Lecture1.—Preliminary notions. Definition of geology expressed from its applications. Division in four s:—1st. Mineralogy. 2d. Paleontology. 3d. Geognosy. 4th. Geogeny. (Only the three first are here treated of.)
First Section.—Mineralogy. Generalities. Distinctive characters of minerals. Fundamental principle of a mineralogical classification. Minerals are distinguished as having characters either exterior, crystalline, chemical, or physical; classification of minerals.
First Section.—Mineralogy. Generalities. Distinctive characters of minerals. Fundamental principle of a mineralogical classification. Minerals are distinguished as having characters either exterior, crystalline, chemical, or physical; classification of minerals.
Lecture2.—First class: Simple bodies forming one of the essential principles of minerals. Genus silica, quartz, sulphur. Second class: Alkali and alkaline salts, potass, soda, &c. Third class: Alkaline earths, and earths. Genus lime. Fourth class: Metals. Iron of various kinds; copper, lead, tin, zinc.
Lecture3.—Fifth class: Silicates of various kinds. Sixth class: Combustibles, minerals.
Lecture4.—Description of various rocks. Classification of rocks.
Lecture5.—Use of rock and stone in the arts, and particularly in the art of construction.
Lecture6.—On the calcination of calcareous stones, lime-kilns.
Lecture7.—Manufacture of artificial hydraulic lime, manufacture of bricks, stucco, or cements.
Lecture8.—Second Section: Paleontology. General division established in zoology and botany. General notions relating to the different kinds of animals and vegetables, of which the remains are found in various geological formations. Third : Geognosy. Lectures 9, 10, 11, 12, occupied with the explanation of the various formations.
Lecture13.—Preliminary notions. Definitions and general considerations. Characteristics of iron, steel, cast-iron, &c.
Lecture14.—On iron ore and the various kinds of fluxes.
Lecture15.—On combustibles. Vegetable combustibles, mineral combustibles.
Lecture16.—Manufacture of cast-iron. High furnaces, different modes of proceeding with vegetable and mineral combustibles.
Lecture17.—Manufacture of iron and steel and the different kinds of iron.
Lecture19.—Making of projectiles, carriages for guns and mortars, axle-trees and anchors. Use of cast-iron for artillery. General notions in moulding. Use of wrought-iron and steel. Materials first made use of for the making of projectiles, and in the casting of cannon-balls, &c.
Lecture20.—On the manufacture of hollow projectiles and the carriages for guns and mortars.
Lecture21.—On the manufacture of axles and anchors.
Lecture 22.—Preliminary considerations. Assay of metals. Fire-arms, manufacture of gun-barrels, describing the various details.
Lecture23.—Bayonets, locks, &c.
Lecture24.—On the making of stocks. Finishing. Rifling small-arms.
Lecture25.—Manufacture of sabres, swords, lances, hatchets, cuirasses, and on the preservation, maintenance, and repair of arms.
Lecture26.—Preliminary notions. Metals proper for the manufacture of ordnance. Composition and properties of gun-metal. Wrought and cast-iron ordnance. Moulding generally. Moulding of cannons.
Lecture27.—Moulding of howitzers. Foundries. Fusion of the metals.
Lectures28, 29.—Boring. Turning. Carving. Turning of the trunnions, &c. Manufacture and reception of bushes. Insertion and replacement of bushes.
Lecture30.—Last operations. Proofs and reception of cannon. Chemical operations. Assay and analysis of the metals employed in the casting of gun-metal; proportion of the several ingredients.
Lecture31.—General notions. Various kinds of powder, &c. On saltpetre and sulphur.
Lecture32.—Charcoal; wood employed; various kinds of charcoal; proceeding followed in making powder in various ways by the pestle.
Lecture33.—Manufacture by mills, &c.
Lecture34.—Influence of the proportion of the several ingredients, and of the manner of making it on its various properties. Preservation, inflammation, and combustion.
