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U. S. MILITARY ACAOeivlV. 
 
 COURSE OF INSTRUCTION 
 
 IN 
 
 ORDNANCE AND GUNNERY 
 
 TEXT. 
 
 BY- 
 
 Captain HENRY METCALFE, 
 
 Ordnance Dep't, U. S. Army, 
 
 Instructor of Ordnance and G winery, U. S. Military Academy. 
 
 SKCOND KDITION. 
 
 ^^ OP TEra"^^ 
 
 UHiyERSITY] 
 
 *^^^ — 1891. 
 

 Copyright, 1891, 
 
 BY 
 
 Henry Metcalfe. 
 
CONTENTS 
 
 CHAPTER 
 
 I. 
 
 CHAPTER 
 
 II. 
 
 CHAPTER 
 
 III. 
 
 CHAPTER 
 
 IV. 
 
 CHAPTER 
 
 V. 
 
 CHAPTER 
 
 VI.- 
 
 CHAPTER 
 
 VII.- 
 
 CHAPTER 
 
 VIII. 
 
 CHAPTER 
 
 IX.- 
 
 CHAPTER 
 
 X. 
 
 CHAPTER 
 
 XI.- 
 
 CHAPTER 
 
 XII.- 
 
 CHAPTER 
 
 XIII.- 
 
 CHAPTER 
 
 XIV.- 
 
 CHAPTER 
 
 XV. 
 
 CHAPTER 
 
 XVI.- 
 
 CHAPTER 
 
 XVII.- 
 
 CHAPTER 
 
 XVIIL- 
 
 CHAPTER 
 
 XIX.- 
 
 CHAPTER 
 
 XX.- 
 
 CHAPTER 
 
 XXI.- 
 
 CHAPTER 
 
 XXII.- 
 
 CHAPTER 
 
 XXIII.- 
 
 CHAPTER 
 
 XXIV.- 
 
 CHAPTER 
 
 XXV.- 
 
 CHAPTER 
 
 XXVI.- 
 
 CHAPTER 
 
 XXVII.- 
 
 CHAPTER : 
 
 XXVIII.- 
 
 CHAPTER 
 
 XXIX.- 
 
 CHAPTER 
 
 XXX.- 
 
 -Definitions. ) 
 
 -Explosive Agents. 
 
 -Ingredients of Gunpowder. , 
 
 -Manufacture of Gunpowder. J 
 
 -Interior Ballistics. 
 
 -Velocimeters. 
 
 -Pressure Gauges. 
 
 -Phenomena of Conversion. 
 
 -Noble and Abel's Experiments. 
 
 -Combustion of Gunpowder in the Air. 
 
 -Combustion of Gunpowder in the Gun. 
 
 -Sarrau's Formula for Interior Ballistics. 
 
 -History of Gunpowder. 
 
 -High Explosives. - / 
 
 -Metallurgy. 
 
 -Projectiles and Armor. 
 
 -Manufacture of Projectiles. 
 
 -Means of Communicating Fire. 
 
 -Gun Construction. 
 
 -Exterior Ballistics. 
 
 -Varieties of Cannon. 
 
 -Artillery Carriages, Principles. 
 
 -Various Artillery Carriages. 
 
 -Horse and Harness. 
 
 -Artillery Machines. 
 
 -Hand Arms. - { 
 
 -Small Arm Ammunition. 
 
 -Small Arms. '- 1 
 
 -Cannon Without Recoil. 
 
 -Accuracy of Fire. 
 
PREFACE TO SECOND EDITION, 
 
 The great advances which have been recently made in our 
 knowledge of the properties of gunpowder have subjugated 
 the " Spirit of Artillery," as this agent has been termed, to a 
 seemingly docile servitude. These, with corresponding 
 improvements in Metallurgy, have led to such changes in 
 nearly all that relates to fire-arms as to make necessary 
 a comprehensive revision of the course of Ordnance and 
 Gunnery, established by the late Colonel James G. Benton 
 in 1861, and modified from time to time by his successors on 
 the Academic Board. 
 
 The subject has outgrown the limits of the small encyclo- 
 pedia in which Benton comprised all that was then essential 
 for the ordinary officer, as well as for the student, to know of 
 the materiel of war. 
 
 It has also lost much of the stability which characterized 
 it when spherical projectiles were still generally employed. 
 The labors of men of science and the energy of inventors 
 are continually extending the boundaries of knowledge and 
 undermining positions which appear most fixed. 
 
 Therefore, instead of giving to the course a descriptiv^e 
 character, it appears advisable to frame it so as to present 
 as simply as possible such of its principles as are the most 
 important, and appear the best established. 
 
 By employing the short time available for this course in 
 teaching such principles, the student, although less familar 
 with existing forms and methods than after the study of the 
 former course, may possibly be better fitted to understand 
 the causes of changes in materiel which are now so frequent, 
 and, as his experience increases, to wisely advise the direc- 
 tion that such changes should take. 
 
VI PREFACE. 
 
 The selection, enunciation and deduction of such princi- 
 ples in a suitable form is rather embarrassed than assisted 
 by the mass of specialized knowledge to be found in the 
 Government reports and in the periodical press. In fact, 
 had it not been for the admirable text-books used at the 
 ^'''Ecole d'' Application de VArtillerie et du Genie^'' at Fontaine- 
 bleau, France, for a set of which the author is obliged to 
 superior military and diplomatic authority, it would not 
 have been possible for him to prepare many of the following 
 pages. 
 
 Graphical methods have been freely used, both to express 
 abstract relations and to avoid description. In order to 
 reheve the memory and to train the student in reading 
 mechanical drawings, it is intended that the more elaborate 
 shall be recited on from the book. 
 
 It has been attempted to give the antecedents of present 
 forms, briefly, but so as to indicate the general lines fol- 
 lowed in their evolution and possibly to anticipate the 
 direction in which their improvement tends. In so doing 
 more stress than heretofore has been laid upon the practice 
 of the workshops; since the history of invention shows 
 that this has had as much to do with the march of improve- 
 ment as a special knowledge of the military necessities of 
 any particular case. 
 
 The thanks of the author are due : 
 
 To Mr. Geo. H. Chase, of the Midvale Steel Works, Phila- 
 delphia, for revising Chapter XV. 
 
 To Captain Z. L. Bruff, Ordnance Department, for the 
 appendix to Chapter XIX, relating to the Elastic Strength 
 of Guns. 
 
 To Private C. August Schopper, of his detachment, for 
 most of the drawings used in illustration. 
 
 West Point, New York, yuly 1, 1891. 
 
 HENRY METCALFE, 
 
Bibliography of the Principal Works Consulted. 
 
 Benton's Ordnance and Gunnery. 6th Edition. 
 
 Mordecai's Revision of Benton. Pamphlets, U. S. M. A. 
 
 McKinlay's Text-Book of Gunnery. British. 1887. 
 
 Cooke's Naval Ordnance and Gunnery. 2nd Edition. 
 
 Text Book of Ordnance and Gunnery, U. S. N, A. 1887 
 
 Noble and Abel's Experiments on Fired Gunpowder. 2 Vols, 1880. 
 
 Proceedings U. S. Naval Insiitute. Current series. 
 
 Encyclopedia Brittanica. 9th Edition. 
 
 Bloxam's Chemistry. 6th Edition. 
 
 Byrne's Metal Worker's Assistant. 1869. 
 
 Goodeve's Principles of Mechanism. 1876. 
 
 Reports of the Chief of Ordnance, U. S, A. 1872 — 1890. 
 
 Ordnance Notes, U. S. A. 
 
 Notes on the Construction of Ordnance, U. S. A. Current series. 
 
 Reports on Naval Progress, U. S. N. 1887 — 1890. 
 
 Principal French Works. 
 Roulin's. Poudres de Guerre et Balistique Int^rieure. 1884. 
 
 do Armes Portatives. 1885. 
 
 Pi^bourg. Fabrication de la Poudre. 1884. 
 
 do Pyrotechnic. 1884. 
 
 Jouffret. Les Projectiles. 1881. 
 Berthelot. Sur la force de la Poudre. 1872. 
 Muzeau. Effets du tir sur les affuts. 1884. 
 Bornecque. Armes ^ repetition. 1888. 
 Malengrau. L'Artillerie a I'Exposition. 1890. 
 Aide Memoire. Artillerie. 1887. 
 
 Referritig to Chapter XII. 
 Meig's and Ingersoll's Interior Ballistics, U. S. N. A. 1887. 
 Medcalfe and Howard. Notes on Construction of Ordnance. N0S.36&42. 
 The above are derived principally from Sarrau's ** Researches on the 
 Effect of Powder," translated in the Proceedings of the U. S. Naval 
 Institute. Vol. X. Whole No. 28. And from ** Researches on the 
 Loading of Fire Arms." 1882. 
 
VIU BIBLIOGRAPHY OF THE PRINCIPAL WORKS CoNStJLtED. 
 
 Referring to Chapter XIV. 
 Abbott's Submarine Mines. i88i. Appendices. 
 Eissler's High Explosives. 1884. 
 Monroe's Notes on Explosives. 1888. 
 
 Referring to Chapter XV. 
 Greenwood's Steel and Iron. 1884. 
 Bauerman's Metallurgy of Iron. 1868. 
 Jean's Steel, History, Manufacture, etc. 1880. 
 Thurston's Text-Book of Materials of Construction. 1886. 
 Chernoff on the Structure of Steel. Note on Construction of Ordnance. 
 
 No. 22. 
 Brinell on the Structure of Steel. Note on the Construction of Ordnance. 
 
 No. 37. 
 
 Referring to Chapter XVI. 
 Proceedings U. S. Naval Institute. No. 56. 1890. 
 Ordnance Construction Notes, 28, 49. 
 
 Referring to Chapter XVII. 
 Ordnance Construction Note, 26. 
 
 Refe'^ring to Chapter XIX. 
 Ordnance Construction Notes, 9, 19. 
 
 Referring to Chapter XX. 
 Bruff 's Ballistics. 1885. 
 Ingalls' Exterior Ballistics. 1886. 
 
 Referring to Chapter XXX. 
 Glennon's Accuracy and Probability of Fire. 1888. 
 
 REMARK. — The unusual method of paging adopted in this work is 
 intended to facilitate its revision, since new chapters can be inserted with- 
 out disturbing the sequence of the following pages. 
 
INDEX 
 
 The heavy figures refer to the number of the chapter, and the lighter 
 figures to that of the page. 
 
 Abbott's experiments, 14, 1. 
 
 Abbreviations, 1, 4. 
 
 Abel, gun cotton, 14, 10. 
 
 Absolute error, 30, '24; force of 
 
 gunpowder, 9, 6. 
 
 Accidents, fuzes, 18, 19; gunpow- 
 der, 4, 1; high explosives, 
 
 14, 1. 
 
 Accles feed, 29, 6. 
 
 Accuracy of lire, 30, 5; estimated, 
 
 30, 23, 35. 
 
 Acoustic telemeters, 30, 11. 
 
 Air, combustion in, 8, 2, 10, 3, 4, 12, 
 3; packing, 7, 4, 21 , 7; re- 
 sistance of, 16, 1, 20, 8; spac- 
 ing, 11, 14; trajectory in, 20, 
 
 18. 
 
 Aluminium in steel, 15, 20. 
 
 Ammonium nitrate, 3, 7. 
 
 Ammunition and arms, relation, 27, 
 1; chest, 22, 28; rapid fire, 
 
 29, 18, 20; small arm, 27, 9, 
 
 28, 19; supply of, 2S, 17. 
 
 Ancient cannon, 13, 1; carriages, 
 
 i8l, 20; gunpowder, 13, 2. 
 
 Analysis of gunpowder, 2, 10, 9, 2, 
 11, 29. 
 
 Angle of fall, 20, 37, 30, 35; of 
 
 draught, 24, 3. 
 
 Animal power, 24, 1, 3, 28, 2. 
 
 Animate objects, 10, 23; areas, 
 
 30, 48. 
 
 Annapolis armor tests, 16, 43. 
 
 Annealability, 15, 23. 
 
 Annealing, 15, 38, 51, 52, 57; vrater, 
 
 15,54. 
 Anvils, forging, 15, 44. 46; for 
 
 ])rimers, 27, 4. 
 
 Armor, kinds of, 16, 36; piercing 
 
 shell, 16, 20, 29, 21; penetration 
 
 of, 16, 36; test for projectiles, 
 
 17. 18. 
 
 Arms and ammunition, relation, 27, 1. 
 
 Artillery carriages, 22, 1; system 
 
 of, a 1,3. 
 
 Assembling cannon, 16, 58. 
 
 Axle, 22, 24. 
 
 B. 
 
 Back gear, 17, 12. 
 
 Backing, armor, 16, 37. 
 
 Back rest, 17, 13. 
 
 IJallistics, interior, 5, 1; exterior, 
 
 20, 1; coefficient (gunpowder) 
 
 12, 13, 28. 21; projectile, 
 
 16, 2, 20, 11, 23; formulae, 20, 
 
 28, 47; tables, 20, 27. 53. 
 
 Balloting of projectile, 16, 15. 
 
 Bands, carrying, 4, 5; rotating, 
 
 16, 12, 15, 17,2,15. 
 
 Barbette carriage, 22, 2, 23, 5. 
 
 Harlow's law, 19, J, 4. 
 
 Barrels, mixing, 4, 5; tumbling, 
 
 4, 4; small arm, 28, 2. 
 
 Bashforth, experiments, 20, 9; 
 
 target, 6, 15 
 
 Basic process. 15, 19, 35, 37. 
 
 Batteries, electric, 6, 15, 18, 5. 
 
 Bayonet, 26, 1. 
 
 Beaten zone, 30, 49. 
 
 Belleville springs, 22, 19, 23, 4. 
 
 Bellite, 14, 16. 
 
 Belts, 17, 12. 
 
 Benton velocimeter, 6, 3. 
 
 Berdan telemeter, 30, 15; primer, 
 
 27,4. 
 
 Berihelot's theory, explosives, 2, 3. 
 
 Bessemer process, 15, 32, 35 j »»« 
 
ind: X. 
 
 Bickford fuze, 18, 2. 
 
 Blacking arms, aS, 29. 
 
 lilack wash, l"?, 3. 
 
 Blasts, size of, 14, 2. 
 
 Blasting fuze, 18, 2; powder, 8, 
 
 7, 9, 9, 2. 
 Blending gunpowder, 4, 13. 
 Blister steel, 15, 14, 30. 
 Blooms, 15, 43. 
 Blow holes, 15, 21. 
 l?o]t guns, 88, a. 
 Bomford's experiment, 7, 15. 
 
 Bore, rocket, 16, 44; and parts 1, 1. 
 
 Boring, 17, 13. 
 
 Bormann fuze, 18, 9. 
 
 Boxer shrapnel, 16, 31, 32. 
 
 Box magazines, 88, 11. 
 
 Brakes, 22, 11, 18. 
 
 Brinell's experiments, 15, 49. 
 
 Brgger's chronograph, 6, 10. 
 
 Breaching, 14, 19, 16, 20. 
 
 Breech, 1, 2. 
 
 Breeching, 24, 7. 
 
 Breech loading, advantages of, II, 16, 
 
 13, 2, 28, 1; projectiles, 
 
 5, 3, 16, 14; small arms, 
 
 28,5. 
 Broad well ring, 21, 7. 
 Bronze, 15, 14, 20, 24, 19, 12; 
 
 quenched, 15, 22. 
 Browning arms, 28, 29. 
 Blown powder. ( See Cocoa.) 
 Bruce feed, 29, 5. 
 Brug^re powder, 1 4, 18. 
 Buffers, 23, 14. 
 Buffington brake, 22, 19, 23, 2; 
 
 carriage, 23, 1. 
 Built up guns, 19, 12,22. 
 Bullet, manufacture, 27, 8; small 
 
 caliber, 28, 2, 20. 
 Burden of ammunition, 28, 4, 28, 18 
 Bursting charges, 14, 7, 19, 16, 20, 26, 
 
 32, 19, 17, 29, 17. 
 Butler projectile, 16, 13. 
 Buttofrifle, 28, 3. 
 
 C. 
 
 Caisson, 22, 29, 23, 2. 
 Cake powder, 13, i, 
 
 Caking, 16, 20. 
 
 Caliber, 1, 1; influence of, 16, 7, 
 
 17; small arm, 28, 2. 
 
 Canet system, 21, 13. 
 
 Canister, 16, 23, 25, 28, 82, 28. 
 
 Cannelures, 27, 8. 
 
 Cannon, 1, 1; B. L., 5, 3, 13, 2; 
 
 construction of, 19, 1, 22; 
 
 dimensions of, 13, 25, 21, 22; 
 
 disabling, 14, 20; metals, 15, 
 
 13, 24; M. L , 6, 3, 13, 2, 21, 
 
 4; nomenclature, 1, 1; 
 
 proportions of, 5, 2, 19, 46; 
 
 varieties of, 21, 1. 
 
 Carbine, 28, 1. 
 
 Carbo-hydrates, 11, 28. 
 
 Carbon, cement, 15, 18, 48; hard- 
 ening, 15, 18, 48; states of, 15, 
 
 48; in steel, 15, 18. 
 
 Carbonizers, 15, 28, 32, 36. 
 
 Carcass, 16, 22. 
 
 Carriages, artillery, 22, 1. 
 
 Cartridge, anvil, 27, 4, 5; cor- 
 roded, 27, 6; limit of size, 29, 
 
 IS; manufacture of, 27, 6; 
 
 metals, 27, 5; origin, 87, 1; 
 
 resizing, 27, 6, 
 
 Case hardening, 15, 27. 
 
 Case shot, 16, 18, 23. 
 
 Castan's powder, 4, 12. 
 
 Casting, 17, 1; cannon, 15, 58, 19, 
 
 12; ingots, 15, 33, 56; steel, 
 
 15, 42. 
 
 Cast iron, 15, 24; projectiles, 
 
 16, 5, 6. 
 
 Cavity in shells, 16, 18, 22. 
 
 Cellular theory, 15, 21. 
 
 Cement carbon, 15, 18, 48. 
 
 Center of impact, 30, 23; marks, 
 
 17, 13. 
 
 Centering projectile, 16, 12. 
 
 Central fire cartridge, 27, 4. 
 
 Chamber, 1, 1, 5, 3. 
 
 Change gear, 17, 12. 
 
 Charcoal, brown, 3, 5, 4, 14, 11, 28 ; 
 material, etc., 3, 1; pre- 
 paration, 3, 2; properties, 3, 
 
 4; — spontaneous ignition, 3, 4. 
 
 Cbase, 1, 3r 
 
INDEX. 
 
 Chassis, 32, 2. 
 
 Chauvenet's table, 30, 36. 
 
 Chest, ammunition, 32, 28. 
 
 Chi (x), coefficient, 11, 20, 13, 28; 
 
 factors of, 13, 29; maximum 
 
 value of, 13, 31. 
 Chilled iron, 16, 5, 17, 6, 9, 14. 
 Chlorates, 3, 7, 14, 19. 
 Choice of formulae, Sarrau, 13, 6. 
 Chromium in steel, 15, 20. 
 Chronograph, Le Bouleng6, 6, 6. 
 Chronoscope, 6, 13. 
 Chuck, lathe, 17, 13. 
 Clips, 33, 9, 33, 6 
 Cluster, 16, 23. 
 Cocoa powder, manufacture, 4, 13 ; 
 
 theory, 11, 27. 
 
 Coefficient, ballistic, 13, 13, 16, •?, 30, 
 
 11, 23 ; of efficiency, 30, 52 ; 
 
 of elasticity, 16, 4, 10, 19,9, 
 
 22; internal ballistic, various, 
 
 11, 19; Wertheims, 19, 2, 3, 25. 
 
 Cold and heat, on high explosives, 
 
 14, 6; rolling, 15, 24, 42; 
 
 shuts, 15,44. 
 Collective fire, 30, 48. 
 Combination fuze, 18, 6, 15. 
 Combustion, condition of, 3, 4; in 
 
 air, 8, 2, 10, 1; in gun, 8, 2, 
 
 11, 1, 4; rates, 8, 2, JO, 3, 13, 
 
 3; volume, 11, 1. 
 
 Commercial values, 3, 9, 14, 2, 31, fi. 
 Common properties, high explosives, 
 
 14,2. 
 Communicating fire, 18, 1. 
 Component parts of arms, 38, 2; 
 
 of ammunition, 37, 8. 
 Composition of gunpowder, 3, 10, 9, 2. 
 Compound cylinder, strength of, 19, 
 
 14, 33. 
 Compressive projectiles, 5, 3, 16, 14. 
 Concrete powder, 4. 11. 
 Concussion fuze, 18, 11. 
 Condie's hammer, 15, 46. 
 Conditions of loading, 13, 16. 
 Cone of dispersion, 16, 23, 26, 30, 49; 
 
 pulley, 17, 11. 
 
 Constants, physical, 34, 2, 38, 16; 
 
 Constitution of steel, 15, 16. 
 Converted guns, II, 21, 19, 8, 31, 3, 
 
 5, 38, 15, 
 Conversion of gunpowder, 3, 1; 
 
 rate of 8, 3, 10, 2, 13, 3; phe- 
 nomena of, 8, 1. 
 Cooling, 15, 21, 49. 
 Cope, 17, 5. 
 Cores, 17, 4, 8, 11. 
 Coring, 15, 56. 
 Corning mill, 4, 11, 13. 3. 
 Counter recoil, 33, 18; shaft, 17, 
 
 12 
 Cradle, 35, 2. 
 Cranes, 1 5, 33, 
 
 Crank axle, 33, 29; kinds of, 39, 7. 
 
 Crozier's deduction, 19, 27; gun, 
 
 19, 18. 
 Crucible steel, 15, 31. 
 Crusher gauge, 7, 4. 
 Crystallization, 15, 21. 
 Cube, elastic, equilibrium, 19, 25. 
 Cubic law, 30, 12, 16. 
 Cup-anvil, 37, 4. 
 Cupola furnace, 15, 25. 
 Curvature of cutting arms, 36, 3. 
 
 Cutting arms, 36, 2; speed, 17, 12. 
 
 Cut-ofl", 38, 11. * 
 
 Cylinder, elastic, equilibrium, 19, 26, 
 
 31; gauge, 17, 17; strength 
 
 of, 16, 19, 19, 6, 31, 33. 
 
 Damascus steel, 15, 55. 
 
 Dangerous fragment, 16, 19 ; 
 
 space, 1, 3, 30, 39, 43, 49, 38, 4 ; 
 
 zone, 30, 49. 
 
 Dank's furnace, 15, 29. 
 
 De Bange gas check, 31, 8. 
 
 Definitions, general, 1, 1. 
 
 Deformation, process of, 7, 3. 
 
 Delayed action fuze, 18, 19. 
 
 De Marre, formula for armor, 16,40. 
 
 Demolition, 14, 19. 
 
 Density, gravimetric, 9, 3 ; of 
 
 loading, 9, 4, 12, 11, 14, 13, 1; 
 
 sectional, 16,1; — spherical, 16,6. 
 Departure, angle of, 30, 2, 45j -i— ™» 
 
 liue Of, 20, 1, 
 
INDEX. 
 
 Depression range finder, 30, 14. 
 
 DesignoUe powder, 1*, 17. 
 
 Detachable magazine, 38, 11. 
 
 Detonation, 2, 3, 4, 14, 3; sympa- 
 thetic, 8, 5. 
 
 Detonator, 3, 5, 14, 3, 18, 3; tube, 
 
 18,2. 
 
 Development of small arms, 28, 17. 
 
 Deviations, 80, 4, 30, 6, 23; causes 
 
 of, 30, 6. 
 
 Dimensions of cannon, changes in, 
 19, 27, 37. 
 
 Dirigibility, 29, 13. 
 
 Disabling cannon, 14, 20. 
 
 Disappearing carriage, 83, 13. 
 
 Dish of wheel, 23, 24. 
 
 Disjunctor, 6, 4, 7. 
 
 Dispart, 1, 2. 
 
 Dissociation, 3, 1. 
 
 Distance, estimation of, 30, 10. , 
 
 Drag, 17, 5. 
 
 Draught, angle of, 34, 3; horse, 
 
 34, 1; of patterns, 17, 4. 
 
 Drawn cartridge, 37, 7. 
 
 Drift, 30, 4, 30, 8. 
 
 Drill cartridge, 39, 20. 
 
 Drop test, 15, 15. 
 
 Drying gunpowder, 4, 12. 
 
 Dog, lathe, ir, 13. 
 
 Ductility, 15, 11. 
 
 Dusting gunpowder, 4, 13. 
 
 Dynamite, 14, 4, 13. 
 
 E. 
 
 Early cannon, 13, 1; carriages, 
 
 31, 20; shrapnel, 16, 30; 
 
 fuzes, 18, 7, 8. 
 Eccentric turning, 38, 29. 
 Economy, coefficient of, 11, 19. 
 Effective work of gunpowder, 11, 11. 
 Effect, factor of, 11, 11, 21. 
 Efficiency of fire, 30, 52. 
 Elasticity, 15, 3, 11; coefficient of, 
 
 15, 4, 19, 22; varying, 19, 9. 
 
 Elastic limit, 15, 4, 19, 22; choice 
 
 of, 19, 33; gtrength of guns. 
 
 Electric batteries, 6, 15, 18, 5; 
 
 primers, 18, 4. 
 
 Electro-welding, 15, 23, 17, 15, 19, 19. 
 
 Elevation, angle of, 30, 1. 
 
 Emergency powder, 8, 4. 
 
 Emmensite, 14, 17. 
 
 Energy, 3, 6, 5, 1, 16, 1, 18, 30, 22; 
 
 of recoil, 19, 19, 33, 4, 38, 16, 39, 
 
 1; of rotation, 16, 3; waste 
 
 of, 9, 10, 11, 8. 
 
 Engelhardt buffer, 33, 18. 
 
 Envelope of cluster, 16, 23; of tra- 
 jectory, 30, 6. 
 
 Equilibrium, equations of, 19, 25, 27. 
 
 Erosion of gun, 9, 13, 19, 20. 
 
 Errors, 30, 6, 22, 24. 
 
 Estimation of distances, 30, 10. 
 
 Eta iv), 11, 19. 
 
 Eureka projectile, 16, 14. 
 
 Eprouvette, 7, 2, 9, 5, 13, 3. 
 
 Expanding projectile, 16, 13. 
 
 Expansion volume, 11,1; volumes 
 
 of, 11, 12. 
 
 Experiments, rule for, 9, 1. 
 
 Exterior ballistics, definitions, 30, 1. 
 
 Explosion, 5i, 1; orders of, 3, 2, 4; 
 
 Berthelot's theory, 3, 3; 
 
 temperature of, 9, 8. 
 
 Explosive compounds, J8, 10; 
 
 gelatine, 14, 15; high, 3, 10, 
 
 14, 1; military, 3, 9; mix- 
 tures, a, 9; reactions, 3, 3; ^— 
 
 strength of, 2, 6; value of, », 8. 
 
 Eye, error of, 30, 7. 
 
 F. 
 
 Face plate, 1 7, 11. 
 
 Facings, 17, 3. 
 
 Factor of effect, 11, 11, 21. 
 
 Fall, angle of, 30, 37, 30, 35. 
 
 Feed case, 39, 5 ; of machine 
 
 guns, 39, 5, 12; screw, 17, 12. 
 
 Fermeture, cannon, 31, 9, 15; small 
 
 arms, 38, 5. 
 Ferreous metals, 15, 13, 24. 
 Ferro-manganese, 15, 28j ^UiQOn, 
 
 15,28, 
 
INDEX. 
 
 Field cannon B L., 21, 17; 
 
 M. L., 81, 4; mortar, 31, 17; 
 
 sight, 30, 3, 
 
 Final velocity, 20, 17. 
 
 Finishing projectiles, 17,10. 
 
 Fire, angle of, 20, 5, 22, 9; arms, 
 
 1, 1; classification of, 20, 5; 
 
 line of, 20, 5; plane of, 
 
 20, 4; works, 14, 1<J. 
 
 Firing, 2, 2; gunpowder, 8, 1; 
 
 high explosives, 14, 3. 
 
 Fiske range finder, 30, 15. 
 
 Fixed carbon, 16, 48; magazines, 
 
 28, 12. 
 Flagler fuze, 18, 17. 
 Flasks, 17, 5, 8, 22, 3. 
 Flatness of trajectory, 1, 3, 20, 23, 
 
 40, 28, 20. 
 Flow of metals, 15, 11, 87, 7. 
 Folded head, 27,3. 
 Follow-board, 17, 5. 
 Food and feed of arms, 27, 1, 29, 12. 
 Force, 2, 7, 9, 7, 11, 2!), 12, 29, 14, 5. 
 Forcite, 14, 14. 
 Forging, 15, 45, 53; cannon, 16, 
 
 56; press, 16, 47. 
 
 Fork, establishing, 30, 21. 
 
 Form of cannon, 6, 2, 9, 13, 13, 2, 19, 
 
 6, 46, 21, 1. 
 Founding, 17, 1. 
 Fractures, 15, 20, 49. 
 Free carbon, 15, 48. 
 French fuze, 18, 13, 16; system, 
 
 21 , 10. 
 
 Freyi-e gas check, 21, 7. 
 
 Friction checks, 22, 11; clutch, 
 
 22, 12; .primers, 18, 3. 
 
 Fioloir, formula for armor, 16, 38. 
 Fulminates, 2, 10, 14, 18. 
 Fulmi-bran, 14, 11. 
 
 Functions, ballistic, 20, 27; experi- 
 mental, 9, 1, 5; independence 
 
 of, 9, 1, 16, 34, 18, 16, 19, 16, 21, 2, 
 19, 22, 22, 23, 24, 6, 26, 3, 4, 27, 4, 
 28, 4, 15, 29, 4, 8, 15, 24. 
 
 Fundamental laws, gun construction, 
 19, 29. 
 
 Furnaces, 15, 25, 29, 39, 45. 
 
 Fusibility, 15, 22. 
 
 Fusse, principles of, 16, J8, 28, la, 7. 
 
 Gadolin's law, 19, 9, 20,44. 
 
 Gardner gun, 29, 7. 
 
 Gaseous fuel, 16, 38. 
 
 Gas checks, 7, 3, 13, 2, 21, 6. 
 
 Gate, 17, 9. 
 
 Catling gun, 29, 2. 
 
 Gauging, 4, U, 17, 17, 28, 25. 
 
 Gautier range finder, 30, 18, 
 
 General coeflicient, gunpowder, 11, 
 20, 12, 28. 
 
 Gerdon fermeture, 21, 15. 
 
 Giant powder, 14, 13. 
 
 Gin, 26, 1. 
 
 Glazing gunpowder, 4, 12. 
 
 Gordon range finder, 30, 20. 
 
 Graining gunpowder, 4, 11, 13, 3. 
 
 Grains, diameter of, 10. 2, 12, 4. 
 
 Granulation of gunpowder, 4, 10. 
 
 Grape shot, 16, 23, 25. 
 
 Gravimetric density, 9, 3. 
 
 Grazed zone, 30, 49. 
 
 Grenades, 16, 20. 
 
 Gribeauval carriage, 32, 25. 
 
 Grinding, 1.5, 21, 17, 14. 
 
 Ground, slope of, 30, 51. 
 
 Guide, rocket, 16, 45. 
 
 Gun, 1, 1; combustion in, 8, 2, 11, 
 
 1, 4; form of, 5, 1; lift, 
 
 25,1. 
 
 Gun construction, theory, 19, 11, 23; 
 Itractice, 15, 56. 
 
 Gun cotton, 14, 2, 8 ; detona- 
 tion of, 2, 6. 
 
 Gunpowder, adapted to gun, 11, 7, 24, 
 12, 16, 32, 13, 3, 6; advan- 
 tages of, 2, II; characteristics, 
 
 12, 2, 22; composition of, 2, 10, 
 
 9,2; concrete, 4, 11,16,21; 
 
 fiat, 4, 12, 13, 5; Fossano, 13, 
 
 5; history of, 13, 1; hexag- 
 onal, 13, 5; ingredients, 3,1; 
 
 machinery, 4, 2; manu- 
 
 ficture, 4. 1; modern, 13, 6; 
 
 modulus of qaickness, 12, 10, 
 
 29; — pebble, 4, 12, 13,5; pris- 
 matic, 4, 15, 10, 4, 11, 6, 13, 4, 6; 
 products of, 2, 10, 9. 6, II, 29; 
 
 -^reaction, a, loj — KodmaB's, 
 
INDEX. 
 
 13, 3; small caliber, «7, 9, 2S, 
 
 21, 22; smokeless, 3, 7, 14, 8, 
 
 15, 88, 22; sphero hexagoual, 
 
 13, 5; work of, 11. 10. 
 
 Gustavus Adolphus, 27, 1. 
 
 Hale rocket, 16, 46. 
 
 Hall rifle, 87, 2. 
 
 Hammers, 15, 45. 
 
 Hand arms, 36, 1 
 
 Hardening, 15, 22, 52; carbon, 15, 
 
 15, 48; strains, 15, 55. 
 
 Harness, 84, 6. 
 
 Heat of gunpowder, ^, 6, 9, 7; 
 
 waste of, 9, 10, 1 1, 8. 
 Hebler, system, 88, 19. 
 Helhofite, 14,16. 
 High explosives, 8, 10, 14, 1; 
 
 for bursting charge, J6, 21; 
 
 use of, 14, 7, 19. 
 
 History of ammunition, 87, 1; 
 
 of gunpowder, 13, 1; of rifling, 
 
 16, 8; of shrapnel, 16, 30; 
 
 of small arms, 87, 1, 88, 1, 16 
 
 Hitting, probability of, 30, 27, 35, 43 
 
 Hollow of wheel, 548, 24. 
 
 Hooke's law, 19, 22. 
 
 Horse and harness, 84, 1. 
 
 Hotchkiss ammunition, 89, 20; 
 
 brake, 88, 12; field carriage, 
 
 89, 20; fuzes, 18, 14; guns. 
 
 81, 16, 17; mounts 89, 1; 
 
 rapid fire gun, 29, 21; revolv- 
 ing cannon, 89, 14; projectile, 
 
 16, 15, 17. 
 
 Housing, pressure gauge, 7, 4. 
 
 Howitzer, 1, 1; siege, 81, 18. 
 
 Hydraulic bufier, 88, 14, 83, : ; 
 
 forgingpress, 15, 47; Jack, 85, 
 
 1; motor, 4, 9, 15, 15, 33, 34, 47, 
 
 17, 14. 
 
 Hydro pneumatic carriage, 88, .18. 
 
 Hypothesis, Barlow, 19, 2; Noble's, 
 
 9,8. 
 
 I. 
 
 Ignition of gunpowder, 8, 1; and 
 
 infl^mmAtioa iu guns, 1 1, 18. 
 
 fuze. 
 
 Igniting charges, 18, 5. 
 Impact, center of, 30, 23; 
 
 16, 18, 18, 6, 11. 
 Immovable layer, 7, 1, 11, 9 
 Incendiary projectiles, 16, 22. 
 Increasing twist, J6, 9, IJ, 15. 
 Incorporation of gunpowder, 4, 7, 16, 
 
 44. 
 Independence of function, 9, 1, 16, 
 
 34, 18, 16, 19, 16, 81, 2, 19, 22, 88, 
 
 23, 84, 6, 86. 3, 4, 87, 4, 88, 4, 15, 
 
 89, 4. 8, 15, 24. 
 Inertia igniter, 18, 10, 16, 17. 
 Inflammation of gunpowder, 8, 1; 
 
 prism, 16, -21. 
 
 Ingots, 15, 34; metals, 15, U. 
 
 Initial tension, 19, 11, 23. 
 
 Initial velocity, 1, 2. 
 
 Inspecting instruments, projectiles, 
 
 17, 17. 
 Interchangeability, 88,25. 
 Internal strain, 15, 21, 55, 19, 12. 
 Interrupted screw, 81, 11. 
 Interrupter, 6, 12. 
 Interstitial volume, 9, 3. 
 
 Iron castings, 15, 24, 26, 27. 
 
 Judson powder, 14, 14. 
 Jump, 80, 2, 3. 
 
 Kalchoids, 15, 14. 
 
 Kinetic measures, 7, 9, 16. 
 
 King carriage, 8Si, 13. 
 
 Krupp fuze, 18, 15; gun, 15, 15, 
 
 81. 6, 9; process, 15, 19; 
 
 steel, 15, 15, 32. 
 
 Lathe, 17, 11; 
 
 13. 
 Lance, 86, 1. 
 Lands. 1,2. 
 Leather, 84, 9. 
 Lead, projectiles, 16, 5, 24 
 Lead of wheel, 88, 24. 
 Lebel powaer, 14, 18. 
 
 variations of, 17, 
 
INDEX. 
 
 Le Bouleng6 Telemeter, 30, 11; 
 
 chronograph, 6, 6. 
 Lee rifle, 38, 7, II. 
 Lemoine brake, 33, 19. 
 Length of bore, 5, 2, 7, II, 11, IJ, 13, 
 
 2, 19, 47. 
 Levers in guns, 27, 6, 28, 6. 
 Light balls, 16, 22. 
 Limber, 23, 27, 23, 2; chest, 22, 
 
 28 
 Limiting values of pressures, 19, 39. 
 Line of departure, J*0, 1; of metal, 
 
 1, 2; of signt, ao, 1. 
 
 Liners, 19, 20. 
 
 Liquation, 15, 16. 
 
 Loam, 17, 3. 
 
 Lock, Springfield, 28, 16, 
 
 Longitudinal stress, 19, 16, 30. 
 
 Longridge gun, 19, 19. 
 
 M. 
 
 MacDonald, Hale rocket, 16, 45. 
 
 Machines, artillery, 25, 1; guns, 
 
 21, 1, 29, I, 12. 
 
 Magazine arms, 27, 3, 28, 9, 13, 14. 
 
 Maitland formula for armor, 16, 38. 
 
 Malleability of metals, 15, 23. 
 
 Malleable castings, 15,27. 
 
 Mandreling, 15. 22, 19, 11. 
 
 Mandrels, forging, 15, 47. 
 
 Manganese in steel, 15, 19. 
 
 Mannlicher rifle, 28, 12. 
 
 Manometric balance, 7, 8. 
 
