they asserted, the day predicted in their priestly records, when the East should wax in power, and men go forth from Judea to rule the world. The Romans, listening credulously to every oracle, foreign or domestic, pointed with exultation to Titus and Vespasian, who issued from Judea to assume the government of the empire. Translate into Greek Verse: Yet a few days, and thee The all-beholding Sun shall see no more In all his course; nor yet in the cold ground, Thy image. Earth, that nourish'd thee, shall claim To mix for ever with the elements, To be a brother to the insensible rock And to the sluggish clod, which the rude swain Shalt thou retire alone.-Thou shalt lie down Translate into Latin Verse: Sweet evening hour! sweet evening hour! Sweet hour! that bids the labourer cease, That gives the weary team release, And leads them home, and crowns them there O season of soft sounds and hues, Yes, lovely hour! thou art the time And God receives and answers prayer. Logics. MR. ABBOTT. 1. The defect which the ancient Sceptics ascribed to the senses was really due to other causes according to Bacon. Specify and explain the different causes which he enumerates. 6 2. Of 'inversio experimenti' Bacon suggests these instances: Calidum per specula intenditur; num etiam frigidum?' 'Item, radii solis supra album dissiliunt, supra nigrum congregantur; num etiam umbrae super nigrum disperduntur, super album congregantur?' Comment on these suggestions. 3. What is Mill's account of what is meant by 'substance'? 4. What ambiguity is exemplified when it is said that two persons are ill of the same disease? Give other instances of the like ambiguity or of confusion arising therefrom. 5. Discuss the question whether circumstances of time belong to the predicate or the copula. What technical advantage is gained by adopting the former view? 6. "The notion that what is primary importance to the logician in a proposition is the relation between the two ideas corresponding to the subject and predicate. . . seems to me one of the most fatal errors ever introduced into the philosophy of Logic." Explain and comment on this remark. 7. Discuss Bain's view of Definition, that the meaning of a general name includes all the ultimate properties of the class named. 8. Bain banishes singular propositions from syllogism; why? 9. "A scientifically-cultivated mind is, in virtue of that cultivation, unable to conceive suppositions which a common man conceives without the smallest difficulty.' What explanations may be given of this 'paradoxical truth' ? 10. “Language is not made but grows." Explain and illustrate this remark. DR. TARLETON. 1. How does Mr. Monck deduce the four rules of the hypothetical syllogism from those of the categorical syllogism? 2. On what grounds, according to Mr. Monck, may it be asserted that the Dictum and the Axioms cannot form the basis of the science of Logic? What is the real basis? 3. The Categories and the Predicables of Aristotle are both lists of predicates. How do the two lists differ as regards the guiding principle of their formation ? 4. What is Mr. Monck's view of the distinction between nominal and real definitions? On what grounds does he differ from Mill on this point? 5. Prove that the only conclusion which can be drawn from two negative propositions, by considering one or both as affirmative, is of the form, Some not-Ys are not-Xs. 6. Describe the three processes by which, according to Jevons, the growth of a language is chiefly effected, and give examples of each. The third is a special form of one of the other two? These two latter imply one another? 7. What, according to Leibnitz, are the four characteristics of perfect knowledge? How is each characteristic explained and distinguished from its opposite ? 8. The syllogistic theory, as founded on the Axioms, may be illustrated by space representations; how? The space representation, as usually drawn, embodies a radical error in reference to the extension of a general term? 9. Describe Jevons' Method of Indirect Inference. If n terms and their contradictories be under discussion, how many combinations containing n elements must be considered? 10. Point out the fallacies in the following arguments: All presuming men are contemptible; this man therefore is contemptible; for he presumes to believe that his opinions are correct. The holders of some of the shares in a lottery are sure to gain a prize; A is the holder of some of the shares, and is therefore sure to gain a prize. What produces intoxication should be prohibited; the use of alcoholic liquids produces intoxication; therefore it should be prohibited. DR. MAGUIRE. 1. How does Mill's view of Induction differ from that of Dugald Stewart and Dr. Whewell? 2. What is meant by Colligation of Fact? Give an instance. 3. How far does Whately connect Syllogism and Induction? How would Mill prefer to state the case? 4. Is the Emperor of Germany mortal? Give the reasons for your opinion fully. 5. A is a strong induction: B is a weak one: what is the effect of these (if any) on each other? 6. State accurately what Mill means by Cause. Mention other meanings of the word. 7. What Sciences are most indebted to the various Methods of Induction? Give instances. 8. What is the difference between Observation and Experiment? To what is each applicable? 9. Explain and illustrate what Mill means by Deduction. 10. Explain and illustrate what he means by Explanation of Laws, Composition of Causes, and Intermixture of Effects? JUNIOR FRESHMEN. Mathematics. A. MR. PANTON. I. Two triangles, whose vertices are C and C', have a common base AB; prove that they are to one another as the segments into which the line CC' is divided by the base. 2. If a, b, c be the sides of a triangle, and l, m, n the distances from the vertices to the centre of the inscribed circle; prove the relation 3. Prove the trigonometrical equation sin2 (A + B) = sin2 A + sin2 B + 2 sin A sin B cos (A + B). 4. Prove the formula a b in a plane triangle, and write down the corresponding logarithmic equa tion. 6. If one person can do a piece of work W1 in the time t1, and if another person can do a piece of work W2 in the time t2; find in what time, both acting together, can do a piece of work W3. MR. F. PURSER. 7. A line AB is cut internally in O, and externally in O', the ratio AO: BO being the duplicate of the ratio AO: BO; prove that 00' is a mean proportional between AO', Bơʻ. 8. The base of a right-angled triangle being given, find the locus of the centre of the square described on either side. 9. Solve the equation x2 + x − 4 + (x + 1) √x2 − 5 = 0. 10. Find x, y from the equations √x (1 − y) + √y (1 − x) = a, √x (1 − x) + √y (1 11. If y = a + bx + cx2, where a, b, c are constants, and if we are given that to the values 1, 2, 3 for x answer the values 1, 10, 100 for y, find the value of y when x = 4. 12. Wishing to ascertain my position, I observe three points A, B, C, which are known to lie in a right line from South to North in the order given; their mutual distances being also known. Prove that, denoting by 0, o the observed angles subtended by AB, BC respectively, the station B will bear West of North by an angle w given by BC cot o AB cot 0 cot w = AC MR. W. R. ROBERTS. 13. Construct a triangle, being given the vertical angle and the segments into which the line bisecting it divides the base. 14. Describe a triangle of given species, whose sides pass through fixed points, so that its area may be a maximum. 15. Prove Ptolemy's theorem by inversion. 16. Given base and sum of sides of a triangle, show that is constant. 17. Solve the equations tan A. tan B x y = 5y? – I, xy + 2 = 4y. 18. Find the square root of 1 + 4xa ̃3 + 2x2 (a3 + 2a ̄3⁄4) + 4x3 + x1a3⁄4. B. MR. PANTON. I. Describe a circle passing through a given point, and cutting harmonically two given finite right lines. |