1. Arithmetic (14 hours), including practice, proportion, percentage, square root, simple interest, the metric system, vulgar and decimal fractions. Candidates for the Lower Grade in Mathematics will be at liberty to take the Arithmetic paper of either the Higher or Lower Grade. When Higher Arithmetic is taken, special mention will be made on the Certificate. 2. Algebra (1 hours), including fractions, factors, square root, equations of the first degree, simultaneous equations of the first degree, easy quadratic equations, easy quadratic surds, problems leading to the above equations. 3. Geometry (2 hours). The subject matter of Euclid, Books I, II, and III, with easy deductions. Demonstrations other than Euclid's will be accepted if they assume no propositions which in Euclid's order are subsequent to the proposition under consideration. Candidates for the Lower Grade may also take the paper in Elements of Dynamics, success in which will be endorsed on the Certificate. No candidate will be allowed to pass in Dynamics who does not pass in Mathematics. The papers in Geometrical Conics, Analytical Geometry, and Higher Dynamics cannot be taken by candidates for the Lower Grade. Higher Grade. To pass in the Higher Grade, a candidate must, at the same examination, pass in each of the four following subjects, † but deficiency in any one paper may, to a certain extent, be compensated by excellence in others. The candidate may also take one or more of the additional subjects, success in which will be endorsed on the Certificate. (Only one additional subject should, as a rule, be taken at this stage.) 1. Arithmetic (14 hours). The whole subject, including questions on Theory. * 2. Algebra (1 hours), including the subjects of the Lower Grade with harder examples, and in addition simultaneous quadratic equations, theory of indices, definitions of cyclical order, symmetry, &c., transformations and identities, test of divisibility by simple factors, ratio, proportion, variation, progressions, problems relating to the above subjects. 3. Geometry (2 hours). The subject matter of Euclid, Books I, II, III, IV, VI, and XI (Propositions 1-21), with deductions. 4. Trigonometry and Logarithms (1 hours). Trigonometry as far as the solution of triangles, theory and use of logarithms. Arithmetic. Candidates may be examined in Arithmetic* alone, in either the Lower or Higher Grade. * No candidate in the Lower or Higher Grade of Mathematics will be excused examination in Arithmetic on the ground of having already obtained a Certificate in Arithmetic, or in the Higher Grade on the ground of having passed in Higher Arithmetic when a pass in the Lower Grade in Mathematics was obtained. + Candidates for any grade must take all the papers belonging to that grade, except as mentioned above under Lower Grade Arithmetic. The use of a book of mathematical tables is allowed, provided it contain no manuscript notes or printed matter other than such as refers to the use of the tables, Each candidate should be provided with a separate book, Candidates who fail to pass in Mathematics may be allowed to pass in Arithmetic if they show sufficient proficiency in that subject. Honours. To obtain Honours, a candidate must, at the same examination, pass with credit in each of the four following subjects, but deficiency in any one paper may, to a certain extent, be compensated by excellence in others. 1. Algebra (14 hours), including the subjects of the Higher Grade with more difficult examples, and in addition the elements of indeterminate co-efficients and partial fractions, inequalities, elementary treatment of maxima and minima, permutations and combinations, the binomial theorem, with positive integral indices, the exponential series and elementary cases of recurring series, together with the application of the simplest tests for their convergency or divergency, the graphic representation of simple algebraic functions, and the elementary theory of complex numbers. 2. Geometry (2 hours), including Euclid with deductions, and the following sections of modern geometry:-Line segments (signs of segments, relations among segments); transversals; properties of the centroid and orthocentre of a triangle and of its circumscribed, inscribed, escribed, and nine-point circles; harmonic ranges and pencils; pole and polar; radical axis; similitude; inversion. 3. Trigonometry (14 hours), as far as De Moivre's theorem, with its application to simple series. 4. At least one of the following additional subjects :-Geometrical Conics, Analytical Geometry, Higher Dynamics. Additional Subjects. 1. Elements of Dynamics (1 hours). Velocity, acceleration, the rectilineal motion of a uniformly accelerated particle, the laws of motion, the composition of forces, equilibrium, the centre of mass (gravity), common machines, work and energy, elementary hydrostatics. 2. Geometrical Conics (1 hours). The properties of the parabola, the elementary properties of central conics, the sections of the cone. 3. Analytical Geometry (11⁄2 hours). The straight line, transformation of co-ordinates, the circle. 