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Q. 56. Describe fully how the metacentric diagram for a ship is con

structed, and state to what uses it is put. Sketch the metacentric diagram for any type of ship with which you are acquainted, and figure on it the metacentric heights for the light and load conditions. Name the type of vessel chosen, and

state the leading particulars of the vessel. About 75 candidates attempted this question, and about one-third of those gave satisfactory answers. The remainder of the answers were generally incomplete. The first part of the question was generally well answered, except that many candidates referred to BM as representing metacentric height. The second part of the question was badly done generally. Candidates in this stage should have a clearer knowledge of metacentric height, and should be familiar with approximate values of the metacentric heights of typical vessels.

HONOURS. Results : 1st Class, 4 ; 2nd Class, 9 ; Failed, 66 ; Total, 79. There was an increase of about 15 per cent. in the number of candidates who sat at the examination in this stage, as compared with last year. The standard of the answers was not so good as last year, and it is suggested that more attention should be given to the syllabus, which is now prepared in considerable detail.

It is again necessary to point out the great lack of neatness in the working of many of the papers, which often resulted in confusion and failure, especially in calculations. Arithmetical errors were far too common, and often from slips in cancelling. Students should be directed to pay more attention to the dimensional units to be employed in a calculation. A very large proportion of incorrect answers were due to carelessness in mixing up feet and inches or pounds and tons in the same formula..

The stability questions were fairly well answered, but the students in this stage onght to shew a more complete knowledge of the properties of the metacentre, and the geometry of the metacentric diagram.

The subject of rolling seems not to be treated as well as is desired ; the questions set were of a very elementary character and should have been treated much better than they were.

The answers to the questions on resistance were generally satisfactory, but the strength questions were poorly done.

The questions relating to the elements of design were, on the whole, well answered, and it is satisfactory to note that several of the candidates had a fair knowledge of the current literature on this branch of the subject. Q. 61. Having given three equidistant ordinates of a plane curve, and

the common interval between them, deduce a rule for calculating the area included between the curve, base line, and two consecutive ordinates. Deduce also a rule for calculating the moment of such an area about one of the end ordinates.

Illustrate your answers by means of a simple numerical

example. Attempted by about 60 per cent of the candidates, and generally well answered. The question refers to Simpson's third, or five-eight rule. In several cases Simpson's first rule was quoted and proved. Q. 62. Prove that for angles of heel for which the sides of a vessel, with ordinary waterlines, are wall-sided, the righting 'lever

,

GZ = (GM + BM tano 0) sin 6, Grepresenting the centre of gravity of the vessel, M the metacentre and B the centre of buoyancy.

A prismatic vessel of rectangular section 30' broad, draws 10 of water, and has a metacentric height of 1. If weights be shifted so as to raise the centre of gravity 15", find the angle to which the vessel will loll over.

Only nineteen candidates attempted this question, and there were about seven good answers. The formula quoted is a very useful one, as the majority of ships may be regarded as wall-sided for small angles of heel. In attempting the second part of the question, it was generally

overlooked that the vessel would loll over until GZ becomes zero, which value substituted in the formula stated, enables to be found. Q. 63. What are the effects of a large sea breaking over, say, a well

deck steamer, or a vessel with bulwarks, the freeing ports being assumed set up with rust, due to neglect ?

A vessel of 700 tons displacement has a freeboard to upper deck of 6. The centre of gravity is l' 6" above water, and its metacentric locus is horizontal. A sea breaking over the bulwarks causes a rectangular area 50' long and 20' broad, on the upper deck of the vessel, to be covered with water to a

depth of 1'. Calculate the loss of metacentric height. A popular question, and generally well answered. Several candidates took the centre of gravity of the vessel as 1' 6" above the water on the upper deck, instead of l' 6" above the water line of the vessel. Q. 64. Show how a curve of statical stability may be practically con

structed from a curve of dynamical stability.
In a particular vessel the dynamical stability
=W. GM. (1

cos 6),
A being the angle of heel from the upright. Deduce the
equation of the curve of statical stability, and the form of
the section of the vessel, supposing it to be of constant section

throughout. Attempted by 18 candidates, and only about four satisfactory answers were given. Many of the investigations were very laborious, and made without success. It was often stated that the integration of a curve of statical stability up to any angle is the dynamical stability at that angle, but it seemed to be quite overlooked that the question asked for the reverse of this process, and that by differentiating the expression given for the dynamical stability, the equation to the curve of statical stability is readily obtained, and the form of the section seen to be circular, unless she be wholly submerged. Q. 65. Obtain an expression for the slope of the tangent to the curve of

metacentres, at any draught, in the metacentric diagram.

A log, of which the section is 2 square, floats with one diagonal vertical. Sketch the curve of metacentres, and

calculate the draughts at which it is horizontal. Only six candidates attempted this question, and the answers were disappointing. The first part of the question is an easy example on the geometry of the metacentric diagram, and the second part should be simple for Honours students. Q. 66. Define “surface of buoyancy,” “surface of flotation," and "

of pro-metacentres.'

