a 12. Describe the phenomena of the seasons (1) to a per sou within the tropics, (2) to a person within the arctic circle. 13. Investigate the position of the stationary points of Venus as seen from the Earth. Do these coincide with the points of greatest elongation? Give a reason for your answer. VI. MECHANICS AND NEWTON. 1. State the proposition known as “the parellelogram of forces.” Given its truth for the direction of the resultant, prove it for the magnitude. Two forces, one double the magnitude of the other, act at a point at an avgle 0, and have a resultant 4lbs, when they act at an angle 180—0 the resultant is 3lbs. Find the forces and the value of cos 0. 2. Find the conditions of equilibrium of a body acted on by forces in one plane. A right circular cone of weight W rests with a point of the edge of its base in contact with a smooth plane inclined at an angle a to the horizon. The axis of the cone is inclined at an angle o to the horizon and a string attached to its vertex passes over a pulley and supports a weight P. The string being horizontal in the position of equilibrium, prove that P = W tan a, and tan 0 = cos a cos B + 4 sin a sin B 4 sin (B — a) where B is the semivertical angle of the cone. 3. Find the position of the centre of gravity of the frustrum of a thin spherical shell contained between two parallel planes. Deduce the position of the centre of gravity of the portion of a homegeneous spherical shell whose inner and outer radii are a and 2a contained between a plane through the centre and a parallel plane at a distance a from the centre. 4. Find the equation of the common catenary. Prove that if t and t be the tensions at two points, the distance of the latter of which from the axis is double that of the former ť csť + c) 2 5. A frame consisting of six equal heavy rods jointed at their extremities has the upper rod fixed in a horizontal position. The middle point of this rod is connected with the ends of the lowest rod by strings of such lengths that the whole forms a regular hexagon. Find by virtual velocities the ten sion of the strings. 6. State the three laws of motion. Deduce the general equations of motion of a particle acted on by any forces. 7. A particle moves in a straight line under the influence of an attractive force equal to f times the distance from a fixed point. Find the position and velocity at any time. If the force be repulsive and the particle be projected from a point at a distance a from the centre with a velocity a N My discuss the motion and the time of reaching the centre of force. 8. A body is projected from a given point in a given direction with a given velocity, and is acted on by a constant force in a constant direction. Find the range and the time of flight on any inclined plane passing through the point of projection. Find the condition that the body may strike the plane per pendicularly. 9. Find the polar differential equation to the path of a particle acted on by a central force. Prove that dr h2 C 2 Pdr. dt 92 Of what general principle is this equation a particular case ? 10. Prove that when a particle is moving freely in a plane curve under the action of any forces the velocity at any point is given by the equation. 22 2F2 where F is the resultant force and 49 the chord of curvature in the direction of F. Prove that this is also true in a resisting medium if F does not include the force of resistance. + . 11. State and prove Lemma IV., and apply it to find the area of an ellipse. 12. Prove the first Proposition of Newton's second Section, and deduce that in any central orbit the velocity at any point varies inversely as the perpen dicular on the tangent from the centre of force. 