4. Higher Dynamics (1 hours). The elements of dynamics, as above, treated with the help of trigonometry, Atwood's machine, parabolic motion of a projectile, composition of forces acting on a rigid body, uniform circular motion, impact, kinetic energy, centre of pressure metacentre. No candidate may take any of the additional subjects who is not a candidate in Mathematics, and no credit will be given for success in any of the additional subjects unless the candidate pass in Mathematics. The results of the examination in additional subjects will, however, in all cases be given on the Schedule of Results. * Candidates for any grade must take all the papers belonging to that grade. 5593. С с Book-keeping and Commercial Arithmetic. To pass in Book-keeping and Commercial Arithmetic, a candidate must pass in each of the following papers : :- 1. Book-keeping (2 hours). Candidates will be required to answer easy questions on the principles and practice of Book-keeping, to frame the books necessary to record a number of transactions of moderate difficulty, to adjust ledger accounts, and to frame balance-sheets and profit and loss accounts. Proper books will be provided. 2. Commercial Arithmetic (2 hours). Arithmetic with special reference to discount, interest, exchange, foreign weights and measures, and such questions as are likely to arise in ordinary commercial transactions. An exercise in calculation, involving speed and accuracy, will be given. December, 1901. NOTE AS TO PAPERS IN ENGLISH. Various representations have from time to time been made in connection with the subject of the examination in English, and these representations have been the subject of careful consideration in the light of the experience of past years. My Lords attach great value to these suggestions, made, as they are, by those whose means of judging are large; and, without intending to intimate any serious change in the methods of examination, they think it will be useful to indicate the views which they themselves have adopted on certain points upon which these suggestions bear. My Lords attach very great importance to this part of the examination, holding that mastery of our own language, and the power of lucid and easy composition, are amongst the most valuable elements in higher education. It has been urged that the mental training involved in English Grammar and Analysis is of little value to those who have studied the principles of grammar through an inflected language. But many of the candidates in the Leaving Certificate Examination have not had this opportunity. In their case the grammatical part of the English examination is important, and the subject forms too constant a feature in the curriculum of the Schools to be ignored. For all pupils, on the other hand, the exercise in paraphrasing is of great importance, not only as a mental discipline, but as training the pupil to grasp the real meaning of what he reads, and indirectly assisting him to acquire facility in composition. The subject of the chronological study of English Literature, and of the degree to which it should be recognised in the examination, is one of great difficulty. It is unquestionable that, as it is not infrequently pursued, this study lends itself to superficial and demoralising cramwork, and my Lords regret to find evidence in the examination that this very largely prevails. They are unwilling either to ignore the subject altogether or to adopt the only remaining course of prescribing a special period or special authors for study. This last course would be opposed to the principle upon which the examination has hitherto been based, and my Lords fear that it might tend to introduce a monotony of curriculum which would be hurtful to the Schools. Whether the argu ments in its favour do not counterbalance these disadvantages is a matter on which they prefer to delay coming to a decision until they have some. further experience. In any case, in prescribing a certain period or certain authors it would be necessary to allow considerable breadth of option to the Schools in selecting the work to be taken up. They think that the following are points upon which the most competent judges would be in agreement, and they wish it to be understood that they will prevail in the conduct of the examination: 1st. The chief and most essential requirement in the examination will be a fair power of writing lucid and grammatical English, such as may prove the candidate to have had an adequate training in composition. 2nd. He will be expected to show such power of paraphrasing as may prove that he has been trained to read with care and thought, and to exercise his mental faculties in endeavouring to discover the meaning of a difficult passage. 