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(6) The point F reached by the foot of the embankment, assu

ming the material removed at A to expand 1. th in bulk. N.B.- The point F on the diagranı is purposely misplaced, and

is not to be copied. Attempted by 25 per cent. Although a fair proportion appeared to know the general lines on which the problem ought to be solved, there were not many complete answers. Even where attempts were made to find the mean height of the area of the cross section of the material A, an inaccurate rule was often employed. Q. 26. A piece of sheet material K has a motion determined by the

condition that the two grooves AA, BB cut in it slide over two pins a, b secured to a fixed plate H. Determine the path traced

on H by the point P carried by K. About 55 per cent. attempted this question, but, unfortunately, in probably quite half the cases an entirely wrong locus was obtained, namely, the ellipse which would have been traced on K by P, a point on H, if the pins a and 6 had moved in the slots of K, while the latter remained fixed ; in other words, many students unconsciously altered the conditions of the problem, an indication of careless reading of the question. Q. 27. A shot having 1:5 units of mass strikes a target with a velocity of

1,200109 feet per second, and rebounds with a velocity of 300110° feet per second. The duration of the blow being estimated at ito of a second, the average force F exerted during the impact (that is the rate of change of momentum) is given by the vector equation.

F=1'5 (1,200,00 – 300110-) = 1do

=(180,00010 - 45,000.10) pds. Find F in magnitude and direction. Attempted by only 20 per cent. It is not easy to determine precisely why this question was not more popular ; teachers are in the best position to do this. Possibly the difficulty lies in interpreting the given vector equation. If so the task of removing the obstacle is surely a simple one. But even some of the candidates, who evidently realised that the difference of two vectors was required, failed to apply the simple rule in order to determine this difference. The subject of vectors is one which teachers must endeavour to deal with in a more efficient manner. Q. 28. In a laboratory experiment a polygon with five hinged joints is

constructed out of strips of sheet metal. This link polygon being placed on a drawing board, forces, which can be measured by the springs S, are applied at the corners. If the figure takes the form shown, and the force A measures 2'08 lbs., what would you expect the forces B, C, D, E to measure.

Show the resultant of the three forces E, A, and B.

Let the force scale be } inch to 0:1 lb. Attempted by nearly 49 per cent. This question was only moderately

. well answered. The first part is a very easy problem, requiring the application of the principle of the triangle of forces five times over. Of those who attempted it many drew a separate triangle of forces for each joint of the frame. Of those who solved the first part only a small proportion afterwards determined the line of action of the resultant of the three specified forces, and of these, many drew a new link polygon for the purpose instead of using the given one. The properties of link polygons are not sufficiently studied experimentally. Q. 29. You are given the projections of a piece of wire AB fixed in the

horizontal plane at B.
(a) Find the true length of the wire and the angles the wire

makes with the two planes of projection.
(b) From the elevation project a new plan of the wire on .

answers.

All except three candidates attempted this. There were certainly many most excellent answers; at the same time the number of worthless results was far too large. It is quite clear that owing to unsatisfactoryor ineffective methods of presenting the subject, many of the candidates had never realised what they had to determine when working this type of exercise. The matter is one which uires very serious consideration by teachers. This branch of the subject possesses inherent difficulties, which, however, are easily surmounted by even the less able students if proper methods of teaching are adopted. As the complete mastery of this particular problem delights a student, and often alters his attitude to the subject as a whole, besides giving him power to successfully attack a multitude of other problems, the teacher cannot devote too much time and trouble in seeing that it is intelligently dealt with. Suitable models for measurement by the student should be employed, as specified elsewhere. Q. 30. The figure shows the size and shape of a rectangular box with the

lid open at right angles along the hinge OY, dimensions parallel O Y and O2 being set off full size, and parallel to OX half size. (a) Draw an end elevation of the box with the lid open at 60°,

that is an elevation on a vertical plane parallel to

20X. (6) From the elevation project a plan. (c) From the plan project a new elevation on a vertical plane

which makes 45° with the first vertical plane. N.B.—The pictorial view is not to be copied, but dimensions

are to be measured from it. Attempted by about 72 per cent. As the question presented no difficulties, from its very nature, there was a large proportion of satisfactory

As in the Stage 1 papers, the thickness and depth of the box were often not shown in the two elevations, while the height of the lid was frequently drawn one-half the correct height. Q. 31. A coal scuttle (with parts omitted) is shown. Draw a plan pro

jected from À A.