Prove that the surface of buoyancy is closed, and wholly concave, to some interior point, and find the limits to its size, as

the displacement of a given ship is varied. Attempted by 28 per cent. of the candidates, but only about five obtained good marks. Many stated that the surfaces of buoyancy and flotation were the surfaces of imaginary cylinders extending throughout the vessel's length. Q. 67. Find the expression which gives the height of the longitudinal

metacentre above the centre of buoyancy, in a floating body, and explain what use is made of this information.

Calculate the longitudinal metacentric height for a square log of fir of specific gravity '5, 18' long and 2 6" side, when it is floating in a position of equilibrium.

curve

This was also a popular question, 83 per cent. of the candidates attempting it. About one-third of the answers were very good ; but it is surprising how many went wrong in one or both of the parts of this comparatively simple question. Many candidates treated the question as referring to transverse inclinations instead of longitudinal, and some jointly considered both transverse and longitudinal. A large percentage of the answers to the second part of the question were based on the assumption that the sides of the log would be vertical when floating in a position of equilibrium, instead of with one diagonal vertical and the other horizontal. Q. 68. Investigate the rolling motion of a vessel in still water, on the

supposition that there is no resistance, and obtain a formula, giving the angle of inclination at any instant. Deduce the time of a single swing:

Calculate, and state in seconds, the time of a single swing of an empty steel circular pontoon, 10' in diameter, floating at mid-depth. The centre of gravity is 6" below the centre of

figure. Twenty candidates attempted this question, and only about three satisfactory answers were given. The answers were generally incomplete. Most of the candidates who attempted the first part of the question simply quoted the formula, instead of deducing it from the equation of motion,

The attempts to answer the calculation were generally laborious and unsatisfactory. Many tried to deduce the radius of gyration of the circular pontoon by working from the moment of inertia of a rectangular figure, whereas by noting that all the material of the steel plating forming the pontoon is distant the radius of the section from the axis, it is at once seen that the radius of gyration is the radius of the section, viz. :-5 feet. Q. 69. State why the ordinary, or short-period, pendulum observations

are untrustworthy, for giving the inclination of a ship in a sea-way. Investigate the error of a short period pendulum in giving the inclination of a ship rolling in still water.

Show how, by means of two such pendulums placed at different heights on the middle line, the axis of still water

oscillations may be ascertained. Attempted by eleven candidates; one or two of the answers were very good, but the others were very poor, shewing that the effects of rolling were little understood. Q. 70. Give a brief outline of Mr. W. Froude's surface friction experi

ments, and state the chief results reached with reference to the variation of resistance due to-(1) variation in character of surface, (2) varying dimensions of the same character of surface, and (3) change of velocity, the dimensions and character of the surface remaining unchanged.

Find the resistance in pounds per ton of displacement, and the horse-power necessary to overcome frictional resistance in the case of a ship 330 long, 58' beam, 23'6" draught and 6,882 tons displacement, when going at 18 knots. Assume that the surface friction of one square foot of the bottom, moving at

a speed of one foot per sec. = '0034 lbs. Another favourite question, 65 candidates attempting it. About one-third of the answers were very good. The failures in the calculation were due mainly to the use of wrong units, or to bad arithmetic. One candidate stated that the resistance amounted to 26472749746 lbs., and that the resistance per ton of displacement is 38321 lbs. Q. 71. State Froude's law of comparison, as applied to the relative

resistance of models and ships. How would you sub-divide the total resistance, offered by the water, to the motion of a ship? To what parts of the resistance does the law not apply?

Two ships of unequal size are made from the same model. Prove that at the speed where the resistance varies as the 6th power of the speed, the same effective horse-power is required to drive both ships at the same speed.

Attempted by 61 candidates. The first part of the question was, in most cases, well done, but the second part was rarely attempted, and generally answered unsatisfactorily. It is an example illustrating the general principle of the economical propulsion of large vessels. Q. 72. A box-shaped vessel 100' long, 35' broad and of 1,000 tons dis

placement, is on the crest of a wave of her own length, 5' high, of which the profile is a curve of sines. The weight of the vessel is uniformly distributed along its length. Construct, to scale, the curves of shearing force and bending, moment, and

state in tons and foot-tons respectively their maximum values. Nineteen candidates attempted this question, but only about five satisfactory answers were given ; the remainder were poor. The majority of the curves were badly drawn, and very little working was shewn. Q. 73. Find the maximum longitudinal stresses (in lbs. per square inch)

upon a section of the vessel referred to in Question 72, assuming the depth of the vessel is 15', and that the plating on the deck, side and bottom is 26" thick. (No allowance need be made for rivet holes.)

