> ! l)(\ ^tnatc---;'}oiuc (i:':iaiuiiuuio!i|laijr iih iB€:o-ei, , \ii (■('. Cornell Unlvarsity Library arV16497 Cambridge senate-house examination paper olin.anx 3 1924 031 426 087 Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031426087 CAMBRIDG1E 1860-61, A COLLECTION OF ALL THE PAPERS SET AT THE EXAMINATIONS FOR THE DEGEEES, THE VARIOUS TRIPOSES, AND THE THEOLOGICAL EXAMINATION : ALSO, THE CHANCELLOR'S MEDALS AND SMITH'S PKIZES: TOGETHER WITH THE LISTS OF CANDIDATES AND OF THOSE EXAMINED AND AFFEOVED. MACMILLAN AND CO. (ZDambritfge : AND 23, HENRIETTA STREET, COVENT GARDEN, HonlJon, 1862. It CAMBRIDGE : PRIKTED BY WILUaM aKTCALFE, OKKEN STRKET. CONTENTS. Page Examination for Chancellor's Medal, (Legal Studies), February, 1861 7 Examination for Chancellor's Medal, (Classical Studies), March, 1861 11 Smith's Prize Examination Papers, January, 1861 16 Examination for B.A. Degree, May, 1861 23 Theological Examination, October, 1860 49 Previous Examination, October, 1860 66 Examination for B.A. Degree, November, 1860 65 Law Degree Examination, Dec&nber, 1860 70 Examination for B.A. Degree, January, 1861 78 Classical Tripos, February, 1861 108 Examination for B.A. Degree, February, 1861 115 Moral Sciences Tripos, February, 1861 120 Natural Sciences Tripos, March, 1861 129 Previous Examination, Lent Term, 1861 1 35 Theological Examination, Easter Term, 1861 162 B.L. Examination, May, 1861 , 175 First M.B. Examination, May, 1861 , 178 Second M.B. Examination, May, 1861 182 INDEX TO THE SUBJECTS, &c. Acts of the Apostles, 34, 35, 36, 37, 51, 66, 118, 164. -Sachylus, Cheop., HO. Aix-la-ChapeUe, Treaty of, 77. Algebra, 43, 44, 45, 46, 61, 68, 80, 116, 147, 148. Anatomy, Comparative, 179. " Human, 178. Aristophanes, Nubes, 11. " Pax, 109. Aristotle, Politics, HI, 113, " Khetoric, 12. Arithmetic, 57, 58, 80, 140, 141, 142. Articles of Religion, 52, 165. Astronomy, 88. Athenseus, 111. B.A. Degree Papers, 23, 65, 78, 115. Blackstoue (Warren's), 71, 75. Burke, for Greek Prose, 12, Butler's Analogy, 173. Chemistry, 181. Christianity, Evidences of, 66, 57, 138, 139. Church of England, Liturgy of, 53, 166. Cicero, Epist. ad Att., 113. " pro Csecina, 75. " pro Cluentio, 13. " pro Milone, 114. " pro Plancio, 112. »' Philippics, 38, 39, 40, 114. Classical Tripos Papers, 108. Conies, 79. Constitutional History, 7, 72, 76, 178. Corinthians, 1st Epist., 164. Demosthenes, Pantsen, 12. " c. Meid., HI. Digest, 70, 73, 176. Diseases, Surgical, 182. Dynamics, 82. Ecclesiastical History of first three Centuries, 64, 168. Economy, Political, 120, 124, 126. England, Constitutional History of, 7, 72, 76, 178. England, Reformation in, 41, 42, 43, 64, 69, 119, 168. Euclid, 24, 25, 26, 27, 59, 62, 66, 79, 116, 143, 144, 145, 160. Euripides, Bacch^, 27, 28, 29, " Furens, 11. Exodus, 170. Gaius's Commentaries, 74. Galatians, Epistle to the, 164. General Paper, 77. Genesis, 169. Gibbon, fi3r Latin Prose, 113. Greece, History of, 113. Green's James IV. for Greek Tri- meter Iambics, 110. Hallam's Const. Hist., 7, 72, 76, 178. Haynes, 75. Herodotus, 66, 111, 118. Hesiod, Theogonia, 109. History, 121, 123, 125. " (Ecclesiastical) of the first three Centuries, 54, 168. " of Philosophy, 128. " of the Reformation in Eng- land, 41, 42, 43, 54, 69, 119, 168. Historical Books of the Old Testa- ment, 60, 163. Homer, Iliad, 109. " Odyssea, 11. Hook's Li ves of Abps. of Canterbury, for Latin Prose, 113. Hooker, for Greek Prose, 111. Horace, Ars. Poet., 13. " Carm., 114. " Epist., 111. Hydrostatics, 30, 31, 32, 33, 67, 84, 116. James, St., Epistle of, 164. John, St., 51, 164. Jurisprudence, 122, 126, 127, 177. Medical, 183. Justin Martyr, 172. Justinian's Institutes, 71, 74, 176. Juvenal, Satires, 68, 112, 114, 117. INDEX TO THE SUBJECTS, &C. Keats' Endymion, for Latin' Hexa- meters, 112. Law Degree Papers, 70, 175. " English, 9. " Hindoo, 177. " International, 8, 77i " Mohammedan, 177. " Roman, 8, 70, 72, 174. Liturgy of the Church of England, S3, 166. Livy, 112. Logic, 122, 124, 126. Lucretius, 111. Luke, St., 61, 151, 162, 153, 154, 155, 166, 157, 168, 164. Mark, St., 61, 63, 64, 164. Martial, 13, 112. Materia Medica, 180. Mathematics, Pure, 91, 99, 103, 106, 106. Mathematical Tripos Papers, 78. Matthew, St., 61, 164. Mechanics, 30, 31, 32, 33, 60, 67, lie, 146, 147. Medal, Legal Studies fbr Chan- cellor's, 7. " Classical Studies for Chan- cellor's, 11. Medical Degree Papers, 178, 182. " Jurisprudence, 183. Medicine, Obstetrical, 182. Mental Philosophy, 121, 123, 127. Moral Philosophy, 120, 123, 126. Moral Sciences Tripos Papers, 120. Nahum, 170. Natural Philosophy, 89, 95, 103, 105, 106. Natural Sciences Tripos Papers, 129. Newton, 88. Ovid, Mctam,, 112. Optics, 84. Paley's Evidences, 66, 57, 138^ 139. " Horae Paulinse, 173. Pathology, 180, 183. Peele's Arraignment 6f Paris, for Greek Elegiacs, 110. Persius, 114. Peter, St., 1st Epist., 51, 169. Pharmacy, 180. Philosophy, History of, 128. Mental, 121, 123, 127. Moral, 120, 123, 125. " Natural, 89, 95, 103, 105, 106. " Political, 121, 123, 125. Phy^ie, Prattice of, 183. Physiology, 178, 179. Pindar, Pythia, 109. Plane Trigonometry, 80. Plato, Charm., HI. Plautus, Aulul., 13. Pliny, Natural History, 113. Political Economy, 120, 124, 126. Previous Exam. Paper, 66, 135. Problems, 86, 93, 97, 101. Propertins, 112. Quintilian, 112. Keformation, Hist, of, in England, 41, 42, 43, 64, 69, 119, 168. Keligion, Articles of, 52, 166. Komans, 51, 171. Home, History of, 114. ' Septuagint, 170. Seneca, 113. Sophocles, (Ed. Colon., 110. " (Ed. Tyr., 150, 161, 162, 153, 164, 156, 167. Smith's Prize Papers, 16. Statics, 82. Tacitus, Annales, 13, 112. " Hist., 151, 152, 154, 155, 157. Tennyson's In Memoriam, for Latin .Alcaics, 112. Terence, Andria, 63. Terentius, Phormio, 111. Tertullian, de Corona Militis, 172. " de Idololatria, 172. Theological Papers, 49, 162. Theocritus, 109. Thucydides, 12, 110. Timothy, 61. Trial, State, 7. Virgil, iEn., 12, 112. Wilkes (John), Trial of, 76. Xenophon, 63, 111. EXAMINATION FOR CHANCELLOR'S MEDAL, LEGAL STUDIES, February, 1861. EXAMINERS : John Thomas Abdt, ll.d., Trinity Hall. Joseph Sharpe, ll.d., Jesus College. Herbert Broom, m.a.. Trinity College. Charles Stuart Calverlet, m.a., Christ's College. CONSTITUTIONAL HISTOEY. 1. "What circumstances had, (it is said,) placed Charles at his accession in antagonism with the people? What views are taken by Clarendon, Guizot, and Hallam, respectively, about the question ' Who was the aggressor' in the quarrel between him and the Parliament? 2. Give a sketch of the rise and principles of the Independents ; and of the circumstances which led to the decline of the Presbyterian party. 3. Compare the situation of the English Church in the latter part of Elizabeth's reign with its situation under James and Charles. i. Give some account of the Council of the North : and of the Star Chamber. When and how was the latter Court abolished ? How far do you consider that Charles himself was answerable for this or any other ' illegal jurisdictions' ? 5. What were the leading topics discussed at Uxbrldge ? and on what grounds does Hallam think that an agreement was out of the question ? What was, on the whole, the ^character of the Long Parliament, as estimated from a survey of its measures, beneficial or otherwise ? 6. Trace the gradual progress of the Republican party from 1645 to 16 18. 7. What considerations may have led Charles to take refuge in Scotland, and how did that step aflfect his position and prospects ? Can any apologies be made for the surrender of him by the Scots ? 8. State briefly any political arguments that have been advanced in &VOUT of the King's execution. THE STATE TEIAL. 1. State any disadvantages to which the prisoner was subjected in the manner and conduct of the trial. What were the leading charges against him ? How did he answer the one concerning billeting soldiers in Ireland ? 2. Give an outline of Mr. Lane's arguments for the defence, and of Lord Digby's objections to the bill of attainder. Has any body been subsequently condemned by bill of attainder ? 8 EXAMINATION FOB CHANCEtLOB's MEDAL. 3. How does Hallam gather that Strafford was 'party in a conspiracy to subvert the fundamental laws and liberties of his country' •- and, if he were, how far would he be guilty of treason ? 4. Whatpart had Strafford taken in the Petition of Eight? What were the origin and objects of that Petition ? What is meant by ' Ship-money' ; and is there any proof that it was countenanced by Strafford i EOMAN LAW. 1. Explain accurately the meaning and object of the Roman diTision of Actions into Real and Personal, with reference to Rights. Why is the term Vindicatio applied to Real actions ? 2. Give a short sketch of the changes in the Law of Actions. 3. Mention the different parts of the Formula, and explain the particular object of each part. 4. Explain fully the effect of the Exeeptio, with reference (o) to the pleadings and (i) the proofs in an action under the formulary system. What changes were introduced herein by Justinian's alterations? 5. By what special plea was our principle of law ' nemo debet bis yexari pro eadem causa' maintained at Rome i 6. Was there any general limitation in time of the Plaintiff's right to sue under the formulary process, and under Justinian's system i 7. Ch. Principio earn esse dico liberam. Xhk. hem ! Ch. Civem Atticam. Thk. hui ! Ch. Meam sororem. Thb. os durum ! Tekeni. Eimuch, Act. it. se. 7. Explain the allusion here to the Actiones Praejudiciales. 8. What was the analogous form of an action of ejectment at Rome? In what important points did the Praetorian remedy differ from that given Jure Civili? 9. "Interdicta omnia licet in rem videaniur coneepta, vi tamen ipsa personalia sunt." D. 43. 1. From the passage in italics can any argmnent be advanced against Savigny's theory, that Interdicts belong to the law of obliffations ? How does he overcome that difficulty, as well as this other that in the Roman Law they are not classed with obligations ? 10. What was the Interdict applied for in Csecina's case? To what set of Judges was that case referred ? Draw a formula embodying the question of fact remitted to them for trial. 11. Is there any reason for supposing that there was a difference between Real actions and Possessory interdicts in the amount of evidence required to support the Plaintiff's claim ? 12. Describe briefly the Actiones Institoria, Exercitoria, and Tributoria. Which was likely to have been the most important of these ftom the peculiar condition of Roman Society ? 13. What was the Sponsio ? How was it introduced into the formula ? 14. Omnia judicia absolutoria sunt. Gaii Comm. iv. 114. Explain this; and state the effect produced by the Litis contestatio upon this principle. INTEENATIONAL LAW. 1. Upon what, considered in an international point of view, is the jurisdiction of Courts of Justice founded ? 2. Can the sovereign prince of one country sue or be sued in the courts of another country ? and if so, state in what cases. EXAMINATION FOIt CHANCELLORS MEDAL. 9 3. ^ a British subieot destroys, in a foreign country, the house and furniture of B another British subject, and A also assaults JS, Under what circumstances can B have a remedy against A in the English Courts, and for which of the above injuries? i. A a, resident in England makes a parol contract with B a British subject resident in France, to employ B as his agent, the agency to be for one year and to commence at and from a future day. By the law of France this contract, although not in writing, can be enforced by the Courts in that country. By the 4th section of the statute of Frauds it is enacted, " That no action shall be brought whereby to charge any person upon any agreement that is not to be performed within the space of one year from the making thereof, unless the agreement upon which such aciion shall be brought or some memorandum or note thereof shall be in writing and signed by the party to be charged therewith." Can B sue A upon the contract, in the English Courts? Give the reasons for your opinion. 5. A debt is contracted in a foreign country by whose laws the debtor is not liable to arrest. The debtor and creditor are both subjects of the country in which the debt is contracted. The debtor comes to reside in England : can the creditor arrest him ? 6. Define a "Judgment in rem" and a "Judgment in personam." Give uistances of the different descriptions of each, and point out whether any of the instances you specify are or are not conclusive in foreign countries. 7. With what system of law must the proofs in the following cases accord ? (1) The due execution of wills and testaments of moveables and immoveables. (2) Deeds or conveyances of property, required to be registered by the law of the country where the property is situate, but not required to be registered by the law of the country in which legal proceeding are pending. 8. How do the courts of justice of one country arrive at the knowledge of the laws of another country ? 9. In what cases can a person resident out of the jurisdiction of the English Courts be sued in such courts ? 10. How can the Judgment of a foreign court be enforced in this country ? 11. Enumerate some of the principal grounds of objection to the en- forcing a foreign judgment. 12. (1) A sues .S in a foreign court and obtains judgment against him. (2) A sues Biaa foreign court and judgment is given for B. B afterwards comes to England : can A sue B upon the original causes of action in the above cases ? 13. State briefly the case of the fugitive slave Anderson. Give the principal argiunents for and against his extradition. ENGLISH LAW. 1 . What is meant by a presumption of law ? Into what two classes are legal presumptions reducible ? Give instances of each. 2. Mention various rules or principles of law illustrating either class of legal presumptions above referred to. 8. To what extent may a relaxation of the strict rules of evidence be allowed on a criminal trial ? 4. " Non refert quid notum sit judici, si notum non sit in formS jndicii/' What is the meaning of this maxim, and how does it practically apply ? 10 EXAMINATION FOR CHANCELLOH's MEDAL. 5. Is a wife admissible as a witness for or against her husband (1) in a civil, (2) in a criminal proceeding ! 6. What was the ancient office of Conservator of the Peace ? And how were Conservators of the Peace appointed ? 7. What are the principal powers given to Justices of the Peace by their Commission? 8. State shortly the ordinary mode of proceeding before a Justice of the Peace on a criminal charge. 9. State the purport of such Statutory provisions as have been enacted during the present reign for the protection of Justices of the Peace in the performance of their duties. 10. "What mode of procedure may be adopted against a Justice who acts corruptly or is guilty of misconduct in the execution of his office ? 11. When will a Justice of the Peace be entitled to Notice of action; and what may be the consequence of omitting to give him due Notice ? 12. Mention three leading principles characteristic of the system of judicial evidence which obtains in this country. 13. "Res inter alios acta alteri nocere non debet." Explain fully the practical operation of this maxim, and indicate its principal limitations. At what early period can it be proved to have been recognized in our Courts ? 14. What is meant by " backing" a warrant issued by a Justice of the Peace for the apprehension of an offender ? When is it necessary that the warrant should be " backed," and when not so ? ADJUDGED TO Lazarus ThrelfaU Baines, B.L., Trinity College. EXAMINATION FOE CHANCELLOE'S MEDALS, CLASSICAL STUDIES, March, 186L EXAMINEES : The Vioe-Chanoellor. Ktchard Okbs, D.D., Provost of King' s College. Wtlliam Whewell, D.D., Master of Trinity College. Henry Wilkinson Cookson, d.d.. Master of St. Peter's College, James Cartmell, d.d., Master of Christ's College. William George Clark, m.a.. Trinity College. (Public Orator.) William Hepworth Thompson, m.a., Trinity College. Charles Kingsley, m.a., Magdalene College, Joseph Barber Liqhtpoot, m.a.. Trinity College. 1. 1. Give a brief sketch of the plan of the Odyssey. 2. Quote from the Homeric poems any inconsistencies in the story which you may remember, and mention any portions which may have struck you as being inferior in poetical merit to the rest. What inference would you draw, respecting the authorship of the poems? 3. Discuss the etymology and signification of the following words : dpKLO^f dtl\t]f ii\ij3aT0^f oiJ\os, nzonevtmiv. 4. Scan the following line : EOiB o TauB' wp/jLaLVE KaT& ippiva Kal Kwra dufiov. II. Translate: Beginning, AvtoI d' els dyopriv k'iov idpooLj ovSi tiv' aWoy, k.t.X, Ending, ovucud ol being assumed to be a function oir and 6. 17. Given the partial differential equations, (P.r0 1 Id' .rcf) ^d.rcj) ^•r-^-^^H^*'-^=° (^)' di* t* '-^ - ^ -^^ = » (=^)' -^ - ^^ -"^ = ° («)• shew how to find a particular form of

, and also / and !/<■, are reciprocal j and thence from the known values of j^e-»* cosca;<& and/" «-»* sineiite deduce those of two other definite integrals. ' 18 smith's prizes, 5. In a rainbow of any order, shew that a small pencil of rajrs in the primary plane in the middle of its course within the drop has its focus at the middle point of incidence, or else at an infinite distance, according as the number of reflections is odd or even. 6. The altitudes of two known stars are taken with a theodolite which is clamped in azimuth, find the latitude of the place, and point out the circumstances which are favourable to accuracy in the determination. 7. In a heliostat of such a construction as to involve but one reflection, shew that a line drawn through any fixed point perpendicular to the plane of the mirror will describe in the 24" an elliptic cone, the section of which by the plane of the equator is a circle which is described uni- formly. Examine the case in which the rays are reflected towards a point the south polar distance of which is'equal to the north polar distance of the Sun. 8. Express the position of the invariable plane of a system of bodies not acted on by forces external to the system in terms of quantities depending on the motions of and the motions about the centers of gravity of the several bodies. 9. A planet circulates in a slightly resisting medium; find the efiect of the resistance on the angle described in a long time, the undisturbed orbit being supposed circular. 10. A uniform flexible and inextensible string at rest in space is pulled by an impulsive force applied at one end in the direction of the tangent; shew that the impulsive tension (r) is determined by the d^T T equation — - =. ■—, , where R is the radius of absolute curvature ; and ds' R' find the components of the initial velocity at any point in the directions of the tangent, radius of absolute curvature, and normal to the osculating plane. 11. A slender fluid ring revolves uniformly round I a center of force situated at its center, the force varying inversely as the square of the distance ; find approximately the form of a section of the ring. 12. If a mass of steel be permanently magnetized in any manner, shew that the effect of the Earth's magnetism upon it will be the same as if it were replaced by a slender bar, fixed relatively to the mass, and uniformly and longitudinally magnetized. What is meant by the magnetic moment of a magnet i 13. When a small flame is viewed by reflection in a slightly tarnished looking glass some way off, at a moderate angle of incidence, a series of coloured bands is seen accompanying the image ; explain the formation of these bands, and calculate their forms. 14. A small solid sphere is contained in an infinite mass of air not acted on by external forces ; assuming that when the sphere moves through the air at rest, along a straight line, with a small velocity v, dv the resistance is expressed by o j- + bv, determine the motion of the sphere produced by an infinite succession of plane waves of sound, in which the disturbance is expressed by a sine or cosine. 15. The motion of an indefinitely extended and slightly disturbed homogeneous elastic medium, not acted on by external forces, nor subject in the position of equilibrium to internal tensions, being determined according to the method of Lagrange by the equation smith's peizes. .19 where «, v, w are the displacements parallel to the rectangular axes of X, y, z, and F is a function of the nine differential coefficients of u, v, w with respect to x, y, z, it is required to express by means of the function V the normal and tangential tensions at any point on planes parallel to the co-ordinate planes. Write short dissertations on the following subjects : (1) On the signification and integration of the equation Pdx + Qiy + Rdz = 0. (2) On Clajraut's Theorem. (3) On the colours of thin crystalline plates in polarized light. By Professor Adams. 1. The coefficients of the algebraical equation /(») = are all integers; show that if /(O) and /(I) are both odd numbers, the equation can have no integral root. 2. Of a series of quantities Oj, u^, a^, &c., the first two are given, and each of the others is a mean proportional between the two immediately preceding it ; find the limit to which a„ approaches as n is indefinitely increased. 3. If m be any positive integer, prove that the integer next greater than (3 + V S)"' is divisible by 2 ^ when m is even and by 2 ' when m is odd. 4. If both X and y lie between the limits — f and + J, and every value between those limits is equally probable, find the probability that the value ot X + y lies between — m and + m, where m is any quantity not greater than 1. 5. A conic section is circumscribed about a given quadrilateral : show that its center always lies in another conic section Which passes through the middle points of the sides and diagonals of the quadrilateral, as well as through the point of intersection of the diagonals and the points in which the two pairs of opposite sides meet when produced. 6. Find the envelope of all chords of a conic section which subtend a given angle at the focus. 7. C is the middle point of an arc ACB of finite and continuously varying curvature, the difference between the radii of curvature at A and B being ultimately m . AB. If R be the radius of curvature at C, show that the chord AB ultimately cuts the tangent at C in a point whose distance from C IS — , m Also show that the angle which AB makes with the tangent at C is ultimately equal to two-thirds of that which the line joining C with the middle point of A.B makes with the normal at C. 8. If X and y be connected by the equation dy and if when x = 0, y = and -^ = 1, find the value of y when x = I , so that the error shall be less than '0001. c2 20 smith's prizes. 9. Investigate the different kinds of contact which exist between a curve surface and its tangent plane at any point according as da^ ' dtf \dxdyl is positive, negative, or zero. In a surface which can be generated in two ways by the motion of a straight line, if the generating lines through any point be projected on the plane of xy, and if a, /3 be the angles which those projections make with the axis of x, prove that d\ d'z 1 „. dxdy , 1 , , ^ „, dxdy - (tana + tan/3) = - -^ , and - (coto + cot^) = - — ^ . dy^ dsi? 10. A, B, C are the angular points of a spherical triangle, A, B', C the middle points of the sides o, b, e which are respectively opposite to them, the center of the sphere ; prove that the volumes of the triangular pyramids OJ'B'C, OAB'C, OBA'C, OCA'S are respectively propor- tional to a h c 1, cos-, cos-, cos-. 11. The surface of a given circle is self-luminous and of tmiform bright- ness ; find the illumination at any point of a plane which is parallel to the plane of the circle and at a given distance from it : supposing, as usual, that the intejisity of radiation from a luminous element in any direction varies as the cosine of the angle between that direction and the normal to the luminous surface. Also find the total quantity of light which falls upon a circle of given radius, the line joining the centers of the two circles being perpendicular to each of the planes. 12. A body moves in a plane about a fixed point under the action of given forces. If the areal velocity and the direction of motion of the body at a proposed point be known, find the semi-latus rectum of the elliptic orbit which has a contact of the second order with the real orbit at that point, its focus being at the given fixed point. Also find the changes produced in an indefinitely smaU time in the eccentricity and in the position of the apse of this elliptic orbit, in terms of the corresponding change of the semi-latus rectum. 13. If the force acting on the Moon relatively to the Earth be resolved into two forces, one in the plane of the orbit and the other perpendicular to the ecliptic, prove that the latter force ds employing the usual notation. Hence derive the equation dh ^ d0 de' ^ * Hv — ' where H denotes twice the Moon's areal velocity. smith's prizes, 21 14. Explain clearly the various means by which we can compare the mass of the Earth, (I) With that of the Sun, ^21 With that of the Moon, (3) With that of a given volume of water, pointing out what are the data on our imperfect knowledge of which the chief uncertainty of the result in each case depends. 15. If («i denote the angular velocity of a body at any time about an axis fixed in space, and ai' the angular velocity at the same time about an axis fixed in the body, prove that at the instant when these two axes coincide dw' dtv^ 'di'"dt' Point out clearly why this needs proof. Also show that at the same instant rf'io' d'o>i dw^ dto, "dp ° IF ■'■ '^'"df ~"''~dF' a^ and <»s being the angular velocities about the other two axes in any rect- angular system. 16. A pencil of common light is incident on the surface of a uniaxal crystal. Shew clearly how to determine the course of the light after re- fraction into the crystal. When the axis of the crystal is in the plane of incidence and makes any given angle with the surface, investigate a formula for finding the angle of refraction of the extraordinary ray corresponding to any given angle of incidence ; and show that in the particular case when the axis lies in the surface, the tangents of the angles of refraction of the ordinary and extraordinary rays are to each other in a constant ratio. By the Master of Trinity. 1. If ABC he a straight line, and on AB, BC, AC, as diameters, semi- circles be described on the same side of the line, find (by a construction) a circle equal to the area bounded by the three semicircles. 2. Also inscribe in this area another circle and find its area. 3. A uniform straight rod hangs in a horizontal position from two vertical strings of unequal lengths : the rod being slightly disturbed but remaining horizontal, find its motion. Shew that the small longitudinal and transverse vibrations will be co- existent and independent. i. Of all spherical segments of equal curved surface, the hemisphere has the greatest content. 5. A great number of small soft spheres in regular arrangement occupy a space ; supposing the space to be compressed so that they become poly- hedrons, what will be the form of the polyhedron, and how much will the space be contracted? 6. Let ABODE be a polygon; produce the sides BA to u, CB to J, DC to e, and so on ; let aB, bC, cD, &c. be levers, resting at their outer extremities a, 6, c, &c. on props, and at their inner extremities B, C, D, &c. each on the next ; weights being hung at a given point of each of the levers, find the pressures at aU the points, A, a, B, b, C, c, &c. (Omi the weights of the levers). 7. Describe Horner's method for the solution of equations. Apply it to solve the equation a^ ~ 2x — 6 = 0, to 5 places of decimals. 22 SMITH S PRIZES. 8. Compare the motion of the nodes and apse of one of Jupiter's satellites with one of Saturn's. 9. Newton (Princ. Lib. i. Prop. 66, Cor. 19) proves that an equatorial ring of water, acted upon by the sun and moon, would have its greatest height at the octants after syzygies : prove this. How does it apply to the tides ? 10. A projectUe, acted upon by gravity, moves in a medium of which the resistance is proportional to the velocity : determine the curve in which it moves, and where it strikes the horizontal plane again. 11. If a cycloidal pendulum oscillate in a medium of which the resistance is as the mth power of the velocity (the density of the medium being small), find the law of decrement of the arcs described in successive oscillations. 12. " Motus soils medius a nodo [lunae] defiuitur per medium propor- tionale geometricum inter motum ipsius soils medium, et motum ilium mediocrem quo sol celerrime recedit a nodo in quadraturis." (Machin, as given by Newton, Princ. Lib. iii. Prop. 33, Scholium). Prove this. 13. Given the requisite 'observations, shew how the parabolic orbit of a Comet moving in the ecliptic, may be found : (the earth's orbit being circular.) 14. Define principal axes of rotation. Shew that every body has three such axes. 15. In the case of an oblique parallelopiped, what are the positions of these axes ? 16. A fluid is acted upon by gravity, and also, at each point, by a horizontal force proportional to the distance from a vertical plane. Shew that equilibrium is impossible, and determine what steady motion is possible. 17. Give Laplace's explanation of the phenomena of Double Refraction. Also Newton's. Shew the errors of both. Give the true explanation. 18. Trace the curves to which the following equations belong : * a;^ — Zxy + y' = ; s* — ixy + y* = 0, a:' — 4a;j + y^ = 0. 19. If a small magnet exist at the center of the earth, what wiU be the law of magnetic dip with reference to th emagnetic equator ? 20. A body moves in a given curve of double curvatiire ; what is the condition requisite that it may be retained in this curve by forces tending to two given centers ? The condition being fulfilled, find the forces to the two centers. If the curve be the regular screw-thread on a cylinder, and the centers two given points in the axis, apply this. 21. At a given time and place a star is observed, and it is found that the azimuth is equal to the altitude and the hour angle equal to the declination. Determine its position. 22. Sum the series 23. Find a quadrangle inscribed in a circle, the diameter being an integer, of which the sides, diagonals, and area are all rational. 24. Give the history of the parallelogram of forces. ADJUDGED TO. First Prize. William Steadman Aldis, B.A., Scholar of Trinity College, Senior "Wrangler. Second Pkize. John Bond, B.A., Scholar of Magdalene College, Second Wrangler. SENATE-HOUSE EXAMINATION PAPERS. EXAMINATION FOR B;A. DEGREE, Mat, 1861. EXAMINERS : Thomas Hughes Eakle, m.a., King's College. Fkancis Thomas Hurst, m.a., St. Catharine's College, George John Boudiee, m.a.. King's College. Churchill Babington, b.d.. Si. John's College. Thomas Samuel Woollaston, m.a., St. Peter's College, John Willis Clark, m.a.. Trinity College, CANDIDATES. Adams Christ's Carpenter Sidney Grove Trin. Addison Corpus Causton Joh. Grylls Joh. Agassiz Joh. Cavill Jesus Gurney Trin. Alder Trin. H. Clarke, R. D. Caius Hall Pet. Allen Trin. Clarke Emm. Hankey, S. A Trin. AUeyne Trin. Climenson Trin. Hargreaves Trin. Alston Joh. Cogswell Sidney Harries Jesus Amherst, Hon . P. Trin. Collings Trin. Harwood Trin. H. Anderson Corpus Corfield Trin. Hawkesworth Trin. Apthorp Emm. Dash wood Christ's Hawkrigg, J. Clare Atherton Joh. Bavey Queens' Hayter rjlTlTn, Atkinson, F. H.Caius Davis Joh. Heathfield Trin. Bagnall Sidney Daw Emm. Henniker Trin. Baillie Trin. Dearsly Caius Henty IVin. Baker Magd. De Robeck Trin. Hodgson Pet. BaUs Pet. Dickinson Caius Hole Christ's Baraford Joh. Dobson 'J'rin. Hopton Trin. Baring-Gould Joh. Dodington Trin. Hose Joh. Barnard Trin. Duke Joh. Hosegood Sidney Beavan Caius Dunn, "W. A. Corpus Hudson, F.W. Trin. Beavan Joh. Dyson Trin. Jamieson Emm. Becher Trin. Elliot Trin. Kempson Emm. Best Joh. Ely Joh. Kershaw Cath. Beverley Joh. Evans Emm. Knox, A. B. Trin. Bishop Christ's Ewen Trin. Lewthwaite Trin. Blake Corpus Fa-flfcett Trin. Mabson l-rin. Blake Trin. Fenn Trin. Makins Trin. Boddington Pet. Forster Trin. Manners-SuttonMagd. Bottom Emm. Frost Trin. Marsden Queens Bowen Caius Gardner Corpus Matthews,W.P.P.Magd Bo wen Trin. Gibbs Trin. Mayne Joh. Bourke,Hon.H.L.Trin. Ginders Joh. McLaughlin Magd. Bragge Trin. Goodchild Emm. Meeking Trin. Brailsford Trin. H. Gorst Joh. Melville Trin. Brent Queens' Gorst Trin. Mirehouse, J. Clare Brymer Trin. Graham Pet. Moncrieff Trin, Butlin Corpus Griffiths Trin. Moore Magd. Carlyon Emm. Grimaldi Caius Morton Trin. 24 EXAMINATION FOE B.A. DEGREE. Muriel Pet. Rule Corpus Thorne Caius Newman Cath. Sargant Trin. ThomhUl Magd. Newall Trin. Savage Caius Tilston Trin. H. Neame Clare Scott Trin. Tooth Trin. Nott Trin. Seaton Trin. Trevelyan Christ's Onslow Trin. Selwyn Joh. Valentine Joh. Outram Cbrist's Shaw Caius Wailes Caius Page Joh. Shepherd, J.W.Trin. Walker Caius Palmour riTnTTi, Shirley Trin. Walker, C. Trin. Pardoe, J. Trin. Simcox Joh. Watkins Trin. Perceval Trin. H. Skeels Emm. Walsh Joh. Pidcock Corpus Slight Joh. Webber Trin. H. Pincott Caius Smith Emm. Wharton Queens' Pomeroy Trin. Staunton Joh. Wilkinson Corpus Powell, D. Trin. Stevenson Trin. Wilkinson Cath. Heeve Christ's Steward Joh. Wilson Queens' Roberts Joh. Stuart Caius Wilson, R. H. Trin. Kobinson Jesus Sturges Emm. Wilson, W D. Trin. Bogers Queens' Tarleton Joh. Wolley Emm. Kowlands, J. Corpus Tate Trin. Yardley Joh. Rowlands, L. J Corpus Tatham Trin. Yeoman • Trin. Rudge Corpus Taylor Queens' Young, T. C. Trin. EUCTTT1. 1. Define a straight line, a plane angle, a sector of a circle. When are triangles said to be similar ? 2. Draw a straight line perpendicular to a given straight line of un- limited length, from a given point without it. 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely the sides opposite to the equal angles in each, then the other sides shall be equal each to each. Shew by means of this proposition that if the angles, which two sides of a triangle produced make with the third side, are equal, the triangle is isosceles. 4. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another. If through a point, equidistant from two parallel straight lines, two straight lines be drawn cutting the parallel straight lines, they wiU intercept equEd portions of these lines. 5. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles. The exterior angles of a quadrilateral, made by producing the sides successively in the same direction, are together equal to the interior angles. 6. Triangles upon equal bases and between the same parallels are equal to one another. If from the opposite angles of a parallelogram straight lines be drawn to a point in the diagonal produced, the triangles, thus formed externally to the parallelogram, are equal. 7. If a straight line be bisected and produced to any point the rect- angle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. If a straight line drawn through the center of a circle bisect a EXAMINATIOBf FOH B.A. DEGREE. 25 straight line which does not pass through the center it shall cut it at right " angles, and conversely, if it cuts it at right angles it shall bisect it. 9. The angles in the same segment of a circle are equal to one another. If two straight lines whose extremities are in the ciroumferenoe of a circle cut one another, the triangles formed by joining their extremities are equiangular to each other. . 10. If two straight lines cut one another at right angles within a circle the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Hence shew that the angle in a semicircle is a right angle. 11. Inscribe a circle in a given square. 12. If the sides of two triangles, about each of their angles be propor- tionals, the triangles shall be equiangular ; and the equal angles shall be those which are opposite to the homologous sides. EUCLID. 1. Define a right angle, a plane superficies, and a segment of a circle. "When are segments of circles said to be similar i 2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal, the angle which is contained by the two sides of the one shall be equal to the angle con- tained by the two sides equal to them of the other. 3. The greater angle of every triangle is subtended by the greater side or has the greater side opposite to it. In an obtuse-angled triangle the greatest side is opposite the obtuse angle. 4. If a straight line falliMLon two other straight lines make the al- ternate angles equal to each oWer, these two straight lines shall be parallel. If two finite straight lines bisect each other the figure formed by joining their extremities is a parallelogram. 5. The three interior angles of a triangle are together equal to two right angles. Divide a right-angled triangle into two isosceles triangles. 6. If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram shall be double of the triangle. Describe a triangle that shall be equal to a given parallelogram and have one of its angles equal to a given rectilineal angle. 7. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part together with the square of the other part. 8. Find the center of a given circle. Only one circle can be drawn through three given points. 9. In equal circles equal angles stand upon equal circumferences whether they be at the centers or circumferences. 10. If a straight line touches a circle, and from the point of contact a straight line be drawn cutting the circle, the angles, which this line makes with the line touching the circle, shall be equ^ to the angles which are in the alternate segments of the circle. The segments into which a circle is cut by any straight line, contain angles whose difference is equal to the incUnation to each other of the straight lines touching the circle at the extremities of the straight line which divides the circle. 11. Inscribe a square in a given circle. 12. The sides about the equal angles of equiangular triangles are pro- portionals and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. 26 EXAraNATION FOR B.A. DEGREE. EUCLID. 1. Define a circle and a parallelogram. State the last axiom. 2. If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to each other ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz. those to which the equal sides are opposite. 3. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Prove the proposition fiiUy for both the interior angles. 4. Triangles upon equal bases, and between the same parallels, are equal to one another. The diagonals divide a parallelogram into four equal triangles. 6. If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle con- tained by these two sides is a right angle. The triangles ABC, DEF, having the angles ACB, DFE right angles, have also the sides AB, AC equal to DE, DF each to each, shew that the triangles are equal in every respect. 6. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. In a triangle, whose vertical angle is a right angle, a straight line is drawn from the vertex perpendicular to the base, shew that the square of either of the sides adjacent to the right Mgle, is equal to the rectangle contained by the base and the segment of it|Pgacent to that side. 7. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side sub- tending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 8. Define the angle of a segment, also the sector of a circle. 9. The opposite angles of emy quadrilateral figure inscribed in a circle, are together equal to two right angles. If from O, the center of the circle inscribed in a triangle ABC, OD, OE, OF be drawn perpendicular to the sides BC, AC, AB respectively, and from any point P in OP, drawn parallel to AB, PQ, PR, be drawn perpendicular to OD, OE, respectively or these produced, shew that the triangles ABC, QRO, are equiangular to one another. 10. A segment of a circle being given, describe the circle of which it is the segment. 1 1 . Describe a circle about a given square. 12. If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another ; and conversely, if the segments of the base have the same ratio which the other sides of the triangle have to one another, the straight line drawn from the vertex to the point of section, divides the vertical angle into two equal angles. If two of the exterior angles of a triangle ABC be bisected by the lines COE, BOD intersecting in O, and meeting the opposite sides in the points E and D, prove that OD : OB : : AD : AB, aad OC : OE :: AC : AE. EXAMINATION FOR B.A. DEGREE. 27 EtJCLID. 1. Define a rigM angle and a rhombus. Give Euclid's Postulates. 2. If two angles of a triangle be equal to each other, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another. In an equiangular triangle the lines drawn to bisect the equal angles will also bisect the opposite sides at right angles. 3. If two straight lines cut one another, the vertical, or opposite angles shall be equal. In any rectilineal figure, the straight lines bisecting any interior angle, and the corresponding exterior one made by producing an adjacent side, are at right 'angles to each other. 4. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles. 5. Describe a square upon a given straight line. 6. If a straight line be divided into any two parts, the square of the whole line . is equal to the squares of the two parts together with twice the rectangle contained by the parts. In a triangle, whose vertical angle is a right angle, a straight line is drawn from the vertex perpendicular to the base, shew that the rectangle contained by the segments of the base is equal to the square of the perpendicular. 7. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. 8. Define the angle in a segment. What are similar segments ? 9. The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. If from O, the center of the circle inscribed in a triangle ABC, OD, OE, OF be drawn perpendicular to the sides BC, AC, JB respectively, and from any point F in OP, drawn parallel to AB, perpendiculars PQ, PR be drawn upon OD and OE respectively, or these produced, shew that the triangle QRO is equiangular to the triangle ABC. 10. Upon a given straight line describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. 1 1 . Inscribe a circle in a given square. 12. The sides about the equal angles of equiangular triangles are pro- portionals ; and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. Straight lines are drawn through the angular points of a triangle parallel to the opposite sides, and through the angular points of the triangle thus formed straight lines are drawn parallel to its opposite sides, and so on ; shew that all these triangles are similar to the original triangle, and any one has its sides bisected by the angular points of the preceding triangle. EUEIPIDIS BAOOH^. Translate the following passages into English Pkose : 1. Beginning, Xoxto*s 6* avriKa viv S&^aTO Qakd/ioi^KpoviSa^ Z'eus' /c.t.X, Ending, Bpojuios tux' av dyri Otatrous. — 1. 95 to 115. Write down the Attic form of every word in the above passage which has undergone alteration. TavpoKipwv : give the nominative and genitive cases. Give some account of the orgiastic worship of Dionysus (explaining the terms thyrsus, cista, and dithyra/mbus), and make such remarks as you 28 EXAMINATION FOR B.A. DEGBEE. deem expedient as to its antiquity and origin, "Write a short history of Thebes, from the earliest times down to its destruction by Alexander. Who restored it ? 2. Beginning, oVav Xd^ri Tts rdJi/ \6ytov dvtip aofpd^j k.t.X. !Ending, f^vPV' Si-Sd^u) tr* tos KoKtlo^ ixei toSe. — 1, 266 to 287. Give the principal tenses of the following verbs: \o/i/3a'i/\Biv, eI:"Aijou : quote corresponding expressions in Latin. isji/oTOTos, ijirKoTBTos : what is the rule for forming the superlative in -OTttTOff and -tOTaTOS ? How do t/KM, Epxofiai., and clp-t differ in signification in Attic Greek ? 