5. The representation in drawing of the laws of the motion of the projectile, the trajectory, inclinations, remaining velocities, durations of the passage. In addition, the scale of the elevations and that of the angles of fire, for an object of aim placed at different distances. 6. An inscription showing all the essential elements by which the projectile and the piece are distinguished. The final tracings of the gun, the projectile, the bottom, and the fuse, must be colored in uniform tints conformably to the table of conventional colors. As to the tracing of the profile founded upon the calculation, it should receive merely an edging of the color which represents the metal used. PROGRAMME OF THE MEMORANDUM ON THE DESIGN FOR ORDNANCE. INTRODUCTION. _Object of the work. Data of the Question._ A. PROJECTILE. _First Section.--Substance, Forms, and Dimensions._ 1. Choice of the metal employed in the manufacture of this projectile. 2. Forms of the projectile. 3. Internal diameter. 4. External diameter. 5. Dimensions of the vent. 6. Diameters of the high and low gauges. 7. Densities of the projectile empty and filled with powder. 8. Weight of the cast-iron ball of the same calibre as the howitzer shell. _Second Section.--Minimum Bursting Charge._ 9. Theoretical bursting charge for the hollow sphere. 10. Effect of the shock of the gases, and of their loss through the vent. 11. Résumé of the results arrived at in this chapter. B. ORDNANCE. _First Section.--Metal, Calibre, and Length of Bore._ 12. Choice of the metal of which the piece is to be formed. 13. Windage of the projectile and diameter of the bore. 14. Effect of the windage on the velocity of the projectile. 15. Length of the bore and charge of powder which satisfy the data of the programme. 16. Résumé of the results arrived at in this section. _Second Section.--Thickness of Metal necessary in order that the Piece may resist the Expansion of the Gases._ 17. Explanation of the method employed to resolve the question of the thicknesses of metal. 18. First propulsion of the projectile, mean density of the gases after this propulsion. 19. Second propulsion of the projectile, mean density of the gases after this propulsion. 20. Third, fourth, &c., propulsions of the projectile, mean density of the gases after each of them. 21. Density and position of the strata (of gas) at the moment of the maximum of mean density. 22. Density of the last stratum for the positions which come after that of the maximum of mean density. 23. Tensions which result from the densities found. 24. Corresponding thicknesses of metal. 25. Résumé of the results obtained. _Third Section.--Profile of the Piece._ 26. Inclosing curve, resulting from the calculations of the second section. 27. Modification rendered necessary by the form of the posterior part of the projectile. 28. Utility of the chamber and its dimensions.