Each Candidate is expected, on entering the Examination room, to proceed immediately to the seat that may be assigned to him; to maintain quiet and silence; to address himself only to the Moderators in case he may require explanation or assistance; and to conform to their arrangements. Answers are to be written only on one side of the paper. A margin of about one inch is to be left on the lefthand side of each page; and the answer to each question is to be begun at the top of a fresh page. The division and number of each question is to be written in the margin opposite the first line of the answer upon each page employed. The Candidate's number is to be put at the corresponding bottom corner of each page. The papers of answers are to be delivered in half sheets with the papers of questions to the Moderators, who will fasten them together, attach their own signs on the right hand top corner, and remove the numbers put by the Candidates. A larger number of questions has been given than it is expected the Candidates can answer in the time allotted. This is done in order that they may have the advantage of selection; and the Examiners wish to impress most earnestly upon the Candidates the necessity of attending to the correctness of the answers, rather than to the number of them. The mathematical subjects must be strictly worked out; the propositions from Euclid and the riders are to be considered as distinct questions, and are to be answered separately. It is not necessary that the questions in Physics, Professional Practice, and Materials should be worked out, in detail, further than is requisite to show that the Candidate has a competent knowledge of the subject; but mere indication of the rule will not be a sufficient answer. It must be clearly understood that the Examiners wish to develope and recognize what the Candidates do fairly know, and not to try and throw difficulties and perplexities in their way. CLASS OF PROFICIENCY. FIRST DAY.-MORNING AND AFTERNOON. DESIGN AND DRAWING. The grand staircase, to a public building, contained in a hall 60 feet by 40 feet; the ground story 25 feet, and the upper 15 feet, high from top of floor to top of floor; the length of tread to be not less than 8 feet. To be in the style which the Candidate has selected; and to be drawn (in pencil will be sufficient) not sketched to a scale of a quarter of an inch to a foot: no colour except Indian ink is to be used. The drawings to consist of at least one plan, and two sections, shewing roof, windows, and other necessary features. The details of construction will be required to be drawn on a subsequent day to larger scales. The Staircase itself is to be considered the important part of the design, and to be carefully studied. SECOND DAY.-MORNING. MATHEMATICS. Arithmetic. N.B. The French mètre is 39-3708 English inches, or 3.2809 English feet. The Tuscan braccio is 22.98 English inches; and the Roman palm 8·796 English inches. 1. Extract the square roots of 443556; of 603729; of 6 to four places of decimals; and of 60 to the same. 2. The usual approximation of French to English measures is to call the mètre 3 ft. 3 in.; how far does this differ from the true decimal? 3. Being unexpectedly called on to measure a length of park wall, and obliged to borrow a 50 ft. tape for the purpose, the length comes out 1510 feet. On bringing home, and proving, the tape, it is found to be 1 inch ths too long; what is the true length when corrected? 4. If 24 navigators can excavate a large foundation in 6 days, when they can work 12 hours a day; in what time can 30 perform the same work in winter, when they can only work 8 hours a day? 5. An Italian architectural work states that a church measures 212 braccia in length; another gives the same length as 545 Roman palms; what is the difference between the two statements? 6. Calculate the following claim against a Railway Company, and write out the same fair as if to be delivered to the umpire. (1.) A ground rent of £12. per annum for 5 years. The reversion to the rack rent of £120. per annum in perpetuity after such term. Less:-15 per cent. for losses, repairs, collection, &c. N.B.-Take the tabular value of the ground rent for the 5 years at 4.579 years purchase; and that of the reversion to the house on the 6 per cent. tables at 16-666 years purchase, less 4.212 years purchase for the outstanding term. (2.) A piece of freehold ground fit for building on immediately, 1240 feet frontage, at 7 shillings per foot per annum, allowing 2 years of rent at a peppercorn and 6 years to cover. N.B.—Take the building ground at 25 years purchase, less 4-452 years purchase, being the deferred period of the peppercorn and 3 years (the mean of 6) to cover. Add 15 per cent. for compulsory sale. Add also your own commission on the whole valuation at 1 per cent. on the first £1000, and per cent. on the remainder. Algebra. 1. Add together (a + b) x + (b + c) y, and (a − b) x − (b − c) y ; also subtract the same from the same, and explain the rule relating to minus brackets. 2. Divide a3 + b3 + c3 — 3 a b c by a+b+c in the ordinary manner, and shew how the same may be done by brackets. 5. An architect invests £6000. for a lady in two mortgages, one at 4 per cent., and one at 5 per cent. He is in the country, and the deeds are with her solicitor, and she wishes to know the amounts of each mortgage separately. She receives as interest £264. per annum in all; what are the respective sums invested? 6. An architect has a large quantity of walling to execute, and finds he has funds enough at command if the same can be done for £14. per rod. If the work be of stone wholly it will cost £20. per rod; if of brick wholly it may be done for £12. per rod. If he uses brick faced with stone; how much of the latter may be used in proportion to the former to bring the work to the prescribed £14. per rod. Euclid. Book 1. 1. What are the definitions of a square, oblong, rhombus, rhomboid, and trapezium? 2. Prop. 5.-Theorem. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles on the opposite site of the base shall be equal. Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44.-Problem. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Book 2. 5. What is the definition of the gnomon of a parallelogram? 6. Prop. 12. Theorem. In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 7. Prop. 14.-Theorem. To describe a square equal to a given rectilineal figure. SECOND DAY.-AFTERNOON. PRACTICAL GEOMETRICAL DRAWING. 1. Assume two lines, and draw a third proportional thereto. 2. Divide a line (say 6 inches long) into thirteen parts by one geometrical operation. 3. The diagram, fig. 1, in the margin represents two fields A and B with an irregular boundary between them; enlarge the same to four times the scale; and draw, with a parallel ruler only, without compasses, an equalizing, or give and take line, so that the boundary between the two fields may be straight, and each have the same contents as at present. 4. Lay down the dimensions on the margin half inch to the foot, and find the centres and draw a four-centred gothic arch, as fig. 2, the circles being tangents to A B, B C, and the curves continuous. 5. In designing some geometrical windows with circles in the heads of the tracery, it is determined to place in one a cinque-foil, and in another three equal and similar pear-shaped figures, find the centres, and draw the cuspings. 6. How are the lines found for the voussoir joints to a true elliptical arch? MENSURATION. 1. The sides of a triangle are 30, 36, and 42 feet, what is the superficial content? 2. The sides of an equilateral triangle measure 4 feet each; those of a square 3 feet each; those of a regular hexagon 2 feet each; a circle girts 12 feet round: what are the respective areas of each of these figures? Shew from this that perimeter is no guide in computing superficial area unless the figure be given. 3. An early English roof is 32 feet span, and rises 27 feet, the collar is half way up the rafter. What are the lengths of the rafters, collars, and king posts, supposing the dimensions given to be outside measure? 27 Ft A 32 F |