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**Benton, Brevet-Col.J.G.."Chapter VIII. Science of Gunnery,"Ordnance and Gunnery (1867)**; 53 Pages, 10 illus. Price 5.00 {Item No. 20508} [Includes: History of ballistics. Initial Velocity: Fundamental questions, Definitions of velocities, By mechanical principles, Practical rule for initial velocity, What effects initial velocity, Determination of initial velocity by experiment, The West Point ballistic machine. Motion of a Projectile in Vacuo: Determination of equations of motion, Practical application of formula. Resistance of the Air: Importance of considering it, Law of resistance, Fall of a projectile in the air. Loss of Velocity by Resistance of the Air: Equations of motion. Form of Projectile: Theory, Experiments of Hutton and Borda, Conclusions. Trajectory in Air: Difficulties of the problem, Didion's method, 1st class, 2d class, 3d class, Comparison of true and calculated trajectories, Trajectory of oblong projectile. Deviation of Projectiles: Nature and causes, Causes which effect initial velocity, Rotation, The effect of rotation, Deviation of oblong projectiles, Summary of deviating causes.]**Benton, Brevet-Col.J.G.."Chapter XIII. Tables of Mutipliers, Tables of Fire,"Ordnance and Gunnery (1867)**; 33 Pages, many tables Price 4.00 {Item No. 20513} [Includes: Tables of Mutipliers: Explanation, Tables 1-5, Table of times calculated for the West Point ballistic machine. [The values of B, I, D, V &c.] [The tables are related to formulas in the Ballistic section of this book] Tables of Fire: Ranges: 6 Pdr. Field Gun, 12 Pdr. Field Gun, 12 Pdr. Field Howitzer, 24 Pdr. Field Howitzer, 24 Pdr. Field Howitzer, 32 Pdr. Field Howitzer, 24 Pdr. Siege Gun, 32 Pdr. Sea Coast Gun, 42 Pdr. Sea Coast Gun, 8 inch Siege Howitzer, 8 inch Sea Coast Howitzer, 10 inch Sea Coast Howitzer, 8 inch Rodman, 10 inch Rodman, 15 inch Rodman, 3 inch Rifle Gun, 3 inch Parrott Gun, 4-1/2 inch Rifle Gun, 24 Pdr. Gun Rifled, 32 Pdr. Gun Rifled, 30 Pdr. Parrott Gun, 42 Pdr. Gun Rifled, 100 Pdr. Parrot Gun, 8 inch Siege Mortar (Model 1861), 10 inch Siege Mortar, 8 inch Siege Howitzer as a Mortar, 13 inch Sea Coast Mortar. Table with angles of depression of an object for different distances and heights of a gun above the water, Table with remaining velocities for Sea coast projectiles: 15 inch shot, 13 inch shot, 10 inch shot, 8 inch shot, 12 inch Rifle shot, 10 inch Rifle shot, 8 inch Rifle shot. Table of experimental firing in 15 inch Columbiad to determine penetration of a solid shot and shell against sand target. Table of results of experimental firing of various projectiles from the Parrott gun against at sand and clay target Table with results of experiments on the penetration of rifle bullets into various substances (using a Enfield Rifle and Lancaster rifled carbine. Table of the cost of guns]**Bruff, Capt. Lawrence."Combustion of a Gun - Interior Ballistics," Ordnance and Gunnery (1896), Chapter I.**; 74 pages, 21 illus. Price 8.00 {Item No.20522} [Includes: 17. Action of gunpowder in a Gun, 18. Equation of pressure curve - Noble and Abel's method, 19. Application of formula (43) - Work of gunpowder in a gun, 20. Equation of pressure curve - Recent hypothesis - Expression for work under this hypothesis, 21. Work of gunpowder in terms of force and weight of charge - Expression for it in terms of length of travel of projectile, 22. Division of work of gunpowder - velocity of recoil, 23. Velocity of projectile - Passive resistances - Limit of length of bore - Influence on velocity and maximum pressures, 24. Sarrau's formulas - General equation of motion of projectile in bore, 25. Transformation of equation (75) - Errors in its deduction and their correction, 26. Deduction of final equation of motion of projectile in bore, 27. Integration of equation (90) - Practical formulas for velocity and pressure - Values of A and B - Characteristics a and b, 28. Maximum pressure on breech on gun - Value of K, 29. Theoretical maximum velocity - Time of burning corresponding to the maximum velocity, 30. Modulus of quickness - value of modulus - Velocity and pressure as functions of this modulus, 31. Limit of use of binomial formula, 32. Monomial formula for velocity, 33. Calculation of the value of t, 34. Determination of the characteristics of a and