[aRcHiBALD] MATHEMATICAL INSTRUCTION IN FRANCE 135 
moving cone on a fixed cone.—Movement of a solid body in space. 
Helicoidal movement.—Relative movements. Theorem of Coriolis. 
13°. Dynamics of a Particle:-—Work. General Theorems.—First 
integrals of the equations of the motion.—Application to the motions 
of the planets.—Movement of a point on a curve or on a surface. Pen- 
dulum in a vacuum and in a resisting medium. Conical Pendulum. 
Geodetic Lines. 
14°. Geometry of Masses: Centres of gravity. Moments of 
Inertia. 
15°. Dynamics of Systems: General Theorems. First Integrals.— 
Energy, Stability of Equilibrium.—Movement of a solid body about a fixed 
axis. Pressure supported by the axis. Compound Pendulum.—Move- 
ment of a solid body about a fixed point.—General movement of a solid 
body.—Law of friction and slipping.—Application of the principle of 
vis viva to machines.—D’Alembert’s Principle.—Lagrange’s Equations. 
—Relative motion.—Percussions. 
16°. Canonical Equations: Theorem of Jacobi. 
17°. Hydrostatics: Equilibrium of a fluid mass. ‘Surfaces de 
niveau.” Pressure on a side plane. Archimedes’ principle. Equi- 
librium of floating bodies. 
18°. Hydrodynamics: General equations of the movement of a 
fluid mass. Bernoulli’s Theorem. Torricelli’s Theorem. 
LESSONS. 
Parts of the programmes from which are drawn the subjects of the 
lessons. 
1.—MATHEMATIQUES SPECIALES. 
Series: Series of positive terms; character of convergence or 
divergence drawn from the study of the expressions: 
= “| Un, nPUn, 

Un 
Absolutely converging series. Convergence of series, with terms alter- 
nately positive and negative, of which the general term decreases con- 
stantly in absolute value and tends towards zero. Numerical examples. 
General Properties of Algebraic Equations: Number of roots of 
an Equation. Relations between the coefficients and the roots. Every 
rational and symmetric function of the roots may be expressed rationally 
as a function of the coefficients. —Elimination of one unknown between 
two equations by means of symmetric functions.—Condition that an 
equation has equal roots. Study of the commensurable roots.—Des- 