 Manufacture of ammunition, 27, 6; 
 of fuzes, 18, IS; of gun- 
 powder, 4, 5; of projectiles, 
 
 17, 1; of small arms, 28, 24. 
 
 Marking gunpowder, 4, 13. 
 
 Matches, 18, 1. 
 
 Maxim aut. machine gun, 29, 8; 
 
 rapid fire gun, 29, 25. 
 
 Mayewski's experiment, 7, 9. 
 
 Mean error, 30, 24, 33; point of 
 
 impact, 30, 23; trajectory, 16, 
 
 23, 30, 6. 
 
 Mechanism, small arm, 28, 5. 
 
 Megagraph, 6, 7. 
 
 MeUing^, 15,24, n,6. 
 
 Metals for cartridges, 27, 5; ord- 
 nance. 16, 13; physical prop- 
 erties of, 15, 13; useful prop- 
 erties of, 15, 15. 
 
 Metallic cartridges, 27, 2. 
 
 Micrograph, 6, 8. 
 
 Mildness, coeflicient of, 11, 19. 
 
 Military explosives, 2, 9. 
 
 Mill cake, 4, 8; gunpowder, 4, 1; 
 
 train, 15, 43; universal, 
 
 15, 43. 
 
 Milling, 17, 13,28,28. 
 
 Mi lis metal, 15, 20. 
 
 Mixing gunpowder, 4, 7, 16, 44. 
 
 Modulus of elasticity, 15, 4, 19, 22. 
 
 Moistening gunpowder, 4, 7 ; 
 molds, 17, 2 
 
 Molding, 17, 1, 10; composition, 
 
 17, 2; tools, 17, 6. 
 
 Molded gunpowder, 4, 10 ; 
 
 press for, 4, 15. 
 
 Moncriefl carriage, 22, 13, 
 
 Morse cartridge, 27, 5, 28, 22. 
 
 Mortar, 1, 1, 21, 17, 19,22; car- 
 
 riage, 23, 7; fire, formula; for, 
 
 20, 6, 8; fuze, 18, 9; wagon, 
 
 22, 28. 
 
 Mounts, for rapid fire guns, 29, 18. 
 
 Mountings, email arm, 28, 5, 
 
 Mu ifi), 11, 19 
 
 Mule, 24, 1. 
 
 Muzzle loading projectiles, 5, 3, 16, 12. 
 
 N. 
 
 Napoleon gun, 21, 4. 
 
 Nasmyth hammer, 15, 45. 
 
 Natural line of sight, 30, 2. 
 
 Nave, 22, 22. 
 
 Nickel armor, 16, 43; in steel, 
 
 15, 20. 
 Nitrates, 3, 6, 12,29. 
 Nitre, 3, 6. 
 Nitro-benzine, 14, 15; glycerine, 
 
 14, 11. 
 Niven's method, 20, 25. 
 Noble's gauge, 7, 4; experiments, 
 
 7, 16, 9, 1; — an(i Abel's law, 
 9,8, 
 
INDEX. 
 
 Nolan range finder, 30, 20, 
 Non-metallic cartridges, fil, 2. 
 Non-recoil guns, as, 18, 29, 1 ; 
 
 mount, 29, 19. 
 Nordenfelt gunpowder, 4, 15; 
 
 machine gun, 89, S; rapid fire 
 
 gun, 29, 24. 
 Nucleus, 30, 6. 
 Number of grains varied, 10, 2. 
 
 Oblong projectiles, advantages of, 16, 
 
 4. 
 Obturating primers, 18, 4. 
 Oil hardening, 15, 53, 57. 
 Open hearth process, 15, 37; 
 
 steel, 16,14,32. 
 Orders of explosion, 3, 2, 4. 
 Ordnance, I, 1. 
 Origin of motion, .1,10. 
 Oxidation, rate of, 15, 37; scale 
 
 of, 16, 17. 
 Oxydizing agents, 3, 6. 
 
 P. 
 
 Pack horse, 84, 1. 
 
 Palliser gun, ai, 5. ' 
 
 Parallax, 30, 11. 
 
 Parrott gun, 21, 5 ; i)rojectile, 
 
 16. 12. 
 
 Parting plane, 17, 4; sand, 17, 3. 
 
 Passive resistances, 11, 8. 
 
 Patterns, 17, 3, 7. 
 
 Pebble powder, 4. 12, 13, 5. 
 
 Peep sight, 30, 4. 
 
 Percussion caps, 18, 2; fuze, 18, 
 
 11. 
 Pemot furnace, 15, 30, 41. 
 Petroleum fuel, 15, 38. 
 Phi dash(g)), 20, 22, 37, 50. 
 Phosphorus in steel, 15, 19. 
 Physical constants, 24, 2, 28, 17; 
 
 properties, 15, 1, 12, 20, 57. 
 Pi (FT), coj^fficient, 11, 27, 12, 29. 
 Picric acid, 1 4, 17. 
 Piemonte S. S., 29, 17, 
 Fiutles, ^^, 9, 36.. 
 
 Piping, 15, 21. 
 
 Plane table, 30, 14. 
 
 Platforms, '4a, 19. 
 
 Pointing, 20, 1, 30, 1. 
 
 Porter bar, 16, 56. 
 
 Ports, 22, 14. 
 
 Potasaum chlorate, 3, 7, 14, 16, 19. 
 
 Potential, », 6, 9, 7; work, 2, 6, 
 
 II, 9, 15, . 
 
 Pouring, 17, 7. 
 
 Powder mills, 4, 1. 
 
 Pratt range finder, 30, 17. 
 
 Precautions in manufacture of gun- 
 powder, 3, 5, 4, 1. 
 
 Premature explosions, 18, 19, 21, 14, 
 28,6. 
 
 Preponderance, 1, 2, 22, 8. 
 
 Press cake, 4, 7; forging, 16, 47; 
 
 powder, 4, 9, 15. 
 
 Pressure curve, 9, 13, 11, 3, 12, 8, 
 19, 46. 
 
 Pressure, exterior limits of, 19, 39; 
 
 formula;, Sarrau, 12, 8, 13; 
 
 gauges, 7, 1, 5; in gun. Noble 
 
 and Abel, 9, 11; ■ high explo- 
 sives, a, 8, 14, 4; piston, mass 
 
 of, r, 6. 
 
 Primers, 14, 3, 18, 1, 3. 
 
 Probability of fire, 30, 27. 
 
 Probable error, 30, 32; rectangle, 
 
 30, 34; zones, 30, 33. 
 
 Products of gunpowder, 2, 10, 11, 29; 
 
 of high explosives, 2, 2, 14, 
 
 4. 9, 12. 
 
 Profiling, 28, 28. 
 
 Profile of i)rojectile, 16, 16, 20, 9. 
 
 Progressiveness, 10, 3, 11, 19. 
 
 Progressive range finding, 30, 21. 
 
 Projection, angle of, 20, 2. 
 
 Projectiles defined, 16, 1; form 
 
 of, 5, 3; manufacture of, 1 7, 1; 
 
 proof of, 17, 16, 18. 
 
 Proposed magazine arm, 2S, 13. 
 
 Proportions of cannon, 5, 2, 9, 13, 13, 
 2, 19, 6, 46. 
 
 Puddled steel, 15, 30. 
 
 Pulls, 15, 44. 
 
 Pulverizing gunpowder, 4, 6, 
 
 Funching armor, 16, 36, 
 
iJ^i)E5t. 
 
 Quadrant an^le, 20, 2. 
 
 Quenching 15, 22, 49. 
 
 Quickness of gunpowder, 11, 7,24, 12, 
 
 10, 12, 29. 
 Quick loader, 38, 13. 
 Quick match, 1 8, 1. 
 
 Rackarock, 14, 15. 
 
 Racking armor, 16, 36. 
 
 Radius of gun, 20, 1. 
 
 Ramsbottam's hammer, 15,47. 
 
 Range, 20, 4 ; to compute, 20, 36; 
 
 finding, 30, 10; table, 30, 
 
 8, 52. 
 
 Rapidity of lire, 27, 2; 28, 1; 29, 1, 7, 
 11, 16, 17, 26, 30, 61; of re- 
 action, 2, 8. 
 
 Rapid firing guns, 21, 1, 29, l, 16. 
 
 Reaction, gunpowder, 2, 10; gun 
 
 cotton, 14, 9; nitro-glycerine, 
 
 14, 12; rapidity of, 2, 8. 
 
 Re- annealing, 15, 67. 
 
 Recoil, angle of greatest, 22, 9; of 
 
 cannon, 11, 18, 19, 19; control 
 
 of, 22, 11; — energy of, 19, 19, 2'^, 
 
 3; extent of, 22, 7, 11, 16; 
 
 force of, 22, 5; mount, 29, 19; 
 
 periods of, 22, 3; pheno- 
 mena of, 22, 8; rotation due 
 
 to, 22, 8; small arms, 28, 16; 
 
 in testing metals, 15, 3; 
 
 work of, 15, 5, 22, 4. 
 
 Refining steel, 15, 52. 
 
 Regenerator, 15, 39. . 
 
 Reheating furnace, 15, 45. 
 
 Remeltlng iron, 15, 24, 
 
 Reinforce, 1,2. 
 
 Resistance of air, 20, 8, 16; of 
 
 cannon, 19, fi, 31, 3:5; passive, 
 
 11, 8; of primers, 18, 4. 
 
 Retardation, coefficient of, 16, 2. 
 
 Reverberatory furnace, 15, 25. 
 
 Revolvers, 28, 23. 
 
 Ricqs register, 7, 15. 
 
 Rifle, 28, 1. 
 
 Rifling, 1, 2, 16, 8, 28, 3, 27. 
 
 Right line method, 30, 41, 45. 
 
 Rigidity of trajectory, 20, 24. 
 
 Rimfire cartridge, 27, 3. 
 
 Rimless cartridge, 28, 23. 
 
 Riser, 17, 9. 
 
 Rockets, 16, 44. 
 
 Rodman's gauge, 7,3; gun, 19,12; 
 
 improvements in gunpowder, 
 
 13, 3; velocimeter, 6, 13, 7, 12. 
 
 Rolls, 4, 3, 
 
 Rolling mill, 15, 43; — ^ table, 17, 17. 
 
 Rotating bands, 17, 15; device, 
 
 11, 16, 16, 12, 15. 
 R^ation of projectile, 11, 16, 16, 12. 
 Rotary energy, 16, 3; furnace, 
 
 15, 37, 41. 
 Rotten steel, 15, 18. 
 Rumford's gauge, 7, 2. 
 Rupture of shells, 16, 19. 
 Russell's interrupter, 6, 13. 
 
 Saber, 26, 2. 
 
 Safe space, 20, 39, 43, 30, 51. 
 
 Saltpeter, 3, 6. 
 
 Sand, molding, 17, 3. 
 
 Sarrau, application, 12, 21, 28 ; 
 
 formulae, 12, 1; on pressure 
 
 gauge, 7, 8. 
 
 Sawyer canister; 16, 25. 
 
 Schulhofl" magazine rifle, 28, 13. 
 
 Screw guns, 21, 17; interrupted, 
 
 21, 10. 
 
 Sea coast cannon, 21, 20; car- 
 riage, 23, 5; fuze, 18. 9. 
 
 S6bert's projectile, 7, 10; veloci- 
 meter, 6. 13, 7, 13. 
 
 Sectional density, 16, 1, 28, 21. 
 
 Segment shell, 16, 33. 
 
 Segregation, 15. 16, 59. 
 
 Sensitiveness of high explo.sives, 14, 2. 
 
 Set of metal, 15, 3; of wheel, 22, 
 
 24. 
 
 Shafts, 22, 28. 
 
 Sheaf of dispersion, 16, 23, 30, 6. 
 
 Shearing plane, 27, 4. 
 
 Shear steel, 15, 30 
 
 Shells, 16, 18; bursting charges, 
 
 14, 7, 19, 16, 20, 33, 19, 17. 
 
10 
 
 1NDE5^. 
 
 Shields for guns, 16, 41, 23, 6. 
 
 Shock, explosion by, 8, 2, 14, 3, 7, 12, 
 15, 16, 16, 21, 18, 11. 
 
 Shortening bore, 7, y. 
 
 Shrapnel, 16, 23, 26; early, 16, 30; 
 
 fire, 16, 34. 
 
 Shrinkage in cannon, 15, 21, 58, 19, 
 12, 15, 23, 41. 
 
 Shuts. 15, 44. 
 
 Side-box, maxim, 29, 27. 
 
 Siege cannon, 21, 17; carriage, 
 
 «3, 3. 
 
 Siemen's furnace, 15, C9; regene- 
 rator, 16, 3!). 
 
 Sights, 20, 1, 28, 4, 20, 30, 1; 
 
 angle of, 20, 2; field, 30, 3; 
 
 heavy guns, 30, 3; line of, 
 
 20, 1; plane of, 20, 4; 
 
 radius, 20, 1; small arm, 28, 4. 
 
 Signal time, 6, 1, 12. 
 
 Silico-Spiegel, 15, 18, 28. 
 
 Silicon as fuel, 15, 35; in steel, 
 
 15,18. 
 
 Similitude, principle of, 1^, 14. 
 
 Sinclair check, 22, 12. 
 
 Singletree, 22, 27, 24, 5. 
 
 Sinking head, 15, 34, 58, 17, 10, 15. 
 
 Single cylinder, strength of, 19, 6, 31. 
 
 Size of grain, 10, 2, 11, 4. 
 
 Slide rest, 17, 11. 
 
 Sling cart, 25, 2. 
 
 Slow match, 18, 1. 
 
 Small arms, 1, 1, 28, 1; ammuni- 
 tion, 27, 1, 9; manufacture of, 
 
 28, 24. 
 
 Small caliber, 28, 2, 20. 
 
 Smokeless gunpowder, 3, 7, 14, 15, 
 28, 22. 
 
 Soaking pits, 15, 43. 
 
 Sodium nitrate, 3, 6. 
 
 Solid head cartridge, 27, 5. 
 
 Solid shot, 16. 18. 
 
 Special irons, 15, 27. 
 
 Specific gravity of gunpowder, 9, 3; 
 of iron, 16, 24. 
 
 Specific volume, 2, 7, 9, 3, 7. 
 
 Spheres of action, 14, 5. 
 
 Spherical case. 16, 31; density, 12, 
 
 31, 16,6, 28,21. 
 
 Spiegeleisen, 15, 28. 
 
 Spindles, lathe, 17, 11. 
 
 Sprengel mixtures, 14, 16. 
 
 Springfield rifle, 28, 15. 
 
 Stationary carriages, 2'4, 1. 
 
 Stadia, 30, 13. 
 
 Static measures, 7, 2 
 
 Steam, comparison to, 11,1; test, 
 
 17,17. 
 
 Steel castings, 15, 42; cast can- 
 non, 15, 58; classification of, 
 
 15, 13, 18; composition of, 15, 
 
 17; constitution of, 15, 16; 
 
 manufacture of, 15, 30; me- 
 chanical treatment of, 15, 4 ; 
 
 molecular treatment of, 15,48; 
 
 projectiles, 16, 6; projectiles, 
 
 manufacture, 17, 14; proper- 
 ties under stress, 15, 22; struc- 
 ture of, 16, 20, 49; working 
 
 properties, 15, 22. 
 
 Stock, cannon, 22, 3, 25; rifle, 28, 3. 
 
 Stone projectile, 16, 5. 
 
 Store wagon, 22, 29. 
 
 Strain diagram, 15,3,8; equalizing, 
 
 19, 9, 19, 23; internal, 15, 21, 
 
 55, 19, 12; as function of 
 
 radius, 19, 3, 29; on gun, 5, 2, 
 
 16,3, 19,1. 
 
 Strength of cannon, 5, 1, 2, 1 9, 6, 31, 33; 
 
 of explosives, 2, 6; of gun 
 
 construction, coeflicient for, II, 
 21. 
 
 Stress and strain, 16, 1, 19, 22; in 
 
 guns, 5, 2, 16, 3, 19, 1. 
 
 String measure, 30, 24. 
 
 Structure of projectiles, 16, 17. 
 
 Studded projectile, 16, 12. 
 
 Successive means, method of, 30, 21; 
 shortening of bore, 7, 11. 
 
 Sulphur, 3, 1; in steel, 15, 20. 
 
 Supply train, '-i'-i, 29. 
 
 Surface of gunpowder, 8, 1, 10, 1. 
 
 Sweep molding, 17, 3, 5 
 
 Swiss method, 30, 27. 
 
 Sword, 26, 1. 
 
 Sympathetic detonation, 2, 5. 
 
 System of artillery, 21, 3; at rest, 
 
 etc, 19, 13, 36. 
 
INDEX. 
 
 11 
 
 Tarage, 7, 7. 
 
 Targets, animate, 30, 48; —— comput- 
 ing, 30, 26; velocity, 6, 14. 
 
 Team, arrangement of horses, 24, 5. 
 
 Telescopic sight, 30, 3. 
 
 Telemeters, 30, 11, 
 
 Temperature of ignition, 8, 1, 14, 3; 
 
 of explosion, 2, 8, 9, 8; 
 
 scale of, 1, 3. 
 
 Tempering, 15, 52. 
 
 Tenacity, 15, 10. 
 
 Testing cannon metal, J 5, 57; 
 
 machines, 16, 1,5; projectiles, 
 
 17, 18. 
 
 Test piece, form of, 16, 2; record, 
 
 15, 2, 8. 
 Thickness of cannon, 5, 2, 9, 13, 19,6, 
 
 19, 45, 46. 
 Thrusting arms, 86, 1. 
 Thurston machine, 15, 6. 
 Tilted steel, 15, 30. 
 Time of flight, 30, 40, 41, fuze, 16, 
 
 18, 18, 6, 10; limits, 6, 8; 
 
 of maximum, 13, 11. 
 
 Tire rolling, 15, 44. 
 
 Tolerance, 4, 11, 17, 17. 
 
 Tonite, 14, 9. 
 
 Torpedo shells, 14, 8, 16, 20, 31, 18. 
 
 Torsional testing, 16, 6. 
 
 Trajectory in air, 30, 18; curva- 
 ture of, 1, 3, 30, 23; elements 
 
 of, 30, 30; flatness of, 1, 3. 30, 
 
 23, 40, 38, 20, 30, 35, 30; mean 
 
 radius of curvature, 30, 23; 
 
 rigidity of, 30, 24; in vacuo. 
 
 30,6. 
 
 Traveling trunnion bed, 33. (. 
 
 "Treatment" of cannon, 15, 57. 
 
 True mean error, 30, 33, 41. 
 
 Trunnions, inclination of, 30, 2. 
 
 Tubular magazines, 38, 10. 
 
 Tuning fork, 6, 12, 7, 13. 
 
 Tumbling barrels, 4, 4; of pro- 
 jectiles, 16, 3. 
 
 Turning angle, 33, 25. 
 
 Twist, 10, 9, 
 
 U. 
 
 U, path of projectile, 11, 10, 14, 13, 1. 
 Units of measure, 1, 3. 
 
 V. 
 
 Vacuo, trajectory in, 30, 6. 
 
 Value of explosives, 3, 8, 14, 2. 
 
 Variables, experimental, 9, 1. 
 
 Varying elasticity, 19, 9. 
 
 Velocimeters, 6, i, 7, 9; Benton, 
 
 6, 3; classified, 6, 2. 
 
 Velocities defined, 1, 2; final, 30, 
 
 17; formula;, 13, 5, 12; 
 
 targets, 6, 14. 
 
 Vents 11, 18, 31, 13; direction of, 
 
 18, 3; rocket, 16, 44. 
 
 Vertex, height of, 30, 36; prin- 
 ciple of, 30, 42. 
 
 Very's formula for armor, 16, 41. 
 
 Vesiculation, 15, 21. 
 
 Volumes of expansion, 11, 12. 
 
 Vulnerability, 30, 50. 
 
 W. 
 
 Wagon, mortar, 33. 28; store, J5J5, 
 
 29. 
 Washed metal, 15, 19. 
 Waste of energy, 9, 10, 11, 8. 
 Water on high explosives, 14, 5, 6; 
 
 annealing, 15, 54; cap, 
 
 18,9. 
 Weather, 30, 9, 30, 10. 
 Weaver formula for armor, 16, 42. 
 Weight of cannon, 6, 1, 19, 19; of 
 
 charge, Jl, 13, 15, 13, 16, 32, 38, 
 
 21; distribution of, «3, 4, 34, 
 
 2, 38, 17; of projectile, 16, 8. 
 
 Weld steel, 15, 14. 
 Weldability of metals, 15, 23. 
 Weldon range finder, 30, 16. 
 Wertheim's coefficient, 19, 2, 3, 25. 
 West Point target, 6, 15. 
 Whitvvorth's forging press, 16, 47; 
 
 projectile, 16, 12, 17; 
 
 steel, 16, 15, 34. 
 Wheel mills, 4, 7; principles <jf, 
 
 33, 21. 
 
12 
 
 INDEX. 
 
 Wheeled carriages, 23, 2. 
 Wiener's powder, 4, iO. 
 Wiliiston harness, 24, 8. 
 Winchedter magazine rifle, 28, 10. 
 Windage, 1, 2. 
 Wind and accuracy, 30, 9. 
 Wire drawing, 15, 44; wound can- 
 non, 19, 17. 
 Woodbridge gun, 19, 18. 
 Woods, physical properties of, 16, 11 . 
 
 Work of gunpowder, 3, 6, 9, 7, 11, 10. 
 Wrapped metal cartridge, 87, 7. 
 Wrought iron, manufacture, 16, 29; 
 projectiles, 16, 5. 
 
 Zalinski gun, 10, 3, 14, 8. 
 Zones in collective fire, 30, 49. 
 Zones, probable, 30, 33. 
 
I. — DEFINITIONS. 
 
 - 07 THr: 
 
 ^TJKITEBSIT 
 
 CHAPTER I, 
 
 DEFINITIONS. 
 
 Ordnance. — A general terra usually applied only to the 
 material of Artillery, but embracing also all warlike stores 
 made according to prescribed regulations or ordinances. 
 
 Fire Arms. — Offensive weapons used to throw projectiles 
 by means of explosives. They are divided into — 
 
 1. Cannon. — Heavy fire arms requiring carriages to sup- 
 port and to transport them. 
 
 2. Small Arms, — Which can be carried by men. 
 Cannon are divided into — 
 
 Guns. — Or relatively long cannon. Gun is used as a gen- 
 eral term for all fire arms. It has probably the same root 
 as engine, meaning a machine. 
 
 Howitzers.. — Comparatively short cannon. 
 
 Mortars. — Very short cannon. 
 
 NOMENCLATURE. 
 
 Bore. — That part of a cannon which is bored out. It in- 
 cludes — 
 
 1. The cylinder or principal portion of the bore.' 
 
 2. The seat of the charge, or the part occupied by the 
 powder. This may be either a continuation of the cylinder 
 terminated by a plane or curved surface; or a cha?nder, the 
 diameter of which differs from tha* of the cylinder of the 
 bore. For breech loaders, the chamber is divided into the 
 powder chamber and the shot chamber. 
 
 Caliber. — The diameter of the cylinder of the bore. It was 
 formerly expressed by the weight of the inscribed sphere. 
 
I. — DEFINITIONS. 
 
 For cannon, this was the weight in pounds of the cast iron 
 shot; for small arms, the number of leaden balls required to 
 weigh a pound. 
 
 Rifling. — Cutting spiral grooves in the surface of the bore, 
 so as to give to the projectile a motion of rotation at right 
 angles to that of translation. 
 
 Lands. — The ridges left between the rifle groves. The 
 caliber of rifles is usually measured between lands. 
 
 Chase. — The long conical portion of a cannon in rear of 
 the muzzle. 
 
 Reinforce. — The thick portion of the body over and imme- 
 diately m front of the seat of the charge. 
 
 Breech. — The mass of metal in rear of the plane of right 
 section at the base of the charge. 
 
 Line of Metal. — The intersection of the upper surface of 
 the piece by an axial plane perpendicular to the axis of the 
 trunnions. 
 
 Dispart. — The difference between the semi-diameters at 
 the muzzle and at the breech. 
 
 Preponderance. — The difference between the moments of 
 the weight in front of, and in rear of, the trunnions. 
 
 Windage. — This is properly the difference between the 
 area of right section of the cylinder of the bore, including 
 the grooves, and the maximum parallel area of right section 
 of the projectile. 
 
 It is usually expressed in linear units as the difference 
 between the diameter of the cylinder of the bore and the 
 diameter of the projectile. 
 
 VELOCITIES. 
 
 Muzzle or Initial Velocity. — Is the maximum velocity of 
 the projectile after leaving the piece, 
 
t. — BEFmiTlONS. 
 
 Remaining Velocity. — Is that at any point of the trajec- 
 tory. 
 
 Terminal Velocity. — Is that at the point of impact. 
 
 The greater the velocity at any instant, the more flat does 
 the trajectory become; and, therefore, the greater is the 
 probability of striking a vertical object at an unknown 
 distance. (See note 1, page 5.) 
 
 The horizontal distance over which, under given condi- 
 tions, a vertical object would be struck, is called the dan- 
 gerous space for that object. 
 
 UNITS OF MEASURE. 
 
 Those used in English speaking countries are unfortun- 
 ately numerous and are apt to cause confusion. 
 
 Units of Temperature. 
 
 Throughout this work the temperatures are expressed in 
 degrees centigrade. 
 
 Units of Length, 
 
 Yards. — For ranges of projectiles. 
 
 Feet. — For measuring velocities and the chords and alti- 
 tudes of trajectories. 
 
 Inches. — For the internal dimensions of guns and for all 
 dimensions of their projectiles. The decimal sub-division 
 of the inch is generally employed. 
 
 Units of Weight, 
 
 Tons. — For cannon, 1 ton =2240 lbs. 
 
 Pounds. — For large projectiles, for their charges and for 
 measuring the pressures (per square inch) of the gases of 
 fired gunpowder. 
 
 In England, pressures are measured in tons per square 
 inch; in France, in kilogrammes per square centimetre; else- 
 where on the continent of Europe in atmospheres. 
 
t. — MFiNitioNS. 
 
 Grains Troy. — For bullets and powder charges of small 
 arms 7000 grains troy=l lb. avoirdupois. 
 
 g is generally taken =32.2 lbs., which is nearly its value at 
 London. 
 
 Unit of Energy and Work, 
 Foot tons=foot pounds-r2240. 
 
 USEFUL MECHANICAL FORMULAE. 
 
 s 
 
 Uniform motion, v=- 
 
 ds 
 Varied motion, v— —r: 
 
 Uniformly varied motion, v=-aJ<^ a-k = a-fj h— — 
 
 % 
 
 . . dv d^s 
 
 Acceleration, af= -T- = -To- . 
 at dt^ 
 
 Intensity of a motive force, I=Ma. 
 
 Intensity of an impulsive force, I^-^MV, 
 
 Measure of work, Q=Wh—flds, 
 
 Measure of energy, E= ^f^^ 
 
 Time of oscillation of a simple pendulum, t=;rA / — 
 
 ABBREVIATIONS. 
 
 S. B. — Smooth bore. 
 
 R.— Rifle. 
 
 M. L. — Muzzle loading. 
 
 B. L. — Breech loading. 
 
 C. I. — Cast iron. 
 
 W. I. — Wrought Iron. 
 S._Steel. 
 
 The caliber is placed first. Example: 
 8 in. B. L. R. S. 
 
1.— i>EpmiTtoNS. 
 
 15 in. S. B. C. I., etc. 
 
 W. w. — Weight of larger and smaller of two masses consid- 
 ered; as of piece in regard to projectile, or of projectile in 
 regard to charge of powder. 
 
 V. V. — Initial and remaining velocities. 
 
 p. — Intensity of gaseous pressure per unit of area. 
 
 r. d. — Radius and diameter of the cylinder of the bore, or 
 of the projectile according to context. 
 
 Note 1. From Michies Mechanics, Article 94, we have — = '^ ^^ 
 See also Chapter XX, p. 22. p "v , 
 
!I. — EXPLOSIVE AGENTS. 
 
 CHAPTER II. 
 
 EXPLOSIVE AGENTS. 
 
 Explosion. 
 
 Is a name given to a series of phenomena resulting from 
 two general causes. 
 Causes of Explosion. 
 
 I. The rapid conversion of a solid or liquid to a gaseous 
 state. This conversion is accompanied by the evolution of 
 heat, due to the nature of the chemical reaction involved. 
 
 II. The rapid dilatation of a mixture of gases by the heat 
 evolved in their combination. Such explosives are not yet 
 generally employed in warfare and are not herein considered. 
 Products. 
 
 The gases evolved in conversion are principally CO2 and 
 CO. These result from the more or less perfect combustion 
 of carbon, which enters into every military explosive under 
 circumstances intended to facilitate its oxidation. 
 Dissociation. 
 
 The tendency at high temperatures of CO2 and other com- 
 plex products to occur in simpler forms, as CO + O, is sup- 
 posed by Berthelot to exert a powerful influence upon the 
 corresponding pressures. 
 
 Dissociation, as this phenomenon is called, whether it pre- 
 vents the formation of the complex product or destroys it, 
 increases the specific volume of the gaseous products; but, 
 since Mariotte's law has been proved not to hold for pres- 
 sures ^ of those found in fire arms, it is supposed that the 
 loss of heat from imperfect combination, or from work done 
 
II. — EXPLOSIVE AGENTS. 
 
 in breaking up the molecules already formed, exceeds in its 
 effect upon the resultant pressure the increase of specific 
 volume cited. External causes may subsequently decrease 
 the temperature and permit recombination with a relative 
 increase of pressure. 
 
 It is found that, when the conversion yields a large pro- 
 portion of CO, the violence or sharpness of the explosion is 
 increased. This is supposed to be due to the rigidity or 
 stability of this gas against diSvSOciation. 
 
 H2 O is, by some, supposed to be subject to dissociation 
 at the temperatures found in explosions. (See Bloxam, Arts. 
 36, 68, 311, Note.) 
 Firing. 
 
 The proximate cause of the reaction resulting in an explo- 
 sion is always the absorption by some portion of the explo- 
 sive of heat sufficient to raise its temperature to the point 
 necessary to start the conversion. 
 
 The source of heat may be external; or, as in spontaneous 
 decomposition, internal. 
 
 The means by which the temperature of the explosive is 
 raised to the critical point may, in general terms, be called 
 firing. 
 
 Firing generally results from the transformation of kinetic 
 energy into heat as a result of arresting the motion of either 
 molar or molecular masses. 
 
 Almost all explosives may be fired by molar shock, if it be 
 concentrated on a mass of the explosive which is sufficiently 
 small. (Bloxam, Arts. 309, 434, 538). 
 Orders of Explosion. 
 
 The energy of molecules in motion depends principally 
 upon their velocity; and the external work done in stopping 
 them, upon their stability of composition. When an explo- 
 sive is fired by contact with incandescent matter, as by a 
 flame consisting of molecules of COg, C, etc., moving with 
 
II. — EXPLOSIVE AGENTS. 3 
 
 relatively low velocities, the explosive is said to be ignited^ 
 and the explosion is called low or of the second order. 
 
 When fired as by fulminate or gun cotton, the conver- 
 sion of which yields a large proportion of molecules of CO, 
 moving with a very great velocity, the explosive is said to 
 be detonated, and the explosion is called high or of \.\\& first 
 order. ■ Explosives which readily detonate are called high 
 explosives. 
 
 Example, Gun-cotton when — 
 
 Order. 
 
 Ignited j unconfined; burns quietly — 
 
 ^ * * ' ( confined; explodes like gunpowder 2nd 
 
 unconfined ) i j vu 
 
 [ explodes with great 
 
 f violence 1st 
 
 Detonated . . . -j or 
 
 ( confined; 
 
 The distinction between the two orders of explosion is 
 only conventional; the phenomena in practice appearing 
 often to partake of the nature of both orders. 
 
 This may explain certain anomalies observed in mining 
 and in artillery. In mines, when the charges are large, the 
 high pressure resulting from the initial explosion, if at a 
 point considerably beneath the surface of the charge, is sup- 
 posed to cause the detonation of the remainder. In cannon 
 the mixing of quick with slow powder produces a similar 
 effect. 
 
 BERTHELOT S THEORY OF EXPLOSIVES. 
 
 Origin of Reactions. 
 
 " Every explosion must be referred to some initial increase 
 of temperature transmitted from particle to particle on the 
 surface of an explosive wave. This wave raises successively 
 all portions of the explosive to the temperature of convei- 
 sion. 
 
II. — EXPLOSIVE AGENTS. 
 
 Propagation of Eeactions. 
 
 Two limiting conditions are supposed to result, viz.: 
 
 1. The condition of combustion. 
 
 2. The condition of detonation. 
 
 These are progressively interchangeable in different de- 
 grees, according as the amplitude and velocity of vibration 
 of the particles forming the surface of the explosive wave 
 are increasing or diminishing. 
 
 Combustion. 
 
 I. The condition of combustion depends upon a reduc- 
 tion of temperature from the free expansion of a portion of 
 the gases resulting from the initial explosion. 
 
 Successive portions of the explosive will thereupon be 
 heated to the temperature of decomposition with a velocity 
 depending upon various conditions; this velocity, compared 
 with that of detonation, is slow. 
 
 Detonation. 
 
 II. On the other hand, the condition of detonation de- 
 pends upon an initial shock, too sudden (sharp) to permit of 
 molar motion of the particles of the explosive. It is, there- 
 fore, transmuted into heat which may raise the contiguous 
 molecules to the temperature of conversion. The result- 
 ing gases arc projected as a single (not periodic) explosive 
 chemical wave traveling throughout the successive layers of 
 the unexploded mass. This wave transforms its energy into 
 heat at each impact, and, by virtue of its acceleration, raises 
 each of the successive layers more rapidly to the tempera- 
 ture of conversion. 
 
 Origin of Orders of Explosion. 
 
 The order of the resulting explosion will depend upon the 
 velocity with which the reaction is propagated; /. ^., the velo- 
 city of the wave surface described. 
 
 The velocity of the wave surface will depend — 
 
n. — EXPLOSIVE AGENTS. 
 
 1. Upon the molecular velocit}^ of the reaction; /. ^., the 
 rate of conversion under constant conditions. 
 
 2. Upon conditions which prevent the free expansion of 
 the gases formed. 
 
 3. Upon the mass and initial temperature of the explo- 
 sive; these affect the rate of cooling. 
 
 The last two conditions may be neglected when, as with 
 the high explosives, the first is fully satisfied. 
 Influence of Detonator. 
 
 It is seen that detonation depends upon a chain of causes 
 which results from the nature of the initial explosion. Herein 
 lies the importance of the nature of the detonator, its mass, 
 and the nature of its own explosion. 
 
 Its conversion should be rapid and evolve abundant heat. 
 The mercuric fulminate is the detonator which is preferably 
 employed. It is less violent than NCI, but yields more heat 
 by its explosion and also much CO. 
 Influence of the Explosive detonated. 
 
 Detonation depends upon the physical condition of the 
 explosive. Its sensitiveness generally diminishes as its den- 
 sity and elasticity increase, since the shock is distributed 
 over a greater mass." 
 
 SYMPATHETIC DETONATION. 
 
 Conditions. 
 
 The instability of the high explosives renders their con- 
 tact unnecessary when the continuous detonation of several 
 charges is desired. The maximum interval permitting ''sym- 
 pathetic detonation," or "detonation by influence," and the 
 order of this detonation, depend upon the elasticity of the 
 intervening medium, the mass of the primitive charge, and 
 the order of its explosion. 
 Examples. 
 
 Calling w the weight of the primitive charge in pounds, 
 and d the maximum interval in feet — 
 
n. — EXPLOSIVE AGENTS. 
 
 In water, d=S w. 
 
 On a firm soil, (/=5 w. 
 
 On an iron rail, ^=10 w. 
 
 When discs of compressed gun-cotton are in contact, the 
 velocity of detonation is said to be over 3J miles per second 
 when the discs are wet, and less than 3J miles per second 
 when they are dry. The incompressibility of the water assists 
 in transferring the shock. 
 
 STRENGTH OF EXPLOSIVES. 
 
 The strength of an explosive, or its mechanical efificiency, 
 may be analyzed by reference to 1, its potential; 2, its force; 
 3, the molecular velocity of its reaction. 
 
 1. Potential. 
 
 The potential of an explosive is the maximum work 
 which a unit weight of it can perform. It is measured by 
 the product of the quantity of heat liberated by the reaction, 
 and the mechanical equivalent of heat; or, Q= J x H. 
 
 The potential is independent of the process of conversion, 
 provided it be complete and its products be constant. 
 
 In practice, these products often vary with the circum- 
 stances under which they are formed, so that the potential 
 realized will also vary. 
 
 Only a portion of the potential can be realized in prac- 
 tice, depending upon the volumes of the gases produced, 
 their specific heats, and the difference between the tempera- 
 tures at which they are formed and to which they are ex- 
 panded. 
 Examples.* 
 
 Theoretical potentials, in foot tons, resulting from the 
 conversion of one pound of each of the following sub- 
 stances: 
 
 * It is required that only the general principles illustrated by this and 
 following tables shall be committed to memory. 
 
II. — EXPLOSIVE AGENTS. 
 
 Name. Foot Tons. Proportion. 
 
 Blasting powder 391 1.0 
 
 Cannon " 609 1.3 
 
 Sporting « 642 1.4 
 
 Gun-cotton 716 1.8 1.0 
 
 Dynamite No. 1 884 2.3 1.3 
 
 Explosive Gelatine 1,235 3.2 1.8 
 
 Nitro-glycerine 1,282 3.3 1.8 
 
 Chloride of Nitrogen 216 0.5 
 
 Anthracite coal 6,170 13.0 
 
 The greater potential of coal is due to its composition and 
 to there being no loss of energy expended in converting in- 
 to gas the compounds of oxygen contained in the other sub- 
 stances. 
 2. Force. 
 
 The force of an explosive, or the pressure per unit of area 
 due to the explosion of a unit of weight in a unit of volume, 
 may be calculated on theoretical grounds from the formula,* 
 
 In which v^ is what is known herein as the specific volume of 
 the gas, viz.: the volume in litres of the gases resulting from 
 firing one kilogramme of powder, taken at 0° C, and at the 
 pressure p^ of one atmosphere ; and c is the specific heat of 
 the gas. 
 
