On the whole, the salary, pension, social position, and scholastic status of the secondary-school teacher in France and Germany seem to combine to give to the profession an attractiveness not to be found in other countries.

TABLE.

In this table it should be noted that: (1) The separation lines between the primary and secondary schools do not always indicate that regular primary instruction ends there, but only that portion of it preparatory to the secondary school in question; (2) five only, of the six years of the course in the realskola of Sweden, suffice as preparation for a gymnasium; and (3) some university courses extend beyond the limits of age in the table, e. g., in Belgium and in Japan.

3 According to the Report of the International Commission on the Teaching of Mathematics in Finland (pp. 5, 6, 21) there appears to be a gap between the primary and secondary
We are told that the normal age of a boy entering the lyceum is 10, and that the average age of the boy entering upon the two-year course of the preparatory school (Ecole
primaire élémentaire or École préparatoire) is 7.
In Wurttemberg the nine classes of the secondary school are numbered I (the first) to IX (the last).

In Russia there is no correlation between elementary and secondary curricula, and while there is nothing to prevent a clever boy whose parents can afford the necessary expense
from passing from a primary school at the age of 10 or 11 into a gymnasium or "real school," it is unusual and often inadvisable. Hence many "real schools" introduce this pre-
paratory year.
The regular course of the "real school" was formerly six years, but this seventh year is now added in most cases,

7 With the great variation of systems in the Cantons no very definite statement can be made with reference to the period covered by primary and secondary instruction. In
the case of Gymnasien the period is usually 13 years, but some Cantons have 11-year and 14-year periods. In Realschulen the general range is 124 years, though there are also those
with 10 and 11 year range. Primary instruction for boys begins at 6 years of age in most of the Cantons, and the usual range of duration is 4 to 6 years. The term "Realschule"
is employed to designate many types. For example, Gymnasium Biel, in Bern; Real section of Kantonschule in Schaffhausen; Collège de Genève; Ginnasio e Liceo in Tessen;
and Collège et Gymnase in Vaud.
More details in this connection may be found in K. Brandenberger's report, pp. 14-25.

APPENDICES.

APPENDIX A.

ENGLAND.

CAMBRIDGE LOCAL EXAMINATIONS, SENIOR STUDENTS.
December, 1915.

GEOMETRY.

(Two hours.)

The answers to questions marked A and B are to be arranged and sent up to the examiner in separate bundles. N. B.-Attention is called to the alternative questions B ix, B x, B xi at the end of the paper.

A.

A 1. In the triangles ABC, DEF, ¿B=LE, LC= ▲ F, and BC=EF. Prove that the triangles are congruent.

Show that the diagonals of a parallelogram bisect each other.

A 2. In a triangle ABC, AD is drawn perpendicular to BC; show that, when the angle C is acute,

AB AC2+BC2-2BC. DC.

Prove that the sum of the squares on the four sides of a parallelogram is equal to the sum of the squares on the diagonals.

A 3. From a point 0 outside a circle two straight lines OPQ, ORS are drawn, the first cutting the circle at P and Q, the second cutting the circle at Rand S. Prove that

OP.OQ=OR.OS.

In the triangle ABC, the angle A is a right angle. From a point D on BC a line DEF is drawn perpendicular to BC, meeting AC at E. and BA produced at F. Show that

DE=BD. DC-AE. EC.

A 4. Inscribe a regular octagon in a circle of radius 2 inches. Produce alternate sides of the octagon, so as to form a square.

Measure the side of the square.

Show clearly all the construction lines in your figure.

B.

B 5. Show that if a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Two circles intersect at A and B. At A, tangents to the circles are drawn, meeting the other circles at X and Y. Show that BA bisects the angle XB Y.

B 6. Two trianglee ABC, DEF are similar, AB and DE being corresponding sides. Show that their areas are in the ratio AB2: DE2.

Through each of two opposite corners of a rectangle perpendiculars are drawn to the diagonal which joins the other two corners. Show that if the three parts into which the diagonal is thus divided are equal, the squares on the sides of the rectangle are in the ratio 2: 1.