*7. Shew that if a rigid body with one point fixed undergo two successive finite rotations, there is one line in the body whose initial and final positions in space are the same.

*8. The unit of acceleration being 6 ft.-sec. units, find (a) the unit of mass, when the derived unit of force is equal to the weight of 20 lbs. ; and (b) the unit of force when the derived unit of mass is a mass of 20 lbs.

*9. A particle of mass m, attached by an inextensible string of length l to a fixed point, moves in a vertical plane through the fixed point in a circle of radius 1. Shew that the smallest value which the velocity of the particle at the highest point of the circle can have is Vlg, and that when it has this value, the greatest value of the tension in the string is 6mg.

*10. A string has its ends fixed at A and B. Another string is knotted to it at C and supports a body of weight W. The inclinations of CA and CB to the horizon are and respectively. Find the tensions in CA and CB when there is equilibrium.

*11. Prove that the rate of change of angular momentum of a system about a given axis is equal to the algebraic sum of the moments of the external forces about that axis.-Adapt this result to the case of a rigid body moveable about a fixed axis.

12. Given the moment of inertia of a rectangle about an axis through its centre of figure normal to its plane, find that of an isosceles triangle about an axis through its vertex normal to its plane.

*13. A uniform rod rests with one end pressing against the inner surface of a fixed smooth hemispherical bowl, whose rim is horizontal, and with the other projecting beyond the rim. It is inclined 30° to the horizon. Find its length in terms of the radius of the bowl.

(Additional for First Class.)

APRIL 22ND, 10 A. M.-12 M.

1. Show that if a body is subjected to a homogeneous strain, there are two sets of parallel planes which remain undistorted after the strain.

2. Prove that the amount of a shear is equal to the excess of the ratio of the shear above its reciprocal; and that if the shear is indefinitely small, its amount is equal to twice the greatest principal elongation.

3. The direction and intensity of the stress at a point of a body across any three planes through the point being given, shew how to determine the stress across any other plane through the same point.

4. Show that the strain produced in a homogeneous isotropic body by a simple longitudinal stress consists of a uniform dilatation together with two distortions, and determine their amounts.— Determine also the linear elongation in the direction of the stress.

Examiner

CHEMISTRY.

PROFESSOR LAWSON.

INORGANIC CHEMISTRY.

TIME: THREE HOURS.

1. Give a precise verbal explanation of the meaning of four of the following Chemical Equations:

(1.) Cu+2 H2SO, Cu SO +2 H2O+SO,·

2

4

=

=

4

2

(4.) 2 Na Cl+H, SO, Na, SO +2 HCl.

2

4

2

4

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(5.) 3 KOH + 4 P+3H,0 = 3 KH, PO2+PH ̧.

(6.) Na NO+H2SO4 = Na H SO+H NO。·

3

2. What is meant by Affinity as distinguished from Cohesion ? Explain fully, with examples. "The capacity of combination which resides in the atoms is called Atomicity. Atomicity is the relative equivalence of the atoms." Explain this fully, with examples.

3. What does Atmospheric Air principally consist of? In what proportions, and in what chemical state, are its constituents? Describe severally, with respect to their chemical chraacters or constitution, the three principal gases forming, or found in, the Air.

4. In what manner may the composition of Water be determined? What is its composition, and what are the weights and volumes of its constituents? Give a careful description of Hydrogen, its discovery, mode of preparation, chemical and physical characters, and method of condensation.

5. In what forms does Sulphur occur in nature? Arrange the principal Metallic Sulphides into groups according to solubility, and indicate the principle upon which is founded the general method of testing for and separating Metals in solution.

6. Modes of occurrence of Iron in nature, and changes which its Compounds undergo spontaneously in the soil and in water. What are the principal Ores of Iron? their chemical composition? Describe the chemical changes that take place in the processes of roasting and reduction in the blast furnace.

7. What are Salts, and how are they formed? Explain the action of Hydracids and Oxacids upon Bases, and show, by equations, the chemical changes that result. What is meant by (1) a Neutral Salt, (2) an Acid Salt, (3) a Basic Salt? Give examples of hydrated or crystallized salts that exhibit characteristic colours, and explain upon what constituent of the salt the colour depends.

8. In what state does Potassium exist most abundantly in nature? What is the source of the compound of Potash that is found in soils? In what form does it exist in the plant? and in the ash of the plant? Upon what does the solubility or insolubility of Calcium Phosphates depend?

(Five questions only to be answered. All are of equal value.)

ORGANIC CHEMISTRY.

TIME: THREE HOURS.

1. In what way may the Atomicity of the Element Carbon be certainly determined? Describe the Mode of Generation, and the Structure, of Organic Molecules, as exemplified in Methane, and the Chlorine Compounds derived from it by substitution. In what way may more complicated Organic Molecules, containing several carbon atoms, be produced?

2. What is the special object of Elementary Analysis of organic bodies? Give process for, or method of, determining the amounts of Carbon, Hydrogen and Oxygen respectively, with any necessary calculations.

3. Compare the Saturated Hydrocarbon, the Simple Ether, the Monatomic Alcohol, the Aldelyde, the Fatty Acid, and the Compound Ether, with respect to their Chemical Constitution.

4. Describe fully the process for preparing Chloroform, explaining reactions. What is the Chemical Constitution of Chloroform, and what are its Physical and Chemical characters or properties? In what way may its presence be detected in cases of poisoning?