 But the uncertainty attending the application of the laws 
 of Mariotte and Gay-Lussac to such high pressures as exist 
 in cannon, and the doubt as to the nature and state of the 
 products of explosion at the epoch of maximum pressure 
 have caused instrumental measurements of pressure to be 
 preferred. 
 
 Examples. 
 
 The following table shows in round numbers the relative 
 force of the explosives named. 
 
 * For the deduction of this formula see page 11. 
 
II. — EXPLOSIVE AGENTS. 
 
 The detonation of gunpowder was accomplished by mix- 
 ing it with dynamite. 
 
 Eelative Force. 
 Explosive. 1st Order. Snd Order. 
 
 Gunpowder 4.0 1.0 
 
 Gun-cotton 6.0 3.0 
 
 Nitro-glycerine 10.0 5.0 
 
 The force of a mixture of high explosives is proportional 
 to the sum of the products of the force of each constituent 
 by the corresponding fractional part of the whole mass. 
 
 A remarkable property of gunpowder (to be referred to 
 hereafter) is that, however its potential may vary with its 
 composition, the force of all compositions is sensibly con- 
 stant. The specific volume of the gases formed seems to 
 vary inversely with the quantity of heat evolved in their 
 formation. 
 
 3. Rapidity of Reaction. 
 
 The temperature increases with the rapidity of the reac- 
 tion. This depends upon the affinity between the combin- 
 ing molecules, and largely upon the state of aggregation 
 of the exploding mass, in so far as it affects the distances 
 between them. 
 
 In certain high explosives, the rapidity of the reaction 
 causes so high a temperature that the gaseous products are, 
 as it were, shot against the w^alls of the envelope with such 
 velocity that the effect seems due rather to a physical shock, 
 than to the elastic pressure of a confined gas. With such 
 explosives tamping is relatively unneccessary. 
 
 VALUE OF EXPLOSIVES. 
 
 As a general rule, the value of an explosive depends: — 
 1. Mechanically; upon its primitive state of aggregation, in 
 
 so far as this affects the ease of handling it in loading; also 
 
 upon its density. 
 
II. — EXPLOSIVE AGENTS. 
 
 V H 
 2. Chemically; upon the value of the ratio —2 — z=iv^T^ 
 
 If, when this is great, the conversion is sufficiently rapid, a 
 high and elastic pressure will succeed the initial shock; this 
 pressure will be well sustained, since the cooHng effect of 
 the envelope will be relatively small. 
 
 The potential of an explosive is thus seen to be the 
 measure of its power of sustaining a given force or pres- 
 sure. 
 Examples. 
 
 The relative importance of potential, force, and rapidity, 
 depends upon the use made of the explosive. 
 
 In order to burst, we use one of high force and density, 
 acting locally like an hydrostatic pressure. 
 
 Chloride of nitrogen detonates with such rapidity that it 
 may simply pulverize the surface of the envelope without 
 rupturing its walls. 
 
 For mining in rock or coal, blasting powder is better than 
 cannon powder, since the end sought is rather the rup- 
 ture of the envelope than the dispersion of the fragments. 
 Its force depends on the great specific volume of the gases 
 generated rather than upon their temperature. 
 
 For blasting in earth, cannon powder is better than blast- 
 ing powder as its potential is higher. Its diminished den- 
 sity, compared to high explosives, distributes the effect over 
 a larger area. 
 
 MILITARY EXPLOSIVES. 
 
 The principal explosives used in warfare are of two 
 general classes: 
 
 1. Mixtures. 
 
 Gunpowder and its like; these are more or less inti- 
 mate mechanical mixtures of combustibles, such as C, S, Sb, 
 with an oxydizing agent, generally a nitrate or a chlorate. 
 
10 ■ II. — EXPLOSIVE AGENTS. 
 
 Explosives of class 1 are relatively stable. 
 
 2. Compounds. 
 
 Nitro-glycerine and gun-cotton and their derivatives. 
 These are chemical compounds, formed by the substitution, in 
 an organic substance of the general form C^ Hy 0„ of 
 3 molecules of NO2 for 3 atoms of H. 
 
 The weak affinity of N renders the NO^ a readily acces- 
 sible magazine of oxygen. 
 
 Explosives of class 2 are called high explosives, and 
 are relatively unstable. In this class are included the 
 fulminatmg compounds. See Chap. XIV. 
 
 GUNPOWDER. 
 
 This is formed of a mixture of KNO3; C, and S, in the 
 proportions of about 75, 15, 10. These proportions are 
 considerably varied in pyrotechnic compositions. 
 
 The conversion of gunpowder is approximately expressed 
 by the following reaction: 
 
 4KN03-|-Q + S=K2C03 + K2S04 + N,-i-2COa4-CO. 
 
 The reaction is really much more complex, and varies 
 with the circumstances attending the explosion, even 
 though great care be taken to make them constant. 
 
 Illustration. 
 
 The parts played by the three ingredients may be im- 
 agined by reference to the forced combustion of coal in a 
 furnace. 
 
 The charcoal, in which form C is introduced, forms the 
 main supply of fuel. The sulphur, owing to the ease with 
 which it is ignited, takes the place of the kindling material. 
 The nitre acts as a bellows forcing in air. 
 
 The sulphur also gives coherence to the grain, correct- 
 ing the friability of a binary mixture of carbon and nitre. 
 
11. — EXPLOSIVE AGENTS. 11 
 
 Advantages and Disadvantages. 
 
 The facility with which, by varying the proportions and 
 the arrangement of the ingredients of gunpowder its 
 conversion may be controlled, and also its comparative 
 stability against accidental ignition, have hitherto com- 
 pensated for its defects. 
 
 These refer to its bulk, the care required in storage, its 
 sensitiveness to dampness, the large solid residue left from 
 its conversion, and the danger attending its manufacture. 
 While for special purposes, where great force is required, it 
 is being supplanted by the high explosives; its value, as a 
 reservoir of potential energy for purposes of propulsion, 
 increases as our knowledge of its properties extends. 
 
 Note to page 7. 
 
 1. From the chemistry we have p v =/o ^^o ( 1 H 7 = — 7 ) . If in 
 
 \ 273 ^Tdl 
 
 this we make v = l, then by definition /= p = — — ^ — - = — . 
 
 •^ ^ 273 273 C 
 
III. — INGREDIENTS OF GUNPOWDER. 
 
 CHAPTER III. 
 INGREDIENTS OF GUNPOWDER. 
 
 COMBUSTIBLES. 
 
 1. Sulphur* 
 Preparation. 
 
 This is refined by distillation. The product is called 
 "flowers of sulphur," or "rock sulphur " or "brimstone," 
 according to the temperature at which the volatile pro- 
 ducts are condensed. 
 Properties. 
 
 If below 115°, minute crystals or "flowers" are formed; 
 above that temperature, the vapors condense in a liquid 
 form, which is cast into moulds. Flowers of sulphur are 
 not used for gunpowder, as they contain SOg and HgSOji 
 which are hygroscopic. 
 
 2. Charcoal, 
 Material. 
 
 Charcoal used for gunpowder is made from wood, the 
 composition of which, excluding water and ash, is repre- 
 sented by CeHioOg, corresponding to the following propor- 
 tions per cent.: 
 
 c, 
 
 44 
 
 H, 
 
 6 
 
 0. 
 
 50 
 
 100 
 
 The object of carbonizing the wood is twofold. 1st. To 
 increase the calorific value of the fuel by increasing the 
 
III. — INGREDIENTS OF GUNPOWDER. 
 
 proportion of carbon. 2d. To increase its calorific inten- 
 sity by facilitating its reduction to powder. 
 Composition. 
 
 Gunpowder charcoal consists of from 55 to 85 per cent, 
 of carbon with varying proportions of hydrogen, oxygen, 
 and ash. Its imperfect distillation leaves varying amounts of 
 hydro-carbons which increase its inflammabiUty, and, owing to 
 the calorific value of hydrogen, may increase its potential. 
 Condition. 
 
 The uniform action of fired gunpowder and the safety of 
 its manufacture depend largely upon uniformity in the 
 condition of the principal fuel which it contains. 
 
 Uniformity is sought by using the same kind of wood, 
 carbonized by the same process; the temperature being 
 raised at the same rate to a point which, for each grade of 
 charcoal, is the same. 
 
 PREPARATION. 
 
 Preliminaries. 
 
 White woods, such as the young willow or alder, which 
 are soft and of rapid growth, are preferably employed, 
 since they yield a charcoal that is inflammable, friable, and 
 free from ash. 
 
 The bark is removed, so as to facilitate drying in the 
 open air, and to free the coal from earthy matter and 
 salts. 
 Distillation. 
 
 The wood is usually distilled in iron retorts, surrounded 
 by flame consisting largely of the gases evolved by the 
 process: Figures 1 and 2. 
 
 For convenience, the wood is charged in slips^ which are 
 cylinders of thin sheet iron. 
 
 The progress of the operation is judged of by test sticks, 
 withdrawn from time to time for examination; by the use of 
 
HI. — INGREDIENTS OF GUNPOWDER. 
 
 a pyrometer, or by the appearance of the flame and smoke 
 as follows. 
 
 Phenomena of Carbonization. 
 
 The rate of distillation being always slow, the character- 
 istics of the product depend principally upon the temper- 
 ature at which the process ceases. Five stages are recog- 
 nized, of which three correspond to useful grades of 
 charcoal. 
 
 I. Up to 150°, desiccation occurs. 
 
 II. At 150°, decomposition begins, and continues as fol- 
 lows: — 
 
 1st. H and O are evolved and unite. 
 
 2nd. Three acid oxides (carbonic, acetic, and 
 pyroligneous acids. — COg; CH3, CO2H; CgH^Og) 
 and an empyreumatic oil of an analogous com- 
 position are evolved. 
 
 3rd. Soot comes forth in heavy clouds. 
 
 4th. The gases burn with a ruddy flame. 
 
 6th. As the proportion of O diminishes, CO re- 
 places CO2, and at 260°, the flame becomes blue. 
 
 The solid products are called brands (Fr. fumer- 
 ons)j which smoke in burning. 
 
 III. From 260° to 270°, brown charcoal is formed. It is 
 smokeless but tough. 
 
 IV. From 270° to 340° is the period of the formation of 
 hydro-carbons; both gaseous, viz.: defiant and marsh gases 
 (Cg H^; C HJ, and in various liquid forms, including coal 
 tar. The gases burn with a yellow flame, which, as the 
 proportion of C diminishes, gradually becomes pale. 
 
 At 280° the liberation of the hydro-carbons changes the 
 charcoal from brown to red (charbon roux); it tends to 
 raise the temperature suddenly to about 340°. 
 
III. — INGREDIENTS OF GUNPOWDER. 
 
 The effect of this rise in temperature is to convert the 
 red coal to the next grade, which is black. The redness 
 of the product will, therefore, depend upon the care taken 
 in regulating the temperature. This is done by drawing 
 the fire, and completing the process by the residual heat. 
 
 The operation is difficult and the product not uniform. 
 
 V. Above 340°, black charcoal is formed in proportions 
 increasing with the temperature, as indicated by the in- 
 creasing whiteness of the flame. 
 
 The effect of increasing the temperature upon the pro- 
 portions of the constituent elements is shown roughly by 
 the following table: 
 
 Max. Temperature.. 150° 260° 280° 350° 
 
 Prr»rln/^fo Dried Brown Red Black 
 
 jrruUUCLb. , Wood, Coal. Coal. Coal. 
 
 Carbon 44.0 68.0 71.0 77.0 
 
 Hydrogen 6.0 5.0 4.5 4.0 
 
 Oxygen 50.0 27.0 24.5 19.0 
 
 Proportion of Weight 
 
 of Dried Wood... 100.0 60 37 30 
 
 Physical Properties. 
 
 The physical properties also change. The higher the 
 temperature — 
 
 the more — the less — 
 
 1. brittle; 1. hygroscopic; 
 
 2. hard and dense ; 2. violent as an ingredient 
 
 3. prone to spontaneous com- of gunpowder — 
 
 bustion — 
 does charcoal become. 
 
 SPONTANEOUS IGNITION OF CHARCOAL, 
 
 Cause. 
 
 The property of charcoal by which it condenses gases 
 within its pores, particularly the vapor of water, may raise 
 its temperature to the point of ignition. This ^ facilitated 
 
in. — INGREDIENTS OF GUNPOWDER. 
 
 by the occluded oxygen and by the increased surface result- 
 ing from pulverization. 
 Preservation. 
 
 To prevent accident, it is cooled slowly, and kept in the 
 stick for several days. To obtain uniformity in the amount 
 of water occluded, it is prepared only as required for use. 
 
 Its power of spontaneous ignition, when pulverized, is 
 destroyed by mixing it with sulphur or nitre. 
 
 MANUFACTURE OF BROWN CHARCOAL BY SUPERHEATED 
 STEAM. 
 
 Process. 
 
 The uniform production of brown charcoal may be 
 accomplished by exposing it for a longer period to a some- 
 what lower temperature than that above assigned as the 
 maximum. For this purpose superheated steam is used, as 
 shown in figure 3. 
 Eetort. 
 
 The retort is a fixed vertical cylinder of boiler iron, 
 jacketed with mineral cotton. (Bloxam, Art. 217.) 
 
 Through perforations in the cast-iron top enters a cur- 
 rent of steam which has been superheated in a coil to about 
 230°. 
 
 The wood is piled vertically on a perforated false bottom 
 made fast to an axial bar, by which the contents can be 
 removed. 
 
 The condensed steam and the water, acids, and tar drain 
 through the pipe shown. 
 Product. 
 
 The process lasts about four hours, being stopped when 
 experience shows that the fibrous structure of the wood is 
 about to disappear. 
 
 The fiber, which is retained for its binding effect on the 
 structure of the powder made from this coal, notably 
 increases the difficulty of pulverizing it. 
 
III. — INGREDIENTS OF GUNPOWDER. 
 
 OXYDIZING AGENTS. 
 
 1. Nitre. 
 Source. 
 
 Only about one-tenth of the supply of nitre is the native 
 Indian product; the remainder comes from the double 
 decomposition of the sodium nitrate with a potassium salt. 
 
 Impurities. 
 
 The principal impurities are the chlorides, the affinity of 
 which for moisture renders them objectionable. Not over 
 ■g-g^ is allowed in nitre used for government gunpowder. 
 
 2. Sodium Nitrate, 
 Advantages. 
 
 1. It is cheaper than nitre for equal weights. 
 
 2. Owing to the relative atomic weights of sodium (23), 
 and potassium (39), 85 per cent, of the. usual proportion of 
 nitre suffices as a supply of oxygen, still further reducing 
 its cost. 
 
 3. If the usual proportion of 75 per cent, be retained, the 
 greater volume of gas evolved increases the force of the 
 powder and adapts it especially for blasting. 
 
 Disadvantages. 
 
 1. The deliquescent properties attributed to the salt are 
 detrimental when the powder made from it is to be stored. 
 
 2. The salt is more soluble than nitre, and, therefore, 
 powder made from it suffers more than ordinary powder 
 from the segregation of the salt by efflorescence. This is 
 due to the acqueous vapor condensed in the pores of the 
 charcoal which the powder contains. When the powder is 
 made on the spot where it is used, as in the excavation of the 
 Suez Canal, this objection need not apply. 
 
III. INGREDIENTS OF GUNPOWDER. 
 
 3. Potassium Chlorate. 
 Disadvantages. 
 
 1. The low temperature of conversion, due to the affinity 
 of chlorine for the metals, renders the powder dangerous 
 when exposed to shock. 
 
 2. Its conversion gives free chlorine, which attacks the 
 bore of the gun and is injurious to the gunners. 
 
 3. It is costly. 
 
 4. The uncontrollable violence of mixtures containing 
 the chlorates relegates them to the category of the high 
 explosives discussed in Chap. XIV. 
 
 They are principally iemployed for igniting other explo* 
 5ives; themselves being ignited by friction. 
 
 4. Ammonium Nitrate, 
 
 This is becoming extensively used in the so-called smoke- 
 less powders for heavy cannon. 
 
 Advantages. 
 
 The products of combustion are gaseous or volatile, so 
 that the smoke is greatly diminished in density, and the 
 entire volume occupied by the powder is available for the 
 expansion of the gases. 
 
 Disadvantages. 
 
 The deliquescence of this salt requires that powder made 
 from it be hermetically sealed. This prevents the use of 
 the ordinary cartridge bags. 
 
IV. THE MANUFACTURE OF GUNPOWDER. 
 
 CHAPTER IV. 
 
 THE MANUFACTURE OF GUNPOWDER. 
 
 ACCIDENTS. 
 
 Buildings. 
 
 Owing to the danger of explosion the buildings are scat- 
 tered as much as possible and are separated by traverses or 
 rows of trees. Figs. 1, 2. 
 
 The buildings are generally constructed with heavy walls 
 on three sides, the remaining side and the roof being as 
 light as practicable, so as not to increase the violence of 
 explosions by unnecessary confinement. Fig. 3. 
 
 Power. 
 
 The machines employed are usually automatic, power being 
 conveyed by canals (fig. 1), or wire rope (fig. 2), radiating 
 from a central steam engine. As a general rule safety is 
 enhanced by slowly operating the machines. 
 
 Precautions. 
 
 The machines are started and stopped from an outside 
 shelter, the completion of the operation being indicated by 
 an automatic signal. Great care is taken to prevent the in- 
 troduction of foreign matter, the workmen being required 
 to change their clothing before entering, and wearing rubber 
 overshoes within the buildings, at the door of each of which 
 is a wet mat. 
 
 All parts of the machines liable to become loose are boxed 
 in. Iron is replaced, wherever possible, by gun-metal, copper, 
 or wood. 
 
IV. — THE MANUFACTURE OP GUNPOWDER. 
 
 Automatic devices are arranged to drench the contents of 
 buildings adjacent to a probable explosion. 
 
 The diffusion of dust is avoided by boxing in those 
 machines which produce it. 
 
 Powder in barrels is always gently handled. It should 
 never be rolled for transportation. 
 
 These details are given to suggest the precautions neces- 
 sary while handling gunpowder in service. 
 
 PRINCIPLES OF THE MACHINES EMPLOYED IN THE MANU- 
 FACTURE OF GUNPOWDER. 
 
 Types. 
 
 In order to derive the benefits of continuous operation, 
 the tools yOX portions of the machines in contact with the 
 material, are preferably of the rotary type. Reciprocating 
 motion is objectionable, in that it wastes energy in revers- 
 ing the direction of the motion at each end of the stroke. 
 
 Classification. — The tools employed may be classified ac- 
 cording to their functions, as follows: 
 
 
 FUNCTIONS. 
 
 NAME OP TOOLS. 
 
 Nature 
 
 
 
 
 
 of 
 Operation. 
 
 
 General. 
 
 Special. 
 
 General. Special. 
 
 
 
 
 U.B011S \l^ 
 
 continuous. 
 
 
 
 fl. disintegration 
 
 intermittent. 
 
 
 
 
 { 2. Barrels tumblins 
 
 contnmous. 
 
 1. 
 
 To divide by 
 
 . 
 
 
 fl. cylindrical 
 
 continuous. 
 
 
 
 1 2. separation 
 
 Sieves ■ 
 
 2. flat 
 
 1 
 
 intermittent by 
 reciprocating 
 motion. 
 
 
 
 fl. mixinff 
 
 Batrels tumbling 
 
 continuous. 
 
 n. 
 
 To combine by-j 
 
 L2. pressure 
 
 fl. rolling 
 Th'^sjifin \ 2- thrusting 
 Pi esses \ (hydraulic) 
 
 continuous, 
 intermittent by 
 reciprocating 
 
 
 
 
 motion. 
 
 ni. 
 
 To convey by 
 
 
 Bands endless 
 
 continuous. 
 
 The rotary tools may be classified as to whether the 
 material lies without or within the tool; as — 
 1st. Rolls. 
 2d. Tumbling or rolling barrels. 
 
IV. — TME MANU^ACTtrkE OF CtJNfOWDEft. 
 
 Rolls. 
 
 The object of a roller or roll is twofold. 
 
 1st. To concentrate a given pressure on a small area of 
 contact. 
 
 2nd. To transfer this pressure to successive areas contin- 
 uously. 
 
 Relative motion between the material and the tool is, there- 
 fore, necessary. 
 Eeduction of Area. 
 
 The reduction of area desired is generally attained by 
 the curvature given to the smooth cylindrical surface of the 
 roll; it may be increased by fluting the surface or by provid- 
 ing it with pyramidal points. 
 
 The effect upon a granular material then resembles crack- 
 ing, rather than the crushing effect of the smooth roller. 
 Transfer of Pressure. 
 
 When the pressure is transferred but slowly, the parti- 
 cles of the material may have time to adjust themselves in 
 their new positions. The effect of the pressure will then be 
 rather to condense the material than to disintegrate it by 
 crushing. 
 Eelative Motion. 
 
 1. When the material is at rest, a single roller is used. 
 Example: a rolling-pin. See fig. 8. 
 
 In practice, the path of the roller is circular, so that its 
 effects may be repeated. 
 
 2. When the material moves, the rollers are in pairs and 
 revolve on fixed axes in relatively opposite directions. Ex- 
 ample: A clothes wringer. See fig. 14. 
 
 In this case, they act but once upon the material, which is 
 carried through them by friction, and fed to and removed 
 from the rollers by its weight. 
 
 To assist in feeding automatically, several pairs of rollers 
 may be placed in tiers, surmounted by a hopper containing 
 
4 IV. — The manufacture op gunpowder. 
 
 the material to be disintegrated. The upper tiers have the 
 coarsest teeth and are placed farthest apart. 
 
 A coffee-mill is a variety of this class. The rolls are ver- 
 tical, concentric, and conical; the outer roll, which is fixed, 
 being the more obtuse. The funnel-shaped space between 
 them serves as a hopper, and as the material descends, pro- 
 duces the effect obtained by the successive tiers above de- 
 scribed. 
 
 Fig. 4 shows a charcoal-mill and sieve. The roll is bal- 
 anced to avoid excessive pressure. 
 
 Barrels, 
 Type. 
 
 Tumbling barrels, as represented in fig. 5, are much used 
 in the arts for abrasion. Their utility depends upon the 
 inter-attrition of the contents. In powder making, besides 
 the material, these often consist of balls, b, b, lifted by ledges, 
 Z, Z, and continually falling back upon the material beneath 
 them. 
 
 When the operation has proceeded far enough, the door 
 JD is removed, disclosing a perforated screen through which 
 the finer portions may gradually escape upon the oscillating 
 sieve, S. 
 
 The product is collected in the drawer Z>/ 
 
 Varieties. 
 
 The nature of the barrel and of the balls varies with the 
 explosiveness of the material and the character of the 
 operation. Thus, the barrel may be of iron with iron balls 
 where an inexplosive material is to be pulverized*; of a 
 wooden skeleton covered with leather, using bronze or zinc 
 balls, when the operation is dangerous; or covered with wire 
 
 *When the material to be disintegrated is very tough, heavy iron 
 cylinders are used instead of balls. 
 
IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 gauze netting, and using wooden balls, where simple com- 
 minution of a friable material is desired. 
 
 By omitting the balls and varying the size of the netting, 
 such barrels may be used as sieves; and, by slightly inclining 
 their axes to the horizon, both ends may be left open, when 
 they will remove the dust. Fig. 4. 
 
 If the barrels be tight and no balls be used, the contents 
 will be merely polished. Such tools are much used in the 
 arts for finishing the surface of rough metallic objects, and, 
 in the manufacture of gunpowder, for glazing it. 
 
 Mixing Barrels. 
 
 Where simple mixture of the ingredients 'is sought, the 
 barrel may contain paddles revolving independently upon 
 its axle, as in a churn, fig. 6. The action of these paddles 
 is also disintegrating, and, where time is important, may 
 replace the more crude pulverizing apparatus described. 
 Advantages. 
 
 The principal advantage of the rolling barrels consists in 
 their cheapness of construction and operation, by which 
 their number may be multiplied, and the eifects of an 
 explosion diminished. 
 
 Carrying Bands. 
 
 These are endless belts of a suitable width, which serve 
 to carry continuously the material from one part of a 
 machine to another. 
 
 If horizontal, a plain band will suffice; but, if inclined, it 
 is furnished with elevator buckets. Fig. 7. 
 
 OPERATIONS OF MANUFACTURE. 
 
 Processes, 
 Nature. 
 
 All the stages of manufacture may be referred to the 
 following essential processes. 
 
b IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 1. Formation of a homogeneous press cake of required 
 density. 
 
 2. Breaking up the press cake into grains of required 
 size and form. 
 
 3. Finishing the grains so formed. 
 
 Operations. 
 
 The necessary operations may be divided into four 
 principal groups, viz.: 
 
 Jl. Pulverizing. 
 2. Mixing. 
 3. Moistening. 
 
 II. Operations relating to press cake. ] \ p"ressi^n°^^^^"^' 
 III. Operations relating to graining, -j \; gjf^/^^"^ 
 
 IV. Operations relating to finishing. 
 
 '1. Glazing. 
 
 2. Drying. 
 
 3. Dusting. 
 
 4. Blending. 
 
 5. Marking. 
 
 X PRELIMINARY OPERATIONS. 
 
 1. Pulverizing, 
 Process. 
 
 The nitre is generally in crystals that are sufficiently 
 fine. Otherwise, this and the other materials are pulverized 
 by any suitable process, either separately under single rolls 
 or by a binary process in a barrel, viz.: the charcoal and 
 sulphur together, or the charcoal and nitre together. 
 
 Object. 
 
 The pulverization should be thorough, so as to reduce 
 the time required for incorporation ; the latter, owing to the 
 cost of the plant and the smallness of the " charges " treated, 
 is the most expensive of the operations. 
 
IV. — THE MANUFACTURE OF GUNPOWDER. 7 
 
 2. Mixiftg. 
 
 The three ingredients may be mixed by hand or in the 
 rolling barrel. 
 
 3. Moistening. 
 Object. 
 
 The object of moistening is generally to assist in the 
 distribution of the nitre; to give consistency to the mass; 
 and to prevent a dangerous rise in temperature during the 
 various operations of manufacture. 
 
 Limits. 
 
 An excess of moisture may cause segregation of the 
 nitre by crystallization, and its evaporation, as in store, may 
 render the finished powder unduly porous. 
 
 On the other hand, extreme desiccation may lead to the 
 re-absorption of hygrometric moisture, which would affect 
 the properties of the powder dried. 
 
 The amount of moisture should never exceed 3 or 4 per 
 cent. It is frequently renewed during manufacture, accord- 
 ing to the state of the atmosphere and to the special object 
 in view. The amount present is determined by desiccating 
 a weighed sample. 
 
 II. OPERATIONS RELATING TO PRESS CAKE. 
 
 1. Incorporating. 
 Object. 
 
 This is intended to unite the dust of the ingredients as 
 intimately as mechanical means permit, and thereby to facili- 
 tate the conversion of the powder into gas. It is the most 
 important of all the operations of manufacture. 
 
 Process. 
 
 The wheel mill (Figs. 8 and 9), used for this purpose, con- 
 sists of two cast-iron cylinders Cy c^ weighing several tons 
 each and acting as single rolls. 
 
b IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 In order that their effect may be exerted throughout the 
 layer of composition, this is made only about one inch thick. 
 
 The risk attending this disposition is diminished by fre- 
 quent careful moistening, and by the eccentricity of the axle; 
 this permits the wheels to rise and fall as obstacles are 
 encountered. The constancy of the resulting pressure in- 
 creases the uniformity of their effect. This arrangement is 
 shown in Fig. 9. 
 
 The arrangement of the wheels upon an axis rotating in 
 a horizontal plane peculiarly adapts them to the require- 
 ments of this operation. For, while both edges of either 
 wheel have the same angular velocity, their paths described 
 in the same time are notably different. Hence, it follows 
 that the inner ed^e will tend to slide backward relatively to 
 the outer edge; giving to the wheel a motion of rotation 
 about an instantaneous vertical axis, combined with that 
 about its permanent horizontal axis. 
 
 The effect is to grind the material nearest to the centre 
 more thoroughly than that nearest to the curb of the 
 trough; because in the former case, the sliding of the wheel 
 repeats the effect of its crushing, and, in the latter case 
 replaces it in part. 
 
 This effect is distributed by means of ploughs preceding 
 the wheels, and by causing the wheels to travel in different 
 paths. 
 
 The process takes about two hours, depending on the 
 quality of the product; it continues day and night, while 
 that of the other machines is confined to daylight. 
 
 Product. 
 
 The product of the wheel mill, called mi7/ cake, unless 
 consolidated by very slow rolling, is friable and of variable 
 thickness and density. These defects are corrected by the 
 next process. 
 
 The perfectness of the incorporation may be tested by 
 
IV. — THE MANUFACTURE OF GUNPOWDER. 9 
 
 flashing a small quantity upon a glass plate. No residue 
 should be left. The stains left by flashing powder on the 
 blue paper used in solar printing are characteristic, and 
 increase the delicacy of the test. 
 Variations in Process. 
 
 In case of necessity the incorporation may be less 
 perfectly performed by the stamp mill (Fig. 13), or by the 
 protracted use of the rolling barrel. (See also page 15.) 
 
 2. Pressing, 
 Object. 
 
 The object of pressing powder is to increase its density 
 as a fuel, and to give it sufficient hardness to resist the 
 formation of dust in transportation. 
 Kind of Press. 
 
 The intensity and uniformity of the pressure required 
 usually demand the action of an hydraulic press, Fig. 10; 
 although, when quantity rather than quality is desired, 
 single or double rolls may be employed. 
 Process. 
 
 To increase the uniformity of the material pressed, the 
 product of the various wheel mills is coarsely granulated 
 and mixed. Then, having been moistened, it is placed in 
 layers between plates which are kept at about two inches 
 apart until the spaces between them are filled. 
 
 The powder is then gradually compressed to about half 
 its former volume; being kept from spreading by hinged 
 side pieces, which, being latched together, form a sort of 
 box. This box is generally vertical, but for convenience is^ 
 preferably horizontal and on the level of the floor. 
 Variations in Density. 
 
 The resulting density increases within limits, with the 
 duration of the pressure and with the amount of trituration 
 which the powder has received. The proportion of mois- 
 
10 IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 ture largely affects the density, since it acts as a lubricant 
 between the particles. The density is not uniform through- 
 out the press cake, being always greatest next to the mov- 
 ing surface. 
 
 To obtain uniform density, upon which it will be seen 
 that the uniform action of powder greatly depends, one 
 must compress equal masses equally incorporated and con- 
 taining equal quantities of water at equal rates into equal 
 volumes. 
 
 Wiener's Powder. 
 
 These requisites are with difficulty attained, owing to the 
 variable hygrometric condition of the atmosphere. It has 
 been attempted to dispense with water for pressing, by 
 heating the powder during this operation slightly above the 
 melting point of sulphur. 
 
 This process, invented by Colonel Wiener, of Russia, 
 renders the gunpowder practically waterproof. 
 
 Effect of Form of Plates. 
 
 The plates between which the powder is pressed are gen- 
 erally flat, in which case the press cake comes from the press 
 in slate-like slabs. The powder, resulting from breaking up 
 these cakes, is called of irregular granulation^ or simply 
 grained powder. 
 
 Modern powders for heavy guns are often pressed be- 
 tween plates, the surfaces of which are regularly indented 
 or ribbed after the manner of a waffle iron (Figs. 11, 12). 
 The resulting press cake may be readily broken up into 
 grains of great uniformity of size and shape. Such powders 
 are said to be of regular granulation. 
 
 Molded Powder. 
 
 When the press cake is made exceedingly small, so that 
 each cake shall make one grain, the powder is said to be 
 molded. See molded J>rismatic, Figure 12. 
 
IV. — THE MANUFACTURE OF GUNPOWDER. 11 
 
 Such powders are made by a number of properly shaped 
 punches and dies simultaneously operated. Fig. 15, post. 
 Concrete Powders. 
 
 The structural homogeneity of the product depends 
 much upon the condition of the material compressed. If 
 the soft mill cake, above referred to, be replaced by that 
 which has already been pressed and granulated, a co7icrete 
 powder is produced; the fine grains composing it being 
 cemented together by the pressure into a mass, the 
 porosity of which is greatest in the middle. The burning 
 of this powder is notably different from that of the homo- 
 geneous mass generally produced. 
 
 OPERATIONS RELATING TO GRAINING. 
 
 Object. 
 
 The object of graining, like that of splitting fire wood, is 
 to increase the initial surface of combustion. 
 Operations. 
 
 The press cake is broken up by a series of rolls (Fig. 14), 
 and sifted between limiting sieves. 
 Principle of Gauging. 
 
 The use of these sieves illustrates a principle common in 
 manufactures; this principle when it is applied tp individual 
 articles, is called gauging. 
 
 Assuming that no two objects can be made of precisely 
 the same size, a certain tolerance is established by the 
 adoption of a maximum gauge, through which each object 
 must pass, and of a minimum gauge, through which no ob- 
 ject may pass. 
 
 The grains which are too coarse or too fine are reworked. 
 
 Special Operations in Graining, 
 
 Regular Granulation. 
 
 These depend upon the kind of grain required. For 
 
13 IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 example, the powders of regular granulation require only 
 breaking up as by hand. 
 Pebble Powder. 
 
 The English cubical, or pebble powder is made by cutting 
 the flat press cake into prisms between ribbed rolls, and 
 then recutting these prisms across their length. 
 Flat Powder. 
 
 The flat French powder (Castan's) is made by roughly 
 breaking a rather thin press cake, so as to make the thick- 
 ness of the cake the minimum dimension of the finished 
 grain. (Fi^. 12.) 
 
 IV. — OPERATIONS RELATING TO FINISHING, 
 
 1. Glazing, 
 Object. 
 
 The object of glazing is to remove the angles and asper- 
 ities of the grain; these would form dust in transportation 
 and facilitate the absorption of moisture in store. 
 
 It compensates for the diminished density of the interior 
 of the press cake from which most of the grains are formed, 
 by increasing their superficial density by their mutual col- 
 lision; it also increases the homogeneity of their struc- 
 ture by the heat which is thus evolved. 
 Process. 
 
 Moisture having been added to give some plasticity, the 
 grains are rolled in a wooden barrel without balls. 
 
 2. Drying, 
 Object. 
 
 The object of drying is to reduce to normal limits, the 
 moisture required in the previous stages of manufacture. 
 Process. 
 
 It is accomplished by passing a current of warm, dry air 
 through successive layers'of powder spread on screens or 
 on shallow trays. 
 
IV. — THE MANUFACTURE OF GUNPOWDER. 13 
 
 The temperature should be increased gradually, to avoid 
 disintegration of the grains. 
 
 3. Dustiftg, 
 Object. 
 
 This is intended to remove the dust resulting from the 
 glazing, and detached from the surface of the grains by 
 drying. 
 
 4. Blending, 
 Object. 
 
 To neutralize unavoidable variations in manufacture, 
 powders of the same size and nature may be blended so as 
 to give certain average results. 
 Process. 
 
 Fine grain powders are mixed according to their densi- 
 ties, and those of larger grain, according to their ballistic 
 properties. Molded powders are blended in charges, grain 
 by grain alternately. 
 
 6. Marking, 
 In the U. S., powders receive certain conventional fac- 
 tory marks, of which the first two letters generally relate to 
 the size and use, and the final letters to recorded variations 
 in the manufacture, or to the date at which certain lots are 
 made. Thus, I. K. A. might mean the first lot of I. K. 
 powder used for field guns; E. V. B. the second lot of 
 hexagonal powder for sea-coast guns, etc. Similar symbols 
 are used abroad and are very convenient. 
 
 VARIATIONS IN MANUFACTURE. 
 
 COCOA POWDER. 
 
 History. 
 
 The most important improvement in gunpowder, since 
 1860, is the invention by the Germans of what, from its 
 color, is called cocoa or brown powder. 
 
14 IV. — THE MANUFACTURE OF GUNPOWDER. 
 
 It is notable for being the first important modification of 
 the long established composition of gunpowder which has 
 proved practically successful, and, as will be seen, for the 
 paradoxical nature of its results. In this country it has so 
 far been used only in heavy cannon. 
 
 Characteristics. 
 
 As made in this country by the Du Pont Powder Works, 
 it differs from ordinary powder; — 
 
 1. In the composition of the charcoal, which is made by 
 steam heat, as described Chap. III. 
 
 2. In the addition during incorporation of gummy carbo- 
 hydrates, such as sugar, dextrine, etc. 
 
 3. In the proportion of the ingredients — 
 
 Nitre, 81.5 per cent. 
 
 Charcoal and Carbo-Hydrates, 15.5 
 Sulphur, 3. 
 
 lOOO" 
 
 4. It is difficult to ignite, requiring in the gun a few 
 prisms of black powder to be built into the cartridge near 
 the mouth of the vent. 
 
 6. When ignited, unconfined, it seems to/j/j^^rather than 
 to deflagrate explosively. 
 
 This and its want of friability make it safe to transport 
 and handle in store. 
 
 6. It is quite hygroscopic, but suffers less from moisture 
 than black powder. 
 
 7. Its ballistic properties are extraordinary, 
 
 8. It gives comparatively little smoke. 
 
 Manufacture. 
 
 This resembles that of all the molded concrete powders. 
 The grams compressed are of the size of mortar powder, 
 and are slightly moistened before pressing. 
 
TV. — THE MANUFACTURE OF GUNPOWDER. 15 
 
 Press for Molded Powders. 
 
 Pressing is done by carefully regulating the motion of the 
 plungers of a duplex hydraulic press, which molds about 
 100 prisms at a time. 
 
 In fig. 15, ^ is a fixed mold plate containing a number of 
 apertures of a cylindrical or prismatic form, into which the 
 perforated plungers, G^ Z, fit. 
 
 Through the axes of the plungers run needles, H, sim- 
 ultaneously operated by the toggle-joint, /, and the supple- 
 mentary cylinder, K. 
 
 A quantity of powder is swept into the apertures, X^ until 
 they, are full. The rams, B^ B' , then approach each other 
 with equal velocities; and as L enters E, ZT rises into L. 
 
 After suitable pressure, L rises; ZT is withdrawn, and G 
 rises; lifting the prism so that it may be swept off into a 
 box. 
 
 The resulting prism has very dense ends, separated by a 
 somewhat porous belt. 
 
