=

sentative crank. Interpretation of the expression = a sin (w + a) or = a sin (a). Plotting the curve of sines from given data. Vectors; meaning of the symbols +, when applied to vectors, and of such expressions as A+ B, A B+ C, A B+CD, etc. Verification by drawing of the bracket law as expressed by the equation A- (B - C) = A − B + C. Meaning of the scalar product of two vectors, with illustrations.

The link polygon. Experimental illustration by means of cords and weights; verification by drawing of the relations which exist between the weights, the form taken by the chord, and the tensions in the segments of the chord. Conditions of equilibrium of a set of forces (the force polygon and the link polygon must be closed).

SOLID GEOMETRY.

General problems on lines and planes, with applications. Their intersections; the angles between them; parallel and perpendicular lines and planes. Alteration of the ground line.

Problems on trihedral angles and spherical triangles, with applications. The regular tetrahedron and octahedron, the sphere, right circular cylinder, and cones. Plans, elevations, and sections of these solids singly or in combination.

To draw the projection of a solid of known form, having given the projections of three of its edges, by applying the principle that parallel lines project into parallel lines, all to the same scale. In this problem the projection is not necessarily orthographic.

The perspective projection of the cube, prism, pyramid, and right circular cone and cylinder, singly or grouped, in simple upright positions. Meaning of such terms as picture plane, point of sight, centre of vision, vanishing point.

HONOURS.

The examination in Honours will be divided into two parts, which cannot both be taken in one year, and no candidate who has not been successful in Part I. (or in Honours prior to the division of Honours into parts) can be examined in Part II. A certificate or medal will only be given when a success in Part II.has been obtained.

PART I.

Candidates must have an intimate acquaintance with the portions of the subject enumerated in the Elementary and Advanced Stages. Questions in the following subjects will also be set :

PLANE GEOMETRY.

Cycloidal and trochoidal curves. The involute of the circle. Tangent, normal, and circle of curvature at any point. Envelopes. Setting out the forms of wheel teeth.

The Archimedian and Logarithmic spirals. The Ionic volute. The setting out of the profiles of cams for mechanisms in which a given motion is required to be obtained.

Additional examples of simple vibration. Easy problems relating to the motion of the slide valve of a steam engine. To compound two simple vibrations of the same period and in parallel directions by adding their representative cranks or vectors. Applications to electrical problems and the motions of machines. The locus of a point whose motion consists of two simple vibrations of the same or different periods in directions inclined to one another.

Plane motions in mechanisms. Instantaneous centre of rotation. Diagrams of velocity and acceleration. Degrees of freedom in plane motions. Vectors. Further applications of the link polygon. Determination of centre of gravity, moment of inertia, and radius of gyration. Co-planar

forces resolved along three given lines. Form of equilibrium of flexible cord or suspension chain under given conditions of loading.

SOLID GEOMETRY.

General problems on the line and plane.

The geometrical solids previcusly enumerated, and solids of revolution of any form. Their projections and sections in various positions and in contact. Simple examples of tangent planes to them. Their interpretations. Developments of their surfaces (when possible), with applications to sheet metal work. Simple cases of their cast shadows, the rays of light being parallel. The perspective projection of these solids in various positions, and of simple buildings or other objects.

PART II.

Questions will be set in the following subjects, in addition to those previously indicated:

Problems relating to the paths, velocities, and accelerations, linear and angular, that occur in the parts of machines such as steam engines, turbines, centrifugal pumps, etc. Straining actions due to such motions. Balancing of machines.

Complex motions in machines analysed and expressed in Fourier series. Special cases, such as valve gears, in which the motion consists approximately of a fundamental simple vibration with a small superposed octave. Diagrams for such cases. Analogous problems in electrical work. Beats. Problems on the general case of motion of a body in space. Degrees of freedom.

Problems on the general case of a system of forces in space. Reduction to two perpendicular forces, and to a single force along the central axis, together with the minimum couple. Braced frames in three dimensions. Simple cases of equipotential lines and surfaces, and of lines of force. Line of resistance in arches and masonry structures. Diagrams of bending moment in metal and masonry arches. Fuller's diagram.

The projections of helical surfaces, including screw threads, spiral springs, and propeller blades.

The use of contours in problems relating to irregularly curved surfaces, such as those of earthworks, ships, etc.

The nature of the curvature of any surface. Euler's Theorem. The ellipsoid. The hyperboloid of revolution and skew bevel wheels. Other Quadric surfaces.

Approximate constructions for sheet metal work for surfaces not developable.

SUBJECT II.-MACHINE CONSTRUCTION AND DRAWING.

(Under revision for 1902–1903.)

This subject includes a knowledge of the form of the parts of machines, the physical characteristics of the materials used in machine construction, the various workshop processes employed in giving the materials the required shape and size, the magnitude of the straining actions to which they are exposed, and the methods of estimating the dimensions necessary to withstand those straining actions.

In addition to this knowledge, the possession of which may be shown by means of written descriptions, freehand sketches and calculations, a candidate for examination in this subject will be required to be able to draw neatly to scale, the whole or part of a machine either from dimensioned sketches, by measurement of an actual machine or model, or from his own design.