Lecture35.—Proofs and reception of powder. Proof of its projectile force. Mortar proof, and various kinds of other proofs to which it is subject. Reception and analysis of powder.
Lecture36.—Preliminary ideas. Objects of the course. Precautions that should be adopted to prevent accident. Mixture of the materials. Manufacture of leaden balls of various kinds. Caps. Fireworks for warlike purposes, used for setting buildings, &c., on fire. Firing cannon and exploding mines.
Lecture37.—Fireworks employed under various circumstances in war. Signal rockets. For illuminating or setting on fire. For explosions. Petards. On ordinary fireworks.
Works of Application.—The works of application which are connected with the course of science applied to the military arts are as follows:—
1st. Study of samples of mineralogical specimens.2d. Study of geological maps to be followed by a memoir.3d. Memoirs on: 1st. Iron and its applications. 2d. Manufacture of cannon. 3d. Manufacture of small-arms and powder.4th. Out-of-door geological excursions to be followed by memoirs.5th. Manipulations relative to moulding in earth or sand.6th. Chemical manipulations.7th. Pyrotechnic manipulations.
1st. Study of samples of mineralogical specimens.
2d. Study of geological maps to be followed by a memoir.
3d. Memoirs on: 1st. Iron and its applications. 2d. Manufacture of cannon. 3d. Manufacture of small-arms and powder.
4th. Out-of-door geological excursions to be followed by memoirs.
5th. Manipulations relative to moulding in earth or sand.
6th. Chemical manipulations.
7th. Pyrotechnic manipulations.
First.—Study of Samples of Mineralogical Specimens.
This study has for its object the determination of the kind of minerals described in the course. It is made in s of ten or twelve Sub-Lieutenants and by attendances of one hour, each Sub-Lieutenant being called upon to reply at least three times.
Second.—Study of Geological Maps, followed by a Memoir.
The study of geological maps will consist in indicating, by conventional colors, the different geological formations of a lithographical map, and to make a in a particular direction. The map will be the same for all, and it will be conceived so as to correspond with the geological formation of France, but the s will differ for each student.
An explanatory memoir will have for its object to call the attention of the Sub-Lieutenants to the most salient facts which will be placed in relief by this study.
One attendance in the halls of study will be devoted to this work.
Third.—Three Memoirs.
Three memoirs on different parts of the course, other than the geological, will be made immediately after the interrogations relative to each . Particular data will be furnished to each Sub-Lieutenant. Three attendances in the halls of study will be allowed for these memoirs.
Fourth.—Geological Excursions.
Three geological excursions will be made in the environs of Metz by groups of ten or twelve Sub-Lieutenants under the direction of the Professor, and at the period of the out-of-door work, so as not to interfere with the current work in the halls. The first excursion will have for its object the study of the lias and lower oolite, met with in the vicinity of Metz. If the time will admit of it, a reconnaissance will be made to the great oolite at Taumont or at Amanvillers.
The second excursion will be made in the direction of Gorze for the study of the lower oolitic formation and to trace it up to Bradford clay, where an important fault occurs in this direction near to Metz. The study of this fault will be the great object of this excursion.
The third excursion will be made in the direction of Forbach, meeting with the lias, chalk-colored freestone, &c.
Three entire days will be devoted to these excursions, and each Sub-Lieutenant will enter his observations in a note-book, and make a certain number ofs, and report the results of these excursions in three memoirs in a specified time.
Fifth.—Manipulations relative to Moulding in Earth or Sand.
These mouldings of projectiles will be made by s of ten or twelve Sub-Lieutenants, two attendances of three hours each being devoted to them, one for ordinary and the other for hollow projectiles.
The manipulations for the moulding of cannon will be executed by the Professor.
All the Sub-Lieutenants will be successively called by s a certain number of times, in order that they may be enabled to render an account of the different states of advancement of the work.
Programme of practical instruction for the casting of projectiles.
1st attendance. Making shot, &c.2d attendance. Making hollow projectiles.
1st attendance. Making shot, &c.
2d attendance. Making hollow projectiles.