 NORDENFELDT POWDER. 
 
 Object. 
 
 To increase the intimacy of the incorporation and to 
 avoid the danger of performing it by mechanical means. 
 
 Manufacture. 
 Charcoal. 
 
 Straw or cotton-wool is carbonized by exposure to a 
 stream of gaseous HCl. 
 Sulphur. 
 
 Dissolved in CS^ and added to Charcoal. 
 Nitre. 
 
 In aqueous solution is gradually added to above. 
 
 The mass is mixed by paddles while in a liquid state, 
 after which the vehicles are distilled and evaporated. The 
 usual operations following incorporation are then pursued. 
 
V. — INTERIOR BALLISTICS. 
 
 CHAPTER V. 
 
 INTERIOR BALLISTICS. 
 
 Division of Ballistics. 
 
 Ballistics, which treats of the motion of projectiles, is 
 divided into interior and exterior ballistics, according as 
 the motion of the projectile within or without the gun is 
 considered. 
 Interior Ballistics. 
 
 The latter science is studied later in the course; but the 
 former is so intimately related to the conversion of gun- 
 powder into gas, that it is expedient to deal with it while 
 the circumstances of this conversion are fresh in our minds. 
 The Gun as a Machine. 
 
 Functionally speaking, the gun is a machine by which the 
 potential energy of the gunpowder is converted into the 
 kinetic energy of the projectile. 
 
 It is well to consider in advance certain elementary prin- 
 ciples relating to the construction of this machine and to 
 the measurement of the energies received and usefully 
 converted. 
 
 FORM OF GUN. 
 
 strength vs. Weight of Guns. 
 It will hereafter appear that, 
 considering a gun to be com- 
 posed of a series of elementary 
 concentric cylinders, the resist- 
 ance which each of these cylin- 
 ders offers to a permanent tan- 
 gential deformation varies in- 
 versely with the square of its 
 radius; or, if S represent the 
 stress, ABy on the interior cir- 
 
 tJ^IVE 
 
 "\ 
 
 O^' 
 
 .-f*\ 
 
V. — INTERIOR BALLISTICS. 
 
 cumference of an elementary area of cross section of the 
 bore, the radius of which is r j and y be the stress from the 
 
 same cause at any other radius, x; then j* = — ^ . This is ex- 
 
 00 
 
 pressed by figure 1. 
 
 But the weight of the elementary longitudinal cylinders 
 increases with the square of their radii. 
 
 It therefore appears, that after a certain point, an increase 
 in the thickness of the walls of the gun adds rapidly to its 
 weight and but slowly to its strength. 
 
 Strength vs. Cost. 
 
 Also, when the diameters of cannon exceed a certain 
 limit, the difficulties of construction attending an increase 
 in diameter, increase much more rapidly than do those at- 
 tending an increase in length. 
 
 Conclusion as to Form of Gun. 
 
 A given amount of energy may, therefore, be most 
 economically transferred from the gunpowder to the pro- 
 jectile, by diminishing the rate of transfer and increasing 
 its duration. 
 
 Considerations relating to the weight and cost of a given 
 cannon having thus determined the most suitable diameter, 
 it should be kept constant for the entire length of the gun, 
 provided that the stress to which it is exposed shall also be 
 constant. 
 
 It is the object of recent improvements in guns, powder, 
 and projectiles, to make this stress as high as it is safe, and 
 to prolong it as far as possible throughout the length of the 
 bore. 
 
 Recent changes in the profile of cannon illustrate the 
 progress which has so far been attained toward realizing the 
 conditions of this ideal gun. 
 
-INTERIOR BALLISTICS. 
 
 FORM OF PROJECTILE. 
 
 Until quite recently, all but experimental cannon were 
 muzzle loaders. 
 
 Until about 1860, they were smooth-bores and fired 
 spherical balls. 
 
 The success of the rifled field pieces in the war between 
 France and Austria led to the general use of projectiles, 
 oblong in shape, but, like the spherical projectiles, smaller 
 than the bore. 
 
 These cannon have been recently replaced by rifled 
 breech loaders, firing projectiles provided with a compres- 
 sible ring slightly greater in diameter than the bore. 
 
 The enlarged chamber, which this form of projectile re- 
 quires, and the resistance which it offers to motion, consid- 
 erably modify the circumstances of the conversion. 
 
 Note. — This chapter is introductory to the seven following chapters. 
 
VI. — VELOCIMETERS. 
 
 CHAPTER VI. 
 
 VELOCIMETERS. 
 
 Object. — In order to study experimentally the transfor- 
 mation of energy from the gunpowder to the projectile and 
 to the gun and carriage, and to measure the kinetic energy 
 residing in the projectile, both as it leaves the gun and when 
 it has done work upon the medium through which it passes, 
 special instruments, known as velocimeters^ chronographs^ 
 chronoscopes, etc., have been devised. 
 
 Importance. — Except where otherwise specified, the fol- 
 lowing discussion relates to the means employed for meas- 
 uring the initial velocity of the projectile. This is the great 
 measure upon which all ballistic predictions are based. 
 
 Constituent Parts. — All such instruments are chronometers 
 and consist essentially of a register and a marker. 
 
 The register has a known velocity relative to that of the 
 marker and receives from it a succession of marks, the 
 time equivalents of the spaces between which measure the 
 periods between certain events. 
 
 The events are the first visible effects produced upon the 
 velocimeter by the arrival of the projectile at certain 
 epochal points. These are often targets. 
 
 Signal Time. — The interval between an epoch and the 
 corresponding event is called the time of transmission, or 
 the signal time. See figure 14. 
 
 The time from any origin to an event = time to the 
 epoch, /, + signal time, G\ and the interval between two 
 events, 8 =(/" + a") - {t' + 6')^{t" -f) + (a' - c'). If 
 G''-a'=Oj t'-t', or r, =d. If a"-a'=Cj r=d-C; if 
 •then r=0, d--C. To diminish accidental variations in C, 
 a is made as small as possible. Knowing s, the distance 
 between the epochal points, and r, the mean velocity of the 
 projectile over the intervening path may be determined. 
 
VI. VELOCIMETERS. 
 
 Functions of Velocimeters. — Conceiving times and dis- 
 tances as being each measured from common origins, we 
 may say that the instruments record differences in instru- 
 mental distance corresponding to differences in time, 
 which differences in time correspond to differences in dis- 
 tance of the projectile from any point upon its trajectory. 
 
 Classification. — The velocimeters may be divided into 
 three general classes according as they are adapted to 
 record: — 
 
 I. One difference in time corresponding to one definite 
 difference of distance of the projectile from a common 
 origin. 
 
 II. Successive differences in time corresponding to sev- 
 eral successive definite differences of distance of the pro- 
 jectile from a common origin. 
 
 III. Continuous differences in time corresponding to con- 
 tinuous differences of distance of the projectile from a com- 
 mon origin. 
 
 Comparison of Classes. — For each fire the instruments of 
 class I determine the mean velocity of the projectile between 
 one pair of points. 
 
 Those of class II determine that between several succes- 
 sive pairs of points. 
 
 Those of class III set forth continuously the circumstances 
 of the motion. 
 
 By taking the epochal points at constant intervals, either 
 of distance or of time, the indications of the instruments of 
 class II may, by interpolation, serve to determine the varia- 
 tions in velocity corresponding to known values of A J or A r 
 and thus to approximate to the law of motion more fully 
 expressed by the record of instruments of class III. 
 
 This method enables the epochal points to be separated 
 further than the construction of the instruments of class III 
 permits. 
 
VI. — VELOCIMETERS. 
 
 CLASS I. 
 
 Events.— In class I the events are those of the falling of 
 certain masses, either freely or with constrained motion. 
 
 The position of the marks indicates indirectly the interval 
 of time separating the events. 
 
 Operation. — Calling the masses respectively a and b, ac- 
 cording to their priority of fall, b is caused to strike a while 
 a is falling. The problem resolves itself into determining 
 the difference between two intervals of time, viz.: 
 
 4=how long a was falling before it was struck. 
 
 /b=how long it took b to strike a. 
 
 Then 4— 4=0=time that a was falling before b started 
 to strike it=:the interval between the starting of a and of b^ 
 which is the time interval required. 
 
 a and b are generally caused to fall by the demagnetiza- 
 tion of electro-magnets in separate circuits, which are broken 
 by the arrival of the projectile at the epochal points. Or 
 they may be made to fall by the cutting of taut threads by 
 which they have been suspended. 
 
 Disjunctor. — An essential appendage to machines of this 
 class is the disjunctor^ by means of which, both circuits being 
 simultaneously broken, the masses a and b are caused sim- 
 ultaneously to fall. 
 
 EXAMPLES OF CLASS I. 
 
 1. THE BENTON VELOCIMETER. 
 
 See figures 1, 2 and 3. 
 
 Description.— This instrument, devised by the late Colo- 
 nel J. G. Benton, the first Instructor of Ordnance and Gun- 
 nery at the U. S. Military Academy, employs either elec- 
 tricity or threads to support a and b. These are similar 
 pendulums suspended at the centre d of the arc b c a so 
 that they are constrained to oscillate in adjacent planes par- 
 allel and close to the face of the arc; this arc, being gradu- 
 ated, forms the register. 
 
VI. VELOCIMETERS. 
 
 That pendulum which lies nearest to the arc carries at its 
 outer end the marker; this is a delicate bent lever pivoting 
 in a plane perpendicular to the arc, and so placed that its 
 inner end, which is lightly covered with printing ink, shall 
 travel close to the register. 
 
 As the pendulums pass each other, a projection on tb.e 
 inner face of the outer pendulum strikes the outer end of 
 the marker and causes it to indicate the point of meeting as 
 at c^ figure 2. 
 
 Inspection of the figure shows 0=4 — 4=time of passage 
 over the arc a o c^ minus time of passage over the arc b ^:=2X 
 time of passage over the arc o c. 
 
 Disjunctor. — The disjunctor in this instrument serves to 
 determine C, the difference in signal times. 
 
 It consists of two flat steel blades, mn, ni'n', secured to 
 the base at m^ 7n' ^ and having their free ends, n^ «', resting 
 upon posts ^, b'^ through which and the blades the electric 
 current passes. 
 
 Between the blades is a powerful bent spring r, provided 
 with a cross piece p q, which lies beneath the blades and 
 lifts them when the spring is released from the latch g. The 
 button Sy having been pressed, contact is made; it is broken 
 by pinching the latch. 
 
 Determination of Time Value of Record. — To determine 
 the time corresponding to a given reading, let / be the 
 length of the equivalent simple pendulum ; v the velocity of 
 the center of oscillation or point b; y the vertical distance 
 passed over by this point; x the variable angle which the 
 axis of the pendulum makes with the vertical; and t' the 
 time necessary for the point b to pass over an entire circum- 
 ference, the radius of which is /, with a uniform velocity v. 
 We then have : 
 
 V=: 
 
 y/2gy. 
 
VI.— VELOCIMETERS. 
 
 Substituting for y its value in terms of x, the above ex- 
 i:)ression becomes : 
 
 ^=V2^^"7cos^ 
 from which it is evident that the velocity of the pendulum 
 increases from its highest to its lowest point. 
 
 The time /' is equal to the circumference of the circle, 
 the radius of which is /, divided by the velocity v; if this 
 value of f be again divided by 360, we shall have very 
 nearly the time of passing over any degree at the height y^ 
 or — 
 
 2 7tl 
 
 t= 
 
 360^2^/ cos ^. 
 
 Calling /" the time of a single vibration of the pendulum 
 of the machine, we have by known laws — 
 
 Substituting this value in the equation above, and represent- 
 ing— 
 
 jg^|by«, wehave 
 
 V COS X. 
 
 To determine /", the pendulums are removed from the 
 machine, and the cylindrical journals about which they re- 
 volve are replaced by others, the bearing surfaces of which 
 are knife edges. Each pendulum is started vibrating through 
 a very small arc. By means of a stop-watch the time of 
 1,000 vibrations may be found. By repeating the operation 
 several times and taking the mean, the time of a single 
 vibration may be determined very exactly. This time for 
 pendulums of recent construction is 0.378 of a second. 
 
VI. — VfiLOClMETERS. 
 
 If now X be made successively equal to 1°, 2°, 3°, &c., 
 and the corresponding values of / be found, we shall have 
 the time of passage of the pendulum over each degree. 
 
 By adding the time of passage over the first degree to 
 that over the second, we shall have the time of passage 
 over an arc of 2°. In the same manner, by adding this 
 latter time to that over the third degree, we shall have the 
 time of passage over an arc of 3°, and so on. 
 
 The following table has been determined in this manner: 
 Table. 
 
 De- 
 
 grefeB. 
 
 Time in seconds 
 
 of passage over 
 
 each degree. 
 
 Sum of times in 
 seconds. 
 
 De- 
 grees. 
 
 Time in seconds 
 
 of passage over 
 
 each degree. 
 
 Sum of times in 
 seconds. 
 
 1 
 
 .00148504 
 
 .00148504 
 
 19 
 
 .00152749 
 
 .02849909 
 
 2 
 
 .00148538 
 
 .00297042 
 
 20 
 
 .00153174 
 
 .03003083 
 
 3 
 
 .00148594 
 
 .00445636 
 
 21 
 
 .00153684 
 
 .0315676T 
 
 4 
 
 .00148673 
 
 .00594309 
 
 22 
 
 .00154213 
 
 .03310980 
 
 5 
 
 .00148775 
 
 .00743084 
 
 23 
 
 .00154772 
 
 .03465752 
 
 6 
 
 .00118001 
 
 .00891985 
 
 24 
 
 .00155361 
 
 .03621113 
 
 7 
 
 .00149019 
 
 .01041034 
 
 25 
 
 .00155980 
 
 .03777098 
 
 8 
 
 .00149221 
 
 .01190255 
 
 26 
 
 .00156630 
 
 .03933723 
 
 9 
 
 .00149415 
 
 .01339670 
 
 27 
 
 .00157313 
 
 .04091036 
 
 10 
 
 .00149033 
 
 .01489303 
 
 28 
 
 .00158029 
 
 .04249065 
 
 11 
 
 .00149876 
 
 .01639179 
 
 29 
 
 .00158780 
 
 .04407845 
 
 12 
 
 .00150142 
 
 .01789321 
 
 30 
 
 .00159565 
 
 .01567410 
 
 13 
 
 .00150433 
 
 .01939754 
 
 31 
 
 .00160388 
 
 .04727798 
 
 14 
 
 .00150749 
 
 .02090503 
 
 32 
 
 .00161248 
 
 .04889046 
 
 15 
 
 .00151089 
 
 .02241592 
 
 33 
 
 .00162147 
 
 .05051193 
 
 16 
 
 .00151455 
 
 .02393047 
 
 34 
 
 .00:63087 
 
 .05214280 
 
 17 
 
 .00151847 
 
 .02544894 
 
 35 
 
 .00164070 
 
 .05378350 
 
 18 
 
 .00152266 
 
 .02097160 
 
 36 
 
 .00165092 
 
 .05543442 
 
 To Compute a Scale of Velocities. — It should be rem.em- 
 bered that the times above determined correspond to but 
 half the difference of the arcs described by the two pen- 
 dulums; therefore, they should be doubled in order to get 
 the time r. 
 
 2. THE LE BOULENGE CHRONOGRAPH. 
 
 See Figures 4, 5, 8, 9. 
 Description. — This velocimeter, invented by Captain Le 
 Boulenge of the Belgian artillery, is the one used generally 
 throughout the world for the determination of initial 
 
Vt. — vfiLO^iMETERg. 
 
 velocities. In it the masses a and b are rods falling 
 freely from electro-magnets E, E' . These are supported 
 on a stand s, so placed that while a may fall through the 
 foot of the stand, the fall of b is arrested by a trigger /, 
 the shock upon which releases a knife-shaped marker m. 
 The edge of this marker lies close to the path of a, so that 
 a very slight movement of it to the right, under the impulse 
 of a powerful spring which is liberated by the fall of b^ 
 produces a mark upon that elementary circle of a which 
 was opposite to 7n at the moment of impact. 
 
 Disjunctor. — Although the operation of the disjunctor is 
 the same as with the Benton velocimeter, its object in the 
 LeBoulenge instrument is quite different. 
 
 It serves, by making r=(9, to determine the value of 4* 
 since then 4=4> o^^ the time that a was falling before it 
 was struck measures the time required for b to strike it. 
 
 This instrument does not serve to determine the signal 
 time, but it may be shown that if the difference in signal 
 times remains constant the time recorded between the 
 events = time between the epochs, or 0=?. 
 
 Operation. — This mark may be made in three ways, as 
 follows: 
 
 1. Release m while a is at rest; the mark will fall at O, 
 which is the origin for future measurements. 
 
 2. By means of the disjunctor, rupture E and E' simul- 
 taneously; the mark will be at some point Z> at a height h 
 above O, corresponding to the time required for b to fall to 
 
 m and for m to mark the rod a. This time is /, 
 
 1 1h 
 
 or the time required for b to strike a. The mark D is 
 called the disjunction mark. 
 
 3. Use as Megagraph. — Rupture E and immediately 
 afterward E'\ the mark will occur, as at R^ at a height /%' 
 above O. This is the usual case in practice. Then 
 
VI. — VELOCIMETERS. 
 
 •v 
 
 2 h' 
 
 = the time during which a was falling before 
 
 i 
 
 it was struck, and t^—t^=Q^ as with the Benton velocimeter. 
 The mark R is called the record mark. 
 
 As a matter of convenience only, the construction of the 
 instrument permits 4 to be made constant =0^ 15, so that 
 a rule may be so graduated, that, for a given interval be- 
 tween targets, the velocity corresponding to a height OR 
 
 s s 
 
 may be obtained by simple inspection, for v =—= 
 
 T 4-OM5 
 
 The instrument so arranged is called a Megagraph. 
 
 (Greek ^eya8,-great.) 
 
 Use as Micrograph. — By raising E' so that the lower 
 end of b may be nearly level with the top of a, D will be 
 made to occur near that section of a which passes m with 
 the greatest velocity. This serves to verify the accuracy 
 of the operation of the disjunctor, of the magnets, and of 
 the marking apparatus; since, if these parts worked with 
 perfect uniformity, successive disjunction marks would be 
 found at the same height above O. The velocity of a at 
 the moment of marking magnifies the visible consequences 
 of deficient uniformity and assists in correcting the causes 
 to which it is due. 
 
 With this arrangement, if b is detached before a^ the 
 mark will be found as at R and Q=t^—t^. 
 
 The advantages of this arrangement for the measure- 
 ment of very small intervals of time give it the name of 
 micrograph. (Greek fxiupoB^-smali.) 
 
 Determination of time limit. — The following reasoning 
 determines the circumstances under which the instrument 
 should be used as a megagraph, or as a micrograph. 
 
 Considering for the moment 0r=r and remembering that 
 we are measuring the interval t=- we see that, with the in- 
 
 V 
 
VI. — VELOCIMETERS. 
 
 strument arranged as a megagraph, r may be greatly dimin- 
 ished by increasing v and reducing s. The mark R will then 
 be made near D where a has but little velocity, and therefore 
 imperceptible differences in h may correspond to considerable 
 differences in r and hence in v. Since the instrument was 
 invented, initial velocities have increased from 1,200 f. s. to 
 over 2,000 f. s. while s may be restricted, as at West Point, 
 so as to be reduced from 50 metres (164 feet, for which interval 
 the instrument was made) to but 50 feet and even less. 
 
 On the other hand, when using the instrument as a 
 micrograph, if r increase unduly, the mark will occur in 
 the same neighborhood as before, and the same conse- 
 quences will ensue. 
 
 It becomes therefore necessary to determine a common 
 time limit within which the instrument should be used as a 
 micrograph and beyond which as a megagraph. 
 
 For this time the mark will, in both cases, occur at the 
 same height above O. For the megagraph, it will be at 
 the height corresponding to 4=r + 0^''*'-.15. 
 
 For the micrograph, since the length of ^=about 0.5 
 metre, the maximum value of /b=:0^®*^-.32; therefore, 4= 
 
 Qsec.32_2'. 
 
 Equating these two values of 4, we have r=0.^®^085 as 
 the value of the time limit. 
 
 Details of the Instrument. 
 
 Chronometer. — Referring to the definitions, p. 1, the 
 rod a is seen to be a register^ the time of fall of which to 
 any distance h below the edge of the knife making the 
 mark (9, is known. 
 
 This rod in this instrument is called the chronometer. It 
 is enclosed by a tightly fitting zinc tube which receives the 
 marks. By turning this tube axially, and finally by revers- 
 ing it, many records may be made before it need be changed, 
 
10 VI. — VELOCIMETERS. 
 
 Registrar. — The rod b is called the registrar. It is much 
 lighter than a. 
 
 Adjustment. — To diminish differences in the time of de- 
 magnetization, the power of the magnets, E, E\ is reduced 
 to a safe minimum, which, by the movable screw-cores con- 
 tained in the magnets, is determined as follows: — 
 
 A definite surplus of power* is assured by attaching to 
 each armature a make-weight in the form of a tube of -^ 
 the weight of the armature. The weighted armature having 
 been suspended from the magnet, the core of the latter is 
 slowly unscrewed until the armature falls. The make- 
 weight is removed before the armature is again applied. 
 
 Disjunction Circle. — When it is desired to read velocities 
 directly from the rule, the value of t^ is made constant by 
 varying the height of fall of b so that the mark shall fall 
 upon a disjunction circle previously traced upon the zinc 
 
 recorder at a height above O = ~ — ^ — • 
 
 Levelling. — The instrument is levelled by using the sus- 
 pended chronometer as a plumb, 
 between the epochs. 
 
 Bregers Improvemen'.s. — In order to diminish variations 
 in o'a— o'b resulting from variations in the method of rupture, 
 depending upon whether the circuit is broken by the dis- 
 junctor or by impact of the projectile on the target wires, the 
 improvements of Captain Breger of the French service 
 tend: — 
 
 1. To diminish differences in the time and velocity of 
 rupture of the two circuits by the disjunctor, which differ- 
 ences are due to the unequal operating of the parts of the 
 disjunctor. 
 
 Such differences are found to make material differences 
 in the times required to demagnetize E, E', in consequence 
 of variations in the intensity of the induced currents follow- 
 ing variations in the method of rupture. 
 
VI. — VELOCIMETERS. 11 
 
 2. Differences in the rate of demagnetization have been 
 avoided by making as nearly equal as possible the masses 
 a and b, and therefore the magnetic states of E and E'. 
 
 These and other minor mechanical improvements have 
 diminished the mean error to ^ of that form.erly found. 
 
 CLASS II. 
 
 Register. — The register in these instruments generally 
 consists of a revolving polished metallic cylinder, the angu- 
 lar velocity of which is known. The surface of the cylinder 
 is preferably smoked, so as to make visible the marks which 
 it receives. 
 
 Marks. — The marks are made in two general ways; — 
 
 1st. By the trace of a quill point held lightly against 
 the cylinder. 
 
 By giving the quill point relative longitudinal motion 
 during the rotation of the cylinder, the trace may be 
 greatly developed helically. 
 
 This trace being developed during the motion of the 
 projectile, the latter's arrival at an epochal point may be 
 signalized by a sudden motion of the quill point along a 
 rectilinear element of the cylinder, causing a jog or offset 
 in the trace. See Fig. 6. The offset is here the mark. 
 
 This motion may be caused by the action of a spring 
 previously in equilibrium with the attraction of an electro- 
 magnet. This magnet is included in a circuit that is broken 
 by the arrival of the projectile at the epochal point. 
 
 If the circuit can be re-established before the next 
 epochal point is reached by the projectile, the quill point 
 will return to the prolongation of the trace, and one quill 
 point will suffice. Otherwise, as in Fig. 6, as many quill 
 points and circuits are needed as there are epochal points. 
 
 3nd. The mark may result from the passage of an 
 induced electric spark caused by the rupture of a primary 
 circuit at each epochal point. 
 
13 VI. — VELOCIMETERS. 
 
 Signal Times. — In order to avoid variations in the time 
 of signaling, it is advisable, in both cases above cited, to 
 include all the epochal points in the same circuit and to 
 provide each of them with the means of renewing the 
 broken circuit automatically before the projectile can arrive 
 at the next point. See Targets, Class II, below. 
 
 When the times to be measured are exceedingly minute, 
 this may not be feasible. Equality in signal times is then 
 sought by increasing the delicacy of the apparatus and 
 is verified by the simultaneous rupture of as many circuits 
 as there are markers to be operated. 
 
 Tuning Fork. — Uniformity in the rotation of the cylinder 
 is either assumed from the accuracy of the apparatus or 
 may be neglected by attaching a tracing quill to one of the 
 tines of a tuning fork, the time of vibration of which is 
 known. 
 
 The trace then takes the form of a harmonic curve, the 
 alternate intersections of which with a median trace, formed 
 when the fork is at rest, mark the ends of each double 
 vibration of the fork. 
 
 The duration of the double vibration is the unit of 
 measure of time; if the velocity of the surface upon which 
 the trace is formed be constant during any double vibration, 
 fractional parts of the intercepted median line will measure 
 corresponding portions of the unit of time. 
 
 The double vibration, instead of the single vibration, is 
 selected as the unit in order to neutralize errors of meas- 
 urement. The median line gives the most definite inter- 
 sections with the harmonic curve. 
 
 Interrupter. — When the total time of the observation re- 
 quires it, the vibrations of the fork F, Fig. 7, may be sustained 
 by the use of adjacent electro-magnets, w, w, the attrac- 
 tion of which separates the tines, /, t, until the rupture of the 
 circuit through the spring R^ releases them. The spring is 
 
VT. VELOCIMETERS. 
 
 13 
 
 used instead of a rigid contact so as to prolong the influ- 
 ence of the magnets. The reaction of the fork due to its 
 elasticity renews the circuit and makes the process con- 
 tinuous. 
 
 This device, as applied to the Schultz Chronoscope, is 
 known in this country as the Russell interrupter. It is due 
 to Captain Russell of the Ordnance Department. 
 
 When the total time of vibration is very short, no inter- 
 rupter is required. In this case the fork may be set vibrat- 
 ing by the sudden withdrawal of a wedge inserted between 
 its tines; it is then abandoned. 
 
 CLASS III. 
 
 In instruments of this class relative motion is given to 
 the register directly by the motion, either of the piece or 
 of the projectile. 
 
 The velocity of the register at any portion of its path is 
 determined by tracing upon it a harmonic curve with the 
 tuning fork, or by giving it a known velocity at right angles 
 to that of the moving part. In either case, a compound 
 curve is traced from which the required relations between 
 space and time may be deduced. 
 
 Examples: — 
 
 If to a gun about to recoil be fastened a bar upon the 
 smoked surface of which the harmonic curve is traced dur- 
 ing the recoil, or if some point of the gun be kept in con- 
 tact with a cylinder rotating at a known velocity about an 
 axis parallel to the direction of the recoil, we may in 
 both cases determine by interpolation the velocities desired: 
 
 For example: — 
 
 Travel 
 
 Time. 
 
 A/ 
 
 A X 
 
 ft. 
 0.00 
 0.02 
 
 0.04 
 
 sec. 
 0.0000000 
 0.0018182 
 0.0023772 
 
 sec. 
 
 0.0018182 
 0.0005590 
 
 f. S. 
 
 11.0 
 35.8 
 
14 VI. — VELOCIMETERS. 
 
 Knowing thus the mean velocities between many pairs 
 of epochal pjints, it is possible by interpolation to deter- 
 mine the accelerations at each of the epochal points and, 
 knowing the mass of the moving object, to determine the 
 intensity of the pressure accelerating it. 
 
 TARGETS. 
 
 CLASS I. 
 
 The epochal points are generally wire screens stretched 
 across the trajectory, as shown in Fig. 9. 
 
 Cannon. — In order to prevent injury to the first screen 
 and to allow for the acceleration of the projectile for a 
 short distance after it has left the muzzle, due to the rela- 
 tively great velocity of the escaping gas, the first screen is 
 put at a distance from the muzzle, which increases with the 
 calibre of the gun. 
 
 When they are situated in the bore of the gun, as in Cap- 
 tain Noble's experiments, Figs. 11 and 12, the wire may be 
 severed by the action of a wedge raised by the passage of 
 the projectile. This arrangement requires the walls of the 
 gun to be pierced radially as many times as there are 
 epochal points. 
 
 To avoid this piercing, the L^tard apparatus. Fig. 10, is 
 devised. It is principally of wood, cemented by resin to 
 the surface of the bore. The head ot the metaUic bolt, a, 
 and the metallic washer, b, are held in contact by the cross 
 pin, c. The impact of the projectile on the point of a breaks 
 the circuit and sweeps the fragments out to the front. 
 
 Small Arms. — For small arms, in order to save the time re- 
 quired in repairing at each fire the distant target, it consists 
 of an iron plate having attached to its back a flat elastic 
 blade, through which the circuit passes as in the disjunctor, 
 Fig. 3. The shock of impact breaks the circuit which is 
 immediately re-established by the elasticity of the blade. 
 
VI. — VELOCIMETERS. 15 
 
 CLASS II. 
 
 Instruments of this class that use but one circuit for all 
 the targets have an arrangement, shown in Fig. 13. 
 
 The weights, IV, depress the free ends of the spring wire 
 staples, df d, f, so that the current may pass from the brass 
 plate, ay to the brass plate, <r, through the staple, bj and from 
 ^ to ^ through d, and so on. 
 
 When one of the threads / is broken by the projectile, 
 the free end of one of the tines of d flies upward, break- 
 ing the circuit for an instant, but renewing it as soon as the 
 upper side of the oblong hole in c is reached. 
 
 The West Point target, figure 15, resembles that above 
 described, but is applied to instruments of Class I. 
 
 A discontinuous copper strip, c, c, c, conveys the current 
 when the flanged copper tubes /, t (cartridge cases), are drawn 
 into place by the weights w, w. 
 
 When a weight is cut the spring, s, lifts its tube and the 
 circuit is broken. 
 
 Compared with fig. 9, the advantages are — 
 
 1. The circuit is broken in the same manner, both by the 
 disjunctor and by the projectile. See page 10. 
 
 2. The tension of the threads and the resistance of the cir- 
 cuit are more constant than when a spHced, continuous target 
 wire is used. 
 
 3. The targets are more readily mended, and the " short 
 circuiting " of leading wires by fragments of the target wires 
 is avoided. 
 
 ELECTRIC BATTERIES. 
 
 These should be as constant as possible. Where storage 
 room permits the employment of a large number of elements, 
 the batteries of the gravity type are preferred, except for pro- 
 ducing the sparks referred to on page 11. 
 
VII. — PRESSURE GAUGES. 
 
 CHAPTER VII. 
 
 PRESSURE GAUGES. 
 Object. 
 
 From the circumstances of the case the transfer of energy 
 from the gunpowder to the projectile is accompanied by a 
 considerable elastic pressure upon the walls of the gun, 
 the effects of which, to be guarded against, require the 
 intensity of the pressure to be known. 
 History. 
 
 Owing to the want of suitable apparatus, pressures were 
 formerly inferred only from the injury resulting to the gun, 
 and it was not until the time of Rodman that this important 
 requisite was supplied. Since then great improvements have 
 been made, some of which will be described. 
 Nature of Pressure. 
 
 The pressure varies at each instant during the passage of 
 the projectile through the bore, and is generally taken to be 
 constant throughout the volume in rear of the projectile at 
 any point of its path. If we adopt Noble's hypothesis, 
 hereafter to be explained, this is equivalent to saying that 
 the gases in rear of the projectile at any instant are of uni- 
 form density. 
 
 But the expansion to the front and rear, in consequence 
 of the motion of the projectile and of the piece, diminishes 
 the density of the successive layers, estimated in both direc- 
 tions from that layer containing the center of gravity of the 
 system. This layer, called the immovable layer, is practi- 
 cally taken at the bottom of the bore, where experiment 
 shows that the maximum pressures occur. See page 17. 
 
VII. — PRESSURE GAUGES. 
 
 General Methods Adopted. 
 
 Two general methods for measuring the intensity of the 
 pressure are employed, viz.: 
 
 1. Statical. 
 
 The statical, in which the elastic pressure is placed in 
 equilibrio with a known resistance. The objections to this 
 method relate to the magnitude of the forces to be measured 
 and to the rapidity with which they vary. It is principally 
 valuable for determining the intensity of the maximum 
 pressure at the point at which the measurement is made. 
 
 2. Kinetic. 
 
 In which the intensity of the pressure at any instant is 
 deduced from the acceleration given to a known mass. 
 
 The objections to this method relate to the minuteness of 
 
 the times to be measured and to the consequences of small 
 
 . . . A''^ 
 errors m measurmg the spaces, smce a= 
 
 By the use of comparatively simple apparatus it permits 
 the law of the variation in pressure to be approximately 
 determined. 
 
 I.-THE STATIC METHOD. 
 Rumford's Plan. 
 
 In 1792, Count Rumford, who made the first recorded 
 experiments on powder pressures, sought to measure the 
 total pressure, P=/ 7t r% of a charge of gunpowder fired in 
 the closed bore of the eprouvefte, Fig. 1, by determining 
 the greatest weight, W, that would be lifted by the gas suffi- 
 ciently to allow the escape of gas to cause an audible report. 
 Conversely, the weight and the volume being constant, he varied 
 
 W 
 the charge. In either case he assumed P— W oi fiz=. r 
 
 But if we represent by /, the time during which the gases 
 were lifting the tenon of the stopper through the height h^ 
 
VII. — PRESSURE GAUGES. 
 
 the general expression Mgl = M = P- JV, (whence 
 
 /i = 
 
 F^W 
 
 df 
 
 t \ '^^ 
 
 yf^ ^ J shows that, / being very small, P must have 
 
 greatly exceeded W in order that h should have had an 
 appreciable value. 
 Process of Deformation. 
 
 This, which is the present method, consists — 
 
 1st. In determining with a press the tarage^ or law con- 
 necting known pressures with the observed permanent de- 
 formations of similar metallic specimens. 
 
 2nd. Exposing a similar specimen to the action of powder 
 gases acting over a known area; observing the resulting 
 deformation, and inferring from the tarage the intensity of 
 the total pressure producing the deformation observed. 
 Methods of Deformation. 
 
 The specimen may be deformed in several ways — 
 
 1. By making a cut, the length of which increases more 
 rapidly than its width. Fig. 2. 
 
 This is General Rodman's plan. 
 
 2. By compressing a cylinder between flat surfaces. 
 This is Captain Noble's crusher gauge, now generally 
 
 employed. 
 
 Both methods are adapted for service either within or 
 without the bore. 
 
 Apparatus, 
 Specimens. 
 
 On account of its homogeneity, copper is generally used for 
 the specimen, although lead, and even silver, are employed. 
 Pistwi. 
 
 The pressures are exerted through a freely moving piston. 
 When firing, a gas check of some kind prevents the gas from 
 leaking past the piston. 
 Gas Checks. — 1. Cup. 
 
 The action of this gas check, which illustrates a principle 
 of frequent application in ordnance, depends upon the 
 excess of the pressure within the cup over that without it; 
 
VII. — PRESSURE GAUGES. 
 
 since any gas that may leak past the edge before it is 
 fully dilated will expand so readily as to have its density 
 greatly reduced in comparison with that of the gas within 
 the cup. 
 
 2. Air Packing, 
 
 Another form of gas check depends upon a number of 
 circumferential grooves, surrounding the stem of a closely 
 fitting piston, Fig. 4. These diminish successively the 
 tension of any intruding gas and delay its progress, until, 
 by the departure of the projectile from the gun, the pres- 
 sure ceases. This principle also is applied in ordnance 
 construction. 
 External Housing. 
 
 For external use the gauge is contained in a housings 
 screwed into the walls of the gun and communicating by a 
 radial hole with the bore. This method is rarely employed 
 at present. ^ 
 
 Internal Housing. 
 
 For internal service a housing, Fig. 3, contains all the 
 parts. The drawing represents a Noble internal crusher 
 gauge, full size. 
 
 A is the specimen; B, the cavity; C the body of the 
 housing, closed by the screw y and the soft metallic gasket K. 
 
 I is the piston, the cross section of which is y^^ of a 
 square inch in area. It is enlarged at E to accommodate 
 itself to the dilatation of A. 
 
 Z> is a cup-shaped copper gas-check acting like a metal- 
 lic cartridge case, and F is a spring to keep the specimen 
 in an axial position. 
 
 Use of Internal Gauge. 
 
 To use the gauge, it is tied to the bottom of the cartridge 
 so that no powder can pass between it and the bottom of 
 the bore. 
 
VII. — PRESSURE GAUGES. 
 
 It is sometimes recessed into the face of the block of 
 breech loading guns, so that full charges may be fired. It 
 has also been similarly recessed into the base of the pro- 
 jectile. 
 Advantages of Crusher over Rodman Gauge. 
 
 The advantages of the Crusher over the Rodman gauge 
 are: 
 
 1. Size. 
 
 The small diameter of the specimen, which enables the 
 size of the housing to be greatly reduced. 
 
 When used internally, the circumstances are therefore 
 more nearly normal, and, when used externally as in Fig. 13, it 
 maybe inserted close to the walls of the bore instead of ex- 
 ternally to the gun as with Rodman's first gauge. Fig. 2. 
 
 In the latter case it was found that the gas developed con- 
 siderable kinetic energy in its passage through the walls 
 of the gun and struck the pi.ston a blow which vitiated the 
 results of the experiment. This action accounts for many 
 anomalies in the early experiments. 
 
 When properly used, the fact that the gases act by a 
 pressure and not by a blow is shown by the sensible persist- 
 ence of form of a specimen exposed to several similar dis- 
 charges, and by the experimental verification of calculations 
 based upon this statical hypothesis. 
 
 2. Surface. 
 
 The flat face of the piston is less liable to injury and 
 admits of duplication more easily than does the Rodman 
 knife. 
 
 3. Tarage. 
 
 It also admits of giving to the specimen a preliminary 
 compression before it is exposed to the action of the gas. 
 
 This, if nearly equal to that expected within the gun, 
 diminishes the velocity which the piston can acquire (see 
 ^ost) ; it also serves to verify the tarage. 
 
VII. — PRESSURE GAUGES. 
 
 EFFECT OF VARYING THE MASS OF THE PISTON. 
 