In future, examples of parts of Dynamo Machines and Motors may be dealt with in this examination.

ELEMENTARY STAGE.

A candidate will be required to draw in simple or orthographic projection neatly in pencil to a given scale, two or more views (sectional or outside), of a simple portion of a machine in common use. The sketches from which the drawings are to be produced will be given. They will in general be incomplete, and be drawn purposely somewhat out of proportion, and the candidate will be required to set off, correctly to scale, dimensions, some of which are given on the view he is drawing, the remainder being obtained from the other views. He will be expected to add parts which are omitted from some of the sketches but shown in shape and size in others. He will further be expected to draw from his own knowledge the fastenings which are suitable for connecting together the machine parts which are the subject of the example, and, in sectional views, to draw lines neatly by freehand to indicate parts cut by the planes of section, taking care to slope the lines on all the parts of the same piece in the same direction, and of contiguous pieces in directions or characters which differ from one another.

In some cases an additional new view (outside or sectional), which is not shown in the sketches will be required to be drawn, and details which are shown in separate detached sketches will be required to be inserted in their proper places in the general drawing.

The various views required must be placed in position so as to project from one another in order to show that the candidate appreciates the fact that he is producing a representation of a solid piece of machinery and not merely copying a sketch. No credit whatever will be given unless the candidate shows some knowledge of projection by drawing two views of at least one subject in their proper relative situations.

Teachers are enjoined not to rely too much on drawings in giving instruction to their classes, but to make use also of actual simple machine parts or models of them.

It is desirable that centre lines should be shown distinctly, and the parts of other lines continued too far, and not needed in the finished drawing, should be rubbed out.

The usual Drawing Office procedure is to keep drawings in pencil, to make tracings in ink, and to photograph these tracings. It is easy to alter the pencil drawing and take new tracings. Students will, therefore, in their classes make only pencil drawings on white paper, and in the 1902 examination and afterwards they will be required to make an ink tracing of a portion of a drawing, the lines being very uniform, with no visible discontinuities where straight lines and arcs of circles touch or proceed from one another. In some offices, it is the practice to have all lines in a tracing fairly thick and of exactly the same thickness. In other offices, lines of two and only two thicknesses are used in the same tracing. In no case ought very thin lines to be employed. It is quite easy to get beginners into. the habit of producing tracings such as would be respected by workmen in the shops.

The following list of examples which have been set in previous years will give a general indication of what may be expected and prepared for :

PARTS OF AN ENGINE. Piston. Hydraulic piston and plunger. Piston rod end and guide block. Cross-head. Connecting-rod. Crank-shaft. Eccentric and rod. Valve-rod end. Spring-loaded steam-valve. Guide bracket for slide-valve rod. Simple form of loaded governor.

PARTS OF A BOILER.-Gusset-stay. Mud-hole door. Water-gauge cock Simple feed-pump.

PORTIONS OF MACHINE TOOLS.-Fast headstock and spindle of a lathe. Tumbler bearing and bracket for the back shaft of a long lathe. Rest for a hand-tool for a lathe. Jaw of a dog-chuck for a lathe. Quadrant for carrying chauge-wheels for a lathe. Ram of a slotting machine. Parallel-jaw vice. MILL WORK. Footstep-bearing for an upright shaft. Joint for segments of large spur-wheel. Bearing for turbine shaft. Wall bracket. GENERAL FITTINGS.-Hooke's coupling. Hydraulic pipe-joint. Union joint.

Ball-bearing for a tricycle.

BESIDES MAKING DRAWINGS, CANDIDATES WILL BE REQUIRED TO ANSWER SOME OF A NUMBER OF QUESTIONS ON MACHINE CONSTRUCTION, and illustrate those answers by sketches. Unless specially instructed to the contrary the sketches should be drawn freehand. The capability of making freehand sketches of parts of machines from memory is of the greatest value to an engineer, and when the sketches are drawn to a tolerable proportion they will be estimated by the examiners at at least as high a value as those drawn more accurately by means of instruments with a much larger expenditure of time.

The details of this portion of the subject may be classified as follows:THE FORMATION OF THE PARTS OF MACHINES WHICH ARE IN MOVING CONTACT:

Constructions suitable to permit of TURNING and SWINGING motions.

Simplest form without special means for refitting after wear, as in fork or knuckle-joint. Use of bushes to facilitate renewal after wear. Use of steps or brasses with caps to facilitate adjustment of the cylindrical surface for wear in one direction. Methods of preventing end motion by pin and groove, collars and recesses as in shafts and eccentric-straps and by simple forms of footstep and pivot bearings.

Method of providing cylindrical an 1 end adjustment together by the use of cones as in lathe.

Constructions suitable for SLIDING motions. Forms of cross section employed for piston-rod guides and in the lathe, planing, shaping, drilling and slotting machines.

HELICAL OR SCREW MOTION.-Construction of a helical curve. Meaning of the terms pitch and angle of thread.

SURFACES SUITABLE FOR ROLLING CONTACT.-Cylinders, frustums of cones and spheres.