If Question 72 has not been worked, assume that over each one-third of the length of the vessel, from each end, two-fifths of the total weight of the vessel and cargo is uniformly distributed, and that the vessel floats in still water.

If the vessel has a continuous bulwark each side, 3' high and 76" thick, what will then be the maximum stresses? Explain

the significance of your result as applying to actual ships. About 28 candidates attempted this question, the first part of which was generally well done. Several of the candidates mixed up the units of the expressions in the formula used to obtain the stresses, and obtained absurd results. The second part of the question was not so well answered, many neglecting the change in the neutral axis of the section, due to the addition of bulwarks. A correct deduction from the difference in the value of the maximum stresses due to the addition of bulwarks was rarely stated. Q. 74. State generally the present rules as to maximum load-line in

merchant ships. Is there any legal enforcement in the case of vessels of foreign nations ? What are the leading considerations in determining the freeboard for any particular vessel? What bearing has the reserve of buoyancy on the stability and

behaviour of the vessel at sea ? Attempted by about 23 candidates, but only two or three answers were satisfactory. Generally the answers were very poor and incomplete. Q. 75. Having given the moulded dimensions of a vessel of known type,

also the specification and designed speed, how would you determine the weights of hull, outfit and machinery, and the light displacement ?

How would you proceed to estimate the weight, and position of the centre of gravity, longitudinally and vertically, of the

transverse framing of a vessel? About one-half of the candidates attempted this question, which was generally very well done ; about thirteen obtaining very good marks. Q. 76. Describe generally the development of turbine machinery from

the naval architect's point of view, as applied to marine propulsion.

What do you consider to be the advantages and disadvantages of turbine engines, as compared with reciprocating engines ?

State, as far as you can, comparative results of any two similar vessels with which you are acquainted, one vessel being fitted with turbine engines and the other with reciprocating

engines. Twenty-one candidates attempted this question, and the answers were generally satisfactory. About five obtained very good marks.

Honours PRACTICAL EXAMINATION. Nineteen candidates who had done sufficiently well in the written examination were summoned to South Kensington to sit for the practical examination in Design.

The designs were, on the whole, good; three or four candidates did exceptionally good work.

It should be noted that the drawing of border lines is not required. Accuracy and neatness of drawing is insisted on, and the inking in of the drawings, though desirable, should not be proceeded with until it has been ascertained that the lines of the vessel are fair. The fairing lines should be left on the drawing. In two or three cases there were arithmetical errors in working the displacement sheet.

Report on the Examination in Applied Mechanics.

In all stages the answering this year on the whole showed a distinct advance, and there was evidence of careful, and in many cases of successful, teaching. Confusion of units is becoming less and less noticeable, but in the higher stages many candidates still mix up feet and inches, or tons and pounds, in one formula, and it is desirable again to draw attention to the fact that constant drill in the working out of numerical examples is the only way of eradicating this evil. It is perhaps too often the custom to allow students to write down a formula, insert numerical data, and then leave the problem unfinished, otherwise candidates would more quickly realise when they had obtained an absurd result, and would either check their calculations or state that a slip must have been made and that the result was an incorrect one. Undoubtedly the best method to secure greater accuracy in arithmetical work would be to insist on attendance at courses of instruction in Practical Mathematics. As in previous years, it was often impossible to determine where students had gone wrong in their arithmetical calculations owing to the untidy and careless manner in which the various steps in the calculations were written down. It should be impressed upon students that accuracy and tidiness in work nearly always go together. The answers to the questions dealing with the method of carrying out certain experiments showed again conclusively that too little attention is paid by many teachers to the careful preparation beforehand of demonstrations in the laboratory. Even where the candidate gave a reasonably intelligent explanation of the method of carrying out an experiment, he was frequently quite unable to state what results would be obtained and how the results would be recorded, and what physical interpretation would be placed upon the results. Hardly any candidate, even in Honours, showed any acquaintance with the fact that in all experimental work the appliances used should be thoroughly tested for accuracy both before and after the conclusion of the experiment, and though the answers to these questions during the last two or three years have steadily shown an advance, there is still a great deal of leeway to be made up. From the replies to Question 26 it is evident that teachers are somewhat prone to neglect at the present day the teaching of the principles of simple mechanism, and it is desirable that more attention should be given to this tranch of the subject. In the elementary classes more time should be given to problems such as that of Question 13. The Examiners would again emphasise the necessity of compelling students always to write down the units in which their answer is expressed. Such statements as “a force of so many foot-pounds” or “a stress of so many inch-tons” are still far too frequent and point to want of care on the part of the teachers.

STAGE 1.
Results : 1st Class, 659; 2nd Class, 507 ; Failed, 541 ; Total, 1,707.
Q. 1. Describe, with careful sketches, only one of the following (a), (6),

(c) or (d) :
(a) The operation of centering, fixing in the lathe, and turning

a shaft or spindle, say about 2 inches diameter and
3 feet long.

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