ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 137 
Applications (confined to the case when the equation is solved with 
respect to a radius vector). Case of the conics. 
Gauche Curves: Tangent. Osculating plane. Curvature. Appli- 
cations to the circular helix. 
Study of surfaces of the second degree with reduced equation: Con- 
dition of the contact of a plane with the surface. Simple problems 
relative to tangent planes. Normals. Properties of conjugate dia- 
meters. Theorems of Apollonius for the ellipsoid and the hyper- 
boloids. Circular sections.  Rectilinear generatrices. The surfaces of 
the second order are unicursal. 
DYNAMICS. 
1. Free Material Point: Principle of inertia. Definition of force 
and mass.! Relation between the mass and the weight. Invariability 
of the mass. Fundamental units. Derived units. Movement of a 
point under the action of a force, constant in magnitude and direction or 
under the action of a force issuing from a fixed centre: 1° proportional 
to the distance; 2° in the ratio inversely as the square of the distance.— 
Composition of forces applied at a material point.2—Work of a force, 
work of the resultant of several forces, work of a force for a resulting 
displacement. Theory of living force. Surfaces de niveau. Fields 
and lines of force. Kinetic energy and potential energy of a particle 
placed in a field of force. 
2. Material Point, not free: Movement of a heavy particle on an 
inclined plane, with and without friction, the initial veolcity acting along 
the line of greatest inclination. Total pressure on the plane; reaction 
of the plane. Small oscillations of a simple pendulum without friction; 
isochronism. 
DESCRIPTIVE GEOMETRY. 
Intersection of Surfaces: Two cones or cylinders, cone or cylinder 
and surface of revolution, two surfaces of revolution of which the axes 
are in the same plane. 
1Tt is admitted that a force applied at a material point is geometrically equal 
to the product of the mass of the point by the acceleration that it impresses on the 
point. 
2]t is admitted that, if several forces act at a point, the acceleration that they 
impress on the point is the geometric sum of the accelerations that each of them 
impresses on it, if acting alone. 
