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II.

Le chêne un jour dit au roseau:
"Vous avez bien sujet d'accuser la nature;
Un roitelet pour vous est un pesant fardeau :
Le moindre vent qui d'aventure
Fait rider la face de l'eau,

Vous oblige à baisser la tête;
Cependant que mon front, au Caucase pareil,
Non content d'arrêter les rayons du soleil,
Brave l'effort de la tempête.

Tout vous est aquilon, tout me semble zéphyr.
Encor si vous naissiez à l'abri du feuillage.
Dont je couvre le voisinage,

Vous n'auriez pas tant à souffrir;
Je vous défendrais de l'orage:

Mais vous naissez le plus souvent

Sur les humides bords des royaumes du vent.
La nature envers vous me semble bien injuste.
-Votre compassion, lui répondit l'arbuste,
Part d'un bon naturel; mais quittez ce souci :

Les vents me sont moins qu'à vous redoutables;
Je plie, et ne romps pas. Vous avex jusqu'ici
Contre leurs coups épouvantables
Résisté sans courber le dos;

Mais attendons la fin." Comme il disait ces mots,
Du bout de l'horizon accourt avec furie
Le plus terrible des enfans

Que le nord eût portés jusque-là dans ses flancs.
L'arbre tient bon; le roseau plie.

Le vent redouble ses efforts,
Et fait si bien qu'il déracine

Celui de qui la tête au ciel était voisine.

Et dont les pieds touchaient à l'empire des morts.

LA FONTAINE,

[blocks in formation]

Drawing a line from A to the upper extremity of the perpendicular at B, and joining this point with summit of that at C, and on to that at D, and thence to E, we have the longitudinal section of an excavation— the heights at B and D being 12 ft., at C 20 ft.; the lengths in chains are—AB= 2.5, BC= 3.5, CD = 1, and DE=0.5; the slopes are 2 to 1, and the bottom width 30 ft.

1. Calculate the cubic content of this cutting by the true prismoidal formula, giving the tabular number of each block.

2. Also mention the two erroneous modes of calculating, and the cubic contents they give, and the relation between all three results; pointing out also the various evils that arise from the miscalculation of these two last methods.

3. Calculate the total quantity of land required for this excavation; point out how the tabular number, for calculating the land required, is obtained in the Text-book; and give this number for the part between B and C.

4. In these three last Questions certain things are assumed for simplification, which but seldom occur in earthworks; mention them, and show that they are immaterial as to the cubic content. So far as the quantity of land is concerned, show how you would obtain the exact amount.

5. Draw up a "Specification" for this excavation, supposing it to form part of a contract, with embankments, &c.; and write out the general stipulations that should be attached to specifications.

6. Supposing that loose rubble rock appeared, from borings or trial shafts, at the bottom of this excavation, beginning at A, and rising to 3 ft. at B, and 6 ft. at C, and 2 ft. at D, disappearing again at E: state what works you would order in this case, and what bottom width might now be adopted, and the cubic quantity of rock to be removed. Draw a transverse section at C, the slope being, as before, 2 to 1 for the upper earthwork. Add the clauses in the specification that are rendered necessary by the rock occurring at bottom.

7. Supposing that at each end of this excavation we had an embankment identical in longitudinal section, would it be cheaper for the contractor to run it all out at the end A or E; and explain the "average lead" mentioned in the Text-book (4ƒ).

8. State the usual average price for earthwork; and separate it into parts which represent the cost of the different operations, stating what is given in the "Collection of Prices" on the subject.

9. Describe the terms-bottom lift, top lift, gullet, battery head.

10. If we had an exact balance between the calculated excavations and embankments on any line of work, we may yet have a deficiency or excess of excavation from the character of the soil; mention the properties of chalk, clay, gravel, and rock in this respect; and state what cubic quantity of embankment the rock in Question 6 might be expected to fill.

11. Describe the peculiar difficulties of the Blisworth excavation through the Oolite; and give a transverse section of the work.

12. Give the geometrical construction by which the angle of the coursing joints in a segmental oblique arch is determined.

13. Deduce the general expression for the value of the axial length of the segmental spiral, comparing it with that of the same in the full semicircular arch.

14. Mention the methods used in practical construction, by which the expense of working and setting spiral courses in oblique arches, of stone or brick masonry, is obviated or diminished.

15. Between what limits of intersection of the axes of road and railway may we build oblique bridges with parallel courses ?-and state the object to be attained by the use of spiral courses; state also the expense, per cubic foot, of the arch-sheeting of each.

16. State succinctly the history of the successive theories of the arch, and the points in which they were severally defective.

17. Describe the experiment by which Barlow proves that there does exist a curve of equal horizontal thrust.

18. Give the construction by which the curve of pressure may be drawn through any ring of voussoirs, supposing it to commence at any known or given points in the bed of the key, and of the skew back at the springing.

19. Trace the curve, in like manner, through the abutment to the arch mentioned in last Question.

20. Deduce the general expression for the thickness of the abutment, noting the meaning of the several letters used, and pointing out the improvements in the statement of the conditions of the problem introduced by this author.

21. From the expression so determined prove that, even though the abutment or pier were indefinitely high, yet that the thickness does not increase beyond a certain limit; give the value of that limiting thickness, and represent it by a geometrical construction.

