works, giving also the different methods of payment on different works which have been laid before you.

[In the following questions, as to the specification of particular works, the answers must give succinctly the quality of the material, and the quality of the workmanship only; all else ought to be given for once in the answer to No. 1 :-]

2. Give a specification for permanent way, double line, including all above the formation level, giving dimensions on a cross section.

3. Draw up a specification for a turnpike road, with footpaths, from the formation level upwards, and add the fencing with quickset hedge, giving dimensions on a cross section.

4. Also for Portland cement, concrete of Portland cement, and ditto used in lieu of mortar. In like manner specify for Roman cement, and its applications; and common mortar of chalk and hydraulic limestone. 5. Specify for a timber bridge to carry either road or railway, adding a statement of the different specifications of the driving of bearing piles; add for the creosoting and painting of the timber.

6. Draw a plan of a course of aisler, showing each stone, and, by descriptive words, lines, and dimensions, indicate all that is required for god workmanship; the courses are from 15 to 18 inches in thickness; set down also, in dotted lines, the position and dimensions of the aisler stones, in the course immediately beneath; the front aisler is backed by rubble masonry. A section of about three courses will also be necessary, the back of the wall to be vertical, the front having a batter of one inch to a foot, the wall being 7 feet thick.

7. Draw a vertical section of a dry stone boundary wall with coping set in mortar, as for the fencing of the site of a reservoir, and show by a sketch in elevation how best it may be carried over a small stream running in a depression of 6 to 8 feet in depth. Also a section of a boundary wall 12 feet in height, all set in mortar, in each case describing in words such particulars as cannot be defined by a drawing, and write a specification of each wall.

8. An embankment for an impounding reservoir, erected across the valley in which a stream to be stored up flows, is 600 feet long and 70 feet in total height at the deepest part. Describe fully the mode of constructing the bank, mentioning all the accessories required for its safe and efficient working, with a transverse section and plan for reference. State the present system of taking off the supply, and the reason for its adoption; and mention the practical method of dealing with the volume of the stream during the construction of the embankment.

9. If compensation in water is to be provided, state the various proportions of the total quantity impounded which are usually assigned, and the methods of providing it; also the mode of testing the quantity delivered to mill owners and riparian proprietors down stream.

10. Give a plan, showing the arrangement of the filter beds for preparing water for domestic use after leaving the store reservoir; mention all the accessories necessary to the complete working of the beds, with a vertical section of the filtering material, and from the rule for the number of gallons per diem which can pass through each square yard of

filtering surface, deduce the total area required to be under operation for a daily supply of 17,000,000 gallons.

11. Give a plan of a screen chamber and a vertical section, with detailed description of the screens, &c., showing such arrangements as will enable an uninterrupted supply to be sent down during repairs or examination of the whole or any part of the equipment of the chamber.

12. If the depth of water flowing over a measuring outfall be increased from 3 inches to 5, compute the increase of the discharge in cubic feet per minute, the length being 10 feet, and draw a cross section of the overfall usually employed for gauging?

13. If the discharge at 3 inches depth in the last question were required to be doubled, what would now be the depth over the sides, and what the number of gallons per day passing down?

14. What is the increased discharge by adding inches to the diameter of a pipe 33 inches in diameter, the fall in each case being 20 feet per mile?

15. Describe and sketch the various different methods of jointing castiron pipes for conveying water under pressure, giving the longitudinal section at the joint; and state the comparative value of each, and the position in which severally they may be advantageously adopted.

16. In the design for a wrought-iron girder, having a clear span of 76 feet, and parallel top and bottom flanges; it is required that the intended uniform load, of 1 tons per foot, should not produce a greater strain than 3 tons per square inch on the upper, and 4 tons per square inch on the lower flange, and at the same time the deflection at the centre, with the above load, is not to exceed 0.912 inch. Calculate the depth the girder must have to meet this last condition, and give a transverse section of the beam at the centre, at one-fourth of the span, and at the bearing, showing, in figures, the dimensions of the top and bottom flanges and the details of the plating, riveting, and connexions with the vertical web, which is to be formed of plates, and the details of the beam at the bearing at each abutment.

17. What general relation between the deflection span and depth may be traced in beams whose flanges are strained as in question No. I? And by it determine at once the deflection of a girder / feet span, h feet depth, and having in the bottom flange a strain of 4ğ tons, and in the upper 3 tons per square inch.

18. A wrought-iron beam 22 feet in clear span supports a vertical cast-iron pillar, the axis of which is 7 feet from one abutment; the pillar is computed to carry 36 tons, and rests on the upper flange of the beam by a base 14 inches square; at this point the beam is 2 feet 6 inches in depth. Compute the total strain in the flanges at this point from this load so applied, and give a detailed sketch of the transverse section at the part where the column rests on the beam; and also a suitable elevation of it, including the bearing at each wall.

19. Draw a diagram exhibiting the shearing strains developed in the girder in No. 18, giving the proof of its applicability, and compute the necessary transverse area to resist shearing at each end of the clear span.

Draw also a diagram, showing the horizontal strains in this beam, No. 18, and give the proof of it. At what point in the shorter segment

is the horizontal strain the same as that at 4 feet from the wall in the longer segment; in each case giving a proof that the forces are represented by the diagram.

