SCHEDULE of MATHEMATICAL SUBJECTS of Examination, fo the Degree of B.A. of Persons not Candidates for Honors. ARITHMETIC. Addition, subtraction, multiplication, division, reduction, rule of th the same rules in vulgar and decimal fractions: practice, simple compound interest, discount, extraction of square and cube roots; decimals, together with the proofs of the Rules and the reasons for processes employed. ALGEBRA. 1. Definitions and explanations of algebraical signs and terms, 2. Addition, subtraction, multiplication and division of simple algebrai quantities and simple algebraical fractions. 3. 4. Algebraical definitions of ratio and proportion. If a bed, then a d=bc, and the converse: and a 7. Geometrical definition of Proportion. (Euc. Book v. Def. 5.) 8. If quantities be proportional according to the algebraical definition, the are proportional according to the geometrical definition. 9. Definition of a quantity varying as another, directly, or inversely, or as tw others jointly. 10. Easy equations of a degree not higher than the second, involving one two, unknown quantities, and Questions producing such Equations. EUCLID. Book I. II. III. Book vi. Props 1. 2. 3. 4. 5. 6. MECHANICS. Definition of Force, Weight, Quantity of Matter, Density, Measure o Force. Definition of Lever. The Lever, Axioms. Prop. 1. A horizontal prism or cylinder of uniform density will produc the same effect by its weight as if it were collected at its middle point. Prop. 2. If two weights acting perpendicularly on a straight lever on opposite sides of the fulcrum balance each other, they are inversely as their distances from the fulcrum; and the pressure on the fulcrum is equal to their sum. Prop. 3. If two forces acting perpendicularly on a straight lever in opposite directions and on the same side of the fulcrum balance each other, they are inversely as their distances from the fulcrum; and the pressure on the fulcrum is equal to the difference of the forces. Prop. 4. To explain the kinds of levers. Prop. 5. If two forces acting perpendicularly at the extremities of the rms of any lever balance each other, they are inversely as the arms. Prop. 6. If two forces acting at any angles on the arms of any lever alance each other, they are inversely as the perpendiculars drawn from the ilcrum to the directions in which the forces act. Prop. 7. If two weights balance each other on a straight lever when it horizontal, they will balance each other in every position of the lever. Composition and Resolution of Forces. Definition of Component and Resultant Forces. Prop. 8. If the adjacent sides of a parallelogram represent the comonent forces in direction and magnitude, the diagonal will represent the sultant force in direction and magnitude. Prop. 9. If three forces, represented in magnitude and direction by the des of a triangle, act on a point, they will keep it at rest. And also of such Questions and Applications as arise directly out of be aforenamed Propositions. Mechanical Powers. Definition of Wheel and Axle. Prop. 10. There is an equilibrium upon the wheel and axle when the ower is to the weight as the radius of the axle to the radius of the wheel. Definition of Pulley. Prop. 11. In the single moveable pulley where the strings are parallel, here is an equilibrium when the power is to the weight as 1 to 2. Prop. 12. In a system in which the same string passes round any numer of pulleys, and the parts of it between the pulleys are parallel, there is n equilibrium when power (P) weight (W) :: 1: the number of strings at he lower block. Prop. 13. In a system in which each pulley hangs by a separate string, nd the strings are parallel, there is an equilibrium when P: W:: 1: that ower of 2 whose index is the number of moveable pulleys. Prop. 14. The weight (W) being on an inclined plane, and the force (P) cting parallel to the plane, there is an equilibrium when P: W :: the height of the plane its length. : Definition of Velocity. Prop. 15. Assuming that the arcs which subtend equal angles at the entres of two circles are as the radii of the circles, to shew that if P and W alance each other on the wheel and axle, and the whole be put in motion, P: WW's velocity: P's velocity. Prop. 16. To shew that if P and W balance each other in the machines escribed in propositions 11, 12, 13, and 14, and the whole be put in motion, : W:: W's velocity in the direction of gravity: P's velocity. The Centre of Gravity. Definition of Centre of Gravity. Prop. 17. If a body balance itself on a line in all positions, the centre of ravity is in that line. Prop. 18. To find the centre of gravity of two heavy points; and to shew hat the pressure at the centre of gravity is equal to the sum of the weights I all positions. Prop. 19. To find the centre of gravity of any number of heavy points; ad to shew that the pressure at the centre of gravity is equal to the sum of e weights in all positions. Prop. 20. To find the centre of gravity of a straight line. Prop. 22. When a body is placed on a horizontal plane, it will stand fall, according as the vertical line, drawn from its centre of gravity, fal within or without its base. Prop. 23. When a body is suspended from a point, it will rest with i centre