Programme of the moulds to be executed by the Professor.
Manufacture of cannon; moulding in earth and the various processes to be carried on.
Sixth.—Chemical Manipulations.
The chemical manipulations are made by s of ten or twelve Sub-Lieutenants.
Nine attendances of three hours each are employed.
1st. To the determination of the specific gravity and real density of gunpowder and to its analysis.2d. To two other analyses of gun-metal, iron-ore, &c.
1st. To the determination of the specific gravity and real density of gunpowder and to its analysis.
2d. To two other analyses of gun-metal, iron-ore, &c.
Seventh.—Manipulations in Pyrotechny.
The manipulations in pyrotechny will be made by the whole division, divided into three brigades. Each brigade will be assembled in one of the halls at the School of Pyrotechny, and will execute the different manipulations indicated in the following programme, under the direction of the Professor, and with the assistance of the master artificers of the School of Pyrotechny. Five attendances of three hours will be employed at these manipulations.
1st Attendance. Munitions for small-arms.Infantry cartridges,Construction of bullets.Constructionof pouches and caps.Constructionof cartridges.Cartridges with oblong bullets.2d Attendance. Ammunition for field guns.Construction and filling of pouches, packing in wood, &c.3d Attendance. Ammunition for siege artillery, &c.Construction and filling of cartridges, &c.Charging hollow projectiles.4th Attendance. Fireworks for war purposes.Construction of matches, quick matches, tubes, fusees for shells and grenades.Construction of signal rockets.5th Attendance. Carriage of field ammunition.Loading and unloading field ammunition chests for cannons, howitzers, and infantry wagons.Construction of ornamental lances and Roman candles.
1st Attendance. Munitions for small-arms.
Infantry cartridges,Construction of bullets.Constructionof pouches and caps.Constructionof cartridges.Cartridges with oblong bullets.
Infantry cartridges,Construction of bullets.Constructionof pouches and caps.Constructionof cartridges.
Cartridges with oblong bullets.
2d Attendance. Ammunition for field guns.
Construction and filling of pouches, packing in wood, &c.
Construction and filling of pouches, packing in wood, &c.
3d Attendance. Ammunition for siege artillery, &c.
Construction and filling of cartridges, &c.Charging hollow projectiles.
Construction and filling of cartridges, &c.
Charging hollow projectiles.
4th Attendance. Fireworks for war purposes.
Construction of matches, quick matches, tubes, fusees for shells and grenades.Construction of signal rockets.
Construction of matches, quick matches, tubes, fusees for shells and grenades.
Construction of signal rockets.
5th Attendance. Carriage of field ammunition.
Loading and unloading field ammunition chests for cannons, howitzers, and infantry wagons.Construction of ornamental lances and Roman candles.
Loading and unloading field ammunition chests for cannons, howitzers, and infantry wagons.
Construction of ornamental lances and Roman candles.
RECAPITULATION FOR THE ARTILLERY AND ENGINEERS.
NL No. of Lectures.+A With Application, 1h. 5m.-A Without Application, 3h. 0m.T Total Credits.I No. of Interrogations.
NL No. of Lectures.
+A With Application, 1h. 5m.
-A Without Application, 3h. 0m.
T Total Credits.
I No. of Interrogations.
* The first series of interrogations relates to mineralogy.† The second to geognosy.
* The first series of interrogations relates to mineralogy.
† The second to geognosy.
The printed Observations column (shown here as footnotes) is ambiguous; the best guess is that both items refer to Geology.
St Studies.Sk Sketches.M Memoirs.E Exercises.Mp Manipulations.H Attendances in halls, 4h. 5m.OD Attendances out of doors, 6h.AL Attendances at the Laboratory:L1 1h. to 2h.L3 of 3h.P Attendance at the School of Pyrotechny 3h.Cr Credits.
St Studies.
Sk Sketches.
M Memoirs.
E Exercises.
Mp Manipulations.
H Attendances in halls, 4h. 5m.
OD Attendances out of doors, 6h.
