EXTRACTS FROM EXAMINERS' REPORTS.

Mathematics. Rev. Canon Heaviside, M.A.

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There is nothing very striking to call forth any special remarks. There is progress, however, and that of a satisfactory kind. As was anticipated, increased attention to the elementary subjects, which form the sound ground-work of Mathematics, has been the salutary consequence of the changes alluded to. There is even a considerable advance in this respect, as tested by a comparison of the result of this Examination with that of July 1863. I find that by my papers in Section I, on a general total, the average marks obtained by each Candidate in July 1863, were 405 18, whilst in January 1864, this average amounts to 460.74. The marks obtained are not only higher among the best Candidates, but the number of those whose marks are extremely low has sensibly diminished. The papers on Mixed Mathematics are never so well done as the papers Pure Mathematics. The present Examination is no exception to this general rule. Nor, by comparison with the Examination in July 1863, do the marks in Section II, in January 1864, exhibit the same improvement as those in Section I. The average of each Candidate examined by myself gives, in Section II, as a result of marks, for July 1863, 174 29, for January 1864, 163 75. The variation is hardly appreciable; still, I think I discern that the higher subjects have not been made so much a matter of speculation as formerly, and I think I may venture to attribute the improvement in the Obligatory Subjects and the stationary average in the Voluntary Mathematics, to the recognition by the Candidates and their Tutors of the truth, which has been so often urged, that it is far more profitable, even for the purpose of getting marks, to master thoroughly the elementary subjects rather than to hurry on prematurely to the higher departments of Mathematics.

Mathematics. Rev. W. N. Griffin, M.A.

The marks in the First Section have been obtained pretty equally on the subjects which that Section embraces, and, therefore, are the best representation of the attainments of the Candidates in their more elementary work. It is satisfactory that so many of them have learned the use of Trigonometry in practical computations.

Few Candidates gain marks of any significance in my third paper. I can understand that many of them have been induced to read partially the subjects of that paper that they might not have the time allotted to it wholly unemployed; but I am confident that they would have raised the total of their marks by increased power and accuracy in the lower subjects, if they had given to these the time spent on Co-ordinate Geometry and the Differential and Integral Calculus.

The weakness of the Candidates appears to arise from their not having worked examples of sufficient number and variety. In all the subjects, in a measure, I am led to this remark; in the physical subjects especially. I would be far from slighting the effort made, and the improvement gained in mastering demonstrations in books; but with a practical profession in view the habit of applying largely the principles thus acquired is obviously of the highest value.

Free-Hand Drawing.-Rev. W. Kingsley, B.D.

The number of Candidates who have presented themselves for Examination in this subject is thirty-three.

The general result of the Examination shows that for the first time almost all the Candidates have been preparing themselves by a proper course of training; very few of the number have failed in producing good elementary work, though at the same time few have become proficients, none of them probably having given much time to the study. Still there can be no doubt that nearly all who have presented themselves have laid a sound foundation, that will make their progress rapid, if they succeed in obtaining admission into the Academy.

The improvement is mainly in the drawings required by the first six questions of the paper: the model-drawing and drawing from nature being still very defective.

French-Monsieur Alphonse Esquiros.

The worst part of the present Examination is the translation of French into English, whilst on the other hand the most commendable one is the translation of English into French.

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Such a fact is so contrary to what has ever taken place before, that it cannot be allowed to pass unnoticed. As a matter of course, more marks are allotted for Composition than for translating French into English. Induced by the prospect of a greater reward, Candidates have perhaps devoted more time and pains to the former exercise than to the latter, in their course of studies. This tendency has its good and its bad sides. Its good side is obvious, and I was very glad to find attempts in the most difficult part of the Examination invested this time with greater prominence and more success than was formerly the case. It should moreover be borne in mind that translating into French and translating into English are twin branches of the same knowledge. A link which is not to be overlooked exists between both exercises; they must go hand in hand, and by neglecting one or the other, instruction would be injured rather than improved.

Those two objects are so closely connected that they cannot be disunited without affecting the results of the Examination. The best method at schools would be, I think, to practise them simultaneously, in translating the same extract first from French into English, and then from English into French. In doing so, pupils would be enabled to catch better the different tone of both languages. This method is not mine; it has been recommended by an English statesman, who, through such a process, mastered the difficulties of the foreign tongue in a short time.

EXAMINATION PAPERS.

JANUARY 1864.

GEOMETRICAL DRAWING.

LIEUT.-COL. SCOTT, R.E.

[N.B.-The whole of the problems are to be carefully inked in, the constructive lines being shown in dots. These need only be sufficiently prolonged to show the mode of construction adopted.

Full credit will be assigned for the perfect solution of the last 6 questions. Candidates taking up Geometrical Drawing as a subject, and not for qualification only, are therefore recommended to consider these before commencing on the first 4 questions.]

1. Draw a straight line 4 inches long, and divide it, by construction, into 5 equal parts.

2. Describe a circle with a radius of 1 inch, and draw a tangent to it by construction.

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3. Construct a triangle having two of its sides equal to 3 inches and 34 inches respectively, and the angle subtended by the longer side equal to 50°.

The triangle is to be inked in with very fine lines, and the length of the third side and the values of the remaining angles are to be neatly figured on the diagram.

4. Draw a straight line 2 inches long, and on it describe the segment of a circle which shall contain an angle of 55°.

5. Draw two straight lines 24 inches apart, and unite them by two curves of contrary flexure, having radii of inch and 14 inches respectively, in such a manner that the curves shall be tangential to each other, and each one of them tangential to one of the two straight lines.

6. Draw a plain scale of 13 feet to an inch, to show feet and inches. Give its representative fraction..

7. The horizontal distance from a point C, of another point A, 30 feet above the horizontal plane in which C is situated, is 300 feet. The altitude of a point B is 55 feet above the same plane and its horizontal distance from C is 150 feet. The angle included between the lines CA and CB is 55°. Find by construction the value of the horizontal angle between these lines, and neatly figure it on the diagram.

8. Describe a circle with a radius of 2 inches. Assume this circle to be the base of a hemispherical mound 200 yards in diameter. Represent on its surface the plan of a pathway ascending the mound at an inclination of 15.

It will be sufficient to show the pathway in a single dark line, and to determine its position by 8 points.