4. Beginning, Kal Tr)v "ApEOje Traifi' ^ Appoviav, Sa[jLapT* kfifittf k.t.X. Ending, KA. ovk ol^a, tIkvov ailiKpoi iiriKovpo^ irarijp, 1. 1356 to 1366. Scan the first line : what have you to remark respecting the scansion ? How are iroX, iroS, and irtj distinguished ? Explain any apparent exception. Distinguish ■ttoS and irov. EHEIPIDIS BACCH^. Translate the following passages into English Pkosb : 1. Beginning, 'Ao-tas diro yaias, k.t.X. Ending, 'EXXaSos el? eupvxopov? AyuiAs tov Bpopiou, — ^1. 64 to 87. Give the Attic form of every word in the above passage which has undergone alteration. Ku^eXus : what are the different forms of this word ? What have you to remark on the quantity of one of the syllables ? Give some account of her worship. cupvxopous : derive this, and investigate the meanings of xop"". (Donald- son, New Crat. § 280.) EKToiros, K.T.k. Quote similar passages from Greek or Latin authors. 2. Beginning, HE. rauT' ovxl ^eiutIs dyxov^^ tfT* a^ta, k.t.X. Ending, 'Ej^toyo^ o' aiu irats KaTaio-j^uuEts ytvos, — 1, 246 to 265. iroXuw yikwi'. Decline the singular of both words : how is the accu- sative governed ? Give some account of the legendary history of Cadmus ; explaining also the parentage of Pentheus, What historical truth seems to underlie the myth of Cadmus ? Make any remarks that you deem expedient about the forms of the letters, and the introduction and disuse of certain letters in the Greek alphabet? Derive alphabet, explaining the meaning of its roots. Give the principal tenses of the following verbs : dpdw^ ^X^* '^^^^^1 yiyi^opai, ^po}, &yw, 3. Beginning, Al. iniQiL fiiv ov5iv, Tmv ipoiv \6ywv kXucdv, k.t.X, Ending, Al. (o Tay, et* eo-tiz; tv KaTaiTTriiTaL Ta^E. — 1. 787 tO 802. What are the significations of oi), ph, and ov pii in Attic Greek? Give examples of their use. Decline the singular of oti^Eis : how much of inflection of the word is in use? Illustrate a line in this passage from the New Testament. What tenses of lo-Tij/ii are transitive, and what intransitive ? EXAMINATION FOB B.A. DEGREE. 29 4. Beginning, ATA. ti S' ov koKiS^ tiSvS', fj tI XvtrripiSs ix" ! 'f.''''^' Ending, AFA. ws £fc\£Xt]cr/uai 7* a irdpo^ t'LirojiEv, 'na.Ttp, 1. 1264 to 1273. What is the force of IBoi ? What variations of accentuation do dis- syllabic prepositions admit, and with what exceptions? What does av signify, when joined with an indicative, optatiye, and suhjunetiye mood ? EUEIPIDIS BACOH^. Translate : 1. Beginning, piirmv 8e Avddiv -rous 'rroXvxpvt^ou^ yvas, k.t.\, Ending, Zt;i/* k^EKavx<^v^' t oVt ydfiovv ei^tiiffatro, — 1, 13 to 31, Suaxt-i^ov. Give the derivation ; what other reading exists ? niyatri, k.t.X. Point out an unusual construction in this clause. o-o balance in the system of pulleys, in which each pulley hangs by a separate string and the whole be put in motion, shew that p : w :: w's velocity in direction of gravity : p's velocity. 6. When a body is placed on a horizontal plane, it will stand or fall, according as the vertical line, dravni from its center of gravity, falls within or without its base. With what restriction is this true of any plane ? A sugarloaf, whose height is twice as great as the diameter of its base, stands on a table, rough enough to prevent sliding, one end of which is gently raised until the sugarloaf is on the verge of falling over, when this 34 EXAMINATION FOR B.A. DEKBEE, is the case, find the inclination of the table to the horizon: The center of gravity of a cone being distant from the base one-fourth of the height. 7. How is pressure at a point in a fluid estimated ? Shew that the surface of every fluid at rest is horizontal. In supplying a town with water, why is the locality of the reservoir selected in the highest position possible ? 8. If a body floats on a fluid, it displaces as much of the fluid as is equal in weight to the weight of the body ; and it presses downwards and is pressed upwards with a force equal to the weight of the fluid displaced. A symmetrical box, weighing 8 lbs., with a weight on the top, floats just immersed in a fluid ; how heavy must the weight be, in order that, when removed, the box may float with only one-third immersed ? 9. Define specific gravity and explain how it is measured. Shew how to find the weight of a body whose specific gravity is known. Find the weight of 64 cubic inches of copper, whose specific gravity is 8'8. 10. Describe the construction of the common air-pump and its operation. What advantage does Hawksbee's possess over the common air-pump ? 1 1 . Shew how to graduate a common thermometer. One thermometer marks two temperatures by 8° and 10", another thermometer by 11" and 14", what wiU the latter mark, when the former marks 16o? ACTS OE THE APOSTLES. Tkansiate : 1. Beginning, "Ai/fijOfS FaXtXatoi, k.t.X,. Ending, aaP^ciTov ixov o&oii, — ehap. i, 11, 12. Parse dyaX-jjepBels, iXtvatTai, Parse and explain the word Aaimi/ot. What place does St. Luke mention in his Gospel as the locality of the Ascension ? How do you reconcile the two statements ? What was the length of a Sabbath-day's journey ? ■ 2. Beginning, ^Ho-av Si irpoaKaprtpovvT^^ t^ SiSa-^^ rtjav ditocToktov^ k.t.X. Ending, KaQ* rifitpav Ty tK*fX»;fffa.— chap. ii. 42 — 47. What different explanations have been given to the words icXaVis toS dpTov ? What is specially meant by toTs ■Tr/joo-euxai! ? What is the difference between KT^iuoTa and u'lrap^tw ? Give the derivation oi ii(pt\6TriTi. 3. Beginning, *Ef Si rats ^]pipai^ TauTais nrXriQw ovTtav TtSv /xaQiiT^tty k.t.X. Ending, Kal T-p StaKovia tou Xoyou irpoiTKapTEp^tyopiEV, chap. vi. 1 — 4. Parse irpocrKaXiaafisvoi, KaTaXsiiffavTa^, iirttrKti/zafffie. What was the difference between the 'EXXtji/io-Tnl and the "Efipaioi ? What is meant by the words SiaKoveiv Tpairt'^aK ? 4. Beginning, 'O di SauXos tTt tftiruiuov diriiXiji Kal 6vov eIs tous p.adijTit TOU ICupToy, K.T.X. Ending, Kal XoXtj0TJff£Ta| trot ti o-e Ssl irotEiv, — chap. ix. 1 — 6. When is Damascus first mentioned in the Bible ? Does St. Paul on any subsequent occasion relate these events differently? What is known of him previous to his conversion? 5. Beginning, ''E^iovrtuv Si Ik t^s irvvayiuyfii twv 'lovSaiwv, k t.X. Ending, ISov aTpstpopLida th Td tflBt). — chap. xiii. 42—46. At what place did this occur ? Draw a map marking the places visited 1 y St. Paul in his Jirst journey. Who are the wpo^rAXvToi ? In what words did our Lord command His Apostles to preach the Gospel especially to the Jews ? EXAMINATION FOK B.A. DEGREE. 35 6. Beginning, 'Hjutpas 8i yzvofiivrii^ k.t.X, Ending, on 'Vmnaiol tlai, — chap. xvi. 35 — 38. Parse diriaraKKOti — a.iro\uQi\T& — i^ayayiTwaav , Derive and explain pafiSoixo^. How did St. Paul come to be born a Roman citizen ? On what other occasion did this privilege save him ? What is the exact meaning of viioKopov ? How long had St. Paul been at Ephesus ? 7. Beginning, 'O Si, OJ natuofial, k.t.X, Ending, 'Ev 6\iyt^ fis tte^Oeis XptaTLavdif yEviadai, chap, xxvi, 25 — 28. Is our Version correct in its rendering of the last words ? What is the accurate meaning of h oXiyw ? 8. Beginning, 'A.vfv6iTov Se rov Xtfilvos virapxovTOi -jrpds irapax^t- /iatriaVj k.t.X, Ending, xaXavavrE^ to ckeuos, outms l^ipovTo. — chap.xxvii. 12 — 17. Explain accurately kuto. Aifia Kal xaTi. x'^pov. What wind is lipoKX-iSaiv ? Does our version translate x"^'^""^"'''^^ '^° o-keuos rightly ? Explain the manoeuvre. 9. " Of the Jews five times received I forty stripes save one. Thrice was I beaten with rods, once was I stoned, thrice I suffered shipvvreck, a night and a day I have been in the deep." — 2 Cor. xi. 24, 25. Shew that though many of the facts here alluded to are not mentioned in the Acts, their omission does not make the narrative less trustworthy. ACTS OE THE APOSTLES. Tbanslate : 1. Beginning, Kal iv tiS crvp-irXftpoCddai Trjv iifxipav Ti}i XitvTr]Koa~ T^S, K.T.X. Ending, Ka9aJs to rrrvBufia kSiSov avTol^ diro(j)diyyETEs ? Where was the wTod SoXofiwuo^, and why was it so called ? 3. Beginning, ^EffT^E^^e Se 6 GefJs, k.t.X, Ending, Kal /xsTotxtto ufidi iirEKEiva Baj3i/\wi/o?, — chap. vii. 42, 43. Parse yiypairTai, irpoaiiviyKaTEt. What is meant by tu /3i/3Xm t—a){x—b){x+c) is the coefficient of :);' in the expansion of (''-Di'-Dhi)"'"- EXAMINATION FOR B.A. DEGREE. 45 Beduce to their simplest forms : a' - g - 20 o' + o - 12 ' « y , y+z-x z+x-y x-y-z 7. Define Ratio. If a straight line be divided into two parts so that the rectangle contained by the whole line and one part is equal to six times the square of the other part ; find the ratio of the parts. 8. When are four quantities said to be proportional ? a a -.b :; c : d, then a : a + b :: ao — be ; ac — bd, 9. Explain fully the meaning of the expression A cc—, and shew that one pair of corresponding values of A and B must be known that any other pair may be determined. 10. Solve the equations : (1) .,'l^.,J±Zl. ar + 4 Sr- -4 (ii) 4x Ts" ix- ^' - 2« (4) x'' a x' 2/'_ * = 2 V 1 • 11. In order to resist cavalry a battalion is usually formed into a hollow square, the men being four deep, but a single company is usually formed into a solid square. If the hollow of the square of a battalion, consisting of seven equal companies, is nine times as large as one of its companies' squares, find how many men there are in a company, assuming every man to occupy the same space. ALGEBEA. 1. ExFLAiN the meaning of "negative quantities," "factors," "coeffi- cients," and "indices." 2. Simplify the expression 4o — [36 — {2a — (4a — 35)}], also 2a-[a-{b(i! + y)-a(l + b)}]. 3. Multiply together H? ~ xy + y' and x^ + xy + y', and find the con- tinued product of »' — y', x' + y',x^ + y^ and x^ + y^. i. Simplify the following : {x - y){3e' - xy -^ f) (x + y){x' + xy + f ) _ x' - y" se' + y' !i?-f ' x^^xY + y'' 5. Divide x*'— (a + b + c + d)!>? + (ab + ao + ad + bc + bd + 0^0^ — {bed + cda + dab + abe) x + abed by a' — (o + 6) a + o4 ; also 3? — 1 by a:"""' — 1. 6. Give the geometrical definition of proportion. If quantities be proportional according to the algebraical definition, they are proportional according to the geometrical definition. 7. If a, b, c, d are proportionals, shew that a + b \b i-.c + did. If a crew, which can row from Baits-^bite to Searle's boat-house in 30 minutes, can row firom Searle's to Baits-bite W 26 minutes, copipare the rates of the stream and the boat. — • . . ; . ., 46 EXAMINATION FOR B.A. DEGEEB. 8. "When is one quantity said to vary inversely as another ? If X varies inversely as y, y directly as z, and x = 1, when 2 = 3, find the relation between x and z. 9. Solve the following equations : (^) 2-3^=4-^6- (2) ---=3. (3) a:' - 2a:y = 24\ (4) oy + Jar = 2a;y"l xy-2y'= i] cy + dx = Zxyi ' 10. A can do half as much work as B, B half as much as C, and together they can complete a piece of work in 66 days, in what time could they singly do the work ? 11. On a side at cricket, consisting of 11 men, one- third more were bowled out than caught, one-half more caught than stumped, and one was run out, how many were bowled, caught, and stumped, respectively ? AIGEBEA. 1. Explain the meaning of "positive quantities," "factors," "coeffi- cients," and " terms." 2. Simplify the expression, 6a - [46 - {4a -(6a - 46)}], also 4a - [2a - {26(a! + y) - 2a(l + 6)}]. 3. Multiply together a;* — x'y' + y* and a:* + x'y' + y* ; and find the con- tinued product of a: — y, a; + y, a:' + y', and x* + y*. 4. Simplify the following : ( a!'-»/')(a;'-aV + y') (a;' * y') (a;* 4 x'y' + y') x> - y- a:' + y« '^ x" - y" ' ar' + ar'/ty** 5. Divide a;' — (a + 6 + c) a;' + (6c + cd + da) x — abc, by x' — {a + 8) x + ab, also x«" - 1 by j:'""' + 1. 6. Give the geometrical definition of proportion. If quantities be proportional according to the algebraical definition, they are proportional according; to the geometrical definition. 7. Give the algebraical definition of proportion. If a crew, which can row from Ely to tlpware in 60 minutes, can row from TJpware to Ely in 55, compare the rates of the stream and boat. 8. When is one quantity said to vary directly as another ? If X varies directly as y, y inversely as z, and a: = 3, when 2 = 4, find the relation between se and z. 9. Solve the following equations : ... a; a; 1 a; 1 .,„, 9 a; „ (1^3---4^r8-^r2- (2) --- = 2. (3) my + nx = 3xy\ (4) 23^ - xy = 101 py + gx = 4xy} ' 2xy - y' = i j ' 10. Three men, whose capacities for work are as the numbers 3, 4, 5, can complete a piece of work in 60 days, in what time could they singly do the work ? U On a side at cricket, consisting of 1 1 men, one-third more were bowled than run out, and three times as many run out as stumped, two were caught out, how many were bowled, "stumped, and run out, respectively ? EXAMINATION FOH B.A. DEGREE. 47 EXAMINED AND APPEOVED- FinST CLASS. Ds Corfield Trin. Ds Atkinson, F. H. Caius Davis Joh. Baker Magd. Dickinson Caius Best Joh. Duke Joh. Beverley Joh. Dyson Trin. Davey Queens' Evans Emm. Fenn Trin. Forster Trin. Gibbs Trin. Ginders Joh. Gorst Trin. Graham Pet. Grove Trin. Griffiths Trin. Grylls Joh. Hawkrigg, J. Clare Harries Jesus Hayter Emm. Hose Joh. Heathfield Trin. Hosegood Sidney Jamieson Emm, Kershaw Cath. Kempson Emm. Lewthwaite Trin. Mayne Joh. Mabson Trin. McLaughlin Magd. Moncrieff Trin. Mirehouse, J. Clare Moore Magd.i Page Joh. Newman. Cath. Palmour Emm. Nott Trin. Rowlands, J. Corpus Pardee, J. Trin. Rowlands, L. J. Corpus Pidcock Corpus Rudge Corpus Powell, D. Trin. Sargant Trin. Roberts Joh. Seaton Trin. Bobinson Jesus Tarleton Joh. Savage Caius Thorne Caius Scott Trin. Trevelyan Christ's Skeels Emm. Wilkinson Corpus Sturges Emm. Wilson Queens' Walker Caius Wilson, R. H. Trin. THIED CLASS, WoUey Emm. Ds Apthorp Emm. Yardley Joh. Balls Pet. Yeoman Trin. Bamford Joh. Young, F. C. Trin. Bishop Christ's Boddington Pet. SECOND CLASS Bowen Caius Ds Adams Christ's Bragge Trin. Addison Corpus Clarke Emm. AUen Trin. Dashwood Christ's Alston Joh. Dobson Trin. Amherst, Hon. P. Trin. Fawcett Trin. Anderson Corpus Frost Trin. Atherton Joh. Gorst Joh. Baillie Trin. Henty Trin. Baring- Gould Joh. Knox, A. B. Trin. Beavan Joh. Manners-Sutton Magd. Blake Corpus Marsden Quewis' Blake Trin. Meeking Trin. Bottom Emm. Morton Trin. Bo wen Trin. Onslow Trin. Brent Queens' Pincott Caius 48 EXAMINATION FOB B.A. DE6BEE. Ds Pomeroy Trin. Ds Ewen Trin. Rule Corpus Gardner Corpus Selwyn Joh. Goodchild Emm. Shirley Trin. Henniker Trin. Staunton Joh. Hodgson Pet. Tate Trin. Hole Christ's Taylor Queens' Hopton Trin. TUstou Trin. H. Matthews Magd. Tooth Trin. MelviUe Trin. Valentine Joh. Perceval Trin. H. Wailes Caius Rogers Queens' Watkins Trin. Simcox Joh. Wilkinson Cath. Slight Joh. Wilson. W. D. Trin. Stevenson Trin. Tatham Trin. POUETH CLASS. Walker, C. Trin. Ds Agassiz Joh. Walker, T. L. Joh. Beavan Caius Webber Trin.H, Brailsford Trin. H. Brymer Trin. ^GROTANT. Clarke, R. D. Caius Hall Pet. Cogswell Sidney Shaw Caius Elliot Trin. Wharton Queens' Ely Joh. SENATE-HOUSE EXAMINATION PAPERS. THEOLOaiCAL EXAMINATION, Octobee, 1860. EXAMINERS : J. A. Jeremie, D.D., Regius Professor of Divinity. E. H. Brotstne, B.D., Norrisian Professor of Divinity. C. S. Ellicott, B.D., St. John's College. H. C. A. Tatlee, M.A., Trinity College. J. S. PuRTON, B.D., St. Catharine's College. T. T. Peuowne, B.D., Corpus Christi College, CANDIDATES FOE THE EXAMINATION IN THEOLOGY. Abbott B.A. Ainger B.A. Andias B.A. Arthur B.A. Bagshaw, 'Rx. for B.A BaUey B.A. Ball B.A. Banks B.A. Bassett B.A. Binyon B.A. Bird B.A. Bramall B.A. Brooks B.A. Broscombe B.A. Bunbury B.A. Butler B.A. Carew LL.B. Gary B.A. Cay BA. Chandler B.A. Chell B.A. Clark B.A. Clementsou B.A. CoUier B.A. Comford B.A. Covey B.A. Crabtree B.A. Cross B.A. Curgenven B.A. D'Almaine B.A. Dawson B.A. De Chair B.A. Dixon B.A. Dowle B.A. Dunning B.A. Eaton B.A. Farman B.A. Christ's Trin. H. Joh. Triu. Joh. C. C. Caius Cath. Trin. Trin. Trin. Joh. Trin. Caius Joh. Sid. Trin. Trin. Enun. Caius Joh. Triu. Enun. Caius Emm. Caius Cath. Pet. Jes. Queens' Christ's Jes. Joh. Emm, Christ's Joh. Joh. Festing B.A. Gilbert M.A. Glegge B.A. Goggs B.A. Graham-Pigott, Ex. for Granger B.A. Green Harrison Head Heale Henham Holmes Jackson Jenkin Jenour Jickling Jones Jones Kemm Kidd King Knight Lambert Lane Latham M.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. Leigh, (Hon. J. W.) M, Lock Marsden Mason Metcalfe Minns Newton S.C.L. B.A. B.A. B.A. B.A. LL.B. B.A. Nimmo-Howard B.A. Nixon B.A. NuttaU B.A. Page B.A. Trin. Triu. Trin. Christ's B.A. Pet. Joh. Joh. Trin. Caius Trm. Christ's Emm. Joh. Joh. Christ's Emm. Pemb. Cath. C. C. Emm. Queens' Caius C. C. Joh. A. Trin. Joh. Joh. Christ's Joh. Joh.' Cath. Joh. Clare C. C. Cath. Christ's E 50 THEOLOGICAL EXAMINATION. B.A. Joh. Stanwell B.A. C.C. Stapleton M.A. Queens' Starky B.A. Jes. Stone B.A. Joh. Stowell B.A. Joh. Symns B.A. Clare Swann B.A. Caius Taylor B.A. Joli. Tibbits B.A. Magd. Tilbury B.A. Sea. Vines B.A. Emm, Vyvyan B.A. Trin. Wale, Ex. B.A. Joh. Walne B.A. Christ's Warlow B.A. Trin. Warwick B.A. C.C. Watton B.A. Trin. WethereU B.A. Joh. Whitley B.A. Clare Williams B.A. Clare Wills B.A. Joh. B.A. Joh. B.A. Trin. H B.A. Magd. B.A. Pet. B.A. Caius B.A. Joh. B.A. Caius B.A. Joh. B.A. Joh. B.A. Emm. B.A. C.C. B.A. Caius for B.A. Magd. LL.B. Emm. B.A. Joh. B.A. Magd. B.A. Magd. B.A. Joh. B.A. C.C. B.A. Joh. B.A. Sid. Falmour Porter Porter Pratt Previt6 Price Price Prowse Baven Kemington Boberts Koberts Bobinson B,owseU Salvin Salwey Sandys Sayer Sellwood Shackleton Shield Squibb HI8T0EICAL BOOKS OP THE OLD TESTAMENT. 1. State in the language of Scripture the causes that led God to punish the earth -with a flood. How long did the waters prevail on the earth, and what incidents took place at the close of the time ?_ 2. Give an account of the life of Abraham up to the birth of Isaac, and state the number and substance of the promises that were made to him during this time. What was it that he believed, when God counted that belief to ^™ for righteousness ? 3. Describe fuUy the events alluded to in the following passages : (a) 'By faith Jacob when he was a dying blessed both the sons of Joseph ; and worshipped, leaning upon the top of his staff.' (Heb. xi. 21.) (8) ' And they m^e a calf in those days and offered sacrifice unto the idol.' (Acts vii. 41.) (y) 'Neither let us commit fornication as some of them committed, and fell in one day three and twenty thousand.' (1 Cor. x. 8.) 4. On what occasions did the following miracles take place; the Leprosy of Miriam, the Budding of Aaron's rod, the Parting of the waters of the Jordan, and the Standing still of the Sun and Moon? 5. Give a brief account of the life and conquests of Joshua, and some notices of the three most famous of the military Judges that followed him. Which of the Judges received more especially direot appointment &om God, and in what way was it vouchsafed i 6. Mention some of the leading events in sacred history that took place during the lives of Eli and Samud. How long did the latter judge Israel, and what was the general character of his judicature ? 7. Give an account of the three great offences of Saul, and the punish- ments that followed. What was the nature of his conduct to David, and in what way did David act towards him in return ? 8. State briefly the events in the life of David during the earlier portion of his reign, and prior to his rule over all Israel, When did this latter portion of Ms reign commence, and how long did it last ? THEOLOGICAL EXAMINATION. 51 9. Enumerate some of the punishments with which God visited Bavid for his sin in the matter of XJriah. Give also an account of his sin in numbering the people, and the circumstances which followed. 10. Give an account of the reign of Jeroboam. What was the prophecy uttered before bim at Bethel by the man of God from Judah, and how was it fulfilled? What was the subsequent sin and punishment of him who uttered the prophecy ? 11. Describe briefly the principal events in the reign of Asa, Ahab, Jehu, and Josiah, and give a full account of the reformation set on foot by the last- mentioned of these kings. 12. State the situation of Shechem, Bethel, the Plains of Moab, Gilgal, the Waters of Merom, Hebron, Kirjath-jearim, Mount Olivet, Eamoth- gUead, and the principal events connected with each of these places. THE GOSPELS AND ACTS; THE EPISTLES TO THE EOMAJSrS AND TO TIMOTHY; AJSTD THE FIEST EPISTLE OF ST. PETEE. 1. Translate the following passages, adding short explanatory notes where required : (a) Beginning, ''EXdovToiv Si avrdiv ah Kairepvaovfi, k.t,\. Ending, dvrl ifiov Kal trov. — Matth, xvii. 24 — 27. (/3) Beginning, Kal irapaTrip^iravTi^ diriaTeiKav iysaQiTov^^ k.t.X, Ending, koI QavfjidtraVTE^ Ivl Tp diroKpitrsi avTou itriyijffav, Luke XX. 20—26. (y) Beginning, Msto fit TaSra ^pwTtjffe tov JliKaTov 6 *IiocrjJ 6 diro ^ApipLadataVf k.t.X. Ending, oti tyyus ^u to fivrjfjLEtov, sdijKav tou 'lijtrovi/^ John xix. 38—42. (5) Beginning, ''EyivsTo 8k iv 'Ikoi/im, k.t.\. Ending, K&Ktl ^a-av zvayy^Xi^ofi^voi. — Acts xiv. 1 — 7. (e) Beginning, To Sk irv^vfia pijTws XJyEi, k.t.X, Ending, Kal t^s KoXijs SiSaa-KoXla^ y irapriKoXovQtjKa^, 1 Tim. iv. 1—6. Illustrate this passage from early Church History. (£) Beginning, IIp£ffj8uTE/povs to^s si; vfilv irapaKaXiu, k.t,X, Ending, Kop-iCiuQe. t6i/ dfXapdvTtvov t^s fio^ijs a-ritpavov, 2. Translate and explain : ^ ^^*- ^- 1— *• (a) Beginning, Has ydp irvpl a\i(T0^ffETa£, k.t.X, Ending, Kal zlpTiviv^rt iv dXX^Xois, — Mark ix. 49, 50. (/3) Beginning, EI ydp trvfi^v-rot ysyovafisv Ttu opjOitipiaTi, k.t.X. Ending, 'O ydp dirodavcuv SsdiKatuTal diro t^5 dfiap'ria'S, Bom. vi. 5, 6. (y) Beginning, Kal o Xdyos avTuiv ols ydyypaiva vofirjv U^^i, k,t,X, Ending, Kal diroaTrlTto diro dSiKia^ iras 6 ovo/jLa^tav to ovofxa XpurTov.—2 Tim. ii. 17—19. 3. "He alone describes on several occasions the look and feeling of the Lord, and preserves the very Aramaic words which He uttered." Illustrate this remark by quotations from the Gospel to which it refers. 4. Define clearly the sense in which St. Paul uses irio-Tis, as distin- guished from v6fio9, in his Epistle to the Romans. 5. Mention the particulars which may be gathered from the New Testa- ment respecting the life and character of Timothy. What hints do we derive from it concerning the duties of the deacons in apostolic times } e2 52 THEOLOGICAL EXAMmAIION. 6. To -what class of converts was the first Epistle of St. Peter addressed? Support your answer )by quotations from it. 1. Describe the position of the following places": Bethlehem— Nazareth — Lydda— Melita— Antipatris — Puteoli— Cenchrea — Thessalonica, State briefly the persons and events with which these names are connected in the New Testament. 8. Explain with derivations : irpo<7ij\vTo^ — ol ypa/xfiaTSL^ — UTroKptTtjs — yievva — SivW^ovxzi top Kwvunra — -Truy/xj; — 7ra/)a/3o\t| — irapoifiia — dvddefia diro tov %piaTOv — e-irio'/coiros— ^ viroTviruifftv txe vytaiifovTuv Xoytav, 9. Retranslate into Gkeek. the following passages from the Authorized Version, and point out any amendments of which they are capable : " Who his own self bare our sins in his own body on the tree." " All Scripture is given by inspiration of God, and is profitable for doctrine." " Charge them that are rich in this world, that they be not highminded, nor trust in uncertain riches, but in the living God, who giveth us richly all things to enjoy." "For if Abraham were justified by works, he hath whereof to glory; but not before God." "And he said unto them. Take heed, and beware of covetousness : for a man's life consisteth not in the abundance of the things which he possesseth." "Almost thou persuadest me to be a Christian." AETICLES OF EELIGION. I. Give some account of the Confession of Augsburg, and shew that it exercised an important influence upon our Articles of Religion. Trace concisely the history of the Articles from the accession of Queen Elizabeth to the year 1571. Have any important changes been introduced since that date? When, and under what circumstances, was His Majesty's Declaration prefixed to the Articles ? II. Shew that the Old Testament supports the assertions of the 1st Article as against 1. Polytheism, 2. Pantheism. 3. Anthropomorphism. III. Article II. (1) Describe very briefly the principal ancient and modem heresies against which this Article is directed. (2) Shew that Christ was foretold in the Old Testament as "very God and very man." (3) Prove from the New Testament that Christ died (a) To reconcile His Father to us. (6) To be a sacrifice for sin. How would you meet the objection that the language of the New Testament writers is not to be understood literally inasmuch as they were "Jews writing to Jews"? IV. How did the Article Of the Holy Ghost stand in the Arfioles of 1552? Have you anything to remark upon the change ? Give a concise account of the controversy on the words Filioque with reference to the Procession of the Holy Ghost, and shew that the language of the Western Church agrees with holy Scripture. By what passages of the New Testament would you prove the Person- ality of the Holy Ghost i Shew that the argument is strengthened by an appeal to the original Greek. V. Write a brief essay on the Article Of the Justification of Man, with a view to "express more largely" (in lie language of the Homily THEOLOGICAL ESAMINATION. SS if you please) the doctrine therein taught, and to shew its agreement with holy Scripture. VI. Article XVI. Of sin after Baptism. How was the subject of this Article treated in the Articles of 1552 ? Give some account of the early heretics whose opinions are here condemned. What reason have we for believing that the Article was directed partly against them ? By what texts and arguments from holy Scripture would you comfort a person distressed in conscience at having committed, as he supposed, the unpardonable sin? VII. Write down the opinion expressed by our Church on the doctrine of Transubstantiation, and establish each point of it by argument or quota- tion. Give the history of the rise and formal recognition of the doctrine in the Church of Rome, and quote if you can the words of the Council of Trent on the subject. What is meant by Consubstantiation ? VIII. Kal ov6e gZs Ti TiSf uTrapxovTwv avT(S ikEysv tSiOV elyat, dW* tJi; auTois airaVTa KOLvd. — Acts iv. 32. E-yoJ 8i \E7e0 vfiLVf fit] 6fi6trat oXtos. — Matt. v. 34. What is the teaching of the Articles on these two subjects ? Shew that it is not contrary to these and other like passages of the New Testament. LITUEGY OF THE CHUECH OF ENGLAND. 1. Mention any errors or defects in the mode of performing Divine Service in the times immediately before the Reformation. Illustrate your remarks by reference to any old Service Books. " These many years past this godly and decent order of the Ancient Fathers hath been, altered, broken, and neglected." Pref. 1549. What "order" is here meant ? What rules are laid down in our Prayer Book for the saying of the Lord's Prayer, the Creed, and for the reading of the Lessons at Morning and Evening Prayer ? 2. Compare the forms of Absolution iii Morning Prayer, the Communion Service, and Visitation of the Sick. Under what circumstances is the last appointed to be used ? 3. What traces are there of the use of a Creed in the New Testa- ment? Give some account of the history of the following clauses : "The Lord and Giver of Life, Who proceedeth from the Father and the Son." Mention some of the days on which the Athanasian Creed is appointed to be said. What errors were the following clauses intended to condemn ? Neither confounding the Persons, nor dividing the Substance — Perfect God and Perfect Man, of a reasonable soid and human flesh subsisting— Who although He be God and Man, yet He is not two but one Christ. 4. Quote passages from the Prayer Book in which the following words are found, and give, where you can, the corresponding Greek and Latin words : Catholic, charity, confirm, contrite, endeavour, heresy, incompre- hensible, justification, mortify, oblations, prevent, Passion, redeem, regenerate, renounce, salvation, schism, tribulation, vocation. 5. What are the proper Lessons for Easter Sunday, Whit Sunday, and AH Saints' Day? Write out the Collect for one of these days. Translate : (1) Deus, cui omne cor patet, et quem nullum latet secretum ; purifica per infusionem Sanoti Spiritus cogitationes cordis nostri; ut perfects te diligere, et digne laudare mereamur. (2) Deus, qui ho- 54 THEOLOGICAL EXAMINATION. dierna die unigenitmu tuum gentibus Stella duce revelasti: concede propitius ut qui jam te ex fide oognovimus, usque ad contemplandam speclem. tuae celsitudinis preduoamur. In what part of our Service are these Collects found ? 6. Explain the meaning of the word Catechism. From what Greek word is it derived ? Quote passages from the New Testament where the word is used. My Baptism wherein I was made a member(l) of Christ, the ehild(2) of God, and an inheritor(3) of the Kingdom of Heaven. (1) Illustrate by reference to St. Paul's language. (2) Confirm this from Scripture, and explain the sense in which you imderstand (3). Compare the whole passage with the language of the Service for the Baptism of Infants. Give accurately the answer to the following question: "What is required of those who come to the Lord's Supper ?" Shew that the same requisites are mentioned in the Communion Service. 7. Mention any changes which were made in successive Prayer Books (1) in the Rubrics of the Communion Service, (2) in the Prayer for Christ's Church MUitant, (3) in the Prayer of Consecration, (4) in the form of words used in delivering the Bread and the Cup. Assign reasons for such changes. 8. What steps does the Rubric direct to be taken before a person of riper years is admitted to Baptism ? When was the Office for Baptism of Adults added to the Prayer Book? Why was it called for specially at that time ? 9. Mention some of the alterations made in the Book of Common Prayer in 1604. Explain by reference to the Preface the principles on which the last Seview was conducted. HISTOET OF THE FIEST THEEE CEJSmjRIES. 1. What traditions were current in the early Church respecting the latter part of the lives of St. Peter, St. Paul, and St. John ? 2. Mention the chief centres of the Christian faith, and give a sketch of the constitution and ritual of the primitive Churches at tibie beginning of the second century. S. Describe the characteristics of the Catechetical School at Alexandria. Who were its chief representatives? 4. Who were the principal adversaries of Christianity during the second century ? Give a short account of the Apologists during the same period. 5. Who was Novatian? What were his opinions? By what name were his followers distinguished ? 6. Write a short account of Cyprian and the chief controversies in which he was engaged. 7. By what natural causes was the progress of Christianity assisted or impeded diuing the first three centuries ? HISTOET OF THE EEFOEMATION IN ENGLAND. 1 . Mention any arguments which have been advanced in support of the Pope's claim to jurisdiction in England. Can you shew from historical facts that suph arguments are unsound ? How did the authority of the Pope make itself felt in England before the Reformation ? THEOLOGICAL EXAMINATION. 55 2. Give some account of the internal condition of the Chnich of England in the 14th and 16th centuries. What was done by Wickliffe to prepare the way for the Keformation ? 3. Give the date of Henry's rupture with tiie Pope, and explain briefly how it was brought about. What do you understand by the Koysu Supremacy in England ? How is it exercised i 4. Give an outline of the life of Cranmer and compare his character as a Reformer with that of Wickliffe. From what motives and with what hopes does it appear that he acquiesced in the Dissolution of the Monasteries i Mention some of the consequences of this measure, 5. What steps were taken to advance the work of the Reformation during the reign of Edward YI, ? How was its progress affected by the political condition of England at this time ? 6. Mention the names of any of the exiles in Queen Mary's reign who returned on the accession of Elizabeth, Give an account of any of their writings. The following is a note by Bishop Bonner : " A.D. MDLIX die mail xxx vocatus ad concilium recusavi praestare juramentum," What oath was this i Determine by the date the circumstance to which he alludes. 7. Give an outline of the life of Archbishop Parker. LIST OF PEESONS WHO PASSED THE EXAMINATION IN THEOLOGY. Abbott Ainger Andras Arthur Bagshaw, E: Bailey BaU Bassett Binyon Bird Bramall Brooks Bunbury Gary Cay Chandler Chell Clark Clementson ColUer Corbet Cornford Covey Crabtree Curgenven D'Almaine De Chair Dowle B.A. Christ's Dunning B.A. Christ's B.A. Trin. H. Eaton B.A. Joh, B.A. Joh. Farman B.A. Joh. B,A, Trin. Festing B.A. Trin. c. for B.A. Joh. Gilbert M.A. Trin. B.A, C. C. Glegge B.A. Trin. B.A. Cains Goggs B.A. Christ's B.A. Trin. Graham-Pigott, Ex. for B.A. Pet B.A. Trin. Granger B.A. Joh. B.A. Trin. Green M.A. Joh. B.A. Joh. Harrison B.A. Trin. B.A. Trin. Head B.A. Caius B.A, Joh. Heale B.A. Trin. B,A, Trin. Heaton B.A. C. C. B.A. Emman. Henham B.A. Christ's B.A. Caiua Holland B.A. Trin. B.A. Joh. Jackson B.A. Joh. B.A. Trin. f Jenour B.A. Christ's B.A. Emman, Jickling B.A. Emman. B.A. Caius Jones B.A. Pemb. B.A, Trin. Kemm B.A. C. C. B.A. Emman. Kidd 3. A. Emman. B.A. Caius King B.A. Queens' B.A. Cath. Knight B.A. Caius • B.A. Jes. Lambert B.A. C. C. B.A. Queens' Lane B.A. Joh. B.A, Jes. Latham B.A. JSnun&na B.A. Emman. iPaspsed Mason in Hebrew. B.A, Christ's 56 PBEVIOUS EXAMINATION. Metcalfe B.A. Newton B.A. Nimmo-Howard B.A. Nixon Nuttall Page Palmour Porter Porter Pratt Previte Price Prowse Kaven B.A. B.A. B.A. B.A. B.A. M.A. B.A. B.A. B.A. B.A. B.A. Benungton B.A. Roberts B.A. Roberts B.A. Robinson B.A. Rowsell B.A. Job. Joh. Clare C. C. Cath. Christ's Joh. C. C. Queens' Jes. Joh. Clare Caius Joh. Magd. Jes. Enrnian, Triu. Joh. Salwey B.A. Sayer B.A. Sellwood B.A. ShackletonB.A. Sqviibb B.A. Stapleton B.A. Stone StoweU Swann Taylor Tibbits Tilbury fVines Vyvyan Walne Warlow "Wattou WethereU B.A. "Wills B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. B.A. LL.B. B.A. B.A. Tiin. Trin. Joh. Clare Joh. Trin. H. Pet. Caius Caius Joh. Joh. Emman, C. C. Caius Emman. Joh. Magd. Joh. Sid. t Passed in Hebrew. PEEVIOUS EXAMINATION, Octobee, 1860. ExAHIITBRS : J. PoKTEE, M.A., St. Peter's College. A. A. Ellis, h.a., Ti-imty College. ' A. Beabd, M.A., St. John's College. J. M. Flbtcheb, M.A., Caim College. A. PoTfNALL, M.A., St. Catharine's College. J. B. Feaeson, M.A., Emmanuel College. B, W. Beatson, m,a., Pembroke College, J. RiCKARDS, B.A., Sidney College. PALEY'S EVIDENCES. 1. How does Paley maintain the assertion that in miracles adduced in support of revelation there is not any such antecedent improbability as no testimony can surmount ? 2. What do we mean, when we say, strictly speaking, that a fact is contrary to experience ? 3. How does Mr. Hume state the case of miracles ? 4. What two points does Paley say are necessary to be made out to support the Proposition which stands at the head of the first nine chapters ? 5. Show that the first teachers of Christianity would find no protection in the general disbelief of the popular Theology. 6. What evidence is furnished by Tacitus as to the activity and BuflFerings of the first teachers of Christianity, and what three things are proved by the passage which Paley quotes from his writings i 7. Show that the account which our Scriptures contain is the story for which the early propagators of our religion suffered. 8. TJnder what division does Paley treat the subject of the Morality of the Gospel ? 9. Show the Originality of Christ's character. PREVIOUS EXAMINATION. 57 10. Facinus est vinciri civem Romanmn ; seelus verberari. — Cic. in Verr. Csedebatur virgis, in medio foro Messanse, civis Romanus, Judices : cum interea nullus gemitus, nulla vox alia, istius miseri inter dolorem crepi- tumque plagarum audiebatui, nisi hsec, Civis Romanus sum. Translate these passages and show how they bear upon the genuineness of the New Testament writings. 11. What would be the real effect of oyerpowering evidence of the truth of Christianity ? , PALEY'S EVIDENCES. 1. What is the modern objection to miracles which Paley felt himself called upon to answer ? Upon what principle does that objection profess to be founded ? 2. On what is the force of experience as an objection to miracles founded ? 3. Prove that there is no solid foxmdation in Mr. Hume's conclusion respecting miracles, by trying his theorem upon a simple case. 4. Write down the two propositions which Paley establishes in the first part of the Evidences. 5. Show that it is highly probable from the nature of the case that the propagation of the Christian Religion was attended with difficulty and danger. 6. To what two points does the information to be drawn from the younger Pliny's Letter to the Emperor Trajan principally relate ? Give the quotation. 7. Show that the story for which the early teachers of our religion suffered, was a miraenious story. 8. What does Paley observe respecting the negative character of our Lord's discourses ? 9 Give instances of the candour of the new Testament vrriters. 10. Judseos, impulsore Chresto assidue tumultuantes, Roma expulit. Sdet. Claud, c. XXV. Quemadmodum eadem catena et eustodiam et militem copulat ; sic ista, quae tarn dissimilia sunt, pariter inceduut. — Seneca, Ep. v. Translate these passages, and show how they bear upon the genuine- ness of the New Testament writings. 11. How does Paley meet the objection, that the Christian miracles are not recited or appealed to in the Epistles of the Apostles so fuUy or frequently as might have been expected ? ARITHMETIC. 1. Find the sum, difference, product, and quotient of 1653125 and 13225. 2. Find the square, and square root of "007569. 3. There are three quantities: (1) 4 miles, (2) 4 furlongs, (3) £2. Multiply one of these by the quotient of the other two ; state accurately the result of the operation, and perform it in as many different ways as possible. ^ 12 4. Multiply 99fff by 324 ; and find the value of ^^ of a week in days, hours, &c. 5. Find the value of '61875 of a £. ; and •10714285 of a cwt. 58 PREVIOUS EIAMINATXOa. 6. State the tests of divisibility of niunbers by 4, 9, and 11 ; and apply them to the ntunber 71016. 7. What is the value of a cargo of Tallow, weighing 516 tons at 51s. 3d. per cwt. f 8. Five per cent, on a given sum amoimtB to £26. 13s. id. Find 4f and 1^ per cent, on the same sum. 9. Define Interest and Discount. What is the Discount on £429. 5s. due 3 months hence at 4 per cent, per annum ? 10. Two Bills for £466. 5s. and £274. 2s. 6d. are due on the 1st and 30th June respectively. What is their value on the 20th June, interest being reckoned at the rate of 6 per cent, per annum ? 11. Divide £3920 amongst 4 persons in the proportions of 2, 4, 6, 8. 12. A speculator sells at a profit of 50 per cent. ; but his purchaser fails, and only pays 10«. in the £. How much per cent, does tie speculator gain or lose by his venture ? 13. 4 and B run a race. .4 starts at the rate of 400 yards a minute, but in every successive minute increases his pace by a yard a minute : B dimi- nishes his pace by the same, and is overtaken by !k in 4 minutes. What was f s pace at starting i AEITHMETIC. 1. Find the sum, difiPerence, product, and quotient of 2756250 and 11025. 2. Find the square and square root of '006084. 3. There are three quantities (1) 6 gallons, (2) 6 quarts, (3) 6 hours. Multiply one of these by the quotient of the other two : state accurately the result of the operation, and perform it in as many different ways as possible. 220 4. Multiply 99f|-f by 274 ; and find the value of — . of a mUe in furlongs, yards. Sec. 6. Find the value of •53125 of a £. ; and '17857142 of a cwt. 6. State the tests of divisibility of numbers by 3, 8 and 11 ; and apply them to the number 370524. 7. What is the value of a cargo of sugar weighing 756 tons at 28s. Sd, per cwt. ? 8. Five per cent, on a given sum amounts to £32. 6s. 6d. Find 5^ and 5^ per cent, on the same sum. 9. Define Interest and Discount. What is the Discount on £328. 5s. due 4 months hence at 3 per cent, per annum ? 10. Two Bills for £273. 15s. and £456. 17s. Sd. are due on the 2nd and 22nd July respectively. What is their value on the 12th July, interest be- ing reckoned at the rate of 6 per cent, per annum ? 11. Divide £3264 amongst 4 persons in the proportions of 1, 3, 5, 7. 12. A speculator sells at a profit of 75 per cent. ; but his purchaser fails, and only pays 5s. in the £, How much per cent, does the speculator gain or lose by his venture ? 12. A and B run a race. A starts at the rate of 400 yards a minute and in every successive minute diminishes his pace by a yard a minute. B increases his pace by the same, and overtakes A in four minutes. What was B'a pace at starting? EBBVIOtrS EXAMISfATIOir. 59 EUCLID. 1. DEriNE angle, and the kinds of angles, figure, rhombus, gnomon, segment, similar segments. 2. The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall be equal. 3. To bisect a given finite straight line. 4. The angles 'which one straight line makes with another upon one side of it, are either two right angles, or are togetiier equal tp two right angles. 5. If one side of a triangle is greater than another, the angle opposite the greater shall be greater than the angle opposite the less. 6. To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 7. In any right-angled triangle, the square which is described on the- side subtending the right angle, is equal to the squares described on the sides containing the right angle, 8. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced is equal to the square of the straight line, which is made up of the half and the part produced. 9. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 10. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced ; the square of the side subtending the acute angle is greater than the squares of the sides containing the acute angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 11. If two circles cut one another they shall not have the same center. 12. To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. 13. Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. EUCLID. 1. Define a plane superficies ; an acute-angled triangle ; a semicircle; parallel straight lines ; and similar segments of a circle. 2. If two angles of a triangle be equal to each other, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another. 3. Draw a straight line at right angles to a given straight line, from a given point in the same. i. Any two angles of a triangle are togethei: less than two right angles. 5. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, 6. Parallelograms upon the same base, and between the same parallels, are equal to one another. 7i If the square described upon one of the sides of a triangle, be equal 60 PREVIOUS ESAMINATION. to the squares described upon the other two sides of it ; the angle coniaineu by these two sides is a right angle. 8. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 9. If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the Une, and of the square of the line between the points of section. 10. To find the center of a given circle. 11. EquEd straight lines in a circle are equally distant from the center ; and conversely, those which are equally distant from the center, are equal to one another. 12. The diameter is the greatest straight line in a circle ; and, of all others, that which is nearer to the center is always greater than one more remote : and the greater is nearer to the center than the less. 13. A segment of a circle being given, to describe the circle of which it is the segment. MECHAJSflCS. 1. Define a force. When is a force known? State the principle of the transmission of force. Is this a self-evident principle or not ? 