 Discussion. % 
 
 Let /* be the variable gaseous pressure on the piston ; R the 
 variable resistance to deformation of the specimen; m the 
 mass of the piston, and v its variable velocity over the 
 path X. 
 
 Let d represent the permanent compression. 
 
 Suppose the piston to be in contact with the specimen 
 and to be indeformable. 
 
 We have: 
 
 ' ^/lPdx-/lRdx. (1) 
 
 2 
 
 When X is a maximum, v—o\ x^^d, and the equation (1) 
 becomes 
 
 /\pdx=f\Rdx. (2) 
 
 Let the curves AFE and BFC in Fig. 5 represent by 
 their ordinates, respectively, the resistances and pressures 
 due to successive values of x, and let x represent only 
 permanent deformation, /. <?., that occurring beyond the 
 elastic limit of the specimen. 
 
 From the nature of powder pressures as hereafter ex- 
 plained, Chap. XI, the pressure curve will be of the general 
 form OABC\ and, if OD—d, we have area 
 
 OABCDrz^f'^^Pdx, 
 
 From the nature of the resistances to deformation, the 
 curve AFE will present no maximum phase, and the curve 
 will be of the general form AFE, such that the area 
 
 OAEn=^ f^'Rdx. 
 
 ■/> 
 
 Equations 1 and 2 show that the resistance curve, at first 
 beneath the pressure curve, rises above it when x has some 
 value = OH, 
 
Vn. — PRESSURE GAUGES. 
 
 The statical value of the ordinate E,D^ corresponding to the 
 maximum compression OD, is determined from the tarage. 
 
 The figure shows that, while ED may be greater or less 
 than IB^ which represents the maximum gaseous pressure, 
 the difference between these two ordinates will depend 
 upon the angle at which the curves intersect. If this angle 
 be such that the difference, P — R, of any two ordinates 
 corresponding to a common abscissa be relatively small, the 
 resistance corresponding to the maximum compression may 
 safely be taken as the maximum gaseous pressure. 
 
 But P-R= ^ ^ ,= ma (3) 
 
 doc 
 
 So that the difference between ED and IB can be 
 neglected only when the mass of the piston is small and the 
 initial resistance to deformation is great and increases rapidly. 
 
 The last two conditions are satisfied by a preliminary 
 deformation of the specimen to nearly the total extent that 
 is expected. Such conditions are represented by figure 6. 
 
 The indications of the gauge will be more correct when 
 the pressure curve approaches parallelism with the axis of 
 X. It will be seen that this occurs rather with slow-burn- 
 ing powders, which give a gradual change of pressure, than 
 with those which act more violently. 
 
 Tarage. 
 
 The preceding discussion shows that the pressures used 
 in determining the tarage must be applied so slowly that the 
 velocity of the piston and of the contiguous parts of the 
 machine may be neglected. Under such circumstances, 
 when the specimen is of pure copper, 8 mm. in diameter 
 and 13 mm. long, the resistance in kilogrammes, T, corres- 
 ponding to a permanent compression in millimetres, E^ is 
 given by the following equation. 
 
VII. — PRESSURE GAUGES. 
 
 ^=551 +531 E, 
 The tarage would accordingly be represented by a dia- 
 gram, such as Fig. 7, the initial ordinate being at the elastic 
 limit, and the co-efficient 531=tan ^, or the reciprocal of 
 the rate of permanent compression. 
 
 V SARRAU'S DEDUCTIONS. 
 
 An elaborate deduction by M. Sarrau, shows by an 
 analysis confirmed by experiment that,^- 
 Slow Pressure. 
 
 I. When the pressure increases slowly, as when the 
 crusher is used in the chamber of a gun firing ordinary 
 gunpowder, the maximum pressure is sensibly equal to that 
 indicated by the tarage. 
 
 ftuick Pressure. 
 
 II. When the pressure is instantaneously, or very sud- 
 denly applied, as with some of the high explosives; or 
 when, with ordinary gunpowder, the crusher is placed in 
 front of the position occupied by the projectile when at 
 rest so that the pressure shall be very suddenly applied 
 when the base of the projectile has passed the mouth of the 
 hole; then the maximum pressure is sensibly equal to that 
 corresponding to half the tarage. 
 
 The correction increases with the mass of the piston 
 employed. 
 
 THE MANOMETRIC BALANCE. 
 
 Object. 
 
 This avoids the perturbations due to the mass of the 
 piston, and permits certain relations between pressures and 
 time to be determined. 
 Simple Form. 
 
 B, figure 8, is a differential piston, the small end of which 
 is in contact with the bore, and the large base of which enters 
 slightly the air-tight cavity C, connected with a manometer 
 
VII. — PRESSURE GAUGES. 
 
 tube, M, in which mercury is kept at any given height by 
 means of air pumped into C. 
 
 A slide, a, is held by friction beneath B against the ten- 
 sion of a spring, r. 
 
 The pressure may be determined within limits by finding 
 at two successive similar fires, the heights of the mercury 
 permitting and preventing the motion of a. 
 
 Compound Form. 
 
 Also by providing, say, ten similar pistons of varying 
 area, moving outwardly from Cj each of them provided, 
 besides the arrangement ra, with some apparatus such as 
 described Chap. VI, for recording the intervals of time 
 corresponding to the motion of the slide a. 
 
 II. THE KINETIC METHOD. 
 
 This consists in determining the rate of change of the 
 pressure from the change in rate of motion of some body, 
 the mass of which is known. This body may be either 
 I, the projectile; II, the cannon; or III, a piston or auxiliary 
 projectile, placed in some radial channel communicating 
 with the bore. 
 
 I. THE PROJECTILE. 
 
 1. Direct Intermittent Method, 
 
 Mayewski's Experiments. Figure 16. 
 
 General Mayewski, of Russia, in 1867, attempted to 
 determine the acceleration of the projectile by attaching to 
 its base a rod which, passing through the breech of the 
 gun, ruptured by means of a projection upon it certain 
 electric currents placed at varying distances from the 
 initial position of this projection. The conditions of each 
 fire were made constant, except as to the portion of the 
 path of the projectile, the duration of which was to be 
 measured. 
 
10 VII. — PRESSURE GAUGES. 
 
 Supposing that x~f[t), he assumed a development 
 
 x=At+Bt^-{-Ct^ + nt'' + Qtc., (4) 
 
 and determined by trial the values for the co-efficients, A, B^ 
 etc., that would satisfy the instrumental values x and /. 
 Then, 
 
 dx 
 dt 
 
 =A^%Bt-{-ZCt^ + ^nt^^-tio. (5) 
 
 d^x 
 a=-^=2B + %Ct+12nt^ + ttc, (6) 
 
 The value of t corresponding to the manimum pressure 
 
 d^x 
 wasfoundby placing— 3 =0, and solving with respect to /; 
 
 then, by substitution in equations (1) and (3), the corres- 
 ponding values of x and a were found. 
 
 The intensity per unit of area of the corresponding pres- 
 sure, is given by the following equation: 
 
 d'^x 
 
 This pressure is only that giving acceleration to the 
 projectile. The results, found by adding to B=p n r^ the 
 pressure found to be required to force the projectile 
 through the bore, gave reasonably close approximations to 
 the results of the statical pressure gauges, altiiough the 
 apparatus was subject to many instrumental errors. 
 
 2. Direct Continuous Method, 
 Sebert's Registering Projectile. 
 
 This method, which is applicable only to comparatively 
 short lengths of bore in guns of large caliber, requires a 
 hollow cylindrical projectile, such as is shown in Fig. 9. It 
 
VII. — PRESSURE GAUGES. 11 
 
 is provided with an axial spindle, S, of rectangular cross 
 section and rotating freely at each end; one of the sides of 
 this spindle is covered with a film of soot. 
 
 A slide M moves freely on the spindle and bears a 
 delicate tuning fork 7^ arranged as described, Chap. VI. 
 
 When the projectile is fired, the inertia of the slide holds 
 it relatively at rest while the projectile passes by; the 
 points of the tines describe such a trace as is shown in 
 figure 10, in which the parallel straight lines represent the 
 traces when the slide is slipped along the spindle, the fork 
 not vibrating. 
 
 The effect of the friction between the slide and the 
 spindle can be shown to be negligible. 
 
 Although the path of the slide is limited to less than the 
 length of the projectile, yet it is within this length of travel 
 that is generally found the maximum pressure, the rate of 
 change in reaching which is one of the most important 
 objects of research. 
 
 By placing the slide at the bottom of the spindle, it may 
 serve to determine the retardation of the projectile in flight; 
 and, by confining it there by a fragile cross-pin to be broken 
 on impact, it may determine the varying resistance found in 
 penetrating a more resisting medium than the air. 
 
 3. hidirect Intermittent Method. 
 Successive Shortening of the Bore. 
 
 The mean of the muzzle velocities of a large number of 
 shots fired under conditions, which, excepting the length of the 
 bore, were identical, could be laid off as the ordinates of a 
 curve of which the abscissae should represent the various 
 paths. The curve would have the form given by Fig. 11. 
 Calling a the acceleration, we have, 
 
 dv dv dx dv /i\ 
 
 dt dx dt dx 
 
12 VII. — PRESSURE GAUGES. 
 
 The figure shows that the subnormal a= corresponding 
 
 ordinate v x tan g? = ?; x -r- • (") 
 
 ^ ax 
 
 Therefore, having plotted the curve expressing 
 v=f(x), 
 the acceleration at the different points along the bore may 
 be determined by finding the corresponding values of the 
 subnormals. 
 
 The experiments enabled positive conclusions to be 
 formed : 
 
 1st. As to the smallness of the advantage gained by in- 
 creasing the length of the bore more than 20 calibers, when 
 quick powders were used. 
 
 2nd. As to the great advantage of progressive powders in 
 guns of suitable length. 
 
 II. THE GUN. 
 
 Advantages. 
 
 Determining the pressure from the acceleration of the gun 
 in its recoil affords certain advantages owing: — 
 
 1st, To the low velocity of the gun compared to that of 
 the projectile; this permits a greater number of observations 
 to be made over a given path. 
 
 2d. To the simplicity of the apparatus, which avoids the 
 mutilation of the piece, and permits it to be used with guns 
 of varying calibers. 
 
 3d. To the aid given in the study of the pressures pre- 
 vailing at the bottom of the bore. 
 
 1. Rodman's Velocimeter , 
 Construction. 
 
 The original instrument of this description was devised 
 by General Rodman. It consisted of a cylinder rotating 
 with a known and uniform velocity about an axis parallel 
 
Vll. — PRESSURE GAUGES. 13 
 
 to that of the gun and close to it, A pointer fastened to 
 the gun traced upon the cylinder during the recoil, a line 
 which, when developed, gave the successive accelerations of 
 the recoil. The gun was hung as a pendulum oscillating 
 in the plane of fire. See figure 17. 
 
 Acceleration of Eecoil. 
 
 For example, let mm' ^ Fig. 12, be the developed circumfer- 
 ence traced by the pointer when the projectile is placed at the 
 muzzle, and the charge uniformly dispersed along the bore ; 
 and let bb' be the corresponding circumference when the charge 
 is in place. Then taking axes of space and time, ^S" and T 
 
 a = 7 — -ri, as in Chap. VI. 
 
 Tlniform Pressure. 
 
 The dotted line represents the parabola which would be 
 traced under the ideal circumstances discussed, Chap. V, 
 / V being straight and parallel to t' v' . 
 
 Rate of Change of Pressure. 
 
 It is evident, from the inclination of the initial portions 
 of the curve, that ihe velocity is actually acquired much more 
 rapidly than is desired. 
 
 2. Siberfs Velocimeter, 
 
 Construction. 
 
 The velocimeter of Colonel Sebert of the French service 
 replaces the rotary cylinder by a broad steel tape, one side 
 of which is smoked, and against which rest the tines of a 
 tuning fork set vibrating by the act of recoil. See Chap. 
 VI. 
 
 Velocity of Recoil. 
 
 The length of any double vibration measured on the 
 tape, divided by the time of the double vibration of the 
 
14 Vll.— PRESSURE GAUGES. 
 
 fork, gives us the mean velocity of recoil over that portion 
 of the path selected; from which, calling, 
 
 qv =z weight of projectile. 
 
 JV = weight of gun. 
 
 «/ = weight of powder. 
 
 2j = velocity of projectile. 
 
 V = velocity of gun. 
 
 We have V= -^ (see Chapter VI). 
 
 Velocity of Projectile. 
 
 Or else, supposing the center of mass of the powder to be 
 moved to the position occupied by the center of mass of the 
 gases, which is equivalent to supposing that half the mass of 
 the powder is added to that of the projectile. 
 
 -= --^r (9) 
 
 Position of Projectile. 
 
 Also, denoting by X the length of recoil at the end of a 
 time t, and x the corresponding path of the projectile. 
 
 Pressure on Base of Projectile. 
 
 The method above described permits the construction of 
 a velocity curve, such as Fig. 11, from which the pressure 
 corresponding to different positions of the projectile along 
 the bore may be deduced. 
 Pressure on Base of Bore. 
 
 Also, the difference between two successive velocities, as 
 determined by the trace of the tuning fork, divided by the 
 common interval of time, would give the mean accelera- 
 tion ; this multiplied by the mass of the gun gives the mean 
 
Vn, — PRESSURE GAUGES. 15 
 
 total pressure on the bottom of the bore during the same 
 interval of time. 
 
 III. AUXILIARY PROJECTILES EXPELLED THROUGH THE 
 WALLS OF THE GUN. 
 
 1. Bomford's Method. 
 
 About 1841, Colonel Bomford, of the Ordnance Depart- 
 ment, prepared a cannon by boring through its walls a 
 series of small holes at right angles to its axis, as in Fig. 13, 
 and placing in each hole a bullet, the velocity of which was 
 instrumentally determined. The pressure at the various 
 points, deduced from the velocities communicated to the 
 balls, determined the form of the old Columbiads. 
 
 This method was objectionable, as it treated the powder 
 pressure as an impulsive force and could not take into 
 account the varying accelerations of the projectile, as is 
 done in the following recent inventions. 
 
 2. Ricqs Register^ Fig. 14 
 
 A cylinder C, revolving with known and uniform velocity, 
 is enclosed in a box B^ through a groove, Z>, in which slides a 
 marker F^ in contact with the piston Z. 
 
 The weight per unit of the sectional area, ^, of (F-Vl^ 
 may be varied at pleasure. 
 
 When the gun is fired, a curve, such as shown, is traced 
 on the cylindery from which, by finite differences, we have 
 
 ^= -,. (11) 
 
 ^= ^(KJf (12) 
 
 8. T/ie French Accelerograph, 
 
 This projects vertically upward a piston, the mass of 
 which may be greatly varied by the addition of weights. 
 
16 
 
 VIT. — PRESSURE GAUGES. 
 
 A fixed tuning fork traces the harmonic curve upon a 
 blackened surface on the piston. 
 
 III. STATIC AND KINETIC METHODS COMBINED, 
 Objections to Kinetic Method. 
 
 It will be seen that the objection to the kinetic method 
 lies in the liability of error in the measurement of the small 
 spaces by which the time record is expressed. 
 
 This limits the method principally to the cases where the 
 pressure changes but slowly, as in those powders known as 
 slow-burning powders. 
 
 Noble's Experiments. 
 
 In 1869, Capt. Noble, R. A., prepared a M. L. gun as 
 .described, Chap. VI. Crusher gauges were placed in the 
 holes leading to the chamber, and the other holes were 
 provided with the apparatus also given in Chap. VI. 
 
 By observation and interpolation, a table of spaces and 
 times was formed so as to make A x constant=6, 10°^, as 
 follows: 
 
 
 
 
 7J ^^ 
 
 
 
 Av 
 
 /- ^ a 
 
 X 
 
 / 
 
 At 
 
 At 
 
 A V 
 
 logdt 
 
 dt 
 
 ^ Ttr^g 
 
 mm. 
 
 sec. 
 
 sec. 
 
 m. s. 
 
 m. s. 
 
 * 
 
 m. s. 
 
 kil. per 
 c=] cm. 
 
 0.00 
 6.10 
 
 0.0000000 
 0.0018182 
 
 0.0018182 
 
 8.85 
 
 
 
 
 
 
 
 0.0005590 
 
 
 7.56 
 
 4.88327 
 
 9891 
 
 271 
 
 12.20 
 
 0.0023772 
 
 
 10.91 
 
 
 
 
 
 
 
 0.0002528 
 
 
 9.02 
 
 4.61517 
 
 22082 
 
 005 
 
 18.30 
 
 0.0026330 
 
 
 19.33 
 
 
 
 
 
 * The values of dt are obtained by interpolation. That of the mean 
 
 acceleration for the first value of Az^, viz., A/= 
 
 0.0023772 
 
 =0.0011886 
 
 would evidently be too large, and the corresponding value for /=186.5 
 would be too small. The method of interpolation is similar to that here- 
 after described in Exterior Ballistics. 
 
VII. — l-KESSTTRE GAUGES. 17 
 
 Fig. 15, represents the curves obtained in a 10 in. gun 
 firing a 300 lbs. projectile with fine (R. L. G.), and coarse, 
 (Pebble) powders. 
 
 The muzzle velocity of the projectile was in both cases 
 practically equal. 
 
 Comparison of Results. 
 
 The calculated pressures agreed closely with those ob- 
 served in the gauges placed near the base of the projectile 
 when at rest; and those observed at the base of the bore 
 considerably exceeded those observed near the base of the 
 projectile. ^^^. Chap. XI. 
 
VIII. — PHENOMENA OF CONVERSION. 
 
 CHAPTER VIIL 
 
 PHENOMENA OF CONVERSION. 
 
 Phenomena. 
 
 For purposes of analysis the conversion of gunpowder 
 into gas may be considered under tliree heads, viz.: Ignition^ 
 Inflammation and Combustion, 
 Definitions. 
 
 By Ignition is meant the setting on fire of a particular 
 point of a grain or charge. 
 
 By Inflamination is meant the spreading of the fire from 
 point to point of the surface of a grain, or from one granu- 
 lar surface to another throughout the charge. 
 
 By Combustion is meant the passage of the inflamed 
 surface throughout the substance of each grain. 
 
 IGNITION. 
 
 Gunpowder is the most refractory of the explosives; it 
 ordinarily requires a temperature of 300°. Its ignitibility 
 varies inversely: 
 
 1st. With the amount of moisture present. 
 
 2d. With the smoothness and sphericity of the surface. 
 
 3d. With its density. 
 
 It also varies with the character of the charcoal. 
 
 COMBUSTION. 
 Definition. 
 
 By velocity of combustion is meant the rate of motion of 
 
 the inflamed surface in a direction normal to that surface. 
 
 Owing to the impossibility of determining this within the 
 
VIII. — PHENOMENA OF CONVERSION. 
 
 gun, the velocity of combustion of different kinds of 
 powder in the open air is taken by the manufacturer as a 
 rude means of comparing their combustibility. 
 Determination. 
 
 If the size of the grain permits the time of its burning to 
 be accurately determined, this simple method is preferred; 
 since it resembles most closely the actual conditions of prac- 
 tice. Otherwise, we may extend the time to be measured 
 by burning, like a candle, a prism of press cake having its 
 sides greased to protect them from the flame; or else, we 
 may use a tube rammed with the pulverized mill cake of 
 the same density as that of the powder to be tested. So 
 determined, the velocity is found to be about 0.4 inch per 
 second. 
 Nature of Combustion. 1. In Air. 
 
 This experiment proves that the composition burns in 
 parallel layers at a uniform rate; so that the combustion of 
 a spherical grain would resemble the peeling of an onion. 
 
 This fact is frequently illustrated on the proving ground, 
 where burning grains of powder are projected from the gun 
 with sufficient force to penetrate deeply into wooden 
 boards. Should they fall in snow, their appearance will 
 plainly indicate the superficial nature ot their combustion. 
 2. In Gun. 
 
 It is important to remember that the velocity of combus- 
 tion within the gun is very much greater and less uniform 
 than that in the open air. The process resembles roughly 
 the absorption of water by a porous substance when under 
 variable hydrostatic pressure. The effect may be, not only 
 to accelerate the velocity of combustion, but also, by break- 
 ing up the grains, to increase the burning surface; as we 
 crush sugar to facilitate its solution. 
 
 The velocity of combustion is supposed to vary directly 
 with the intensity of the gaseous pressure. 
 
VIII. — PHEKOMENA OF CONVERSION. 
 
 CIRCUMSTANCES AFFECTING THE VELOCITY OF COMBUSTION 
 
 IN AIR. 
 
 Varying Conditions. 
 
 Under similar circumstances the velocity of combustion 
 of homogeneous powder is constant. It varies however, 
 with the purity^ proportions^ incorporation^ density and con- 
 dition of the powder as follows; 
 
 1. Purity. 
 
 The nitre and sulphur should be pure, or nearly so. The 
 part that charcoal plays depends upon its combustibility. 
 This is determined by finding the velocity of its combus- 
 tion, when incorporated with a due proportion of nitre in 
 such a tube as above described. 
 
 2. Proportions. 
 
 By varying the proportions, all velocities up to 0.55 inch 
 per second can be obtained. 
 
 The proportions usually adopted are those that give the 
 greatest volume of gas in a given time, because the mass 
 burned is the greatest, and because each unit of mass gives 
 the greatest volume of gas. 
 
 3. Incorporation. 
 
 Prolonging the incorporation increases the velocity at a 
 rate which increases as the proportions approach those 
 adopted. 
 
 4. Density. 
 
 With each set of proportions a density is soon reached 
 that corresponds to the maximum velocity. Beyond this 
 density the velocity varies inversely as the density, at a rate 
 which increases as the proportions approach those adopted. 
 
 The increase in superficial density due to glazing dimin- 
 ishes the velocity of combustion; provided that the dust 
 formed in the process be removed. 
 
VlII. — PHENOMENA OF CONVERSION. 
 
 5. Condition. 
 
 The velocity increases with the porosity of the powder. 
 See page 2. The porosity may result from the evaporation 
 of water, alcohol, or vinegar, added to the substance before 
 pressing it. When porosity is carried to the point of fria- 
 bility, the consequences described, page 2, may be expected. 
 
 AVhen oils, gums, or resins are added, or when an excess 
 of water remains in the composition, the velocity of com- 
 bustion is diminished. An excess of water permits the nitre 
 to segregate and to neutralize the effects of incorporation. 
 
 Re7nark< 
 
 These variations should be carefully studied, as upon 
 them depend the most important characteristics of gun- 
 powder. 
 Emergency Powder. 
 
 For example; during the Franco-German War of 1870, it 
 was found necessary to increase, far above their normal 
 capacity, the product of the powder mills remaining in the 
 hands of the French. 
 
 This was accomplished by reducing the time of incor- 
 poration under the wheels, besides calling into use the stamp 
 mills and rolling barrels formerly employed for this pur- 
 pose. 
 
 The effect of less thorough incorporation upon the 
 velocity of combustion was neutralized by reducing the 
 density of the powder. 
 
 This answered well where the powder was not intended 
 to be stored, and where the capacity of the chambers in 
 which it was to be fired permitted a corresponding increase 
 in the volume of the charge. 
 
 The differences of the effects upon the gun and its pro- 
 jectile, resulting from varying the phenomena of combus- 
 tion, are described in Chapters X and XI. 
 
VIII, — PHENOMENA OF CONVERSION. 
 
 INFLAMMATION. 
 Hypothesis. 
 
 The inflammation of a single grain is generally assumed 
 to be instantaneous, and so is that of a charge of powder; 
 unless the time of its inflammation bears so considerable a 
 ratio to that of its combustion that the total time required 
 for the conversion of the charge into gas is sensibly in- 
 creased. 
 
 Experiment. 
 
 The nature of the process may be studied by determining 
 the time required to inflame trains of powder of known 
 lengths under various conditions. 
 
 Varying Conditions. 
 
 The velocity of inflammation is found to vary: 
 
 1. With the disposition of surrounding bodies. 
 
 2. With the size and shape of the grains. 
 
 3. With their composition and constitution. 
 
 1. Confinement. 
 
 The heated gases, evolved by ignition, follow in their ex- 
 pansion the line of least resistance. If they are confined, 
 so that this line coincides with that along which the powder 
 is disposed, its rate of inflammation is increased. Thus, the 
 velocity of inflammation of a train is increased by firing it 
 in a tube instead of in the open air. It is still further 
 increased when the cross-section of the tube is not entirely 
 filled; and when the bottom of the tube, near which the 
 train is ignited, is closed, as in a gun. 
 
 2. Size and Shape of Grain. 
 
 The size and shape of the grain affect both the force 
 propelling the gases and the resistances which they encoun- 
 ter. In the first case, the size and shape of the grain affect 
 the amount of gas evolved in equal successive times and 
 also the ignitibility of the unburned grain; in the second 
 
VIII. — PHENOMENA OF CONVERSION. 
 
 case, they affect the size and shape of the spaces between 
 the grains. So that, in fine powder, although the gaseous 
 pressure may be greater, the resistance to the passage of the 
 wave of inflammation may also be greater. In coarse pow- 
 der the converse may be the case. The velocity of inflam- 
 mation should therefore be determined by experiment. 
 
 It is now much less important than when muzzle loading 
 guns were in use. 
 
 If the charge be made of mealed powder compressed, 
 there will be no interstices; and the velocity of inflammation 
 and that of combustion will be the same. 
 
 If it be of concrete powder, the velocity of combustion of 
 the entire grain will be that of the inflammation of the con- 
 stituent grains, and will be greater than that of the com- 
 pressed mealed powder above referred to. 
 
 This ratio was found to be as 1.4 to 1.0. 
 3. Composition and Constitution. 
 
 The velocity of inflammation is affected by variations 
 in the purity and proportions of the ingredients, in the 
 thoroughness of their incorporation, and in the density of 
 the powder, in so far as these affect its velocity of combus- 
 tion and its susceptibility to ignition. 
 
IX. — NOBLE AND ABEL's EXPERIMENTS. 
 
 CHAPTER IX. 
 
 NOBLE AND ABEL'S EXPERIMENTS. 
 
 From 1868 to 1874, Captain Noble, R. A., and Mr. F. Abel, 
 the chemist of the British War Department, made a series 
 cf experiments upon gunpowder that have become his- 
 torical. 
 
 NATURE OF THE EXPERIMENTS. 
 
 These experiments were conducted on the principle, 
 general in all experimental comparisons, of keepmg all con- 
 ditions constant except that of the variable under consideration. 
 
 Although their ultimate object was to determine the 
 behavior of fired gunpowder in the variable volume behind 
 the projectile in a gun, this principle required that their 
 preliminary experiments should be conducted in closed 
 vessels, the capacity of which was invariable and accurately 
 known. 
 
 VARIABLES. 
 
 They accordingly varied: — 
 
 1. The composition of the powder. 
 
 2. The size of its grain. 
 
 3. The mass of gunpowder exploded in a given volume, 
 or the density of loading. 
 
 FUNCTIONS. 
 
 Under these different circumstances they observed: — 
 
 1. The maximum pressures per unit of area. 
 
 2. The composition and condition of the products of 
 combustion. 
 
2 IX. — NOBLE AND ABEL's EXPERIMENTS. 
 
 3. The specific volume of the gases formed, viz^ at a 
 pressure of one atmosphere and at 0°. 
 
 4. The quantity of heat evolved by the combustion. 
 
 CONCLUSIONS. 
 
 From the observed states of the functions corresponding 
 to particular values of each variable they sought to 
 determine the law expressing the relation between pres- 
 sures, volumes and temperatures in closed vessels, with the 
 view of applying it to the variable conditions existing in 
 guns. 
 
 METHODS FOLLOWED IN THE EXPERIMENTS. 
 
 VARIABLES. 
 
 1. Composition of Powders. 
 
 Four of the six kinds of powders tried were approxi- 
 mately of the usual composition. The others differed 
 notably as seen by the following table: 
 
 COMPONENTS. POWDERS. 
 
 Four English. Spanish. Blasting, 
 
 Nitre, 74 
 
 Carbon, 12 
 
 Sulphur, 10 
 
 Water, H, O, Ash, etc., 4 
 
 100 100 100 
 
 2. Size of Grain. 
 
 The principal experiments in which the size of grain 
 entered as a variable were those in which comparisons 
 were made between R. L. G. (Rifle, large grain) and the 
 Pebble powders referred to Chap. VII. The linear dimen- 
 sions of these powders were about as 1 to 3. 
 
 3. Density. 
 
 It is evident that the results of the experiments were 
 largely dependent upon the relation existing between the 
 
 75 
 
 62 
 
 9 
 
 18 
 
 12 
 
 15 
 
 4 
 
 5 
 
!X. — NOBLE AND ABEL's EXPERIMENTS. 
 
 mass of the charges and the volumes in which they were 
 fired. This requires a discussion of the density of powder 
 which is named under three heads. 
 
 1. Specific Gravity. 
 
 By density simply, or d, we mean the specific gravity of 
 the press-cake, or that of the individual grains, referred to 
 water. This in practice ranges from 1.68 to 1.85. The 
 maximum attainable density calculated from that of the 
 ingredients of gunpowder united in their ordinary propor- 
 tions, is 1.95. 
 
 2. Gravimetric Density. 
 
 By this term, or y^ we mean the density referred to water 
 of grained powder, including its interstitial volumes; or, 
 calling w, the weight in pounds of one cubic foot of the 
 loose powder. 
 
 ^~ 62.425 ^^ 
 
 The gravimetric density is sometimes expressed by the 
 weight in ounces of one cubic foot of the loose powder. 
 
 The gravimetric density of powder is important when it 
 is to be used in a limited 'volume as in the cartridges for 
 breech-loading small arms and in explosive projectiles. It 
 is evident that the form of grain and the amount of settling 
 affect the interstitial volumes and hence its value. For 
 loosely piled powder of irregular granulation it is about 0.9. 
 
 Specific and Interstitial Volumes. 
 
 The amount of the interstitial volumes, which, as seen in 
 Chap. VIII, affects the rate of inflammation, may be de- 
 termined as follows: 
 
 Let F, represent the volume of the powder when loose; 
 v,^ its specific volume, or its volume when compressed to a 
 uniform density, 6 ; and v' ^ the sum of the interstitial volumes : 
 then, since w = F y = z^, (5. 
 
IX. — NOBLE AND ABEL S EXPERIMENTS. 
 
 d : y :: V W or v=y -k- (2) 
 
 whence v'= F-v= F ^^"^^ (3) 
 
 Ordinarily, d is about 1.8; and, when the powder is loosely 
 
 y 
 piled, V is about 0.9. In such a case v=v^= -^. 
 
 Noble conducted his experiments with powder so closely 
 packed that y was sometimes equal to unity: in such a case 
 v' was sensibly equal to 0.44 F. 
 
 3. Density of Loading. 
 
 By this term, or A , we express the relation between the 
 mass of a charge of powder and the volume in which it is 
 fired. 
 
 If the values of S and y were constant, it would suffice to 
 say that the cavity holding the powder was, say, one-half, 
 three-quarters full, etc. This was the method adopted by 
 the early experimenters. 
 
 But the quantity of matter in a given volume of grained 
 powder may vary from both the causes named. 
 
 The value of A is therefore taken as the ratio of the 
 weight of the powder fired, to the weight of water at its 
 maximum density which would fill the volume in which the 
 powder is fired. Calling this volume expressed in cubic 
 feet F, and expressing w^ as before, in pounds, we have 
 
 w 
 ^ ^ Fx 62.425 (^^ 
 
 It is usual to give the linear dimensions of guns in 
 mches; therefore calling z;= Fx 1728, the volume in cubic 
 inches, we have 
 
 • ,^^^ (5) 
 
 This value of A is of constant application and must be 
 remembered. 
 
IX. — NOBLE AND ABEL's EXPERIMENTS. 
 
 APPARATUS. 
 
 The vessels employed were strong steel cylinders as 
 shown in Fig. 1. Each one contained a firing plug, F^ with 
 a conical stopper, /, insulated from 7^ by a washer, w, and by 
 sheet of tissue paper wrapped around its body. Another 
 conical screw plug, P, carried a crusher gauge, C. 
 
 The object of the form given to F and P was to facilitate 
 their removal; since a very slight motion would free them 
 from the walls. 
 
 The charge was ignited by an electric igniter, /. 
 
 After the firing the vessel was immediately conveyed to a 
 calorimeter; or a smaller vessel. Fig. 2, could be fired 
 under water. 
 
 FUNCTIONS. 
 
 1. Pressures. 
 
 These were determined by the crusher gauge, and the 
 observed results compared and corrected by the methods 
 used in experimental research. 
 
 2. Nature of Products. 
 
 Small samples of gas were drawn off for analysis through 
 the tube, E, opened by slightly unscrewing the valve e. 
 
 The initial liquidity of the non-gaseous products was 
 determined by tipping the cylinder in various directions 
 soon after the explosion, and by observing the appearance 
 of the solid crust when the vessel was finally opened. 
 
 3. Volume of Gases. 
 
 The specific volume of the gases was determined by a 
 gasometer. Fig. 3. The long wTench, w, passing through 
 the stufhng-box, sb^ was used to unscrew P^ immediately 
 after the explosion. 
 
 4. Heat. 
 
 The quantity of heat evolved by the conversion was 
 determined by immersing the vessel in a calorimeter con- 
 
6 IX. — NOBLE AND ABEL'S EXPERIMENTS. 
 
 taining a known weight of water of known temperature, 
 and by noting the resulting rise in temperature. 
 
 RESULTS OF THE EXPERIMENTS. 
 
 STATES OF THE FUNCTIONS. 
 
 1. Pressures. 
 
 For all kinds and sizes of powder the pressure was found 
 to be practically constant for equal densities of loading, or 
 the force o( SiW the powders was the same. When A=l, 
 the force was about 6,400 atmospheres, or 43 tons, or 
 96,000 lbs., per square inch. 
 
 2. Products. 
 
 The following table* gives, by weight per cent, the mean 
 proportions of the products resulting from many experiments; 
 
 PRODUCTS. KINDS OF POWDER. 
 
 Gaseous. Tour English. Spanish. Blasting. 
 
 CO2, 
 
 CO, 
 
 N, 
 Various, 
 
 Total Gaseous, 
 
 Non-Gaseous. 
 
 K, CO3, 
 K2SO4, 
 Ka S, 
 Various, 
 
 Total Non-Gaseous, 66 62 49 
 
 From the appearance of the cavity after firing, the non- 
 gaseous products were supposed to be suspended at the 
 instant of the explosion as a highly heated liquid spray 
 which eventually assumed a solid form. In cooling it was 
 
 26 
 
 25 
 
 23 
 
 3 
 
 1 
 
 15 
 
 11 
 
 11 
 
 9 
 
 4 
 
 1 
 
 4 
 
 44 
 
 38 
 
 51 
 
 34 
 
 22 
 
 19 
 
 12 
 
 30 
 
 
 6 
 
 6 
 
 17 
 
 4 
 
 5 
 
 13 
 
 *NoTE. — The relative proportions of the total gaseous products and of 
 CO, should be learned. See Chapter II, 
 
IX.- 
 
 supposed to shrink from about 0.6 the volume of the entire 
 charge, or 0.6 F, page 3, to about 0.3 V. 
 
 Confining our attention to the typical English powders it 
 is significant to observe that very nearly the same propor- 
 tions were concluded to exist between the volumes occu- 
 pied by the gaseous and non-gaseous products at the instant 
 of the explosion, as were found to exist between the weights 
 of these products and between the interstitial and specific 
 volumes of the charge. 
 
 That the non-gaseous products did not, by their volati- 
 lization, augment the volume of the gases was inferred from 
 their behavior when exposed, solid, in a Siemen's furnace, 
 to a temperature of about 1700°. At this temperature 
 which, although the highest available, was about 700° lower 
 than that determined by calculation, the solids swelled to 
 nearly twice their volume, but did not volatilize. 
 
 3. Volumes. 4. Heat. ^ 
 
 The relations between the specific volumes of the gases 
 and the calorific values of the powders appear from the 
 following table which illustrates the curious fact, noted in 
 Chap. II, that their product is approximately a constant 
 quantity. The volumes are referred to that occupied by tlie 
 powder when A = 1. See note 1, page 13. 
 
 Kind of Powder. Specific Volumes. Heat Units Products, 
 
 or vq. or H. 
 
 English powders, 264 737 194568 
 
 Spanish powder,, 234 767 179478 
 
 Blasting powder, 360 517 186120 
 
 Had the experimenters known the specific heat of the 
 
 products of combustion when at a constant volume, or C^, 
 
 the absolute temperature of the conversion, or Tq, might 
 
 have been determined from the general equation, 
 
 If 
 
IX. — NOBLE ANt) ABEL*S EXPERIMENTS. 
 
 but, although the same products were always formed, they 
 occurred in such varying proportions, even when all the 
 conditions were as nearly as possible identical, that no 
 certain conclusions could be made. Chap. II, page 7. 
 
 Also, by taking the mean specific heats of the mean of 
 the non-gaseous products, when in a solid form, and also of 
 the gases, a temperature was computed which was mani- 
 festly too great. The experimenters accordingly adopted 
 the following course in which the deductions of theory are 
 corrected by experiment. 
 
 Temperature of Explosion. 
 
 Assuming the general equation for the work of perma- 
 nent gases subjected to changes in temperature, or — 
 
 pv=^rt, (6) 
 
 in which r is a constant, and t is reckoned from absolute 
 zero; let us express/ in atmospheres. 
 
 The preceding table gives for the English powders a 
 mean value of r= (264 = v) (1 =/) v (273 = /) = 0.967. 
 
 Substituting the values of v and / for A zz: 1, we have — 
 /= (6400) (0.4) ^ 0.967 = 2646° absolute, = 2373° C 
 
 This was verified for varying values of A and by the ex- 
 posure to the temperature of the explosion of very fine 
 platinum wire which melts at about the temperature above 
 determined. 
 
 CONCLUSIONS. 
 Fundamental Hypothesis. 
 
 The remarkable compensation between the volumes of 
 gas generated and heat evolved permitted Noble and Abel 
 to apply to these gases the laws of Mariotteand Gay-Lussac; 
 provided, that from the volume of the chamber in which the 
 explosio7i occurred was subtracted the volume occupied by the 
 non-gaseous residue. 
 
IX. — NOBLE AND AP>EL S EXPERIMENTS. 9 
 
 Remarks. 
 