22. No one proportion of depth of key to span of arch (of whatever curve that may be) holds good for the whole range of spans found in practice, but we may deduce it from trustworthy examples. Thus give the depth of the key in terms of the span, for a stone arch of 200 ft. span, and for every 30 ft. less successively.

23. Calculate the horizontal thrust of an elliptical arch, 60 ft. span,

20 ft. rise, 25 ft. wide, with depth of key to be assigned as in last Question; the stone, granite.

24. Prove the expression by which the last Question was calculated, and state the three conditions necessary to the stability of any voussoir in an arch.

25. Give the approximate value of the horizontal thrust in very flat castiron arches, tracing clearly the several steps by which it is attained.

26. In conducting experiments on the ultimate resistance to compression, many circumstances must be attended to, which, in those upon the ultimate resistance to tension, are not essential to good results. State these, and trace out the effect upon the laws of each thence resulting; and, by a sketch of the transverse section of a wrought-iron beam, show that the same circumstances must be attended to in practical construction.

27. State the value of the resistance to compression of cast-iron given in the Proposition, § 99, and on what data that number has been attained.

28. State the average ratio of tensile and compressive resistances in cast-iron, giving the highest and lowest values of this ratio, and the name of the iron works respectively as given in the Table in the Text Book; also the remark given upon the results of the earlier and later experiments.

29. An experimental pillar of cast-iron, inch diameter, and 60.5 inches long, was broken with a compressive force of 143 lbs.; another of the same diameter, and 3.78125 inches in length, required 15,107 lbs. to break it. Calculate the power of the length to which the strength is proportional on these data.

30. Give the practical rule for the strength of solid and hollow uniform pillars of cast-iron of different length and diameter, deduced by Mr. E. Hodgkinson from his experiments; and state clearly the meaning of the numerical constant, what it is, and what it represents. Design a castiron pillar, 25 ft. high, to carry 80 tons.

31. Define the term "Elasticity" of materials. State its laws; and the manner in which it is introduced into the formulæ for the strength of wrought-iron beams. Also the "Set" and its laws.

32. Give the results of Mr. E. Clark's experiments on limestone, sandstone, and brickwork, as to compressive resistance; the manner of failure observed in each, and dimensions of the block used.

33. Describe the self-acting arrangement for measuring the expansion and contraction of the tubes of the Britannia Bridge from change of temperature; and state the greatest observed motion of the continuous tube from this cause.

34. Describe the manner in which a continuous bearing on the surface of the rails is provided for at the entrance of the tubes, notwithstanding their expansion and contraction. Also the construction of the instrument by which the deflection of the tubes (when completed and in place) was measured under any stationary or passing load.

35. Give a sketch and statement (similar to that in the Text-book) of the manner in which the several spans were finally united in one continuous tube, and the resulting effects on the deflections that were observed

36. Define the "circular inch," and prove the rules given

1. For a round rod of any diameter, the square of the diameter, taken in quarter inches, is the breaking weight in tons.

2. Half this quantity is the weight in pounds per yard.

37. The effect of the wind on the tubes during violent storms had been a subject of anxiety with many persons, lest the pulsations of a gale of wind might become isochronous with the resulting vibrations of the tube, and thus create an amount of oscillation that would be injurious. The result of an experiment before the tube was floated, namely, ten men pressing against its side, acting in unison, and keeping time with the vibrations, proved it unfounded. Also, in the experiments on the large model, an experiment is described, intended to decide this. Give both in full detail.

38. At the recently opened Glasgow Water-works a deep valley is crossed by a pipe 4 ft. in diameter, the delivery end is at a depth below the other, giving a fall at the rate of 5 ft. per mile; calculate the discharge in gallons in 24 hours.

39. Give a description and sketch of the method of obtaining a nearly constant discharge through a fixed orifice under a varying head, used in the irrigation works in Lombardy.

40. At what depth of the sheet of water, flowing over a weir, is the velocity at a mean, and what proportion of the bottom velocity is it?

41. A beam 40 ft. long between the abutments has a weight of 35 tons applied at a point 10 ft. from the abutment; what is the total pressure on each abutment, the beam itself weighing 8 tons ?

42. What is the horizontal strain at the other point 10 ft. from the abutment, arising from this applied weight?

43. If the 35 tons were uniformly distributed over the span of 40 ft., what would be the horizontal strain at these same points?

44. Calculate the diagonal tension on a tension bar in a lattice girder, joining any assumed points in the top and bottom of the beama. When the weight is uniformly distributed.

b. When all suspended at the centre.

45. A uniform beam rests on abutments and an intervening central pier of support; calculate the pressures upon the abutments and pier. 46. And calculate the effective length of each span.

47. A uniform wrought-iron beam, 80 ft. clear span, and 6 ft. extreme depth, has a top cell 15 inches square outside, metal inch thick; bottom plates 23 inches wide, thickness 2 inches, sides inch thick. Calculate the strength, as in the "large model," and by the method of Mr. E. Hodgkinson, neglecting the angle irons.

DR. APJOHN.

1. What is the general rule for determining the atomic volume of a substance, and what elements have the same atomic volume with oxygen? 2. Explain practically and theoretically the process for preparing nitric acid from nitre, and the modification it should undergo when nitrate of soda is substituted for nitrate of potash.

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