2. Enunciate the parallelogram offerees. Assuming that it is true for the direction of the resultant, prove that it is true for the magnitude of the resxdtant. 3. If two parallel forces acting at given points of a straight lever, and in the same direction, keep the lever at rest ; prove that tiie forces are inversely proportional to the distances of their points of application from the frilcrum. Eind also the pressure on the fulcrum. One end of a poker rests on a smooth horizontal plane, and the other is supported by a string attached to it and fastened to a fixed point. Find the tension of the string, and the direction in which it will hang. i. Enumerate the different kinds of levers, and give examples of each, pointing out in each case whether mechanical advantage is gained or lost. 5. A body is supported on a smooth inclined plane, by a force acting parallel to the plane ; prove that the power is to the weight as the height of the plane to its lengl^. Find also the pressure on the plane. Under what circumstances can the power, the weight, and the pressure on the plane, be all equal to one another ? 6. Describe the common balance, and state briefly what are the requisites of a good balance. Describe the method of double weighing or any method by which the defects of a balance arising from inequality in the arms, can be completely obviated, 7. Find the condition of equilibrium in that system of pullies in which the strings are parallel and in which each pidly hangs by a separate string. 8. A uniformheavyladderrestswithoneextremityonasmoothhorizontal plane, and the other on a smooth vertical wall, and is kept from slipping by a string attached to the bottom of the ladder and to a. point in the horizontal plane, shew that the tension of the string is equal to TF— , where PREVIOUS EXAMINATION. 61 W is the weight of the ladder, a the distance of the foot of the ladder &om the wall, and i the distance of the top of the ladder from the ground. 9. Define the term center of gravity. Explain the method of finding the center of gravity of a number of heavy particles situated at given points. Shew from your method that every system of heavy particles has only one center of gravity. 10. Piud the center of gravity of a triangular lamina of imiform thickness and density. Will the sam^ point be also in general the center of gravity of the perimeter of the triangle ? 11. If a body rest on a horizontal plane, shew that it will stand or fall according as the vertical line through its center of gravity falls within or without the base. Construct a parallelogram, which shall just rest in equilibrium wit^ one side resting on a horizontal plane. 12. Distinguish between stable and unstable equilibrium and give instances of each. Shew that if any part be cut off from a sphere by a plane the sphere vrill rest in stable equilibrium on a horizontal plane on the convex, surface. ALGEBEA. 1. Add together (a — 2i)^, o (o + 25 — 6c), 5 (2a — 44 — 3c) and subtract the result from (2a + i) (a — 3c) . 2. Prove the rules of signs in Multiplication, by investigating the form of the product of o — 6 and c — d, in the case when o > 6, and c> d. 3. The product of two expressions is 'i.a^y' + 2aV + 2y V - a* - j/* - si, and one of them isK + y — «; find the other. 4. Prove that the difference of the squares of a number composed of two digits, and of the number formed by inverting these digits, is equal to 99 times the difference of the squares of the digits. 5. Beduce to their simplest forms : 5 h «+ — a: + - a and add together a\-h- c a + b - c a' - V c + + b - e c - a {b - c)(e- a) a - b 6. Solve the equations : x-2 _ l{x-l)-^(x - 5) 5 2 + 1(22- 28) = !/. (4) -%f = l. a b x' y' _ ab a b a + 6 ' 62 PREVIOUS EXAMINATION. 7. A rectangular room is 3 feet longer than it is broad, and is 10 feet high. If by adding 3 feet to the length, 3 feet to the breadth, and 2 feet to the height, the cubical content of the room is doubled, find the length and breadth of the room. 8. "When are four quantities said to be proportional ? What value must be given to a; in order that a; + 1 : 2a! + 1 : : 3a! - 1 : 2ai + 8 ? li a : b ;: b : c :: c : d, prove that a : c :: a' : b', and a: d :: a^ : b^. 9. A and B run a race. A gives B a start of 100 yards and overtakes him in i minutes. Afterwards A gives B a start of 30 seconds and over- takes him in 7 minutes. Supposing the rates of running to be uniform throughout, find the rates at which A and B ran. Find also how many yards start, in addition to a start of 20 seconds, A must give B, that they may run a dead heat of a mile. 10. It is between 3 and i o'clock ; find the two times when the hands include the angle of an equUateral triangle, and the interval between these times. 11. The Cambridge TJmversity Volunteer Eifle Corps can be formed into a hollow square 8 deep, and may also be formed into a hollow square 10 deep. The front presented in the latter formation has 1 man less than the front in the former formation. Find the number of men in the corps. Shew also that the corps may be formed into hoUow squares respectively 1, 2, 3, 4, 5 and 6 men deep. EUCLID, BOOKS IV. and "71. 1 . When is a rectilineal figure said to be inscribed in a circle ? Prove that any parallelogram inscribed in a circle must be rectangular. 2. When is a straight line said to be placed in a circle ? Prove that the diameter is the greatest straight line that can be placed in a circle. 3. Describe a circle about a given triangle. 4. Inscribe an equilateral and equiangidar hexagon in a given circle. 6. What relation must exist between two quantities in respect to (1) kind and (2) magnitude, in order that a ratio may subsist between them ? When are four quantities said to be proportionals ? 6. Define duplicate ratio. What ratio is the duplicate of 4 to 9 ? 7. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally ; and con- versely, if the sides, or the sides produced, be cut proportionally, the straight line which joins the paints of section shall be parallel to the remaining side of the triangle. 8. From a straight line cut off any part required. Divide a straight line into three equal parts. 9. Find a mean proportional between two given straight lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. In two similar triangles the ratio of the triangles is equal to the ratio of their sides. What is that ratio ? 11. In right-angled triangles, the rectilineal figure described upon the side opposite to the right angle, is e^ual to the similar and similarly desraibed figures upon the sides cpntaining the right angle. PEEVIOtJS EXAMINATION. 63 XENOPHON, ANABASIS, I. H. TaANSLATE : lib. I. cap. iv., 4, 5. 1. Begmningi *EyT£u6£i/ k^eXavv^i crTadfiov £va, k.t.X, Sndingy TpiaKovra ftvptdda^ cTjOaTtas, Translate : lib. II. cap. v. 29, 30. 2. Beginning, 'EjSoiiXtTO Sk Kal 6 KXiapxas, k.t.X, Ending, Kal twv dWuiv GTpaTLWTWv ois StaKotriot, Parse, T£tx»I, et^EiffT^KSCol/, diro^L^atrzuv^ wcto, Iei;ai, (TTpaTlwTttil/, Give the derivations of ^Xi/Sotoi, iKiro£ii>v, \0x07ds. Decline vous. Give the date of the expedition of Cyrus. XENOPHON, ANABASIS, I. H. Translate : lib, I. cap, vii., 18 — 20. 1. Beginning, 'Ei/rauOa Kupos ^iKavdv KoKitras t6v ' AfiirpaKtoaTtjVj k.t.X. !Ending, cttI dfia^tSu r(yovTo Kal viro^uylutv , Translate : lib. II. cap. iv, 21—23. 2. Beginning, 'Akouo-os &k Tavra 6 KXeojoxos, k.t.X, Bndingi ws ol x^vKdrrovT^^ airTiyyeXXoi/. Parse T/otcxiXious, /u.ax*'-^''"'"t 'JM^P**'''* ?i)LieXTjjii£i;os, ^psTo, Give the derivations of aXTjCsutrTjs, apfxaTo^^ viro^vyttov, Siwpvxo^, diroffTpotfirj. TEEBNCE'S ANDEIA. I. Transiate into English: Act I., So. i., 110 — 126. Beginning, So. Quid ais i Si. Kedeo inde iiatus, atque eegre ferens, etc. Ending, Sine nunc meo me vivere interea modo, 1. Diceret. Explain the construction here. 2. Parse iUi, eomperisse, cedo, 3, Derive sedulo. n. Translate into English: Act II., Sc. iv., 1—8, Beginning, Si. Keviso quid agant, aut quid captent consilii, etc. Ending, TJnum esse verbum, si te dices ducere. 1. Parse and explain the words Qui differai te, 2, Conjugate revise, and decline solm. TERENCE'S ANDEIA. I. Translate into English : Act II., Sc. ti., 1 — 11. Beginning, Dav. Hie nunc me credit aliquam sibi faUaciam, etc. Ending, Etenim ipsus secum earn rem reputavit via. 1. Vaxae restitisae, potin' es. 2. Conjugate (fesino. 3. Deiiye prorstis, soUicitudo, II. Translate into English : Act V., Sc. iii., 11 — 24. Beginning, Pam. Me miserum ! Si. Hem ! modoue id demum sensti, Paniphile ? etc. Ending, Chreme ? Ch. At tandem dicat sine. Si. Age, dicat ; sino. 1. PaiBB aliqiio pacto, mi pater, viceris, 2. Derive and conjugate macero, indigeo. 3. Derive and explain the use of imo, olim. GOSPEL OF ST. MAEK. 1. Explain the meaning and derivation of the word EuayyeXiov. State what you know of the author of this Gospel. With what cir- cumstances does he open his nanative? 64 PREVIOUS EXAMEIATION. 2. Translate : chap. ii. 1—5. Beginning, Kol -ttoKlv BlarjXdiv c£e KawEpvaov/i ii iiiupiSu- k.t.X. Ending, &ia}VTal crou al d^aprtat trov. Parse X'^^^o'^j irpoatyyitrai^ &(piivvrat. 3. Translate : chap. iv. 26—32. Beginning, Kai iktytv, OStios IittIi/ ^ pairiXiia tou 6cou, k.t.X. Ending, tA -jrETSH/d tou oujual/ou KaTatTKT]voiti, Give the principal tenses of the following verbs : pKaa-rivn, pLnKuutiTai, vapaSiSf diroarTkWst, 4. Translate : chap. viii. 27 — 30. Beginning, Kal k^Xdsv 6 'Ifja-ous Kal ol fiaOrjral avTOVf ic.t.\. Ending, tva fiijSevl Xiyuiffi irspl avTov, Compare this accoimt with that given of the same occurrence by any- other Evangelist. Derive 'I?;crous, /lio0»)t^s, Ba'TTTtcT^s, IIsTpds, Xpiffros. 6. Parse the following words : ^'ifraro, dipnKtv, cyttpai, )vat. Explain t6v dpxvyov t^s 5*"^^. 2. Translate : chap. v. 33—40. Beginning, 01 Sk dKoinravTt^ SiitrpiovTOy k.t.X, ]Binding, koI oVeXytray avTovv, Xtywy eli/at Ttva iavrov. Where is this phrase used elsewhere in the Acts, and in St. Paul's Epistles ? Parse &vrtpiQi\^ dirovrtiTt^ iatruTS, >T, SeipavTS^, What other mention have we of Gamaliel in the Acts ? 3. Translate: chap. ix. 10— 21. Seginning, 'Hv Si tis paQriTris kv Aa/jiatrKtS ovofiaTi 'Ayawms, k.x.X. Ending, kirl Toiis dp\t£peZ^ ; Parse dKii/coa, ^, dtriirTaXKk. What account does St. Paul give of himself after the recovery of his sight ? 4. Translate: chap, xviii. 1 — 11. Beginning, M£Td fie rauTa x^iotcrOsIff 6 IJauXos c/c toiv ^Adrjvtav^ k.t.X. Ending, SiSdtTKiav iv aujois tov Xtryoo too Qbov, Parse SiaT^Tax^vat. How does St. Paul mention elsewhere that he had baptized Crispus, and whom does he add besides as having been baptized by his owp. hand? HEEODOTUS. BOOK m. 1. Whekb was Herodotus born, and when did he live? What was the extent of his travels ? 2. Translate : bk. in. cap. 6, 7.^ Beginning, T^ Sk 6\lyoi Ttjov is AiyvirTov vavnWouivwv titvtvwKaa-ij k.t.X. Ending, -ttiVtis 5ous te Kal 8&^d/xevos nrap' avToS, (a) Parse ivvevwKaat, aa^aVTS.^^ irapiKa^oVy TryOo/ieyos. (6) Give the Attic Greek for dvaiaiiwSvTai, iiriipoiTeuiv, darjjaXtitji. (c) Derive Siiiiapx«^, iTfioM. Where \yas Memphis ? EXAMINATION FOR B.A. DEGREE. 67 3. >Translate : bk. iii. cap. .41. Beginning, Touto iiriKs^dfJLavo^ 6 HoXvKpdTrj^, k.t.X, !Ending, dirtKOfievo^ Se es tA oiKtaj (rufiipop^ i-^iqTO, (a) Farse eVtXE^a/isyos, uttct^Osto, dvayayzlVf daijdsiri, (6) Derive KEifi-^Xia, (c) Relate the previous part of the story of Amasis and Polycrates. 4. Translate; bk. iii. chap. 115, U6. Beginning, AijiTai /itp vuu svTET^ 'Ao-iTjEVxaTiaieio-iKol ci/t^ A*j3uj7, k.t.X. ^Ending, xal triravLtoTaTa ex^iw avTai. (a) Parse clirat, ot/cao-i, voltjQev. (b) Kao-o-txEpt^ts. What is the modem name of the district thus called by Herodotus ? What river is probably meant by the Eridanus ? (c) Give the Attic Greek for TeptKA.ijtouo-ai, kv^tKOfxai, irotijTito, MEOHAJSnCS AND HYDE0STATIC8. 1. Define Force, and shew that forces in Statics may be completely represented by straight lines. 2. If two forces, acting perpendicularly on a streiight lever in opposite directions, and on the same side of the fulcrum, balance each other, they are inversely as their distances from the fulcrum : and the pressure on the fulcrum is equal to the difference of the forces. What are the conditions necessary in order that three' forces acting perpendicularly on a straight rod without weight, may balance each other ? 3. If two forces acting at a point are represented in direction and magnitude by two sides of a parallelogram, the diagonal through the point will represent their resultant in direction. Having given the direction and magnitude of the resultant of two forces acting at a point, and also the direction of one and the magnitude of the other, find a geometrical construction for determining the magnitude of the one and the direction of the other force. 4. Investigate the conditions of equilibrium on the wheel and axle. How does the thickness of the rope affect thte mechanical advantage when a weight is raised by means of a windlass or similar contrivance ? 5. If a body balance itself on a line in all positions, the center of gravity is in that line. When is the equilibrium of a body said to be stable, and when unstable? 6. The pressure at any point of a fluid of uniform density is pro- portional to its depth below the surface of the fluid. If a vessel of any form the bottom of which is horizontal, be filled with fluid, the pressure on the bottom is the same as though the sides were vertical. 7. If a body fl.oat on a fluid it displaces as much of the fluid as is equal in weight to the weight of the body : and it presses downwards and ia pressed upwards with a force equal to the weight of the fluid displaced. What further condition mus't be satisfied in order that the body may be in equilibrium ? 8. Describe the common Hydrometer, and explain the method of employing it to compare the specific gravities of two fluids. 9. Explain the construction of the Common Barometer. Shew that the pressure of the atmosphere is accurately measxired by the weight of the mercurial column. If the level of the mercury in the cistern be at the zero point of gradua- tion when the reading of the barometer is 30 inches, and the area of the horizontal section of the cistern = n times that of the tube, determine the correction to be applied when the reading of the barometer is 30 + r inches. 10. Describe tiie construction of thecommon-lifting-pumpanditsoperation, f2 68 EXAMINATION FOR B.A. DKGBEE. ALGEBRA. 1. Pro7e that o' X a' = o*. Enunciate the general proposition of which this is a particular case. 2. Divide iaJ'b' + 2 (Sa* - 26*) - a6(So» - lli») by ia' + 2a6 - 6». 3. Simplify the following : .J, g' + iify + 2zy' + y' U - y x-^yl ' \x-y x+y)' 4. Resohe 4 (o6 + erf)' -' («« + J' _ c" - d»)' into four factors. 5. If a number be divided into any two parts, shew that the difference of the cubes of the parts, together with the product of the less part into the sum of the squares of the parts, is equal to the product of the other part into the difference of the squares of the parts, together with the continued product of the number and the two parts. 6. Solve the following equations : 2a: - 3 4i - 5 „ 3'' = 6- 7. When are four algebraical quantities said to be proportional? If o, b, c, d satisfy your definition, shew that a? + Zab + b' : b' :: c' + Sod + d' : d'. 8. A person who is travelling eastwsirds at the rate of 3 degrees a day has a watch which loses half a minute a day, how far has he travelled when Ms watch seems to be 50 minutes too slow? N.B. A watch which ia carried eastwards appears to lose one hour for every 15 degrees. 0. At a rifle-match the winner's score was four times the difference between his score and the greatest number of points that could be won, and the sum of his score and the greatest number of points was equal to the square of the same difference ; what was the winner's score, and what the greatest number of points ? JUVENAL, SATIRES m. AND X. 1. Teamblatb the following passages : (a) Quosdam prsecipitat subjecta potentia magnse Invidiae. What instances does Juvenal adduce in support of this assertion ? (i) Caius erit Verri, qui Verrem tempore quo vult Accusare potest. What were the principal charges brought against Verres ? By whom was he defended? (c) Ergo supervacua hseo aut pemiciosa petuntur, Propter quae fas «3t genua incerare Deorum. Compare this passage with ^AW rfroi fiiv TaOra dsoiii iv yovvatn Ketrai, — II, P. 514. and 'A.W' eis flsou's x/"i tout' duapT^aavr' ixsiu, — EuR. Phcen. 717. Js the same custom alluded to in each of these passages ? EXAMINATION FOR B.A. DE6BEE. 69 (d) Divitia hie servi claudit latus ingeuuorum • Pilius : alter enim, quantum in legione tribuni Accipiunt, donat Calvinse vel Catienae, Explain the expression " claudit latus." When was pay first granted to Roman soldiers ? What proportion was assigned to a tribune ? (e) Sic libitum vano, qui nos distinxit Othoni. Give the date of the introduction of this law of Otho. What was the distinction drawn in it ? (/) prsestare tributa clientes Cogimur, et cultis augere peculia servis. What was the relation between the Cliens and Patronus in the earlier days of Rome ? How were these relations subsequently modified ? [g) Quid Crassos, quid Pompeios evertit, et Ulum, Ad sua qui domitos deduxit flagra Quirites ? What is the date of the 1st Triumvirate ? How was this connexion severed? Derive Quirites. (A) Bed ille Cannarum viudex ac tanti sanguinis ultor, Annulus. I, demens, et saevas curre per Alpes, TTt pueris placeas, et declamatio fias. Explain the several allusions in this passage. 2. Translate: Sat. iii., 171—184. (A) Beginning, Pars magna Italiae est, si verum admittimus, in qua, etc. Ending, Faupertate omnes. Quid te moror i Omnia Romse Cum pretio. Translate: Sat. x., 65— 81. (B) Beginning, Pone domi lauros, due in Capitolia magnum, etc. Ending, Continet, atque duas tautum res anxius optat, Panem et Cireenses. HISTOEY OF THE ENGLISH EEFOEMATION. 1. State the nature and extent of the Papal Supremacy in England at the beginning of the reign of Henry VIII. Give a brief account of the measures by which it was superseded in his reign. How far did the royal supremacy take its place ? 2. Describe the contents of the Act of Six Articles, and the circum- stances which gave rise to it. 3. Enumerate the Sacraments of the Church of Rome. What course did the English Reformers pursue with respect to them ? How did they define a Sacrament? 4. Give some account of the principal German Reformers who were consulted by the English divines in the reign of Edward VI. 5. State the principal facts in the lives of Sir T. More, Latimer, and Jewell. Name some of their works. 6. Who were the chief martyrs in the persecution under Queen Mary ? State particulars respecting the death of Cranmer. 7. Mention the principal points of difference between the first and second Prayer Books of King Edward VI. Give their dates. 8. What were the Lambeth Articles ? With what view, and under what circumstances were they framed? 9. Relate the events which induced Hooker to write his ' Ecclesiastical Polity.' Mention other works of similar character published in the same reign. 10. Give some account of the Hampton Court Conference. What was its result ? ( 70 ) LAW DEGREE EXAMINATION, December, 1860. EXAMINEES : J. T. Abdt, Li.D., Trinity Hall. Joseph Shahpb, il.d., Jems College. Heebert Broom, m.a., Trinity College, C. S. Calvbriey, M.A., Christ's College. EOMAN LAW. 1. Give the definition of Jus Gentium contained in the Institutes. Is there anj' distinction between the Jus Gentium of the CiTU Law and Modem International Law ? 2. Was a child born of a free father and a slave mother free by the Roman Law? What was the rule of the English Law as to the children of a free father and k villein mother ? Shew what was the effect of the English rule with respect to the extirpation of Villenage. 3. Define 'Dos,' and state the rights of the husband thereto. 4. What was the ' Jus Postliminii' ? Give an instance of its applica- tion to Modern Law. 5. Enumerate the kinds of Capitis diminutio, and describe the effect of each. Explain the term Caput in the Roman Law. 6. State what were the duties of the Tutor and Curator respectively. When and how did their duties cease ? 7. In whom is the property in the sea shore vested by the Roman and English Law? Have private persons any rights in the sea shore by either system of law ? 8. Define Servitudes, and give their principal divisions with examples of each kind. Explain ' iter,' ' actus', ' via,' and ' aquseductus.' 9 What was TJsucapio, and to what did it extend ? State the alterations which were made by Justinian in the law by which the fact of possession was converted into the right of ownership. 10. What were the various kinds of Roman Testaments? Give the formalities requisite to the validity of each. 11. Enumerate the principal persons who were incapacitated from making Testaments. 12. By what means might a Testament be either ' ruptum' or ' irritum'? Explain the distinction between 'ruptum' and 'irritum.' DIGEST. Book I. Tit. n. TSANSLATE : Beginning, Facturus legum vetustarum interpretationem, etc. Ending, Sed communi nomine appellatur jus civile. Beginning, Deinde quum esset in civitate lex duodecim tabularum et jus civile, etc. Ending, Honorarium dicitur, quod ab honore Prsetoris veuerat. Beginning, Capta deinde Sardinia, mox Sicilia, etc. Ending, Postea sediles senatusconsulto creabantur. 1. What were the 'actiones legis'? Who was Cnseus Flavins, and what had he to do with them ? Was any addition made to them by another person afterwards ? 2. How many Prsetois were there at the first establishment of the office, and why was the number increased ? LAW DEGREE EXAMINATION. 71 JUSTINIAN'S INSTITUTES. Books I. II. I. Translate, explaining briefly " dedititios" ; "Latinos"; Junianos"; and " multis modis additis.' 1. Beginning, Et dedititios quidem per constitution em nostram ex- pulimus, etc. Ending, quae sola est in prsesenti, prsestari. — Sook i. tit. v. 3. What -were the provisions of the Lex Julia Norbana ? Which one is referred to when Justinian says, " In ipso ultimo spiritu animam simul et libertatem amittebaut" ? 2. Beginning, Non tamen cuicumque volenti manumittere licet, etc. Ending, qualibet ex causa heres non extiterit. — Book i. tit. vi. 1. Explain briefly "in fraudem creditorum manumittit" ; "heres;" " necessarius." 3. Beginning, Sed hodie, ex nostra constitutione, etc. Ending, causa cognita adrogatio permittitur. — Book i. tit. xii. 2. On -what principle were women unable to adopt? Explain briefly "personam", and "adrogatio." 4. Beginning, Sed et servus proprius testamento, etc. Ending, Proprius autem servus inutiliter eo modo tutor datur. — Book I. tit. xiv. 1. To what is "libertatem directam" opposed ? 5. Beginning, Quod autem lex ab intestato vocat ad tutelam adgnatos, etc. Ending, cum is qui datus est tutor, vivo testatore decesserit. — Book I. tit. xvi. 2, To support what principle did the law step in in this case ? 6. Et qui poiestatem habent aliquam, se excusare possunt [a tutela]. Book I. tit. XXV. 3, What other excuses were allowed ? Explain briefly the Italicized words. 7. Beginning, Si tamen alienam purpuram vestimento suo quis intexuit, Ending, etquibusdamaliispossessoribus possunt. — Bookii. tit. i. 26. Explain briefly " vindicari" and " condici." 8. Denique et si in adrogationem datus fuerit miles, vel filiusfamilias emancipatus est, testamentum ejus que^i ex nova mUitis voluntate valet, neo videtur capitis deminutione irritum fieri. — Book ii. tit. xi. 5. Mention some of the soldier's testamentary privileges. 9. Beginning, Hereditas plerumque dividitur in duodecim uncias, etc. Ending, suam hereditatem dividere. — Book ii. tit. xiv. S. 10. Beginning, Si peculium legatum fuerit, etc. Ending, et ex eo reliqua inferre, — Book ii. tit. xx. 20. Explain briefly " peculium." 11. Compare vsus with usvsfritetus^ legatum with * legacy* ; and explain briefly the following phrases: servus peena, statu liber; semel heres semper heres ; servitus servitutis esse non potest, WAEEEN'S BLACKSTONE. 1. Define " Municipal Law." And state the ordinary twofold division of it adopted by English lawyers. 2. Specify various general customs which obtain in this country, and have the force of law. 3. Which is the oldest of our Statutes now operative ? 4. What, according to Blackstone, are the "constituent parts of a Parliament" ? 72 LAW DEGREE EXAMINATION. 5. What is meant by " allodial" land ? Is there any such in England ? 6. " Fraud will vitiate everything." Illustrate this proposition. 7. What was sought to be affected by Mr Fox's Libel Act ? Was this statute declaratory or enacting ? 8. Distinguish between libel and slander, and between slander actionable per se and slander actionable on proof of special damage, 9. What are the three ingredients in a valid contract ? And in what does a contract differ from a tort ? 10. Explain shortly the policy of the legislature in enacting the Statute of Frauds, (29 Car. II. c. 3). 11. How may murder be distinguished from manslaughter ? Put instances of homicide not felonious. 12. "Actus non facit reum, nisi mens sit rea," put various states of facts illustrating this maxim. 13. Mention the Three Superior Courts of Common Law and Courts having Appellate Jurisdiction in common law cases. HALLAM'S CONSTITUTIONAJL HISTOET. 1. What was the dispensing power claimed by the sovereigns of England ? and how far was it consistent with the ancient law ? 2. State briefly the principal resolutions which were passed in the Convention Parliament yrior to the presentation of the Bill of Rights. 3. What were the principal provisions in the Bill of Kights r and state the points in which it differed from the Declaration of Kights, 4. By what proceeding was the punishment of Sir John Fenwick effected, and in what respects didit contravene the ordinary course of the law ? 5. By whatmeansis this country secured from the abuse of miUtarypower? 6. What were constructive treasons ? Give examples, and state the arguments applicable to each. 7. What alterations were made in the law of treason during the reign of William the Third ? 8. How was the libeirty of the Press secured during the reigns of William the Third and his successors ? 9. State what Acts were passed during the reigns of William the Third against, and in favour of, toleration in religion. 10. On what occasion and when was the Act of Settlement passed? What were its principal provisions i U. What was the proceeding against SachevereU, its cause, and its result ? Give an analysis of the chief arguments for and against his prosecution. 12. What was the war of the succession? Shortly describe the negociations for pacification, and give the reasons for and against the peace of Utrecht. 1 3. State briefly the causes which led to the diminution of the personal authority of the crown. EOMAN LAW. 1. , TRANSLATE the following passage of Gains : Constant autem jura ex legibus plebiscitis senatus consultis constitutioni- bus Principum, edictis eorum qui jus edicendi habent responsis prudentium. Define the sources of the Civil Law enumerated in the above passage. What was the ' Jus edicendi' and who possessed it ? Whence was the obligatory force of the ' Constitutiones Principum' derived ? 2. What was the contract of ' emptio et venditio' ? What were the remedies, by each party, by the Roman and English system of laws, for LAW DEGREE EXAMINATION. 73 a breach of such contract respecting a chattel, and what could be recovered in an action for breach of such contract ? 3. Si quis a non domino quern dominum esse crediderit, bona fide fundum emerit, vel ex donatione aUave qualibet justa causa aeque bona fide acceperit, natural! ratione placuit fructus quos peroepit, ejus esse pro cultura et cura ; et ideo si postea dominus supervenerit, et fundum vindicet, de fructibus ab eo consumptis agere non potest. Does the doctrine asserted in the text accord with the English law ? In what cases, according to the latter system of law, can the lawful owner recover the profits which have accrued to the holder, and by what means ? 4. Define 'Traditio.' What were the requisites to its validity, and to what did it extend ? Does the similar proceeding in the English Law have an equally extensive effect ? 5. What was the ' longi temporis possessio' ? To Which of the following cases does it extend ? and give your reasons for your opinion. (1) Immoveables taken by violence in the possession of original wrongdoer. (2) Immoveables taken by violence in the hands of a bona fide possessor. (3) Things stolen in the hands of a bona fide purchaser without notice, (4) Immoveables taken through the absence or negligence of real owner and conveyed to a bona fide possessor. 6. What are the periods of time after which no action can be brought by the law of England for the recovery of lands and goods respectively ? Apply the English law to the cases stated in the last question. 7. Describe briefly the principal proceedings in a Roman action during the reign of Justinian. 8. What is the meaning of an Issue in an English action at law ? By what means were issues arrived at, both by the Roman and English systems ? Give examples, and state who were the persons to try such issues. 9. Define ' damnum infectum.' What were the measures provided by the Roman Law against ' damnum infectum' ? ^'s house adjoins and is supported by B's house ; B allows his house to become in disrepair, whereby it is probable that within a short time it will fall down and A's house with it. Has A any remedy in Roman or English Law to compel £ to repair his house ? 10. What were the various forms of marriage, and by what modes and for what causes might marriage be dissolved ? 11. Between what relations were marriages prohibited by the Civil Law S How were the degrees of relationship computed ? 12. State the various modes by which illegitimate children might be legitimatised. Are any of those modes allowed by the English Law ? DIGEST. Book XXX. Tit. i. Teanslatb, adding any such brief notes as may be necessary : Begirming, Quod in rerum natura adhuc non sit, etc. Ending, nihilominus recte a legatario vindicabitur. Beginning, Plane ubi transferre voluit legatum in novissimum, etc. Ending, utputa si Titio et servo proprio sine libertate. Beginning, Qusesitum est : si filiusfamilias qui filium habebat, etc. Ending, si alieuatus a testatore fuisset, legatum ad emtorem pertinebit. Beginning, Ab omnibus heredibus legatum ita erat, etc. Ending, quod unusquisque et sibi et coheredi suo dare damnatus videretur. ^ 1. A testator leaves a horse to B imagining it to be his own : it tUms 74 LAW DEGREE EXAMINATION. out however to telong to C. Would this legacy be valid ? "Would it be valid if the testator at the time of the legacy knew that it was C's? Give your reasons for each answer. 2. How does a Modus differ from a Condition ? 3. Explain briefly the terms ' dies eedit' and ' dies venit' with reference to legacies. JUSTINIAJST'S INSTITUTES, BOOK n. GAIUS'S COMMENTARIES, BOOKS I. H. I. Tbansiate: 1. Beginning, Finitur autem ususfructus morte fructuarii, etc. Ending, qu8e res consolidato appellatur. — Inst. tit. iv. 3. On what principle was the usufruct extinguished by ' consolidatio' ? 2. Beginning, Denique et si in adrogationem datus fuerit miles, etc. Ending, nee videtur capitis deminutioneirritum fieri. — Inst, tit.xi. 5. Mention some of the testamentary privileges accorded to soldiers. 3. Beginning, Hereditas plerumque dividitm- in duodecim uncias, etc. Ending, suam hereditatem dividere. — Inst. tit. xrv. 6. What would be the effect of a testator assigning definite parts to some of his heirs and not to others ? 4. Sed si instituto heredi et cohered! suo substituto dato alius subs- titutus fuerit, divi Severus et Antoninus sine distinctione rescripserunt ad utramque partem substitutum admitti. — Inst. tit. xv. 3. 5. Beginning, Si peculium legatum fuerit, etc. Ending, et ex eo reliqua inferre. — Inst, tit, xx. 20. II. Explain the phrase "nuUi res sua servit," and give the meaning, and probable origin, of the term " suus heres." III. What were the objects of the " Lex Palcidia," and of the " senatus- consultum Trebelliauum" ? Translate : 1. Beginning, Non tamen cuicumque volenti manu mittere licet, etc. Ending, quam si vindicta aput consiliiuu justa causa manu missionis adprobata fuerit. — Comm. book i. 36. Compare the term ' legatum' with our ' legacy.' 2. Beginning, Item si quis per populum, etc. Ending, set etiam liberi ejus in ejusdem fiimt potestate tanquam nepotes. — Comm. book i. 105—107. How did children escape depairia potestate? 3. Beginning, Sed jura praediorum urbanorum in jure tantum cedi possunt; etc. Ending, et in jure cessionem recipiunt. — Comm. book ii. 29—31. How does ' usus' differ from ' ususfructus' ? What are stipendiaria, tributaria pradia ? i. Beginning, Idem- contingit et in frumento quod in solo nostro ab aliquo satum fuerit, etc. Ending, utique si bona fide possessor fueris. — Comm, book ii. 76-78. How did Justinian decide the question pending between the Proculeians and Sabinians? Explain "bonorum possessio." 5. Beginning, Item qui filium in potestate habet, etc, Ending, filia adcrescendo ex dimidia parte fit heres. — Comm. book II. 123, 124. LAW DEGREE EXAMINATION. 75 M. TULLIUS CIOEEO PEO O^aiCINA. Translate, explaining wherever necessary : 1 . Beginning, Qui igitur convenit, etc. Ending, non quid actum sit, quaerere. — cap. 3. Explain what modes of proceeding were open to Caecina. 2. Beginning, Huic CEesennise fundum in agro Tarquiniensi, etc, Ending, Sed hunc fructum mature fortuna ademit. — cap. i. 3. Beginning, His rebus ita gestis, P. Dolabella praetor interdixit, etc. Ending, sed etiam profiteri videatur, recuperatores ?— cap. 8, 9. Why may the interdict de vi armata have been preferred in this case ? 4. Beginning, In eum quid dicam, nisi id quod negare non possit ? etc. Ending, sed ad explendam damnationem praesto fuisse. — cap. 10. 5. Beginning, Ego, quod mihi videretur, etc. Ending, sed id quod dicitur, valebit. — cap. 28. 6. Beginning, Lex usum auctoritatem fundi jubet esse biennium, etc Ending, si velit, jumentum per M. Scauri Tusculanum. — cap. 19. Explain the line of argument here, and the reason of its adoption. 7. Beginning, At est aliquando contra judicatum, etc. Ending, multisque peritissimis hominibus, auctoribus uteretur. — cap. 24. What was the cause in question, and in support of what principle is it appealed to here ? 8. Beginning, TJt vero jam, recuperatores, etc. Ending, Numera, quam multa in ista defensione falsa sint, Piso. — cap. 31. Mention any of these alleged fallacies. Give any illustrations that occur of the maxim ' exoeptio probat regulam.' Explain recuperatores, feciales ; jure judicioque, jure mancipii : and give corresponding Latin expressions to "vested right," " right of road," "statute law," " common law." What is the meaning of Lucretius's line, " Vitaque mancipio nulli datur, omnibus usu" ? BLACKSTONE, VOL. I. AND HATNE8. 1. Explain the nature of the remedies available to a subject against the Crown by our,constitution. 2. In what cases may the maxim, "nullum tempus occurritregi," be applicable (') in civil, {') in. criminal proceedings ? 3. Under what circumstances will a Writ of Habeas Corpus be an appropriate remedy? What is meant by suspending the Habeas Corpus Act i and how may this be done ? ■1 . What was decided in the Case of Monopolies 1 1 Coke Kep. 85. 5. What is meant by a wife's " equity to a settlement" ? And how did this privilege originate ? 6. What degree of moral guilt attaches, in your opinion, to one who violates or acts counter to the provisions of a statute passed in regard to a matter in itself indifferent ? 7. Specify various classes of cases which are vrithin the jurisdiction of Equity but excluded from that of a Court of Law. 8. In what respect does the province of a Judge in Equity essentially differ from that of a Common Law Judge ? 9. What powers are derived from his Commission by a justice of tliePeace? 76 LAW DEGEEE EXAMINATION. 10. Mention various incidents which attach to a corporation aggregate at common law. 11. What do you understand by the " lex et consuetudo parliamenti" ? In what remarkable cases has this law been in conflict with the " lex terrae" ? 12. Whatis the Mutinjr Act? How frequently is it passed, and what, generally, is the nature of its provisions S CONSTITUTIONAL HISTOEY. 1. "Septenstial Parliaments were at first a direct usurpation of the lights of the people." (Priestley.) How does Priestley support this dictum ? Is it true? Give abrief account of this bUl, and the reasons for its introduction. 2. Lord Stanhopebroughtforward(A.D. 1718) " An act for strengthening the Protestant interest." What biU was this? What was its fate? On what other occasion was the attempt to carry out the same object renewed ? 3. What was "the fable of Captain Jenkins's ears"? What political use was made of this story ? 4. State briefly the arguments of Holt, L.C.J., in the case of Ashby v. White. What other important case of privilege was discussed some few years after this, and what was the opinion of the judges in this case ? 5. Hallam asserts that Jacobitism with the majority was a modification of the spirit of liberty in the natibn. Is this dictum in your opinion true ? If so, how is it supported by the facts ? If not, state your reasons for objecting to it. 6. What was the object of the Habeas Corpus Bill of 1758 ? What addition was made by it to the Act passed in the reign of Charles II. ? 7. What was the "Family Compact" ? Mention shortly its terms. What was the purport x)f the secret convention attached to it ? 8. " Wilkes's case arose on the legality of General Warrants." What case is here alluded to, and what was the result of the debate in the House of Commons on the subject above italicized ? 9. Mention as many of the persons as you can remember to whom the letters of Junius have been attributed. State which of these names you prefer, and your reasons for the preference. What weight would you attach to the evidence of handwriting in the controversy about the authorship ? 10. Give a short account of the political events that led to the American war of independence. What was the conduct of Lord Chatham and Mr. GrenvUle respectively at this crisis ? TRIAL OF JOHN WILKES. 1. State as nearly in the language of the original as you can the warrant of commitment in the information against WiUies for the publica- tion of No. 45 of the North Briton. What were the two objections raised to its Legality ? 2. How were these objections overruled? 3. Taking the same facts, draw a warrant of commitment that would have brought the case within the terms of the second of these objections. 4. "The case of writing and publishing seditious libels has been resolved by both Houses not to be entitled to Privilege." (Blackstone.) Was this point raised in Wilkes's case ? If so, what view was talier of it by the Court ? LAW DEGREE EXAMINATION. 77 INTEENATIONAL LAW, AND TEEATT OF AIX-LA-OHAPELLE. 1 In what respects is a treaty between two nations analogous to a contract between individuals ? 2. In what relation does a treaty between two countries stand to -International Law generally ? 3. Shew by reference to history that the sanction of the legislative power in a state may be necessary for giving validity and efficacy to a treaty. 4 Specify various modes recognised in diplomacy, whereby the mission of a minister at a foreign court may, during his life, be terminated. 5. State shortly the effect of a declaration of war upon contracts existing between subjects of the belligerent powers. What effect has a declaration of war upon a partnership comprised of subjects of the two belligerents ? 6. Upon what grounds were the works of art deposited in the Louvre during the wars of the French Revolution restored to the Countries from which they had been taken ? 7. Explain what is meant by perfect and by imperfect neutrality. Give instances of the latter species of neutrality. 8. In whom, according to the theory of our Constitution, is vested the power of declaring war and of making peace? And how is the power practically limited ? 9. Explain the cause of the war between Great Britain and Spain which commenced in the year 1739, and state when that war was termi- nated, and by what treaty. 10. Specify the principal powers engaged in the hostilities put an end to by the treaty of Aix-la-Chapelle. 11. What causes or events mainly induced the English Government to negotiate for peace a.d. 1748 ? Mention also the European powers which shewed themselves most disinclined to join in the negotiations, and state the reasons why they were averse to doing so. 12. Mention the more celebrated treaties on which that of Aix-la- Chapelle was based. 13. Were the geographical boundaries of the principal states of Europe materially affected by the last-named treaty ? GENEEAL PAPEE. (o) 1. What is a ' custom of the country' or ' local custom' } vrhat efficacy has it ? and what qualities are essential to its validity ? 2. What advantages does a Court of Equity possess in deaKng with fraud over a Court of Law, assuming the case sub judice to be within their concurrent jurisdiction ? (6) 1. War having broken out between two powers, is concluded by a treaty of peace. What is the effect of this treaty in regard to claims or rights in question between the contracting parties not specifically ad- justed and settled by the treaty ? 2. What are the privileges accorded to a public minister or ambassador accredited to a foreign state during the period of his residence in the country to which he is accredited ! What are the exceptions to the • immunity thus extended ? (c) 1 . Mention shortly the provisions of Mr, Grenville's Bill for regu- lating the trial of controverted elections ? What part did the ministry of the day take in the debates ? 78 THE MATHEMATICAL TRIPOS. 2. A makes a speech in Parliamrait imputmg improper conduct and motives to B, a private individual, and charging him with unprofessional and dishonest practices : A afterwards publishes his speech, and is indicted for a libel. Would this indictment hold on the obieotion that members of parliament are protected from all charges against them for anything said in the house. (d) 1 . Define Caput, Persona. How is the existence of capitis dmnimitio reconoileable with the principle " civitatem nemo unquam ullo populi jussu amittit invitus" ? 2. Mention the weak points, if any exist, in Caecina's case, and explain the way in which Cicero endeavours to counteract their effect. (e) 1. What was an luterdictum under the Roman Law? Explain the proceedings in connection therewith, and shew how they differed &om those in an Actio. 2. What was the law of Accessio among the Romans ? A paints a picture of great value upon the canvas of B, A being at the' time ignorant of the fact that the canvas is B's property. To whom, by English and Roman Law, does the picture belong ? FIRST CLASS. Bayford, \ ^„ Trin. H. Barter, ] ^*- Trinity Buszard Trinity HONOURS. SECOND CLASS. Bignold, Trin. H. Trench, Trinity Boult, Trinity THIRD CLASS. Goddard, Trin. H. Wilkinson, Jesus Hartley, Jahvrin, EXAMINED AND APPEOVED. St, .Tohn's Caius I MacLeod, WiUiams, H. Trin. Hall St. John's EXAMINATION FOE, B.A. DEGKEE, January, 186L MODERATORS : Peeoival Frost, m.a., St. John's College. Augustus Vatjghton Hadlbt, m.a., St. John's College. EXAMINERS : Henry William Watson, m.a.. Trinity. College. Edward John Route, m.a., St, Peter's College. CANDIDATES FOE MATHEMATICAL HONOTJES. Abbott Airy Aldis AUen, E. K. Armitage Barclay Bechaux Bond, J. Boys Bradley Buckley Joh. Trin. Trin. Trin. Emm. Trin. Trin. Sidney Magd. King's Caius Joh. Budd Pemb. Dalton Caius Bull Queens' Davies, T. C. Trin. Burney Trin. Dodd Trin. BusheH Joh. Dover Jesus Channell Trin. Edwards Emm. Cheyne Joh. Edwards, T. J .Trin. Churchill Joh. Fawcett Trie H Clarence Trin. Pinlaison Jesus Cole Christ's Flather Joh. Cooke Joh. Foster Joh. Copestake Christ's Francis Joh. Corrie, J. 0. Trin. Freeman Joh. THE MATHEMATICAL TRIPOS. 