 This conclusion, although simplifying the labors of the 
 experimenters, and useful for a general discussion like the 
 present, is now believed to depend upon a compensation of 
 errors. 
 
 It is now believed that the solid products are volatilized 
 and probably dissociated, and it is known that Mariotte's 
 law does not apply to the pressures observed in guns. 
 
 Still the latest researches lead to practically the same con- 
 clusions reached by these experimenters. 
 
 EXPERIMENTS IN GUNS. 
 
 The experimenters found that when the gases expanded 
 into a varying volume, as in the gun, results similar to those 
 above described were found, vk.: 
 
 1. Products. 
 
 That the nature and proportions of the products remained 
 the same as in a closed vessel. 
 
 2. Working Substance. 
 
 That the work on the projectile may be considered to be 
 due to the elastic force of the permanent gases. 
 
 3. Source of Energy. 
 
 That the heat evolved by the non-gaseous residue main- 
 tains the gases at a constant temperature during their expan- 
 sion, which, therefore, is isothermal. 
 
 This is essentially the hypothesis of Hutton, made a cen- 
 tury ago. For want of suitable apparatus Hutton erred 
 greatly in his deductions from this hypothesis, 
 
 4. Theoretical Work. 
 
 The total theoretical work of the permanent gases, when 
 indefinitely expanded, was computed to be about 486 toot- 
 tons per pound of powder. 
 
10 IX. NOBLE AND ABEL's EXPERIMENTS. 
 
 This is nearly the result given by the table on page 7. 
 Only from 13 to 20 per cent, of this work can be realized 
 in practice. See note 2, page 13. 
 6. Loss of Heat by Absorption. 
 
 The quantity of heat lost by absorption was approxi- 
 mately determined by plunging into a calorimeter a field 
 piece, after firing from it a number of rounds in rapid suc- 
 cession. 
 
 The loss was found to vary directly with the ratio of the 
 cooling surface to the weight of the charge, and also with 
 the time of travel in the bore. 
 
 It varied, per unit of weight of the powder fired, approx- 
 imately as follows: 
 
 Gun. Loss in H. ^ Energy. 
 
 10 in. M. L. R. 25 3.5 
 
 12 pdr. B. L. R. 100 14.0 
 
 0.45 in. B. L. R. musket' 250 35.0 
 
 6. Pressures. 
 
 The experimenters confined themselves to the prediction 
 of velocities. The determination of the actual intensity of 
 the variable pressure during the progressive combustion of 
 the powder in a volume varying with the position of the pro- 
 jectile during combustion was determined in only a few 
 special cases. The important law by which this pressure 
 varies, upon which modern guns are constructed, was left 
 unsolved. 
 
 The methods of M. Emil vSarrau, of the ^'- D^partement 
 des Poudres et Salpltres^'' which depend rather upon dynam- 
 ical than chemical laws, corrected, like those of Noble and 
 Abel, by experiment, are now generally followed where ac- 
 curate prevision, both of pressures and velocities, is required. 
 
 The older methods are adopted in this text, as they permit 
 the presentation of some of the more important phenomena 
 of fired gunpowder in a relatively simple form. 
 
IX. — NOBLE AND ABEL's EXPERIMENTS. 11 
 
 DEDUCTION OF THE VARIABLE PRESSURES IN A 
 
 GUN. 
 Hypothesis. 
 
 It has been shown in Chapter VIII. that the conversion 
 of gunpowder is not instantaneous. Yet, on account of the 
 difficulty of determining the circumstances of the motion of 
 the projectile during the period of combustion, or x=q) (t) 
 and the rate of combustion under the varying pressure to 
 which the powder is exposed, or gz=/ (t) it is best to begin 
 by assuming that the conversion is instantaneous, and to cor- 
 rect the results of computation by experiment. See note 3, 
 page 13. 
 
 Assuming then, the proportions of solid and gaseous pro- 
 ducts previously given, and that the change in pressure is 
 due to the change in volume in rear of the projectile (which, 
 under the isothermal hypothesis, acts like a piston moving 
 with variable velocity under some external force), we may 
 deduce the following relation between the pressure and the 
 mean density of the products of the explosion. 
 
 Let / represent the intensity of the gaseous pressure in 
 tons per square inch, and 
 
 Wy the weight of the charge in pounds; 
 
 Vf the variable volume behind the projectile in cubic 
 inches; 
 
 v'f the volume occupied by the non-gaseous products in 
 cubic inches; 
 
 <^, the density of these products referred to water; 
 
 d, the density of the gases referred to water and supposed 
 to remain at a constant temperature. 
 
 jff, the ratio -^ assumed under Mariotte's law to be con- 
 stant. 
 
 Deduction. 
 
 From the general expression for density we have 
 
12 IX. — NOBLE AND ABEL's EXPERIMENTS. 
 
 ^ 0.44 wx 27.68 12.18 a/ , 
 
 d— -. = -J- ; and 
 
 v—v v—v 
 
 ^, 0.56 wx 27.68 , \h.hw 
 
 d'^ -, •••^^--^7-; and 
 
 ^ 15.5 w 
 
 " — n^' 
 
 Multiplying both numerator and denominator of the value 
 of/ by 
 
 27.68 2.2724 
 
 12.18 z;~ V 
 
 , we have 
 
 p=R ^ -. (7) 
 
 2.2724-1.2726 -^ 
 
 The ratio, R^ is found, by experiment, not to be absolutely 
 constant; but, by selecting from Noble's experiments in 
 closed vessels, suitable values of / and A in pairs, and by 
 substituting these values in Eq. (7), we may obtain two 
 equations, containing two unknown quantities, from which 
 we find (See note 4, page 13.) 
 
 7?=32.18 ^'=0.824. 
 
 These values substituted in Eq. (7) give, after reduction, 
 _ 1 * 
 
 A 
 Which, for convenience, may be placed under the form 
 
 /= 1 (9) 
 
 0.0025571 - -0.048 
 
 w 
 
 Equations (8) and (9) give remarkably close approxi- 
 mations to all but the very highest pressures found in Noble's 
 experiments in closed vessels. 
 
 *log 0.070618 ="3.8489170. flog 0.0025571 = 3^4077557. 
 
IX.— NOBLE AND ABEL's EXPER1M£NTS. 13 
 
 COROLLARIES. 
 
 V 
 
 1. By substituting in Eq. (9) proper values for ^= — ^>we 
 
 may construct a curve, as in fig. 4, which will give the pres- 
 sures at different points along the bore of the gun under the 
 assumptions noted, page 11. 
 
 Should the piece be chambered, the value of x\ the re- 
 duced length of the chamber =.Yo\vimQ. of chamber-^ ;r t^ must 
 replace its measured length. 
 
 2. It is evident that the value of the initial ordinate is 
 determined by the value of the density of loading, A. 
 
 3. Also that, knowing by experiment the intensity of the 
 maximum pressure, and the charge, we may determine 
 approximately the corresponding position of the projectile. 
 
 __ ^ [l+(/X 0.04 8)1 
 Smce X — ^^py^ 0.0025571 ' 
 
 4. Also that we may determine the charge required to 
 burst a closed vessel, like an explosive projectile, when its 
 resistance to rupture is known. 
 
 NOTES. 
 
 1. Page 13. — The experimenters ascertained that the erosion of the 
 bore, caused by the rush of the gases past the projectile, increases directly 
 with the factor H, and inversely with v^. 
 
 Since modern steel guns fail rather from erosion than from bursting, it 
 is possible that the large values of H, now generally sought, may be 
 ultimately diminished in favor of z/q. 
 
 That is, that the guns have a surplus of strength that may profitably 
 be used to favor their endurance under erosion. 
 
 2. Page 10.— Taking y=1390 ft. -lbs. for !« C we have 
 Q=-U[= '^^TXISQO ^ ^g,^ 3 Qj. 94 ^^^^^ oi4:%Q. foot tons. 
 
 2240 2240 
 
 3. Page 11. X and a signify respectively the variable space passed 
 over by the projectile and the variable surface of the burning grains com- 
 posing the charge. Chap. XI, pp. 2, 3, 4. 
 
 4. Page 12. — For recitation at the board the numerical values after 
 Eq. (7) may be represented by symbols. 
 
X.— eoMStrstiON IN Alft. 
 
 CHAPTER X. 
 
 COMBUSTION IN AIR. 
 
 Single Grain. 
 
 We know from the experiment in Chap. VIII that in air, 
 gunpowder burns only superficially, so that the burning 
 under these circumstances of a spherical grain may be 
 likened to the exceedingly rapid peeling of an onion. 
 
 Considering, for the present, all solid grains to be repre- 
 sented by their equivalent spheres, the radius of any sphere 
 will be equally shortened in equal successive times, but the 
 surface and the volume will vary in a higher ratio to the 
 time. 
 
 Accordingly let Fig. 1 represent the central section of 
 a hom.ogeneous spherical grain burning with a uniform 
 velocity of combustion which in the variable time, /, will 
 reduce the original radius R, to r, and the original surface 
 iS", to s. Let the time required for the combustion of the 
 entire grain be r. 
 
 Then ^: j::i?2 : ;^::t2 : (r-/)2, or 
 
 ^=^{r-t)\ (1) 
 
 By differentiating Eq. (1) with respect to s and / we have 
 
 It may be shown from Equations (1) and (2) that the 
 curve, Fig. 2, expressing the relation s=/{f), is a parabola 
 referred to a system of rectangular axes; one of which, the 
 axis of times, coincides with the tangent at the vertex of the 
 parabola, and has upon it the origin, O, at a distance from 
 the vertex =r. 
 
X. — COMBUSTION IN AIR. 
 
 The rate of change of the ordinate of the curve is the 
 same as that of the surface of the burning grain. 
 
 The summation of the successive ordinates of the curve, 
 corresponding to any value, /, will be equal to the area 
 O Ssf; and since the ordinates represent the correspond- 
 ing successive surfaces, this area will be proportional, either 
 to the mass or volume of the grain which has been burned 
 up to the time /, according as the density of the powder is, 
 or is not considered. 
 
 y'' dw 
 sdtj-j- =s, or the rate at 
 
 which the mass of gas is increasing at any instant,or the 
 rate of conversion, is proportional to the corresponding 
 surface.* 
 
 The total area O S r= — - — will be proportional to the 
 
 o 
 
 original mass or volume of the grain. 
 Number of Grains Varied. 
 
 Such a relation, once established, would be true for all 
 equal grains composing a charge, and would therefore be 
 true for the whole charge, but the rate of conversion would 
 vary with the size of the charge as shown by curves 1 and 
 2, Fig. 3. In these, 1, represents such a curve as shown in 
 Fig. 2, for a single grain; and 2, the same for n grains com- 
 posing a charge. 
 Size of Grains Varied. 
 
 If, in a charge of a given weight composed of spherical 
 grains of a given density, the -size only, of the grains be in- 
 
 *If the grain be not homogeneous, and burn with a variable velocity 
 the rate of conversion will vary with the product of the surface, J, of the 
 density, b, and of the velocity of combustion ft), or 
 
 = J X X w. 
 
 dt 
 
 In this case the curve will no longer be a parabola, 
 
X. — COMBUSTION IN AIR. 
 
 creased, the sum of the granular surfaces, ^ S, will be in- 
 versely proportional to the radius of the grain. 
 
 •For W=n v d, and v= — jr— .-. W= 
 
 or^= 
 
 3 3 ' 
 
 3 W 1^ 
 
 nS ' r 
 
 or r 
 
 If we represent by ^ the sum of the initial granular 
 surfaces of a charge, and by 6 the sum of the successive 
 granular surfaces of the same charge during its combustion; 
 Fig. 4 may represent by curves 1 and 2, respectively, the 
 relation G=f {f) for charges of equal weights composed of 
 grains of different sizes. 
 Objections to increasing Size of Grain. 
 
 The effect of increasing the size of the grain is to make 
 the powder relatively slow ; or, as it is called with reference 
 to its action in the gun, 7nild or progressive. This diminishes 
 
 the value of --z- by increasing the value of r. 
 
 The objection to this will hereafter appear; it will suffice 
 here to say that it may require the gun to be of inconvenient 
 length. 
 
 Alternatives. 
 
 The following methods have been proposed for regulating 
 the rate of conversion without, in all cases, increasing the 
 value of r. 
 Constant Rate. 
 
 1. A constant rate would evidently be attained by form- 
 ing the powder as a prism and confining the burning area to 
 that of its cross section. This result is approached in the 
 Zalinski pneumatic gun, in which compressed air from a 
 large reservoir, expands continuously into the volume be- 
 hind the projectile. Also in the steam engine. 
 
X. — COMBUSTION IN AIR. 
 
 2. An approximation to a constant rate, with a small value 
 of r, has been sought by forming the powder into volumes 
 of which two dimensions considerably exceed the ihird. The 
 French, Castan, powder and the American, LX, powder are 
 so formed. 
 
 Increasing Eate. 
 
 The rate of conversion may be increased by causing the 
 burning surface to increase: 
 
 3. By igniting the grain from the interior, and protecting 
 the exterior surface from the flame by forming the grains 
 into hexagonal prisms closely packed together, fig. 5. The 
 perforations are continuous flues, facilitating inflammation. 
 
 This is Rodman's powder. 
 
 4. By diminishing the density of the grain toward its 
 center, Chap. III., or by facilitating its disruption after 
 ignition. 
 
 These cases may be represented by the correspondingly 
 numbered lines on figure 6. 
 
 COROLLARY. 
 
 Supposing the charge to consist of n equal spherical grains, 
 the proportion of the whole charge that will be burned in the 
 variable time, /, may be determined as follows : 
 
 The original volume of the charge is, F= n ^ i: R^ \ or, 
 assuming, as before, that the velocity of combustion is unity, 
 V=z n -^ TX r^, the unburned volume at the end of the time, 
 
 t,v7'i\\hev,-n^7T{r—ty=,v{l—[\ - Therefore, the 
 volume burned will be, z/'= V—Vf^z V\ 1 — ( 1 — - j (4) 
 
 Similarly w' = ^F 1— ( 1— ^)' 1 - (5) 
 
 The curve whose ordinates express the relation w' z=. f {t) 
 will be of the form shown in figure 7, and figure 1, chap. XII. 
 
XI. — COMBUSTION IN A GUN 
 
 CHAPTER XI. 
 COMBUSTION IN A GUN. 
 
 PRESSURES. 
 
 Comparison to Steam. 
 
 For purposes of illustration, the action of gunpowder, 
 when burning in a gun, may be compared to that of steam 
 in the cylinder of a steam engine; and the pressures,/, at 
 different lengths of travel, x, of the projectile in the bore, 
 may be represented by the ordinates of a curve which 
 expresses the relation jf=f [x), in the manner used in the 
 indicator diagram of the steam engine. 
 
 The operation may be conveniently analyzed by dividing 
 the volume of the bore into two portions, viz.: 
 
 1st. That through which the elastic gases are being 
 evolved from the burning powder, called the combustion 
 volume. 
 
 2d. That through which these gases are expanding under 
 the elastic potential acquired during combustion. This may 
 be called the expansion volume. 
 
 Thus, the circumstances during the passage of the pro- 
 jectile through the combustion volume correspond to the 
 admission of steam to the cylinder of a steam engine, and 
 the completion of the combustion to the action of the valve 
 which cuts off the supply of steam. The subsequent expan- 
 sion in both cases is limited by the length of the cylinder. 
 
 This important difference exists; that the expansion, 
 which in steam is treated as adiabatic (without loss 
 of heat except from external work), and which, there- 
 fore, leads to a loss of temperature due to the work done, 
 
XI. — COMBUSTION IN A GUN. 
 
 is, in the gun, supposed, from Noble and Abel's experi- 
 ments, to be isothermal^ and, therefore, under Mariotte's 
 law. 
 
 DISCUSSION. 
 
 Hypotheses. 
 
 In the following general discussion we will, for simplicity, 
 begin by assuming that the projectile starts freely from its seat. 
 We will neglect the variable volume of the liquid residue 
 and that of the powder remaining unburned at any time. 
 
 We will also assume that the inflammation is instanta- 
 neous. See Chap. VIII. 
 Notation. 
 
 Taking the origin of co-ordinates at the origin of motion; 
 X will represent either the path of the projectile or the 
 volume described by the translation of its maximum crosr 
 section. 
 
 The volume of the chamber, ^, or the initial volume, is 
 composed of two volumes, viz.: 
 
 c, the volume actually occupied by the charge of powder 
 including its interstitial spaces. 
 
 c\ any excess of volume besides that required to hold 
 the charge. Therefore, k=zc-\-c\ and, for the reduced 
 
 k 
 length of chamber^ we have x, -=l ^ , in which r is the 
 
 radius of the bore. We shall first take c' = O. 
 
 Let w represent the weight of a charge of powder which 
 will be consumed in a time r, and let w' be the variable weight 
 of w converted into gas at the end of any time /. 
 
 Let (S represent the corresponding sum of the burning 
 surfaces as in Chap. X, and '2 the sum of the initial sur- 
 faces. 
 
 Let / represent the variable intensity of the gaseous 
 pressure per unit of area on the base >f the projectile; and 
 
XI.— COMBUJ^TION m A GUN. 
 
 assume any particular value o. / to be uniform throughout 
 the volume occupied by the gases, the density of which is d. 
 
 Let/ be taken in such units that R^ Chap. IX, be equal to 
 unity. 
 
 Let W represent the weight of the projectile, the radius 
 of the cross section of which is r\ the variable velocity of 
 which, in the bore is v\ and, at the muzzle of the gun is V. 
 
 Let q and Q represent the quantities of work done upon 
 the projectile to give it the velocities v and V. 
 
 FORM OF PRESSURE CURVE. 
 
 Upon firing the charge the combustion volume is gradu- 
 ally filled with gas, the density of which will vary directly 
 with w' and inversely with x-\-c\ so that we may write 
 
 w' 
 
 Differentiating this equation, considering /, w* and x as 
 variables, and dividing through by dx^ we have 
 dp __ 
 
 dx x-\-c 
 
 1 i dw* w* \ 
 '^c\dx x^cX 
 
 (2) 
 (3) 
 
 But, since q=f p dx^ 
 
 dp _ _1_^ / dw'—dq \ 
 dx ~ x-\-c \ dx J 
 Or, dividing both numerator and denominator of the 
 expression in the parenthesis by dt and remembering that 
 dw' 
 
 dt 
 
 Similarly, 
 
 dp _ 1 / dq \ 
 
 dx '~ {x^c)vy dt )' W 
 
 dp 
 
 No simple law has yet been discovered connecting (T, x 
 and /, and these equations cannot, therefore, be integrated; 
 
XT.— COMBUSTION m A GUN. 
 
 but, remembering that (T is a decreasing function, and q 
 an increasing function of /, a conception may be had of the 
 form of the curve, the ordinates of which express the 
 relation /=/ (^). 
 
 The inclination to the axis of X will be greatest at first 
 
 when 6 is large, and x and ~- =p v are small. It will be 
 
 Oy or / will be constant, when the gas is evolved just fast 
 enough to compensate for the increasing volume. From 
 this point the conversion is not rapid enough to keep up 
 the maximum pressure, so that the pressure will fall off 
 until a=.Oy as at «, Fig. 1, from which point the curve will 
 be an hyperbola with the axis of X as an asymptote, since 
 p becomes equal to a constant, w, divided by x-\-c. By 
 the law of continuity, a should be a point of inflexion and a 
 point of tangency between the combuscicn and the expan- 
 sion curves.* 
 
 The same results will follow when / is taken =/' {t), ex- 
 cept that the inclination of the tangent to the curve will 
 vary more gradually. 
 
 I. PRESSURES DURING COMBUSTION. 
 
 Effect of Size of Grain. 
 
 Although we do not know the law which, in the gun, con- 
 nects (T=/(/) and x = Qf (/); experiments with Noble's and 
 Ricq's apparatus demonstrate that, when nearly equal charges 
 of powder, a and b, in which H^ > Z^^ are fired ; for small 
 
 ♦The parenthetical expression refers to the relation between the poten- 
 tial energy of the unburned powder and the kinetic energy of the projec- 
 tile ; for n, the potential energy of the charge must always be equal to 
 7r = /(CT), that residing in the unburned charge; -]- q=f^ (v), the work 
 already done at any instant; -\-e=/^^ (/), the work which the elastic 
 potential of the gases is capable of doing; or H =7r -j-q-\-e. 
 
XI. — COMBUSTION IN A GUN. 
 
 values of x and /, cp (/) changes but slowly for considerable 
 variations in/" (/). 
 
 The small change in the form of cp (t) for a given change 
 in the form of / (/) is probably due, on one hand, to the 
 relative constancy of the initial resistances to motion, or 
 the molecular work (Michie, Art. 25), and on the other hand, 
 to the great changes in / {t) resulting from the cumulative in- 
 fluence upon the velocity of combustion of high pressures 
 when (7 is large. Chapters VIII., X. 
 
 If, therefore, during the critical period of combustion, we 
 assume that qp (/) is nearly constant for all sizes of grain; 
 V, and therefore ^, may be taken as independent of o. Con- 
 sequently, Eq. 4 shows that during combustion, the inclina- 
 tion of pressure curves corresponding to different values of 
 Z will be an increasing function of a ; or for equal charges, 
 the smaller the grain, the steeper the curve. Similar reason- 
 ing shows that it will also be higher. 
 
 Experiine7ital Illustration. 
 This may be re'presented by fig. 2, derived from Noble's 
 experiments, in which a represents, by its ordinates, the suc- 
 cessive surfaces of a charge of fine-grained powder burned 
 in the air, its initial portion only being represented. The 
 curve a' shows the effect produced upon its burning by con- 
 finement in the gun. Let b and b' similarly represent the 
 varying surfaces of an equal charge of coarse-grained 
 powder. Let a and /3 be corresponding curves representing, 
 by their ordinates, the velocities acquired by the projectile at 
 any time, /. For any time /, the area under a' or b' = 
 
 J a dt=w' ; and similarly the area under a ox (i=J vdt—.x-^c. 
 
 Under the circumstances named, although Z^=*^ Zy,, the 
 curves a. and |3 were nearly coincident in their initial por- 
 tions. These, which we shall term the v curves and the a 
 curves, have the axis of time m common. 
 
XI. — COMBUSTION IN A GUN. 
 
 At any time /, which is less than tb, the time required for 
 the combustion of the powder ^, the ratio, =/» is less 
 
 for the coarse grained powder than for the fine. At t^ ^^d 
 Tb expansion begins ; at r^ the pressures from the two pow- 
 ders will be nearly equal to each other, since the same weight 
 of powder in each case is burned in nearly equal volumes. 
 
 Similar effects would follow the changes in a, indicated in 
 Chap. X., from whatever cause the rate of change of o was 
 varied. 
 
 The best results would be attained when both the <j and 
 V curves coincided in such a line as ^, fig. 2, since we 
 would then have the constant pressure sought for in the 
 ideal gun. 
 
 The effect upon pressures of varying the size of grain, or 
 the rate of burning in charges of equal weight, would be 
 represented by the curves a, b^ k, in fig. 3, in which the nota- 
 tion of fig. 2 is preserved. 
 
 Additional Illustration, 
 
 The principle is illustrated in figure 10, in which curves a 
 and b (which to avoid confusing the drawing are omitted), may 
 be imagined to result from Equation (5), Chapter X, and a' 
 and b' to be constructed from a and b^ in the manner indi- 
 cated in figure 2. The curves a and ^ express the relation 
 x=f' (/) as in figure 2 they expressed v=.f{t). 
 
 The ordinate t y' represents the proportionate part w', of 
 the original weight of the charge, w^ (represented by O 7v), 
 that has been burned in the time O t\ and / z' the volume, x, 
 through which the projectile has moved in the same time. 
 Similarly for the curves b' and /?. 
 
 The line ^^ is parallel to O T^ and at a distance from it, on 
 the scale of the axis JT, that is proportional to the volume of the 
 
 chamber.. Then^p-p-^ = -^ = ^=A.- and similarly 
 for the curves b' and ^. 
 
X!. — COMBUSTION IN A GUN. 
 
 In figure 2 it is not possible to represent the constant of 
 integration, c, 
 
 2. PRESSURES DURING EXPANSION. 
 
 The locus of the pressures at the end of the several com- 
 bustion periods is the hyperbola H, fig. 3, the intersection of 
 which, with the axis of P^ is at a height (9/, corresponding 
 to 43 tons per square inch, and the parameter of which de- 
 pends upon the weight of the charge. Thus, the hyperbola 
 H' would be the locus for a charge greater than w, and its 
 vertical asymptote would be at a distance from 6?= —Xi—c 
 See figure 5. 
 
 Remarks. 
 
 1. The relative constancy of the v curves, in spite of con- 
 siderable variations in /, may be explained by considering 
 the gunpowder as a reservoir of potential energy. In this 
 
 — ^ — J , SO that v=J\^w')y while we 
 
 have seen that/=/^^(w'). 
 
 2. It is probable that the work done during combustion 
 is proportional to the weight of the charge. 
 
 ADAPTATION OF POWDER TO GUNS. 
 
 The preceding discussion shows that if the size of the 
 grain remains constant, the pressure increases with the size 
 of the charge. 
 
 In order to compensate for this, General Rodman pro- 
 posed to increase the size of the grain as the caliber of can- 
 non of the same class increased. 
 
 This is the basis of the modern practice requiring special 
 powders for special guns. 
 
XI. — COMBUSTION IN A GUN. 
 
 PASSIVE RESISTANCES. 
 
 Returning to fig. 1, we see that the area limited by the 
 pressure curve, the axis of X, and the muzzle ordinate at w, 
 will represent the work done by the powder under the cir- 
 cumstances named. 
 
 The greater portion of this work appears in the kinetic 
 energy of translation of the projectile; and, for simplicity in 
 the following discussions, all the work will be considered to 
 have been so transformed. 
 
 The difference between the work of the pressures and the 
 energy of translation, which, in practice, may amount to 
 about ten per cent, of the former, is due to the work of the 
 passive resistances ^ including the waste. 
 
 Eesistances. 
 
 The work of these resistances is equal to the sum of the 
 following quantities of work: 
 
 1. That done in giving rotation to the projectiles in rifled 
 guns and in causing recoil. 
 
 2. That done in permanently deforming the projectile and 
 the gun. The former is practically confined to rifled pro- 
 jectiles and is greatest in breech loaders. 
 
 3. That done in overcoming the friction of the projectile, 
 and in distributing the charge in the form of gas through- 
 out the bore. 
 
 Waste. 
 
 4. The waste is due to the absorption of heat by the walls 
 of the gun, and to the escape of the gases past the projectile 
 and through the vent. 
 
 Graphical Representation. 
 
 So that if we take a pressure curve, as in fig. 4, and draw a 
 line R R\ so that the area under it, corresponding to any 
 length of path x, shall represent the work of the passive re. 
 sistances during the motion of the projectile over that path, 
 
XI. — COMBUSTION IN A GUN. 
 
 the segment r/, of any ordinate x p, will represent that por- 
 tion of the total pressure which gives acceleration to the 
 projectile and imparts to it kinetic energy proportional to 
 the area included between the two curves and any limiting 
 ordinate. 
 
 Remarks. 
 Band. 
 
 In breech-loading guns the initial resistance is consider- 
 able until the rotating band has entered the rifling; there- 
 after the resistance diminishes rapidly. 
 
 Example: In a 9.5 in. B. L. R. a charge of over 4 pounds 
 of powder failed to move the projectile; but a slight increase 
 in the charge gave it considerable velocity. 
 "Waste. 
 
 The loss of energy from absorption of heat by the gun 
 increases with the slowness of the powder; since with slow 
 powder the velocity of the projectile is less at the moment 
 of maximum temperature or pressure. 
 
 It varies inversely with the calibre, since with charges of 
 the same proportions the weight of the charge varies with 
 r*, while the surface varies nearly with r^. 
 
 The escape through the vent probably increases with the 
 slowness of the powder. 
 
 Instantaneous Pressure. 
 Variability. 
 
 From the discussion, Chap. VII., it is evident that the pres- 
 sure at any instant throughout the volume in rear of the pro- 
 jectile is not uniform, but increases toward the bottom of the 
 bore, as represented by the variable line/o/- Fig. 4. 
 
 Neglecting the passive resistances, the intensity of the 
 variable pressure at the bottom of the bore, generally known 
 as/o> can, by analysis, be shown to be very nearly equal to 
 
 / 
 
 (w \ 
 
10 
 
 XI COMBUSTION IN A GUN. 
 
 Considering the passive resistance/o is taken =// 1 + yTvi- 
 
 Supposition. 
 
 For an elementary discussion, like the following, such 
 
 differences in the instantaneous pressure, and the effect of 
 
 the passive resistances, once understood, maybe neglected. 
 
 So that the pressure at any instant upon the bottom of the 
 
 bore will be assumed to be that exerted at the same instant 
 
 on the base of the projectile, and all of it is supposed to be 
 
 utilized in giving motion to the projectile. 
 
 JV 
 The difference, p n r' a, evidently tends to compress 
 
 . . . ^ 
 
 the projectile in the direction of motion, and its effect will be 
 
 most felt at the base of the column of metal moved. 
 
 Except in the next discussion, in which actual free vol- 
 umes are considered, the origin of co-ordinates is always 
 taken at the origin of motion; viz., at that section of the 
 bore occupied by the base of the projectile when the gun is 
 fired. 
 
 WORK OF FIRED GUNPOWDER. 
 
 It is not necessary in practice to separate the work of 
 combustion from that of expansion; but the total work which 
 may be expected from a given charge of powder may be 
 determined in the following manner. 
 Total Potential Work. 
 
 In fig. 3 the area included between the ordinate O P^ the 
 axis of X, and the hyperbola H at infinity, will represent 
 the total amount of work which this charge could perform. 
 Calling this i2, we see, from Chapter IX., that expressing, 
 as is usually done, work in foot-tons, and w in pounds, 
 
 /2=486 w. 
 Actual Potential Work. 
 
 If, instead of expanding the powder gases to infinity, we 
 limit the useful work of the expansion by placing the muzzle 
 
XI. — COMBUSTION IN A GUN. H 
 
 as at m^ we shall have an area which will represent the 
 maximum potential work under the conditions existing in 
 the gun. 
 
 This, which in practice is not much over — , we will call Q. 
 
 Effective Work. 
 
 Now, if we fire the charge w in a gun, we shall give a 
 certain velocity F to a projectile W. Calling the amount 
 of kinetic energy so realized E^ we have 
 
 E=. 
 
 2^x2240 
 The ratio, -— = F, is called the factor of effect. It is 
 
 used, as hereafter explained, in anticipating the results of 
 certain changes in the piece and ammunition. 
 
 Fig. 3, shows by the triangular areas above the curves, 
 a, ^, k, the principal reason why 7^ < 1. 
 
 F is further diminished by the passive resistances. 
 
 MEASURE OF Q. 
 
 To deduce a formula for the potential work of the 
 powder gases when expanded in a gun of a definite length, 
 or the equivalent of the area Q^ we use the general equation 
 
 ^—^dx. (6) 
 
 Substituting the ;i^alue of /, from Eq. 3, Chap. IX, and 
 for brevity replacing 0.0025571 by «, and 0.048 by by we 
 have, since all linear dimensions are given in inches, 
 
 G" (inch-tons) = ^ 
 
 na d* 
 
12 
 
 XI. — COMBUSTION IN A GUN. 
 
 (2" (inch-tons) ='^ ' '^^ 
 
 Takinrj, in this case, the origin of co-ordinates at tne 
 bottom of the bore, integrating between x^, and x' , corre- 
 sponding to O' O and O' m^ fig. 1; substituting the value 
 
 of a^ and remembering that Q= ■^— , we have, 
 
 ^'-23.9 ^3 
 
 e= 75.04 tt/, log ~ . (7) 
 
 ^,-33.9 -, 
 
 Volumes of Expansion. 
 
 The subtractive term above, appears from the form of the 
 equation and can be shown to be the reduced length of the 
 residue,* or 
 
 />=33.9^; (8) 
 
 pand x^/—x^—p: — =z n ^ number of 
 
 volumes of expansion, an important characteristic of a gun. 
 It is convenient to remember that p=: about -j^ the length 
 of the cartridge, if its diameter =d above. 
 
 Equation 7 may, therefore, be written under a form con- 
 venient for general discussion. 
 
 (2=75.04 w. log«. * (9) 
 
 The calculus shows that the curve, the area between 
 which, the asymptote, and two ordinates is proportional to 
 the logarithm of the extreme abscissa, is an hyperbola, 
 which is the result reached, page 4. 
 
 * For the smokeless powder referred to in Chapter III, p will be prac- 
 tically = 0, n will diminish, and so will /o for equal values of w. The 
 effect, as hereafter discussed under Air spacing, will be to make the powder 
 more progressive ; unless the powder belongs to the class of high explo- 
 sives and its explosion is of a high order. 
 
XI. — COMBUSTION m A GUN. 1^ 
 
 Consequently if, as in fig. 5, we assume axes of P and 
 iV", we may construct various hyperbolas depending upon 
 the value of w^ such that the areas under them will give^ 
 the corresponding values of Q. 
 
 VARIATIONS. 
 
 1. In Weight of Charge. 
 
 The hyperbolas intersecting at the point P, Fig. 5, and 
 Equation 7, show the effect upon x,; x' \ x,,; x"; p; n; 
 Q ; and /, resulting from variations in w. 
 
 Inspection of the figure shows that an increase of 7Cf to 
 7£/ =: -f 7i>, decreases n from about 12 to 7, or about ^ ', 
 the total length of the bore x' =z x" remaining constant, as in 
 a muzzle loader. 
 
 Owing to the effect on n of variations in w, Q will not in- 
 crease in direct proportion to w. But, in a given gun, log 
 n diminishes so much less rapidly than w increases, that we 
 may for simplicity assume that n is constant; and, taking a 
 constant ratio between n and x, we may replace the axis of 
 iV^by that of X, and complete the figure by drawing upon 
 it combustion curves, as in Fig. 6, so that for the same weight 
 of charge the areas under the combustion curves are equal, 
 without regard to the size of grain. See Remark 2, page 7. 
 
 2. In Size of Grain. 
 
 The curves a' a" , refer to different weights of the same 
 kind of fine grained powder, which are supposed to be 
 burned through at about the same point of the bore. Curve 
 a", refers to a weight w of coarse grained powder. 
 
 Consideration of Fig. 6, shows how, by increasing both 
 the weight of the charge and its inherent progressiveness, 
 we may obtain a pressure curve, the work area under which 
 may equal and even exceed that due to the fine grained 
 powder, without incurring the risk attending the high pressures 
 to which it gives rise. 
 
14 XT.— COMBUSTION IN A GUN. 
 
 In other words, we approach the conditions required in 
 the ideal gun, by effectively diminishing the value of n. 
 
 For, comparing curves a" and b" ^ figure 6, it is evident 
 that the latter is the more progressive, or more nearly parallel 
 to the axis of X, and that this results from expansion begin- 
 ning further down the bore. Neglecting the areas under the 
 combustion curves, the inclination of which in the diagrams 
 is purposely exaggerated, the effect is practically the same as 
 if the powder had been instantaneously burned in a volume, 
 c -\- c', greater than c, page 2, by the volume through which 
 the projectile had moved before expansion began. We would 
 
 x' p 
 
 then have n' =: , , — < n. See Air Spacing, 
 
 x, + c'—p 
 
 3. In Length of Bore. 
 
 While, in all cases in practice, an increase of O m increases 
 Q and F, the proportionate advantage from the increase of 
 O m increases with the progressiveness of the powder. 
 
 The limit of useful increase of O mis determined by the 
 intersection of the line of pressures with that of resistances. 
 Fig. 4.* 
 
 In many works on Gunnery the importance of Om^ or the 
 path traversed by the base of the projectile in the bore of 
 the gun, is overlooked; or it is left to be inferred from the 
 total length of the bore. 
 
 In the more recent and advanced works it has a specific 
 symbol u by which it will be hereafter recognized. 
 
 AIR SPACING. 
 Variations in A. 
 
 We have so far assumed the powder to be fired in its own 
 volume. If we assign to the charge a volume greater than 
 that required to contain it by the volume ^', page 2, the 
 
 *This applies to small arms. For heavy cannon the increased weight 
 of piece resulting from the prolongation of the bore, can generally be 
 used to better advantage elsewhere. 
 
XI. — COMBUSTION IN A GUN. 15 
 
 value of A will diminish. Eq. 8, Chap. IX., shows that the 
 initial pressure will also diminish, and so, under given con- 
 ditions will Q. In such a case, Eq. 1, will take the form 
 
 /= j — , and the curve expressing the relation 
 
 x-\-c-t- c' 
 
 p =/ {x) will be such as shown in fig. 7. 
 
 Curve 1 expresses, by its ordinates, the varying pressure 
 when A is large, and curve 2 the same function when A is 
 small, the weight of the charge being the same in both cases.t 
 
 It will be observed that the effect of air spacing is princi- 
 pally felt when c^ is large, compared with x^ that is, when cs 
 and/ are relatively large. 
 
 Also, since by differentiating Eq. 1, regarding w' as a 
 
 df) 11) 
 
 constant and x + k=-\^ we have -^ = r-^^; the inclination 
 
 aA. Ar 
 
 of curve 2, will be less than that of curve 1. The values of 
 
 Q and B will therefore both be smaller for curve 2. 
 
 Increase of Charge. 
 
 If u is fixed, this effect is compensated for, as before, by 
 increasing w. This produces the effect shown in the dotted 
 curve, 3, fig. 7. 
 
 APPLieATIONS. 
 
 Air spacing is principally applied to muzzle-loading can- 
 non on account of the necessary limit to their length imposed 
 by the requirements of loading. It results spontaneously from 
 
 t To familiarize himself with the principles involved, it is recommended 
 that the student construct curves 1, 2, 3, as follows : 
 
 1. Assume a maximum pressure of say 24 units and<:=l; c^ = o', 
 10=1; thenfor jr = l,/ = 12; for x=2, / = - =8, and so on. 
 
 2. Take c^ =1.-, /& = 2; w=:l, as above; then for x = o,p^=12i 
 for x = 2fp = Q, and so on. 
 
 3. Take^=l and w = 1.5; then for x = o, p=-=18', forjr=l, 
 / = 12, as in No. 1; forx = 2, /=9 (greater than No. 1). No. 3 will 
 continue above No. 1 to oo. The powder is more progressive, and n is 
 decreased. 
 