Draw a development of the cylindrical part AA of the scuttle,

omitting the curve where it intersects the conical foot. Attempted by 50 per cent. The proportion of correct and carefully executed solutions was rather small, though the method of obtaining both plan and development seemed to be generally understood. Q. 32. You are given a map of a portion of Snowden to a scale of one

inch to the mile, contoured in feet above sea level, and showing the line of the railway from Llanberis station to the summit of the mountain. By means of tracing paper and a pricker, or otherwise, measure the length of the railway. If the average slope of the line is 1 foot rise in x feet of length, what is x? Where is the railway steepest, and what is its inclination to the horizontal at this place?

A curve CC is begun, showing the height MP above sea level of any point P on the railway, distant O M miles from Llanberis station as measured along the railway line on the map. Com

plete this curve. About 40 per cent. attempted this question. Some very satisfactory answers were given in response to the first part of the question. In completing the curve CC showing the height of any point on the line, many candidates appeared to consider it sufficient to plot the heights of a few points, e.g., the stations, and then to draw a fair curve through these ; curves obtained in this way showed only very inadequately the varying slope of the railway. Q. 33. A star in the north has an angular elevation of 30° above the

horizon, and one in the south-east an elevation of 60°. Deter. mine the plane containing the stars and the spectator, and measure its inclination to the horizontal, and the direction in degrees north of east of the lines of steepest slope up the plane. About 12 per cent. attempted this, and almost invariably the answers were correct. The candidates choosing this were clearly those who thoroughly understood their work, for as a rule they were successful in attacking the other questions which they selected.

Report on the Examination in Machine Construction

and Drawing

STAGE 1. Results : 1st Class, 1,718 ; 2nd Class, 1,724 ; Failed, 1,706 ; Total, 5,148.

The number of candidates in this stage was 5,148, being about 41 per cent. greater than in 1905. The quality of the work was equal to that of recent years, and in many schools was excellent. But there are still far too many instances of schools in which the teaching, is evidently of the most slipshod character. In these cases the work is rough and untidy; the candidates are unable to draw correctly the simplest of machine details such as nuts or keys, they cannot insert dimensions properly, do not understand the meaning of section lines, and sometimes are ignorant of projection. Candidates so taught are quite unfitted to proceed to the higher stages of the subject. To remedy this, copies should be sparingly used in class, the efforts of the students being directed rather to the sketching and drawing of actual machine details, a collection of which should be procurable from manufacturers in the neighbourhood, and the work should be confined to simple fastenings and the like, until these can be neatly and accurately represented. Some detailed criticisms of the work in Stage 1 now follow.

TRACING.
Trace in ink on the tracing paper supplied the eye-bolt shown on

Diagram X. Insert the dimensions and print the title as shown.
The lines should be very black, of uniform and moderate width,

and as continuous as possible. On the whole the tracing was well executed, but many candidates used weak ink or drew fine lines, showing that they had not been taught the requirements for printing purposes. Others wasted time by first drawing the copy in pencil and then tracing that instead of the original drawing. A few did the tracing by freehand or in pencil and in consequence received no credit for this portion of their work.

Example 1.

1 -INCH BEARING. The diagram gives dimensioned hand-sketches of details of a simple bearing. Draw full size, inserting dimensions :(a) An elevation corresponding with A, but in section, adding

the cap and one of the į" studs. (6) An elevation, projected from (a), looking on the face indicated by the arrow.

In this view the cap, cap screws, and the studs should be shown. (c) A plan. N.B.-Do not draw the pictorial view, nor the parts separated as

in the diagram. Dotted lines, representing hidden parts, are not

required. This example was the one generally chosen, and in a large number of schools the work was uniformly good, with very few failures, and more than half the candidates passing in the first class. In many cases, however, and in some schools throughout, bad work was prevalent, the teaching being evidently most faulty. Thus, soft blunt pencils were used ; centre lines were omitted or erased ; dimension lines were too frequently placed close up to the main lines of the drawing, or were crowded together, or the written figures were small and scarcely legible. Again, many candidates have very hazy notions about the use of section lines. It was quite common to find a view, otherwise good, spoiled by being completely covered by such lines, like a flat wash over an elevation. And it was quite as common to find a view ruined by some such muddle of cross hatching as could conceivably be obtained by taking a number of part section planes, one behind the other. But perhaps the most striking evidence of defective teaching

seen in the many grotesque attempts to insert the the stud. Too many candidates lost marks by drawing the plan out of projection, and occasionally the example was cancelled because the views were scattered over the sheet'in defiance of the rules of projection. The plotting of dimensions to scale was good throughout.

was

Alternative Example 2.
END OF A CONNECTING-LINK OF AN AIR COMPRESSOR.
Make full size separate scale drawings of details, with dimensions
as follows :-
(a) A longitudinal and an end view of the rod end A. The

screw thread may be drawn in the manner shown.
(6) Three views of the nut B.
(c) Three views of the wedge C.

