Indication of the geometrical problem, of which the partial differential equation expresses analytically the enunciation. Integration of the partial differential equations to cylindrical, conical, conoidal surfaces of revolution. Determination of the arbitrary functions.
Integration of the equation d2u dy2 = a2 d2u dx2. The general integral contains two arbitrary functions. Determination of these functions.
Lessons 17–23. Applications to Mechanics.
Equation to the catenary.
Vertical motion of a heavy particle, taking into account the variation of gravity according to the distance from the center of the earth. Vertical motion of a heavy point in a resisting medium, the resistance being supposed proportional to the square of the velocity.
Motion of a heavy point compelled to remain in a circle or cycloid. Simple pendulum. Indication of the analytical problem to which we are led in investigating the motion of a free point.
Motion of projectiles in a vacuum. Calculation of the longitudinal and transversal vibrations of cords. Longitudinal vibrations of elastic rods. Vibration of gases in cylindical tubes.
Lessons 24–26. Applications to Astronomy.
Calculation of the force which attracts the planets, deduced from Kepler’s laws. Numerical data of the question.