3rd. He must also show a comprehension of grammatical principles, and a general acquaintance with the leading grammatical rules under some system in current use. 4th. In regard to English Literature, my Lords think that candidates may be expected to have some acquaintance with the authorship and period of the leading masterpieces of our literature. This need involve no multiplicity of biographical or bibliographical detail, and they think it may be acquired with no undue burden of time or labour. But any answers which show that the study of English Literature has been interpreted to mean the committing to memory of lists of authors, and their books,—and the answers of pupils so trained seldom fail, by an occasional absurdity, to give evidence of such training-will be treated with the utmost rigour, and will not be held to compensate for deficiency in the essential parts of the examination. On the other hand, such answers as show independent reading, careful and methodical instruction, or intelligent criticism, will be accorded full weight in adjudging marks in the case of the Higher and Honours Grades. In the Lower Grade, my Lords cannot expect any such results, and they propose that this part of the subject shall form a comparatively unimportant element in the examination in that Grade. 5th. With regard to History and Geography, my Lords have little to add to the remarks which they have made in previous years. These subjects enter largely into the curriculum of many Schools they are required by many of the bodies by whom passes in the Leaving Certificate Examination are recognised; and my Lords are unwilling to do anything which would discourage the continuance of such instruction. They endeavour to give a wide option in the questions set, and to afford opportunity to all who have not entirely neglected the subjects to show a knowledge of them in some branch or other. More than this they have not demanded, and do not propose to demand, as a necessary condition of a pass; but more extensive knowledge will receive ample recognition. December, 1901. 5593. CC 2 NOTE AS TO PAPERS IN MODERN LANGUAGES. My Lords desire to remind School Authorities of the terms of the Circulars issued on 15th June and 1st August, 1901. While neither commercial nor literary questions will in future be included in the ordinary French and German papers of any grade, their Lordships are prepared, in the event of candidates coming forward, to have special papers set in Commercial French and Commercial German. No candidate will be admitted to this separate examination in either language unless he has already passed in the Higher Grade in the language in which he desires to be examined. The general grouping and arrangement of the ordinary papers will henceforth be somewhat as follows:-The papers for the Lower and Higher Grades will each be divided into two sections, instead of several as heretofore. The first section will consist of translation and composition, the second will contain questions in grammar and (in the case of the Higher Grade) such elementary philology as is really helpful in grammatical study. No candidate will be allowed to pass who does not attain a certain minimum in translation and composition. The papers set for Honours will be entirely distinct from that set for the Higher Grade. They will be two in number, the first consisting mainly of composition, and the second of translation and more advanced grammar and philology. My Lords do not propose in the meantime to discontinue the practice hitherto followed of allowing unsuccessful candidates for Honours in Modern Languages to pass in the Higher Grade, provided their work bears witness to a level of attainment corresponding to that required for a pass in the Higher Grade on a Higher Grade paper. Candidates in the Lower and Higher Grades will be required to reproduce in French or German a story that has been read aloud to them in English. This test will not, in future, be applied to Honours candidates. Instead, they will be afforded an opportunity, in the first Honours paper, of showing their powers of free composition in an essay on some simple theme. My Lords are fully alive to the importance of the oral side of Modern Language teaching. In one or two cases they have already refused to admit to the examination candidates from Schools where the report of the Inspector who visits the School shows that pronunciation has been neglected. Their Lordships are of opinion that in the near future it may be both possible and desirable to increase the stringency of their requirements in this respect. December, 1901. NOTE AS TO LATIN AND GREEK PAPERS. My Lords have considered the various remarks submitted to them from time to time in regard to the examinations in Latin and Greek for the Leaving Certificate. In the past, complaints have been made that in certain grades the papers set have sometimes been of undue difficulty. Without pronouncing any opinion as to this, my Lords agree that it is undesirable to set any test which is of an involved or confusing character. But, while anxious to avoid undue difficulty, my Lords cannot hold out the hope that the test applied in judging the answers to such papers as may be set will be relaxed. One of the objections to undue difficulty |