SURFACES FOR A COMBINATION OF ROLLING AND SLIDING CONTACT. --Elementary information relative to the forms of spur and bevel wheels. CONSTRUCTIONS TO PERMIT OF THE APPLICATION OF THE URGING FORCES AND THE WORKING RESISTANCES TO THE MOVING PARTS AND THE REGULATION OF THOSE FORCES.

FOR THE APPLICATION OF PUSHING FORCES by means of steam, air or water pressure :Simple forms of pistons, plungers, and stuffing boxes. Use of leather in hydraulic work. Simple forms of slide, lift, and screw-down valves, and two-way turn cocks.

FOR THE APPLICATION OF PULLING FORCES by means of belts and ropes --Forms of pulleys of simple construction with radial and curved arms. Forms of periphery to retain belt or rope by rims, barrel-shaped surface and grooves, also by the use of forked guides. Methods of connecting the ends of a belt or rope.

Use of an idle or loose pulley and shifting fork for the purpose of ceasing the pulling force.

METHOD OF CONSTRUCTION OF THE PORTIONS OF A MACHINE IN PARTS TO FACILITATE THE MANUFACTURE AND REFITTING AFTER WEAR, AND THE USE OF FASTENINGS TO JOIN THE PARTS TOGETHER :-

BY THE USE OF RIVETS :-Forms of Rivets. Junction of plates by single and double riveting in chain and zigzag with lap and butt joints Process of closing the rivet, and caulking the joint. Use of iron and steel of angle, tee, and channe! sections to strengthen and stiffen plates, and to unite plates. BY THE USE OF SCREWS.-Bolts with various forms of heads and nuts. Studs and screws. Use of washers. The Whitworth and square form of screw threads. Raised threads. Right and left-handed threads. Method of preventing nuts from working loose. Prevention of bolts from turning when screwing up the nut. Forms of spanners.

BY THE USE OF COTTERS.-Draw of cotter and clearance. Use of gib. Methods of preventing cotters from working loose.

BY THE USE OF KEYS.-Sunk saddle, and feather keys. Methods of withdrawing keys.

METHODS OF CONSTRUCTION BY PARTS OF THE FOLLOWING PORTIONS OF MACHINES:

THE FRAME OF A MACHINE.-Use of chipping strips when two or more parts of a frame have to be united. Simple forms of pedestals, and methods of securing them to frame. Simple forms of hangers, brackets, and wall boxes, the structure of the building itself being a part of the frame. Methods of securing frames to foundations.

Elementary knowledge of the construction of a boiler and the necessary fittings. Gusset and bar stays. Methods of making the joints of pipes for conveying steam and water under pressure. Flange, socket, and union joints. Use of a centring ring in a cylinder cover.

THE PRIMARY PIECES OF A MACHINE.-Connection of the parts of a shaft. Crank-pin to crank-arm and arm to shaft. Box and flange couplings. Connection of the two parts of an eccentric sheave. Meaning of terms eccentric radius and travel of valve. Connection of the parts of sliding pieces. Piston to rod, rod to crosshead or guide block, and slide-valve to valve-rod.

SECONDARY PIECES.-Parts of a connecting-rod. Construction of an eccentric-strap and rod.

PHYSICAL CHARACTERISTICS OF THE COMMON MATERIALS USED IN MACHINE CONSTRUCTION.-Elementary information as to the relative strength, durability under wear, resistance to corrosion, and capability of being cast or forged of iron, steel, brass, and copper. Any question which may be set on the strength and proportions of machine parts will be of a very elementary character.

WORKSHOP PROCESSES.-Elementary information of the processes by which the desired shape is given to machine parts, including the use of the lathe, the planing, shaping, slotting and drilling machines.

ADVANCED STAGE.

Will include all that has been detailed for the Elementary Stage. The example to be drawn to scale will be a piece of machinery of more complicated construction, requiring the candidate to possess more capability of reading drawings; and the greater part of the drawing required will consist of views not shown, but which will have to be deduced from information given in other views; also the candidate may be required to design a portion. A greater facility of execution will be expected to be shown by a larger quantity of drawing of a better finish than for the Elementary Stage.

The following is a list of examples which have been set in some previous years:

PARTS OF AN ENGINE.-Link reversing gear. Regulator-valve. Hydraulic engine. Double-ported slide-valve. Crank-shaft bearing for horizontal engine. Cylinder for corliss-engine.

PARTS OF A BOILER.-Giffard's injector. Safety valve. Double acting

pump.

MILL WORK.-Wall-fixing with shafts and bevel wheels. Collar-bearing for suspended vertical shaft.

GENERAL FITTINGS.-Valve box and valves of pump for charging an hydraulic accumulator.

TO ANSWER THE QUESTIONS a more intimate detailed knowledge of the parts of machines previously enumerated will be required, and of the following in addition :

:

THE FORMATION OF THE PARTS OF MACHINES WHICH ARE IN MOVING CONTACT :

Constructions suitable to permit of TURNING and SWINGING motions. Various forms of the ends of connecting-rod and links. Method of taking up the wear of the brasses of a link so that the length may remain constant. Bearings constructed with complete provision against wear in any direction. Pedestals constructed so that the steps are free to set themselves in true