(d) Three views of the head D.
N.B.-No credit will be given for drawing the parts assembled,

as in the diagram. Dotted lines, representing hidden parts, are

not required. When this example was selected, which was comparatively seldom, it was generally taken by the better candidates, and so was often well done. What failures occurred were for the most part attributable to the candidates ignoring the very clear instructions and drawing the parts assembled as in the diagram, and not in separate detail, as required.

a

Questions, only two to be answered.
The Sketches in answer to these questions should be drawn freehand

on the squared foolscap paper, the lines on which may be taken as

4-inch apart. Good use was made of the squared paper, and it was satisfactory to find that freehand sketching was almost universal. Q. 11. Sketch full size, inserting dimensions, two views of a wheel boss,

fixed to a shaft by means of a sunk gib key, as follows :-
Diameter of shaft

2"
Diameter of boss

4"
Length of boss
Width of key
Depth of key

Taper of key, }" per foot. This question was fairly well answered. The two principal defects were in making the key way extend only part way through the wheel, and in not extending it in the shaft a sufficient distance to allow of the insertion or withdrawal of the key. Q. 12. Name the materials of which the parts of Example 1, and

the several parts A, B, C, D, E and F of Example 2 would be

constructed. This question was also frequently well answered, but occasionally most unsuitable materials were named, such as cast iron for the rod end or for the bolt.

Q. 13. Sketch full size, inserting dimensions, a l" rag bolt or Lewis

bolt, suitable for securing the frame of a machine to a stone

foundation. Explain how the bolt is fixed in the stone. Very few really good sketches were received. Bad proportions were the rule. The hole in the stone was often parallel, and when undercut it might be too small at the top to allow of the insertion of the bolt. Moreover, the nut was often shown screwed down on to the top of the lead tilling, showing no room for a flange. Q. 14. Explain briefly, with sketches, how you would set out, drill, and

tap the hole marked H in Example 1, on the diagram. Candidates had not much power of description, though it was evident that many had used a drilling machine. Few, however, employed the holes in the cap for marking out the required tapping holes. Q. 15. Sketch in section the armature of a small drum wound motor,

showing clearly how the stampings are secured. This question was seldom attempted, indicating that a knowledge of electrical work is not very common.

STAGE 2. Results : 1st Class, 671 ; 2nd Class, 1,669 ; Failed, 1,474 ; Total, 3,814.

The work sent in showed clearly that the students had not sufficiently sketched from actual machine parts. There has been too much working from copies. Much better work would result if copies were banished altogether from the course of instructiсn and their place taken by actual machine details, even of the simplest kind. This method of working would improve the freehand sketching, would cultivate the habit of reading a drawing correctly, and would train the student to observe details and machinery of every kind and description.

The quality of the drawing was generally poor. Clumsy lines, the result of a blunt pencil, and the bad joining up of curves to lines were persistent features of the work. The tracing was, however, fairly well done.

Example 3, Diagram Y.

ADJUSTABLE FOOTSTEP BEARING.
Draw to scale and complete the two projections partly shown in

Diagram Y. Example 3, and also draw a vertical section through
line E F, correctly projected, looking in the direction of the arrow

marked G. Scale, size. No dotted lines need be shown and figured dimensions need not be

inserted. A large proportion of candidates who tried this example failed to realize the real arrangement of the footstep, bearing from the views given, and did little more than set out to scale the views given on the diagram. There were some notable exceptions, however, in which the views were correctly drawn, sectioned, and lined in neatly.

Alternative Example 4, Diagram Y.

LIFT VALVE.
Draw, full size, an outside view corresponding to the vertical

section shown in Example 4, Diagram Y. Draw also a sectional
plan through line C D, with the spindle K removed. Finally draw
a sectional elevation taken through the centre line, looking in the

direction of the arrow marked H.
Also make a plan and the two end elevations of the spindle marked

K, all the necessary dimensions being shown on it.
Seale, full size.
No dotted lines need be shown and figured dimensions need not be

inserted in the three first views.

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