b, 35. Effect of variation of elements of loading upon velocity and maximum pressure, 36. Change of velocity when maximum pressure remains constant - fixed powder chamber, 37. Relative variation of velocity and time of combustion - Of velocity and maximum pressure - Limits of modulus - Useful practical formulas, 38. Pressure curves in guns - Noble and Abel's method - Mayevski's method, 39. Longridge's method, 40. Pressure curve by Sarrau's formulas, Determination of velocity by experiment - General principles - Targets for cannon - For small arms, 42. The ballistic instruments - Description of the Le Boulenge chronograph, 43. Arrangement of wires - Working of instrument - Disjunction, 44. Arrangement of wires for small times - Disjunctor - Measuring rule, 45. Adjustments - Use - Objections to the instrument - Breger's improvements, 46. Schultz chronoscope - Marsel Deprez registers - Bashforth tragets, 47. Determination of pressures by experiment - Static method - Discussion - Conclusions, 48. Rodman and Noble gauges - Advantages of Noble, 49. Determination of pressures by the dynamic method - Noble and Abel's method - Letard's apparatus - Sebert's velocimeter]**Bruff, Capt. Lawrence."Exterior Ballistics," Ordnance and Gunnery (1896), Chapter VI.**; 28 pages, 3 illus. Price 3.00 {Item No.20539} [Includes: 194. Definitions, 195. Forces acting on a projectile - Circumstances of motion - Drift, 196. Form of trajectory - Causes affecting resistance - Form - Cross section - Density of the air, 197. Relation between velocity and resistance - Experiments, 198. Method of determining resistance, 199. Modification of general method - Results - Resistance, 200. Trajectory in air - Nomenclature - Equations of motion, 201. Method of integrating equations A - 1st Step, 202. Method of integration of equations (A) - 2d Step, 203. Simplification of equations (291), (292), and (293) - Method of calculating the functions which enter them, 204. Relation between x and y, 205. Modifications of general formulas for the whole range X - For the summit of the trajectory, 206. Auxiliary formulas, 207. Explanation of ballistic tables, 208. Auxiliary tables - Values of f (zV), z, and V, 209. Examples of use of auxiliary tables - Ballistic coefficient]**Bruff, Capt. Lawrence."Practical Problems," Ordnance and Gunnery (1896), Chapter VI.**; 15 pages Price 1.50 {Item No.20540} [Includes: 210. Kind of fire to which formulas apply - Problem I - Use of Equation D, 211. Problem 2. - Use of equations (316) and (321), 212. Problem 3 - Time of flight, 213. Problem 4 - Angle of inclination, 214. Problem 5 - Height of trajectory - Maximum height, 215. Problem 6 - To determine the dangerous space - Rule of double position, 216. Example, 217. Rigidity of trajectory - Drift, 218. Problem 7 - Mortar fire - Modified equations - Calculation] [Practical problems for Bruff's article on Exterior Ballistics]**Bruff, Capt. Lawrence."Probability of Fire," Ordnance and Gunnery (1896), Chapter VIII.**; 23 pages, 8 illus. Price 2.50 {Item No.20548} [Includes: 293. Division of sheaf of trajectories - Law of error - Probability curve - Principles upon which form of curve depends, 294. Equation of the probability curve - Properties of the curve - Limits, 295. Equation of the probability curve - Properties of the curve - Limits, 295. Modulus of precision h - Use of table I, 296. Probable error - True mean error - Relation between probable and true mean errors, 297. Probable zone - Examples - Comparison of mean and true mean errors, 298. 25 percent rectangle - Probable rectangle - Rectangles of any percentage, 299. Examples - Measure of accuracy of guns - Calculation of probable rectangle from mean error, 300. Use of probable error in calculating probabilities - Use of table II - Example, 301. Probability of hitting any plane figure, 302. Right line method, 303. Value of probability by the right line method]**Lissak, Ormond M.."Interior Ballistics," Ordnance and Gunnery (1915), Chapter III**; 87 pages, 6 illus. Price 9.00 {Item No.20563} [Includes: Scope, Investigations, Gravimetric density of powder, Density of loading, Reduced length of powder chamber, Reduced length of initial air space, Problems. Properties of perfect gases, Mariotte's law, Gay Lussac's law, Characteristic equation of the gaseous state, Problems, Thermal