19 Gabb Joh. Maclachlan Trin. Smart Joh. Griffith Emm. McDowell Pemb. Smith; G. Clare Harwood Triu.H. Mathews, A.D .Joh. Sweeting Trin. Hawkins Joh. Mozley King's Tanner Corpus Heath Trin. H. Newton, W. Joh. Thelwall Trin. Hedges Joh. Pattrick, F. Magd. Thomas, E. L Trin. Helt Trin. Peers, J. W. Cath. Thompson Trin. Hensley Christ's Pierpoiut Joh. Thomson Joh. Hieru Joh. Quilter Pet. Thurlbourn Emm. Hoare Joh. Bichmond Pet. TiUard Joh. Hornby Pemb. Rippin Joh. Tomlin Caius Hudson Joh. Robertson Trin. Townend Trin. Hughes, A. 0. Trin. H. Romilly Caius Trench Trin. Hughes Emm Rouse Trin. Twentyman Christ's Hulbert, C. A. Caius Scriven Joh. Valentine Job. Jones, J. B. Trin. Sharpe, H. J. Joh. Venn Caius Kitchener Trin. Shepherd,C.W.Trin. Warlow Joh. Lane Trin. Shuttleworth Caius WilUams, L. .Toh, Leach Caius Singleton Pemb. Wilson, W. S Joh. Levin Cath. Skinner Trin. Wilson, W. R . Trin. EUCLID AND CONICS. 1. Ip a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. If ABC be a triangle in which C is a right angle, shew how, by means of the first book, to draw a straight line parallel to a given straight line so as to be terminated by CA and CB and bisected by AB. ii. In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides and the straight fine in- tercepted between the perpendicular let fall upon it from the opposite angle and the acute angle. If ABC be a triangle in which C is a right angle, and DE be drawn from a point D ia. AC at right angles to ^ 6 ; prove, without using the third book, that the rectangles AB, AE and AC, AD will be equal. 3. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line vrith the line touching the circle shall be equal to the angles which are in the alternate segments of the circle. Two circles intersect in A and B, and CBD is drawn perpendicular to AB to meet the circles in C and D ; if EAF bisect either the interior or exterior angle between CA and DA, prove that the tangents to the circles at E and F intersect in a point on AB produced. iv. Inscribe a circle in a given triangle. Describe a circle touching the side BC of the triangle ABC and the other two sides produced, and prove that the distance between the points of contact of the side BC with the inscribed circle, and the latter circle is equal to the difference between the sides AB and AC. 5. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 80 THE MATHEMATICAL TRIPOS. From the angular points of a parallelogram ABCD perpendiculars are drawn on the diagonals meeting them in. E, F, G and B respecti-vely ; prove that EFGH is a parallelogram similar to ABCD. vi. Draw a straight line at right angles to a plane from a given point in the plane. Prove that the shortest distance between two opposite edges of a regular tetrahedron is equal to half the diagonal of the square described on an edge. vii. In the parabola prove that SY is a mean proportional between SA and SP. P^ is a focal chord, and upon PS and pS as diameters circles are described j prove that the length of either of their common tangents is a mean proportional between AS and Pp. 8. In a parabola the rectangle contained by four times the focal distance SP and the abscissa PVis equal to the square on the semi-ordinate QV. If j4Q be a chord of a parabola through the vertex A, and QR be drawn perpendicular to .rfQ to meet the axis in .R ; prove that AR vrillbe equal to the chord through the focus parallel to AQ. ix. From the foci S and fi of an ellipse SY and HZ are drawn at right angles to the tangent at P ; prove that Y and Z are in the circumference of the circle whose diameter is the axis major. If AQ be drawn from one of the vertices perpendicular to the tangent at any point P, prove that the locus of the point of intersection of PS and QA produced wiU be a circle. 10. If PN be an ordinate of the semi-axis major CA of an ellipse whose center is C, and if PTthe tangent at P meet the axis produced in T, prove that CN. CT= CA'. If Y, Z be the feet of the perpendiculars from the foci on the tangent at P ; prove that the circle circumscribed about the triangle YNZ will pass through C, 11. If from a point P in an hyperbola straight lines PH, PK be drawn parallel to the asymptotes and meeting them in H and K respectively ; prove that the rectangle contained by PH and PK wiU be invariable. If the tangent at P meet one asymptote in T, and a line TQ be drawn parallel to the other asymptote to meet the curve in Q ; prove that if PQ be joined and produced both ways to meet the asymptotes in R and R', RBf will be trisected at the points P and Q. xii. A right cone is cut by a plane which meets the cone on both sides of the vertex ; prove that the curve of intersection is an hyperbola. If the curve formed by the intersection of any plane with a cone be projected upon a plane perpendicular to the axis ; prove that the curve of projection will be a conic section having its focus at the point in which the axis meets the plane of projection. ARITHMETIC ALGEBEA, AND PLANE TEIGONOMETET. 1. A PERSON having to pay ^1045 two years hence invests a certain sum in the three per cent, consols, to accumulate interest until the debt shall be paid, and also an equal sum the next year. Supposing the investments to be made when consols are at 73, and the price to remain the same, what must be the sum invested on each occasion tiat there may be just sufficient to pay the debt at the proper time ? 2. At the siege of Sebastopol it was found that a certain length of trench could be dug by the soldiers and navvies in 4 days, but that when only half the navvies were present, it required 7 days to dig the same THE MATHEMATICAL TRIPOS, 81 length of trench. Shew that the nawiea did six. times as much work as the soldiers. 3. Define x™ when m is an integer, and prove that US'", a;" = x"*" where m and n are integers. Taking this equation as the definition of x*" when m has any value, deduce that (x")" = x""". 7-2 V(10) Change the fraction -rr; — ;; — ,..„., , , ..„, into one m which the ^ V{7-2 V(10)} + 5- V(10) denominator is rational. 4. Define the arithmetical and geometricsd means hetween two given numbers. Prove that no two unequal numbers can have their arithmeticEd and geometrical means equal. If « be the sum of an odd number of terms of a series in geometrical progression, and s' the sum of the series when the signs of the alternate terms are changed ; prove that the sum of the squares of the terms will be equal to + ss according as the signs of the odd or even terms be changed. 5. If a and (3 be the roots of ox" + ia: + c = ; prove that the equation a p yihoae roots are -=. and - will be /3 a , 2ae-b' , „ a' + a; + 1 = 0. ac Solve the equations : (3x - 1)2 + (4x - 2)' = (5x - 3)', (x + o) V(l + x) = 3 (x - 1) + 2o, x' + y' + xy' + x'y = 4 XS + j,3 = 8 }• 6. Prove the Binomial Theorem for a positive integral index. If a^ be the coefficient of x' in the expansion of (1 + x)" ; prove that ii) according as « is an even or odd integer. vii. Define the characteristic and mantissa of a logarithm. Investigate a rule for finding by inspection the characteristic of the logarithm of a number, which is either greater or less than unity. Given that log2 = •30103, and logS = •4771213, find the integral values between which x must lie in order that the integral part of (1*08)* may contain four digits. viii. Define tan^l for any value of A, and give the changes of sign and magnitude of tan 4 for values of A whict change gradually from 90° to 270°. Trace the chemges of from A = OtoA = 180°. cos A Give a geometrical construction for dividing an angle into two parts whose tangents shall be in a given ratio. • -D ^x. ^ i. A l-cos2^ , //l-cos2^\ .„ , IX. Prove that UnA = -^^^ = + ^(_-__) . ^^i^^ the double sign. If tan^jl = V(2) + 1, find cos 2^1 and thence the general value of ^4. 82 THE MATHEMATICAI- TRIPOS. X. Prove that the tangents of -i - and — r- are in arithmetical pro- gression, ,, . -D . n lono i.1. ^ 2 1 - cos^ + cos^ + cosC If ^ + B ^C= 180°, prove that ^ = ■=: i— =. ^ C 1 - oosC+ cos^ + cos5 tan 2 If sin{a + /3) cosy = sin(a + y) eos/3, prove that either /3 — y is a multiple of ir, or a an odd multiple of— . xi. Show how to solve a triangle by the use of logarithmic tables when two sides and the included angle are given. If 6 = a{V(3) — 11 and C = 30° find A and B. If in a triangle the feet of the perpendiculars from two angles on the opposite sides be equally distant from the middle points of those sides, the other angle will be 60° or 120°, or else the triangle will be isosceles. xii. Find the radius of the circle circumscribing a given triangle. Prove that if it be equal to the perpendicular drawn from one of the angles on the opposite side, the product of the sines of the angles adjacent to that side is \. STATICS AND DYNAMICS. 1 . Define the resultant of two forces ; prove the parallelogram of forces so far as the direction of the resultant is concerned, when the forces are commensurable. If the parallelogram of forces be true for any two forces making a given angle witii each other, prove that it will be also true for any two forces making any other angle with each other. 2. If three forces acting on a body be in equilibrium, prove that their lines of action will meet in a point and that each force vrill be proportional to the sine of the angle between the Hues of action of the other two. Deduce from this proposition the conditions of equilibrium when the forces are parallel. Two equal rods AB, AC without weight are connected by a hinge at A and are placed in a vertical plane resting on a smooth sphere so that the point A is vertically over the center O. A heavy ring slides on a string attached to the two ends 3 and C, the length of the string being twice that of either rod. If BD be the perpendicular drawn from B on .40 produced, prove that in the position of equilibrium AO.AD = 2.BD', supposing the sphere to be so smeJl that the string is clear of it. iii. Investigate the distance of the center of gravity of any number of bodies from a given plane, in terms of the distances of the centers of gravity of the bodies from that plane. Prove that the center of gravity of a triangle is the same as that of three equal particles placed at its angular points. Perpendiculars are drawn from the angular points of a given triangle ABC upon the opposite sides, and another triangle is formed by joining the feet of these perpendiculars ; prove that, if^j, y, rbe the distances of the center of gravity of this triangle from the sides opposite to A, B, and C, p £ r a' cos(Ii -C)~ b'cosl.C-A)' c' cog(^ - £)' iv. Two given weights are connected by a string which passes over a pulley, one hangs freely and the other rests on a rough inclined plane, THE MATHEMATICAL TRIPOS. 83 find the directions of the string when the latter weight is on the highest and lowest positions consistent with equilibrium. If the weights be such that when a is the inclination of the plane, X the angle of iriction, the inclinations of the string to the plane in the highest and lowest positions be s and K respectively, prove that . , s 4 X tanX tan'— ^r— = - . 2 tana V. Explain the principle on which a measure of the sensibility of the Common Balance may be chosen ; and find how the seusibUity of a balance may be increased, without affecting the stability. vi. In the system of pullies in which each pulley is suspended by a string attached to a fixed beam, the strings being parallel, prove that the principle of Virtual Velocities holds, if the weights of the pullies be neglected, and also if their weight be taken into account. Prove also, that the same principle holds, and that the equilibriiim is unstable, when two weights balance which are joined by a heavy string passing over the top of an inclined plane, one portion of the string resting on the plane and the other being vertical. vii. State the Second Law of Motion. Deduce from this law that it is correct in calculating the position of a projectile projected with a velocity », to assert that the space traversed in the time < is ^ in a vertical direction, and vt in the direction of projection. viii. Explain how Attwood's machine is employed to illustrate the third law of motion. If, instead of allowing both weights to hang freely, one of them is moved by a single moveable pulley, the strings being parallel, find the acceleration of each weight. li P = Mfhe the relation between the pressure, mass, acceleration, find the unit of time, when the unit of space is two feet, an d the unit of pressure is the weight of an unit of mass. 9. If a particle describe a parabola under the action of gravity, prove that the square of the velocity at any point of the orbit will be proportional to the distance of the particle from the focus. If C be the center of curvature corresponding to any point P of the particle, prove that the vertical velocity of C will be proportional to the time elapsed since P was at the highest point of its orbit. 10. Two elastic balls moving in the same direction but with different velocities impinge directly upon one another, find their velocities after impact. 11. If a particle slide down a smooth curve in a vertical plane under the action of gravity, and if v, v' be the velocities of the particle at two points whose altitudes above any horizontal plane are y, y' , prove that s''-e» = 2?(y'-j,). A smooth circular cylinder of given height h and whose radius is a is divided into two equal, parts by a plane through the axis which is vertical, and one part is removed. A particle is projected horizontally with a given velocity from one extremity of the upper rim. Prove that the greatest possible velocity of projection in order that the particle may reach the ground before it leaves the semi-cylinder 's ira W ( ;^ j , and supposing the velocity greater than this, find the point where it will strike the ground. g2 84 THE MATHEMATICAL TRIPOS, 12. Prove that the time of a complete oscillation of a particle in a smooth cycloid, whose axis is vertical, is 2^ */( -J, where a is the radius of curvature at the vertex. A number of cycloids are drawn through a given point A and having their vertices situated on a given curve and their axes vertical. Prove that if the given curve be a cycloid whose vertex is at A and whose axis is vertical, the time of descent from A down all the cycloids to the given curve will be the same ; and that whatever be the form of the given curve, the cycloid down which a particle will slide in the greatest or least time will have the tangent at A parallel to the tangent drawn to the given curve at the point where the cycloid meets it. HYDEOSTATICS AND OPTICS. 1, Peove that the difference of the fluid pressures at any two points within a vessel containing fluid of uniform density varies as the diflerence of the depths of the points below the surface. How is this proposition modified if the vessel contains layers of imiform fluids of different densities which do not mix ? Three fluids whose densities are in Arithmetical Progression, fill a semi- circular tube whose bounding diameter is horizontal. Prove that the depth of one of the common surfaces is double that of the other, ii. Show how to find the resultant vertical pressure of a heavy homo- geneous inelastic fluid upon any portion of the surface of a body immersed in it. A double funnel formed by joining two equal hollow cones at their vertices stands upon a horizontal plane with the common axis vertical, and fluid is poured in until its surface bisects the axis of the upper cone. If the fluid be now on the point of escaping between the lower cone and the plane, prove that the weight of either cone is to that of the fluid it can hold as 27 : 16. 3. If a body be partially or totally immersed in a uniform fluid, show that the resultant fluid pressure on the body is equal to the weight of the fluid displaced, and acts vertically upwards through the center of gravity of the fluid displaced. An equilateral triangle ABC, of weight W and specific gravity coto — 1, where a is the critical angle for the medium of which the prism is composed. 11. Determine the geometrical focus of a pencil of rays after direct refraction through a lens, the thickness of which is neglected. The ends of a glass cylinder are worked into convex spherical surfaces whose radii are each equal to the length of the cylinder, prove that the geometrical focus of a pencil after direct refraction through the ends of 86 THE SIATHEMATICAL TRIPOS. u' 1 ft' — 1 the cylinder is determined by the equation = — - — — , where « and V u r V are measured from the face nearest to the origin of light and r is the length of the cylinder, xii. Describe the simplest form of the Astronomical Telescope, and trace the course of an oblique pencil to the eye of an observer. If the eye-glass be fitted in the extremity of a jjol^hed tube whose diameter and length are respectively equal to the diameter and focal length of the eye-glass, find the effect of flie tube on the ragged edge when the stop is removed. PEOBLEMS. 1. The circles which touch the sides AC, BC of a triangle at C, and pass through B, A respectively, intersect AB in E and F. Lines ijrawn from the centers of the circles inscribed in the triangles ACF, BCE parallel to CF, CE, respectively, meet AC, BC in P, Q. Prove that CP is equal to CQ. 2. If X, J/, z be real qtiantities, prove that a' {x — y) (x - z) + 6' (y - x) (y — z) + c* (z - x) (z — y) will always be positive provided that any two of the quantities a, b, e are together greater than the third. 3. A mixture of gold with » different metals contains r per cent, of gold and r^, *•,, r,. .7„per cent, of the other metals. After repeated processes, by which portions of the other metals are taken away, the amount of gold remaining unaltered, the mixture contains s per cent, of gold and «,, a^, s^.-'„ per cent, of the other metals. Find what per centage of each metal remains. 4. If ACB be a triangle having a right angle at C, and AE, BD drawn perpendicular to AB respectively, meet BC, AC produced in E and D, prove that tanC£Z) = tax^BAC, and the triangle ECD is equal to the triangle ACS. V. A beacon is due west of a lighthouse and three miles distant from it. The channel of a river is given by the condition that a vessel shall enter due south of the lighthouse, at such a point that the lighthouse and beacon shall subtend 60° at the vessel, and shall continue to do so until the beacon is north-west, when the channel remains straight in the last direction in which the vessel was sailing until it is due south of the beacon. Prove that the straight part of the channel is {V(3) + 1} miles. vi. Two parabolas have a common axis and vertex, and their concavities turned in opposite directions, the latus rectum of one is eight times that of the other ; prove that the portion of a tangent to the former, intercepted between the common tangent and axis, is bisected by the latter. vii. Tangents to an ellipse are drawn from any point in a circle through the foci, prove that the lines bisecting the angle between the tangents, all pass through a fixed point. 8. A sphere of radius a is supported on a rough inclined plane, for which the coefficient of friction is /«, by a string of length - , attached to it and to a point in the plane. Prove that the greatest possible elevation of the plane in order that the sphere may rest when the string is a tangent is 2tan~i/u; and find the tension of the string and the pressure on the plane in the limiting position of equilibrium. 9. The barrel of a rifle sighted to hit the center of the bull's eye, which is at the same height as the muzzle and distant a yards from it, would be inclined at an elevation a to the horizon. Prove that if the rifle be wrongly sighted so that the elevation is a + 6, 6 being small compared THE MATHEMATICAL TEIPOS. 87 ■witli a, the target will be hit at a height — -; — B above the center of the bull's eye. If the range be 960 yards, the time of flight 2 seconds, and the error of elevation 1", the height above the center of the buU's eye at which the target will be hit will be nearly ^th of an inch. X. The portion of a right cone cut ofiF by a plane will only just balance on a horizontal plane with the shortest side VA in contact ; prove that the vertical through A in that position divides the opposite side VS in the ratio 3 : 2. 11. Three smooth, equal, and perfectly elastic spheres P, Q, R are situated on the circumference of a circle, M being equally distant from P and Q, but farther from each than they are from each other. If they be simultaneously projected with equal velocities towards the center, prove that R will just pass between P and Q without interruption. xii. A ball of elasticity e is projected obliquely up an inclined plane so that the point of impact at the third time of striking the plane is in the same horizontal Une as the point of projection. Prove that the distances from this line of the points of first and second impact, are in the ratio 1 : e. xiii. A straight Ime is drawn from the center of an ellipse meeting the ellipse in P, the circle on the major axis in Q, and the tangent at the vertex in T. Prove that as CT approaches and ultimately coincides with the semi-major axis, PT and QT are ultimately in the duplicate ratio of the axes. 14. The tangent at any point P in an ellipse, of which S and H are the foci, meets the axis-major in T, and TQR bisects HP in Q and meets SP in R ; prove that PR is one fourth of the chord of curvature at P through S. XV. Two particles are revolving in the same direction in an ellipse, under the action of a force tending to the focus. Prove that the direction of the motion of one as it appears to the other is parallel to the line bisecting the angle between their distances from the foci. xvi. The sides of a rectangle are in the ratio ir : 4, and semicircles are described on the longer sides as diameters. Prove that, if the rectangle be immersed in water, with one of the shorter sides in the surface, the pressure on the two parts external to both semicircles will together be equal to that on the part common to them. 17. A plane rectangular lamina is bent into the form of a cylindrical surface of which the transverse section is a rectangular hyperbola. If it be now immersed in water so that first the transverse, secondly the con- jugate, axes of the hyperbolic sections be in the surface, prove that the horizontal pressure on any the same immersed surface will be in the two cases the same. xviii. A hoUow cylinder is closed at one end and open at the other, and a fixed stop perpendicular to the axis divides the cylinder into two equal parts cutting off the communication between the parts ; the weight of the whole cylinder is half the weight of the water which it would contain. Prove that if the cylinder be placed mouth downwards in water the depth of the stop in the position of rest will be only half as great as if a hole had been made in the stop. xix. Two hollow cones, filled with water, are connected together by a string attached to their vertices which passes over a fixed pulley ; prove that, during the motion, if the weights of the cones be neglected, the total pressures on their bases vrill be always equal, whatever be the forms and dimensions of the cones. If the heights of the cones be h, h', and heights 88 THE MATHBMATICAIi TEIPOS. mh, nh' be vinoccupied by water, the total normal pressure on the base dviring the motion will always be in the ratio »* + » + 1 : rf + ra + 1. XX, A refracting medium is worked into a prolate spheroid in which the axis is n times the distance between the foci. Prove that if a ray be incident parallel to the axis, its deviation after emergence at the opposite side will be twice the angle which the notmal at the point of emergence makes with the axis, 21. Two similar and similarly situated ellipses are traced on a plane such that the square on the distance between their centers is equal to the sum of the squares on the radius of each, dravm in the direction of the center of the other. A luminous point is placed at the center, and a convex lens at any point on the circumference, of one ; prove that the image wUI lie on the circumference of the other if the principal focus does. 22. If the azimuth of a star at its rising be equal to the N.F.D. of the Sun at 6 a.m. to a spectator in 45' north latitude, prove that the declination of the star wiU. be equal to the altitude of the Sun, and the hour single of the star to the south azimuth of the Sun. NEWTON AND A8TE0N0MY. 1. EsTTTNOiATE aud provc Newton's first Lemma. A and B are two fixed points, CD is a fixed straight line, and cd Is another straight line moving subject to the condition that the rectangle under the perpendiculars upon it from A and B is equal to the rectangle under the corresponding perpendiculars upon CD, If the lines CD and cd intersect in P, prove that, ultimately, the angle AFC wUI be equal to the angle BPD. 2. Enunciate and prove Newton's fourth Lemma. Prove that the surface generated by the revolution of a semi-circle round its bounding diameter is to that generated by the revolution of the same semi- circle round the tangent at ttie extremity of the diameter in the ratio of the length of the diameter to the length of the semi-circle. 3. The vanishing subtenses of the angle of contact in all curves which have finite curvature at the point of contact are ultimately in the duplicate ratio of the chords of the conterminous arcs. AB is an arc of finite curvature at A, and a point P is taken in it such that AP : PB in the constant ratio of m : k. At A, P, and B tangents AT, TPR, and BR are drawn and AB is joined ; find the ultimate ratio of the area ATRB to the segment APB as B moves up to A, and prove that this ratio is a minimum and equal to 9 : 8 when P bisects AB. 4. "When a body revolves in an orbit subject to the action of forces tending to a fixed point, the areas which it describes by radii drawn to the fixed center of force are in one fixed plane, and are proportional to the times of describing them. A body is describing an ellipse round a center of force in one of the foci. Prove that the velocity of the point of intersection of the perpendicular from that focus upon the tangent at any point of the orbit is inversely proportional to the square upon the conjugate diameter. V. A particle describes an ellipse with an .acceleration tending to the center, prove that the acceleration is proportional to the distance. If a triangle ABC be inscribed in tiie ellipse so that its center of gravity coincides with the center of the ellipse, prove that the velocities of the particle when at the angular points A, B, C will be proportional to the opposite sides of the triangle, and also that the times from AtoB,B to C, and Cto it will be equal to each other. THE MATHEMATICAL TEIPOS. oS 71. A particle describes an oval orbit about a center of force S ; when tke particle is at any point P the center of force is suddenly removed to anoUier point S ; determine the new law of force in order that the particle may continue to describe the same orbit as before. If T, T be the periodic times before and after the change, and if SS' being produced meet the tangent at P in Q, prove that T:T\: S'Q : SQ. If the new center of force be so taken that the new law of force be always an integral power of the distance, prove that the locus of the centers of force about which the same oval orbit can be described will consist of a series of straight lines finite in length. vii. Explain the changes in the length of the day which occur in the course of the year at a place within the arctic circle. In what part of the heavens wUl a star be seen, whose right ascension is 30° and declination 0°, at six o'clock in the evening at midwinter? At what o'clock will the star set ? Find also the sidereal time of the setting. viii. What is the error of coUimation in the transit instrument ? Why is this error of more importance in this instrument than in the mural circle ? Explain how electro-magnetism is employed in making observations of the time of transit of a star. ix. Shew how to determine the distance of the Moon from the Earth- Can the same method be applied to the Sun or any of the fixed stars ? Obtain roughly the numerical value of the parallax of the Moon. X. Explain the cause of aberration ; and prove that all the stars are displaced by aberration towards the same point on the celestial sphere. At what season of the year is the aberration of a star least whose right ascension is 90° and north declination 60° ? 11. What are meant by the Lunar ecliptic limits ? Shew how to find them. If the orbits of the Moon and of the Earth be supposed to be each circular and in the same plane, investigate the efiect of the finite velocity of light upon the real and apparent times of the beginning and ending, and upon the duration, of a lunar and solar eclipse respectively. 12. Explain the Moon's phases. If on the day of one of the equinoxes the Moon be half fuU, prove that to a spectator at the equator, she will rise with the line bounding her visible disk horizontal. NATUEAL PHILOSOPHY. 1 . Find the resultants of any number of forces acting upon a rigid body, and deduce sufficient conditions of equilibrium. If P, Q be two forces whose directions are at right angles, prove that the distances of the central axis from their lines of action are as P' : Q'. 2. Investigate the position of the center of gravity of an area, the boundaries of which are given by equations in polar co-ordinates. Prove that the center of gravity of the arc of a Lemniscate whose equation is r'=(s* cos 26 is in the line bisecting the angle between the lines drawn to the extremities of the arc from the node. 3. Investigate the equation of the curve in which a uniform string hangs from two fixed points under the action of gravity. If (J be the distance between the two points, a the inclination to the horizon of the line joining them, and I the length of the string, prove that, when I— a is very small, the horizontal tension is equal to the weight of a portion of the string whose length is —, ; . ^ . ^ ^ 2V(3) V(P-o') iv. A particle of mass m moves in one plane under the action of forces, 90 THE MATHEMATICAL TEIPOS. whose resolved parts parallel to two fixed rectangular axes Ox and Oy, are X and Y respectively ; prove the truth of the equations df~m' dF'm' If the axes of reference be moveable in the plane according to any law, and if 6 and 6' be their respective inclinations at any instant to a line fixed in the plane, and v^ and Vy be the velocities of the particle at that instant resolved parallel to the axes, prove that % -«,oosec(e'- a) ^-z,, cot (0'-e) ^= ^, dt " ^ ' dt ^ ' dt m *o ,o ^, d0 ^ , ., ., d9' Y -=-" + «^ cosec (0' - 61) — + »„ cot (0' - 61) — = - . at dt dt m V. A particle is describing a curve luider the action of forces tending to a fixed center. From this center a line is drawn representing the in- stantaneous velocity of the particle in direction and magnitude. Prove that the locus of the extremity of this line is the polar reciprocal of the ciirve described by the particle turned through a right angle. If the polar equation of the original curve be of the form where a and h are any constant quantities, prove that the extremity of the line drawn as above described will move with an acceleration which always tends to the center of force and is proportional to its distance from that center. vi. A particle moves under the action of given forces in a very fine smooth tube of given form which revolves uniformly about an axis perpen- dicular to its plane. Investigate the equations for determining the motion of the particle. An elastic string has one end attached to a point in the interior of a smooth circular tube, the circumference of which is equal to twice the natural length of the string. The string is then stretched completely round the tube, and a material particle is attached to the free end. If the tube be now made to revolve uniformly round an axis passing through the point of attachment of the string and perpendicular to the plane of the tube, find the velocity of the particle when the string has regained its natural length. 7. Find the couple which is required to keep a body, floating in a fluid, in a position inclined at a small angle to the position of equilibrium, a plane with respect to which the body is symmetrical being vertical. If M be the metacenter, H, S the centers of gravity of the fluid dis- placed in the position of equilibrium, and in the position of displacement through an angle 6, respectively, prove that the difference of distances of H and H' from the first plane of fioatation is \ HM. 6' very nearly. viii. A fiexible surface of any form is exposed to the action of fluid. Find the relation between the pressure, tensions, and curvature at any point. If a flexible vessel in the form of a surface of revolution with its axis vertical contain heavy fluid at rest, prove that, generally, whenever the tension parallel to the meridian through any point is a maximum or minimum, it will be equal to the tension perpendicular to the meridian at that point. 9. Investigate the positions of the primary and secondary focal lines. THE MATHEMATICAL TRIPOS. 91 ■when 51 small pencil of light is obliquely refracted from a luminous point below the surface of still water. How would a small white stone at the bottom of a piece of water appear to be coloured on a bright day ? and what would be the effects on the appearance, if it were seen through a straight slit in a screen placed on the surface of the water, when the slit is in the vertical plane contairwug the eye and the stone, and when perpendicular to it, respectively? X. Describe Flamstead's method of determining the position of the first point of Aries, and state the corrections to which the required observations must be subjected. 11. Shew how to iind the time at any place, whose geographical situa- tion is unknown, by observations of equal altitudes of a star before and after passing the meridian. What advantages has this method ? If the latitude of the place is known, and equal altitudes of the Sun are taken before and after noon, prove that the correction for the change of declination may be found from the formula — A/i. tanZ -I- Bf^ tan 5, where A and B are independent of I and S and may be tabulated for different in- tervals of time between the observations, /n being the change in the Sun's declination in 24 hours. xii. Find the errors in right ascension and declination due to parallax. PURE MATHEMATICS. 1 . If ;9 be a prime number and N be prime to p, then N"'^ — I is a multiple of p. If pCn denote the number of combinations of p things n together where p is a prime number, prove that p.iCn + ( — 1 )""' is divisible by p. ii. If «j, = a» + S, prove that the sum of n terms of the series whose (n + l)th term is where k is a given quantity is 6 + OK 1 1 Why cannot this method be applied to determine the sum of the harmonic series 1 + J + J + . . ? Prove that the sum of n terms of this harmonic series beginning at the «th becomes equal to log 2 when n increases without limit. 3. Solve the equation s" — 1 = where » is a positive integer, and shew that if » be a prime number, all the roots may be exhibited in a series of consecutive powers of any one of the imaginary roots. What is the meaning of a primitive nth root of unity ? State the number of primitive »th roots, if « = pgr . . iv. Shew how to determine whether a given equation has any equal roots. Prove that the roots of the equation a* + ^gx' + rx + s = 0, cannot be all real if jS + r^ be positive. 5. If i>„a;" + p^.ix"~^ + + Piic + P^—f (*)j shew how to sum the series i)„sinne + ;j,^isin(n- 1)6+ + p^^nS + p^- If a pair of compasses, the distance between whose points is always a, be moved on by turning round each leg alternately, the arcs described being IT 2'ir Stt a -—, a -—, o r— &c. m order, prove that when two consecutive pomts in 2n 2n "^ 92 TUB MATHEMATICAL TBIPOS. about which the compasses turn first lie in a straight line with the first point, then the distance of the latter of the two points firom that first point IB o cot — . in vi. In any spherical triangle, prove that sin a _ sin 6 sin e sin^ sin 5 sinC' and that each of these ratios is equal to " * '^ ^ -a 2 cos - . cos - . cos - . tan M, u u Z where K is the radius of the small circle circumscribing the triangle. Give a geometrical construction of a spherical triangle of which three given points shall be the middle points of the sides. 7. Investigate the equation of a straight line in the form X cos a + y sin a — ^ = 0. Determine the relation between p^, p^, p^, if the three straight lines acosffli+y sin Bi— j)i = 0, arcosOj+ysinaj— Pj=0, xcosa^+ysina^—p^=0, meet in a point, and shew that the same relation will hold between T'l, r^, rj the distances of the feet of the perpendiculars p^, p^, iJjSfrom the common point of intersection. 8. From the definition, determine the polar equation of a conic section referred to a focus as pole. If ABC be a triangle inscribed in a conic section so that the focus S is the center of the circle inscribed in the triangle, prove that A B C A B C cos— cos— cos— COS— + cos— + cos — 2 2^222 "sa"^ "sb" ^ ~sc ^ sz ' where SL is the semi-latus rectum. 9. Investigate the equation of an hyperbola referred to its asymptotes as axes of co-ordinates. A series of hyperbolas having the same asymptotes is cut by a straight line parallel to one of the asymptotes, and through the points of intersec- tion lines are drawn parallel to the other, and equal to either semi- axis of the corresponding hyperbola, prove that the locus of their extremities is a parabola. X. Investigate the equations of a straight line in the form X -a _i/ -b _z- c I ni n ' Prove that the general equation of all planes passing through this straight line is X- a y -h _ /x - a z - c\ 1 m \ I rt )' where X is an arbitrary constant. Find the equation of the plane passing through a given straight linfe and parallel to another straight line. xi. Shew how to find the plane diametral to a given straight line in a surface of the second degree when its equation is given in the most general form. THE MATHEMATICAL TRIPOS. 93 Determine the nature of the surface a' + y" - a' + 2y« + 2zx - 2xy + 2a! + 23» + 2« = a', and find the magnitude and direction of its principal diameters. xii. Determine the relations which exist between the co-ordinates of the extremities of any three conjugate diameters in an ellipsoid. If closed polyhedrons of the same number of faces be inscribed in an ellipsoid, such that if (», y, z,), (», y, z^) he the co-ordinates of the ex- tremities of any edge RS, where L^}is a given quantity, then the volumes of all these polyhedrons will be equal. Thence prove that the volume of the paiaUelopiped formed by three conjugate diameters is constant. PEOBLEMS. 1. Shew that the number of ways in which m» things can be divided among m persons so that each shall have n of them, is . ~r^ . 2. If ABC be a triangle whose sides touch a parabola, and^, q, r be the perpendiculars from A, B, C on the directrix, prove that p tanA + qtajiB + r tanC= 0. iii. If the lines which bisect the angles between pairs of tangents to an ellipse be parallel to a fixed straight line, prove that the locus of the points of intersection of the tangents will be a rectangular hyperbola. iv. Three hyperbolas are drawn, whose asymptotes are the sides of a tri- ingle ABC, taken two and two, prove that the direction of their three com- aon chords pass through the angular points A, B, C and meet in a point, vhich will be the center of gravity of the triangle, if the hyperbolas touch me another. 5, A, Paxid B, Q are points taken respectively in two parallel straight lines, A and B being fixed and P, Q vaiiable. Prove that if the rectangle AP, BQ be constant, the line PQ will always touch a fixed ellipse, or a fixed hyperbola, according as P and Q are on the same or opposite sides of AB. vi. A uiiifonn string hangs in the form of a loop by two small rings with- out weight from a smooth circular wire placed with its plane vertical, shew that the longest string, which is consistent with the rings remaining apart, is 2a sin' 6, a being the radius of the circle, and 9 being determined by the equation log (cot I] = cotO cosecS. vii. Trace the oiirves whose equations are xy^ — i^y' — ay^ + aV = 0, and r = a (cos26 — sin 6). Find the multiple points in the last curve. 8. If a given line be an equiconjugate diameter of an ellipse, the locus of the foci is a lemniscate. ix. The locus of the middle points of chords of a lemniscate, drawn parallel to the axis, is a curve, whose equation is y = > . . /, g _ „ ., . if 2o be the length of the axis. 94 THE MATHEMATICAL TRIPOS. Trace the curve, and account for the branches which extend beyond the lemniscate. X. Prove that the volume of that portion of the solid, bounded by the surface whose equation is i'« + ay' = « (»* - «•), 8 which lies on the positive side of the plane o£xy, is — ira'. 21 11. Prove that vl = (- ^Tx^^ ^^JmI ^j^ere z = -, and hence inte- dz" ^ ' dx" X grate the equation a;'" -i = ay. xii. Two particles revolve in the same direction in an oval orbit round a center of force S which divides the axis unequally, from the extremities of a chord PQ through the center of force : prove that, when they arrive in positions R, T respectively, such that the angle RST is a minimum, the time from R to the next apse will be an arithmetic mean between the times from P to the next apse and to Q from the last apse. 13. An elastic string, whose mass is ma and unstretched length a, is con- fined -^fithia a straight tube, to one end of which it is fastened and which revolves with uniform angular velocity w in a horizontal plane. Shew that the length of the string when in relative equilibrium is a — j — where 6 = o(o^/(— ),X. being the tension required to double the length of the strmg. xiv. Any number of strings are revolving uniformly about a vertical axis through a point to which the strings are attached ; prove that, if, in a position of relative equilibrium, the tensions at the highest points be all equal, the other ends will lie in a paraboloid. XV. A rough right cone is placed so that the inclinations to the hori- zontal of the highest and lowest generating lines are y and y', prove that, if 6 be the greatest inclination to the vertical plane through the axis, in which a particle can rest on the surface, and \ be the angle of friction, . ,6 cos 7 - cos X, tan'- = '- r- . 2 cosY + cos\ 16. A frustum of aright cone, whose vertical angle (2o) lies between 30" and 60", is made by a plane bisecting the axis and parallel to the base, and has its interior surface polished. If a luminous point be placed at the center of its base, prove that the radius of the bright circle formed on a screen passing through the point where the vertex would have been and perpendicular to the axis, will be a cot (30° + a), cot (30" - a), where o is the radius of the base. xvii. A bright circular wire, of radius a, is placed upon a table, and a luminous point moves upwards from any point A in the wire with uniform velocity « ; an eye is placed vertically over the point B in the diameter AB, shew that the line joining points P, P' at which the light is reflected to the . . v' eye moves with a velocity whose acceleration is — , and that if the eye be • V at a height 2a, the distance BP increases with velocity -77^ . 18. The observed distances of a comet from the Svm r, / as it passes its THE MATHEMATICAL TRIPOS. 95 Nodes are the one too great and the other too small by the same small quan- tity. Prove that the approximate error in the calculated longitude of the perihelion, measured along the comet's orbit, is -j-. — t> a^d '^^ ^^ perihe- lion distance - r +r xix. In passing from one place to another, so that the curve is always inclined to the meridian at flie same angle, shew that the tangents of the con- stant angles of inclination for the path which goes direct from one to the other, and for those which go once, twice, and more times round the earth, will be in arithmetic progression. 