The following Extracts from the Reports of the Examiners will show the character of the Examination, and may be useful guides to future Candidates.

Mathematics.-Rev. Canon Heaviside, M.A.

So far as the result of my own marks is concerned, irrespective of those of my mathematical colleague, which are not known to me, this Examination will not bear a favourable comparison with that of July 1864. In a previous report I expressed an opinion that as regards the marks obtained by the Candidates in Section I., they had probably reached an average from which there would be, in future, no very considerable departure. The present Examination, however, does not bear out this anticipation, for by every test that I can apply. I find that my papers have not been so well done in January 1865 as in July 1864. A few items will illustrate this statement. In July 1864 in Section I, the marks of one Candidate reached 900, 2 others obtained 800 and upwards, 7 others 700, 20 others 600, and the average number of the marks obtained by all the Candidates (115 in number) in this part of the Examination reached 461. In the Examination just terminated, no Candidate obtained 800 marks. only two 700, 17 others reached 600, whilst the average obtained by all the Candidates (122 in number) has fallen to 423. In the voluntary subjects, including Section II and the Mixed Mathematics, the difference is even more striking. In July 1864 one Candidate's marks exceeded 500, and the marks of three others exceeded 400, whilst at the present Examination no Candidate reached 400 marks, and on the whole the average has fallen from 162 in July 1864 to 125.4 in January 1865. Had this defect in the voluntary subjects been compensated by an increased value in the marks of Section I, I should consider it a matter of congratulation, as indicating improved attention to the elementary and grounding subjects; but it must be confessed that the whole survey of the Examination points to the conclusion of a falling off in the mathematical attainments of the Candidates. I cannot attribute the change to any increased difficulty in the questions I proposed, nor to any unconscious increase in the length of time required for the answers to be given. I set no question in Section I that was not solved during the Examination, and this I always consider the fairest test that the questions were not beyond the range of the Candidates' acquirements. It may be that increased attention has been paid to other subjects, and this

may account for the Mathematical decadence; if so, the average abilities of the Candidates may not have deteriorated, notwithstanding the variation in the Mathematical marks.

Although this comparison with July 1864 is not favourable to the Examination just concluded, it must not be supposed that the mathematical attainments of the Candidates are so low as to render the pursuit of their studies at Woolwich difficult or discouraging. I consider that any Candidate who obtains 400 marks with me in Section I may with industry at the Academy pass with credit the appointed course in the prescribed time. As a large number of Candidates have reached this standard and gone beyond it, I do not doubt but the successful competitors on this occasion will be found duly qualified in Mathematics at their final examination at Woolwich, and will ultimately obtain their commissions with advantage to the public service of the country.

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

The answering in Section I is hardly to my mind so satisfactory as it was in the Examination of July last, and I cannot ascribe this decline to increased difficulty in the questions, inasmuch as in propositions of Euclid, and other questions set in an equally plain form, marks are too often deducted. In Mixed Mathematics there appears to be improvement. Ignorance and misapplication of the principles of Mechanics are not so frequently exhibited.

It will probably not disappoint the Council that the marks obtained in the Second Section of Pure Mathematics are scanty. The course included in this Section is extensive, and the questions cannot all be elementary. Only forty-two Candidates gain marks, and twenty-five of these have less than one-fifth maximum.

I continue the tabular comparison which I offered in a former Report:—