unit, Specific heat, Relations between heat and work in the expansion of gases, Isothermal expansion, Adiabatic expansion Noble and Abel's experiments, Apparatus, Results of the experiments, Relation between pressure and density of loading, Temperature of explosion, Relations between volume and pressure in the gun, Theoretical work of gunpowder Formulas for velocities and pressures in the gun, Principle of the covolume, Differential equation of the motion of a projectile in a gun, Dissociation of gases, Ingall's formulas, Combustion under variable pressure, Velocity of the projectile while the powder is burning, Velocity after the powder is burned, Pressures, Values of the constants in the equations, The force coefficient, Values of the X functions, Interpolation, using second differences, Characteristics of a powder Application of the formulas Determinations from measured interior velocities, Problem 1, Problem 2, The action of different powders, Quick and slow powders, Effects of the powder on the design of the gun Determinations from the measured muzzle velocity and maximum pressure, Problem 3, The force coefficient, Problem 4 Table of United States Army Cannon]**Lissak, Ormond M.."Exterior Ballistics," Ordnance and Gunnery (1915), Chapter IX**; 81 pages, 11 illus. Price 8.00 {Item No.20569} [Includes: Definitions, The motion of an oblong projectile, Determination of the resistance of the air, Mayevski's formulas for resistance of the air, Trajectory in air, ballistic formulas, The ballistic coefficient, The functions, Formulas for the whole range, The ballistic elements, The rigidity of the trajectory, Secondary functions, Ballistic tables, Exterior ballistic formulas, Interpolation in Table II, Double interpolation formulas, The solution of problems, Problems, Correction for altitude, The effect of wind, The danger space, Method of double position, The danger range, Curved fire, High angle fire, Calculation of the coefficient of reduction, Perforation of armor, Range tables, Curvature of the earth Accuracy and Probability of fire, Accuracy, Probability of fire, Probability curve, Probably zones and rectangles, Probability of hitting any area Appendix: The use of Table II, Ingall's Ballistic Tables. Description of Table II, Deduction of formulas for double interpolation, Double interpolation formulas, Double interpolation in simple tables, Use of the formulas]**Straith, Major Hector."Definitions," Treatise of Artillery (7th Edition)(1858), Chapter I**; 19 pages, 3 illus. Price 2.00 {Item No.20813} [Including: Matter, Motion, Velocity, uniform, variable, accelerated and retarded. Attraction of cohesion, of gravitation. Weight: a measure of mass, Density, Specific gravity, Inertia, Force, instantaneous, continuous, constant, variable. Moving free, Accelerating force, Motion under a constant force, Under several forces, Heat, Effects of heat, Expansion, Liquefaction, Vaporization, Latent heat, Specific heat, Alterations of temperature attending chemical combination, Friction and percussion sources of heat, Conduction, Radiation, Gas, Air, Weight of air, Pressure, Elasticity, The air gun, Relations of pressure, volume and temperature]**Straith, Major Hector."Resistance of the air to moving bodies," Treatise of Artillery (7th Edition)(1858), Chapter II**; 11 pages, 2 illus. Price 2.00 {Item No.20814} [Including: It arises from the joint action of several causes: 1st Motion imparted to its particles; 2nd, Condensation in front of an rarefication behind the moving body; 3rd, Friction. Experimental determination of the amount of the air’s resistance, The whirling machine, Experiments of Robins, Of Hutton, Practical inferences thence deduced, Ballistic pendulum, Employed to determine the air’s resistance, Table of the air’s resistance to a 2-inch ball, Terminal velocity, Determination of terminal velocity of a ball of any diameter, and of any specific gravity, Table of terminal velocity of iron shot]**Straith, Major Hector."Rotation of Projectiles," Treatise of Artillery (7th Edition)(1858), Chapter III**; 15 pages, 3 illus. Price 2.00 {Item No.20815} [Including: Definition of rotation, Action of a charge of powder on a accurately spherical shot of uniform density, On an eccentric ball, Producing oscillation of the shot in the bore and rotation after leaving it, Relative positions