13. Show that every apsidal distance divides a central orbit symmetrically. Examine the locus of all possible positions of the centre of force, if the curve described is an ellipse. For the other subjects, viz., the GOSPEL OF S. John, the ACTS OF THE APOSTLES, PALEY's EVIDENCES, and NATURAL THEOLOGY, Candidates for Honours take the papers for Students not Candidates for Honours. ADMISSION AND FIRST YEAR EXAMINATION IN THEOLOGY. For Admission. I. LATIN GRAMMAR. 1. Distinguish between unquam, usquam, ubique oblitus, oblitus-clava, clavus--vellitis, velitis simulo, dissimulo. 2. Give the derivation and literal meaning of apricus, stipendium, case, peculiar, solemn, grammar, syllable, consonant. 3. Decline supellex, paterfamilias, jecur, sus, dens, , gigas, comes. 4. Give the chief rules for the oratio obliqua. Turn the following into oratio obliqua : Quantum possum, te ac tua vestigia sequor. Hoc faciam, sed vos non facietis. 5. Explain the terms. Cardinal and Distributive num bers, Heteroclite nouns, Deponent verbs, Syntax, Syncope, Tense. 6. Parse Fungar-tædet-fieri—recepisset-contuleris -morere-adultus-faxit-sirit. 7. Do adjectives alone admit of comparison? Give the degrees of comparison of nequam, magnificus, dubius, dives, pius, pauper, senex. 8. What constructions have the following verbs, and what are their meanings : Animadverto—caveo consulo-moderor-tempero-do? 9. Give the chief tenses of: abdo—frango—rumpo tribuo - fulcio fatiscor-ulciscor—reor—domo juvo—prandeo. 10. Explain the following figures of speech, and give instances : Alliteration-Litotes—Synecdoche-Hypallage Zeugma. Accidentia and evenientia. and exsul. securus. For Admission and First Year. II. THE GOSPELS OF ST. MARK AND ST. JOHN, THE ACTS OF THE APOSTLES. 1. Explain the following passages, and point out any errors or doubtful renderings in the English version. Give the original Greek where you can : “ An alabaster box of ointment of spikenard very precious." “When he thought thereon he wept.” “ He came unto his own and his own received him not." “ And other sheep I have which are not of this fold : them also I must bring, and they shall hear my voice, and there shall be one fold and one shepherd.” ναι. “And on the Sabbath we went out of the city by a river side, where prayer was wont to be made.” “ The law is open and there are deputies." 2. Translate accurately, with notes upon the words or phrases in brackets :- και ουκ ήδύνατο. ο γάρ Ηρώδης έφοβείτο τον Ιωάννην, ειδώς αυτόν άνδρα δίκαιον και άγιον, και συνετήρει αυτόν]: και ακούσας αυτού, [πολλά επoίει] και ηδέως αυτού ήκουε. Και ανέβη προς αυτούς εις το πλοίον, και [εκόπασεν] ο άνεμος, και λίαν εκ περισσού εν εαυτοίς εξίσταντο, και εθαύμαζον, ου γάρ [συνήκαν επί τοις άρτοις]: ήν γάρ ή καρδία αυτών πεπωρωμένη. Και επηρώτησε τον πατέρα αυτού, Πόσος χρόνος έστιν ως τούτο γέγονεν αυτώ ; ο δε είπε, Παιδιόθεν και πολλάκις αυτόν και εις πυρ έβαλε και εις ύδατα, ίνα απολέση αυτόν αλλ' εί τι δύνασαι, βοήθησον ημίν, σπλαγχνισθείς εφ' ημάς. ο δε Ιησούς είπεν αυτώ, Το ει δύνασαι πιστεύσαι: πάντα δυνατά το πιστεύονται. 3. Translate and explain the following words and phrases :-τίλλοντες τους στάχυας – σπεκουλάτωρα – ένοχος-άλεκτοροφωνίας-διά της τρυμαλιάς της ραφίδος εισελθείν --έχετε εν εαυτοίς άλας ραπίσμασιν αυτόν έβαλλον. 4. Write a short life of St. Mark. 5. Note any particulars that are common to the Gospels of St. Mark and St. John and are not found in the other Gospels. How should we most naturally account for the minute particulars by which both Gospels seem to be characterized ? 6. Translate accurately : 'Εγένετο άνθρωπος απεσταλμένος παρά θεού, όνομα αυτώ Ιωάννης, ούτος ήλθεν εις μαρτυρίαν, ίνα μαρτυρήση περί του φωτός, ίνα, πάντες πιστεύσωσι δι' αυτού φωτός ήν το φως το αληθινόν, και φωτίζει πάντα άνθρωπον ερχόμενον εις τον κόσμον. What other ways are there of taking the last sentence ? “Απεκρίθη ο Ιησούς και είπεν αυτοίς, Λύσατε τον ναόν τούτον, και εν τρισίν ημέραις έγερώ αυτόν. είπον ούν οι |