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For the purpose of examining the Grammar School, I set the following papers, viz:—

A trigonometry paper for the first division.

A Euclid paper for the first division, consisting of questions from the first four books.

A paper in arithmetic, algebra, to quadratic equations, and elementary mechanics, for first and second divisions.

A paper in arithmetic and algebra to simple equations, for third and fourth divisions.

A paper in arithmetic for fifth, sixth, and seventh divisions.

A paper in arithmetic for eighth and ninth divisions.

The papers have been answered on the whole, satisfactorily. The trigonometry paper was fairly done. It was of a very elementary character. The questions in mechanics were confined to the definitions, and the answers for the most part showed that the boys thoroughly understood them. The Euclid was well done, out of the sixteen papers sent in, ten were above the average. Gould in the first division, and Stifle and Cotterill in the second, sent in capital papers. The algebra and arithmetic questions in the higher divisions were well done. In the first division Gould did an excellent paper, both in arithmetic and algebra, and the average of the answers to the papers set to the first and second divisions is good. The arithmetic and algebra paper set to the third and fourth divisions has been also well done. This paper is nearly the same as that set to the highest class at the High School, and the answers to the questions show a decided advantage on the part of the College.

When, however, we come to the lower divisions, the advantage is the other way. The arithmetic paper set to the fifth, sixth, and seventh divisions at the College, is the same as that set to class two, and the senior division of class one, at the High School, and the average of the High School is here decidedly superior to the College, not only in the amount, but in the quality of the work done. The answers of the College boys of the eighth and ninth divisions are also inferior to those of the High School boys of the junior division of class one, to the same kind of questions.

Although, however, the junior boys of the College have not done so well as those of the High School, they have done on the whole, creditably.

The first, second, third, and fourth divisions, have done very good papers in arithmetic, as well as in the higher branches of mathematics.

The High School has five mathematical divisions.

Class three, senior division, consists of two boys, who have read algebra to the end of simple equations, the first two and half of the third book of Euclid, Tate’s mechanics and arithmetic.

Class three, junior division, consists of fourteen boys, who have read the first sixteen propositions of the first book of Euclid, algebra to division, and arithmetic.

Class two, class one, senior division, and class one, junior division, consist of forty-five boys in all.

The total number of the boys examined in the High School, was sixty-one.

I set the following examination papers for the High School, viz:—

A paper in mechanics for class three, senior and junior divisions.

A paper in Euclid for class three, senior and junior divisions.

A paper in arithmetic and algebra for class three, senior and junior divisions.

A paper in arithmetic for class two, and class one, senior division.

A paper in arithmetic for class one, junior division.

The paper on mechanics was very well done. Tate’s mechanics, the book read at the High School, does not so much teach the principles of mechanical science, as provide formulae and examples useful for students of engineering. A boy by learning the rules by heart, can work the examples given in the book with little or no knowledge of the science. I think the boys would acquire a sounder knowledge of mechanics if they were taught theoretically as well.

The Euclid paper was done fairly. The boys are not so advanced as the boys at the College and the average of the work done is not so good. Thornton in the senior division of the third class, and Deans in the junior, did very good papers. The arithmetic and algebra paper set to class three, senior and junior divisions, was the same as the arithmetic and algebra paper set to divisions three and four at the College. Although it was fairly done, the answers are inferior to those of the College boys. Only five boys of the junior division answered any questions in algebra. Thornton and Atack in the senior division, and Deans and Ambrose in the junior, did good papers. All the lower divisions of the High School, who did arithmetic only, did exceedingly well; the only fault that could be found, was that some of the answers were not worked out so fully, or written so neatly, as they should have been.

I do not think that the High School takes a proper place either in algebra or geometry, but it is impossible that any progress can be made, if, as I am informed is the case, one hour a week only is given to each of these subjects. I shall be happy to give any further information that you may require.

I have the honour to be, sir,

Your obedient servant,

Joseph Skene Williams, M.A.,

Examiner.