20. Design a cast-iron beam, in lieu of that of wrought iron, mentioned in No. 18, and having the same load applied at the same point, using 4 as a coefficient of safety.

21. Design a cast-iron pillar to carry the load, as in No. 18, with 6 as a coefficient of safety. The height of the column is required to be 16 feet, and the top of it adapted to carry the ends of cast-iron beams and another pillar resting on it.

22. Draw up a specification for material and workmanship in the above wrought-iron girder, and a specification for the girder and pillar of cast iron, Nos. 20, 21, omitting all adjectives such as "best quality," &c., and "according to the drawings," &c., noting only the workmanship and material.

23. The floor of a corn warehouse is supported by beams of American led pine timber 18 feet in clear span and 13 inches deep by 10 inches wide, spaced 8 feet apart, centres. What depth of corn, weighing 60 lbs. per bushel, may be placed on these floors, using in the computation the constant 145 (E. Clark's Experiments), and taking 4 as the coefficient of safety.

24. Compute the weight (either the total weight, or weight per 8 feet of length) of the flooring in the last question, the area being 18 feet wide and 56 feet long; the main beams, having a bearing of 18 inches on each wall, are crossed by joists 9" by 2", placed I foot apart centres, the boarding being I inch thick. Allow, in addition, 2 per cent. for bridg ing, overlap of joints, nails, hoop iron, tounging, &c.

25. Describe fully the experiments on timber (E. Clark) which have led to the constant in No. 23, and the manner of deducing it. What reason may be adduced to account for this constant differing from that of Barlow ?

26. Describe also the experiments of the same author on the deflection of timber, and arrive at the constant for that of red pine, the observed deflection being 0 13 inch per ton laid on; and assuming that the deflection of a beam uniformly loaded is five-eighths of that arising from the same load applied at the centre, compute the deflection of the beams in No. 23, when loaded with the depth of corn, as determined by the answer to that question.

27. Give the details of the construction of the Dock walls at Great Grimsby docks, and point out their appropriateness to the nature of the site.

28. Show that the results of the experiments on retaining walls at Kingstown coincide with the usual formula for the thickness of walls vertical in the elevation and at the back, and with the earth filling on the level of the top of the wall. On what theorem as to the friction of bodies resting on an inclined plane is that formula based, and give a proof of the theorem by a geometrical construction, and point out its place in the deduction of the formula for the thickness of vertical walls.

29. Describe the best construction for a coffer-dam in a tidal river, on rock which crosses the course of the stream and must be removed for the improvement of the navigation.

30. State the particular circumstances of the locality at the site of the coffer-dam at Great Grimsby docks, and the improvements introduced in its construction by Mr. Rendel, and describe the dams abutting on the shore at each end of the coffer-dam.

SCHOOL OF

ENGINEERING.

MIDDLE AND JUNIOR CLASSES.

MECHANICS AND HYDROSTATICS.

MR. GALBRAITH.

1. Investigate the position of the centre of gravity of a quadrilateral, two of whose sides are parallel.

2. Define moment of inertia, and show the relation which exists between the moments round parallel axes.

3. Find the moment of inertia of a plane triangle round an axis in its own plane, and passing through the vertex.

4, Define angular velocity, and prove the equations

5. Prove that y, the acceleration of angular velocity, is expressed as follows:

6. Define centrifugal force; express it in terms of the velocity and radius, and also in terms of the periodic time and radius.

7. Calculate the pressure against the outer rail of a curve whose radius is one-eighth of a mile, the weight of locomotive being 15 tons, and the rate of travelling 40 miles an hour.

8. A cylindrical vessel, 10 feet in diameter, and 19 feet high, is filled with water: calculate the total pressure against the cylindrical part, and show the points of application of the resultant pressure.

9. A plane triangle is immersed in water, one side coinciding with the surface; find the position of the centre of pressure.

IC. A sphere, 10 feet in diameter, is filled with gas whose specific gravity is 0.512; calculate the weight in lbs. of the gas, if its temperature be 140° F. and pressure 31 inches. Convert the data into equivalent metric values, and from them calculate the weight in kilograms.

MIDDLE CLASS.

OPTICS.

1. Deduce from first principles the expression for the deviation of a ray of light in passing nearly perpendicularly through a thin prism.

2. How is this expression used in order to find the expression for the deviation in passing through a thin lens?

3. Define the centre of a lens, and show how its position may be found.

4. What is meant by the words, focus, conjugate focus, real focus, virtual focus, and show the different methods for connecting together the positions of the conjugate foci of a thin lens.

5. Explain the principle on which the pocket lens assists the eye in examining small objects; express its magnifying power.

6. Explain the terms, dispersion and achromatism. How is dispersive power measured, and how may an achromatic combination of two thin lenses be made?

2. Find, by aid of logarithms, a third proportional to (127) and

72.34. 8.39

3. The sides of a triangle are 483·976 and 541°83, and the contained angle is 37° 41' 30", determine its area.

6. Find, by Mac Laurin's theorem, the three first terms in the expansion of tan x in a series of ascending powers of x.