16 XI. — COMBUSTION IN A GUN. 
 
 the ease with which their projectiles, particularly those 
 which are spherical, take up their initial motion. It was 
 probably to diminish this that the sal^of, a cylindrical block 
 fastened to the rear of spherical projectiles, was formerly 
 employed, although other reasons are generally assigned for 
 its use. 
 
 Until about 1880, when the EngUsh government began 
 to adopt exclusively the breech-loading principle for heavy 
 cannon, air spacing was largely employed for s/wrf, thick 
 muzzle-\oa,dmg cannon, firing large charges of ^uick-huYn- 
 ing powder. It was secured by making the diameter of the 
 chamber greater than that of the bore. This was objec- 
 tionable in sponging and it weakened the gun. 
 
 It was made constant by providing the projectile with 
 stops, which held it at an invariable distance from the bottom 
 of the bore. But this, although beneficial in preventing the 
 great variations in pressure and velocity which, from care- 
 less loading, are apt to occur in ordinary muzzle-loading 
 guns, increases the length of the gun in the region of its 
 greatest diameter. 
 
 It is still employed to some extent in breech-loaders, but 
 is yielding in importance to the means now employed for 
 regulating the combustion of gunpowder. 
 
 EFFECT OF THE ROTATING DEVICE. 
 
 If the initial motion of the projectile be restrained by the 
 compression of the rotating device,/ will have an initial 
 value at least equal to the resistance offered to deformation, 
 and, since the powder is burned under higher and more 
 constant pressures, n will be greater and more constant 
 than when the projectile is free to move. 
 
 ADVAIsTAGtS OF BREEuH-LOADING GUNS. 
 
 General Advantages. 
 
 1. The simplicity and exactness of the method by which 
 the value of n may be regulated. 
 
XI. — COMBUSTION IN A GUN. 17 
 
 2. The ease with which u may be increased without inter- 
 fering with the operations of loading. 
 
 3. As will be hereafter shown, the compressible pro- 
 jectiles used in breech-loaders are more accurate than the 
 loosely fitting projectiles employed in muzzle-loading guns. 
 
 In spite of the greater simplicity of construction and of 
 operation of muzzle loaders, these advantages have com- 
 pelled the adoption of breech-loading cannon. 
 
 Tactical Advantages. 
 
 The tactical advantages of breech-loaders are also greater. 
 Among these are — 
 
 1. Greater facility in securing cover for the piece behind 
 defenses, and for the gunners behind the piece. 
 
 2. Less danger and difficulty in loading, since but one 
 charge can be inserted at a time, and the operation of spong- 
 ing is less important than with muzzle loaders. 
 
 3. Greater facility in examining and caring for the bore. 
 
 4. Greater facility in adjusting the charge or fuze after 
 loading. 
 
 5. ImmovabiUty of the projectile in marching. This per- 
 mits batteries to come into action rapidly, when under fire. 
 
 6. The rapidity of fire is increased for large pieces. 
 
 The price paid for these advantages is the difficulty of 
 getting officers and men capable of working the cannon with 
 sufficient care. 
 
 OBJECTIONS TO INCREASING WEIGHT OF 
 POWDER. 
 
 The preceding discussions show that we compensate for 
 small values of 7i by corresponding increases in the value of w. 
 
 The objections to this are as follows. 
 
 1. We increase the waste of powder, as the steam en- 
 gineer does that of his coal by failing to work his steam ex- 
 pansively. This may be of importance when storage capacity 
 is limited, as on ships and in the field, and it tends to dimin- 
 ish the value of ?y, hereafter explained. 
 
18 XI. — COMBUSTION IN A GUN. 
 
 2. The work done in distributing the gas throughout the 
 bore increases with the weight of the charge and the length of 
 u. Some charges now weigh half as much as the projectile. 
 
 3. We increase the tension of the gases within the gun at 
 the instant of the departure of the projectile. This tends 
 to accelerate the recoil and to perturb the flight of the pro- 
 jectile ; since, owing to their small mass, the gases leave the 
 gun with a higher velocity than that of the projectile. 
 
 4. Considering the gun to consist of a number of staves, 
 like those of a barrel, the moment of the pressures about the 
 breach is increased on account of their greater level arm. 
 
 5. Variations in / and «, due to accidental variations in 
 the velocity of combustion, may endanger the safety of the 
 piece or affect its accuracy. 
 
 IGNITION AND INFLAMMATION IN GUNS. 
 
 The importance of these phenomena has largely decreased 
 with the adoption of the breech-loading principle. 
 
 When muzzle-loading cannon, firing free projectiles with 
 
 charges of fine grained angular powder were generally used, 
 
 .1 . . time of inflammation , 
 
 the ratio -— ^ , — was large. 
 
 total time of conversion 
 
 To reduce this as much as possible, so as to increase the 
 value of n^ the charge was ignited near its middle. It was 
 found that ignition in rear tended to waste energy by moving 
 the forward portions of the unburned charge ; while that in 
 front reduced the velocity by the premature movement of the 
 projectile. 
 
 With breech-loaders the charge is always inflamed before 
 the projectile has moved. 
 
 The shape and size of the grain and the use of a special 
 priming of quick powder placed near the vent, reduce the value 
 of the ratio of times above referred to so much, that the 
 position of the vent is determined by other considerations. 
 
XI. — COMBUSTION IN A GUN. 19 
 
 MEASURES DEPENDING UPON THE MUZZLE 
 ENERGY OF THE PROJECTILE. 
 
 1. MILDNESS OR PROGRESSIVENESS. 
 
 P =: / TT r^ is called the variable total pressure. 
 
 In this, and in subsequent similar expressions, r is expressed 
 in the same linear units as those of the area upon which / is 
 estimated. 
 
 When/ has its maximum value, as indicated by the pres- 
 sure gauge, and taken = /„ ; the maximum total pressure is 
 P' = x' p', Fig. 8. 
 
 The area under the pressure curve divided by u gives the 
 
 mean total pressure P,-=^ — = m p,. 
 
 u 
 
 The effective length ox u' = — = O x". 
 
 Therefore, if we represent the following ratio by ju, we 
 have, since E = P' u' = P, u, 
 
 ^ = ^^'!L^^^ ^^' . (10) 
 
 ^ P' u P' u ^gp.-ar'u 
 in which /^ and JVare expressed in the same units, and g, u 
 and Fin the same units. 
 
 This coefficient /x, which measures the ratio of the area 
 under the curve to that of the circumscribed rectangle, may 
 be taken as the measure of the mildness or progressiveness 
 of the action of the gunpowder under the circumstances of 
 any particular case. 
 
 The limit of the ratio for all ordinary powders is evidently 
 unity, and would be reached only in the ideal gun. 
 
 2. ECONOMY. 
 
 -p 
 7) = — is a valuable datum for comparing the economy or 
 
 w 
 
 efficiency of various powders. 
 
 
^0 XI. — COMBUSTION IN A GtjM. 
 
 It appears from figure 3 that the greater is the efficiency, 
 the greater is the maximum pressure ; or that the violence of 
 gunpowder increases with rj. Also from figure 2, that the 
 smaller the value of r, or the quicker is the gunpowder in a 
 given gun, the larger will be the value of t]. 
 
 It would be more consistent to follow the method adopted 
 for jLt, the value of which is independent of any particular 
 metrical system \ but in order to avoid dealing with large 
 numbers, and because of the general use of the term " foot- 
 tons of energy per pound of powder," we shall write 
 
 3. GENERAL COEFFICIENT. 
 
 The preceding discussions show that all expedients intended 
 to increase the progressiveness of powder decrease the muzzle 
 energy resulting from the conversion of a given weight of the 
 explosive ; or decrease rj. 
 
 Thus, when, as in figure 3, we increase the size of the grain, 
 or vary its form, composition or density so as to increase r ; 
 or when, as in figure 7, we diminish /^ by decreasing A, we 
 decrease the Factor of Effect ; and therefore, in order to ob- 
 tain the muzzle energy required, we must increase the weight 
 of the charge, as shown in figure 6. 
 
 In order to compare the performance of different powders 
 fired under the same conditions, or of the same powder fired 
 under different conditions, it is proposed to use a general co- 
 efficienty known as x '• which, since fi and r] are both desir- 
 able, will be proportional to their product ; and which, since 
 they tend to vary inversely with each other, will have an 
 approximately constant value. 
 
 This relation may be expressed by writing 
 
 X-iin= ^^mp.TTiP uw' ('^^ 
 
XI. — Oo^rBusTloW in a gun. 61 
 
 It will be hereafter more fully discussed. 
 
 4. STRENGTH OF GUN CONSTRUCTION. 
 
 // = -j^ , in which IV' is the weight of the gun (in the 
 
 same units in which IV, the weight of the projectile, is expres- 
 sed) measures the height through which the gun would have to 
 fall in vacuo to acquire energy equal to that residing in the 
 projectile at the muzzle of the piece. 
 
 Thus the old 10 in. S. B. C. I. gun had a value of ^ = 300 
 ft. When strengthened by a rifled steel tube that reduces its 
 caliber to 8 in. we have the "converted" 8 in. Rifle, for which 
 A is about 350 ft. 
 
 For the new 8 in. B. L. R. Sfee/, h is nearly 500 ft. 
 
 6. FACTOR OF EFFECT. 
 
 The meaning and derivation of this have already been 
 explained. 
 Use. 
 
 It is used for anticipating the effect of changes in the 
 interior form of a piece, or in its ammunition, upon the 
 muzzle energy of the projectile. 
 
 It differs from the use of x ^"^ its factors in taking no 
 heed of the maximum pressure involved in the result. 
 Conditions. 
 
 It is necessarily assumed to remain constant during the 
 variations, the effect of which is sought; and consequently, 
 the conditions under which it is employed should be as 
 nearly alike as circumstances will allow. 
 
 These conditions relate to the type of gun, of powder, 
 and of projectile employed • 
 
 Owing to the greater constancy of A, and to the high 
 initial pressure required to move the projectile from its 
 seat, it is better adapted for use with breech-loading than 
 with muzzle-loading cannon. 
 
M. L. R. 
 
 B. L. R. 
 
 30 
 
 60 
 
 50 1 
 
 
 65 
 
 75 
 
 ^ 80-85 
 
 85 
 
 
 22 XI. — COMBUSTION IN A GUN. 
 
 The factor of effect increases with the size of the gun, as 
 seen by the following table, giving its approximate value, 
 in certain individual cases. So much depends upon the kind 
 of powder used that only the most general conclusion can 
 be drawn: 
 
 Factor of Effect Per Cent. 
 
 Muskets, 
 Mountain Guns, 
 Field " 
 
 Medium " 
 Heavy " 
 
 APPLICATIONS. 
 
 1. Variations in w and a . 
 
 1. Suppose it be desired to estimate the change in the 
 muzzle velocity to be expected in a given gun from certain 
 charges in a/ or A. 
 
 The values of E and Q, under known conditions, have 
 been determined; and therefore, 
 
 F= -yr is known. 
 
 Determining, from Eq. (7), Q' under the new conditions, 
 we have-£''=i^ Q'. On firing we should find approximately — 
 
 V=JJEl^. (13) 
 
 2. Untried Gun. 
 
 2. Suppose that we desire to estimate the muzzle velocity 
 of a given projectile to be fired from a new and untried gun, 
 of which we have only the drawings. 
 
 We select the record of some gun of as nearly the same 
 type as possible, assume F=F\ and proceed as before. 
 
 3. Dimensions of Guns. 
 
 3. The inverse problem may also arise; viz., to determine 
 the interior dimensions of a gun of any required power. 
 
XI. — COMBUSTION IN A GUN. 23 
 
 Eq. (7) may be placed under the form — 
 
 w 
 
 Q=l!6Mwlog (l4) 
 
 ^,-23.9,-^ 
 
 The calibre and the density of loading, A, are always 
 assumed, the former depending upon the service, and the 
 latter upon the strength of the gup; therefore, since 
 
 27.68 w 
 
 A = 
 
 V=7C — X,, 
 
 110.72 «; (15) 
 
 ' TT ^2 A 
 
 We have, therefore, two problems: 
 
 1. Assuming u to find the necessary values of w and x^, 
 
 2. Assuming iv to find u. 
 
 The difficulty of simplifying an expression of the form 
 of Eq. (14) requires these solutions to be made by trial. 
 In the first case, taking F from some similar gun, we have 
 
 01 =■ —=r- Then, assuming successive values of w, we insert 
 
 them and the corresponding values of x^, determined from 
 Eq. (15) into Eq. (14) until a suitable value of Q^ is obtained. 
 
 In the second case, we proceed as before, substituting 
 successive values of u. 
 
 The initial approximations to the value of u will be facili- 
 tated by reference to the value of n, usual in guns of the 
 type proposed. 
 
 EXAMPLES FOR PRACTICE. 
 
 1. The 3.20 B. L. W. I. Chambered Rifle, in which x,^ 
 12 in.; u= 56.1 in.; 3 lbs. I. K. powder = ze/, gave to a I'Z 
 lb. projectile, F= 1548/.^. 
 
^4 XI. — COMBUSTION IN A GUN. 
 
 Determine its factor of effect; 
 
 j,_ E _ 199.3 _ 
 
 2. Estimate V for a 13 lb. projectile to be fired from 
 the new 3.20 B. L, Steel Chambered Rifle with a charge of 
 3.75 lbs. I. K. powder. 
 
 From the drawings we find that the volume of the cham- 
 ber, which is a truncated ellipsoid terminated by various 
 cylindrical and conical surfaces, when diminished by the 
 volume of that portion of the projectile which lies within it, 
 = 123.157 cubic in. Similarly, the length of the rifled por- 
 tion of the bore, when increased by that of the projectile 
 lying within the chamber,^ 73.24 in. Therefore, ^^= 15.31 
 in., x' = 88.55 in; and in the case supposed n = about 12 as 
 before. 
 
 We find (2' = 303.9 ft.-tons, ^=247.4 ft.-tons, and 
 F=1657/.J. 
 
 By experiment, F= 1662 f.s. 
 
 The difference falls within that usually found when all 
 the conditions are as nearly constant as possible. 
 
 DISCUSSION OF THE COEFFICIENT X. 
 
 A study of many records shows that when the conditions 
 of loading approach those sanctioned by experience, the 
 value of X expressed in the units assumed varies from about 
 24.0, when the powder is so quick* with relation to the gun in 
 which it is to be used, that the weight of the powder is only 
 about one quarter the weight of the projectile ; to about 35.0, 
 when the powder is so slow that 7a may be safely increased 
 to about one half the weight of the projectile. 
 
 * The remark on page 6 shows that the same powder may be quick in 
 some guns and slow in others. Thus the powder suitable for a field 
 piece would be too slow for a musket, and too quick for a siege piece; 
 and in two siege pieces of the same caliber, this powder would be quicker 
 in a gun, than in a howitzer or mortar. 
 
XI. — COMBUSTION IN A GUN. 25 
 
 It is rare to find a value of x ^vith any form of black pow- 
 der greater than 28.0; while with cocoa powder it often 
 approaches 35.0. Furthermore, these values approach con- 
 stancy, as will be seen from the table on following page. 
 
 The approximate constancy of x enables conclusions to be 
 drawn from otherwise perplexing data. Thus, in the 7.0 in. 
 Howitzer in Table I., it might be difficult to decide which 
 was the better powder, L. X. B. or I.. K. K.; but the values 
 of X show that the former is to be preferred. 
 
 If we assume axes of ?/ and fj, as in fig. 9, we may refer to 
 them as asymptotes certain hyperbolas which will limit all 
 reciprocal values of rj and ^ for each kind of powder. Thus 
 powder /^, for any assigned value of 7] or fi will give a higher 
 value of [J, OT rj than powder a. 
 
 0( the two principal ballistic data, viz.: Fand /„, the 
 former is much more easily and certainly obtained than the 
 latter. Indeed, unless the pressure gauges are carefully pre- 
 pared by experienced observers, their indications are fre- 
 quently mconsistent. 
 
 Therefore, a known value of x ^'^^Y be employed to check 
 the records of the pressure gauges, or to replace them; for, 
 having observed V, we have 
 
 ^" ;^ 2240 ^^77^/^ 7/ ^ ^ 
 
 Also, having ascertained by experiment the value of \i^ or of 
 7\ for any powder of which we know the coefficient x^ ^^^ may 
 estimate the weight of the charge of that powder required to 
 give to a projectile of any desired weight the maximum 
 velocity which the limit of pressure imposed by the construc- 
 tion of the piece permits, or 
 
 The density of loading will be regulated by this value oi p^. 
 As will be shown in Chapter XII., the value of X-, for the 
 
26 
 
 XI. — COMBUSTION IN A OUN. 
 
 
 
 Sphere Hex'l powder. 
 Converted gun. 
 Steel gun. 
 
 Flat powder. 
 
 Black Prism. 
 
 Hexagonal. 
 
 Reported "good." 
 Reported "good." 
 Rep. "entirely too quick" 
 Rep. "entirely too slow." 
 
 ^ 
 
 '^o:rrt-iM<Ma:QOOor'Cooscoco(MTrioocc<M 
 
 (M (M CI C-l (M <M C^l (M (M Ol (M (M (M (M fM CO CO CO CO 
 
 5r 
 
 OiO(M-«^iCOQ00iOt^OC00i0i»r5i0.«OO 
 
 oooi-ioooitooiCiTt^inTfmt^co'oicot^TtiQO 
 
 a_ 
 
 
 < 
 
 i-HOOOt-OOOiOOOOOiOOC<IO-<fCO 
 
 'X)ooiOin)0?oor-oooo(Mio<x>OTj<T(i 
 
 (Mt-kOOOOOS-^OO-VOiC^rHCDCDlOOOtD 
 
 tooDOoso^-rjiascoiooocooot-fMeoocooo 
 
 (M(MCO(MCOC0CCC0COr-i(M(M(MCqcOC0COC0<M 
 
 ^ 
 
 t-OCCOOOiOiOOlOCOt'tftOSOOiOT-Ht-CO 
 «OrHCOC0C0Tf<(MtOtOTtiO5(MQ0C0<X)<MC0C0C0 
 
 PL. 
 
 icooooooooio»a»rsicoo 
 ocoeocoincocotoioooooocoosososr-i 
 
 rH ri C^l (M (M CO 
 
 pi 
 
 g 
 
 9 
 
 COOOlOOOOOOOCTOt-' 
 
 lo ift ift in o o 
 
 lOCOCOCOCOCOfMiflTtitDOiOSOSCOTfOOOr-l 
 
 
 : : i : : i^'.i : i ! : : i : :** ; ; 
 
 M w w w w >< ^ 'i ^ >< >< ^ wV >^ izi ^' <i p=3 
 
 vj k4 fj KH* w h4 c» S 6 J J J J h k cu d>Q^ d» 
 
 
 S 
 
 3 
 
 urj in u'. o o CO o lo »o o 
 
 COOOCOCOCOCO-^TtiTtiOOOOrM(M''<!lHTj<-<:j3TlJ 
 (M ^ (M (M (M (M ^ (M (M -< — r-H r^ — -*(?} (M -M (M 
 
 8 
 
 ITS lO iQ O 
 lft-X)(M(M(M(MOOQOOOQOOOCOOOOOt-t-C-l> 
 
 ■^tOCOCOCOCOOSOSOCOCOCOCOCDOlOlClOlO 
 
 '«.S 
 
 coeococococoidu^int-^r^iT-t^ooQOGdGOOOGO 
 
 ^ 
 
 3 
 
 
XI. — COMBUSTION IN A GUN. 27 
 
 same powder fired in the same gun, will increase as the ratio 
 — mcreases ; but a nearly constant expression called 11 will 
 
 result from multiplying the computed value oi xhy j — j ^ or 
 
 \ W / /„ a u wl 
 log 6^=6:2161. 
 
 By comparing different values of IT, we may compare the 
 performance of different powders in the same gun, even when 
 fired with different charges, provided the weight of the pro- 
 jectile is constant, which is usually the case.* 
 
 THEORY OF COCOA POWDER. 
 
 The facts that, although almost all possible combinations 
 of the ingredients of ordinary black powder have at different 
 times been tried without decided advantage over those gen- 
 erally adopted; and that, as we have seen, the changes in 
 manufacture which have had as their object an increase in \i 
 have necessarily correspondingly reduced ?/, indicate that the 
 difference in the action on the brown powder is due to some 
 marked difference in the chemical composition of its charcoal. 
 
 This was for some time a secret for which it is said that the 
 British Government paid a large sum. Without requiring 
 such payment, the Messrs. Du Pont, of Wilmington, Dela- 
 ware, the manufacturers of a powder that has shown itself to 
 be nearly equal to that made abroad, have furnished the basis 
 of the following theory as to its peculiar behavior. 
 
 * So many of the records require the value of u to be assumed from the 
 proportions of the gun, and so doubtful is the accuracy of many of the 
 pressures recorded before the theory of the pressure gauge was well 
 understood, that the constancy of x ^o"" ^ given gun and powder is best 
 seen from an analytical discussion in Chapter XII. The table is given 
 rather for illustration tha\. for proqf. 
 
28 XI. — COMBUSTION IN A GUN. 
 
 The charcoal made by superheated steam contains a large 
 proportion of free hydrogen and much more in relatively 
 unstable combination. 
 
 The carbo-hydrates^ as are termed the resin, gum and 
 sugar added during manufacture, are also magazines of 
 hydrogen. 
 
 The effect upon the velocity of combustion, due to the 
 presence of the gum and to the high density of the powder, 
 and possibly also some of the phenomena of dissociation 
 under high pressures, prevent the sudden liberation of the 
 hydrogen and its combustion when x^ Eq. (1), is small. 
 
 The hydrogen combines as the pressure wanes, and tends 
 to sustain the pressure and to increase both 7\ and //, whereas 
 in black powder they must vary inversely. 
 
 The water formed serves to precipitate the smoke, the solid 
 particles of which are entangled in a condensed spray of 
 liquid gum following the projectile. 
 
 To this may be added, as a theory more generally accepted, 
 that the large proportion of nitre tends to prevent the forma- 
 tion of CO, thus reducing the volume of the gases first formed, 
 and diminishing the violence of their action, or increasing \ji„ 
 On the other hand, the excess of nitre may tend to increase 
 7\ on account of the more perfect combustion of the charcoal 
 and the high calorific value of the hydrogen which it contains. 
 
 The precautions usual in manufacture are taken to affect the 
 size, shape and density of the grain and the amount of moist- 
 ure it contains, so as to increase its progressiveness. 
 
 That these precautions alone do not account for its peculi- 
 arities appears from the fact, that while a prism of black 
 powder burns in the open air in \\ seconds, and a similar 
 prism of brown powder burns in 10 seconds, equal charges 
 of the brown powder give equal or higher muzzle energies 
 than the black powder without exceeding their maximum 
 pressures. 
 
XI. — COMBUSTION IN A GUN. 29 
 
 English Experiments of 1890. 
 
 1'hese furnish the following data from which the effects of 
 the composition of the powder may be observed. 
 SoHd residue per cent : 
 
 Permanent gases per cent of volume : 
 
 7\ oi permanent gases above 
 Heat units per kilogramme 
 /= v^ H. (Chap. IX, page 7) ratio 
 Specific volumes of water vapor 
 
 
 Black. 
 
 Brown. 
 
 K.CO, 
 
 m 
 
 64 
 
 Kir CO, 
 
 — 
 
 14 
 
 s 
 
 9 
 
 — 
 
 K,S 
 
 15 
 
 — 
 
 KSO, 
 
 10 
 
 22 
 
 iim(3 • 
 
 100 
 
 100 
 
 UIIlC . 
 
 CO, 
 
 47 
 
 51 
 
 CO 
 
 16 
 
 3 
 
 H,S 
 
 3 
 
 — 
 
 ZTand CH^ 
 
 4 
 
 4 
 
 N 
 
 30 
 
 42 
 
 
 100 
 
 100 
 
 
 278 
 
 198 
 
 
 721 
 
 837 
 
 •atio 
 
 1.0 
 
 0.83 
 
 
 41 
 
 122 
 
XII. — SARRAU S FORMULAE FOR INTERIOR BALLISTICS. 
 
 CHAPTER XII. 
 
 SARRAU'S FORMULAE FOR INTERIOR 
 BALLISTICS. 
 
 The deductions of M. Emil Sarrau permit a very accu- 
 rate solution of many important problems affecting the 
 interior form and the method of loading cannon. 
 
 By methods which are too elaborate for present instruc- 
 tion, Sarrau deduces four general formulae for pressures 
 and velocities. 
 
 Notation. 
 
 The units in the following notation are based upon those 
 adopted in the publications of the Ordnance Department, 
 U. S. A. Some changes are made in the notation to make 
 it agree with that previously used in this work. Where 
 Sarrau's notation differs, it is given in brackets. 
 
 Let 
 V. (v) Muzzle velocity, in feet per second, 
 /o (F^ Maximum pressure on bottom of bore in pounds 
 
 per square inch. 
 / {P) Same on base of projectile. 
 d. (c) Caliber in inches. 
 u. Length of the travel of the base of the projectile in 
 
 the bore, in inches. See Chapter XI, page 13. 
 W (/) Weight of projectile in pounds. 
 w {n) Same of powder. 
 A Density of loading. 
 
 d Specific gravity of the powder. 
 
 N' The granulation of the powder, or the number of 
 
 grains per pound. 
 
2 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 
 
 / Force of powder when A = 1, Chapter II, page 7. 
 
 r Time of combustion of a single grain, referred to a 
 
 standard grain as unity. See page 5. 
 
 S Initial volume in cubic inches; the same as F,Chap- 
 
 ter IX, foot page 3. This volume generally 
 differs from the capacity of the powder chamber 
 since the base of the projectile may occupy some 
 of this space. 
 
 8 The reduced length of the initial air space which is 
 
 equal to v' (Chapter IX, page 3) + ^' (Chap- 
 ter XI, page 2). 
 
 We have z=S — v. but 
 
 4 ' 
 
 e 27.68 7£/ , 27.68 7£/ ,, . 
 o.= and z^,= : therefore 
 
 A 
 110.72 w 
 
 (i4) 
 
 a and / (Sarrau uses \ instead of /). 
 
 These are two numerical coefficients depending on 
 the form of the grain, which are functions of the 
 ratio of the least dimension of the grain to its 
 other dimensions. See page 3. 
 
 a and fi. Two very important characteristics depending 
 on the nature of the powder; viz, both on its form 
 and the time of its combustion. Their values are 
 obtained from the following equations : 
 
 m 
 
 ^= r (3) 
 
 Owing to their preponderating effect in the prin- 
 cipal equations which follow, a is known as the 
 
XII. — SARRAU'S FORMULif: FOR INTERIOR BALLISTICS. 3 
 
 pressure characteristic^ aod p as the velocity char^ 
 acteristic. 
 A, B, M, K. Certain empirical constants to be determined 
 
 by experiment. 
 Form of Grain. 
 
 If we develop Equation 5, Chapter X, according to the 
 
 ascending powers of — the development may be placed 
 under the general form * 
 
 j=/w=<.i(i_/i+«i;+&c. . . . .) (4) 
 
 This may be shown to apply to other forms of grain 
 
 besides the sphere, the coefficients of — varying with the 
 
 form of the grain and by their values characterizing the 
 mode of combustion in so far as it is affected by the form 
 of grain. 
 
 I. For spherical grains it readily appears that 
 a; = 3; /= 1; m = Yi, 
 The coefficient m is neglected as insignificant. 
 
 Besides the spherical grain, which includes not only true 
 spheres, but grains the form of which approaches that of a 
 sphere, such as cubes, hexagonal powders and those of 
 irregular granulation ; powders are classified as to form, as 
 parallelopipedons and pierced cylinders. Both classes in- 
 clude the forms most closely resembling the type, e. g. L. X. 
 powder would belong to the former, and pierced prismatic 
 powder to the second class. 
 
 * In the above equation replace — by jr, then 
 f {t) =z\— {X — x)^ =^^ X — 2, x" ■\- x^ 
 
 = 3-(i — + -') = T [1-7+1(7)'] 
 
 For grains of other forms a similar but more extended method is followed. 
 
4 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 II. For the parallelopipedon, if x and j^ represent the ratios 
 of the least dimension of the grain to its other two dimensions 
 
 the development of the corresponding function of — will give 
 
 T 
 
 the following characteristic values for the coefficients a and /, 
 
 a 
 If the base of the grain be square, x — y^ and 
 
 a=.\-\-%x; I— •• 
 
 a 
 
 III. For the pierced cylinder, x represents the ratio of the 
 thickness of the walls of the cylinder to its height, or con- 
 versely; the lesser dimension being divided by the greater 
 in either case. The cylinder is supposed to burn all over 
 at once. The following are the values of the coefficients 
 for the pierced cylinder described: 
 
 a=:l-{-xj 1= -. 
 a 
 
 Since the ratio x has generally given to it a value of J 
 we may form the following table. 
 
 TABLE I. 
 
 Values of ^ 
 
 Form of Grain. a I 
 
 I. Cubical; Spherical; Hexagonal; 
 
 Irregular granulation 3.0 1.0 3.0 
 
 II. Parallelopipedon ; flat powder 2.0 g 3.2 
 
 III. Pierced prism or cylinder, one hole f J 4.5 
 
 By substituting these values of a and / in Eq. (4) we may 
 
 represent graphically, as in figure 1, the variations in the 
 
 rate —=^o for grains of equal weight but of different forms, 
 burning in the same time t. 
 
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 If the rate of conversion is uniform, Eq. (4) becomes 
 
 t 
 f {t)-=.a- and /, /? and y (post) reduce to 0. 
 
 T 
 
 Size of Grain. 
 
 The mean diameter of irregular grains results from know- 
 ing their specific gravity and granulation as follows* 
 
 /6x27.68\i / 52.86 \1 
 
 For powders of regular granulation a similar method may 
 be preferred to the actual measurement of their dimensions. 
 
 VELOCITY FORMULA. 
 Monomial formula for quick powders 
 
 '=Ma (i) 
 
 Binomial formula for slow powders 
 
 (A) 
 
 in which 
 
 F=Aa(wu)^^-^y[l-rl (B) 
 
 The choice of the formula to be employed in any case 
 depends upon the value of y. With a given gun and pro- 
 jectile this depends upon the value of /3 and therefore, 
 under the conditions of loading, /3 measures the quickness 
 of the powder. 
 
 The form of the function y shows that its value depends 
 largely upon the gun as well as upon the powder. Conse- 
 
 *Ca\\v=s -—the volume of the mean grain, the weight of which in 
 pounds is w : then 
 
 ^vze;-i 27.68- '^^vrd^. 
 
6 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 
 
 qiiently the same powder may be quick in some guns and 
 slow in others. Chap. XI., p. 24. 
 
 When y > 0.273, Equation (A), should be employed, and 
 conversely for Equation (B). The two equations give but 
 little difference in results when the conditions make y 
 approach 0.273. 
 
 Referring to the value of /?, Equation (3), it appears 
 that the value of y cannot be known until r has been deter- 
 mined. It is evident that the methods described in Chapter 
 VIII are not sufficiently accurate, so that the following 
 practical method is adopted. 
 Determination of Constants. 
 
 A well defined molded powder is taken as a standard and 
 its values of / and r accepted as unity. For this powder 
 
 the values of a and (i, Equations (2, 3), reduce to y a and /, 
 which can be measured by the means described, page 3. 
 
 To determine the value of M in equation (A) we substi- 
 tute the value of F obtained as the mean of several fires in 
 a gun in which the standard powder is relatively quick, and 
 solve with respect to M. 
 
 In equation (B) we proceed similarly for A and B, select- 
 ing two very dissimilar guns and taking their conditions of 
 loading so as to cover as wide a difference of limits as is likely 
 to occur in practice. 
 
 Choice of Formula. 
 
 Inasmuch as the values of A^ B, J/, are true for all 
 powders, and since (Chapter IX, page 6) the force of all 
 nitrate powders may be taken as constant, and in this case 
 equal to unity, equation (A) may be written 
 
 --(0'(v)- 
 
 S 1 ,1 8 
 
 and placing 
 
 M^^^ = X (7) 
 
Xll. — {JARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 7 
 
 we obtain 
 
 r = «*/-3X«. (8) 
 
 If this value of r substituted in that of y, Equation (6), makes 
 'y> 0.273, Equation (A) may be used; but if it makes y< 
 0.273, Equation (B) must be employed. 
 
 To determine the true value of t for use in Equation (B) 
 requires a method of approximation which .s too long to be 
 given here, but can be found in the works mentioned in the 
 bibliography. This will not generally be necessary, as the 
 characteristics may be determined directly, as hereafter ex- 
 plained. 
 
 The value of r for the standard powder is approximately 
 equal to the time of its burning in air at the rate of about 
 0.4 inch (1 decimeter) per second. Other values of r will 
 therefore have approximately their values in air. 
 
 Rejnark. — The first term in liquation (B) represents the 
 ideal case in which the form of the grain is such that the 
 rate of conversion (Note, foot page 2, Chapter X.,) is uni- 
 form. The second term is sub tractive and represents the 
 effect of the decrease of the rate of conversion, or of the 
 burning surface, when the grains have the forms required in 
 practice. It is evidently an advantage to have the second 
 term as small as possible. 
 
 Empirical Constants. 
 
 The numerical values of A^ B, M^ the determination of 
 which has been incidentally described, depend only upon 
 the units of measure adopted for dimensions and masses. 
 
 In the Ordnance Department, the units being respectively 
 the inch, for internal dimensions of guns; the foot, for 
 velocities per second, and the pound, the constants have 
 the following values given by their logarithms : 
 
 log A = 2.56635 ; log ^= 2.80964; log M= 2.84571. 
 
 The other terms in the formula require no change ; since 
 the effect of changes in the units by which the different 
 
8 XII. — SARRAU's FORMULA FOR INTERIOR BALLISTICS. 
 
 elements of loading are measured, is compensated for by the 
 numerical value of the empirical constants. 
 
 PRESSURE FORMULA. 
 
 The following equations are employed to determine the 
 pressures on the base of the projectile and on the base of 
 the bore. 
 
 p=Ka^£u ( Ww)^d-\ (Q 
 
 in which log ^=3.96198. 
 
 /o=^o «' A W^ wU-^, (P) 
 
 in which log ^o=4.25092. 
 
 Equation (C) is obtained by differentiating the equation 
 for velocity and determining the maximum acceleration of 
 the projectile; it can be verified only by the apparatus 
 described Chapter VII. But equation (D) can easily be 
 verified by the pressure gauge. See Chapter XI, pp. 8 — 9 
 
 PRESSURE CURVES. 
 
 In designing guns it is indispensable to know something 
 about the pressure at other points along the bore than that 
 at which the maximum pressure occurs. 
 
 In Chapter IX we have considered an approximate solu- 
 tion; but Sarrau's formula furnishes us a method which is 
 much more accurate. 
 Expansion Curve. 
 
 If in equation (B) we call 
 
 J,=Aaw^\^-jP^j f (9) 
 
 M.=BJ3^^> (10) 
 
 For the same gun, conditions of loading and powder, 
 equation (B), becomes by writing, v, the velocity at any 
 
XII. SARRAU'S FORMUL/E FOR INTERIOR BALLISTICS. 9 
 
 point of the bore, for F, the muzzle velocity, and calling u 
 the variable length of travel of the projectile. 
 
 v^A^u\{\-B^u\). (11) 
 
 If we differentiate equation (11) with respect to v and u^ 
 and divide by dt^ we have 
 
 ^ = (|^,«-|-J/(,^,«-j)^ =/(«)$. (12) 
 
 in which -y- = v and -^ = acceleration of the projectile, or 
 at at 
 
 dv i) 7T d^ <"" 
 
 calling/, the variable pressure on the projectile ; —=<-L- ^, 
 
 From this follows 
 
 Combustion Curve. 
 
 It is not recommended to depend upon the values of /, 
 
 u 
 thus deduced for a travel of the projectile of less than ^ ; 
 
 because the velocity formula is not considered reliable for 
 such small values of u as those existing during the com- 
 bustion period. Chapter XI page 1. 
 
 The form of the pressure curve in the initial portion may 
 be determined as follows. 
 
 It appears from the following table based upon the analy- 
 sis of Sarrau that the displacement of the projectile corre- 
 sponding to the maximum pressure, or C/", is equal to 0.6 Zy 
 equation (1). This gives us the locus of this pressure and 
 equation (C) gives us the intensity. It remains then to find 
 the form of the portions of the curve in the neighborhood 
 of the point of maximum pressure. This is obtained from 
 the following table which gives the proportion of the 
 maximum pressure exerted at points near the displacement, 
 Uj above. In this table the variable jo represents the ratio 
 
10 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 u d"^ y • • 
 
 _, and — v^ values proportional to the acceleration, since 
 z dx^ 
 
 X, in this case represents a certain function of /. It has no 
 
 connection with the quantity x, on page 3. 
 
 TABLE II. 
 
 ^0 
 
 
 y^ 
 
 
 JVo 
 
 d^y. 
 
 dx^ 
 
 0.1 
 
 0.180 
 
 0.6 
 
 0.710 
 
 1.25 
 
 0.651 
 
 .3 
 
 .605 
 
 .7 
 
 .705 
 
 1.50 
 
 .621 
 
 .8 
 
 .665 
 
 .8 
 
 .700 
 
 1.75 
 
 .590 
 
 .4 
 
 .693 
 
 .9 
 
 .692 
 
 2.00 
 
 .563 
 
 .5 
 
 .700 
 
 1.0 
 
 .680 
 
 2.50 
 
 .513 
 
 That is to say that after the projectile has travelled over 
 a distance equal to the reduced length of the initial air space, 
 the pressure is -||- of the maximum; etc. 
 
 It is supposed that the pressure on the wall adjacent to 
 the base of the projectile is to that upon the base, as 10 is 
 to 7; so that by multiplying the pressures just determined 
 by 1.43 it is easy to determine the probable intensity of 
 the corresponding pressure on the walls of the bore. 
 
 QUICKNESS OF POWDER. 
 
 Sarrau has established for powders fired under various 
 conditions of loading certain moduli of quickness which 
 express their relative quickness under these conditions. 
 See page 5. 
 