20. A particle is placed on a rough plane lamina which is initially hori- zontal, and which is moveable about a horizontal line through its center of gravity. Shew that the particle will begin to slip when the plane has turned through an angle tan"' ——5 rj-j , M being the coefficient of friction, 2o the length of the plane perpendicular to its axis of revolution, c the distance of the particle from that axis, and M smd m the masses of the lamina and particle. 21. A ring is constrained to remain in a vertical plane, and to be always in contact with a rough horizontal plane, by passing through a smooth fixed ring at the extremity of a horizontal diameter. A weight equal to - th of the weight of the ring is attached to it at the other extremity of the horizontal diameter. Shew that the weight will just reach the horizontal plane if the coefficient of friction be either of the roots of the equation NATTJEAL PHILOSOPHY. 1. Ip a pencil of light be incident on a small reflecting or refracting surface whose semi-diameters in the primary and secondary planes are X-i, Xj respectively, and if tij, v, be the distances from the surface of the primary and secondary foci, prove that the distance v of the circle of least confusion from the middle point of the surface will be given by the formula A.J + As Xj A^ Prove also that this section of the reflected or refracted pencU is a circle only when the surface is an elUpse ; and that there is in that case another circular section parallel to the former and whose position may be found by changing the sign of \j in the above expression. ii. Describe the experiment by which Newton eSected the decomposition of white light. If the prism be placed at first in a position of minimum deviation for the red rays and afterwards for the violet rays, in which case do we obtain the longer spectrum , the distances of the screen and prism from the aperture being unaltered ? iii. If the Moon's culminating altitude at any place on any day be observed to be A, and her declination an horary motion in declination be o" and m" respectively, prove that the interval expressed in seconds between her culmination and transit over the meridian of the place will be nearly 96 THE MATHEMATICAL TRIPOS. m COB A sml"'cos* sin(^ - S)' Hence explain how, by the aid of a sextant and the Nautical Almanac, the longitude of a place may be determined. i. If the sphericity of tie Earth be neglected, prove that the refraction of a star will vary as the tangent of the apparent zenith distance. This result is found to agree with observation if the zenith distance be not very large. Explain how this agreement is proved to exist. T. If a particle move in a resisting medium under the action of a central force, prove that the velocity at any point is that due to one-fourth of the chord of curvature through the center. Two homogeneous spheres are composed of different substances, and move in a medium, the resistance of which is proportional to the velocity, imder the-action of their mutual attraction which is any function whatever of the distance between their centers. Prove that if their radii be inversely proportional to their densities, their center of gravity will either remain at rest or else move in a straight line, according to the original circumstances of projection. 6. Enunciate and prove the principle of the conservation of areas. If a system of particles mutually attracting each other and under the influence of no external forces be initially at rest ; prove that if at any lime they all become rigidly connected the system so formed wiU be at rest. vii. If at any time i, the co-ordinates of a point in a mass of fluid in motion be x, y, z, the velocities of that point parallel to the co-ordinate axes be u, v, to, and p the density at that point ; prove that the equation of continuity of the fluid is dp djpu) d{pv ^ d(pio) ^ dt dx dy dz ' If a bomb-shell explode at a very great depth below the surface of the ■ sea, prove that the impulsive action at any point of the water will be inversely proportional to the distance of that point from the center of the shell. 8 If a particle describe an ellipse about the focus, trace the effect on the further apse of a small disturbing force, acting in the direction of a normal to the orbit, during one complete revolution. If a particle describe an ellipse of small eccentricity about the focus, and if it be disturbed by the attraction of a very distant center of force, prove that the ellipse will tend to place itself witii the major axis perpen- dicular to the direction of the force. ix. Given that m' „ = a [1 _ + e cos (c0 - o) + m' cos {(2 - 2m) - 2/3} z + Vne cos {(2 - 2m - c) - 2^ + a} + i/me* cos{(2 - 2m - 2c) « - 2^ + o} - |mV C0B(me + /3 - S)], dt lb' T=-~sm2(e-e'). Investigate the inequality in the longitude called the Variation. THE MATHEMATICAL TRIPOS. 97 10. An elastic string whose unstretched length is I, has its extremities fixed at two points whose distance is I', and the string is very slightly- disturbed from its position of rest. Prove that the transversal vibrations will travel along the length of the string in the time*/ — and the longitudinal VIW -~ where Wis the weight of the string, T its tension, and ffE E the modulus of elasticity. If two strings of lengths I, I', and of different elasticities E, K, be attached together and the other extremities be fastened to two fixed points ; prove that, when E and E' are very great, the pitch, T, of the notes which may be sounded wUl be given by the equation 277-; ^'"'^T_I! a' 2^~ H'' ""^ a' according as the vibrations are longitudinal or transversal, where a, a are the velocities of transmission along the two strings. PEOBLEMS. 1. AD bisects the angle ^ of a triangle ABC, and is produced to P, so that the difference of the angles PBC and PCB is a maximum, shew that their sum is iA. 2. If a series of parallel plane sections of an ellipsoid be taken, and on any sections as base a right cylinder be erected, shew that the other plane section, in which it meets the ellipsoid, will meet the plane of the base in a straight line whose locus will be a diametral plane of the ellipsoid. 3. Through a given point (x,,, y,, «,,) a series of chords are drawn to an ellipsoid, whose equation is in such directions that the line of intersection of the tangent planes at the extremities of each chord is perpendicular to the chord. Prove that these chords must all lie upon the conical surface of which the equation is (V-c')x, ^ (o'-o')y„ ^ (a'-6')^„ _^_ «-»o y-Va "-h Prove also that the envelope of the lines of intersection of the tangent planes, drawn as above described, is a parabola, which is the intersection of the polar plane of (a;„, t/„, z,) with the cone of which the equation is V{(y - c') xx^ ^ VKc' - a') yy,) ^ V{(a' - y) i,a„} _ ^ a h c 4. ABC is an indefinite material straight line of uniform thickness and density. The portion AB repels and BC attracts with a force varying inversely as the square of the distance. Prove that if a particle be placed H 98 THE MATHEMATICAL TKIPOS. anywhere in the perpendicular to AC through B, and be then left to move under the action of the attracting line, the velocity at any point P of its path will be proportional to V{(log, cot JPSO)}. 5. Prove that the problem of finding the position of equilibrium of a solid cone on any elliptic base, floating in a heavy fluid, is the same as that of drawing normals to a hyperboloid of two sheets from an internal point. 6. Two particles of equal weight are connected by a string of length 21, which passes over a fixed pulley, and they rest on a smooth inclined plane, /3 is the inclination of the two portions of the string to the plane when the particles are together, and a that of the plane to the horizon. Prove that, if they be slightly displaced, the length of the simple isochronous pendulum will be I cos/3 sin a sin'/3 ' 7. Three small rings of equal mass are fitted on three smooth rods, which are parallel and in the same plane, one being half-way between the other two. Prove that, if they be subject to mutual attraction, according to the law of gravitation, and placed so that the line joining any two of liem is very nearly perpendicular to the rods, the middle ring and the center of gravity IT of the other two vidll oscillate in a time . and the other two relatively V (>)/'; to each other in a time , ._ , , ua being the attraction at a distance a. V (5/x) 8. A straight rod is just immersed in a vertical position in water, the critical angle of which is a, and an eye is placed at a given distance from that extremity of the rod which is in the surface of the water. Prove that, when the eye is in such a position that the image of the rod subtends at the eye a maximum angle, the ray, by which the lowest extremity of the rod is made visible, is incident upon the water at the angle cos"^ V{cosa). 9. The internal surface of a right cylinder is grooved by lines parallel to the axis : prove that, if a luminous point and the eye be placed on opposite generating lines, a bright curve will be seen, which is the inter- section of the cylinder with two hyperbolic paraboloids. 10. A refracting medium consists of layers of spherical surfaces of equal refracting power each of which touches a plane at the same point, and the refractive index for each surface varies inversely as the diameter of that surface. Prove that, when a ray of light passes through the medium in a plane containing the common diameter, the chord of curvature at any point of the path, dravm in the direction of the center of the surface corresponding to that point, is twice the distance of the point from the common tangent plane, and also that the projection of the radius vector from the common point of contact upon the direction of the ray is constant. 11. A sphere is pressed between two perfectly rough parallel boards which are made to revolve with the uniform angular velocities Q and £2' about fixed axes perpendicular to their planes. Prove that the center of the sphere describes a circle about an axis which is in the same plane as the axes of revolution of the boards, and whose distances from these axes are inversely proportional to the angular velocities about them. Shew that, when the boards revolve about the same axis, their points of contact will trace on the sphere small circles, the tangents of whose THE MATHEMATICAL TRIPOS. 99 angular radii will be - x ^z — rr? , a being the radius of the sphere, and c that of the circle described by its center. 12. A irame, formed of four equal uniform rods loosely jointed together at the angular points, so as to form a rhombus, is laid upon a smooth hori- zontal plane and a blow is applied to one of the rods in a direction at right angles to it. Prove that the frame will begin to move as a rigid body provided the middle point of the rod which receives the blow be equidistant from the line of action of the blow and the perpendicular dropped upon the rod from the center of gravity of the frame. Prove also that, in this case, the initial angular velocity of the rod which receives the blow is Jth of what it would have been had it been unconnected with the remaining rods. 13. A uniform wire is bent into the form of a circle whose center is C, and two points A and B at the extremity of a diameter are fixed. The wire is then heated, so that it expands uniformly throughout, and assumes an oval form whose semi-axis major is CD. The tendency at any point to become straight being proportional to the curvature at that point, prove that CD is a harmonic mean between the radii of curvature at A and D. Prove also that, if the expansion of the wire be very small, the increase of its whole length will be to the greatest diametral increase as ir'- 8 : t — 2. 14. A uniform heavy elastic string hangs from a point by one extremity, and begins to move from such a state that all its parts are unstretched; the tension of any portion of the string, if stretched to double its natural length, is the weight of a portion whose unstretched length is I, and c is that of the given string. Prove that a complete oscillation of all parts will take place in a time ... ■ , the lowest point oscillating through a space -j , and that, during each such oscillation, any portion, whose initial distance from the point of sus- pension was nc, win twice move with uniform velocity for a time , „ Z . PUEE MATHEMATICS. 1. Define the terms differential coefficient, and partial differential coefficient, and shew how to obtain the partial differential coefficients of the first order of an implicit function of two independent variables. Pind the differential coefficients of sina; and logaS respectively, and prove that if p, q, r, s, t be the partial differential coefficients of the first and second order respectively obtained from the equation z=f{x,y), and 3-^ be a partial differential coefficient obtained from the equivalent equation then ^J = __{^'i_2pys + /,-]. 2. State the conditions necessary for the truth of the equation F{x^ + h)- -F(xi) _ F'*' (z, + eh) f(x, + h)-f(x,) ~ f"'(x,-^eh)' and deiuce Taylor's theorem from this equation. 100 THE MATHEMATICAL TRIPOS. I If ^0, A^, &o. be the successive coefficients in the expansion of e' prove that _mx A^ n + 3. If /(a) be a continuous function of *, shew how to determine the values of x which render / (x) a maximum or minimum, and deduce tests for distinguishing between the cases of maximum and minimum. If the sum of the squares of the sides of a triangle be s' and the product of the perpendiculars from the extremities of one of the sides upon the other two bep', prove that the ratio of these two sides will be a maximum when the angle between them is cos '-^ . 4. When is one curve said to have a contact of the n* order vfith another curve ? Find an expression for the radius of the circle having a contact of the second order with a given curve at a given point. If r and p be the radius vector and radius of curvature at any point of a plane curve, 8 and their respective inclinations to the prime radius, and s the length of the arc measured from some fixed point ; prove that cPsdr - cPrds '"'' " dcji'dd - de'd^ ' ' 5. Shew how to find the locus of the ultimate intersection of a family of curves whose equations involve one arbitrary parameter. Prove that the equation of the locus of the mtimate intersection of the lines defined by the equation X cos 20 + y sin 29 = 2a cos 9, where a is a given constant, is {x' + y'- ay = \iaV. 6. Trace the curve obtained in the last question, and prove that the radius of curvature at any point is three-fourths of the perpendicular from fhe origin upon the tangent at that point. vi. Integrate and prove that rr / rl-a'Ca' + j/')! , , ttT l-a», l + a1 jjyJi-T^r^Tw} '"'^ = ra I" ^ — '"s—a} ' the limits of integration being y = to y ='/(!— a') and a = to x = 1. A solid is botmded by two paraboloids having a common focus and their principal diameters coincident and in the same direction, and by a sphere whose center is at the common focus. Prove that the volume is 27r .^ c' ^ } (a - h), where ia and ih arc the latera recta of the paraboloids, and c is the radius of the sphere. THE MATHEMATICAL TRIPOS. 101 vii. If an oyal curve roll on a straight line, prove that the area traced out in one complete revolution by any point O in the curve will exceed the area of the curve by Jj r^d\lr, where r is the distance from O of any point P of the curve, and yjf is the angle which the tangent at P makes with some fixed line in the curve. Apply this method to find the area of a cycloid. If sen. oval curve A roll upon an equal and similar curve B so that the point of contact is a center of similitude for each, then the whole area traced out by any point O when A has made a complete revolution is twice the area which would have been traced out if the curve A had rolled on a straight line. viii. Solve the simultaneous difierential equations about a horizontal axis, and the direction of the former make an angle a with the axis of the latter, shew that the angle through which the direction of motion of the center has turned when perfect rolling begins is , 2aio cos a tan ' : — . o» - 2aiu sin a 11. If a ray of light whose direction is a tangent to a surface of the second order be reflected at a homofocal surface, the direction of the re- flected ray will be again a tangent to the surface. THE MATHEMATICAL TBIPOS. 103 12. If one of the principal axes of a cone ■which stands on a given base be always parallel to a given right line, the locus of the vertex is an equilateral hyperbola or a right line according as the base is a central conic or a parabola. 13. A surface is generated by the motion of a variable circle which always intersects the axis of x and is parallel to the plane of y, z. If r be the radius of the circle at a point on the axis of x, and S the inclination of the diameter through that point to the axis of z, prove that the principal radii of curvature at the point are given by the equation p'r +p' (^p — r) = 0, dx when p is the value of — at the point. 14. A rough horizontal plane lamina is capable of rotating freely round a vertical axis. If a heavy particle of mass m be placed at any point upon it, and an angular velocity <« be given to the plane, shew that the length of the arc traversed by the particle on the plane when it just comes to rest relatively to the plane will be m (w — m') ; the inclination of the plane in which 8 is measured to a plane fixed in the body, / the impressed couple about the instantaneous axis, K the impressed couple about the normal to the plane in which 8 is measured, A the moment of inertia about a diameter and (0 the instantaneous angular velocity : prove that A-^, = I, Aw sinO ^ = X. df dt Hence prove that, if the sphere be acted upon by a constant couple whose axis is always perpendicular to the instantaneous axis, and always in the same fixed plane in space, the instantaneous axis vrill describe this fixed plane in space, and a certain right cone in the body, each with uniform angular velocity. 100 THE MATHEMATICAL TRIPOS. 6. If the motion of a mass of elastic fluid be such that every particle is moving towards or from the same fixed point and v be the velocity at the time < of a particle which is at that time at the distance r from the fixed point. Prove that Hence deduce the equation = 1 {F{:r + at) 4/(r - aQ} in the case of the propagation of sound emanating ftom a center of dis- turbance. vii. In the complete developement of ii in a series of simple cosines, shew that the order of the term in which the argument is (^' — gn) « + a is ^ -< J. In the calculation of the constant part of R, shew that additional terms will be introduced if the mean motion of one planet be double that of the other. viii. Prove that in a doubly refracting crystal, there are two directions in the plane front of a wave of light traversing the crystals in which if the vibrations tate place, the light will be propagated without separation. PUEE MATHEMATICS AND NATURAL PHILOSOPHT. 1. What fundamental assumption is made in the usual theory of pro- babilities, if the mathematical definition of a probability be consistent with the ordinary meaning of the term ? An event has happened which must have arisen from some one of a given number of causes : investigate the probability that it arose from an Eissigned cause. An event may happen from different causes at any time at every point in an infinite straight line, and is known to have happened once at every point at some time or other. The probability of its happening between the dis- tances X and « + a* from a fixed point « /(») &x, and if it happen between these points the probability of its happening between the times t and < + 4i a F{x,t). St. The event is known to have happened once at least between the times t^, and t^. Pind the probability that this took place between the distances a and i irom the fixed point, ii. Solve the difierential equations : i> = ?0 («). xr+{x + y)s + yt + '2,{p + q) =0. li a particular integral of any equation of the second order be found of the form (x, y, z, p, q, a, 6) = with two arbitrary constants, prove that a more genersd integral may be found by writing for 4 any arbitrary function dib of a, and then eliminating a between the equations (^ = 0, — = 0, 3. Pind the principal radii of curvature at any point of an ellipsoid, and shew that if p be one of these radii and p the perpendicular from the center on the tangent plane, the point will lie on a homofooal surface provided ^/o be constant. If three homofocal surfaces of the second degree intersect in a point, the centers of principal curvature, at the common point, of any one are the poles with respect to the other two of the tangent plane to the first at that point. THE MATHEMATICAL TEIPOS. 107 iv. A body under the action of any forces is free to turn about a fixed point at which, two of the principal moments are equal. Investigate the equations of motion with reference to rectangular axes, one of which is the axis of unequal moment at O and the other two turn about as origin in any given manner. 6. Shew roughly that the Solar must be less than the Lunar precession, and that considering Solar nutation alone the inclination of the pole of the Earth to the pole of the ecliptic is least at the solstices and greatest at the equinoxes. Assuming the motion of the pole of the Earth parallel to the Moon's orbit, produced by the Moon's action, during a sidereal revolution to be 67r'^ sins' cose Tw (« + 1) ' i being the inclination of the Earth's axis to the pole of the Moon's prbit, T the time of a, sidereal revolution, investigate the Lunar precession of the equinoxes. da, 2na? dR , , ., VI. Assummg the expression — -' = -— deduce the expression dt ." »E for — -^ . If the general term of the disturbing function R be Pe« . f'* cos { {pn, — qn) t + p^ — qs.' — kw + k'w'}, where n and »' are not commensurable with each other ; prove that neither a nor n will be affected by any secular inequality. State the physical cause of the secular acceleration of the Moon's mean motion, and shew that its existence is not contradicted by the above pro- position. 7. An infinite cylinder of radius a is moving with a constant velocity v, in a homogeneous and inelastic fluid, which is acted on by no external forces, so that any point in its axis travels along a straight line perpendicular to the axis. Shew that initially the velocity, relative to the cylinder, of a . a' particle of fluid at a distance r from the axis is — v, and that the initial relative lines of motion lie in cylinders touching the plane in which the axis travels. viii. A plane wave of light polarized in the plane of incidence falls on a plane refracting medium. Assuming the genercil equation of motion to be d'w _ J Id'w d'vA 'df'"' W ^ df) ' where the axis of z is perpendicular to the plane of incidence, and to is the disturbance of any particle, prove that if the coefficient of the incident wave be unity, those of the reflected and refracted waves will be respectively sin(t - r) , 2 cosj sinr - — ^^ — ■ and ■ sin(i + ?-) sin(4 + »') where i and r are the angles of incidence and refraction. If the incident light be white, are the colours of the refracted light mixed in the same proportion? Has the result been confirmed by any experiments ? 108 CLASSICAL TEIPOS. LIST OF H0N0E8 AT THE BACHELOE OF AETS' COMMENCEMENT. »•» In all cases of equality, the names are bracketed. ■Weanglebs. DsALDIS Trin. 2 Bond Mag(] 3 Hudson Job. 4 Hensley Christ's 5 Freeman Job.. 6 Sharpe Joh. 7 Bushell Joh. 8 Pattrick Magd. 9 Hiem Joh. 10 Thomson Joh, 1 1 Thompson Trin. 12 Kitchener Trin. 13 Budd Pemb. r Gabb Joh. \ Eomilly Caius 16 Bechaux Sidney 17 McDoweU Pemb. 18 Cheyne Joh. 19 Mozley King's 20 Hornby Pemb. 21 Dalton Caiiis j Davies Trin. \Lane Trin. 24 B,ouse Trin. 25 Tomlin Caius 26 Channell Trin. (Bradley Caius \ Scriven Job; 29 Rippin Joh. 30 Thurlbourn Emm. 31 Valentine Joh. /Griffith Emm. \ Matthews Joh. 84 Armitage Emm. Senior Optimes. Ds Williams Joh. fChurchiU Joh. \ Sweeting Trin. 38 Helt Trin. 39 Shuttleworth Caius 40 Buckley Joh. 41 Abbott Joh. / Cole Christ's t Skinner Trin. 44 Hawkins Joh. 45 Tillard Joh. 46 Finlaison Jes. 47 Smart Joh. 48Bodd Trin. 49 Pawcett Trin.H ( Corrie Trin. \ Levin Cath. ( Cooke Joh. s Hughes, t W. O. P. Emm. 54 Barclay Trin. f Newton Joh. t Thomas Trin. {Clarence Trin. Richmond Pet. 59 Leach Caius 60 Smith Clare 61 Dover Jes. 62 Edwards Trin. C Bull Queens' { Shepherd Trin. (^ThelwaU Trin. ( Robertson Trin. I Twentyman Christ' si JiTNioR Optimes. Ds QuUter Pet. 69 Heath Trin.H. 70 Burney Trin. /Airy Trin. \Boys King's 73 Edwards Emm. / Jones Trin. \Pierpoint Joh. f Bagge Trin. ( Singleton Pemb. 78 Fremcis Joh. /Flatber Joh. \ Hedges Job. 81 Townend Trin. 82 Hoare Joh, 83 Venn Caius / Maclachlan Trin. \ Wilson,W.R.Trin. 86 Wilson,W.S. Joh. 87 Warlow Joh. 88 Foster Joh. {Copestake Christ's Hulbert Caius 91 Peers Cath. 92 Hughes.A.O. Trin.H. 93 Tanner Corpus CLASSICAL TKIPOS, Febeuaet, 1861. EXAMINERS : J. S. Wood, b.d., St. John's College. Edwabd Balston, M.A., King's College, W. M. Gdnson, M.A., Christ's College. W. J. Beamont, m.a , Trinity College. CANDIDATES FOE THE CLASSICAL TEIPOS. Abbot Airy Athawes Austen Leigh Benn Joh. Trin. Clare King's Joh. Borrett Boulton Boys Brown, J. E. Budd King's Trin. King's Joh. Pemb. Bushell Channell Churchill Cleasby Cobb Joh. Trin. Joh. Trin. Trin. CLASSICAL TKIPOS. 109. Cornish King's Ingham Trin. Smith, G. V. V. Crosse Trin, Kitchener Trin. Stephenson Dalton Caius Harsden Queens' Storr Dayis Caius Mozley King's Straffen Dineley Trin. Newton Joh, Taylor, T. Dodd Trin. Nicholas Joh. Trevelyan Eafle Joh. Northey Trin. TurnbuU Edwards Tiin. Pidcock Corpus Twentyman Forster Trin. Pierpoint Joh. Twist Geary Corpus Raban Emm. Valentine Gery Emm. Richmond Pet. Walsham Haidy Christ's Rowlands Corpus Warren Hedges Joh. Sanderson Clare Whalley Hoare Joh. Shepherd Trin. Yeoman Howard Trin. Smith By Mr. Clare Gwnaon. , Cains Christ's Trin. Cath. Joh. Trin. Trin. Christ's Magd. Joh. Magd. Joh. Trin. Trin. Tbanslate into English Peose, and answer the questions appended to each passage: A* Beginning, Aoiai ftiv M£i'EXaw Aprjyoi/s^ sitrl dsdiav, /c.t.X. Ending, "^pS'' i-rap oii toi 'jtuvtz^ iiraiviofjLEv deal aXKoL, HoMEE, Iliad, IV, 7 — 29. 1. Analyse the words dXaXicofisuTiU, tpiXofifulln^, vapniuPXinKi, tfeuXowi^, EXo^^i ^'"■'V"?'"'- 2. Explain fully the construction Toloi/ TOK /uueow EEiirss; and shew by examples that it is equally compatible with the Attic idiom whether we regard tov as a mere definite article, or as a demonstrative pronoun. Give the full force of this predicative in the following passage : 2to/jL(z T* sppri^sv x«A*«S^, ^fvvTsBpdvtaTat S' dirav, iriKpOTaTovs ISovTt Secfiou^ Tois l/jiois. 3, Shew that iiraiviw bears its primitive meaning in this passage. Discuss Buttmann's derivation of aniv, dximv. B. Beginning, *Ei/0a Oeoijf x^oviov irpotrBsv Sofxai ?Jx^evT£S, k.t.X. Ending, kuL p* oo-tis if/EvSttrai, 'OXupLiria fiw/ia-r' e-jfovTijoi/, Hesiod, Theogonia, 767 — 783. 1. From what sources is Hesiod supposed to have derived the materials for his Theogony ? C Beginning, "Eo-xe ToiauTav iityaXav avarav, /c.t.X. Ending, airipfiaros avdopdv dtaruitjiv vXav, PiNDAE, Pythia iii. 24 — 37. 1, Account for the quantity of aiarav here. "What are the primary meaning and original form of arij ? Has the periphrasis Xfnia KopmviSos any special reference to the usual application of this term ? 2, Remark on the form Too-erais. 3. Give the derivation and various meanings of o/ioijuaKeTos, 4. In what various forms does the root of sraOpou appear J Z), Beginning, XO. '2 irodiivti toU SlKaiois Kal yEiapyoii f'tfiipa, k.t.X. Ending, Kal Tpiaivovv tiJ SocsXXti Sii yjiomv to yriSiov. Abistophanes, Pax, 556—570, 1, Illustrate the idiom ^v Spa, 2. Does the last line but two admit of more than one rendering ? E. Beginning, AI, Xw, rt rd dpfiaK6i/ eo-tii/ dfiaxaviovTo^ ejocotos, k.t.X. Ending, AsvKaivaiv 6 xpovo^. 'jroiijii ti ^eT, ds yovv yXtopov, Theooeiics, xiv, 62— r . Does the 5th line require any emendation ? 110 CLABSiOAI. "riSiPOb. By Mr, Beamont. Translate into English Prose : 'EIIEI fi' i.'jr£fxvrf6pta, ♦gV dvdpi Xaot^ EireiKOTw^ tri^a^, Tioi 5' ddipfiavTov ia-TLav SofiuiVf yvvaiKtiav dToXfiov alxfJ^dv. KaKdSv de irpEcr^E^ETai to Anp-viov dvr. y . A-oyw, youTat Si Sri irdOo^ Kara- •JTTVtFTOVt "^Kaa^EV de TIS TO dtivdv aS AtjfivloiffL nri^fiatriv, QEocTTvy^ria d* dyet (3poTwv dTtfiwdiv o^x^Tttt yei/os, eri^EL yAp oStk to 8viT(f>i\k9 6£ots, Tt TtSuB* ovK ei/5t«:o)S dyBipuo ; TO 6' ayx* '^vEv/xoviou ^i(pov vrp. S', diavTalav d^UTrsu/ces ovra dial A'lKa^' TO fiT] QifiK y&p *oii Xa^ nriSoi TraTovp-tvov t6 irav Atos (Fkjias iraptK^avTOi oi dEfiia-TcJs. AiKas S' ipEiSETat irvQfiijVj dvT, ^, wjooxoXkeuei 5* AXtra ^atryavovpyo^* TEKVov d* iirEitrtpipEi dopLOnriVf *SK 5' alfiaTtav m-aXaLTiptov TLVEt fxvaos Xpouo) KXvrd. ^vncofpptav 'Epii/us, -^scH. Choeph. 612-640. Give various readings or emendations of the passages marked with asterisks. Translate : Beginning, Tout* itTTlv ^Stj KdiroBavp.d a, and — a x bi 2. Multiply together 27»3 - 27oV' + 9ac' - c« and 9(s' + 6ac' + c*, and divide the result by a' — — . 3. Simplify the following expression : 1 - 2ex + e' ex -^ e* 1 ^ + . 1 - ex 1 + ez 4. Divide x^+x^g+a^z—xyz—y'z—yz' by ai'—yz, and x* by x — . y* y B, When are four quantities said to be' proportional in Algebra?- If a, b, 0, d satisfy this test, and a + b + c + d = s, shew that «{s - (6 + c) } = {« - (o + c)}{s - (o + 6) }. 6. If four quantities are proportional according to the algebraical definition they are proportional according to the geometrical definition. Prove this, and explain the nature of the difficulty which arises in the proof of the converse proposition. 7. Solve the following equations : a; + 1 5 - X ^^^2-4 - = » (^) x-ba-l^i ^«>r?-' a: - y = 2. i2 116 EXAMINATIOa FOE B.A. DEGREE. 8. If any six consecutive nxunbers be takeii, the first of which is odd, the difference between the sum of the squai'es of the even and odd num- bers is equal to three times the sum of the two middle numbers. 9. A person died leaving a certain sum to be divided equally between his two daughters (one of whom has married a frenchman) and to be in- vested for their benefit in Consols and French 3 per cents respectively. The trustees bought the former at 92 and the latter at 68, and it was found that the latter investment produced £84 a year more than the former. Required the amount of the legacy (income-tax lOd. in the pound). MECHAJnCS AND HYDEOSTATICS. 1. Defike weight. Explain clearly how statical forces are estimated and compared. 2. If two forces, acting perpendicularly at the extremities of the arms of any lever balance each other, they are inversely as the arms. How may the magnitude and direction of the pressure on the fulcrum be determined ? 3. If two forces acting at a point are represented in direction and magnitude by two sides of a parallelogram, the diagonal through the point will represent theii resultant in magnitude. Two given forces act at a point, within what limits can their resultant vary? 4. In the single moveable pulley when the strings are parallel, there is equilibrium when W = IP. Investigate the mechanical advantage in the Spanish Barton, the con- struction of which is as follows : A string fixed at one end passes under one and above another moveable pulley and the power acts at the other end. Of these two moveable pulleys the first supports the weight and both are connected by a string which passes over a iixed pulley attached to the same beam as the first string. Both strings are parallel. 5. Find the center of gravity of a triangle. Any number of triangles are described on the same base and between the same parallels ; on what line will all their centers of gravity be ? 6. Explain clearly what is meant by the term "pressure at a point" of a fluid, and describe an experiment for proving that if the pressure at any point of a fluid be increased, the pressure at every other point will be equally increased. 7. If a body be immersed in fluid the resultant of the fluid pressures is vertical and equal to the weight of the fluid displaced. Hence determine the conditions of equilibrium of a floating body. 8. Describe the Hydrostatic balance, and shew by means of it how to find the specific gravity of a solid which will not sink in water. 9. Prove that the pressure of the atmosphere is accurately measured by the weight of the column of mercury in the barometer. How is the reading of the barometer affected by the temperature of the mercury at the time of the observation ? 10. Explain the method of filling and graduating a common thermometer. EUCLID. 1. White dovm a list of the symbols which are not admissible in geometry, and give your reasons for excluding them. 2. Define a semicircle, a triangle, and an oblong. When are two magnitudes said to be equal to each other ? EXAMINATION FOR B.A. DEOREE. Ill 3. The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall be equal. 4. Bisect a given rectilineal angle, that is, divide it into two equal angles. Divide a given right angle into three equal parts. 6. All the interior angles of any rectilineal figure together with four light angles are equal to twice as many right angles as the figure has sides. Shevr that any angle of an equilateral pentagon is to a right angle in the ratio of 6 to 5. 6. Equal triangles upon equal bases, in the same straight line, and towards the same parts, are between the same parallels. Shew that in flie figure for the proposition in the third question, the line joining the points taken in the sides produced is parallel to the base. 7. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 8. Find the center of a given circle. 9. Draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. Point out the step in which the problem given in the previous question is employed in this one. 10. Cut off a segment &om a given circle, which shall contain an angle equal to a given rectilineal angle. H. The sides about the equal angles of equiangular triangles are pro- portionals ; and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. If from the vertex C in a triangle ACB, which has the angle ACB a right angle, a line CD be drawn perpendicular to AB, shew that CD is to AC diS BC is to AB and as BD is to BC. JUYENAL, SAT. HI. abd X. I. Tbanslate the following passages: (a) Torrens dicendi copia multis Et sua mortifera est facundia. What instances does Juvenal adduce in support of this assertion? {i) Bidenda poemata malo Quam te conspicuse, divina PhUippica, famae Volveris a prima quae proxima. Are any of the poemata of Cicero stiU extant? Against whom were the Philippics of Cicero directed ? Why called Philippics ? (c) Prima fere vota et cunctis notissima templis Divitise, crescant ut opes, ut maxima toto Ifostra sit area foro. Derive templum, cunctus ; and distinguish between divitise, opes, and pecunia. Why toto foro ? {d) Da testem Romse tam sanctum, quam fuit hospes Numinis Idaei ; procedat vel Numa vel qui Servavit trepidam flagranti ex Eede Minervam. Explain the allusions in this passage. What especial distinction was granted to him " qui servavit, &c." ? («) Exeat, inquit. Si pudor est, et de pulvino surgat equestri, Cujus res legi non sufficit. 118 EXAMINATION FOR B.A. DEGREE. What was the inferior limit of a Roman knight's income ? To what "lex" is allusion here made? By whom introduced?, (/) Quam timeo, victus ne poenas exigat Ajax, tJt male defensus. "What different interpretations have been assigned to this passage ? Which do you prefer? (y) Bomanus Graiusque ac barbarus endoperator. Quote instances of illustrious generals here referred to, (A) Vive bidentis amans et culti villicus horti, TJnde epulum possis centum dare Pythagoreis. £st aUquid, quocumque loco, quocumque recessu, TTnius sese dominum fecisse lacertee. What were the peculiar tenets of the Pythagoreans? Explain and illustrate the expression "unius dominum lacertse." II. Translate : iii. 140—153. Beginning, Protinns ad censum, de moribus ultima fiet, etc. Ending, Quam quod ridiculos homines facit. Translate : x. 88—102. Beginning, Hi sermones, etc. Ending, Frangere pannosus vacuis sedilis TJlubris ? HEEODOTUS. Book HI. 1. Dbaw a map of Egypt, and indicate the position of the following places: Memphis, Thebes, Elephantine, the Lake Moeris, Fatumos, Canopus, Pelusium, Sais, Heliopolis, Busiris. Where was Herodotus born, and when did he live ? 2. Translate : cap. 25. Beginning, 'E-tte/ te Se aTpaTEVofievo^ iyivtTo kv Bi'ij^tftrt, k.t.X. Ending, o ^ikv kir' AtStoTras (rTo\os ovtw eTrpti^e. (a) Parse i^avSpairoSLtrafXEvovSj k/x'jrpiitFatf die\f]\u6Ei/ai, fiTrsXEXoiiTEE, iSlTE'ts, KaTapdi, (b) Derive yvwtrtjitaXEty, i\\tj^p(/)a7iT). (c) Give the Attic Greek for irouufiims, iwowkUiv, l-irptj^E. 3. Translate : cap. 98. Beginning, T6v Si -j^pvtrdv rovrov tov iroWov ol 'IvSol, /c.t.X, Ending, ws dwpriKa kvdvviovtri, (o) Parse Elpripkvov^ tdfitv, dfjL^trwui, KaTairXk^aVTES, (6) Derive x^iiy^ria, ai/aToXat, 6p.6rivai, (6) On what river was Susa ? Has its position been accurately deter- mined by modern travellers ? (c) Enumerate the principal Greek colonies in Southern Italy mentioned by Herodotus. ACTS or THE APOSTLES. 1. Tbanslate : chap. i. 1—8. Beginning, fov fiiv Tpiarov \6yoif iironitrdfiriv irEpl TrdvrutVy k.t.X. Ending, koI eo>s EcrxoTou ti)s yn'. EXAMINATION FOR B.A. DEGREE. 119 (1) Illustrate the words oh •n-apiirTtiirsv . . .Ttjs ^ao-iXetas tou 6eo5 from the Gospel. (2) Relate the circumstances under which the Gospel was first preached in Samaria. (3) Parse el/TctXa/xei/os, TrapiiTTr\trzVj and £0£to. 2. Translate : chap. ix. 10—16. Beginning, 'Hw &i tis |Uo6fiTiis iv Ao/ioo-Km ovoixan 'Avaviai, k.t.X. finding, otra SeZ avTov virip rov owo/AaTos fiov Traflfili'. " (1) Describe the situation of Damascus. (2) Givesome acoountof thelifeof Saulbeforehisfirstmissionaryjourney. (3) Give the derivation of p.a6iiTrit, i^oviyia, and ExXoyij. 3. Translate : chap. xiii. 46—50. Beginning, ILa^prjvLaadfjLEvoL 5s 6 HavXos Kal 6 'Bapvd^ai elirow, k.t.A.. Ending, Kal E^i^aXov aurous dird trnv opitou avrtat/, (1) Who was Barnabas? (2) Explain t&s iripoiiivas yvvaiKas, and give the derivation of Eiio-xii^oi/as. 4. Translate : chap. xvii. 1 — 9. Beginning, AioSiOaavTe^ Sk Trjv *A.fii'n-o\iv Kal 'A-TroWioviav, k.t.X, Ending, TLal ka^oi/Tes to iKavov irapi tou 'Id'iment tried is to be mentioned, the result of it and the conclusion dffavynfrom it, and finally the con- clusion drawn from the whole, 37. State the substance of De Senarmont's explanation of the difference of the angle between the optic axes in mica and also in topaz j and give an account of the experiments on which this explanation is founded. 38. Describe the volcanic products G, H. 39. In what way has Elodea canadensis (Anacharis Alsinastrum of NATURAL SCIKNCES TRIPOS. 131 Babington) becomeso abundantly diffused within the very fewyears it hasbeen observed in Britain: as we have only the female plant in this country? Are any of our native aquatics increased in the same manner ? 40. Compare the brain of a mammal with the chain of ganglia which represents it in fishes. 41. State the reactions of Nitric Acid with (1) Zinc, (2) Ammonia, (3) Hydrosulphuric acid, (4) Calomel. 42. Name the systems of the crystals represented by the models A, B, C... ; the hemihedral forms that occur ; the number of simple forms of which each is a combination ; and the number effaces in each simple form. 43. Distinguish the cases in which colour may be safely used as a character for discriminating minerals from those in which it fails. Point out the precautions which must be employed in fixing the meaning of the names of colours proposed by Werner. 44. Mention the strata of the secondary system in which mammalian remains have been found, and assign to each stratum the genera which have been found in it. 45. Name the species of the British fauna known to have become extinct, since the period of the Boulder-clay. 46. Name the mineral substances most abundantly distributed in sedi- mentary rocks. Which of them occur in nodular and concretionary states ? 47. Suppose the divergence of the fundamental spiral on a cone to be determinable from observations on 8 dextrorse and 5 sinistrorse secondary spirals, what will it be ? Explain how you arrive at the conclusion. 48. What Organs have been observed to assume the condition of Tendrils ? State an example of each kind. 49. Give instances (1) of animals of the same or closely allied species existing naturally under very diverse external circumstances, (2) of animals the distribution of which is limited to particular geographical areas. 50. Name the bone marked (a;). With what other bones is it articulated ; and what purpose does it serve ? Illustrate its use by examples of its presence, absence, and varieties in different species of mammals. 61. Are the movements of the Hydra and other polyps to be regarded as voluntary r Give reasons for your opinion. 52. Explain, and illustrate by other facts the following facts : (1) that a wall in sunshine is hotter than the neighbouring air, (2) that the heat of the sun may be easily concentrated by a burning glass, but not that of a common fire. 53. Explain how the equivalent of chlorine is determined. 54. Define a zone, and find the indices of a face common to two zones in terms of the indices of the zones. 55. Describe the processes by which DaubrSe formed crystals of quartz, felspar and spinelle. 56. Explain the principles of Lyell's classification of Tertiary strata, and point out the precautions requisite in applying them. 57. Under what circumstances are tiie coal measures supposed to have been deposited? 58. Give an account of the Fossil Flora of the Portland beds. 59. In which of the following Orders do albuminous and exalbuminous seeds occur ? Violacese, Alismaoese, Rosacese, Umbelliferae, RanunouiacefB, OleaceEe, Cupuliferae, and LeguminosEe, 60. Examine the skeleton placed on- the table. State the class and order of the animal, and what you know of its habits. Point out also its principaJ. relations to other orders and classes. k2 132 NATURAL aCIENCES TRIPOS. 61. Describe the type of the nervous system in Articulated animals. Describe and explain the movements which have been observed in a centi- pede when a portion of its nervous chord has been removed from the middle of its trunk. 62. Give a concise general account of the power of evolving heat pos- sessed by different classes of animals ; and shew by a comparison of different groups, and of the same animals under different circumstances, that the heat evolved is proportionate to the perfection and activity of the respiratory process. 63. Explain how to prepare pure nitrate of silver &om standard silver. 64. What is fractional distillation? Explain how one of a mixture of two volatile substances may be separated by this means, and give examples of the application of this method. 65. In the rhombohedral system find the angle 111, hJel in terms of the angle 111, 100 ; and shew that the faces in the zone 111 are perpendicular to the face 111. 66. Shew that pyrite, galena, and quartz have been found associated with , substances of such a nature as to preclude the supposition that they were in those cases crystallized at a very high temperature. 67. Point out the principal causes which affect the climate of a district, and how they affect it ; and how movements in the earth's crust cause the climate of any particular district to vary from time to time. 68. What indications at the surface would lead you to suspect a fault ? 