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1. What various readings have the support of MSS. in the following passages : -S. Matt. xix. 17; Acts, ii. 47 ; xx. 28; xxvii. 14; Eph. v. 30; Col. ii. 2?

2. Give a brief statement of the arguments as to the genuineness of the received text of S. Mark, xvi.; and of Acts, viii. 36–39.

3. (a) Remark briefly on S. Paul's use of prepositions, as exemplified by such a text as Rom. iii. 22.

(6). Write a note with this view on Gal. ii. 16, as compared with Phil. üi. 9, and Col. ii. 12.

4. Distinguish between, and illustrate where necessary, the significations of the following words :-ου, μή; έτερον, άλλο (e.g. in Gal. i. 6, 7); πλύνω, νίπτω, λούω; θεοσεβής, ευσεβής, ευλαβής, θρήσκος, δεισιδαίμων, αληθής, αληθινός; Εβραίος, Ιουδαίος, Ισραηλίτης.

5. (a). State the force of tãs with and without the article; showing the sense, according to this rule, of the following passages :—S. Matt. ii. 3; viii. 34; Acts, ii. 36 ; Gal. vi. 6; Eph. iii. 15; Col. iv. 12.

(6). Write a special note on Eph. ii. 21; and illustrate this case by a well-known text.

6. Translate and comment grammatically on Gal. iv. 12-14; Eph. iv. 9; Col. i. 19; Eph. vi. 17, with special reference to the rule as to the gender and number of the relative pronoun, supplying further examples similar to Eph. i. 23, and Phil. i. 28.

7. Translate and explain Acts, xv. 20; Gal. v. 17; Col. ii. 20-23.

8. Write a brief note on each of the following passages :--S. Matt. ii. 23; xxiii. 35; S. Mark, xi. 13; 8. John, xx. 21.

9. Translate and explain the words and phrases—'Aßßă, ó Tarno, Rom. viii. 15; ενεβριμήσατο τω πνεύματι, 8. John, xi. 33; κατά τον έσω άνθρωπον, Rom, vii. 22; ανάθεμα έστω, Gal. i. 8; την κατατομής, Phil. iii. 2.

10. Compare briefly :-S. John, xix. 14, and S. Mark, xv. 25; as well as the different accounts of S. Paul's conversion.

11. S. Paul employs three terms to express the redemptive agency of Christ; quote passages in which they respectively occur.

12. Develop, in the form of an essay, the doctrinal signification of Eph. i. 20–23; Phil. ii. 5-11; Col. i. 15-17.

BEDELL IRISH SCHOLARSHIP EXAMINATION:

PROFESSOR O'MAHONY.

Translate the following passages into Irish :

Matt. v. 13-16.
Rom. xiii. 1-7.
1 Tim. vi. 13-17:

1. Write in Irish the fourteenth and twenty-eighth Articles; and gite Scripture proofs thereof.

2. State briefly the traditionai account as to the period when, and the persons by whom, the Irish letters were invented.

3. Whence is derived the most curious information respecting the literary character of Ireland before St. Patrick's time?

4. Give an account of the first printed Irish Grammar.

5. What are the peculiarities which distinguish the Erse, or Gaelic of Scotland, from Irish ?

6. In what consists the principal difference between the Munster and the other dialects of the Irish language?

7. In what positions is the letter s not aspirated ?

8. What are O'Donovan's particular rules for the formation of the genitive case plural of the second declension ?

9. Conjugate the verb teiðim.

10. What are the simple and idiomatic meanings of the prepositions o and reac?

11. How may derivative substantives be classed according to their terminations

12. Give an abstract of the rules for the government and collocation of pronouns.

SCHOOL OF ENGINEERING.

JUNIOR CLASS.

DR. SALMON

1. Differentiate

2

+ + 4% - æ log to

I + 2 ava 2. Differentiate

5
tan 1x

log
4

2+1 and reduce the answer to a single fraction.

3. Expand by Maclaurin's theorem &* cOS X.
4. When is a tan 0 + b cot O a minimum?
$: Find the value of

83 — * -V1-2 when t = 0.

I-COS X

6. Integrate
dax dat

dx

dx 2x + 3' 242 +9' 32+x+T' 7*3++1 7. Construct the line of intersection of two planes both parallel to the ground line.