of centres of gravity and form influencing velocity and direction of rotation, Deflections of balls in which a motion of rotation is combined with a motion of translation in air, Deflections are toward that direction in which the anterior hemisphere is rotating, Deflections prevented by rotation about an axis coincident with the line of flight, Principles of the rifle, Robin’s experiments on these subjects]**Straith, Major Hector."Ordnance," Treatise of Artillery (7th Edition)(1858), Chapter VI**; 20 pages, 3 illus. Price 2.00 {Item No20818} [Including: Action of the charge of powder in the bore of a gun, Necessary relations between the mass of the shot and the gun, Motion of a ball in the bore of a gun, Length of the bore, Table of lengths of gun and charges to produce maximum velocities, Disposition of the metal in a gun, External form, Position of trunnions, Preponderance, Windage, Chambers, Tangent scale, Metal suitable for the construction of guns, Cast iron, Bronze, Their comparative value, Wrought iron, Celebrated wrought-iron guns, Manufacture of guns, Casting, Turning, Boring, Bouching, Proving]**Tschappat, William H.. "Interior Ballistics,"Ordnance and Gunnery, Chapter IV., New York: John Wiley & Sons, Inc. (1917)**; 68 pages, 3 illus. Price 7.00 {Item No.20733} [Including: Scope. Early Investigations. Energy of Combustion of Nitrocellulose. For Ennea-Nitrocellulose Per cent of Nitrogen 11 966. Effect of Moisture and Volatiles. Specific Rate of Combustion. Effect of Granulation. Volume Burned, when, a Thickness pi is Burned. Single-perforated Cylindrical Grain of Length Greater than Web. Burning Surface when a Thickness pi is Burned. Burning of Grains of Different Forms. Consideration as to the Best Form of Grains. Distribution of Energy of Powder in the Gun. Energy of Translation of the Projectile. Energy of Translation of the Unburnt Charge and Gases. Energy Used in Overcoming Passive Resistance. Total Amount of Energy Converted into Work. Pressures. Energy Lost to the Gun as Heat. Reduced Length of Powder Chamber. Energy Remaining in the Gas as any Instant. Determination of Velocity as a Function of z. Experimental Vertification Equation. Differential Equation of Travel as Function of z. Determination of Travel During Time Powder is Burning. Discussion of Equation. Determination of Travel after Powder is all Burned. Special Case of Multiperforated Cylinderical Grains. Le Duc‘s Formula. Graphical Method of Integration of Equation. Determination of Pressure. Data of Form A. Calculations of Form B. Example 2. Design of Powder Grain for a Given Gun. Design of a Gun.]**Tschappat, William H.. "Exterior Ballistics,"Ordnance and Gunnery, Chapter IX, New York: John Wiley & Sons, Inc. (1917)**; 68 pages, 9 illus. Price 7.00 {Item No.20738} [Including: Definitions, The Motion of an Oblong Projectile. Determination of the Resistance to the Air. The Ballistic Coefficient. The Altitude Factor. The Reducing Factor. Trajectory in Air, Ballistic Formulas. Solution of Equations. Formulas for the Whole Range. Computation of the Functions. Secondary Function. The Principle of the Rigidity of the Trajectory. Table II, Artillery Circular M. Determination of C from Firings. Computation of C without Firings. Range Table Conditions. Range Corrections for Variations in C. Range Corrections for Variations in o1/o. Range Corrections for Variations in V. Range Corrections for Change in Weight of Projectile. Range Correction for Tide. Deflection Corrections. Perforation of Armor. The Danger Spaces. The Danger Range. Formulas for Velocities less than 825 F.s. Curved and High angle Fire. Zones in Mortar Fire. Range elevation and Range Velocity Curves. Conditions for 12 inch Steel Mortar. Example 16. Example 18. Computation of Range Table without Firings. Perforation of Armor. Accuracy. Probability of Fire. Probability Curve. Equation of the Probability Curve. Illustration of the Use of the Table. Probable Zones and Rectangles. Probability of Hitting any Area.]