Euclid, Mechanics, and Hydrostatics, according to the annexed schedule.

10. That no person shall be approved by the Examiners, unless he shew a competent knowledge of all the subjects of the Examination.

11. That there shall be three additional Examinations in every year; the first commencing on the Thursday preceding AshWednesday, the second on the Thursday preceding the Division of the Easter Term, and the third on the Thursday preceding the Division of the Michaelmas Term.

12. That in these additional Examinations the distribution of the subjects and the hours of the Examination shall be at the discretion of the Examiners, the subjects being the same as at the Examination in the preceding January.

13. That no person shall be allowed to attend any Examination whose name is not sent by the Prælector of his College to the Examiners before the commencement of the Examination.

14. That in every year at the first Congregation after the 10th day of October, the Senate shall elect four Examiners, (who shall be members of the Senate, and nominated by the several Colleges according to the cycle of Proctors and Taxors) to assist in conducting the Examinations of the three following terms.

15. That two of these Examiners shall confine themselves to the Classical subjects, and two to Paley's Moral Philosophy and the Acts of the Apostles.

16. That the two Examiners in the Mathematical Subjects, at the Examination in January, be as hitherto the Moderators of the year next but one preceding; and that at the other three Examinations the Moderators for the time being examine in the Mathematical Subjects,

17. That each of the six Examiners shall receive £20. from the University Chest.

18. That the Pro-Proctors and two at least of the Examiners attend in the Senate-House during each portion of the Examination in January.

SCHEDULE OF MATHEMATICAL SUBJECTS of Examination, for the Degree of B.A. of Persons not Candidates for Honors.

ARITHMETIC.

Addition, subtraction, multiplication, division, reduction, rule of three; the same rules in vulgar and decimal fractions: practice, simple and compound interest, discount, extraction of square and cube roots, duodecimals.

ALGEBRA.

1. Definitions and explanation of algebraical signs and terms. 2. Addition, subtraction, multiplication and division of simple algebraical quantities and simple algebraical fractions.

3. Algebraical definitions of ratio and proportion.

4.

:

If a b c d then ad bc, and the converse:
also bad

c,

and a c :: bd,

and a + b : bc+d: d.

7. Geometrical definition of proportion. (Euc. Book v. Def. 5.) 8. If quantities be proportional according to the algebraical definition, they are proportional according to the geometrical definition.

9. Definition of a quantity varying as another, directly, or inversely, or as two others jointly.

EUCLID.

Book I. II. III.

Book vi. Props. 1. 2. 3. 4. 5. 6.

MECHANICS.

Definition of Force, Weight, Quantity of Matter, Density,
Measure of force.

Definition of Lever.

The Lever.

Axioms.

Prop. 1. A horizontal prism or cylinder of uniform density will produce 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 kind of levers.

Prop. 5. If two forces acting perpendicularly at the extremities of the arms 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 balance each other, they are inversely as the perpendiculars drawn from the fulcrum to the directions in which the forces act.

Prop. 7. If two weights balance each other on a straight lever when it is 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 component forces in direction and magnitude, the diagonal will represent the resultant force in direction and magnitude.

Prop. 9. If three forces, represented in magnitude and direction by the sides of a triangle, act on a point, they will keep it at rest.

Mechanical Powers.

Definition of Wheel and Axle.

Prop. 10. There is an equilibrium upon the wheel and axle when the power 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, there 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 number of pulleys and the parts of it between the pulleys are parallel, there is an equilibrium when power (P): weight (W): 1 the number of strings at the lower block.

Prop. 13. In a system in which each pulley hangs by a separate string and the strings are parallel, there is an equilibrium when P: W:: 1: that power of 2 whose index is the number of moveable pulleys.

Prop. 14. The weight (W) being on an inclined plane and the force (P) acting 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 centres of two circles are as the radii of the circles, to shew that if P and W balance each other on the wheel and axle, and the whole be put in motion, P: W:: W's velocity: P's velocity.

Prop. 16. To shew that if P and W balance each other in the machines described in Propositions 11, 12, 13 and 14, and the whole be put in motion, P: 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 gravity is in that line.

Prop. 18. To find the centre of gravity of two heavy points; and to shew that the pressure at the centre of gravity is equal to the sum of the weights in all positions.

Prop. 19. To find the centre of gravity of any number of heavy points; and to shew that the pressure at the centre of gravity is equal to the sum of the weights in all positions.

Prop. 20. To find the centre of gravity of a straight line. Prop. 21. To find the centre of gravity of a triangle.

Prop. 22. When a body is placed on a horizontal plane, it will stand or fall, according as the vertical line, drawn from its centre of gravity, falls within or without its base.

Prop. 23. When a body is suspended from a point, it will rest with its 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 is 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 sides vertical, be filled with fluid, the pressure upon the bottom will be equal to 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 as is equal in weight to the weight of the body; and it presses downwards and 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 part immersed the whole body :: the specific gravity of the body: the specific gravity of the fluid.

:

Prop. 9. When a body is immersed in a fluid, the weight lost: whole weight of the body: the specific gravity of the fluid : the specific gravity of 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. Elastic Fluids.

Prop. 12. Air has weight.

Prop. 13. The elastic force of air at a given temperature varies as to 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 airpump 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.

In order to check the practice of Degrading, which has, of late years, been so frequent, a Syndicate was appointed to take the same into consideration, and they made the following Report, which was confirmed by Grace of the Senate, Feb. 27, 1829.

1. That no person who has degraded, be permitted to become a Candidate for University Scholarships or any other Academical Honors during his Undergraduateship, or for Honors in the Mathematical Tripos, unless he shall previously have obtained special permission for so doing, from a Syndicate hereafter to be appointed for that purpose.

2. That the Syndicate do consist of the Vice-Chancellor, the Public Orator, the Greek Professor, and the two Moderators for the time being, who shall be invested with full power to examine into the cases of applicants for permission to become candidates for Honors after they have degraded, and to grant or withhold such permission, as they may think proper.

3. That this Syndicate do meet on a certain day in October in each year, of which notice is to be given by the Vice-Chancellor,