AL Attendances at the Laboratory:
L1 1h. to 2h.
L3 of 3h.
P Attendance at the School of Pyrotechny 3h.
Cr Credits.
RECAPITULATION OF THE CREDITS OF INFLUENCE.
Lectures,n of Lectures,95Works of Application, 135230.
Lectures1 and 2.—Short account of the general principles which serve as a base for the application of mechanics to machines, under the compound ratio of their establishment and of the calculation of their effects.
Lecture3.—General composition of a factory; power, recipient, transmission of movement, tools. General method of calculating the effect of forces in a complete factory.
Lectures4, 5, and 6.—Theoretical rules and the results of experiments concerning the flow of liquids. (Particular reference is made to the principles which relate to the large orifices of machines moved by water.)
Lecture7.—Gaugingof the volumes and valuation of the dynamical power of water-courses which feed machines.
Lecture8.—Theory of the effect of water on hydraulic wheels. Determination of the elements of the calculation.
Lectures9 to 13.—Application of the general theories to the principal hydraulic recipients. Conditions of the maximum, relative to the useful effect of each kind. Results of experiments, &c. (With reference to turbines, those which are most generally employed in the artillery workshops must be adverted to.)
Lecture14.—Comparative abstract of the usual properties of various hydraulic “recepteurs.” Operations that must be carried on in order to arrive at their results and to their reception in manufactories.
Lecture15.—Physical ideas relative to the use of the vapor of water as a motive power. Theoretical bases of the calculation of the effects of steam-engines. Force exerted by the compression and expansion of elastic fluids.
Lectures16 to 18.—Practical notions and results of experiments relating to the effects and to the usual properties of the principal systems of steam-engines in use, as to the employment, reception, and maintenance in workshops.
Lecture19.—Resistance to compression: 1st, by gradual pressure; 2d, by shock. Results of experience. Application to wooden and cast-iron supports, and to the foundations of machines. Stocks of hammers.
Lecture20.—Resistance to traction. Application to the shank of a piston, to bolts, chains, cordage, and leather straps. Resistance to flexure. Practical formulæ for calculating the transverse dimensions of the wooden or cast-iron arms of hydraulic wheels, of the catches or sails.
Lecture21.—Continuation of the resistance to flexure. Practical formula for calculating the dimensions of the several parts of such machines. Cranks, winches, and handles in wood or in metal.
Lecture22.—Resistance to torsion. Practical formulas. Results of experiments relative to the resistance of wood and metals to boring and turning. Resistance of cast-iron plates to clipping.
Lectures23 and 24.—Of blowing machines. General expression of their useful effect. Conditions of the maximum effect. Ventilators; their use in workshops and galleries of mines. Practical bases of their construction. Blowing machines with a piston. Description. Calculation of the effects and results of experiment.
Lectures25 and 26.—Description and properties of alternative and circular sawing machines. Practical rules for their establishment. Results of experiments concerning the motive power they require, the useful effect obtained, and the resistance of various kinds of wood to the action of the tool. Results of observation relative to the work in shops by hand-saws.
Lectures27 and 28.—Machines which act by shocks. Practical formula for the calculation of the loss of acting force in the shock. Description and usual properties of various kinds of hammers employed in workshops. Results of experiments proper for serving as the base for the establishment of lever hammers and pestles in powder manufactories. Results of calculation and observation relative to hammers and pestles moved directly or by the transmission of a movement by steam.
Lecture29.—Grindstones for powder manufactories. Rapidity suitable to the different parts of the work. Means of obtaining it. Calculation of the necessary motive power. Sharpening grindstones for the manufacture of arms. Ventilation.
Lecture30.—Lathes and drilling bits. Description. Rapidity of movement and form of the tools, according to the nature of the matter and kind of work. Results of experiments concerning the motive force required, and its relation to the useful effect obtained. Composition of a workshop of turning-lathes for an arsenal of artillery.
