[ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 101 
Geometry.—Translation, rotation, symmetry, homology and simili- 
tude, solids, areas, volumes, poles and polars, inversion, stereographic 
projection, vectors, central projections, etc. 
Conics.—Ellipse, hyperbola, parabola, plane sections of a cone or 
cylinder of revolution, ete. 
Descriptive Geometry.—Rabatments—application to distances and 
angles—projection of a circle—sphere, cone, cylinder, planes, sections, 
shadows.—application to topographical maps, etc. 
Kinematics.—Units of length and time. Rectilinear and curvi- 
linear motion. Translation and rotation of a solid body. Geometric 
study of the helix, ete. 
Dynamics and Statics—Dynamics of a particle, forces applied to 
a solid body, simple machines in a state of repose and movement, etc. 
Cosmography.—Celestial sphere, earth, sun, moon, planets, comets, 
stars—Co-ordinate Systems, Kepler’s and Newton’s laws, etc. 
One of the most striking things in this scheme, as compared with 
American method, is to find arithmetic taught in the last year of the 
lycée course. Note too, that from the Cinquiéme on, it has been taken 
up in connection with instruction in geometry and algebra. Indeed, 
this method of constantly showing the interdependence or interrelation 
of the various mathematical subjects was one of the interesting and 
vaulable characteristics of French education as I observed it. For 
example, I happened to be present in a classroom when the theory and 
evaluation of repeating decimals was under discussion. After all the 
processes had been explained, problems which led similarly to the con- 
sideration of infinite series and limits were taken up. By suggestive 
questioning a pupil found the area under an are of a semi-cubical para- 
bola and the position of the centre of gravity of a spherical cap. With 
us it is not till the graduate school of the university that the boy is 
taught the true inwardness of such processes as long division and 
extraction of roots; but in France, arithmetic is taught as a science and 
the éléve leaving the lycée has a comprehending and comprehensive 
erasp of all he has studied. 
The increasing general interest in practical education is reflected 
in the French method of teaching geometry with frequent illustration 
involving discussion of the form or relation between the parts of objects 
met with in every day life. Rather curiously, the method employed 
in at least some German gymnasien, of demanding that a pupil demon- 
strate even the more complicated propositions of geometry without any 
reference to a figure on a blackboard, does not seem to obtain in France. 
Curiously, because there can be no doubt of the fine exercise of mental 
concentration required of the members of the class who first build up in 
imagination the construction as indicated by one of their number and 