5. What is a Carbohydrate? Give examples. Where, and how, are the Carbohydrates formed, and from what inorganic compounds? What subsequent changes do they undergo under action of heat, acids, &c. ?

6. Describe the process of Alcoholic Fermentation, noticing particularly the nature of the substances liable directly or indirectly to this process, and the chemical changes involved. Detail fully the physical and chemical characters of Ethyl Alcohol.

7. Describe the process of Saponification. What is the chemical constitution or nature of an Animal Fat? of Soap? of Glycerine? of Nitroglycerine? of Oleomargarine? Oleine? Palmitine?

8. What is the essential distinction between the Fatty Series of organic compounds and the Aromatic Series? Describe Benzole with respect specially to the theory of its constitution. What is the action of Chlorine and Bromine upon it? What is Aniline?

The first question to be answered, and any four of the others, (five in all). All are of equal value.

PRACTICAL CHEMISTRY-ADVANCED COURSE.

TIME FOUR HOURS.

1. The solution A contains two (2) Acids and five (5) Bases. Separate them so as to ascertain definitely what they are, and write out results. Should you fail to determine with certainty any Base or Acid supposed to be present, state what you consider to be the probable cause of failure. [The Bases were HgO, CdO, MnO, BaO, K O. The Acids HCl, HNO ]

2

3

2. Mineral Water Sample No. 1. Determine whether it contains Cl, Br, I. [The Water Samples were artificially prepared from Distilled Water, with known amounts of impurity.]

3. Find specific gravity of Well Water, No. 2.

f

4.

Ascertain presence or absence of Pb, Fe, Ca, in samples of Tank Water marked Nos. 4, 5, 6.

5. Determine amount of Solid Residue in sample of Lake Water No. 3, and proportions organic and inorganic.

Either the first question only to be taken,rest of the paper.

-or the whole of the

PRACTICAL CHEMISTRY,-ELEMENTARY COURSE.

TIME: FOUR HOURS.

x, X, 1. Find Acid and Base in each of the Salts numbered 1 2 &c., and, in any case of failure or uncertainty, point out probable or possible cause.

[The samples of Salts given out included all the ordinary or important Salts, consisting of Bases and Acids usually tested for in a Practical Course. The standing of the respective Candidates was determined from the number of accurate determinations made of Bases and Acids,—corresponding deductions being allowed for errors.]

BOTANY.

TIME THREE HOURS.

1. In what sense is the Cell to be regarded as the unit in Vegetable Anatomy? What is essential to its vital activity? Describe the Cell Wall, its markings, modifications in consistency (mucilaginous, &c.). What Carbohydrates are dissolved in the cell sap?

2.

Point out the principal Modifications of cells in form and structure, (1) of the fundamental or parenchymatous system; (2) of the fibro-vascular system; (3) sieve or cribrose cells; (4) latex cells.

3. Describe the structure of the Stem, with special regard to the arrangement of its tissue elements, and mode of growth.

4. Describe Protoplasm, as regards its chemical and physical characters, its movements, relations to temperature, and moisture, "continuity.'

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5. Describe the Leaf, with respect to its several parts, its structure, as regards the layers of tissue-elements, and its functions.

6. Process of Reproduction in (1) Seminiferous Plants; (2) Sporiferous Plants.

7. Give an outline of the Natural System of Classification of the Vegetable Kingdom.

8. Distinguish comparatively, by structural characters the following Natural Orders :-Ranunculaceae, Nymphæacea, Cruciferæ, Leguminosa, Rosacea.

Five questions only to be answered. All are of equal value.

B.

ARS POETICA.

Translate Trin. II. 4, vv. 128-145.

HEAUTONTIMORUMENOS.

HORACE EPISTLES,

1. Explain any (a) forms, (b) phrases, (c) allusions that need notice in this passage.

2. Translate and write explanatory notes on the following:

a. Ubi mortuos sis, ita sis ut nomen cluet.

b. Cena hac annonast sine sacris hereditas.

C.

Cave sis tibi ne bubuli cottabi crebri crepent.

3. Quote some Greek words used in a Latin form in this play.

Translate: Heauton. III. 2, vv. 38-50.

1. Supply ellipses and explain syntax where necessary in this

b.

passage.

Qui nuper fecit servo currenti in via.

Decesse populum. Distinguish this from the ordinary construction of facio.

Sed quid crepuerunt fores

Hinc a me? quisnam egreditur? huc concessero.

Translate and write a note on crepuerunt fores, giving the opposite phrase and the Greek equivalents.

tense of concessero.

C.

(Chremes): Sustulisti (puellam).

Explain the

Syrus: Sic est factum,

domina, ergo herus damno auctus est.

Translate and explain this as it stands and with the various corrections, (1) ego for ergo, (2) minor for domina, (3) domine for domina.

3. The Prologue classifies this play and contrasts it with others. The Didascalia notes the time and occasion of its performance. 4. Quote some proverbs from this play.

C.

1.

Translate: a. Georg. I., vv. 71-77.

b. Georg. IV., vv. 281-294.

a. Arcadii memoranda inventa magistri.

b. Pellaei gens fortunata Canopi.

Explain the allusions.

2.

What difficulties are found in the second Extract?

3.

a. Namque sub Oebaliæ nemini me turribus altis.

b. Aut Athon, aut Rhodopen, aut alta Ceraunia telo.
Write geographical notes.