The first lecture is devoted to the explanation of the different kind of signals used under various circumstances; on the method of measuring bases and angles, and the principles on which these operations are performed; and concluding with the description and mode of using certain instruments for measuring angles. The second lecture continues and enlarges on the subject of the measurement of angles, horizontal and vertical, with different kinds of instruments. The third lecture relates to the corrections and reductions which must be made to observed angles, such as the correction for the eccentricity of the instruments, to the reduction of the angles to the horizon, and to the center of the station, and also on the adjustments of the instruments, or the application of corrections for certain errors. The fourth lecture discusses the calculation of the triangles and their errors, and points out the best organization that can be given to the triangulation, and the exactitude which can be expected from it. The fifth lecture also relates to the calculation and the development of the triangulation, and explains the nature of the geodesical operations for the map of France. The sixth lecture explains the manner of observing for, and determination of the azimuthal bearing, for the orientation of the triangulation. The seventh lecture has reference to the convergence of meridians, calculation of rectangular co-ordinates, sundry problems, and geodesical leveling. The eighth lecture shows in what manner the barometer is made use of for the determination of differences of altitude, the nature of the corrections to be applied to the instrument, and the degree of exactitude to be found in the results of this process. The ninth lecture points out the order in which geodesical calculations should be performed and the verifications which should be exacted. The Second Section contains five lectures or exercises, and they have for their object to familiarize the students with the use of the various kinds of instruments employed in carrying on the operations which have been shortly described in the first section. The Third Section relates to the practical application of the preceding principles, and mostly consists of geodesical applications. SECOND PART.--COMMON TO THE ARTILLERY AND ENGINEERS. The First Section consists of lectures given in the amphitheatre, and relates to reflecting instruments, such as the sextant, reflecting circle, and the method of using them, and also on the principles of dialling, and its connection with various problems in astronomy; describes also the different kinds of dials. SECOND SECTION.--PRACTICAL EXERCISES. In which the students are called upon, in the presence of the Professor, to adjust the sextant, and to use it in connection with an artificial horizon for the measurement of the angle between any two objects of the altitude of these objects above the horizon, and also the same altitude.