69. Describe the specimens A, B, C, D, confining yourself to such of the following particulars as can be observed on them : !1) Leaves. Position : Insertion : Arrangement : Form : Stipulation. 2) Inflorescence. Character : Bracteation. (3) Flower. Each of the Ploral whorls, in respect of the numerical rela- tion of the organs, their insertion, and form. Placentation and inversion of the ovules, unless too inconspicuous for ready observation. (4) Natural Class and Order : stating reasons for determining the latter. (5) Geographic distribution of the Order. (6) Economic products of importance in the Order. 70. Discuss the question whether the Dog and Wolf should be regarded as of the same or different species. 71. Describe the Electrical Organs of the Torpedo, and the conditions for their action. What very remarkable peculiarity has been observed by Bilharz in the nerve which supplies the electrical organ of the SUurus ? 72. In what respects do capillary vessels differ from small arteries and veins ? Describe the process of their development in growing parts or in the repair of injuries. 73. Explain ftdly how you would proceed to make an analysis of Acetic acid ; and to determine a rational formula for the same. 74. Explain the preparation of ferrocyanide and ferricyanide of pot- assium. Shew the propriety of these names. When a given volume of cyanogen vapour is transmitted through a glass tube containing oxide of copper and ignited, what are the volumes and nature of the resulting gases ? 75. Measure the angle between the marked faces of the crystal cemented to the axle of the goniometer. 76. Enumerate the principal minerals which enter into the composition of meteorites. How does Joule accoimt for the high temperature they possess on reaching the surface of the earth? 77. Enumerate the varieties of metaiporphism observed in rocks. Shev NATURAL SCIENCES TBIPOS. 133 by reference to examples that metamorpliic rocks are of various ages, and (^plain why they are more abundant among the older rocks. 78. Name the metamorphic specimens X, Y, and state their chief British localities, and the rocks with which they are associated. 79. Describe the specimens E, F, O, H, confining yourself to such of the following particulars as can be observed in them. fl) Leaves. Position : Insertion : Arrangement : Form : Stipulation. (2) Infloresoence, Character : Eracteation. (3) Flowers. Each of the floral whorls, in respect of the numerical relation of the organs, their insertion, and form. Placentation and inversion of the ovules, unless too inconspicuous for ready observation. (4) Natural Class and Order : stating reasons for determining the latter. (5) Geographic distribution of the Order. (6) Economic products of importance in. the Order. 80. Describe generally the groups of animals which form connecting links between Molluscs and Zoophytes. 81. Indicate the chief bodily characteristics of man as compared with other animals, particularly with the apes which approach him most closely. 82. Describe the blood corpuscles of mammals (adult and embryonic), and compare them with the blood corpuscles in other classes of vertebrate animals. Has any relation been observed between the size of animals and that of their blood-corpuscles ? Examine under the microscope the specimens ot blood-corpuscles marked A, B, C, and determine the Classes of the animals to which they respec- tively belong. 83. What is the relation between the vapour volumes and equivalents of bodies ? Explain how the vapour density of a volatile liquid is determined. 84. Kefer to their chemical types Olefiant gas, Kakodyl, Ether, Fousel oil, Aldehyd, and give the chief analogies which lead to this reference. 85. Correct the following statements which recent observations have proved to be erroneous, that Graphite and Ripidolite (of von Kobell) are rhombohedral, that- DathoUte is prismatic, that Autunite (yellow XJranite) is pyramidal, that Boracic acid and Magnesia are the only essential constitu- ents of Boracite, and that Silica, Alumina, and Glucina are the only essen- tial constituents of Euclase. 86. What difference is there between the magnetic properties of different varieties of Fe^O-^ ? 87. State the mean density of the earth, and explain distinctly how it is determined. 88. Explain the grounds for the three great divisions of fossiliferous rocks. 89. Describe the specimens /, J, K, L, (Fruits and Seeds), noticing each integument, and other subordinate parts capable of being determined by inspecting the Fruit, Seed, and Embryo separately. 90. Refer the cryptogamic specimens a, 6, u . . to their orders. 91. Mention instances of Plants which exhibit sensible movements analogous to the movements in the higher animals. Define the limits within which the analogy holds, and point out where it fails. 92. Describe the processes of formation, detachment and renewal of Antlers. Describe also the other kinds of horns which grow on the heads of Mammals. 93. Describe the stomachs of a Ruminant Animal, and the mode of their action. 134 NATURAL SCIEHCES TEIPOS. 94. State the relation between blue and white Indigo, and describe some mode of preparing an indigo vat, and explain the chemistry of the process. 95. In what respects does chemical a£5nity differ from other physicsd forces ? Shew by examples that other forces interfere with chemical action. 96. Draw a figure of a combination of a cube and dodecahedron in the cubic system and the figure of a combination of the rhombohedrons 100, Oli, Ul. 97. The analysis of 100 parts of a mineral yielded Chlorine 2-41, Arsenic acid 18-47, Phosphoric acid 3-34, Oxide of lead 76'47, Lime 0'50. Construct a formula for the mineral ; the equivalents of Phosphorus, Arsenic, Chlorine, and Lead being in the ratios 31 ; 73 : 35-5 : 103-5. 98. State the generic names of the fossils A, B, C. .. ; and the forma- tions to which they belong. 99. ExplEiin the atmospheric actions in disintegrating and removing the surface of the earth. 100. How has the formation of Latlciferous Vessels been accounted for ? and what is the nature of the fluids contained in them ? 101. Explain the formation and destination of Cambium in the stems of woody Exogens. 102. Examine the skins of birds marked A, B, C,...., and refer them to their respective Orders eind Families. 103. Describe the process of formation of the Shells of Molluscs. Explain the terms right-handed and left-handed as applied to univalve shells. 104. The power of reproducing parts that have been lost or destroyed varies much in difierent classes of organised beings, and at different stages of the existence of the same being. Cite facts in evidence, and generalise them. 105. What is the mode of preparing ^un-co^ton ? and what the nature of that compound i 106. State and explain how common phosphate of soda is prepared from bone-earth. 107. Give the chemical formula expressing the constitution of rock-salt. In what directions does it cleave? What are its properties as regards the transmission of radiant heat } Describe an experiment illustrative of these properties. Enumerate the substances that can be considered isomorphous with it. 108. Mention the crystals in which it has been shevra that a change of temperature alters the angle between certain faces, and give an account of the observations by which this change of angle is established. 109. Explain the mode of aggregation of the ingredients in mineral veins, and state the theories which have been proposed to account for it ; and give an account of any experiments which appear to support them. 110. Describe the phenomena which accompany earthquakes, and give a brief account of the chief theories to account for them. 111. Mention the requisites essential to the germination of seeds ; and describe the chemical changes that take place during their germination. 112. Contrast woody-fibre with cotton- wool. 113. Examine the Skull marked A. To what animal, or order of animals does it belong ? 114. Give a general account of the aquiferous or water- vascular system existing in some of the lower animals, and a more particular description of its type in some one limited group. 116. Are Nutrition and Secretion in animals essentially dependent on nervous agency ? Give reasons for your opinion. PBEVIOUS EXAMINATION. 135 116. Explain the method of means in Induction ; and illustrate by its application to some one of the laws of Natural Science. 117. Define an element in Chemistry and when two bodies may be deemed identical in substance. Point out the axioms or assumptions involved in your definition. 118. Give an historical sketch of the theories of combustion. 119. State Sir John Herschei's views on the subject of selecting names for minerals ; and those of Dr. Whewell on the terminology of Mohs, and the language in which the forms of crystals can best be described. 120. What was the method of investigation in Geology insisted on by William Smith? Trace the efiects of his views on the progress of Geology ii'om his time. 121. Give sketches of the Botanical Systems of Ray zmd De Candolle. 122. Give general outlines of the Classification of animals by Aristotle, Linnseus, and Cuvier in his latter works. 123. Explain the terms Conditions of Existence (Cuvier) and Subordination of Characters. Illustrate with examples. 124. Every component part of a complex organised body has an individual life and limited duration of its own, in a great degree irrespective of the condition of the entire body. Illustrate this general fact with particular examples, and give examples of the influence of external agencies upon the length of life of the constituent parts. EXAJ^mSTED AND APPEOVED. FIRST CLASS. Bradford Cath. SECOSD CLASS. THISD GLASS. I Barnard Emman. | Townseud Trin. PEEVIOUS EXAMINATION, Lent Teem, X861. EXAMINERS : John Eigo, b.d. St. John's College. Thomas Hughes Eable, m.a. King's College. James Portee, m.a. St. Peter's College, Abihub Aybes Ellis, m a. Trinity College. Abthub Beard, m.a. St John's College, John Mabtineau Fletcheb, u.a. Caius College, John Robebt Seeley, m.a. Christ's College. Adcock Humph. Alston Ainslie Pemb. Alvis Alder Trin. H. Anderson Alderson Joh. Andrews Aldis Trin. Arden, A. H. Alexander,A.B.Clirist's Ash Alexander Trin. Asplaiid, J. L Allison Sidney Asplaud, R. Allison Trin. Austen CANDIDATES. Clare Christ's Trin. Joh. Christ's Joh. Sidney Sidney Joh. Austen-Leigh Austin Babington Bacon, J. G. Bacon, W. Baker, R. Barker Barnes Baron King's Sidney Clare Clare Clare Corpus Corpus Joh. Joh. 136 PHEVIOUS EXAMINATIOJT. Eathuist Trin. Clarke Christ's Bayne Trin. Clarke Caius Beadon Joh. Clarke Pemb. Beedham Clare Cliff Joh. Bell Caius Clowes Trin. Bertlin Trin. H. Collins Christ's Beaant Emm. Connor Cath. Bettison Corpus Cooke, C.E.B .Trin. Bigwood Joh. Cooke, J. M. Trin. Birch Caius Cookson Jesus Birtwell Queens' Cope Trin. Blaauw Trin. H. Cornford Trin. Blumberg Trin. H. Cotterill Joh. Body Joh. Crampton Trin. Bolton Trin. Crewdson Trin. Bourke Trin. Crosthwaite Caius Bowes- Watson Trin. Cruwys Emm. Boyd Christ's Currey Trin. Boy ton Magd. Curtis Joh. Bradney Trin. Dalrymple Trin. Brady Trin. Dalton Clare Branson Caius Darby Trin. Broad Caius Davies Joh. . Bros Joh. Davies, J. H, Trin. Brown Trin. Davies Cath. Brown, E. A. Caius Deane Trin. Brown Joh. De Montmorency Trin. Brown Trin.H. Dent Trin. Brown,J.W.I] . Caius De Putron Caius Browne Trin. Dewe Cath. Browne Caius De "Wend Joh. Brownjohn Clare Deverell Trin. Buchanan Trin. Dickinson Joh. Buokell Joh. Dickinson Trin. Bulwer Pemb. Dixon Christ's Burnett Queens' Dixon Caius Burrows Cath. Douet Corpus Buxton Trin. Dunlop Trin. Cadman Christ's Dunn Corpus Campion Caius Dyne King's Carey Joh. East Trin. Carpenter Corpus Edwards, J. Trin. Carrington Joh. Edwards, T. Trin. Carroll Trin. Edwards Pet. Carter Christ's Edwards,N.W . Trin. Carter Trin. Elderton Corpus Caitwright Joh. EUames Trin. Casson Christ's Evans Trin. Chalk Pet. Everett Trin. Chancellor Clare Evett Pemb. Charles Christ's Fairclough Christ's Child Enun. ^ Falkner Joh. Churchill Trin. Featherstonhaueh Trin. Clark Caius Fellows Magd. Fison Caius Fontaine Joh. Forbes Trin. Foster Pet. Foye Jesus Francillon Trin. H. Frere Trin. Gael Trin. Gardner Trin. H. Garfit Trin. Garrett, T. (sen.) Caius Garrett T. (jun.) Caius Gaskell, C. M. Trin. Gaskell, T. K. Trin. Geach Trin. Gibbs Trin. H. Glennie Trin. Goodacre Pemb. Goold Trin. Graham Jesus Graves Trin. Green Caius Green Trin. Greene Christ's Grimley Trin. Guest, A. E. Trin. Guest, A. F. Trin. Guinness, F. Joh, Guinness, K. Joh, Gurdon Trin. Gurnhill Emm. Haigh Christ's Hale Sidney Hambro Trin. Hamilton, C. Trin. Hamilton, J. Trin. Hamilton Pet. Hampton Queens' Hanbury Clare Hankey Trin. Hanson Trin. Hardcastle Trin. Hargrove Emm. Harris Emm. Hawkins Trin. Hawthorn Trin. Heathcote Trin. Hensley Trin. Hewitt Corpus Hickman Joh. Hilleary Joh. Hoare Trin. Hnckin Joh. Hodgets Emm. PREVIOUS EXAMINATION. 137 Hodgson Corpus Lock Trin. Pixell lloUis Trin. Long Trin. Plowden HoUond Trin. Lorimer .Toh. Plumtre Honeysett Joh. Ijowther Trin. Pooley Hope- Grant Trin. Luckock Corpus Prance Hopkins Sidney Lumley Trin. Pratt Hopkinson Clare Lush Trin. Pretor Horsfall Christ's Lyon Trin. Price Houldsworth Trin. Mackenzie Trin. Pritchard Hughes Jesus Madan Trin. Procter Hulbert Caius Maddy Joh. Purton Hulbert Cath. Marsh Trin. Quarringtou Hunt Caius. Marshall Trin. H. Ranken Huxtable Christ's Martin Trin. Ransford Isaacson Clare Marton Trin. RatcUffe Jeffery Trin. H. Mason Cath. Rees Jenner Trin. H. Mason Pemb. Reynolds Jenkins Jesus Maurice Caius Richards Johnson Trin. Mayo Trin. Ridsdale Johnson Joh. McGiU Christ's Roberts Jones Trin. McNeile Trin. Roberts Jones, W. T. Queens' McVicar Trin. Rogers Jones Joh. McWilliam Caius Rolph Jones Queens' Mellor Trin. H. Romer Kamey Trin. Metcalfe Joh. Roose Kennedy I'rin. H. Miller Pemb. Rose Kent Trin. Mirehouse Clare Rose Kiuleside Emm. Mitton Cath. Rothschild Kinsey Emm. Monokton Trin. Rounthwaithe Knight Caius Monk Jesus Roworth Lang Trin, Moore Pet. Rudd Lane Joh. Moorsom Trin. Rust Larbalestier Joh. Murray Trin. Rycroft Latham Trin. Myers Queens' Sale Laundon Caius Neil Trin. H. Salter Laurie Caius Neville Clare Salusbury Lawson Trin. NiehoUs Joh. Sanderson Leatham Trin. Nixon King's Sankey Leather Joh. Nottidge Emm. Savory Leavens Queens' Oakley Trin. Soholfield Ledger Corpus Ormrod Emm. Scvilthorpe Lee Caius Outram Christ's Sedgwick Lee Trin. Page Christ's Sevier Lee Joh. Pardoe, J. Trin. Shaw Lee Magd. Pardee, W. Trin. Shepherd Leeke Trin. Parsons Clare Shickle Leeson Down. Partington Trin. Sidgwick Legge Pet. Patch Clare SiUitoe Le Sueur Pemb. Peareth Cath. Simpson Lewis Corpus Peel Christ's Simpson Lewis Emm. Pennington Pet. Simpson Lewthwaite Trin. Pierce Corpus Skinner Lloyd Trin. Piffard Jesus Slater Lobley Trin. Pinches Joh. Smith Trin. Trin. Sid; Joh. Trin. Trin. Trin. Joh. Joh. Christ's Trin. Cath. Caius Clare Trin. Joh. Caius Sid. Caius Queens' Trin. Caius Trin. H. Trin. H. Jesus Emm. Queens' Trin. Joh. Emm. Joh. Pemb. Trin. H. Emm, Clare Emm. Corpus Trin. Trin. Trin. Pet. Caius Trin. Trin. Trin. Humph. Trin. Pemb. Pet. Trin. Pemb. Clare Queens' Trin. 138 PREVIOUS EXAMINATION. Smith Corpvs Tate Queens' Walker Trin. Smith Caius Tatham Trin. Wallis, J. H. Joh. Smith, E. A Christ's TatershaU Queens' Wallis.W.M Joh. Smith- Marriott Trin. Taylor Cath. Ward Joh. Smyly Trin. Taylor Trin. Ward Trin. Snowdou Joh. Taylor Queens' Ward Queens' Spencer Jesus Tebbs Trin. H. Warner Trin. H. Spencer £mm. Teevan Trin. H. Washington Trin. Spurlinp Trin. Thomas Trin. Wason Caius Stable Pet. Thompson Joh. Wayne Trin. Stanning Trin. Thompson Trin. Webb Caius Steele Joh. Thompson Cains Webster Emm. Stenning Trin. Thomley Trin. H. Wells Emm. Stephen Christ's Thornton Trin. Went Christ's Stephenson Joh. Thynne Trin. Wheatoroft Caius Sterling Trin. Tomlinson Clare Wheeler Trin. H Stevens Joh. Towers Pemb. White Sid. Stevens Magd. Townend Trin. Whitehead Joh. Steward Trin. Treffrey Magd. Wilkins Joh. Straton Trin. Tuck Emm. Wilks Trin. Strutt, Hon. H.Trin. Turner Caius Willan Joh. Sturge Trin. Turner Sid. Williams Emm. StuTges Trin. Tweddle Clare Wilson King's Swann Caius TJsborne Trin. Withers Corpus Swann Trin. Vaizey Trin. Wood Trin. Swinhoe Christ's Valentine Joh. Wright Trin. Talbot Trin. H. Waddell Trin. Wyon Corpus Tancock Sid. Walford Trin. Yearsley Trin. Tarletou Joh. Wallace Trin. Young Caius Tarratt Trin. Walker Trin. H. EVIDENCES OF CHEISTIAISIITY. 1. State the proposition to which Paley confines himself in the former part of his work, and describe briefly the process by which he establishes it. 2. The case of miracles is called a contest of opposite improbabilities. How is it so ? In stating this, what considerations does Mr. Hume omit, and what evade ? 3. What position did Religion occupy among the nations of Greece and Rome ? Shew that this must have been imfavourable to the spread of Christianity. 4. Quote passages from the Gospels which represent Our Lord Jesus Christ to have foretold the persecutions of his followers. How does Paley employ these passages to prove the reality of these sufferings ? 6. What features of the narrative of the Acts of the Apostles are con- firmed by the letters left behind by the Apostles ? 6. What considerations make it highly probable that the story for which the early preachers of Christianity hazarded their lives was a miraculous one 1 7. What four considerations are employed to shew that the story con- tained in the Scriptures of the New Testament is the story promulgated by the Apostles ? 8. State the second Proposition established by the Author. On what groimd does he lay out of the case the supernatural powers attributed to Pythagoras and Apollonius Tyaneus ? 9. Shew that the general credibility of the Evangelical miracles is not PEEVIOtJS EXAMINATION. 139 destroyed by the fact that some may be liable to the objections which the Author urges against heathen or post-Apostolic miracles. 10. Give instances of the candour of the Evangelists. 11. Shew the value of the history of the Resurrection. 12. Does Paley establish the necessity of being a Christian ? EYIDENCES OF OHEISTIAOTTT. 1 . What opinion with regard to the Deity does Paley assume to be held by those with whom he is arguing? Accepting the truth of such opinion, estimate the probability of a miraculous Revelation. 2. What does Paley mean by arguing from the nature of the case ? De- feud on this ground the sincerity of the first propagators of Christianity. 3. Sum up concisely the argument from the nature of the case by which Paley supports the truth of his first proposition. 4. Quote passages from the letters attributed to the early followers of Jesus Christ, which prove them to have been written by men labouring under persecution and sufiering. Shew how unreasonable it is to imagine them to be forgeries. 5. Name the immediate followers of the Apostles from whose writings Paley extracts quotations. Give the substance of their testimony. 6. Sum up the historical evidence which compels us to believe that the early teachers of Christianity exerted great industry, and underwent great suffering. 7. How does Paley estimate the historical value (1) of the Pirst and Fourth (2) of the Second and Third Gospels ? 8. What does Paley mean by setting aside, in the proof of his second Proposition events depending on naked history ? Shew that the Christian miracles do not come under this head. 9. Give examples from the Gospels of the benignity, the devoutness, and the lenity of our Saviour's character. 10. Mention any acts or remarks of Our Lord which exhibit strong in- ternal evidence of reality and truthfulness. 11. What distinctions does Paley draw between the spread of Mahomet- anism and that of Christianity ? 12. What portion of the Evidences do you consider to approach nearest to a demonstration, and what to fall farthest short of it ? EVIDENCES OP OHEISTIANITY. 1 ■ Shew clearly upon what grounds we may say that a miraculous his- tory ought not to be rejected at first sight. 2. Give concisely Mr. Hume's objection to the reality of miracles. What does Paley consider its strongest point ? Where in the book is that point discussed ? 3. Quote the passage from Tacitus which bears direct testimony to the cruelties undergone by the early Christians at the hands of the Roman Government under Nero. What recent objection has been made to the value of this testimony ? 4. Sketch briefly the account given by the writer of the book called " The Acts of the Apostles," of the progress of the Christian religion from the death of the Founder, down to the stoning of Stephen. 6. What heathen writer does Paley quote in evidence that the early pro- pagators of Christianity submitted to new rules of conduct? Give his words as nearly as you can. 140 PBEVIOUS EXAMINATION. 6. What circmnstances of the life of oiir Lord are disclosed by the writ- ings of the Apostles ? What point of our argument do these allusions confirm ? 7. For what object does Paley in the process of his argument employ the testimony of the Gospels ? Shew how valuable they are for this purpose. 8. In appreciating the credit of a miraculous history what distinctions may be admitted besides those which relate to the evidence ? 9. Shew how our Saviour laid stress on the regulation of the thoughts. What inference may be drawn from this i 10. What does Paley mean by the Identity of Christ's character, and to what points of identity does he call our attention ? 11. Shew that the story of the Resurrection cannot be accounted for on the supposition of fraud or enthusiasm in those who first affirmed its truth. 12. Meet those objections to the reality of miracles which are drawn from the regularity of the Laws of Nature. EVIDENCES OE CHEISTL/miTT. 1. Can general experience be urged as an objection to the reality of miracles ? 2. Setting aside historical evidence, what reception may we reasonably suppose the propagators of Christianity met with at the hands of the Jews ? 3. What inference does Paley draw from the statements quoted by him from the writings of Tacitus, Suetonius, &c., bearing upon the persecutions of the Christians under Nero ? i. What remarks does Paley make upon the character of the narrative contained in the Acts of the Apostles ? 6. What four observations does Paley make upon the history of the foun- dation of Christianity, as we read it in the writings of its earliest adherents ? 6. Shew that it appears by the Gospels themselves that the story they relate was public at the time they were written. 7. Under what circumstances does Paley suppose the books of the New Testament Scriptures to have been composed ? 8. What Christian miracles does Paley mention as being impossible to resolve into a false perception ? 9. What does Paley mean by the negative character of our Lord's dis- courses, and what instances of it does he give ? 10. Give a summary of the Chapter upon the originality of our Saviour's character. 11. Shew that a believer need not be discouraged by the absence of some effects of the Christian Religion which a sanguine temperament might from its character have been led to anticipate. 12. What is meant by the Rationalistic and Mythical modes of explain- ing away the miracles of our Lord and his Aposties ? How do you account for Paley's not noticing them in detail ? AEITHMETIC. 1. Add 375 to 493 and explain the process. 2. Employ short division in dividing 663072 by 5760. Write down the remainder and compare the process by which 663072 grs. may be reduced to lbs., oz., and dwts. Troy. 3. Add f, 1}, f and divide the sum by i + i^ (J - }). 4. What fraction of 2 owt. 14 lbs. is J of 2 qrs. 14 lbs. ? Find the rent of 226 ac. 1 r. 19 p. at 13a. 2irf. per rood. 5. Reduce £2. 17s. 4Jrf. to the decimal of £7. Also add -275 of a bushel to 725 of a quarter, and find the value at 6s. Sd. per bushel. PREVIOUS EXAMINATION. 141 6. Extractthesquarerootof 17424 and of 175-260564. The length of a rectangle is three times its breadth and its area is 5804 yds. ; what is the length in feet? 7. If 12 Carlinibe worth is. Id. and a Napoleon be worth 16s.; how many Carlini ought to be received for 15 Napoleons ? 8. If 5 men with 7 women earn £7. 13s. in 6 days, and 2 men with 3 women earn three guineas in the same time ; in what time will 6 men with 12 women earn £60 ? 9. What is meant by interest and discount ? Find the interest on £474. 13i. id. at 4 per cent, per annum, for 3J years, simple interest. 10. A tradesman who is ready to allow 5 per cent, per annum, compound interest, for ready money, is asked to give credit for two years. If he charge £27. Us. 3d. in his bill, what ought the ready money price to have been ? 11. A person invests £2000. 16s. Id. in the 3 per cents, at 90|. What is the income derived by his investment i A person invests in the 3 per cents, so as to obtain 3 per cent, clear on his investment when there is an income-tax of 7d. in the pound. What per oentage clear does he obtain if the tax be doubled ? 12. If the price of barley be 6s. Id. per bushel and the cost of malting a quarter of barley be 2s. 2d. how much malt is made from 621 quarters of barley, supposing the malster to pay 24s. 2d. tax per quarter of malt and gain 5 per cent, on the whole of his outlay by selling malt at 77s. IJd. per quarter ? AEITHMETIC. 1. Feom 1861 take 1423 and explain the process. 2. Employ short division in dividing 195477 by 7920. Write down the remainder and compare the process by which 195477 inches may be reduced to furlongs, yards, feet, and inches. 3. Add i, 2J, i and /i and divide the sum by J -I- J (J — J). 4. What fraction of 2 sq. yds. 7 ft. is j of 2 sq, yds. 6 ft. ? Find the value of 72 cwt. 3 qrs. 17 lbs. at £1. 4s. 6d. per cwt. ? 5. Reduce £3. las. O^d. to the decimal of £9. Also add 1'275 of a yard to 3'75 of a foot and find the value at 3s. 4d, per foot. 6. Extract the square root of 21025 and of 210-358669. The length of a room is twice its breadth and the area is 1152 feet, what is its length ? 7. If 10 scudi be worth 52-5 francs and 16 shillings are worth 20 francs ; how much in English money will be equivalent to 46 scudi ? 8. If 3 men with 4 boys earn £5. 16s. in 8 days, and 2 men with 3 boys earn £4 in the same time ; in what time will 6 men and 7 boys earn 20 guineas ? 9. State the meaning of Interest and Discovmt. Find the sum which will produce £146, Us. l^d. interest in 4^ years at 3 per cent, per annum, simple interest. 10. A tradesman who is ready to allow 4 per cent, per annum, compound interest, for ready money, is asked to give credit for two years. If he charge £22. 10». 8d. in his bUl ; what ought the ready money price to have been ? 11. A person invests £1839. 18s. 3d. in the 3 per cents, at 91 J, What is his income derived from the investment ? A persoii invests in the 3 per cents, so as to receive 3 per cent, clear on lis investment when there is an income-tax of 9d. in the pound. What per centage does he receive if the tax be increased to Is. in the pound } 12. If the price of barley be 6s. per bushel and the cost of malting a 142 PIIEVIOUS EXAMINATION. quarter of barley be 2s. lOrf.: how much malt is made from 621 quarters of barley, provided the malster pays 25s. tax per quarter of malt and obtain S per cent, on the whole of his outlay by selling malt at 78s. per quarter ? AEITHMETIO. 1. What number subtracted from three hundred and sixty-five millions twenty-seven thousand and forty-five will leave seventy-three thousand one hundred and five ? 2. Define a vulgar fraction, and shew that a fraction is not altered in value if the numerator and denominator be multiplied by the same quantity. Arrange in order of magnitude the fractions ^, J^f and H^, and express the difference of the first two as a fraction of the difference of the last two. 3. State the rules for the conversion of a terminating and a circulating decimal into their equivalent vulgar fractions. Express as vulgar fractions in their simplest forms •0375, •328 and -238 - -328. 4. Find the value of f of f, of £1 14s, -I- f of ^125 of £1 10s. + 8i of •U9 of 5s., and express the result as a decimal fraction of £20. 5. A grocer buys a chest of tea containing 432 lbs. at 3s. 9f d. per lb. He sells 360 lbs. at 4s. id. per lb., and the remainder, which is injured, at half the cost price per lb. Find his total gain. 6. Explain the statement of a question by the " Double Rule of Three." If the penny loaf weigh 6 oz. when wheat is 5s. per bushel, what should be the weight of the shilling loaf when wheat is 7s. 6d. per bushel ? 7. A pond whose area is 4 acres, is frozen over with ice to the uniform thickness of 6 inches ; if a cubic foot of ice weigh 896 oz. avoirdupois, find the weight of ice on the pond in tons. 8. The wages of 12 men, 24 women, and 30 children amount in 6 days to £25 13s. If the wages of a man, a woman, and a child be in the ratio 3 : 2 : 1, find the wages of each per day. 9. Find the interest of £2962 10s. from the 30th Dec. 1860, to the I3th March, 1861, at 4 per cent, per annum. 10. What is discount ? and what is the present worth of a bill ? Find the present worth of a bill of £2750 due 5 months hence and dis- counted at 7^ per cent, per annum. 11. If 9 per cent, be lost by selling a horse for £78 15s., what will be gained or lost per cent, if he be sold for £90. 12. In the University boat race of 1860, the Cambridge crew rowed 39 strokes per minute, and the Oxford crew 41 ; but 19 strokes of the former were equal to 20 of the latter. The Cambridge crew rowed over the course in 25 minutes and the length of the course was 4 miles. Find the number of feet and the number of seconds by which the race was won. 13. What sum must a man invest in the 3 per cents, at 91 J, in order to have a clear income of £230, afterpayinganincome-taxof lOd. in the pound? AHITHMETIC. 1 . What number must be added to sixty-nine thousand, four hundred and twenty-seven, to produce three hundred and twenty-five millions, seven thousand and twenty-one ? 2. Define a vulgar fraction, and prove that a fraction is not altered in value if the numerator and denominator be multiplied by the same quantity. Arrange in order of magnitude the fractions „%, i^Ai fVt. and express the difference of the fii-st two as a fraction of the difference of the last two. PREVIOUS EXAMfiflATION. 143 3. State and prove the rule for the multiplication of decimal fractions. Multiply -01385 by 61-37 and divide the result by 2'77. 4. Find the value of ? of -^, of £1 18s. + loi -375 of 15s. + | of -429 of 8s. Sd. 4 9i 3 5 , and express the result as a decimal fraction of £5. 6. The Examination for Mathematical Honours commences each year at 9 o'clock on the 1st Tuesday in January. In 1861, the Examination commenced on January 1st. Pind the number of seconds which -will have elapsed from the commencement of the Exami- nation in 1861 till its commencement in 1862. 6. A man purchases a bale of cloth containing 80 yards at £1 12s. per yard. He sells half of it at an advance of 25 per cent. ; two-fifths of it at an advance of 4s. per yard, and the remainder which is injured at half the cost price ;' find his total gain, and his gain per cent. 7. Explain the mode of stating a question in the "Double Rule of Three." If the penny-loaf weigh 6oz. when wheat is at 6s. per bushel, what should be the price of a loaf weighing 4| lbs. when wheat is at 7si 6d, per bushel ? 8. A cubic foot of gold is extended by hammering, so as to cover an area of 6 acres. Find the thickness of the gold in decimals of an inch, correct to the first two significant figures. 9. Find the interest of £808 6s. Sd. from the 1st January 1861 to May 27th 1861, at 4| per cent, per annum. 10. What is discount ? and what is the present worth of a bill ? Find the discount on a bill of £461 15s. 10|rf. due three months hence, and discounted at 7J per cent, per annum. 11. If 6 per cent, be gained by selling a horse for £79 10s. ; how much is lost per cent, by selling him for £69 ? 12. In the University boat-race of 1860, the Cambridge crew rowed 39 strokes per minute, and the Oxford crew 41 ; but 19 strokes of the former were equal to 20 of the latter. The Cambridge crew rowed over the course in 25 minutes, and the length of the course was 4 mUes. Find the number of feet and the number of seconds by which the race was won. 13. A man invests £8063 in the 3 per cents, at 91f, the brokerage being i per cent. ; what wUl be his clear income, after an income-tax of lOd. in the pound is deducted ? EUCLID, I. n. m. 1. Define a plane rectilineal angle, and a circle i and enunciate the postulates. 2. The angles at the base of an isosceles triangle are equal to each other ; and if the equal sides be produced, the angles on the other side of the base shall be equal. ' 3. Bisect a given finite straight line, that is, divide it into two equal parts. 4. Make a triangle of which the sides shaU be equal to three given straight lines, but any two whatever of these must be greater than the third. 5. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles | and the three interior angles of every triangle are together equal to two right angles. 6. Triangles upon the same base, and between the same parallels, are equal to one another. 144 PRE' \L\jLia rd.&j\jsiLaAii\jat 7. If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two aides of it ; the angle contained by these two sides is a right' angle. 8. If a straight line be divided into any two parts, the rectangle con- tained by the whole and one of the parts, is equal to the rectangle contained by the two parts, togefher with the square of the aforesaid part. 9. Describe a square that shall be equal to a given rectilineal figure. 10. Define a sector of a circle, and similar segments of circles. 11. Find the center of a given circle. 12. If two circles cut one another, they shall not have the same center. 13. The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 14. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle con- tained by the segments of the other. EUCLID, I. n. ni. 1. Defiite a right angle, and parallel straight lines; and distinguish between a postulate and axiom. 2. If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to each other ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz. those to which the equal sides are opposite. 3. Bisect a given rectilineal angle, that is, divide it into two equal angles. 4. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. 5. Any two sides of a triangle are together greater than the third side. 6. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 7. In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. 8. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. 9. Divide a given strsiight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. 10. Define a segment of a circle, and the angle in a segment. 11. If a straight line drawn through the center of a circle bisect a straight line in it which does not pass through the center, it shall cut it at right angles : and conversely, if it cuts it at right angles, it shaU bisect it. 12. If one circle touch another internally, they shall not have the same center. 13. The angles in the same segment of a circle are equal to one another. 14. If &om any point vrithout a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it. EUCLID, I. II. in. 1. Depine a plane angle, a sector of a circle, and a polygon. When are magnitudes assumed to be equal ? PREVIOUS EXAMINATION. 145 2. If two angles of a triangle be equal to one another, the sides also ■which subtend, or are opposite to, the equal angles, shall be equal to one another. 3. Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. 4. If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. 5. All the exterior angles of any rectilineal figure are together equal to four right angles. 6. The opposite sides and angles of parallelograms are equal to one another, and the diameter bisects them, that is, divides them into two equal parts. 7. If the square described upon one of the sides of a triangle be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle. 8. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts together with the square of the aforesaid part. 9. Divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. 10. If two circles touch each other externally, the straight line which joins their centers shall pass through the point of contact. 11. Draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. 12. The opposite angles of any quadrilateral figure described in a circle, are together equal to two right angles. 13. Cut off a segment from a given circle, which shaU contain an angle equal to a given rectilineal angle, EUCLID, I. II. m. 1. What is an axiom ? Define an acute-angled triangle, a gnom.ou, and similar segments of circles. 2. Shew how to draw from a given point a straight line equal to a given straight line. 3. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be cqusd to the angle contained by the two sides equal to them, of the other. 4. The greater side of every triangle is opposite to the greater angle. 5. If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other. 6. Parallelograms upon the same base, and between the same parallels, are equal to one another. 7. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 8. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 9. In every triangle, the square of the side subtending any of the acute 146 PREVIOUS EXAMINATION, angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line inter- cepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Prove this when the perpendicular falls without the triangle. 10. If in a circle two straight lines cut one another which do not both pass through the center, they do not bisect each other. 1 1 . The angles in the same segment of a circle are equal to one another. 12. In equal circles, equal circumferences aie subtended by equal straight lines. 13. If a stTEught line touches a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle. mechaot:cs. 1. What is meant by Weight, and the moment of a force about a point ? Forces can be properly represented by straight lines. 2. Define a Lever. If two weights acting perpendicularly on a straight lever on opposite sides of the fulcrum balance each other, they are inversely as their distances from the fulcrum ; and the pressure on the fulcrum is equal to their sum. Two weights, 12 lbs. and 8 lbs. respectively at the ends of a horizontal lever 10 feet long balance. How far ought the fulcrum to be moved for the weights to balance when each is increased by 2 lbs. ? 3. If two weights balance each other on a straight lever when it is horizontal, they will balance each other in every position of the lever. 4. Enunciate the parallelogram of forces, and, assuming the direction of the resultant, shew that the statement is true of the magnitude. Two strings each making an angle of 30° with the vertical line support a weight. Compare the weight and tensions of the strings. 5. Graduate the Common Steel Yard. What effect is produced on the graduation by increasing the specific gravity of the material of the yard ? 6. In a system in which the same string passes round any number of pullies, and the parts of it between the puUies are parallel, there is an equilibrium when power (P) : weight {W) : : 1 : the number of strings at the lower block. Prove that P : W = Ws displacement : P's displacement. 7. Describe the Wheel and Axle and compare P and W. 8. What is an inclined plane ? A weight of 12 lbs. rests on an inclined plane when a force of 6 lbs. parallel the plane acts on it. Find the pressure on the plane. 9. Define the center of gravity of a body. If a body balance in any position about a fixed straight line in it, the center of gravity is in that line, 10. When a body is suspended from a point, it will rest with its center of gravity in the vertical line passing through the point of suspension. A wire is bent into the form of a triangle and hangs from one angle with the base horizontal : shew that the triangle is isosceles. 11. A sphere rests between two inclined planes and the pressure on one which is given in position is double that on the other. Construct the position of the other plane and shew that the inclination of the given plane is less than the third of a right angle. PREVIOUS EXAMINATION. 147 MECHANICS. 1. Dehne Force. State how it is measured, and shew that forces can be properly represented by straight lines. 2. De6iie a Cylinder. If two weights acting perpendicularly on a straight lever on opposite sides of the fulcrum balance each other, they are inversely as their distances from the fulcrum ; and the pressure on the fulcrum is equal to their sum. The length of a horizontal lever is 12 feet and the balancing weights at the end are 3 lbs. and 6 lbs. respectively. How far ought the fulcrum to be moved for equilibrium if each weight be placed 2 feet from the ends of the lever ? 3. If two forces acting at any angles on the arms of any lever balance each other, they are inversely as the perpendiculars drawn from the fulcrum to the directions in which the forces act. 4. State the parallelogram of forces. Three forces represented in magnitude and direction by the sides of a triangle can keep a point at rest. Two strings at right angles to each other support a weight and one string malies an angle of 30° with the vertical line. Compare the tensions of the strings. 6. Graduate the Common Steel Yard. What effect is produced on the graduation by increasing the moveable weight ? 6. In a system in which each pulley hangs by a separate string, and the strings are parallel, there is an equilibrium when P : W : : 1 : that power of 2 whose index is the number of moveable pullies. If there be three pullies of equal weight (to) and P is equal to W, find W. 7. Describe the wheel and axle, and, assuming the relation of P and W, shew that P:W=: W's displacement : P's displacement. 8. Compare P and W on an inclined plane when P acts parallel to the plane. Determine the pressure on the plane. 9. Define the center of gravity of a system of bodies. Find the center of gravity of a triangle. A triangle suspended from an angle has its base horizontal ; shew that the triangle is isosceles. 10. When a body is placed on a horizontal plane, it will stand or fall, according as the vertical line, drawn from its center of gravity, falls within or without its base. 11. A sphere rests between two inclined planes and the pressure on one which is given in position is half that on the oliier plane. Construct the position of the other plane. ALGEBEA. 1. Phove that ffl — (J — c)=o — 6 + ciu the case when b> c and a > bo. Simplify the expression : •2ffi - (35 + 2c) - [SS + 6 (6 - c) + 5c - {2a - (c + 26)}]. 2. Define a"*, when m is a positive integer, and prove that a;" x a:" =3;""" K being also a positive integer. 3. Multiply o' + iahx + 46V by a» - iabx + 46=a;» ; and divide 6 (x3 + a?) + ax («» - o") + a? {x + a) by (a + 6) (x + a). 148 PREVIOUS EXAMINATION. i. Simplify the expiessions : 5 3(a:-l) and 1 3 ' 2x~ a 2x + 3 6(x + 2) a b h-a x(x b' -l)(«+2)' 6 + a b' b" a' 5. Add together the fiist and fourth, and also the second and third of the quantitieB 1 1 1 1 X + 3a' *4-o' X- a' x-3a' and subtract the latter sum from the former. Por what positive values of x vrill the result be positive ? 6. When are four quantities said to be proportional ? 'Will the quanti- ties 7, 22, 8, 25 satisfy your definition ? Determine x in order that 4 + a : 2a! + 8 : : 2a; - 1 : 3a; + 2. 7. Ha: b :: id, prove that a + b : a ~ b :: c + d : c — d, and that a Vinuf + ru?) 8. Solve the equations : X-\ 1 fx-6 14- 'IX\ x~y 7 "2 8' (1) 1-1 1 r x-5 14 - 2a: \ "^ "si 4 ~ 5 ]' ,„, 2a: - 1 2a; - 3 1 „ (3) x'-xy + y'^lSA (4) x>yz=^a/ a; - y = 1. J a;y'« = 6, ieyz' = c. 9. In the Astronomical clock, where the hours are marked upon the dial from 1 up to 24 ; find the time between 8 and 9 o'clock when the hands are together. lOi What is the price of eggs per dozen, when two less in a shilling's worth raises the price one penny per dozen ? 