**Division of Military Engineering of the International Congress of Engineers. "Interior Ballistics, with Bibliography of Exterior and Interior Ballistics," by Capt.J.M.Ingalls, First U.S. Artillery. Columbian Exposition (1894),**; 28 pages, bibliography Price 3.00 {Item No.6123} [Includes: Definition and Object, Interior Ballistics, History, Robins’ Experiments and Deductions, Hutton’s Experiments, D’arcy’s Method, Rumford’s Experiments with Fixed Gunpower, Rodman’s Inventions and Experiments, Count De Saint-Robert’s Hypotheses, Formulas for pressure and work of unit weight of powder, upon the hypothesis that no heat is received from the non-gaseous products, Noble and Abel’s Experiments, Theoretical work effected by gunpowder, according to Noble and Abel, Sarrau’s formulas for velocity and pressure, Sarrau’s Formula for the maximum pressure on the breech, Influence of the Characteristics, Bibliography of Exterior Ballistic Machines, Bibliography of Interior Ballistics.American, Bibliography of Ballistics.Italian, Spanish, German, Dutch, Danish, Portuguese, English, French]**XXII.****Royal Engineers, Corps of."Gunnery,"Aide Memorie to the Military Sciences (1860), Vol.2**; 7 pages Price 1.00 {Item No.20377} [Includes: Introduction, The properties of matter to be considered in reference to gunnery, Movement of bodies, The parabolic theory, Laws and rules of gunnery deduced from experiment and practice]**Royal Engineers, Corps of."Projectiles,"Aide Memorie to the Military Sciences (1862), Vol.III**; 18 pages, 14 illus. Price 2.00 {Item No.20447} [Including: Introduction, General principles of motion, Ballistic pendulum, Gun pendulum, Whirling machine, Electro ballistic apparatus, Velocity, Recoil and strain, Resistance and retardation, Final or remaining and terminal velocity, Deviations of projectiles from smooth bored ordnance, Rifling, Causes of deviation, Experiment with the gyroscope, Advantages of elongated projectiles, Charge]**War Department, Ordnance Office.**Essen, 1881. Translated by Lt.E.L.Zalinski, 5th Artillery; 19 pages, 14 tables Price 2.00 {Item No.5180}**"Krupp’s Ballistic Tables. Text of Krupps Table for the Calculation of Horizontal Remaining Velocities and Times of Flight of Elongated Projectile**s," Ordnance Notes.—No.180 (Washington, 10 March 1882)**War Department, Ordnance Office. "Deviations of Small Arms Projectiles. The vertical deviations of the point of fall of small arms projectiles from the point aimed at which the latter point is above or below the horizontal plane through the point of fire, making use of the equation of the trajectory," Ordnance Notes.---No.225 (Washington, 6 October 1882)**by Captain John E.Greer, Ordnance Department; 5 pages, 1 illus. plus 2 plates of illus. Price 1.00 {Item No.5225}**War Department, Ordnance Office.**; 3 pages Price 1.00 {Item No.5228}**"Determination of the Value of “C.” Didon’s Formula for Computing the Elements of the Trajectory in Air,"**by Capt.John E.Green, Ordnance Department, U.S.A.. Ordnance Notes.—No.228 (Washington, 18 October 1882)**War Department, Ordnance Office. "**Being a continuation of Ordnance Notes 148 by Major George W.McKee; 3 pages, illus. Price 1.00 {Item No.5290}**Bartletts Formulas,"**Ordnance Notes.—No.291 (Washington, April 18, 1883)**War Department, Ordnance Office.**(Translated from the Memorial de Artilleria, by Lt.Orin B.Mitcham)(Addendum to Ordnance Notes No.152, but self contained); 7 pages, with tables Price 1.00 {Item No.5301}**"Theoretical and Practical Ballistics—Addition to the New Method for Solving Problems of Fire,"**by Francis Siacci, Capt.in the Italian Artillery. Ordnance Notes.—No.301 (Washington, 15 June 1883)**Ordnance Department. "Dynamics of Interior Ballistic as Affecting Recoil Design - The Parabolic Trajectory,"Ordnance Department Document No.2035 Theory and Design of Recoil Systems and Gun Carriages (September 1921), Chapter II.**; 54 pages, 1 illus. Price 6.00 {Item No.20202} [Includes: Introduction, Dynamic relationships in interior ballistics, Equivalent mass of projectile, Equivalent mass of powder charge, Equivalent mass of the recoilless parts, Energy equation, Expansion of powder gases, Torque reaction of the projectile, General description, Elementary theory, Leduc's Formula, Recapitulation of the various formulas originating from Leduc's formula, Dynamics of recoil during the travel of the shot up bore, Expansion of the gases after the shot has left the bore and its effect on the recoil, Recapitulation of principle formulas, of interior ballistics, pertaining to recoil design, Leduc's formula, The parabolic trajectory]

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