;

Q. 26. AB is a rod projecting horizontally from A, a point in a wall C is a point in the wall below 4, and D is a point in AB CD is a strut with smooth attachments at C and D. Let a weight W be hung from B; show in a diagram, the forces which keep AB at rest, and draw a triangle for them.

In the particular case when

AC=AD=AB÷2,

show that the thrust of the strut is

2 W √2.

Also find the force tending to pull AB away from the wall, and the line along which it acts.

A few-about ten of the students treated this question well, showing correctly in diagrams the forces and the relations between them. Most of the others failed to treat rightly the action at 4.

Q. 28 A body moves through a distance of 6 ft. and is acted on by a force P, which varies continuously, and has at first a value of 5 lbs.; at the ends of the successive feet its values are 8, 10, 11, 9, 4, 1 lbs. Find the number of foot pounds of work done, and the mean value of P. Illustrate your results by a diagram drawn to scale.

Very few knew Simpson's Rule, and consequently did not get the area of the graph as accurately as the data permitted.

Q. 29. A body slides down a smooth inclined plane, find the acceleration and the pressure on the plane.

If the plane were rough, how would the roughness affect the acceleration? Would the pressure be affected?

Find the acceleration and the pressure on the plane in the case in which the length of the plane is three times its height, and the coefficient of friction is.

Was fairly well done.

Q. 30. Draw a diagram to show all the forces acting upon a marble which moves freely in a horizontal circular tube with uniform acceleration f; taking the marble to weigh 1 oz., and the diameter of the circle to be 1 foot.

If the tube is in a vertical plane and the marble starts from rest at the highest point, find the pressure on the tube when the marble is at its lowest position.

Was seldom well answered.

Q. 31. An inclined plane AB and a point P above it are given. Of all straight lines drawn from P to AB, find that along which the desent is made in the least time.

Let t denote the time in which a body would fall vertically from P to AB, and t, the time down the line of quickest descent; show that

where a denotes the inclination of the plane.

Was fairly well done. However, the first part of the question is to be found in many text books, and the second part does not require much geometry.

Q. 32. Write down and explain the equation of work and kinetic energy. A weight of 2 lbs. falls from a height of 1 foot upon the head of a vertical nail, weighing oz., in a horizontal wooden board, and drives it in inch; find the average resistance of the wood.

Was several times answered approximately, i.e., the mass of the nail was neglected.

9897.

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DIVISION II. (FLUIDS.)

STAGE 1.

Results 1st Class, 39; 2nd Class, 32; Failed, 22; Total, 93.

There were few candidates. Over 50 per cent. were well prepared for the examination.

Q. 10. State Boyle's law and explain the nature of the limitations to which it is subject.

A piston is situated in the middle of a closed cylinder a foot long and there are equal quantities of air on each side of it. The piston is pushed gradually until it is at a distance of 1 inch from one end. Compare the pressures on each side of the piston.

From this question it was evident, as frequently pointed out in these reports, that many candidates did not realize that Boyle's law refers to a given mass, or quantity, of air.

Q. 9. Describe a Nicholson's Hydrometer, and explain how it is used for finding the specific gravity of a solid body.

A Nicholson's Hydrometer is found to sink to the standard point (a) when 720 grains and a certain body P are in the upper pan; (b) when 765 grains are in the upper pan and P in the lower pan. What conclusion can you draw from these data? What more must you know before you can infer the weight of P and its specific gravity?

Q. 11. Explain how the column of mercury in a barometer is supported, and why the column is sometimes higher and sometimes lower.

It is given that the elastic force of the vapour of water at 60° F. equals the pressure of 052 inches of mercury. A barometer stands at 30'15 in. and the temperature is 60° F. Suppose that a little water-enough to occupy about a tenth of an inch of the tube-got into the barometer and came into the vacuum space at the top of the mercury; how would it affect the reading of the barometer, and why? How would the reading be affected if the temperature rose, and how, if it fell?

Q. 12. A tube 61 inches long, closed at one end and open at the other, is held upright in a vessel of mercury. At first the closed end is 30 inches above the surface of the mercury, which is on the same level within and without the tube. The tube is raised slowly. Explain why the surface of the mercury in the tube rises.

If the barometer stands at 30 inches and the closed end of the tube described above is raised to 60 inches above the surface of the mercury, what is the height of the mercury within the tube, above the surface of the mercury outside the tube?

The answering to these three questions gives rise to the remark that candidates should be taught not to give irrelevant detail in answering, The question should be carefully read in order to see the precise point, and the answer then directed to it. A short time spent in instructing students in a proper method of answering would be well employed.

There were only 12 candidates and the quality of the work was good. Some want of accuracy in calculation was shown in the answering of Question 29.

Q. 29. Describe a diving bell.

A cylindrical bell, 7 feet in height, is lowered until the top of the bell if 26 feet below the surface. If the water rises 2.9 feet within the bell, find the height of the mercury barometer, assuming the specific gravity of mercury to be 136.

Report on the Examinations in Navigation and in Spherical and Nautical Astronomy.

NAVIGATION..

STAGE 1.

Results 1st Class, 3; 2nd Class, 15; Failed, 4; Total, 22.

The number of papers sent in, viz., twenty-two, was slightly larger than usual.

The practical questions were fairly well answered, and the definitions asked for were generally given correctly, but otherwise the knowledge of theory was but small.