Lecture31.—Boring. Machines for cutting and boring. The form of the tool and the rapidity of its action must depend on the nature of the material and the kind of work. Results of experience concerning the motive power required, and its relation to the useful effect obtained, principally for the boring machines of the manufactories of arms and of foundries. Boring machines, disposal of them in an arsenal.
Lecture32.—Flatteners. Machines for centering, for making screw holes. Descriptions. Different rapidity of the work, dependent on its nature and that of the material. Results of experiments concerning the amount of the motive power and its relation to the useful effect obtained.
Lecture33.—Proceeding to be followed in the preparation of the sketches of a machine. Observations on the effects of machines, their duration, original cost, and cost of maintenance, mode of making, &c. Indications of the difficulties which are met with, and means which should be employed.
Lecture34.—Project of a factory (specially for the sub-lieutenants of artillery.) Legal conditions respecting the erection of factories. General mode of proceeding with the project. Choice of motor machines dependent on local circumstances and the nature of the work to be performed.
Lecture35.—(Special for the sub-lieutenants of artillery.) Determination ofthe effects supported by the pieces, whose dimensions should be calculated in applying the practical formula of the resistance of materials. Selection of materials.
Lecture36.—(Special for the sub-lieutenants of artillery.) Principal assemblages of various pieces of machines. Building, foundations, supports of trunnions and pivots.
SECTION SECOND.—WORKS OF APPLICATION.
Survey of Workshops.
This survey of workshops comprehends:—
1st. Figured sketches and observations made on the ground.
2d. Drawing of the whole and of details shaded.
3d. A memoir containing an accurate description of the machines and workshops, the calculation of the dynamical effect, the exposition of the mode of fabrication, and, in general, the results and consequences of the observations made on the spot. It must be executed by each, conformably with the particular programme, and to the instruction which will be given to him. He is allowed for this work thirty-four days.
Project of Machines.
This work, executed immediately following the preceding, by the sub-lieutenants of artillery only, has exclusively for its object the establishment of a workshop for the service of the artillery, comprehending the driving machines and the principal operators; or, if there be time, the improvement of the workshops of the same arm, described in the preceding work. This project must be executed conformably to the particular programme given to each sub-lieutenant. It comprehends; 1, sheet of drawings: 2, a memoir. Twenty-six days are allowed for this work,
RECAPITULATION.
NL No. of Lectures.CL Credits for Lectures.+A With application.-A Without application.C Total Credits.I No. of Interrogations.
NL No. of Lectures.
CL Credits for Lectures.
+A With application.
-A Without application.
C Total Credits.
I No. of Interrogations.
RECAPITULATION.
D Sheets of drawings.M Memoirs.Att Attendances.H In the halls.O Out-of-doors.C Credits.
D Sheets of drawings.
M Memoirs.
Att Attendances.
H In the halls.
O Out-of-doors.
C Credits.
* 1 note book.† 1 note book 2 sheets
* 1 note book.
† 1 note book 2 sheets
RECAPITULATION.
The course on construction is divided into four parts.
The first part relates to the elements of masonry and the principles which should regulate the form, dimensions, and the construction of walls, and the different parts of buildings; it contains eighteen lectures.
The second part is devoted to the architecture of military buildings—twelve lectures.
The third part supplies the theory of the stability of construction, and is divided into—
1st , relating to the resistance of materials—six lectures.
2d, relatingto the stability of walls of revetments and arches—nine lectures.
The fourth part applies to constructions in water—twenty lectures.
The course is very nearly the same for the Artillery as for the Engineers.
Lectures1, 2, and 3.—Relate to the elements of which masonry is composed, such as the different kinds of stones, usual dimensions, manner in which good stone may be known; bricks, lime, cement, sand, mortar, stucco, mastic plaster, asphalte, &c., and to the general considerations relating to foundations, and the different kinds of walls under various circumstances.
Lecture4.—Treats of sustaining walls and the probable effects of the pressure of the earth. Of the conditions which must be fulfilled to insure stability. Various formulæ on the subject. Details of construction and on the proper material to be used.