8. Construct the angle between two intersecting lines. 9. Draw a tangent plane to a cylinder from a given point outside it. 10. Draw a tangent to the helix parallel to a given plane.

i. Solve the system of equations,

2+y+%= 10, 2X - Y+%= 7,

i-y +32 = 4. 2. Find an angle whose tangent is four times its sine. 3. Find in degrees and minutes x from the equation

sin (a + 0) = 2 sin 2, being given sin 0=.

4. Being given tan A= }, tan B = }, tan C= }; find the tangent of the sum of the three angles.

5. Find the three angles of the triangle whose sides are 854.692, 412.728, 656.212.

6. Find the base angles and base of a triangle whose sides are 1532.09, 1000, and contained angle 20°.

7. Calculate the logarithm of 2 in Napier's system. 8. Trace the curve

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1. Explain the process for preparing oxygen from chlorate of potash ; and calculate the weight of oxygen which one avoirdupois ounce of the salt should yield.

2. What is the precise action of muriatic acid on peroxide of manga. Dese? 3. If a substance upon analysis was found to consist of

Sulphuric acid,
Alumina,

9.27
Potash,

8.46 Water;

38.88

.

43.20

99.81 how would you investigate its atomic constitution and représent it by a formula ?

4. What circumstance would enable you to conclude that a solution of chloride of calcium would decompose, and be decomposed by, one of phosphate of soda?

5. Give in symbols the reactions of the two salts just mentioned on each other.

6. Explain the constitution of a limestone which on being properly burned would yield a hydraulic mortar.

7. What are the salts which confer hardness on waters? Why, generally speaking, are hard waters partially softened by boiling ?-and what is Clarke's process for determining the degree of hardness of a water?

8. Describe and explain the process for preparing liquid muriatic acid. 9. Describe and explain the process for procuring nitric acid.

10. How would you make an exact analysis of a mixture of oxygen, nitrogen, carbonic acid, and aqueous vapour?

11. Write the formula of felspar (orthose), and specify the differences between this mineral and albite.

12. What is the formula, and what the crystalline system, of the mineral called galena ?-and how by chemical means would you demonstrate the nature of the metal which it includes ?

13. Specify the two uniaxal systems, and give the crystallographic characters of each.

14. Give the notation of the octahedrons in the second and fourth systems.

15. Write the formulæ of common pyrites, of magnetic pyrites, and of mispickel; and mention the system in which each is found.

BISHOP LAW'S MATHEMATICAL PREMIUM.

SIR WILLIAM ROWAN HAMILTON.

A.

QUATERNIONS.

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1. Let A B, A,B2, ... AnB» be any given system of posited right lines, the 2n points being all given; and let their vector sum,

AB=A1B1 + A2B2+. + An Bn, be a line which does not vanish. Then a point H, and a scalar h, can be determined, which shall satisfy the quaternion equation,

HA1. A1B1+...+H An. AnBn=h. AB; namely by assuming any origin 0, and writing,

041. A1Bit..+0An. AnBn 041. A Bit.. OH = T

h=s AiBit..

AiBit.. 2. For any assumed point C, let

Qc= CA1. A1B1+..+ CAn. AnBn; then this quaternion sum may be transformed as follows,

Qc= QH + CH. AB= (h+CH). AB; and therefore its tensor is,

TQc=(h2 + CH2). AB, in which AB and CH denote lengths.

3. The least value of this tensor TQc is obtained by placing the point Cat H; if then a quaternion be said to be a minimum when its tensor is such, we may write

min. Qc = Qa=h. AB; so that this minimum of Qc is a vector. 4. The equation,

TQc=c = any scalar constant > TQA, expresses that the locus of the variable point C is a spheric surface, with its centre at the fixed point H, and with a radius r, or CH, such that

r. AB=(TQc2 TQA?)!=(c? – h2. AB2)}; so that H, as being thus the common centre of a series of concentric spheres, determined by the given system of right lines, may be said to be the Central Point, or simply the Centre, of that System. 5. The equation,

TVQc=i =any scalar constant > TQA, represents a right cylinder, of which the radius = (013 - h2. AB+){ divided by AB, and of which the axis of revolution is the line,

VQc= QA = h. AB;

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