECHANICS: Fluids a. Pascal's law of fluid pressure. The hydraulic press. Pressure varying with depth and density of the liquid. Total pressure on the bottom of a vessel. c. Principle of Archimedes. d. Specific gravity of solids and liquids. e. Gases-relation between pressure and volume. f. Atmosphere pressure, buoyancy, the barometer, pumps for liquids and gases. Solids- a. Principle of moments. Parallelogram of forces (Resolution of forces, rectangular only). b. Newton's laws of motion. Force, momentum, velocity, acceleration. Uniformly accelerated motion, when initial or final velocity is zero. c. Mechanical work. Energy-potential and kinetic. Conservation of energy. d. Machines: Principle of work applied to machines, mechanical advantage, friction, efficiency. (Use terms, effort, and resistance.) Lever, wheel and axle, pulleys, inclined plane. e. Uniform circular motion; centrifugal and centripetal forces qualitatively illustrated. f. Law of universal gravitation. Relation of weight to mass. Center of gravity. III HEAT: a. Heat a form of energy. Temperature, Centigrade and Fahrenheit scales. b. Conduction, convection, and radiation. c. Expansion of solids, coefficient of linear expansion. d. Change of state. Fusion, the melting point. Vaporization, boiling, evaporation. Light, luminous bodies, illuminated bodies, transparent, translucent, and opaque bodies. b. Rectilinear propagation of light in a homogeneous medium, shadows, pinhole camera. c. Photometry. Intensity of light (source) and intensity of illumination distinguished. Law of inverse squares. d. Reflection. Law of reflection. Regular and diffused reflection. Plane and spherical mirrors, position and character of images. e. Refraction. Laws of refraction (qualitative). Refraction by plates, prisms, and lenses. Lenses: Converging and diverging, conjugate foci, principal focus, principal axis. Position and character of real and virtual images formed by converging lenses. Dispersion, color and the spectrum. Applications: The camera, the human eye, the compound microscope, the telescope. VI MAGNETISM: a. Magnets, permanent and temporary. b. Polarity, magnetic attraction and repulsion. c. Magnetic induction, magnetic field and lines of force, permeability. d. The earth as a magnet, compass, declination, dip. VII STATIC ELECTRICITY: a. Electrification by friction; two kinds. b. Electrical attraction and repulsion; electroscopes. c. Conductors and insulators; electrification by induction. VIII CURRENT ELECTRICITY: a. Simple voltaic cell. Electrochemical action. Local action and polarization; prevention of polarization. b. Types of cells (Daniel, Leclanché). Relation between direction of current and lines of magnetic force. Electromagnets, ampère turns (qualitative). The electric bell and the telegraph. VIII CURRENT ELECTRICITY-Continued. e. Resistance. The ohm. Ohm's law. The volt. Power-the watt and the watt hour. f. Heating effects. Fuse wire and electric heater. Arc and incandescent lamps. g. Measuring instruments: Galvanometer, ammeter, voltmeter, resistance box. h. Series and parallel connection of cells, lamps, etc. i. Fall of potential in a circuit. j. Electromagnetic induction. Direction and magnitude of the induced electromotive force. Simple two-pole dynamo and motor. Simple alternating and direct current generator. MECHANICS: LIST OF EXPERIMENTS. 1. Weight of unit volume of a substance, prism or cylinder. 2. Principle of Archimedes. 3. Specific gravity of a solid body that will sink in water. 4. Specific gravity of a liquid, two methods (bottle and displacement methods); or, 5. Specific gravity of a liquid by balancing columns. 6. Boyle's law. 7. Density of air. 8. Hooke's law. 9. Strength of material. 10. The straight lever, principle of moments. 11. Center of gravity and weight of a lever. 12. Parallelogram of forces. 13. Four forces at right angles in one plane. 14. Coefficient of friction between solid bodies on a level and by sliding on an incline. 15. Efficiency test of some elementary machine, either pulley, inclined plane, or wheel and axle. 16. Laws of the pendulum. 17. Laws of accelerated motion. HEAT: 18. The mercury thermometer-relation between pressure of steam and its temperature. 19. Linear expansion of a solid. 20. Increase of pressure of a gas heated at constant volume; or, 21. Increase of volume of a gas heated at constant pressure. 22. Heat of fusion of ice. 23. Cooling curve through change of state (during solidification). 24. Heat of vaporization of water. 25. Determination of the dew point. 26. Specific heat of a solid. SOUND: 27. Velocity of sound. 28. Wave length of sound. 29. Number of vibrations of a tuning fork. LIGHT: 30. Use of photometer. 31. Images in a plane mirror. 32. Images formed by a convex mirror. 33. Images formed by a concave mirror. 34. Index of refraction of glass; or, 35. Index of refraction of water. 36. Focal length and conjugate foci of a converging lens. 37. Shape and size of a real image formed by a lens. 38. Magnifying power of a lens. 39. Construction of model of telescope or compound microscope. MAGNETISM AND ELECTRICITY: 40. Study of magnetic field. 41. Magnetic induction. 42. Study of a single fluid voltaic cell. 43. Study of a two-fluid voltaic cell. 44. Magnetic effect on an electric current. 45. Electrolysis. 46. Laws of electrical resistance of wires-various lengths, cross-section, and in parallel. 47. Resistance measured by volt-ammeter method. 48. Resistance measured by Wheatstone's bridge. 49. Battery resistance-combination of cells. 50. Study of induced currents. 51. Power or efficiency test of a small electric motor. LABORATORY NOTEBOOK. While the College Entrance Examination Board does not require the submission of the candidate's laboratory notebook as part of the examination in physics, it requires the submission of a teacher's certificate descriptive of the candidate's work. The notebook should be forwarded directly to the proper authorities of the college or scientific school that the candidate purposes entering. TEACHER'S LABORATORY CERTIFICATE. In lieu of the presentation of the laboratory notebook, the candidate must submit to the College Entrance Examination Board a certificate in the following form: (School) (Post-office address of school) (Date) (College or scientific school that candidate purposes entering) I certify that during the academic years.. (Name in full) has personally performed and properly recorded in a suitable notebook equivalent to ... periods of 60 minutes each. each, equivalent to ... periods of 60 minutes each. ...... School. periods of ...... minutes each, periods of ...... minutes Half the number of hours given to laboratory work plus the full number of hours given to lectures and recitations is equal to The teacher may here enter the final grade of hours.1 (Signed). 1 To meet the board's requirement the number of hours here entered must be at least 120. |