of gravity in the vertical line passing through the point of suspension HYDROSTATICS. Definitions of Fluid; of elastic and non-elastic Fluids. Pressure of non-elastic Fluids. Prop. 1. Fluids press equally in all directions. Prop. 2. The pressure upon any particle of a fluid of uniform density proportional to its depth below the surface of the fluid. Prop. 3. The surface of every fluid at rest is horizontal. Prop. 4. If a vessel, the bottom of which is horizontal and the side vertical, be filled with fluid, the pressure upon the bottom will be equal t the weight of the fluid. Prop. 5. To explain the hydrostatic paradox. Prop. 6. If a body floats on a fluid, it displaces as much of the fluid a is equal in weight to the weight of the body; and it presses downwards an is pressed upwards with a force equal to the weight of the fluid displaced. Specific Gravities. Definition of Specific Gravity. Prop. 7. If M be the magnitude of a body, S its specific gravity, and Wits weight, W = MS. Prop. 8. When a body of uniform density floats on a fluid, the par immersed the whole body :: the specific gravity of the body: the specifi gravity of the fluid. Prop. 9. When a body is immersed in fluid, the weight lost whole weight of the body :: the specific gravity of the fluid: the specific gravity o the body. Prop. 10. To describe the hydrostatic balance, and to shew how to find the specific gravity of a body by means of it, 1st, when its specific gravity is greater than that of the fluid in which it is weighed; 2ndly, when it is less. Prop. 11. To describe the common hydrometer, and to shew how to compare the specific gravities of two fluids by means of it. Prop. 12. Air has weight. Elastic Fluids. Prop. 13. The elastic force of air at a given temperature varies as the density. Prop. 14. The elastic force of air is increased by an increase of temperature. Prop. 15. To describe the construction of the common air-pump and its operation. Prop. 16. To describe the construction of the condenser and its operation. Prop. 17. To explain the construction of the common barometer, and to shew that the mercury is sustained in it by the pressure of the air on the surface of the mercury in the basin. Prop. 18. The pressure of the atmosphere is accurately measured by the weight of the column of mercury in the barometer. Prop. 19. To describe the construction of the common pump and its operation. Prop. 20. To describe the construction of the forcing pump and its operation. Prop. 21. To explain the action of the siphon. Prop. 22. To shew how to graduate a common thermometer. Prop. 23. Having given the number of degrees on Fahrenheit's thermometer, to find the corresponding number on the centigrade thermometer. That the Questionists who are Candidates for an Ordinary Degree only, and not for Honors, and who pass, be arranged by the Examiners into four Classes, namely, a fourth, fifth, sixth, and seventh, according to merit, the names in each Class being arranged alphabetically; and that these Classes be published in the Senate-House on the Friday preceding the general B.A. Admission'. REGULATIONS Concerning the PROFESSORS' EXAMINATIONS, an additional Condition for the ordinary B.A. Degree appointed by Grace, Oct. 31, 1848. 1. That, at the beginning of each academical year, the Vice-Chancellor shall issue a Programme of the subjects, places, and times, of the several Professors' Lectures for the year then to ensue. 2. That all Students, who, being Candidates for the Degree of B.A., or for the Honorary Degree of M.A., are not Candidates for Honors, shall, in addition to what is now required of them, have attended, before they be admitted to Examination for their respective Degrees, the Lectures delivered during one Term at least, by one or more of the following Professors: Regius Professor of Laws, Woodwardian Professor of Geology, Jacksonian Professor of Natural and Downing Professor of the Laws of Downing Professor of Medicine, Professor of Political Economy; and shall have obtained a Certificate of having passed an Examination satisfactory to one of the Professors whose Lectures they have chosen to attend. The Professors by whom these certificates are to be given, wish to make known to those Members of the University whom it may concern, the subjects of the Examinations on which the certificates will be given, and the books which may be consulted as a preparation for them. It is to be understood, in general, that each Professor will deliver, in his public Lectures, a large portion of the information which he will require in his Examination; and that the books here recommended are to be consulted in the way which the Lectures relative to each subject respectively point out. The books on the respective subjects are to be regarded as a preparation in addition to that supplied by the Lectures on the corresponding subject. In stating the nature of the Examination, the method will be followed, where it can conveniently be done, which was adopted by the University in 1837, to define the nature and extent of the Examination then instituted in Mechanics and Hydrostatics; namely, to refer to a Syllabus of the portion 1 For Schedule of the order of days, &c. at the Examination, see pp. 14, 15. |