Q. 2. Describe the Mariner's Compass, explaining particularly the terms: Bowl, Binnacle, Lubber Point, Gimbals.

Two ships A and B are at anchor, the true bearing of A from B being known to be N. 70° E., and the variation of compass 15° 20′ W.

If the compass bearing of B from A is found to be S. 87° W., find the deviation.

In several cases the first part of the question was very well done, but the answers to the easy numerical example which formed the second part were often inaccurate.

Q. 3. Explain what is meant by parallel sailing, and investigate the formula employed.

Two ships in latitude 40° S., which are 300 miles apart, each steam due North at 10 knots. After what interval will they be 350 miles apart?

The answers generally were unsatisfactory, and none of the candidates appeared to be acquainted with the easy trigonometrical proof of the formula employed.

Q. 5. Describe the Traverse Table, and explain its use.

By means of this Table solve the equations

(1) x=191 sec 49°

(2) 118=146 cot y,

explaining the processes employed.

The descriptions given of the Traverse Table were somewhat vague, and the useful applications of the Table to the solution of plane right-angled triangles in general seem to be very generally neglected.

Q. 8. A ship sails from Vigo (lat. 42° 15′ N., long. 8° 40′ W.) S.W. W. until she finds herself in lat. 37° 27′ N. What is then her longitude?

In this, and other of the practical questions, much confusion was evident as to the distinction between departure and difference of longitude, which cannot be too strongly impressed upon the beginner.

9897.

C 2

STAGE 2.

Results 1st Class, 8; 2nd Class, 22; Failed, 9; Total, 39.

The results in this Stage were of an average character, and a few excellent papers were sent in. The practical questions were upon the whole very correctly worked, and the theoretical knowledge shewn was perhaps a little more satisfactory than usual.

SPHERICAL AND NAUTICAL ASTRONOMY.

STAGE 1.

Results 1st Class, 1; 2nd Class, 2; Failed,

; Total, 3.

Only three papers were received in this Stage, all of which showed a fairly satisfactory knowledge, and one obtained 74 per cent. of the total marks. No candidate availed himself of the option to substitute questions in Spherical Astronomy from Section III. for the practical questions in Nautical Astronomy from Section II.

STAGE 2.

Results 1st Class, 4; 2nd Class, 12; Failed, 1; Total, 17.

Of the 17 candidates, four took the questions in Spherical Astronomy, and the papers of two of these were very good.

In the remaining 13 papers the practical work from Section II. was generally well done, but the theoretical portion was less satisfactory. The practical question (No. 32) on fixing a ship's place by the method of position-lines was very correctly worked by nearly all those who attempted it, but the equally useful method of fixing position by a combination of a single position-line with the bearing of a known point of land (No. 25) seems not so well understood.

It would perhaps be well if it were impressed on students that it is unnecessary to correct elements from the Nautical Almanac to the tenth of a second, as such minute accuracy has no meaning in nautical calculations, and much time is lost thereby.

NAVIGATION AND SPHERICAL AND NAUTICAL ASTRONOMY.

STAGE 3.

No papers were received in this Stage.

HONOURS.

Result 1st Class, -; 2nd Class, 1; Failed, -; Total, 1.

One paper only was sent in, the questions answered being taken wholly from Section A., Navigation and Nautical Astronomy. Slightly more than half marks were awarded to the paper.

Report on the Examinations in Practical Plane and
Solid Geometry.

EVENING EXAMINATION.

The number of candidates in this subject continues to increase, the rates of increase in comparison with the numbers last year being 5 per cent. in Stage 1, 9 per cent. in Stage 2, 27 per cent. in Stage 3, and 12 per cent. in Honours.

As regards quality, the work in Stage 1 was very satisfactory, except for a prevalent weakness in two portions of the subject, viz., in problems on the construction and tangency of circles, represented by Questions 2 and 5, and in problems on the line and plane, for illustration of which refer to Question 10. The same faults were noticed in last year's report, and have not yet been rectified in the classes. The defective answers to these three questions are mainly responsible for the smaller proportion of successes this year. In other parts of both Plane and Solid Geometry, and in vector work, a large amount of good work was done.

In Stage 2, the answering was not so good as in 1906, which was an exceptionally good year. This was partly owing to the character of the examination paper, and partly to a want of thorough knowledge in the. more abstract and fundamental parts of Solid Geometry, as tested by Questions 28 and 32 on the line and plane. This portion of the subject merits more attention than appears to be given to it, and probably requires improved methods of teaching. Questions 26 and 27, on vectors, would no doubt present new features to many candidates, so that the comparatively low average marks obtained for them was to be expected. On the whole the work gave evidence of a large amount of earnest and efficient teaching in the subject.

In Stage 3 and in Honours the answering was even better than in 1906; in Stage 3 especially, the questions proved to be better within the capabili ties of the well-taught student.

Detailed criticisms of the answers follow.

STAGE 1.

Results 1st Class, 574; 2nd Class, 602; Failed, 752; Total, 1,928. Q. 1. Take from the tables the chord and tangent of 22°. Construct an angle of 22° by using the value of the chord, and a second angle of 22° by using the tangent. Verify the results by measuring the two angles with your protractor, writing down, to the first decimal, what each angle measures.

The values of the chord and tangent were usually taken correctly from the tables, and in most cases a proper construction was used for the angle, but the radius was often taken too small to ensure any great accuracy.