Lecture5.—Refers to the manner of facing masonry. Openings in walls, windows. Partition-walls.
Lecture6.—On cylindrical arches, vaults, key-stones. Formulæ for the calculation of the thickness of piers of an arch or vault. Construction and use of tables for the calculation of the thickness. Construction of arches and vaults in different materials.
Lecture7.—Arches continued, flat arches, plate bands, &c.
Lecture8.—On the woods used in construction. On the influence of the soil on its quality. Characteristics of good wood. Preservation of wood. Proper wood for constructions.
Lecture9.—Flooring. Beams. Girders. Joists. Ceilings.
Lecture10.—Staircases, conditions respecting. Construction of different kinds of staircases, part of masonry, wood, &c.; steps. Construction of landing-places, &c.
Lectures11 and 12.—Roofs in carpentry. Conditions which should be satisfied. Composition of the roof of a building. On the different kinds of roofs.
Lecture13.—On the different ways of joining pieces of wood or timber together.
Lecture14.—On permanent kinds of roofing. Conditions which should be fulfilled by good roofing. Composition of roofing. Tiles, lathing, cut slates, ridge tiles, hollow tiles, Dutch tiles. On slate roofing. Metallic roofing. Metal mostly used. Precautions to be taken with reference to all metal roofing.
Lecture15.—Details relating to inhabited buildings. Cellars. Privies. Drainage. Chimneys; cause of their smoking. Most favorable forms of the flues, pipes. Bake-house, hearth.
Lecture16.—On joinery and locksmiths’ work. Flooring of different kinds. Doors. Camp-beds. Racks and mangers in stables. Shutters.
Lecture17.—Apparatus for heating and for cooking food. Hearth, ash-pan. Grate-flues. Amount of surface to be given to heating apparatus. Furnace of kitchens in barracks. Summary notions on the heating and ventilating of buildings. Calorifiéres with hot air, steam, and hot water.
Lecture18.—Plan of a building. Projections adopted for the representation of a building. Plans, s, and elevations. Order in which the measurements should be made, and the sketch prepared. Height at which the horizontal plane of projections should pass, &c.
Lecture1.—Decoration, without making use of the orders of architecture. Principal conditions relating to decoration. Symmetry, regularity, simplicity, unity, and apparent soliditity. Proper character. Proportions of the façades. Height of the stories. Basements. Horizontal chains or fillets. Vertical chains and pilasters. Proportions of the doors and windows. Arcades and arched windows. Cornices, pediments.
Lecture2.—Distribution of buildings. Considerations that should have weight in the distribution. Number composing the edifice. Circumstances that guide in the disposal of masses. Conditions that should be satisfied in placing a building. Locality and suitable dimensions. Relations that should exist between them. Interior and exterior communications. Stories on the same floor.Position of the large rooms. Separation of the rooms. Position and arrangement of staircases. Verification of stability.
Lecture3.—Conditions to be fulfilled in the distribution of the principal military establishments. Arsenals. Polygons for drill. Military establishments to the School of Bridges.
Lecture4.—Foundries. Manufacture of arms.
Lecture5.—Refining saltpetre. Powder. Powder magazines. Details relative to the construction of lightning conductors.
Lecture6.—Infantry and cavalry barracks.
Lecture7.—Hospitals. Military prisons and penitentiaries.
Lecture8.—Storehouse for corn. Store-pits. Storehouse for fodder. Preserving houses.
Lecture9.—Cisterns. Filtration.
Lecture10.—Military tribunals. Guard-house. Gates of cities. Hotels and dwelling-houses. Officers’ quarters.
Lecture11.—Preparatory to the execution of a project for a building. Method of proceeding. Composition of the sketch; approximate surface of all the locality; separation into symmetrical groups in the case of several buildings; number of stories; surface of the ground floor; length and breadth of the building between its walls; distribution of each story; verification of the relation between the stories. Elevation of the building. Sketches. Memoir. General details, and details of execution.