11. An officer can form the men in his battalion into a solid square, and also into a hollow square 12 deep. If the front in the latter formation ex- ceed the front in the former formation by 3, find the number of men in the battalion. 12, Two trains start at the same time from two towns, and each proceeds at a uniform rate towards the other town. When they meet, it is found that one train has run 108 miles more than the other, and that if they continue to run at the same rate, they will finish the journey in 9 and 16 hours re- spectively. Find the distance between the towns, and the rates of the trains. ALGEBRA. 1. Pkovb that a — (b + c)=a — b—cin. the case when a>b + c. Simplify the expression 5a - 7 <6 - c) - [6o - (3J + 2c) + 4c - {2o - (i + 2c - a)}]. PREVIOUS EXAMINATION. 149 2. Define x" when m is a positiye integer and prove that {«"')" = «°"', » being also a positive integer. 3. Multiply a' - 2ab + 6" + e* hy a" + 2a6 + 6« - c» and divide b (a;3 _ oS) ^. ax {x' - a») + (jS (a - a) by (a + 6) (a; - a). i. Simplify the expressions : 1 1__ 1 1 2(z-l)' 4(a:-l)'''4(a; + l) {x - If (x ^^ \)' and ft , 6' 6"^ o a a a a b _ a _ 6' i a b a' 6. Add together the first and last of the three fractions 1 1 _1_ a: " £1 X z + a and subtract &om the sum twice the second. For what values of x will the result be positive? 6. When are four quantities said to be proportional ? Find two numbers in the ratio of 3 : 4, and such that if each be increased by 6, they shall be in the ratio of 4 : 5. 7. lia : b :: c : d; prove that ad = be and that ma + nb ; ma — nb •.; mo + nd : mc — nd. 8. Solve the equations : \x-Z ix-W /3 14 - 2z\ \0-x ^' 5 2 \4 8 /" (2) i^±l_?^:il_s = o, (3) (4) 3 (a: - 5) 2a: -8 2 ft' + c'-a' 2 36 18 + i + y a? + 2xy + y^ 12; 2 (a + 6 -c)(a -A + c) = 4, 2. I «» - 2a;y + y* x - y 9. In the Astronomical clock, where the hours are marked upon the dial from 1 up to 24 ; find the two times between 6 and 7 o'clock when the hands are at right angles, 10. What is the price of eggs per score, when 10 more in half a crown's worth, lowers the price 3d. per score ? 11. An officer can form the men in his battalioil into a hoUow square 4 deep, and also into a hollow square 8 deep. If the &ont in the latter formation contain 16 men fewer than in the former formation; find the number of men in his battalion ? Shew that the battalion can be formed into 3 other hollow squares only.' 12. Two pedestrians start at the same time from two towns, and each walks at a uniform rate towards the other town. When they meet, it is found that one has travelled 96 miles more than the other, and that if they proceed at the same rate, they will finish the journey in 4 and 9 days respec- tively. Find the distance between the to wns, and the rates of walkiiijj per dsiy , 160 PREVIOUS EXAMINATION. EUCLID, IV. VI. 1. When ia a circle said to be inscribed in a rectilineal figure ? Inscribe a circle in a given triangle. 2. Describe a square about a given circle. 3. A circle is inscribed in a triangle ABC, and a triangle is cut off at each angle by a tangent to the circle. The sides nf the three triangles so cut off are together equal to the sides of ABC. 4. Inscribe a circle in a given equUateral and equiangular pentagon. 5. When are four magnitudes proportional ? If the sides of a triangle, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the re- maining side of the triangle. ' 6. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 7. From a given straight line cut off any part required, Bivide a straight line into three equal parts. 8. Similar polygons may be divided into the same number of similar triangles. 9. The parallelograms about the diameter of any paraUelc^ram, are similar to the whole, and to one another. 10. Describe a rectilineal figure which shall be similar to one and equal to another given rectilineal figure. EUCLID, rv. VI. 1. When is a rectilineal figure inscribed in a circle ? In a given circle inscribe a triangle equiangular to a given triangle. 2. Inscribe a circle in a given square. 3. If a circle can be inscribed in a quadrilateral figure, the sums of the opposite sides are equal. 4. Inscribe an equilateral and equiangular pentagon in a given circle. 5. When are four magnitudes proportional ? If a straight line be drawn parallel to one of the sides of a triangle, it shall out the other sides, or these produced, proportionally. 6. If the sides of two triangles, about each of their angles, be propor- tionals, the triangles shall be eqmangular, and have their equal angles op- posite to the homologous sides. 7. From a given straight line cut off any part required. Divide a straight line into five equal parts. 8. Assuming that similar polygons may be divided into the same number of similar triangles ; shew that the triangles have tla same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. 9. The parallelograms about the diameter of any parallelogram, are similar to the whole, and to one another, 10. In right-angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle. SOPHOCLES. (ED. TTE. Translate: 408—425. Beginning, Ei Kal Tvpavvsis, e^ifftoTlov tA yovVf k.t.X. Ending, a a' i^io'tavsi aai re Kal tois \.n9ai, daiirXtvaa'S, l^iamTEov, KaTaio-ap. Explain this last line. Translate: 1186—1191. Beginning, *Iw ytvtal ^porcoi/, k.t.A.. Ending, Kai So^avr' diroKXiuai. SOPHOCLES. CED. TYE. Tbanslate: 390—403. Beginning, 'Ettei, poviis. atviyiia. Explain the allusion. fioKdv. What is the present indicative of this verb ? Produce examples of a similar change of form. Give the cognate tenses of dSas. Parse yuioTou and lyums. Translate: 863—871. Beginning, EI not ^wsiii (pepovrif k.t.X. Ending, ov&k yrjpaa-KEi, What is the derivation and exact meaning of aWnp ? Mention any forms in this passage which are not Attic. TACITUS, HIST. I. Tkanslatb : cap. 13. 1. Beginning, Potentia principatus divisa in T. Vinium, etc. Ending, prona in eum aula Neronis, ut similem. Translate : caps. 69, 70. 2. Beginning, Haud facile dictu est, etc. Ending, sacramento Vitellii accessisse, "P axBe priaOai ? (2) TLvpriviov. Give the Latin name of this man in full. (3) How do you solve the chronological difficulty which meets us in ver. 2 ? II. Translate : chap. xii. 54 — 59. Beginning, "E\e7e M Kal toIs o-)(koi^, k.t.X. Ending, ews ov Kal Td EcrxaTOi* Xetttov diro^ws, (1) Where else in the New Testament does the word Kaitrwv occur, and what is it taken to mean i (2) Explain the use of the words ios ipyatriav, III. Parse and derive ^yE/xovciSoj'Tos, fisnpijtTTtvfJiii/Ti, laTrapyavtaisf , KaraXvpLari, dvtrfiiSi/, irpuKTopi, TACITUS, HIST. I. Translate: caps. 47, 48. 1. Beginning, Exacto per scelera die, etc. Ending, ut prior occideretur. Translate : cap. 76. 2. Beginning, Primus Othoni fiduciam addidit ex Illyrico nuntius, etc. Ending, Carthaginem ceterae civitates secutee. Parse adnitentibus, hasisse, qutssitis, cognitum est, formido, orto, ohtulerat. What were the duties of the pri6 jfs. Derive and explain axi/uos. Explain the use of the optative future tense. Parse ixTtpriS^s, wspirXij- cflEts, /i£0£yTi, 'irpovv\ov i^etrTEfifiivov, Parse TrpotrvfiEda and aiTTE-irdat, What cases may irpo? take, and in what different meanings? Derive dyopdj ^ovvofio^. Translate: 911—917. Beginning, Xw/oas ayaKTEs, 86^a fioi TrapECTdQjj, k.t.X. Ending, dK\* ectI Toif XEyovTos, el i^d/3ov& Xiyoi, SOPHOCLES. (ED. TYE. Tkanslate: 640—561. Beginning, ^Ap' oijxl fitopou Ictti Touyx^V'JM^ ^°^t '^•ir'.X, Ending, KP, tiaKpol iraXaioi t* av /lETjOtjOeiEi/ yjiovoi. Derive Suvfuvrij audaSlaVf iyxtipr\^a^ acl>avTo^f i/o/i£^£(S. Parse ETrtiOes, ivTaKOvtrov, xpsttj, elpTJ'adal, Explain, the construction of olo-fl' ms ■iroiririii.cpiai 'A/3ia'. Explain this by reference to the Old Testament, II. Translate : chap, xvii. 1 — 4. Beginning, ETwe ^e nrpd^ tous /xoStitAs, w.t.X. Ending, Xsywi/, Metki/ow, i<^?i(r£ts avTtS, (1) Compare with this the parallel passage in St. Matthew. By what parable does our Lord there enforce His precept ? (2) Explain the words jiiuXos ouikos. III. Parse and derive irB'jr\ripopd^, eVel irpiirmv ccpue, k.t.X.. !Ending, i/aoTs, eV 'lerfitjuoO te fiavr&la trirodiS, Parse KaBe'trTOTe, n-jooiritVESa, irTto-Sat. Derive Su(rd\yriT09 and iyopaiai, ws OeXowTos ai/, k.t.X. Explain the use of dv, Explain the use of fxh oi. Explain ^CrXov iJ^etFTefinivov, opat piv fipLoii. Point out the U which answers to this iiiv. Translate: 1132—1140. Beginning, K.oiSiv yt BaSna, SiairoT', dW iyvi aaEv^Etr9aL Sokbl^. Parse "TrvQoto opyavstaSje'^EjOeTs, ifiifx\^(a^ irapritFta^ iff^i, ElpydtrSaij (^sv^cirdai. o-Tsyw, What part of the verh is this, and why ? Explain the construction ofotx<«> t^px^<^<''Ot&^- Derive Ivfiv, TeXtovn^, 158 PBEVIOUS EXAMINATION, GEEEK TESTAMENT. GOSPEL OP ST. LUKE. I. Translate : chap. xi. 1—4. BegilUUBg, Kai syevsTO iv tuJ iXvat a^Tdv iv Toirtp Tti/i irpotriVj^ojltvoVf k.t.A, Ending, <^\X*i pvaai ?7juas diro tou irovrjpov, (1) Mention other passages in this Gospel where it is recorded that our Lord was praying. (2) Note any variation between the words of the Lord's Prayer as given in this passage and in St. Matthew. (3) Explain t6v aprov tov iiriovtrLov, (4) What appears to be the true meaning of toO irovtipoC ? II. Translate: chap. xiv. 15 — 24. Beginning, 'AKOvrras S' tis twu cvvavaKtipivrnv raS-ra elirtK auTiS, k.t.\. Ending, rwv khkXtj^uei/wi/ yEvtrErai fiov tov Seiirvov, Compare this parable with the similar one in St. Matthew's Gospel. III. Parse dirS pi5s, yEfiiaSy, iraptjrriiiivoii, a(ps9, tiaEviyKrfs, Derive ijipayiioti^. EXAMINED AND APPEOVED. PIEST CLASS. Ainslie Pemb. Bowes-WataonTrin. | Clarke Alder Trin. H. Boyd Christ's Clarke Alderson Joh. Boyton Magd. Cliff Aldis Trin. Brady Trin. Clowes Alexander,A.B.Christ's | Branson Caius Collins Alexander Trin. Broad Caius Connor Allison Sid. Bros Joh. Cooke, C.E.B Allison Trin. Brown Trin. Cooke, J. M. Alston Clare Brown, E. A Caius Cookson Alvis Christ's Brown Joh. Cope Anderson Trin. Brown Trin. H. Comford Andrews Joh. Brown, J. W.D. Caius Crampton Arden, A. H Christ's Browne Trm. Crewdson Austen Joh. Browne Caius Crosthwaite Austen-Leigh King's Brownjohn Clare Currey Austin Sid. Buchanan Tiin. Curtis Bacon, J, G. Clare Buckell Joh. Dalton Baker, B,. Corpus Bulwer Pemb. Darby Barker Corpus Burrows Cath. Davies Barnes Joh. Buxton Trin. De Putron Baron Joh. Cadman Christ's Dew6 Bathurst Trin. Campion Caius De "Wend Beadon Joh. Carey Joh. DevereU Beedham Clare Carrington Joh. Dickinson Bell Caius Carter Christ's Dickinson Bertlin Trin. H. Chalk Pet. Dixon Besant Emm. Chancellor Clare Dixon Birch Caius Charies Christ's Dcjuef" BirtweU Queens' Child Emm. Dnnlop Body Joh. Clark Caius Dunn Bolton Trin. Clarke ChrUt's Dyne Caius Pemb. Joh. Trin. Christ's Cath. .Trin. Trin. Jesus Trin. Trin. Trin. Trin. Caius Trin. Joh. Clare Trin, Joh. Caius Cath. Joh, Trin, Joh. Trin. Christ's Caius Corpus Trin. Corpus King's PREVIOUS EXAMINATION. 159 East Trin. Jenner Trin. H. Pretor Trin. Edwards, J. Trin. Jenkins Jesus Price Joh. Edwards, T. Trin. Johnson Joh. Pritchard Joh. Edwards Pet. Jones Trin. Purton Trin. Eldertou Corpus Jones Queens' Quarrington Cath. Evans 'I'rin. Karney Trin. Ranken Caius Everett Trin. Kennedy Trin. H. Bansford Clare Evett Pemb. Kent Trin. Ratcliffe Trin. Eairclough Christ's Kinleside Emm. Rees Joh. Palkner Joh. Kinsey Emm. Reynolds Caius Fison Caius Knight Caius Ridsdale Caius Pontaine Joh. Lang Trin. Rogers Caius Francillon Trin. H. Larbalestier Joh. Bolph Trin. H. Gael Trin. Laurie Caius Romer Trin. H Garrett,T.,sen.Cams Ledger Corpus Rose Emm. GaskeU, C. M.Trin. Lee Caius Rounthwaite Joh. Glennie Trin. Lee Joh. Rudd Joh. Goodacre Pemb. Leeke Trin. Rust Pemb. Green Caius Leeson Down. Sale Emm. Green Trin. Le Sueur Pemb. Salter Claxe Greene Christ's Lewis Corpus Salusbury Emm. Grimley I'rin. Lewis Emm. Sanderson Corpus Guinness, P. Joh. Lobley Trin. Scholfield Trin. Gurdon Trin. Lowther Trin. Sculthorpe Pet. Guinhill Emm. Luckock Corpus Sedgwick Caius Haigh Christ's Lush Trin. Shaw Trin. Hale Sid. Mackenize Trin. Sidgwick Trin. Hamilton, C. Trin. Mao Vicar Trin. Sillitoe Pemb. Hampton Queens' Maddy Joh. Simpson Pet. Hanbury Clare Marsh Trin. Simpson Trin. Haukey Trin. Marton Trin. Simpson Pemb. Hanson Trin. Mason Cath. Slater Queens' Hardcastle Trin. Mason Pemb. Smith Trin. Hargrove Emm. McGill Christ's Smith Caius Harris Emm. Mc NeUe Trin. Smith, E. A. Christ's Hawkins Trin. Mc William Caius Smyly Trin. Hawthorn Trin. Metcalfe Joh. Snowdon Joh. Heathcote Trin. Moore Pet. Spencer Emm, Hensley Trin. Moorsom Trin. Spurling Trin. Hewitt Corpus Murray Trin. Stanning Trin. Hickman Joh. Neil Trin. H. Stenning Trin. Hilleary Joh. Nicholls Joh. Stephen Christ's Hoare Trin. Nixon King's Stephenson Joh. Hoekin Joh Nottidge Emm. Stevens Joh. HoUis Trin. Oakley Trin. Stevens Magd. Hollond Trin. Partington Trin. Steward Trin. Hopkins Sid. Patch Clare Straton Trin. Horsfall Christ's Pennington Pet. Strutt,Hon.H . Trin. Hulbert CaiuB Pierce Corpus Sturge Trin. Hulbert Cath. , Pinches Joh. Sturges Trin. Hunt Caius Plumptre Sid. Swann Caius Huxtable Christ's Pooley Joh. Swann Trin. Isaacson Clare Prance Trin. Talbot Trin. H. Jcffery Trin. H. Pratt , Trin. Tancock Sid. . 160 PREVIOUS EXAMINATION. Tarleton Joh. Turner Caius Webb Caius Tate Queens' Turner Sid. Welle Emm. Tattershall Queens' TJsbome Trin. Wheateroft Caius Taylor Trin. Vaizey Trin. White Sid. Tebbs Trin. H. Valentine Joh. Whitehead Joh. Teevan Trin.H. Waddell Trin. Wilkins Joh. Thomas Trin. Walford Trin. Wilks Trin. Thompson Joh. Walker Trin. H. Willan Joh. Thompson Cains Walker Trin. Williams Emm. Thornley Trin. H. Warner Trin. H. Wilson King's Thynne Trin. Washington Trin. Wood Trin. TomlinBon Clare Wason Caius Wyon Corpus Towera Pemb. Wayne Trin. Young Caius Tuck Snini, SECOND CLASS. Ash J,oh. Hamilton Pet, Outram Christ's Aspland, J. L. Sid. Hodgetts Emm. Peel Christ's Babington Clare Hodgson Corpus Pixel! 'J'riu. Bacon, W. Clare Hopkinson Clare Richards Sid. Bettison Corpus Jones, W. T . Queens' Rose Queens' Bigwood Joh. Jones Joh. RothschUd Trin. Burnett Queens' Laundon Caius Smith Corpus Cartwright Joh, Leavens Queens' Stable Pet. Casson Christ's Legge Pet. Swinhoe Christ's CotteriU Joh. Lloyd Trin. Tarratt Trin. Davies, J. H. Trin, Lorimer Joh. Thompson Trin. Deane Trin. Lyon Trin. Thornton Trin. De Montmorency Trin. Madan Trin. Townend Trin. Dent IMn. Mellor Trin. H. Tweddle Clare Frere Trin. Miller Pemb. Ward Trin. Garfit Trin. Mitton Cath. Wheeler Trin. H. Graves Trin, Monckton Trin. Withers Corpus Guinness, R. Joh. Myers Queens' Hamilton, J. Trin. NeviUe Clare Examined in Additional Subjects and approved. Aldis Trin. BertUn Trin. H. Cadman Christ's Alexander, A.B , Christ' s Besant Emm. Campion Caius Alexander Trin. Birch Caius Carey Joh. Allison Sid. Birtvrell Queens' Carrington Joh. Allison I'rin, Bolton Trin. Carter Trin. Alston Clare Boyd Christ's Cartwright Joh. Anderson Trin. Boyton Magd. Chancellor Clare Andrews Joh. Brady Trin. Child Emm. Austen Joh. Broad Caius Clarke Christ's Austen-Leigh King's Brown Trin. Clarke Caius Bacon, J. G, Clare Brown, E. A, Caius Clarke Pemb. Bacon, W. Clare Brown Joh. Clowes Trin. Baron Joh. Brown Trin.H. Collins Christ's Eathurst Trin. Brownjohn Clare Connor Cath. Bayne Trin. Buchanan Trin. Cookson Jesus Beadon Joh. Buckell Joh. CotteriU Joh. Beedham Clare Burrows Cath. Crampton Trin. Bell Gains Buxton Trin. Crewdson Trin. PREVIOUS EXAMINATION. 161 Crosthwaite Caius Isaacson Clare Richards Sid. Carrey Trin. Jeffery Trin. H. Ridsdale Caius Dalrymple Trin. Jones Trin. Rogers Caius Dalton Clare Jones Queens' Rolph Trin. H. Darby Trin. Kennedy Trin.H. Romer Trin. H. Davies, J. H. Trin. Kent Trin. Rose Emm. Deane Trin. Kinsey Emm. Rothschild Trin. De Montmorency Trin. Knight Caius Rounthwaite Joh. Dent Trin. Lang Trin. Rudd Joh. Deverell Trin. Larbalestier Joh. Rust Pemb. Dixon Christ's Leavens Queens' Sale Emm, Dixon Caius Ledger Corpus Salter Clare Dunlop Trin. Lee Caius Sanderson Corpus Dunn Corpus Lee .Joh. Scholfield Trin. Dyne King's Leeke Trin. Sedgwick Caius East Trin. Le Sueur Pemb. Shepherd Trin. Elderton Corpus Lewis Emm. Sidgwiek Trin. Everett Trin. Lobley Trin. Simpson Pemb. Evett Pemb. Long Trin. Smith Trin. Pairclough Christ's Luckock Corpus Smith, E. A. Christ's Falkner Joh. Lumley Trin. Smyly Trin. Fison Caius Lush Trin. Snowdon Joh. Fontaine Joh. Mackenzie I'rin. Spencer Jesus Francillon Trin.H. Mac Vicar Trin. Spencer Emm. Gael Trin. Marton Trin. Spurling Trin. Garat Trin. Mason Pemb. Stanning Trin. Garrett, T.,sen.Caius McGill Christ's Stephen Christ's Gaskell,T. K . Trin. McNeile Trin. Stevens Joh. Green Trin. Mc William Caius Stevens Magd. Greene Christ's Mellor Trin. H. Straton Trin. Grimley Trin, Metcalfe Joh. Strutt, Hon. H. Trin. Guinness, F. Joh. Mirehouse Clare Sturge Trin. Guinness, R. Joh. Moore Pet. Sturges Trin. Gurdon Trin. Moorsom Trin. Swaim Caius Gumhill Emm. Murray Trin. Talbot Trin. H. Haigh Christ's Myers Queens' Tancock Sid. Hale Sid. NeU Trin. H. Tarratt Trin. Hamilton, C. Trin. Nixon King's Tattershall Queens' Hankey Trin. Nottidge Emm. Tebbs Trin. H. Hardoastle Trin. Oakley Trin. Teevan Trin, H. Hargrove Emm. Peel Christ's Thompson Joh. Harris Emm. Pennington Pet. Thompson Caius Hawkins Trin. Pierce Corpus Thornley Trin. H. Heathcote Trin. Plumptre Sid. Towers Pemb. Hensley Trin. Pooley Joh. Turner Sid. Hewitt Corpus Prance Trin. Usbome Trin. Hickman Joh. Pratt Trin. Vaizey Trin. Hoare Trin. Pretor Trin. Waddell Trin. Hockin Joh. Price Joh. Walford Trin. HoUis Trin. Quarrington Cath. Wallace Trin. HoUond Trin. Kanken Caius Walker Trin. H. Hopkins Sid. Ransford Clare Wallis, J. H. Joh. Hulbert Caius Ratcliffe Trin. Wallis, W. M. Joh. Hunt Caius Rees Joh. Warner Trin. H. Huxtable Christ's Reynolds Caius Washington Trin. • M 162 THEOLOGICAL EXAMINATION. Webb Caius Wilkins Joh. Wilson King's Wheeler Trin.H. Wilks Trin. Wood Trin. White Sid. WUlan Joh. Wyon Corpus Whitehead Joh. WiUiams Emm. YoiiTiB Caius. THEOLOGICAL EXAMINATION, Easter Teem, 1861. EXAMINERS : WrUiiAM Selwtn, B.D., Margaret Professor of Divmiiy. Thomas Jaerett, m.a., Eebrew Professor, John Bioo, b.d., St. John's College. John Smyth Furton, b.s., St. Catherine's College. Thomas Thouason Pebownb, b.d., Corptis Christi College. Akthur Atbbs Ellis, m.a., Trinit!/ College. CANDIDATES. Abell Ambrose Appleton Arden Armitsge Athawes Attwood Baker Baldock Beales Benson Berry Bigg Blissard Blofeld Bothamley Bower Boys Braithwaite Brereton Brown Brown Barney Castley Chichester Clark Clark Clayton Clint Coldham CoUison Cornish Cottam Curtois Custance Dawson Day Dickson B.A. Sid. B.A. Corpus B.A. Joh. B.A. Christ's B.A. Emman. B.A. Clare B.A. Emman. B.A. Caius B.A. Trin. B.A. Joh. B.A. Magd. B.A. Pemb. B.A. Caius B.A. Emman. B.A. Trin. B.A. Trin. B.A. Trin. B.A. King's B.A. Clare B.A. Joh. B.A. Caius B.A. Cath. B.A. Trin. B.A. Pemb. B.A. Trin. B.A. Joh. B.A. Magd. B.A. Emman. M.A. Trin. HA. King's B.A. Pemb, B.A. Sid. B.A. Pemb. B.A. Sid. B.A. Joh. B.A. Christ's B.A. Joh. B.A. Trip. Dixon B.A. Joh. Dover B.A. Jes. Edlin B.A. Trin. Edwards B.A. Emman. Evans B.A. Corpus Flather B.A. Joh. riintoff B.A. Emman. Fowler B A. Trin. Francis B.A. Joh. Francis BJ^ Emman. Fullerton B.A. Emman. Geary B.A. Corpus Gray M.A. Trin. Griffith B.A. Emman. Grist Bji.. Joh. Gunter BJ\.. Joh. Hardy B.A. Christ's Harvey B.A. Christ's Harvey B.A. Joh. Hodgson B.A. King's Holley B.A. Trin. H Holmes B.A. Emman. HoweU B.A. Cath. Hudson M.A. Trin. Hulbert B.A. Caius Hunnybun B.A. Cuus Ingles B.A. Trin. Jenkin B.A. Joh. Johnston B.A. Trin. Jones BJi.. Cath. Jon«s B.A. Joh. Kelly LL.B. Trin. H. KemUe B.A. Trin. Kershaw B.A. Joh. Langshaw BJ^. Trin. Leach B.A. Caius Lock S.C.L. Joh. Marsden B.A. Joh. THBOliOQICAL EXAMINATION. 163 Marsden Marshall Massy Mathews May Meres Monk Morse Nelson Newton Nicholls Nlsbet Nixon Noble Norgate Northey Parez Pearse Pearson Pemberton Pettitt Pierpoint Pinuey Potts Pretyman Price Quilter Rigby Rogers Rogers Royds HISTOEICAL BOOKS OF THE OLD TESTAMENT. 1. Give an account of Isaao, stating parlxcnlarly (1) the circumstances under whieh his name was first given, (2) the promises made to him. 2. Narrate the history of Jacob from the time of his marriage with Rachel. 3. State the regulations under which the Levites were substituted for the first-born of the children of Israel. What was the portion assigned to the Levites in the promised letnd, and wherein did their tenure of property differ from that of their brethren ? 4. What injunctions were given to Moses concerning numbering the people? 5. Illustrate and make your remarks on (1) Oen. zxxL 7. "And your father hath deceived me and changed my wageS' ten times." (2) Joshua xxi. 21. "For they gave them Shechem toiih her aulntrbs in Mount Ephraim to be a city of refuge for the slayer." 6. Write a short account of Gideon and his descendants. What ceremonies and procIamacioDS were enjoined by Moses relative to ent^ing on war ? 7. Give a history of Saul down to the time of his rejection. What injunctions did Moses give for the King of the Israelites andjby what Kings were any of them disregarded ? m2 B.A. Emman. Royds LL.B. Pet. Sainsbury B.A. Joh, Salvin B.A. Joh. Sanders B.A. Christ's ■ Sandys B.A. Eraman. Scholefield B.A. Trin. Shaw B.A. Trin. Sheffield B.A. Jes. Sheild B.A. Emman. Shepherd B.A. Joh. Sitwell B.A. Jes. Skipworth B.A. Corpus Slater B.A. Joh. Sparrow B.A. Corpus Stanwell B.A. Trin. Starky M.A. Pemb. Steward B.A. Caius Taylor Todd B.A. Cath. B.A. Cath. Turnbull B.A. Trin. Twist B.A. Joh. Walbran B.A. Caius Wale M.A. Joh. Walsham B.A. Trin. Warwick B.A. Joh. Watkins B.A. Pet. Watson B.A. Trin. Webb B.A. Trin. Williams M.A. Clare Winslow B.A. Trin. Wood B.A. Christ's B.A. Trin. B.A. Christ's B.A. Joh. B.A. Corpus Emman. B.A. Trin. B.A. Trin. H. B.A. Clare B.A. Trin. B.A. Joh. B.A. Emman. LL.B. Trin. H. B.A. Clare B.4. Joh. B.A. Magd. B.A. Trin. B.A. Joh. BA. Trin. B.A. Trin. B.A. B.A. Magd. Pemb. B.A. B.A. B.A. B.A. Magd. Magd. Magd. Caius LL.B. Christ's B.A. Joh. B.A. Christ's B.A. Caius B.A. Joh. 164: THEOLOGICAL EXAMINATION. 8. " The God that answereth by fire, let him be God." Bescribe the condition of Israel when Elijah made this appeal. Mention othei' instances when the acceptance of a sacrijfice was indicated by the falling of fire from heaven. 9. Enumerate the leading events in the history and time of Hezekiah. 10. Describe the restoration of the Jews to Palestine, and the struggles attending the rebuilding of the City and Temple. 11. Mention the Geographical position of Gilgal, Bethel, Mount Ebal, Ashdod, Dan, and Hebron, with some single circumstance relative to each. THE FOUR GOSPELS AND THE ACTS, THE FIEST EPISTLE TO THE COEnSTTHLANS, THE EPISTLE TO THE GALATIANS, THE EPISTLE OP ST. JAMES. 1. Shew that St. Mark's Gospel, as compared with the other three, is calculated to supply a distinct want of the Church ; and also that it is en- titled to be regarded as an original and independent work. 2. What is to be gathered &om the opening verses of the Acts of the Apostles as to (1) the proper subject of the Book, and (2) its relation to the Gospel history ? 3. Translate with brief notes where you think them necessary : (a) Beginning, Kai KaTafiatvoin-tov avTtov Awo tov opovs, k.t.X, Ending, oVt irspl 'Iwavvou tou fiatrTttrrov eIitcv auTois. St. Matth. xvii. 9—13. What event had immediately preceded these words ? On what Old Tes- tament authority did the scribes say that Elias must first come i How far is John the Baptist to be identified with Elias i (d) Beginning, Kal i&v 6 6(t>Qa\fj.6^ vou aKav&oKi^rf o-e, k.t.X, Ending, ical ilpnviiiTt iv iWnWoK, — St. Mark ix. 47 — 50. Derive and explain. ysEKKo. What other word is rendered 'hell' in our English Version? What is the difference of meaning between the two? (c) Beginning, NCi/ jj ij/uxti p-ov TerapaKTaf K.T.X, Ending, woi/tos sXicua-ct) irpi^ ipavTov, — St. John xii. 27 — 32, At what period of our Lord's life were these words spoken, and what request called them forth ? Shew that the concluding sentence of the pas- sage stands related to that request. Have we any earlier example of this mental struggle which has been called the passio inchoata t (rf) Beginning, 'Avoi^a^ 6e Ilcrpos tA oTopa Hinv* k.t.X, Ending, oti 6 Beds ^v ptT* auToC. — Acts x. 34 — 38. Punctuate and translate this either according to the authorised version or in any other way that you prefer. (fi) Beginning, 'E-TrtKou/jias o5v ti/xww t^s irapa tov ©too, k.t.X. Ending, itai toIs IBvstri.. — Acts xxvi 22, 23. 4. In which of his apostolical journeys did St. Paul first visit Corinth i Draw a rough map of the countries traversed by him in that journey, and mark upon it his route. How long was his first residence at Corinth? Mention the' principal heresies and disorders to confute and correct which his first EpisUe to that Church was written. 6. Translate : (a) Beginning, El H rii koKeT 4^as t(oi» initrraiv, k.t.X, Ending, Mtjufirat pov yii/Eo-OE, xaQus xdyio Xjoio-tov, 1 Cor. X. 27, xi. 1. Explain where necessary the connection of the argument. (6) Beginning, Ka0* rjpipau aVodi/^a-Kco, k.t.X. Ending, irpos ivrpoiriiv lipiv \iyui. — 1 Cor. XV. 31 — 34. THEOLOGICAL EXAMINATION. 165 To what do you refer Ka-ri avipuinrov i9ripwfiaxn<"i i" 'Eipiirw? 6. By whom and under what cixeumstanoes was Galatia first evange- lised ? What condition of the Churches there called forth St. Paul's Epistle to them? Shew that the different doctrinal tone of that Epistle and the Epistle of St. James is to be accounted for by the differing requirements of the persons to whom they were respectively addressed. 7. Translate with brief notes as before : Beginning) "EireiTa Sid StKaxEo-o-ajoaji/ e'tmi/, k.t.\. Ending, tfiol y&p ol @okovut&^ ovdiv irpoTavldEUTO, — Gal. ii. 1 — 6. 8. To which of the persons of that name mentioned in the New Testa- ment do you ascribe the Epistle of St. James ? Give the grounds of your decision, and in accordance with it state what is known of the writer. 9. Translate as before : (a) Beginning, rivicrBs Si -TrotTjTal \6yoVj k.t.X. Ending) outos fiaxapLm ev Ty iroitio-ti aurov eo-Toi. — Jas. i. 22 — 25, (6) Beginning, 'ISov tmv liriraiv Tobs x^^tvoys eis Ta aTOfiaTa ^aWofitv Tpos TO "n-Eidea&at auTous tlfiiVf k.t.X, Ending, Kal \oyi^op.Evii viro t^s yttvvijs. — Jas. iii. 3 — 6. 10. Retranslate into Greek, amending the English Version where you think it necessary : Simon, Simon, Satan hath desired to have you that he might sift you as wheat : but I have prayed for thee that thy faith fail not. When he speaketh a lie he speaketh of his own, for he is a liar and the father of it. I am the good shepherd, and know my sheep, and am known of mine. As the Father knoweth me, even so know I the Father : and I lay down my life for the sheep. Which is the chief city of that part of Macedonia, and -a colony . . And he was eaten of worms, and gave up the ghost . . We took up our carriages. But he himself shall be saved ; yet so, as by fire. Ye see how large a letter I have written unto you with mine own hand. Do ye think that the Scripture saith in vain, the spirit that dwelleth in us lusteth to envy ? 11. Establish the truth of the following statements, and shew what use may be made of them : a. There is a difference in the quarter &om which opposition to the Gospel of Christ proceeded, as represented in the Gospels and in the Acts, most characteristic of truth, though most unobtrusive in itself. b. The Epistle to the Galatians and the Acts of the Apostles were written without any communication with each other ; yet the Epistle by recital, implication, or reference, bears testimony to many of the facts contained in the history. ARTICLES OF EELIGION. . 1, To what circumstances do the ' Articles of Religion' owe their origin ? Trace the various stages through which they passed before they assumed their present form. Is it fair to regard them as ' a solitary standard of doctrine' ? 2. Compare the Articles of 1552 with the present Thirty-nine ; and ac- count for the differences which you notice. 3. What is the history of the Document known as ' the Lambeth Arti- cles' ? Was it ever authoritative ? 4. Give proof from Holy Scripture, (1) That the Holt Ghost is God j (2) That He is a Person. 5. Into what three sections does Article II. naturally divide itself? 166 THEOLOGICAL EXAMINATION. Quote the words of it which relate to the Atonement, and render a Scriptural proof of them. 6. In what /our aords does Hooker briefly comprise ' all that antiquity- has handled as touching the person of Jesvs Christ' ? Specify the heresies to which he refers, and the Councils in which they were condemned. 7. What is the history of Article III? In what sense do you understand it r Upon what passage of Scripture is it based ? 8. Investigate the meaning of the words Canon, and Apocrypha. Quote the words of Article VI. which relate to the Canon of Scripture. Establish the Canonicity of the books of the Old Testament. 9. (o) "In Vetere Testamento Novum latet, In Novo TcBtamento Vetus patet." — St. Augutiiniia. Shew that this is substantially the doctrine of the Church of England in Article VII. (|3) " Quare male sentiunt qui veteres tantum in promissiones tempora- lias sperasse confingunt." In what form has the error here condemned reappeared since the Kefor- mation ? Shew that it is unscriptural. 10. (a) Date the Nicene Creed, and mention the circumstances which led to the framing of it. When did it assume its present form ? {£) " I believe in the Holt Ghost. The Lord and Giver of Life." Write down the original of this clause, and quote any passages of the Greek Testament from which these Titles may have been derived. 1 1 . Investigate the Authorship of the Athanasiau Creed, and write down the original of the following clauses : (1) ** The Father incomprehensible, the Son incomprehensible, and the Holt Ghost incomprehensible. (2) " Perfect Gob and Perfect Man, of a reasonable soul and human flesh subsisting." 12. Write down the Latin words of Article IX. and (assuming them to be of co-ordinate authority) give reasons for preferring the Latin to the English form. Briefly sketch the history of the Pelagian Heresy. 13. Examine theteachingof the Homily referred to in the Article ' Of the Jiutijication of Man.' Distinguish between '^esin/bnnts' aixA',fidesformata.' Shew that the doctrine of this Article is in harmony with the teaching of St. Paul and St. James. 1 4 . Illustrate from the History of tlie Chiirch the position, that ' General Councils have erred even in things pertaining unto God,' In what sense must you construe the word ' General' ? 15. How does it appear that Transubstantiation ' overthroweth the nature of a Sacrament' i Distinguish the Romanist from the Lutheran doctrine of this Sacrament. Examine the meaning of the word ' Sacrament.' How does our Church distinguish between ' the two Sacraments of the Gospel' and * those five commonly called Sacraments' ? Enumerate these last. THE UTHRGY. 1. Akbanoe the contents of the Prayer-book according to the fourfold division given in its title. Give the names of the corresponding Latin Service-books, and trace, if you can, the origin of those names. Explain the term ' Use.' What are the ' Sealed Books' ? 2, (a) "In Uauiibus An. In Ula die stillabunt montes dulcedinem ..P>. Dominus regnavit . . CapiMum. Eora est jam nos de somno surgere . . Bymnut. Vox clara ecce intonat. Vers. Vox clamantis in deserto. Bes. THEOLOGICAL EXAMINATION. 16T PaTateTiamDomSni... Omtio, Excita qusesantus Domine. Memoria de sancta Maria. Missus est Gabriel angelus." . . (J) " Deinde dicitur offertorium." (fl) "Beinde accipiat sacerdos infanteni per latera in manibus suis, et intenogato nomine ejus, baptizet eum mb irina immersione," Explain the terms printed in italics in the above rubrics. Describe the chief characteristics of a Missal at the beginning of the reign of Henry VIII. 3. Compare the Order for Daily Morning Prayer as settled at the last revision with the same Order as it stood in 1549. 4. The Presbyterians in 1661 objected to the following phrases in the Prayer-book: — 'deadly sin'; ' sudden death' ; 'all that travel'; ' with my body I thee worship' ; ' till death us do part.' Shew that their objections were ill-founded. 5. Trace the principal changes in the Office for Confirmation from 1549 to 1662. State clearly the origin and meaning of the rite of Confir- mation, and support your answer by quotations from the present office. 6. The Prayer of Consecration in the Office for the Holy Communion consists of three parts. What are they ? 7. Give an outline of the two Offices for the Ordering of Deacons and of Priests, and state the main points of difference between them. 8. Give the history of the following rubrics : (o) " At Morning Prayer, instead of the Psalm ' O come, let us sing &c.,' these Anthems shall be sung or said." (i) "To take away all occasion of dissension and superstition .. it shall suffice that the Bread be such as is usual to be eaten." (c) First, let the Minister of the Parish (or, in his absence, any other lawful Minister that can be procured) with them that are present, call upon God..." 9. Quote Scriptural authority for the following extracts, and comment briefly on the doctrines involved in them : (a) " Grant that we being regenerate, and made thy children by adoption and grace, may daily be renewed by thy Holy Spirit." (b) " God, who as at this time didst teach the hearts of thy faithful people, by the sending to them the light of thy Holy Spirit." (c) " Then we are guilty of the Body and Blood of Christ our Saviour ; we eat and drink our own damnation, not considering the Lord's Body." (d) " Baptism representeth unto us our profession." 10. Explain the terms— Rubric — Quinquagesima Sunday— Octave- reading, saying, singing— Vigil — Dominica in albis — Bogation flays^Chrism — Chrisom. 1 1 . Write out the Collect for Easter- day, and illustrate it from Scripture. What are the proper Lessons appointed for Morning and Evening Prayer on that day? Point out the bearing of each on the festival. 12. When, and for what purpose, is the Commination appointed to be read ? In what points does this Service difier iwom the other forms in the Prayer-book ) 13. Translate into Latin : (o) " The glorious company of the Apostles praise thee : the goodly fellowship of the Prophets praise thee: thenoblearmyof Martyrspraise thee." (A) " O GodtheFather.ofheaven.havemercyuponusmiseraWesinners." (c) " O Lord God, who seest that we put not our trust in any thing that we do ; mercifully grant that by thy power we may be defended against all adversity." (Collect for Sexagesima Sunday). Explain the wording of this Collect, as it stood in the Sarum Missal. 168 THEOLOGICAL EXAMINATIOBT. EOOLESIASTICAJL HI8T0EY. FIE8T THEEB CENTURIES. 1. What predictions or allusions occur in the New Testament respecting any heresies which were subsequently developed in the primitive Church ? 2. What particulars may be gathered from the New Testament and the early fathers concerning (1) the places, (2) the seasons, and (3) the forms of Christian worship in primitive times ? 3. State what you know of the history of the Church in Alexandria, and of its leading theologians in the second century. 4. Give some account of Marcion and his opinions. 5. State the views of Cjrprian on the imity of the Church, How do they differ from those of the modern Church of Rome ? 6. Give a sketch of the history of the Church during the reign of Diocletian, and trace the origin of his persecution. THE EEPOEMATION IN ENGLAND. 1 . Give a brief account of the Lollards and their opinions. State the particulars of the death of William Sawtrey and of Lord Cobham. 2. What was Wycliffe's view of the Royal Supremacy ? Mention any statute affirming the Supremacy before the time of Henry VIIL Mention the successive enactments of Henry VIII. concerning Appeals. 3. Give some account of the Suppression of the Monasteries imder Henry VIII. What was the general effect on the condition of the Country ? i. Mention some of the books which, were precursors of the Reformation. Make observations on the " Bishops' Book " and Pole's Book " De XTnitate Ecelesiae." Describe the religious condition of England in 1636. How does the state of parties develop itself in the Articles of 1536 »i the view taken (1) of the Sacraments (2) of the use of Images (3) of the intercession of Saints ? 5, Write an account of Bishop Fisher, Anne A^^bw, and Joan Bocher. 6. Mention any points in which Bncer ajad MelEtncthon influenced the English Protestants. Describe the condition of the Reformation ^t the death of Edward VI. 1. Point the following passage : -lE^M-bD i»\M 2p»'' npb -lOMb pb-'aa nnrnM v^aw>^ sps"' NT'i : nrn lasn-bs nw nwv la'^aMb -iejsjst i3''2»b mn"< -ia«''') : owbtt; biiana ia» i33''S n^m pb •'23-iis : Toy n">nsT imbinbi Trn^M V"'^'''^ ^w aps-i-bN ]nb ■i)3N'''i : laMs-bM rtiwn nsbbi bmb w-ip'^'i aps"' nbE7'''i ••nbs') awbw baro "'bM •i32"'S-"'5 p'^ss ''3Q-nM •'D2N nsn : p''2N-n« >m^v •'ns-bsn o vnyii nariMi : •'nnr n'^rt law lana-sbi n'^aa mwv Tnat^a-nM ^bnm -"n bnn p^asi '^^b>^ Tistj? rv^n^ nnpa -ia«i ns-OM : •>ia» »-inb D>nbs ]S2n-b3 "nb"*! "riocw ir^n'^ a-^ipv naw'' na-Dsi anpa ^Msn-bs n3?3 M''") : ''b"in't p'^ns napa-ns ONnbN bs"*! : D"Ti2T Q''ip3, Qiips ]S2n-by wivri -iK?« n3!£a Qtc nntca -ids bs-n'^n bwn ''23« : ib n^y pb Viwbs 3TO1 HNTn v~i«n-p ms mp nns -n: db? '^b n-na nbnsi pbn lab ii^n ib n^-iiawm nsbi bm ism : -jmbia baN"--! la-iDa -"a ib laatrna mnoa «ibn . : 13'>2n n-'na "la'^nsa D'^nbs b'^sn it»« itryn-bD o : i2SDD-n« bi3«-Da : ntt?^ TbM d^bs ia« nffi'M ba nnyi la'-aibi «in i:b ana'^T : a>baan-bs rti;2-n«i V3n-n« nec^i 2p»i cap''! t£?3-i -!££?« ■)2''3p napa ©an w« W3Tb3-n«i in:pa -ba-ns ibn pbi t i5?3D ns-iM r2« pn2i-b« Hub ms psa 332''i : n^nwb ie^s ffQnnn-ns bm 232m i3«2-ns rnb : Nin n-Q '^3 lb n^ian iba-by '^a-iMn pb ab-riM aps'' V33-ns □a?"'') -in3n-nM nar"-! ap^i ibnffi'wba'i «in ma-""! np'^i : aps'^ n-a o "'ti^btrn ova pbb la^i : isban in -inn in« pSTi a'a"! ns3£» Tn inns ^fT'i i^s? vn«TiM -laN"'") nb'^bn abnn >a-iNn pb-b« D-'nbw m^ii : isban pb 3tt;''i : vn-fv mtaa apyi-ns nmn-]Q -f? -ia2;n ib -inn vnN-DN vpn ]nbi -inn ibnwnH ypn npyi-i npyi-ns anam ■'nnbriN n33m n'^rsv na nps'^b pb -laM^T : lyban ■Nbi TIM naam mnb n«nn3 nab : mn nvntrn ''n3n-n« ''3n£»Ki3 Nbi :-n3nm Finn a''T'E7m nna2;n inbirsi ibrnan nwsb "-T bsb-E;'' :to» nbnon nnv in3nb'i ''3nbpE73b "jb -iaE;n -lawb "^bN -law t»a« Q3''n« '^nbsi »-i canas F)Dna-in nnbn 7bn nn»i : y-i-i:s7 mraa nps'^-as nma : "-nbs-ns nnaa nab -ynw n^nb nnaona 2. Translate into Hebrew : (1) Now, as soon as he arose in the morning, he saddled his ass, and set out, to go to the place of which his sons had told him. (2) Shall I find room, in your father's town, for my men to lodge ; and will there be fodder for my camels ? (3) He was rich in neat cattle, sheep, and camels, and had many slaves both male and female. (4) She lived sixty- four years, and had twelve sons and three daughters. (5) Having encamped at night on the bank of the river, they crossed over as soon as the sun rose. (6) He feared lest the enemy should fall on his men, and slay them with the edge of the sword, and carry captive the women and children. (7) We sold our brother for thirty pieces of silver, and now his blood is required at our hands. (8) Where have ye hidden the cup of my lord ? 3. Translate into Hebbew: Beginning, EuXoyri-rds 6 Geos, k.t.X. finding, ol nrzpi rrfl sis i/juas y&pvTO^ irpo(j>riT£v&avTES. — 1 Pet. i. 3. 1. Translate : (1) Gren. xxi. (2) Gen. xlii. 2. Analyse the following verbs : ■«nan -i3*"i ^inntst n"'n3 !is-inn,N-T''i 170 THEOLOGICAL EXAMINATIOIf. 3. Affix the pronoun their, m. to the plural of the following nouna : •ban T< )-)wb boa n'w bnA ra it3. •: V T ' T T T 4. Translate, adding Buoh notes as you think needful : (l)Ps. ii. 10 — ^12. (2) Pa. iv. (3) Ps.xviii. 4—16. (4) Ps. xxii. 13-19. (5) Ps.xxxv. 7—17. (6} Ps. xlv. THE SEPTUAGHNT. BOOK OF EXODUS. Translate and explain the passages cited, and mark any pecuHaritiea in the language, tracing them to their origin. 1. Beginning, TLari^ri 8k r\ Ovydrfjp ^apaw kovtratrBai. eVl top irora- Itoiff le.T.X. Ending, t^v firjTlpa tov 'jraiSiov, — ii,. 5—7. 2. Beginning, Kol cItte Mioutr^^ Trpos tov Oeov, k.t.X, Ending, «ai p.vr\fxa cte o fiiWcK \a\i{ios -TTpds Meuuo'^p, Xiyutv, iSov SiStaKO, ere Qeov ^apatOj^ Koi 'A.apo)v 6 dStXipo^ cov t en-at trov nrpotpinTf}^. — vii, 1, 6, Beginning, Kal 'TrapaSo^dirijolv i-p ^fiipa ekswij ttiv yrjv Vea-ip., k.t.X, Ending, 6 QeAs iratrtj? Ttjv y»7s, — viii. 22. 7, Kal s^apwt Maputo Ttjv Kapdtav auroS. — ^vlii. 32. ''B^apuvdri tj KapSia ^apati, — ix. 7. *Effic\i5pui/£ 3e Kupio? T^v KapStav ^apaw. — ix, T2, 8, Begimiing, Kal Sis\Ev* ^fi(Sv yivofisuov optifiivy Koyov yap Tiva TTpo/SaWoyTES, Xoyov ytvvwfiiU, oii kut' diroropriv, aJs iXaTTOiQiivaL Tov kv ilfj.1v \6yoVf irpo^aWofxtvoi, "What is Justin attempting to illustrate here ? IV. Beginning, Tt ttote 5' eo-tI <^iXoffo0ia, k.t.X, Ending, /Uias oOtrri^ TauT»)s iirKTTijp.rjs. — cap. 2. Give some account of the philosophical schools here alluded to, and explain their connection with the career of Justin. V. "What heresies are mentioned by name in this dialogue ? Give an account of them. VI. "What is the original of the following sentence ? ' A.uiiyysi\afi£v ivavTlov aVTOv w'i irai&ioVf ws pi^a f'v y^ fin/fw(rjj. "What Greek versions of the Old Testament were extant when Justin wrote ? "Which does he quote ? Can you give the other versions of this passage ? VII. Translate, explaining the allusions to the Old Testament. (o) Kal ol iv vrjcTTeia Sk Tpdyoi Svo opoiot /CEXfiuffOtyTes yii/to-Oat, wv o sis dTtytrofjLtrdLOi iyiviTO, 6 Sk eTEpo^ eU irpavt^opdUf Ttvv dvo trapovaiwv Tov ILpiarTov KaTayysXta ijo-ai/. (ff\ Kal yap to kokklvov ^dfxfia irepiTtQivat aUTOis ivtTei\aTO u/uTy, 'iva Std TOVTOV fih \^dii vpd^ Xafipduri tov dsov. Kal {pvXaKT^piov kv vp.iari XfiirTOTct'TroK yEypa/xfikvtov 'j^apaKTiipwtv Tivoav^ a nravTmi dyia vooupsv Eti/ai, 'jrepiKsiadai. vfias EKiXeuo-E, Kal Sid TOUTcav duainirdav vfidi dsl fivrip.r\u ixttv TOV 0£ou, dpa TE Kal zK^yxoy iv Tail KapSiat^ v/xdiv, VIII. Translate with brief explanatory notes : Beginning, nal y&p ^pwpaTojv tlviuv dvixeirQai vpoirkTa^ev vpXv, k,t,\, Ending, ou'x t^^ k^ftysiads •iritTT£VTiov, — cap. 20. IX. Translate :_ duSpa^ ekXektous dir6 'lepovtrdKijfi sKXi^dpevoi tote i^eirtpL^aT£ fls nrdaav Tiiv yijv Xsyoi/Tes alpBcriv ddEOV XpiiTTlaviSv ire^tivkvaL. KaTaXiyoVTii TE TavTa d'TTsp KaG* l}/j.iSv ol dyvooSvTE^ ^juas -ttoj/tss Xiyovtriv, Illustrate this statement by reference to other Patristic testimony. Does it receive any support from any passages of the New Testament ? BUTLEE'S AJSTALOGT AND PALET'S HOE.^! PAULINA, I to V. 1. "What is the design of Butler's Analogy? State in what respects Butler regards Analogy as available for the defence of Religion, 2. Reply to the objection which urges that several observations in favour of a future life are equally applicable to the case of brutes. 3. Our trials, difficulties and dangers, in our temporal and our religious capacity are evidently analogous. 4. The present world is peculiarly fit to be a state of discipline for the improvement in virtue and piety of such persons as wUl set themselves to improve. 5. Reply to the objection that there is some peculiar presumption, from analogy, against miracles after the settlement and during the continuance of a course of nature. 6. Mention a way of arguing, which, though just with regard to other writings, is not applicable to the prophetic parts of Scripture. 7. The disorderly exercise of some of the miraculous powers conferred on the Early Christians produces no objection against their being really miraculous. 174 THGOLOOICAL EXAMINATION. 8. How does Butler meet objections against the wisdom, justice, and goodness, of Christianity i 9. The difficulties in which the evidence of Keligion is involved, form no more just ground of complunt than the external circumstances of temptation to which some persons are exposed. 