Compressible soil. The resultant of all the forces should pass through the center of the base. Size of the footing of the wall or depth of the foundations to arrive at the result. Possibility of the wall slipping over the base of the foundations. Use of the buttress to prevent this movement. Graphical method to determine the depth of the foundations. Depth of the foundations in unstable soil. 12. Pressure of arches. Case of cylindrical arches. Explanation of the theory of the pressure of arches. Point of application of the pressure in the five modes of possible rupture. Expression for the pressures and resistances by rolling or slipping. Proceeding to be followed to find by calculation the pressures and resistances. 13. Geometrical determination of the pressures and resistances by rolling. Explanation of the solution of this question. Construction of lines proportional to the surfaces of the voussoirs. 1st. In the case of an arch. Extrados without coping or additional weight. 2d. In that of an arch with extrados in the form of coping, and with or without additional weight. Construction of the verticals passing through the center of gravity of the voussoirs. Abstract of the operations to be performed. Determination by geometrical means of the pressure and resistance against slipping. 14. Co-efficient of stability of arches from the springing. Manner of finding the outline of an arch for a certain given co-efficient. Stability of a cylindrical arch on its piers. Thickness of the piers. Considerations relative to the value of the co-efficient of stability. Stability of an arch on the base of its foundations. Filling in and depth of the foundations of piers. Extension of the geometrical methods serving for the determinations of the pressures and thicknesses of piers in case of cross vaulting, arcades, and spherical vaulting. 15. Investigation by analysis of the pressures and resistances of an arch. 1st. Hypothesis of a plat-band; stability at the springing charge necessary on the coussinet; stability of the plat-band on its piers; thickness of the piers. Squaring of a tie-beam of iron which annihilates the pressure. 2d. Hypothesis of a semicircular vaulting with arched extrados. Pressures and resistances. In similar arches the pressure is proportional to the square of the radius. FOURTH PART.--HYDRAULIC CONSTRUCTION. 1st. Classification of ground on which it may be necessary to place a foundation. Soundings. Their object. Various kinds of sounding line. Dams in earth, and in wood and earth combined. Case of an unstable foundation. Construction on rock. Thickness of dams and of the clay work. General disposition of a dam. Bottom-springs. Means of choking or smothering them or of diverting them. Use of sunk dams. Service bridges. Their height and disposition. Railways in great constructions. Their disposition.