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ROAD AND BRIDGE CONSTRUCTION AND

MAINTENANCE.

FIRST PAPER.

The Board of Examiners.

1. Draw up specifications for the following works:(a) Construction of 20 chains of road across swampy land, the surrounding country being loamy, and metal being obtainable.

(b) Kerbing, channelling, and tar-paving for 10 chains of a town street 50 feet wide, near Melbourne.

(c)

Wood-paving of 10 chains of a 66-ft. street, also near Melbourne.

(d) Supply of maintenance metal for a town for a period of twelve months.

2. Draw half-longitudinal section, quarter plan, and sectional elevation of a skew brick culvert, having 30 square feet waterway, to be placed under a road embankment 20 feet in depth, the formation width of the road being 50 feet, and the angle of skew 45°.

ROAD AND BRIDGE CONSTRUCTION.

SECOND PAPER.

The Board of Examiners.

Design an iron girder bridge, with suitable approaches, for the case outlined in plan herewith. The width of bridge to be 36 feet clear, viz., 24-feet roadway, and two footpaths of 6 feet each.

Give half elevation, half longitudinal section, half plan and cross section showing decking and roadway. Give also details of the more important joints.

HYDRAULIC AND SANITARY ENGINEERING. The Board of Examiners.

1. Write a specification for a pipe-laying contract in connection with an urban Waterworks Trust. The contract to provide for supply of all valves, fittings, and material (except pipes) necessary for the works. Pipes used (which will be supplied by the Trust) 6", 4", and 3′′ diameter.

2. A city with a population of 35,000 concentrated in an area of 2 square miles and not receiving any drainage or sewage from other districts, is carrying out a scheme for drainage on the water carriage system, the sewage being conveyed to a farm ten miles distant. At the point where the branch sewers unite the surface is at R. L. 200

and the inverter of sewers at 180. The general surface level of the sewage farm is 185, the country between the city and farm having a gradual slope towards the latter. For the first two miles the outlet sewer passes through bluestone country.

(a) Give a complete working cross section of the outlet sewer you would adopt.

(b) Give a rough section showing the levels and grades to which it should be constructed.

(c) Show where the necessary pumping plant should be placed.

(d) State what indicated horse-power the plant

should have.

Give

your reasons for

your answers.

3. (a) Give a sketch-design for a timber weir suitable for raising the water in a river 25 feet above ordinary summer level. The river may be assumed to be 300 feet wide, and to have clay banks and bottom, the latter six feet below summer level. No danger need be anticipated from backing flood waters on private property, &c. (b) Give full particulars of filtration works you would deem suitable for a town with population of 10,000, obtaining a water supply by pumping from the lower reaches of a large navigable river (such as the Murray), on the banks of which the town may be assumed to be built.

(NOTE.-One division only of (3) to be attempted.)

EXAMINATION FOR THE DEGREE OF

MASTER OF ARTS.

SCHOOL OF MATHEMATICS.

PURE MATHEMATICS.

The Board of Examiners.

1. Prove Lagrange's theorem for the expansion of F(z) in powers of y where x = x + y p (z).

Shew that the co-efficient of x" in the expansion of (1-2 px + x2)−1 is

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2. Shew how the method of undetermined multipliers is applied to the solution of problems of maxima and minima.

Find the maxima and minima values of x2 + y2+z2 where

ax2 + by2 + cz2 + 2 fyz + 2gzx + 2hxy = 1. lx + my + nz = 0.

3. Find the equation of the osculating conic at a given point of a plane curve.

Prove that the locus of the centre of a conic having contact of the third order with a given curve at a given point is a straight line.

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where f(x), F(x) are rational integral algebraical functions of x and f(x) is at least two degrees lower in a than F(x).

Prove that

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5. Shew how to change the variables in a triple integral.

Transform the integral

SSS V dx dy dz

by the substitution

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6. Shew how to depress the order of a homogeneous ordinary differential equation.

Solve the equation

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P dx + Qdy + R dz = 0

may have a single primitive.

Integrate the equation

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(bz — cy) dx + (cx − az) dy + (ay — bx) dz = 0.

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