Lecture12.—Discussion before the abstraction of the measurements and the preparation of the estimate of the building.
1. Resistance of prismatic bodies to extension and compression. Elasticity of bodies. Modulus of elasticity. Limits of permanent efforts. Resistance to extension and compression of stone, bricks, and analogous materials; also of wood and metals. Applications.
2. Transverse resistance. Some cases in which it is brought into play. Results of experience. Resistance of bodies submitted to the effects of transversal flexure. Results of experience and conventions. Conditions of equilibrium of bodies submitted to efforts directly transversal to their length. Direction and value of molecular efforts. Equation of the axis of the body. Equation of the squaring. Discussion of these equations.
3. Geometrical method for determining the inertia. Application to the research for the inertia of various s. Applications of general equations of equilibrium and of squaring to straight pieces.
1st. A horizontal piece set in a frame at one extremity, and subjected to a weight acting at the other extremity, with a uniform vertical effect.2d. Horizontal beam placed upon two supports, and subjected to a weight acting at its center, and with a uniform vertical effect.3d. Beam placed horizontally on two supports, and having two equal weights symmetrically placed with respect to its center.4th. Beam placed horizontally on two supports, and subjected to a weight acting at any point whatever throughout its length.5th. Horizontal beam fixed at both its extremities, and subjected to a weight acting at its center with an equal vertical effect.6th. Horizontal beam placed on three points of support, at unequal distances, and weighted with two weights acting at the middle of the intervals between the supports.7th. Vertical beam fixed at the foot, and charged with a weight acting at a certain distance from the axis of the beam.
1st. A horizontal piece set in a frame at one extremity, and subjected to a weight acting at the other extremity, with a uniform vertical effect.
2d. Horizontal beam placed upon two supports, and subjected to a weight acting at its center, and with a uniform vertical effect.
3d. Beam placed horizontally on two supports, and having two equal weights symmetrically placed with respect to its center.
4th. Beam placed horizontally on two supports, and subjected to a weight acting at any point whatever throughout its length.
5th. Horizontal beam fixed at both its extremities, and subjected to a weight acting at its center with an equal vertical effect.
6th. Horizontal beam placed on three points of support, at unequal distances, and weighted with two weights acting at the middle of the intervals between the supports.
7th. Vertical beam fixed at the foot, and charged with a weight acting at a certain distance from the axis of the beam.
5. Solids of equal resistances. Most suitable form for cast girders. Applications of the formula of equilibrium and squaring to various kinds of carpentry.
6. On polygonal roofs. Conditions respecting them. Arched roofs, pressure, &c. On the stability of walls required to resist the pressure of roofs.
SECOND SECTION: ON THE STABILITY OF REVETMENT WALLS AND ARCHES.
7. On the pressure of earth. Explanation of the theory on Coulomb’s system. Investigation of the pressure of earth by analysis. Hypothesis necessary in order to simplify the calculations. General formula of the value of the pressure, &c. Equations of stability and equilibrium under the hypothesis of slipping and rolling.
8. Simplification of the general equations of equilibrium in three particular cases. Determination of the co-efficient of stability in Vauban’s profile. M. Poncelet’s formula for calculating the thickness of revetment walls with perpendicular face. Transformation of the profile of a revetment to another of equal stability. Vauban’s counterforts, &c.
9. Geometrical method for determining the pressure of earth, whatever may be the profile of the wall and of the earth, taking into account the friction of the earth on masonry. Geometrical determination of the amount of the pressure. Proceeding for the determination, by geometry, of the thickness of a revetment wall at the level of the exterior ground.
10. On buttresses. Geometrical determination of the buttressing of earth, and of its momentum. Simplification of the geometrical constructions of the pressure, of the buttressing, and of their momenta under certain hypotheses.
11. Points of application of the pressure and of the buttress. 1st. In the case of a terrace sloping less than the natural slope of the ground. 2d. In the case of the ordinary revetments of fortification.
On the stability of the foundations of revetment walls.
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 theverticals 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.