10. "Agreement between letters bearing the name of an ancient author and a received history of that author's life does not necessarily establish the credit of either." Justify this statement and from the circumstances deduce a test of truth applicable to every supposition in the case. 11. Give the arguments based on the following passage : Rom, XV. 19, " So that from Jerusalem and round about unto Illyricum I have fuUy preached the Gospel of Christ." 12. Acts xix. 21, 22, "After these things were ended Paul purposed in the spirit, when he had passed through Macedonia and Achaia, to go to Jerusalem ; saying, after I have been there I must also see Rome ; so he sent into Macedonia two of them that ministered unto him, Timotheus and Erastus." What use does Paley make of this i How many visits to Corinth does Paley recognise? State your own view and point out how far Faley's arguments ought to be modified on the supposition of his being mistaken, 13. The opening of the second Epistle to the Corinthians exhibits a connection with the Acts of the Aposties which alone would satisiy some persons that the Epistle was written by St, Paul and under the circum- stances mentioned in the history. 11, "The Epistle to the Gulatians and the Acts of the Apostles were written without any communication with each other," EXAMINED AND APPEOVED FOE HONOURS, The Names in each Class are arranged in Alphabetical Order. MIDBLE BACHELORS, COMMENCING BACHELOI Cl,ASS I. Ds * Botbamley Trin, Class I, Class II. Ds Brown Clayton Evans t Grist Marsden Pettitt Shaw ,3 i %A^ 3 3 Class IL Ds Blofeld Trin. Clark Joh, Class III. Ds Howell Ni(dioll8 Nixon CatK Joh. Corpus Class HI, Ds Northey Trin, * Scbolefield Prize for Biblicsal Greek. + Distrngnishedln Hebrew. B,L. EXAMINATION. ITS EXAMINED AND APPEOVED. Ds AbeU Sid. Ds Hardy Christ's Ds Rogers Ambrose Corpus Harvey Christ's Royds Arden Christ's Harvey Joh. Sainsbury Armitage £mman. Hodgson King's Sal-vin Athawes Clare Hudson Trin. Sanders Attwood Emman. Hulbert Caii)3 Sandys Baker Caius Hunnybun Caius Scholefieia Benson Magd. Ingles Trin. Sheffield Blissard Emman. Jenkin Joh. Sheild Bower Trin. Jones Cath. Shepherd Boys King's Kelly Trin. H. Sitwell Braithwaite Clare Kemble Trin. Skipworth Brereton Joh. Langshaw Joh. Slater Brown Cath. Leach Caius Sparrow Castley Pemb. Marshall Pet. Stanwell Clark Magd. Mathews Joh. Starky Clint Trin. Meres Emman. Steward Coldham King's Monk Tiin. Taylor Cornish. Sid. Morse Trin. Todd Curtois Sid. Nelson Jes. TumbuU Custance Joh. Newton Emman. Twist Day Joh. Noble Joh. Walbran Dickson' Trin. Parez Pemb. Wale Dover Jes. Pierpoint Joh. "Walshara Flintoff Emman, Pinney Caius Warwick Fowler Trin. . Potts Joh. Watkins Francis Joh. Pretyman Trin. Webb Geary Corpus Price Joh. Williams Gray Trin. Quilter Pet. Winslow Griffith Emman. Rigby Trin. Wood Trin. Trin. Trin. Christ's Joh. Corpus Emman. Trin. H. Clare Trin. Joh. Emman. Trin. H. Clare Joh. Magd. Trin. Joh. Trin. Trin. Magd. Pemb. Magd. Magd. Magd. Caius Joh. Christ's Caius Joh. B.L. EXAMINATION, May, 1861. EXAMINERS : J. T. Abdt, IL.D., Trinit;/ Ball. Joseph Shasfe, lx.d., Jesita College, Heebert Broom, m.a., Trinity College. C. S. Calteblet, M.A., Christ's College. Brigstock Buck Climenson HaU Trin. Clare Trin. Magd. CANDIDATES. Hopkins Emm. Mac LaugKIin Magd. Porch Trin, EOMAN LAW. Salts Joh. Tremaine Pet. Westby Magd, 1. Entjmeeatb the principal modes of acquiring property peculiar to the Roman Law. 2. State the Roman Law with respect to the use of, and theproperty in, the banks of a river. 3. Define " Traditio," To what species of property ^d it apply? (O B.Li. EXAMINATION. . 4. Define " Res Corporales" and " Res Incorporales." Do these definitions accord with those of Corporeal and Incorporeal tiings in the English Law ? 5. What was " TJsusfructus" ? Point out some of the modes by which t might be terminated. 6. Define "TJsucapio" and "Possessio longi temporis." After what leriods could, according to the law at the time of Justinian, the ownership le acquired by possession^ 7. What were the forms of testament in use anterior to the time of ustinian S Describe the formalities requisite to the validity of each. 8. Describe fully the form of testament in use at the time of Justinian. 9. Define " Substitutio vulgaris" and "Substitutio pupiUaris." 10. What was the " actio de inofScioso testamento" i In what cases could it be brought, and when was the right to it ztinguished i 11. What was a " Fideicomraissum" ? Define "Pidei committens, " ' Heres fiduciarius," and " Pideicommissarius." 12. What were the provisions of the Lex Paloidia and the Senatus- onsultum Pegasianum i INSTITUTES or JUSTINIAN. Tbanblate : 1. Beginning, Non tamen cuicnmque volenti manumittere licet : etc. Ending, vel qui, datis libertatibus, desiturus est solyendo esse. -Lib. I. tit. 6. 2. Beginning, Est autem capitis deminutio prioris status mutatio : etc. Ending, est capite deminutus. — Lib. i. tit 16. 3. Beginning, Is vero, ad quem ususfruetus fundi pertinet, etc. Ending, Recte enim colere, et quasi bonus paterfamilias uti, lebet.— Lib. ii. tit. 36. 4. Beginning, Liberis suis impuberibus, etc. Ending, id est, duariun hsereditatum.— Lib. ii. tit. 16. DIGEST, Book I., Tit. n. Tbanslate : Beginning, Pacturus legum vetustaium interpretationem, etc. Ending, evidentiorem praestant intellectum. Beginning, Post originem juris et processum cognitum, etc. Ending, non erat fas ultra sextum mensem retinere. Beginning, Et quum plaouisset leges quoque ferri, etc. Ending, Ita rursus respublica suum statum recepit. Beginning, Servius quum in causis orandis primum locum, etc. Ending, reliquit autem prope centum et octoginta Kbros. 1. What is meant by the Municipal Law of England? Into what two classes is it divisible ? 2. Define " tenement," " hereditament," " chattel." 3. Distinguish between the "absolute" and "relative" rights of in- iividuals. * i. Mention any recent instance of a conflict between the Courts of Law md the House of Commons in regard to privilege asserted by the latter. 6. What is the ordinary twofold division of property ? 6. " Caveat Emptor." Put cases illustrating the legal meaning of this onaxim. 7. When are slanderous words actionable without proof of special damage? B.L. EXAMINATION. 177 8. What is the Writ of Habeas Corpus ad sulg'iciendum ? XTuder what circumstances is it e£Eicacious ? 9. Mention instances to shew that mercantile usages and customs have become blended and incorporated with our Commoil Law. 10. In what respects does a " simple" differ from a " special" contract? 11. " Nemo debet bis vexari pro eadem causa." How is this maxim to be understood ? Are there restrictions on its appUcabiUty ? 12. Put various states of facts in each of which an act primd facie criminal may be excused or justified. 13. What right is vested by our Common Law in the finder of lost property? 14. What is the supposed derivation of the term " felony" ? And what incidents are peculiar to it under our Common Law ? GENEEAL JUEISPEUDENCE AND HINDOO AND MOHAMMEDAN LAW. 1. Give Bentham's definitions of the Principle of Utility, and of Sym- pathy and Antipathy. State your reasons for approving or condemning these principles. 2. Define the Sanction of a Law, and mention Bentham's four Sanctions. 3. Distinguish between ' direct' and ' indirect' methods of preventing crime. HINDOO LAW. 1. A MAN having two sons leaves all his property to the younger ; is this gift valid ? If the gift has been made, can it be set aside ? 2. What is the general principle of law (applicable to alt the schools,) with reference to the order of succession ? What is the true meaning of this principle ? 3. Does the Boman and English maxim ' consensus non concubitus facit nuptias' hold any place in the Hindoo jurisprudence ? What is the pecu- liarity of the Asura and Gdndharva marriages ? i. State briefly the legal position of an adopted son with reference to (a) his natural and (6) his adoptive family. 5. Which of the maxims ' caveat emptor,' ' caveat venditor' is recognized in the Hindoo law of contracts ? A walks into JS's shop and asks to look at a piece of cloth, which on inspection is perfectly good ; A accordingly orders it to be sent to his house, but instead of that piece of cloth another of an inferior description is forwarded : what remedy has A got in this case ? besides that remedy, can B be punished in any way ? MOHAMMEDAN LAW. 1. In the Mohammedan law of inheritance what is meant by the ex- pressions Increase and Ketum? 2. What is the rule with reference to ' commorients' i Does it resemble at all the English rule on the subject ? 3. How is the Contract of sale effected ? What is the Mohammedan rule on the subject of warranty? 4. How far is consent necessary to the Mohammedan contract of marriage ? What are the conditions required of the contracting parties ? 5. Two persons having entered into a contract by deed, a dispute arises between them ; at the trial the deed is offered in evidence, but is found to be informal : what is the effect of such informality upon the contract ? N 178 FIRST M.B. EXAMINATION. HAILAM, CONSTITUTIONAL HISTOET OP ENGLAND. 1. On -what grounds did the Parliament limit the King's revenue, and how far -vras his consequent ' dissatisfaction' reasonable ? Explain the general principle of an Appropriation Act, such as was then passed. 2. How was the resumption of the King's Irish grants Reeled ? Does he appear to have been guilty of an unconstitutional act on this or on any other occasion ? 3. What was in William's time, and what is now, the state of the law ofHbel? 4. What led to the anti-popery Act of 1700 : what were its provisions, and why does Hallam stigmatize it as " disgraceful" ? 6. Give a sketch of the original constitution of the Privy Council, and of the way in which it became superseded by the Cabinet. 6. What was originally the distinctive character of ' whigs' and ' tories' ? What does Hallam mean by calling the Act of Settlement " the complement of the Revolution and the Bill of Eights" ? 7. Discuss the justice of the impeachments of Oxford and Bolingbroke, and state the points in dispute between the Houses in the case of Ashby and White. 8. What attempts have been made, and on what grounds, to establish triennial Parliaments ? What was, and is, meant by ' parliamentary privi- lege' ? Mention any important cases on record of commitment for breach of privilege. 9. Give a brief account of the Scottish Court of Session. 10. How was the state of Scotland, and how was that of Ireland, es- pecially affected by the fall of the Stuarts ? EXAMINED AND APPEOVED. Brjgstock Trin. Buck Clare Climenson Trin. Hall Hagd. Hopkins Emm. Mac Laughlin Magd. Porch Trin. Salts Joh. Tremaine Pet. Westby FIRST M.B. EXAMINATION, May, 1861. EXAMINEES: '?' W. Clark, m.d.. Trinity College. H. J. H. Bond, m.d., Corpm College. H. B. IjEeson, M.A., Caim College. W. H. Dkosieb, m.d., Caius CoUege. C. Lestourqeon, M.A., Trinity College, C. C. BABQtoioir, M.A., St. John's College. G. D. LrvEiNO, M.A., St. John's CoUege. CANDIDATES. W. B. Cheadle B.A. Caius J. J. Mackenzie. J. C. Fish B.A. Caius Caius HUMAN ANATOMY AND PHYSIOLOGY. 1. Give the origin and insertion of the muscles acting on the eyeball ; state distinctly! the various movements produced by these muscles, and the sources from whence they derive their Nerves. FIKST M.B. EXAMINATION. 179 2. Give the anatomy of the Testis ; where is this organ situated ip. foetal Life, and how is the Tunica Vaginalis formed ? 3. Mention briefly the points of attachment of the Diaphragm. State accurately the situation of its openings ; and enumerate the objects which respectively pass through them. 4. Describe briefly the course of the pneumo-gastrio nerve and its prin- cipal branches. What inferences have been drawn &om experiment regard- ing its function ? 5. How are the two sounds of the Heart produced i and what theories have been formed regarding the cause of its rhythmical action ? 6. Show irom Anatomy and experimental inquiry that the fifth pair of nerves resembles a spinal nerve, and give the situation of the various Gan- glia met with in the course of these nerves. 7. What do you understand by the term Vascular glands ? State what is known of the minute Anatomy and function of any one of them. 8. A segment of a transverse section of a long bone (properly prepared) is placed under a microscope ; explain fully (illustrated if you please by dia- gram) the objects presented to view. How are long bones said tp increase a. In length. b. In breadth? 9. Give a general description of a rib. Point out some of the pecu- liarities by which the ribs are distinguished one irom another, and the object gained by such diflerenoes. 10. Describe the shoulder-joint. State accurately the humeral attach- ment of those muscles immediately surrounding it, and the influence which each of them has upon the motion of the joint. 1 1. Give the origin, and describe the course of the arteries which supply the large and small intestines with blood, and mention the principal situa- tion of BruTiner's, Feyer's, and the Lieberkiihnian glands. 12. In dissecting the Neck, what are the various objects progressively brought into view in order to expose the Scalenus Anticus muscle i COMPAEATIVE ANATOMY AND PHYSIOLOGY. 1. Describe the paxticulais of structure which shew that the Bchi- noderms form a group of animals essentially separate from the Polyps and Acalephs. 2. What difierence of position with regard to the skeleton is assumed by the nerves and the ambulacral canals in the EcMni and the Asterise ? 3. Shew that the nervous ring surrounding the mouth of Echinoderms does not represent the ring surrounding the oesophagus of Arthropods and Molluscs ; or, otherwise, state in what position the central parts of the nervous system are to be found in the first named group. 4. A respiratory organ may be formed in any part of an animal where the circulating fluid can be brought into near contact with the medium in which the animal lives. Illustrate this by noting the position of the respi- ratory organs in several orders of Crustaceans. 5. Describe, in the common cockle, the pallial chamber vrith its syphons, the course of the afferent current which conveys the oxygen for respiration : the passage of that currant into the intra-branchial chamber (which describe) and its exit thereirom into the expiratory portion of the pallial chamber. What is the moving force which effects the passage of the fluid inwards and outwards ? 6. In these Molluscs is the heart arterial or venous ? In the dibranchiate Cephalopods what additional moving power is introduced ? 7. Name the lobes, single or in pairs, which make up the brain in 180 FIRST M.B. EXiMlNATIOK, osseous fishes. What parts of the brain of Mammals do they represent, according to the observation of the ftetal development in the latter ? 8. Of what bones in Birds is the osseous belt composed to which the Humerus is appended ? 9. By what considerations are hoiiiologous parts or organs determined in animals, by what analogous parts ? In what animals alotie can relations of homology exist ? Are the following analogous or homologous organs, viz. the gills of a fish and the lungs of a bird— the wings of a bird and the pectoral fins of a fish i MATEEIA MEDIOA AND PHAEMAOY. 1 . In collecting the different parts of plants, to be used as medicine, what rules should be observed as to the time of gathering, the preparation, and the preservation of them ! 2. Describe the usual processes for the preparation of Tinctures. What menstrua are used, and how may the strength of these be conveniently tested ? 3. What is the general character of Mixtures in Pharmacy? Give some examples of mixtures. Why should they be made at the time they are prescribed ? 4. In -what different forms is Iron used in Medicine, with what views, and in what doses ? 5. What do you consider to be the usual modes of operation of such medicines as increase particular secretions ? Apply your views to explain the operation of mercurial preparations. 6. Which of the following infusions — Inf. Calumbae, Inf. Cinchonas, Inf. Khei, Inf. Rosse, — are chemically incompatible with Sulphate of Iron, Carbonate of Soda, Tartrate of Antimony, and Bichloride of Mercury severally, and with each other ? Give instances of medicines which are sometimes prescribed with advantage though they contain substances that react on one another ; account for this. 7. In what doses are the following given, and what are their several physiological effects — Camphor, Jalap, Acid. Sulph. Dil., Sp. Ammon. Arom., L iq. Ammon, Acet. Magnes, Sulphas, Quinse. Disulph., Ol. Eioini., Tinct. Digital ? 8. In what forms is Iodine most often used internally, and in what doses ? What inconveniences are likely to attend a too free use of it ? 9. Why is the strength of medicinal Hydrocyanic Acid very liable to vary ? What precautions should be taken in preserving it S Which of the various modes of preparing it do you prefer, and why ? 10. Explain the advantages of combining in the same medicine substances the operation of which is similar. Give examples. In addition to the above there was a viva voce Examination. PATHOLOGY. 1. Define, in reference to Pathology, the following terms instancing each, Temperament, Predisposition, Diathesis, Type, Dyscrasia, Cachexy, 2. In what does the essential nature of true Hypertrophy consist distin- guishing it from the spurious form ? What are its causes ? To what extent does hypertrophy of organs affect their functions ? Describe some of its occasional effects on contiguous organs. 3. What are the physical characters of pus f What its chemical re-action? Give the microscopical description of the pus-corpuscle before and after FIRST M.B. EXAMINATION. 181 treatment by acetic acid. Can it be distinguished from a mucous or lymph corpuscle ? What changes does pus undergo in a chronic abscess or cyst ? i. What condition o? the minute arteries of the brain is frequently met ■with in cerebral apoplexy ? Describe the appearance of an old apoplectic clot when the patient has survived the attack a considerable time. 6. How do you distinguish true ossification from mere calcareous dege- neration ? In vfhat localities or organs are they severally most frequently met with ? What is eburnation and where is it usually found ? 6. Specialize the different pathological states or lesions which severally impair each of the following conditions necessary for maintaining the normal state of the respiratory fimction, viz. — Ingress of the air to the hmgs gene- rally — its access to the vesicular structure — circulation of the blood through the capillaries of the vesicle— the alternate expansion and contraction of the lungs as dependant firstly on the. pulmonary structure itself and secondly on the mechanism of the thorax — innervation and cerebral influence. 7. To what disorders primary and secondary, and to what structural changes are the lymphatic glands especially hable? Does the minute anatomy of these organs, as at present ascertained, throw any light on the peculiarity of their pathology ? 8. What are the chief pathological conditions determining the softening of organs, especially of the brain, stomach, liver, and spleen i Describe briefly this kind of lesion as it presents itself in each of these organs res- pectively. 9. Mention the causes which most usually give rise to anamia. What are the general symptoms attending it ? How do you account for the in- creased excitability of the nervous system which frequently accompanies it ? 10. Point out the several states or conditions of secreting organs that conduce severally to excessive or defective secretion. Explain, with ex- amples, how defective secretion may become a source of constitutional disturbance, when the secreting organs are excretory also, 11. Describe briefly the different morbid changes in structure and form that are foiind to occur in the valves of the heart, pointing out the causes that may induce these, and the sets of valves most frequently affected by each, 12. Give an account of the various morbid states that may give rise to Hsematemesis. How will the prognosis be modified where it can be made out to which of these the haemorrhage is due? CHEMISTEY. 1 . Explain the decomposition of water by Zinc and Sulphuric Acid, and give a symbolic formula thereof, 2. How are the Sulphates of Magnesia, Lime, Baryta, and Strontia to be chemically distinguished from each other 9 3. Describe and explain the preparation of Iodine. 4. How may Potash and Soda and their salts be mutually distinguished ? 6. Mention some of the most common natural products which contain Sulphur, stating the other substances with which it is combined in each case. Describe and explain one or more methods of preparing alkaline sulphides. 6. Give an account of the properties of Carbonic Acid ; and explain how it may be detected in a mixture of gases. How may it be distinguished from Carbonic Oxide, from Nitrogen, from Sulphurous Acid, from Cyanogen ? 7. State the chemical constitution of the rust of iron, and of copper. Explain how " galvanized iron" is able to resist the action of the atmosphere. 8 . What is the action of Chlorine upon the following substances : ( 1 ) Soda, (2) Protosulphateoflron, (3) Hydrosulphuric Acid, (4) absolute Alcohol? 182 SECOND M.B, EXAMINATION. 9. Besciibe tind explain the preparation of Tartaric Acid. Why is it said to be a bibasic acid? State the constitution of tartar- emetic, and point out the anomaly in its constitution, and mention some analogous compounds. 10. What is wood-spirit, and how obtained? Compare its chemical relations with those of Alcohol. 11. Describe the preparation and properties of defiant gas. 12. 10 graios of Acetate of Silver yielded by incineration 6-462 grains of pure silver, and another 1 grains yielded by combustion with Oxide of Copper, 5'277 grains of Carbonic Acid, 1"620 grains of water ; deduce from thence the equivalent and formula of Anhydrous Acetic Acid. 13. What are the four principal Types to which Oerhardt refers organic compounds ? 14. How may the quantity of Alcohol in fermented liquors be readily determined without distillation i There was alio a practical examination in anah/sis. EXAMINED AND APPEOVED. W. B. Cheadle B.A. Caius { J. J. Mackenzie Caius J. C. Pish B.A. Caius SECOND M.B. EXAMINATION, May, 1861. EXAMmEBS : H. J. H. Bond, m.d., Corpus College. W. W. PiSHBR, M.D., Dawning College, H. J. HiviiANii, M.D., Pembroke CoUege. J. J, Mackenzie Caius T. B. Partridge B.A. Joh. CANDIDATES. W. W. W. Andrew B.A. Caius P. W. Latham B.A. Down. K. Liveing M.A. Christ's SURGICAL DISEASES AND OBSTETEICAL MEDICINE. 1. What local effects are produced by Scalds and Burns, and how would you treat them } To what constitutional symptoms and internal lesions do deep-spated Bums generally give rise ? 2. What do you understand by the term Abscess ? In what respect does the Abscess arising from the common boil differ from that arising &om a scrofulous affection of a subcutaneous gland ? What is your opinion respecting the opening of Abscesses in general ? and mention some of the cases in which that treatment ought to be adopted. 3. Describe the symptoms which distinguish the following diseases of the eye. Cataract, Glaucoma, Amaurosis. On the lesion of what parts of the eye do they respectively depend i 4. What congenital disorder do the roof of the Mouth and the TJvula sometimes offer, and what inconveniences proceed therefrom ? What symp- toms does an elongated Uvula give rise to, and how would you treat the complaint ? M ention some of the causes on which Dysphagia may depend. 6. Explain the meaning you attach to the following terms, Caries, Exostosis, Necrosis. To what constitutional conditions is Caries most frequently due? SECOKD M.B. EXAMINATION. 183 6. Describe tlie tissues which respecti'vely characterize the following Morbid Growths, Polypi, Schirrous Cancer, Medullary Sarcoma. What effects do they give rise to in the neighbouring parts ! Is the removal of them by means of an operation usually followed by permanent success ? 7. To what disease is the term Hernia Humoralis applied, and on what causes does it chiefly depend ? How would you distinguish it from Hydrocele ? In what does the operation for the cure of the latter disease consist ? 8. State your opinion respecting the ef&cacy of Paracentesis in Empyema and Ascites. 9. On wbat local and general conditions may Leucorrhoea depend 5 By what means may ulceration of the Os Tinese be observed and what treat- ment is usually adopted in such cases i Describe the symptoms which accompany Prolapsus TJteri. 10. Describe the stages of Natural Labour. What conditions in Labour require the interference of art, either by the hand alone, or armed with the forceps ? To what complaints is the female peculiarly liable after parturition? 11. In what parts is the Embryon usually lodged in Extra-Uterine Pregnancy? Mention the disorders of development the foetus most fre- quently exhibits, and describe the conformation of the skull in congenital Hydrocephalus . 12. What is meant by the term Abortion, and ■?rbat precautions should females, who have been subject to miscarriage, take during pregnancy ? MEDICAL JTJEISPEUDENCE. 1 . Describe the symptoms of poisoning by Opium : and mention the tests for Morphia and Meconic acid, 2. What do you consider to be a poisonous dose of the extract of Belladonna ? What are the symptoms of poisoning by this substance, and the most appropriate treatment ? 3. In what respect does Oxalic acid differ from other vegetable acids ? Por what salt is it occasionally mistaken, and how would you detect its presence in an organic mixture ? i. Mention the different salts that are usually contained in spring water, and state how each may be detected. 5. Explain the various modes of dying by Asphyxia, Asthenia, Syncope, and Co/reo ; and describe the post mortem appearances found in each case. 6. In the case of a dead body found submerged in water, how would you determine whether or not death was caused by drowning ? 7. What means would you adopt for restoring animation in a body that presented the characters of apparent death from submersion in water ? 8. What is the meaning of the term atelectasis ; and from what causes is it supposed that this condition may proceed ? 9. Enumerate the various predisposing and exciting causes of Insanity : and name those diseases that are most Uable to be mistdcen for this affection. 10. Indicate the leading symptoms of the following forms of Insanity, Mania, Monomania, Dementia, and Amentia. PATHOLOGY AND PEACTICE OP PHYSIO. 1. Compare the physical conditions presented by the lung or a portion of lung in cadaveric congestion, oedema, first and second stage of pneumonia, and pulmonary apoplexy. 2. What are the various conditions to which Hmmatwia may b& referred ? State the diagonsis and the appropriate treatment in each of the varieties of its occurrence. 184 SECOND M.B. EXAMINATION, 3. Give the diagonsis between ascites, pregnancy, and ovarian dropsy ; and describe succinctly the different varieties of ovarian tumors. 4. What are the local peculiarities of the acute inflammation in gout? What are the physical characters and chemical nature of the so-called chalky cleposits? What tissues do they principally invade, and how are they distinguishable irom the lesions produced by rheumatic arthritis ? What are the conditions of the blood and the urine in gout, and how according to recent views do these conditions suggest an explanation of its pathology ? 5. What are the symptoms, pathology, and treatmentof lead-poisoning? What other disease does it occasionally predispose or give rise to ? 6. State some of the principal grave disorders, general or local, which are simulated by hysteria, and how in each case the diagnosis may be determined. 7. As a general rule in Therapeutics in what class of diseases and in what stage of the same disease would you enjoin bodily rest, and on the contrary under what circumstances would you recommend bodily exertion ? 8. How do you explain the frequently almost entire absence of fat in the diabetic patient ? Describe the different modes in which various organs are invaded by a morbid development of fat. Can you trace any correspon- dence between these differences and the different modes under which fat or its analogues permanently or temporarily occur as normal constituents or products of various tissues or organs r 9. Can you assign any probable explanation to account for the stage of incubation in certain diseases, as in variola, scarlatina, hydrophobia ? Des- cribe the different phases, with their dates, of the variolous pustule, and give the diagnosis between the efflorescence of scarlatina and rubeola. 10. What treatment would you adopt in protracted cases of BrigMs disease ? What is the significance of the diminution of the albuminuria and decrease of the specific gravity of the urine when they are observed to occur in the course of this disease ? 11. Describe an attack oi cynanche parotideea. What grave disorders are occasionally incidental to it ? 12. Describe a paroxysm of onjimi^ecio/'ts. How would you treat it ? EXAMINED AND APPEOVED. W. W. W. Andrew B.A. Caius J. J. Mackenzie Caius P. W. Latham B.A. Down. T. B. Partridge B.A. Joh. E. Liveing M.A. Christ's W. UETOALFB, FRINTSB, OKEKH eVREETj CAMBRIDGE. MACMILLAN AND CO.'S FOR COLLEGES AND SCHOOLS, The series o/Cambridge Class-Books fok the use op Colleges and Schools, which heme been issued at intervals during the last ten years by Macmillan and Co., is intended to embrace all bramches of Mathematics, from the most elementary to the most advanced, and to keep pace with the latest discoveries in mathematical science. Of those hitherto ptoblished the. sale of many thousands is a sufficient in- dication of the manner in which they have been appreciated by the public, A further series of a more simple character, adapted to the use of the lower classes in schools, is in course of preparation. 1. Arithmetic and Algebra in their Prin- ciples and Applications. WITH NTJMEEOUS EXAMPLES, SYSTEMATICALLY ARRANGED. £y BARNARD SMITH, M.A. Fello-w of St. Peter's College, Cambridge. Eighth. Edition. 696 pp. (1861). Crown 8vo. strongly hotmd in cloth. I OS. 6d. The first edition of this work was published in 1864. It was primarily- intended for the use of students in the Universities, and for Schools which prepare for the Universities. It has however been found to meet the requirements of a much larger class, and is now in use in a large number of Schools and Colleges both at home and in the Colonies. It has been found of great service for students preparing for the Middle-Class and Civil and Military Service Examinations, from the care that has been taken to elucidate the principles of all the Eules. Testimony of its excellence has been borne by some of the highest practical and theoretical authorities ; of which the following from the late DEAN PEACOCK may be taken as a specimen. " Mr. Smith's "Work is a most useful publication. The Rules are stated with great clearness. The Examples are well selected and worked out with just sufficient detail without being encumbered by too minute explanations ; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work." 1000. 23 12. 61 2 CAMBRIDGE CLASS BOOKS 2. Arithmetic for the Use of Schools. By BARNABB SMITE, M.A. New Edition (1861), 348 pp. Crown 8to. strongly bound in clotJi. 4«. 6d. Answers to all the Questions. KBIT to the above, containing Solutions to all the Questions in the latest Edition. Crown 8vo. 392 pp. Second Edition. ( 1 860). 8s. 6d. EXERCISES IN" ARITHMETIC. 104 pp. Crown 8vo. (i860) 2«. Or with Answers, 2«. %d. Also sold separately in 2 Parts price 1«. each. Answees, &d. To meet a widely expressed wish, the ARITHMETIC was published separately from the larger work in 1851, with so much alteration as was necessary to make it quite independent of the ALGEBRA. It has now a large and increasing sale in all classes of Schools at home and in the Colonies. A very copious collection of Examples, under each rule, has heen embodied in the work in a systematic order, and a Collection of Miscellaneous Papers in all branches of Arithmetic hare been appended to the book. The EXERCISES have been published in order to give the pupil examples of every rule in Arithmetic, and a great number have been care- fully compiled &om the latest University and School Examination Papers. 3. Algebra. FOE THE USE OF COLLEGES AND SCHOOLS. - By I. TOBMUNTJER, M.A. Fellow and Head Lecturer of St. John's College, Cambridge. Second Edition. 516 pp. (i860), strongly bound in cloth. 7«. 6d. This work contains aU the propositions which are usually included in elementary treatises on Algebra, and a large number of Examples for Exercise. The author has sought to render the work easily intelligible to students without impairing the accuracy of the demonstrations, or contracting the limits of the subject. The examples have been selected with a view to illustrate every part of the subject, and as ihe number of them is about sixteen hundred amd fifty, it is hoped they will supply ample exercise for the student. Each set of examples has been carefully arranged, commencing with very simple exercises, and proceeding gradually to those which are less obvious. Hacmillan and Co. FOR SCHOOLS AND COLLEGES. 3 4. Arithmetic in Theory and Practice. FOR ADVAKCED PUPILS. By J. BROOK SMITH, M.A. St. Jolm's College, Cambridge. Paet I. Crown 8vo. cloth. 3s. 6fl!. This ■work forms the first part of a Treatise on Arithmetic, in which the Author has endeavoured, from very simple principles, to explain in a fuU and satisfactory manner all the important processes in that subject. The proofs have in all cases been given in a form entirely arithmetical : for the author does not think that recourse ought to be had to Algebra until the arithmetical proof has become hopelessly long and perplexing. At the end of every chapter several examples have been worked out at length, in which the best practical methods of operation have been care- fally pointed out. 5. A Short Manual of Arithmetic. By C. W. UNDERWOOD, M.A. Vice-Principal of the Collegiate Institution, Liverpool. Fop. 8vo. 96 pp. (i860), limp cloth. 2s. 6(?. The object aimed at by the Compiler of this Mamual is to bring before jimwr students so much of the Theory of Arithmetic as may be fairly ex- pected of them, and to present it in such a form that the study of th^ Science may become to some extent a wrnitaJ, training. It is rather a Gramma/r of Arithmetic than a treatise on that subject, and should for the most part be committed to memory. It will be found well adapted for vv>& voce examination, and enable candidates to prepare themselves for the Local University Examinations. The Definitions are briefly and carefully worded. Each rule is stated so as to include the proof of it where this was possible, Cambridge and lioudon. 4 CAMBEIDGE CLASS BOOKS 6. Plane Trigonometry. FOE SCHOOLS AND COLLEGES. By I. TODHUNTER, M.A. Second Edition. Crown 8vo. 279 pp, (i860), strongly bovind in cloth. 5s. The design of this vork has heen to render the suhjeot intelli- gihle to beginners, and at the same time to afford the student the opportunity of ohtaining all the information which he mil require on this branch of Mathematics. Each chapter is foUowed by a set of examples; those which are entitled Miscellaneous ExampUa, together with a few in some of the other sets, may be advantageously reserved by the student for exercise after he has made some progress in the subject. As the Text and Examples of the present work have been tested by considerable experience in teaching, the hope is entertained that they will be suitable for imparting a sound and comprehensive knowledge of Plane Trigonometry, together with readiness in the application of this knowledge to the solution of problems. In the Second Edition the hints for the solution of the Examples have been considerably increased. 7. Spherical Trigonometry. FOR THE TTSE OF COLLEGES AND SCHOOLS. By I. TOBETJNTER, M.A. 112 pp. Crown 8vo. (1859), strongly boimd in clotli. 4*. 6rf. This work is constructed on the same plan as the Treatise on JPlane Trigonometry, to which it is intended as a sequel. Considerable labour has been expended on the text in order to render it comprehensive and accurate, and the Examples, which have been chiefly selected from University and College Papers, have all been carefully verified. Macmillan and Co, FOR SCHOOLS AND COLLEGES. 5 8. Plane Trigonometry. An Elementajet Teeatisb. "WITH A NUMEROUS COLLECTION OF EXAMPLES. By B. B. BBASLEY, M.A. Head Master of Grantliam School. io6 pp. (1858), strongly bound in cloth. 3*. 6d. This Treatise is specially intended for use in Schools. The choice of matter has been chiefly guided by the requirements of the three days' Examination at Cambridge, with the exception of proportional parts in logarithms, which have been omitted. About four hundred examples have been added, mainly collected from the Examination Papers of the last ten years, and great pains have been taken to exclude from the body of the work any wmoh might dishearten a beginner by their difficulty. 9. Plane and Spherical Trigonometry. ■WITH THE CONSTRUCTION ANB USE OF TABLES OF LOGARITHMS. By J. 0. SNOWBALL, M.A. Late Fellow of St. John's College, Cambridge. Ninth Edition, 240 pp. (1857). Crown 8to. 7*. dd. In preparing a new edition, the proofs of some of the more im- portant propositions have been rendered more strict and general ; and a considerable addition, of more than two hundred examples, taken principally from the questions in the Examinations of Colleges and the University, has been made to the coUeetiou of Examples and Problems for practice. Cambridge and Loudou. CAMBRIDGE CLASS BOOKS 10. Elementary Treatise on Mechanics. WITH A COLLECTION OF EXAMPLES. By 8. PARKINSON; B.B. Fellow and Praelector of St. Jolin's College, Camtridge. Second Ediiioic. 345 pp. (1861). Crown. 8vo. cloth.. qs.dA. The Author has endeavoured to render the present Tolume suitable as a Manual for the junior classes in TTniyersities and the higher classes in Schools. With this object there have been included in it those portions of theoretical Mechanics which can he conTeniently investigated without the Differential Calculus, and with one or two short exceptions the student is not presumed to require a knowledge of any branches of Mathematics beyond the elements of Algebra, Geometry and Trigo- nometry. A collection of Problems and Examples has been added, chiefly taken from the Senate-House and College Examination Papers — which will, it is trusted, be found useful as an exercise for the student. In the Second Edition several additional propositions have been incorpo- rated in the work for the purpose of rendering it more complete, and the Collection of Examples and Problems has been largely increased. 11. Elementary Hydrostatics. WITH NUMEEOXJS EXAMPLES AND SOLUTIONS. By J. B. PHEAR, M.A. Fellow and late Mathematical Lecturer of Clare College. Second Edition. 156 pp. (1857). Crown 8to. cloth, ^s. 6d. "An excellent Introductory Book. The definitions are very clear; the descriptions and explanations aie sufficiently fuU and intelligible ; the investigations are simple and scientific. The examples greatly enhance its value." — Enslish JotonaIi op Education. This Edition contains 147 Examples, and solutions to all these ex- amples are given at the end of the book. SCacinillan and Co. FOE SCHOOLS AND COLLEGES. 7 12. Analytical Statics. WITH NUMEEOtrS EXAMPLES. By I. TOBRVNTER, M.A. Second Edition. 330 pp.. (1858). Crown 8 vo. cloth. lOs. 6(?. In this ■work will be foimd all the propositions which nsually appear in treatises on Theoretical Statics. To the different chapters il&les are appended, which ha^ve been selected principally &om the University and OoUege Examination Papers ; these will furnish ample exercise in the application of the principles of the subject. 13. Dynamics. A Treatise. By "W. P. WILSOK, M.A. Professor of Mathematics in the tTniversity of Melbourne. 176 pp. (1850). 8vo. 9«. 6(jt. This Treatise contains the fundamental principles of the science, with their application to the motion of particles and to the simpler cases of the motion of bodies of finite magnitude. 14. Dynamics of A Particle. "WITH NUMEROUS EXAMPLES. By P. G. TAIT, M.A., and W. J. STEELE, B.A. Late FeUows of St. Peter's College, Cambridge, 304 pp. (1856). Crown 8vo. cloth. io«. 6cl. In this Treatise will be found all the ordinary propositions connected with the Dynamics of Particles which can be conveniently deduced without the use of D'Alembertf s Principles. Throughout the book will be found a number of iUustratiTe Examples introduced in the text, and for the most part completely worked out ; others, with occasional solutions or hints to- assist the student, are appended to each Chapter, Cambridge and Loudon. ' 8 CAMBEIDGB CLASS BOOKS 15. A Treatise on Attractions, La Place's Functions, and the Figure of the Earth. By J. H. PRATT, M.A. Archdeacon of Calcutta, late Pello-w of GonTille and Caius College, Cambridge. Second Edition. Crown 8to. 126 pp. (i 86 i). cloth. 6s. 6d. In the present Treatise the author has endeavoured to supply the want of a work on a subject of great importance and high interest — -La Place's Coefficients and Functions and the calculation of file Figure of the Earth by means of his remarkable analysis. No student of the higher branches of Physical Astronomy should be ignorant of Laplace's analysis and its result — " a calculus," says Airy, " the most singular in its nature and the most powerful in its appUoation that has ever appeared." 16. Dynamics of A System of Rigid Bodies. ■WITH NUMEROUS EXAMPLES. By HBTFABl) JOEN ROUTS, M.A. Fellow and Assistant Tutor of St. Peter's College, Cambridge. 33(5 pp. (i860). Crown 8vo. cloth. io«. 6d. Contents: Chap. I. Of Moments of Inertia. — II. D'Alembert's Prin- ciple. — III. Motion about a Fixed Axis. — IV. Motion in Two Dimen- sions. — V. Motion of a Eigid Body in Three Dimensions. — VI. Motion of a Flexible String. — ^VII. Motion of a System of Rigid Bodies. — ^VIII. Of Impulsiye Forces. — IX. Miscellaneous Examples, The numerous Examples which will be found at the end of each chapter have been chiefly selected from the Examination Papers set in the University and Colleges of Cambridge during the last few years. ISacmillaii and Co. FOE SCHOOLS AND COLLEGES. 17. A Treatise on Optics. By S. PARKINSON, B.B. Tellow and Assistant Tutor of St. Jolin's College, Cambridge. 304 pp. (1859). Crown 8to. ios. 6d. The present work may be regarded as a new edition of the Treatise on Optica, by the Eev. W. N. Griffin, •which being some time ago out of print, was very kindly and liberally placed at the disposal of the author. The author has freely used the liberty accorded to him, and has re-arranged the matter with considerable alterations and additions — especially in those parts which required more copious explanation and illustration to render the work suitable for the present course of reading in the University. A collection of Examples and Problems has been appended, which are sufficiently numerous and varied in character to affijrd an useful exercise for the student : for the greater paxt of them recourse has been had to the Examination Papers set in the University and the several Colleges during the last twenty years. Subjoined to the copious Table of Contents the author has ventured to indicate an elementary course of reading not unsuitable for the require- menta of the First Three Days in the Cambridge Senate House Ex- aminations. 18. Geometrical Treatise on Conic Sections. WITH A COPIOUS COLLECTION OF EXAMPLES. By W. S. BREW, M.A. Second Master of Blackheath School. Second Edition. Crown 8vo. cloth. 4*. 6y By n. A, JslUii,UA:N', M.A. Iji; pp. ^ SENATE-HODHE MATHEMATICAL PKt ISif-"!. Th Tl^l;K,i': \ \ i \\