 The modulus of a powder forms an important independ- 
 ent characteristic which is of considerable help in establish- 
 ing auxiliary equations of condition for the solution of 
 problems in Interior Ballistics. 
 
 It may be shown from equation (B) that if, among the 
 variables in the second member, r alone be caused to vary, 
 the function, F, will pass through a maximum state. 
 
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 11 
 
 In practice this is not absolutely true ; for, as already 
 stated in Chapter XI, the smaller the time of combustion, 
 the greater the number of volumes of expansion in a given 
 gun, and hence the greater the kinetic energy due to a 
 given charge. 
 
 Equation (B) is derived by a process of approximation, 
 and its physical significance cannot therefore be rigorously 
 interpreted. It serves to show, however, that there is a 
 limit below which the reduction in r has but a very slight 
 effect upon the velocity, and which it is inadvisable to pass; 
 because, as r diminishes past a certain point, the velocity 
 increases very slowly; but the maximum pressure very 
 rapidly. 
 
 The value of r corresponding to the maximum value of 
 Fis obtained by placing equal to zero the first differential 
 coefficient of the second member of equation (B) regarded 
 as a function of r and solving with respect to r.* 
 
 Denoting this value of r which is called the time of the 
 maximum (velocity?) by Tj we have 
 
 r. = 3^((^. (14) 
 
 a 
 
 In a given piece a powder behaves as a slow powder 
 when the time of its combustion, r, is notably greater than 
 
 * Equation B may be written, 
 
 V=C\p{t)=^CiT-\ — RT-\\ 
 in which 
 
 .=.£(i^ c=. (/«)»(.„)» (A); 
 
 Hence 
 
 — =C(— ^r 2-\-\Rt 2) 
 
 by placing —- =0. 
 
 a T 
 
 r,=.S^^SJ^'JKpl 
 
 (U) 
 
12 XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS. 
 
 that which in the particular arm corresponds to the theoret- 
 ical maximum of velocity. Further, two powders fired in 
 different pieces should be considered as equivalent as far as 
 regards quickness if their times of combustion are propor- 
 tional to the times of the maximum for the two pieces 
 employed. Consequently we may call the ratio 
 
 ^ = ^ (15) 
 
 the modulus of quickness under the particular circumstances 
 under which the powder is fired ; since the more nearly does 
 Tj equal t, the more nearly does q approach unity.* 
 
 Under this view we may adopt the following arbitrary scale 
 for the classification of powders : 
 
 
 TABLE 
 
 III. 
 
 
 Value of Modulus. 
 
 
 
 Nature of Powder, 
 
 1.0 
 
 
 
 Very quick. 
 
 .9 
 
 
 
 Quick. 
 
 .8 
 
 
 
 Medium. 
 
 .7 
 
 
 
 Slow. 
 
 .6 
 
 
 
 Very slow. 
 
 Since the above classification was proposed by Sarrau, it has been 
 found advisable to extend the value of the modulus in both directions. 
 For long Sea Coast guns it now runs as low as 0.4, while it has been 
 found advantageous in the B.L. mortars to increase it to 1.3. 
 
 In any case we have 
 
 (W u)^ 
 q=^Bp^—^=dy. (16) 
 
 VELOCITY AS A FUNCTION OF THE MODULUS. 
 
 By introducing q in place of r in equation (B) we may 
 obtain a new and useful monomial equation of the general 
 form 
 
 * The modulus of quickness also is designated by Sarrau as x. 
 
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 
 
 13 
 
 V=^A^,B)-^(l{y±^^ (17) 
 
 in which /(^) may be taken as Nq^\ N being some con- 
 stant.* See page 28. 
 
 Collecting the different empirical constants under one 
 head, which we may call M, and ascertaining that for the 
 particular form of / (q) employed we have 
 
 n = i^fZ^.; (18) 
 
 we find that equation (17) reduces to 
 
 In equation (A') V varies with n\ that is, with the 
 modulus, ^, upon which by equation (18), n depends. It may 
 be used as an approximation, as on page 6, by giving to 7t a 
 constant value under conditions of loading which are such 
 that the modulus is comprised within certain limits. 
 
 *This equation shows that under given conditions of loading the initial 
 
 //a\\ 
 velocity is proportional to I -y I . 
 
 This factor is called the ballistic coefficient. It depends both upon the 
 force of the powder and the form of the grain. If the force be considered 
 constant, the ballistic coefficient depends only on the form of the grain. 
 
 By transforming Equations ( 2, 3) we have 
 
 ^ -T-J' 
 
 It will be observed from Equations (C^), (D^), that the pressure varies 
 with the square of the ballistic coefficient. This relation imposes a prac- 
 tical limit to increasing the velocity by the increase of this coefficient. 
 
 The ballistic coefficient of the powder must be carefully distinguished 
 from the ballistic coefficient of the projectile to be hereafter discussed. 
 
14 XII. — SARRAU*S FORMUL.*^ FoR tJJtERlOR BALLISTICS. 
 
 It is convenient to remember that n increases as q de- 
 creases: when ^=i\-, ^=-J; and when ^=3^, n:=\* 
 
 It is considered that these are the limits imposed by 
 practically satisfactory conditions of loading. See page 21. 
 By making q—^ equation (A') reduces to the form of 
 equation (A), which was thus derived. 
 
 Since q—'6y and since the value of q=^ is taken to be 
 about the highest modulus that can be profitably employed, 
 we see why the maximum value of y on page 5, has 
 been determined =3^-^-3=0.273.* 
 
 MAXIMUM PRESSURE AS A FUNCTION OF THE MODULUS. 
 
 By substituting for - in the value of a', equation (C), its 
 value — derived from equation (14), Sarrau finds 
 
 ^=^(3^)-^^^(v)^. (C) 
 
 and similarly 
 
 A = ^o(3^r -/-(»^) ^(v) i- («) 
 
 PRINCIPLE OF SIMILITUDE. 
 
 Two guns are similar when all their homologous linear 
 dimensions are proportional to their calibers. Chapter 
 XVI, page 17. 
 
 The similitude is extended to the loading when the 
 weights of the powder and of the projectile are proportional 
 to the cube of the calibers, and when the grains of powder 
 have the same form, composition, density, etc., and their 
 
 ^Although not so named, it is convenient to think of n as the modulus 
 of slowness. 
 
Xlt. — §ARRAU*S FORMULife fOR iNtEklofe 6aLUSTICS. 15 
 
 dimensions are proportional to the calibers. Consequently 
 the numerical coefficients a^ /, must have the same values, 
 and the value of r must vary proportionately with the caliber. 
 
 The principle of similitude enables the following proposi- 
 tion to be proved, viz. : 
 
 In similar gims, similarly loaded^ the velocities and pressures 
 corresponding to distances passed over, which^ measured ifi cali- 
 bers, are equal, are respectively equal to each other. 
 
 For, let us consider two guns having calibers respectively 
 
 equal to d and to d' such that d' z:^ B d, and substitute in 
 
 d' 
 Eq. (16), (17), the ratio d z= — raised to powers varying with 
 
 d 
 
 the quantity considered, as follows : 
 
 From the conditions of similitude we have 
 
 w:w' :: W: w^':: d^ : d'\ 
 
 or 
 
 7e> - W ~ \ d ) —^ ' 
 
 u' d' 
 and Ji = 4_ = 6>. 
 
 u d 
 
 In Eq. (17) the factors A, B, A, N, and the ballistic co- 
 efficient will be eliminated by division, so that substituting 
 
 for — |- , (03)i = $1 and so on, we have 
 
 I q' r 
 
 Similarly in Eq. (16) since /? =r --, zr — j Q. 
 
 T \ q' 
 
 Now if T varies with the caliber, —j- = —^, and — = 1, 
 
 T ~"6I 
 
 or V= V, 
 
 Since the muzzle may be taken at any distance the propo- 
 sition is proved as to velocities and can be shown to be true 
 as to pressures by the similar treatment of Equation (C). 
 
16 XII. — SARRAU'S FORMUL.^ FOR INTERIOR BALLISTICS. 
 
 But if the same powder is used in two similar guns of 
 
 r V d'^ 
 
 different caliber — r- = 1 and -yit- = (QY = -7—. 
 t' V d^ 
 
 Consequently, for the same powder in similar guns, the ve- 
 locity varies as the ^z**^ power of the caliber. 
 
 Equation (D) similarly shows that when the same powder 
 is used in similar guns the pressure varies as the caliber. 
 
 This is a more exact explanation of the practice of vary- 
 ing the size of the grain to suit the gun than that given 
 Chapter XI, page 7. 
 
 INFLUENCE OF THE CONDITIONS OF LOADING 
 UPON VELOCITIES AND PRESSURES. 
 
 General Statement. 
 
 Let us consider as constant for any gun the quantities d^ 
 u, IV, and as constant for any powder its force and form of 
 grain, or/, a and /, i.e., its ballistic coefficient. 
 
 The quantities which may then be varied so as to affect 
 the velocities and pressures are w, A and r. 
 
 There are an infinite number of sets of values of these 
 variables which will give the same velocity with different 
 maximum pressures, or the same pressure with different 
 velocities. The pressures considered are those upon the 
 breech of the gun. 
 
 The following practical rules result from differentiating 
 the Napierian logarithms of the above named variables in 
 Equations (17) and (D'). In equation (17) the differential 
 of the Napierian logarithm of the function of ^ which it 
 
XII. — SARRAU'S FORMULi^: FOR INTERIOR BALLISTICS. 17 
 
 contains can be shown to reduce to the form * 
 
 '^l0ge/(?)=-«^, (19) 
 
 and in equation D', 
 
 d\oz,q= -—-; (80) 
 
 therefore 
 
 d V dw d b. dr 
 
 
 dpo dw d l\ d t 
 po ~^ w "^ A ~r 
 
 (21) 
 
 (22) 
 
 These equations enable us to determine the variations 
 in velocity and pressure corresponding to very small incre- 
 ments of the variables w, A and r. 
 
 The influence of each variable on the value of the velocity 
 and pressure is measured by the coefficient which multiplies 
 the relative variation of each variable in the above equations. 
 
 In Equation 21 the coefficients of , , and are 
 
 respectively § ; \\ n = ^ S^T^ ' 
 
 bince a = — ; a^ = == — (/ — 
 
 ^ r T T T 
 
 dq dr 
 
 Also d log. f (q) = d loge N q-=J-S^L^ 
 
 A/ q'^ 
 
 d q^ n q^~^ dq 
 
 d T 
 
 =.11 d loge <] = '' 
 
 The increments here discussed are small finite differences made in ad- 
 justing practically the conditions of loading. For considerable differences 
 Equations (A, B, etc.), should be employed. 
 
18 XIT. SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 The third coefficient varies with r and is equal to for 
 T i^ Tj. Its value increases with r, but does not exceed ^ 
 except when q is less than -^ which is not likely to happen 
 in the ordinary conditions of practice. 
 
 Comparing equations (21) and (22) it appears that while 
 in equation (21) the variables are arranged in the order of 
 their relative importance, in equation (22) the influence of 
 w on the maximum pressure is less than that of A or r. 
 
 Let us consider as a fundamental condition that the maxi^ 
 mum pressure remains at a constant value determined by the 
 strength of the gun, and suppose but two of the quantities 
 Wy A and r to vary at a time, the third remaining constant. 
 
 First Case, a and r variable, w constant. 
 
 The equations reduce to 
 
 d t. dt ^ 
 
 -^ = — and (23) 
 
 %'{^y-^ («) 
 
 Therefore, if A is varied by changing the size of the 
 chamber for a given charge, the time of burning must 
 change correspondingly to the density of loading. In such 
 a case, if ^>-5%, T increases with A. Hence the conclu- 
 sion: In order to obtain the greatest velocities we should 
 use high densities of loading and slow powder. 
 
 Second Case. z£^ and r variable ; A constant. (M. L. gun.) 
 
 Equation (22) becomes | = , (25) 
 
 and equation (21) ^ = f (J - «) ^ , (26) 
 
 * That is, that if we increase w by 10 per cent ; then, to fulfill the fun- 
 damental condition, r must be increased ^, or 7.5 per cent. 
 
XII. — SARRAU'S FORMULi*: FOR INTERIOR BALLISTICS. 19 
 
 It follows from equation (18) that since when q is equal 
 to 0, « = J ; and that when q is greater than 0, n is less than 
 J, the factor (J — n) is always positive and therefore that the 
 velocity increases with the charge of powder, and that the 
 maximum pressure will not be exceeded provided that the 
 time of its combustion be regulated as required by Equation 
 (25). 
 
 Third Case, w and r variable in a chamber of constant 
 capacity. We have supposed in the preceding cases that 
 the volume of the powder chamber can be increased or 
 decreased at will, and in designing guns to perform certain 
 work the conclusions reached are useful. Suppose however 
 that we desire to improve the conditions of loading of an 
 existing cannon. In this case, since 
 
 A = 
 
 27.68 w , d t. 
 
 wp nivp 
 
 dw 
 
 (27) 
 
 o A 
 
 and therefore 
 
 
 
 
 
 dV ,dw dr 
 
 
 (28) 
 
 
 dr dw 
 
 r -* w' 
 
 
 (29) 
 
 
 dV ... ^dw 
 
 
 (30) 
 
 in which (^— «) is positive. 
 
 Therefore, if the chamber is large enough, we may in- 
 crease the velocity without changing the pressure by using 
 a larger charge and a slower powder. 
 
 Examples. 
 1. Suppose with a slow powder (;/ = |) we wish to increase 
 
 F by 10 per cent, -^ = j^ .= ^ = ^ ^ ... ^«, = 
 53.3 per cent, and = — 53.3 = 93 per cent. That is, we 
 
20 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 would use nearly double the charge of double the size of 
 grain ; assuming that r is proportional to the size of the grain. 
 2. Using a quick powder {fi = g) and 
 
 ~V = To = 32" loo •'• ^"^ =" ^^ P"' "'""'' ^"^ ~r -= ^^ 
 per cent. Or we would use about one-quarter greater charge 
 of less than one-half greater size. 
 
 Fourth Case, w and A variable and r constant. 
 
 This corresponds to the use of the same powder in guns 
 having different chambers. 
 
 From the conditions we have 
 
 ~ = -i~' (31) 
 
 y=A'^- (3.) 
 
 That is to say; that if we fix the size and shape of the 
 grain, and wish to increase the velocity, we must increase 
 both the weight of the charge and the volume of the 
 chamber. 
 
 General Remark, 
 
 A review of the preceding cases shows that whenever t 
 varies, F is a function of n and also of either wov A according 
 to which one of these is variable. 
 
 THE EFFECT UPON PRESSURES AND VELOCITIES OF 
 VARYING THE TIME OF COMBUSTION. 
 
 If in equation (21) we allow only r to vary, we have 
 
 _=-;._. (33) 
 
 The value of n increases as the modulus decreases; conse- 
 quently the same relative variation of the time of combustion 
 has a greater influence upon the velocity as the powder be- 
 comes slower. See Chapter XI, page 18. 
 
XII. — SARRAU'S FORMUL/K FoR INTERIOR BALLISTICS. 21 
 
 (34) 
 
 Now, suppose the pressure to vary; under the conditions 
 equation (22) reduces to 
 
 dp^ _ _ ^^ . 
 
 Combining this, with equation (33) we obtain the very simple 
 relation 
 
 ^=.^%. (35) 
 
 V p^ 
 
 which expresses a relation between velocities and pressures 
 
 similar to that between velocities and times of combustion, in 
 
 Equation (33). 
 
 It has been stated page 12, that the values -^ and ^ 
 may be considered as the limits that the modulus should not 
 pass. The choice of these limits is justified as follows. 
 When the modulus is greater than -^ the relative variation 
 of the velocity depends upon n in equation (35) which under 
 these circumstances only becomes \ of the relative variation 
 of the maximum pressure. Consequently, a sensible incre- 
 ment of the velocity is obtained only with a considerable 
 increase in the pressure and the energy acquired by the pro- 
 jectile is imparted at an increased risk to' the gun. This 
 grows less as the modulus diminishes from -^^ ; because 
 the value of n increases; but then, from Equation (34), the 
 relative variation of the velocity corresponding to the same 
 relative variation of the time of combustion increases, as 
 shown by Equation (33), so that the influence of accidental 
 irregularities of the powder upon the velocity continually 
 grows greater. 
 
 It is then advisable to fix an inferior limit for the modulus 
 so as to preserve uniformity in velocity. 
 APPLICATIONS. 
 
 1. To determine the characteristics a and y5 of a powder. 
 
 The most practical method is to use according to circum- 
 stances either equations (A) or (B) in connection with equa- 
 
S^ Xlt.— SARRAu's FORMULA FOk INTERIOR BALLlStlCS. 
 
 tion (D), and to substitute in these equations for V and p^ 
 the mean of several measured velocities and pressures ob- 
 tained under invariable conditions of loading. 
 
 We have then two independent equations involving but 
 two unknown quantities, a and /?; these may then be deter- 
 mined without reference to their separate factors. 
 
 By the theory, the characteristics are entirely independent 
 of the gun. In this respect, and also in that they give us 
 numerically the influence of all the elements of firing, Sarrau's 
 formulae are more useful than those, like Noble's, described 
 in Chapter XI. 
 
 Having determined accurate values for the characteristics 
 of a powder, we may compute the velocity and pressure to 
 be expected in any gun whose dimensions are known, when 
 the conditions of loading are given; and conversely, the 
 dimensions may be determined. 
 
 Within reasonable limits of variation of the quantities 
 entering them, the accuracy of the formulae has been abun- 
 dantly verified. 
 
 EXAMPLES. 
 
 1. To find the characteristics of Du Font's P. N. (Brown 
 Prismatic) powder from a single firing of the 8 inch B. Iv. 
 Steel Rifle. For its dimensions see Table IV. 
 Data. 2£/=110; fr= 289; A =0.980 ; z/= 1878; /„= 36000; 
 ^/ = 195.75. Equation (D) gives us 
 
 «2= i^ — - =0.9706=log-il.98704. 
 
 An application of the test mentioned page 6, will show 
 that the binomial form.ula is applicable; although this might 
 be assumed for powders of this kind. If then we write 
 equation (B) so as to combine in each term the quantities 
 relating to the gun and the conditions of loading, we may 
 reduce it to the form 
 
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 23 
 
 XF=a-a(3V or jS^"""^^, 
 
 a V 
 in which Fis measured and 
 
 — = — > (- /v and Y= — ^^ -. 
 
 Substituting in the above the known values of a, X, V 
 
 and K we find 
 
 log i3 = 1.33725. 
 
 Another method is to fire the same powder under very 
 dissimilar sets of conditions in which W^ w, u, d shall have 
 different values and to determine the values of V under 
 these conditions. 
 
 We may thus obtain two formulae of the form of the above 
 value of XV; as these involve but two unknown quantities, 
 the characteristics sought may be determined. 
 
 This method avoids all uncertainty attending the oper- 
 ation of the pressure gauge; but the former method is gener- 
 ally preferred as the conditions more nearly resemble those 
 of practice, and introduce the customary unit of measure- 
 ment of pressure, 
 
 2. To compute the muzzle velocity to be expected from 
 the 8 inch B. L. Steel Rifle for the preceding powder. 
 Data. 7i/=105; A =0.935; /^=289. 
 
 Computati( 
 log B = 
 log^ = 
 log W\ = 
 log u^ = 
 log d-' = 
 
 )n of y, 
 
 2.30964 
 1.33725 
 1.23046 
 1.14585 
 1.09691 
 
 Computatic 
 log^ = 
 
 log a = 
 log wt = 
 log A^ = 
 log u^ = 
 log IV-^ = 
 log d-^ = 
 log(l-;K) = 
 log F = 
 V = 
 
 m of V. 
 2.56635 
 
 1.98704 
 0.75795 
 1.99276 
 0.85939 
 
 log y 
 
 y = 
 
 l-y= 
 
 1.12011 
 0.13186 
 0.86814 
 
 1.38477 
 1.77423 
 1.93859 
 
 
 3.26108 
 1824.3 
 
24 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 By actual measurement Fwas found to be 1825. 
 
 3. To compute the maximum pressure on the breech 
 under the same conditions as in No. 2. But with a powder 
 {PO) of which the characteristics are different, viz.: — 
 a=log-il.97701; y5=log-il.28978. 
 
 log^o 
 
 = 
 
 4.25092 
 
 log a* 
 
 = 
 
 1.95401 
 
 log A 
 
 = 
 
 1.97102 
 
 log w^ 
 
 = 
 
 1.51589 
 
 log Wi 
 
 = 
 
 0.61523 
 
 log ^-2 
 
 : 
 
 2.19382 
 
 log A 
 
 4.50089 
 
 A 
 
 = 
 
 31688 
 
 From actual firing under the above conditions the mean 
 value of A as determined by two independent pressure 
 gauges was 31700 lbs. 
 
 4. In order to avoid injury to valuable cannon, it is custom- 
 ary at the Proving Ground to make a preliminary trial of 
 new powders in what is called the proof gun. 
 Data. w=35.9; «^=181; A =0.8988; ^=8; A=20420. 
 Find the value of A to be expected when 
 
 ze/=90; «^=300; A =0.8018; ^=8. 
 The first set of data give in Equation (D), 
 log a2:=0.18085, 
 hence, we find for the second set of data, 
 A=41174 lbs. 
 In actual firing the mean value was found to be 41055 lbs. 
 
 Useful Tables. 
 
 The following tables give the dimensions of various cannon 
 of the U. S. land service with the characteristics of different 
 powders tried in them and the resulting pressures and 
 velocities both computed and as verified by measurement. 
 
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 25 
 
 They will be useful in solving problems hereafter. 
 Table IV. 
 
 Pow- 
 der. 
 
 Gun. 
 
 d 
 inches. 
 
 u 
 
 inches. 
 
 W 
 
 lbs. 
 
 w 
 lbs. 
 
 A 
 
 V 
 
 feet per 
 sec. 
 
 11 ^'' 
 lbs. per 
 
 eq. in. 
 
 LX... 
 
 3'^20B. L. rifle.. 
 
 3.2 
 
 73.2 
 
 13 
 
 3.50 
 
 0.857 
 
 1,649 
 
 31,000 
 
 LXB. 
 
 ....do 
 
 3.2 
 
 73.2 
 
 13 
 
 3.75 
 
 0.827 
 
 1,756 
 
 35,150 
 
 IKD.. 
 
 ....do 
 
 3.2 
 
 73.2 
 
 13 
 
 3.50 
 
 0.857 
 
 1,680 
 
 29,100 
 
 1KB.. 
 
 ....do 
 
 3.2 
 
 73.2 
 
 13 
 
 3.50 
 
 0.857 
 
 1,663 
 
 30, £^00 
 
 KHC. 
 
 12^^ mortar 
 
 [2.0 
 
 91.6 
 
 610 
 
 50.0 
 
 0.821 
 
 932 
 
 22,000 
 
 MW.. 
 
 ....do 
 
 12.0 
 
 91.6 
 
 610 
 
 48.0 
 
 788 
 
 959 
 
 26,250 
 
 EVF. 
 
 S^^B.L. R Conv.. 
 
 8.0 
 
 98.5 
 
 183 
 
 45.0 
 
 0.792 
 
 1,488 
 
 32,650 
 
 PiV... 
 
 8'^B.L. R. S 
 
 8.0 
 
 195.75 
 
 289 
 
 110.0 
 
 0.980 
 
 1,878 
 
 36,000 
 
 NM.. 
 
 12'^B.L.R.C.L.. 
 
 12.0 
 
 273.5 
 
 800 
 
 265.0 
 
 0.827 
 
 1,688 
 
 26,350 
 
 NV3.. 
 
 ....do 
 
 12.0 
 
 273.5 
 
 800 
 
 265.0 
 
 0.827 
 
 1,718 
 
 26,890 
 
 NR... 
 
 ....do 
 
 12.0 
 
 273.5 
 
 800 
 
 265.0 
 
 0.827 
 
 1,826 
 
 32,990 
 
 NVi.. 
 
 ....do 
 
 12.0 
 
 273.5 
 
 800 
 
 265.0 
 
 0.827 
 
 1,760 
 
 26,625 
 
 NVa.. 
 
 ...do 
 
 12.0 
 
 273.5 
 
 800 
 
 265.0 
 
 0.827 
 
 1,756 
 
 28,000 
 
 IB... 
 
 3^M7 M L.R.W.I. 
 
 8.175 
 
 74.6 
 
 10.5 
 
 5.469 
 
 0.814 
 
 1,983 
 
 25,000 
 
 OB... 
 
 12^^ mortar 
 
 12.0 
 
 91.6 
 
 610 
 
 52.0 
 
 0.854 
 
 987 
 
 25,250 
 
 oc... 
 
 ....do 
 
 12.0 
 
 91.6 
 
 610 
 
 52.0 
 
 0.854 
 
 942 
 
 19,750 
 
26 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 
 
 :S 
 
 o 
 
 s ^ 
 
 s 
 
 tH 
 
 g 
 
 a 
 
 ^ 
 
 ^ ^ 
 
 JO 
 
 JO 
 
 JO 
 
 CO 
 
 ^ 
 
 
 
 
 ■I-H 
 
 GO 
 
 
 
 lO 
 
 ^ 
 
 
 CJ 
 
 
 00 
 
 oo 
 
 lO 
 
 CQ 
 
 ^ CD 
 
 
 bo 
 
 2 
 
 CO 
 
 <- 
 
 o c^ 
 
 CO CO 
 
 
 00 
 
 f- 
 
 
 CO 
 
 CD 
 
 {^ 
 
 
 t- 
 
 
 o 
 
 CD 
 
 CD to 
 
 -* CO 
 
 CC 
 
 03 
 
 '^ 
 
 CO 
 
 OS 
 
 00 
 
 OS 
 
 00 
 
 00 
 
 00 
 
 
 o 
 
 O 
 
 o c 
 
 o o 
 
 c 
 
 o 
 
 o 
 
 o 
 
 It-I 
 
 l-rH 
 
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XII. — SARRAU'S FORMULiE FOR INTERIOR BALLISTICS. 27 
 
 
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28 XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 
 
 DISCUSSION OF THE COEFFICIENT X^ 
 
 If in Equation (10), Chapter XI, we replace r^ by we 
 
 4 
 
 have after reduction, r =. Tc^rr, — rr ji •> 
 
 in which u is expressed in feet. But since internal meas- 
 ures are given in inches we may avoid errors in practice by 
 writing this 
 
 12 
 
 in which G = nctAi\ 2 • 
 2240 g^ n 
 
 If in Equations (17) and (D^) we replace the ballistic co- 
 efficient by C, and collect the constants in both equations 
 so that 
 
 3 (3 ^)W 3 ^ ' 
 
 these equations will read 
 
 _^ ^C wl A^' d^ td N q"" ,^„. 
 
 ^ =" ^ w^ • ^ ^ 
 
 ^°==-^ Wi did ' (^^) 
 
 Substituting these values in Equation (36) we have 
 
 X=Za N^ q^--^ (-^y (39) 
 
 in which Z = ^-^ = log-^ 0.7394, viz., 5.488. 
 
 The factor N, which in Equation (17) was taken as con- 
 stant, is not absolutely so.* Its value is given in Sarrau as 
 
 /(,)=iV," = Z^i^>. (40) 
 
 By substituting the value of N impHed in Equation (40) in 
 
 q rt 
 
 ♦ For values of f between yp and -^ ,iV"varies only from 1.012 to 1.056. 
 
XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 29 
 
 the factor N* /""' in Equation (89) and calling the result- 
 ing value Q, we have 
 
 This reduces Equation (39) to ^ 
 
 ^ = ^^'e(-|^)*. (42) 
 
 Discussion of the Factors of X. 
 
 Of the four factors producing %'. Z is a constant ; C 
 depends solely upon the powder; that is upon its force and 
 the form of the grain ; Q depends upon the suitability to 
 the gun and projectile of the kind of powder employed ; 
 
 — j depends solely upon the circumstances of the particu- 
 lar fire considered. Hence, to compare the intrinsic proper- 
 ties of different powders fired in the same gun, we may 
 compare their respective values of 
 
 The relation between ^ and ^ is shown in figure 2, from 
 which it appears that while Q is sometimes an increasing and 
 sometimes a decreasing function of q ; for values of q be^ 
 tween fj^ and -j^, ^decreases slowly from its maximum value 
 of 1.245, corresponding to ^ = ^q, to a value of 1.159, 
 corresponding to ^ = -^j* 
 
 If the force of all nitrate powders were truly constant, 
 
 C = —- = -jj- would depend for its value solely upon the 
 
 form of the grain ; and, since within ordinary limits Q does 
 not vary greatly, we would expect nearly equally good re- 
 
 * From this we may conclude that for ordinary approximation the mean 
 of these values, or ^ = 1.2 may be used. Also that it is not well to 
 depart much from the inferior limit of g established by Sarrau. 
 
30 XII. — SARRAU'S FORMULAE FOR INTERIOR BALLISTICS. 
 
 suits from black or brown prismatic powder. But, in the 
 following illustration, taken from one of the best black pris- 
 matic powders recently tried, we find /to be so small that C 
 does not much exceed the value oP 3.0 deduced from 
 Table I, for ordinary powders of irregular granulation. 
 
 We may therefore conclude that the advantage of cocoa 
 powder consists in its maintaining its force at nearly unity* 
 without becoming so quick (or slow ; figure 2) as to cause its 
 value of Q to become unduly small. These considerations 
 indicate in a general way that its peculiar properties are due 
 to the nature of the fuel it contains. 
 
 Illustrations. 
 
 The following data, derived from experimental records, 
 illustrate the principles discussed : 
 
 COMPARISON OF POWDERS. 
 
 Gun Sin. B.L.R. 8in.B.L.R. 
 
 Powder, kind Bl. prism. Br. prism. 
 
 Powder, name O. I. N. Ger. cocoa. 
 
 W. 45.0 289.0 
 
 Sph. Density 2.9 4.5 
 
 V, 1852 1875 
 
 A 33075 35900 
 
 u 119.8 195.75 
 
 a 1.5 1.5 
 
 / 1 ^ 
 
 * ^ 3 
 
 a" 2.45 0.93 
 
 (i 0.78 0.21 
 
 /. 0.70 0.96 
 
 r 0.43 1.59 
 
 C 3.16 4.45 
 
 q 0.70 0.38 
 
 * See Table V, in which the last six powders are cocoa* 
 
Xli. — gARRAU*S FORMUL.fi FOR INTERIOR feALLtSTICS. SI 
 
 Q 1.23 1.12 
 
 X observed 28.28 34.32 
 
 X Equation (40) 28.44 34.87 
 
 n 21.26 27.39 
 
 Ratio of n 1.00 1.29 
 
 If we exchange powders only, we have — 
 
 Powder Ger. cocoa. O. I. N. 
 
 q 0.19 1.47 
 
 Q 0.73 0.50 
 
 II 17.95 8.55 
 
 Ratio of n 2.10 1.00 
 
 That is, that while each powder is best suited to the gun in 
 which it is actually used, the cocoa powder would be better 
 for general use, and might profitably be adapted to the siege 
 rifle by reducing the size of the prism so as to diminish r and 
 increase Q. 
 
 MAXIMUM VALUE OF X, 
 
 The value of 11 before deduced, enables us to solve some 
 very important problems in internal ballistics. 
 
 As an example, let us consider the question of how, with 
 our present knowledge of gunpowder, we may attain the 
 maximum value of X' Also, let us apply this to a gun the 
 construction of which limits p^ ; the spherical density of the 
 projectile being known and the value of ?/ being expressed 
 
 8 IV 
 in terms of the caliber or // rr n d, Let s = — -— be the 
 
 spherical density of the projectile.^ The maximum value 
 of C^ being 4.5, figure 2 shows that the maximum value of 
 IT, and hence of x^ will require ^ = 0.6. 
 
 The maximum value of tj will depend on that of A. The 
 
 * See Chapter XVI, page 6. 
 
82 Xn. — SARRAU*S FORMULi^ FOR INTERIOR SAlLISTICS. 
 
 specific gravity of some powders is now such that a value of 
 A =: 1, has been reached. We may consider this a maxi- 
 mum, as it is rarely exceeded. After deducing general equa- 
 tions, we will apply them to a typical gun based on the 8-in. 
 B. L. R. Steel, in which j =z= 4.5 ; ^/ = 24, and take the 
 maximum value for /„ as 36000 lbs. per square inch, that 
 being what the records indicate to be a desirable limit. 
 
 1. Proper Weight of Charge. 
 
 By substituting the values assigned for JV, A, d, t^, q in 
 Equation (D'), it leads to the following ratio : 
 
 ^=[log"'n.lll9^']S (44) 
 
 In which, by substituting the special typical values assumed 
 for /(J, n and i", we have w = 0.2 W. 
 
 In the 8-in. rifle this would reduce the charge of powder 
 about one-half. 
 
 2. Proper Size of Grain. 
 
 If in Equation (16) we place q =s 0.6 and assign values as 
 above, we have for a general equation, since / = J 
 
 r = log " ^2.0799 (^s n)h d. (45) 
 
 This shows that, as before stated, the size of the grain 
 should, in similar guns, vary directly with the caliber. For 
 the 8-in. rifle, this makes % = 1.0, or, from the preceding table, 
 the size of the grain should be about 68 fo of its present linear 
 dimensions; the force of the powder being unity, and the 
 form remaining unchanged. 
 
 3. Maximum velocity. 
 
 The maximum value of H = 5.488 X 4.5 X 1.245 = 30.73. 
 
 But U = X \ wA = x-:7a 3- = 30.73. 
 
 By substituting the value of wl deduced from Equation (44) 
 
XII. — SARRAU'S FORMULA FOR INTERIOR BALLISTICS. 33 
 
 and reducing, we have* 
 
 V= Tlog-^ 2.7355 ^^ ]' ' (46) 
 
 Which in the type-gun gives 
 
 F= 1716, or ;^=: 46.48. 
 The largest value of % Y^^ attained with this gun is about 
 35.0 ; showing an efficiency of about 80 per cent. 
 
 Remark. 
 
 For sea coast guns, in which the bulk and weight of the 
 charge is of no special consequence, since the guns are sta- 
 tionary and magazine room is ample ; the waste of the powder 
 and the increased volume of the chamber necessitated by the 
 present use of very large charges may be neglected in favor 
 of the high muzzle energies required. But as the caliber of 
 the gun decreases, and its mobility increases, the necessity for 
 reducing the weight of the charge becomes more important. 
 This is especially true in the loading of magazine small arms, 
 the efficiency of which requires the weight of the ammuni- 
 tion to be reduced to a minimum ; so that the number of cart- 
 ridges that the soldier may carry will be as great as possible. 
 
 * This is independent of the caliber as would be expected from the 
 principle of similitude, x may also be shown to be independent of the 
 caliber, by substituting values of W and w in terms of s, and of « in 
 terms of d. 
 
XIII. — HISTORY OF GUNPOWDER. 
 
 CHAPTER XIII. 
 
 HISTORY OF GUNPOWDER. 
 
 Origin. 
 
 Knowledge of the properties of nitre as a supporter of 
 combustion are attributed to the accidental kindling of the 
 embers of a camp fire by the salt, often, in India, found effer- 
 escent upon the surface of the ground. As sulphur is not 
 essential, its first employment cannot be conjectured. For 
 its binding properties honey was used at an early date. 
 Early Use. 
 
 The use of gunpowder was at first confined to fireworks 
 and rockets. These are mentioned in Chinese records over 
 2000 years old, and seem to be indicated in the account of 
 Alexander's invasion of India at about the same epoch. 
 
 The transition from its use in a paper tube, or bamboo 
 cane, to cannon of different sizes is indicated by the etymology 
 of the latter name. The barrel of any fire arm is in French 
 called canon. 
 Early Cannon. 
 
 The first use of gunpowder as an agent for propelling pro- 
 jectiles is assigned to the Moors at the siege of Baza in Spain, 
 about 1325; twenty-one years before the battle of Crecy. 
 This is about the time that the chemist monk, Berthold 
 Schwartz, of Freiburg, is said to have discovered its pow- 
 ers by the accidental ignition of a ternary mixture, lying in 
 a mortar and covered with a stone. 
 
 Owing to the weakness of the early cannon — which were 
 constructed after the manner of ordinary barrels, sometimes 
 
XIII.— HISTORY OF GTJNPOWDER. 
 
 of iron bars welded together longitudinally and hooped with 
 iron tires, and sometimes even of wood, wrapped with 
 rope — efforts at first were directed to reducing the strength 
 of the new agent. 
 
 Early Powder. 
 
 Therefore, although the best proportions had long been 
 known, it was often composed of equal parts of the three 
 ingredients, and sometimes mixed with saw-dust, resin, sand, 
 or ashes. 
 
 It was often mixed and ground by hand as required, and 
 was used in the form of a fine meal or powder^ from which 
 its name is derived. 
 
 The diminished velocity of inflammation resulting from 
 the use of meal powder favored the end in view; but, since 
 the cartridge was yet unknown, the condition of this powder 
 made it so inconvenient to load the long guns then used 
 that the efficiency of artillery was much impaired. 
 
 Early Breech-loaders. 
 
 To overcome this difficulty in loading, cannon at a very 
 early date were made to load through the breech. But the 
 arts at that time afforded no means of preventing the escape 
 of gas through the joint so formed, and such cannon are 
 comparatively rare. 
 
 It will be seen hereafter that the practical utilization of 
 this principle depended upon the discovery of the self-sealing 
 gas cheeky the best form of which exists in the metallic 
 cartridge case, now used for small arms. 
 
 But for this essential improvement m^any of the systems 
 now In vogue are but repetitions of these ancient forms, not 
 only in principle, but in many details of construction aad 
 operation. 
 
 The reciprocal evolution of the gun and its ammunition 
 is a striking illustration of the law of continuity. 
 
Xllf. — mSTORV OF rttlKfOWDER. 
 
 Men have probably always been equally ingenious in util- 
 izing the accumulated capital of knowledge at their com- 
 mand; but the successful application of even simple princi- 
 ples requires, in many cases, the parallel development of 
 apparently unrelatec arts. 
 
 Intermediate Stage. 
 
 It was not until near the close of the 16th century that 
 cannon, first of copper or its alloys, and then of cast iron, 
 were made strong enough to resist the pressures due to the 
 use of the grained powder, the use of which had hitherto 
 been confined to muskets. This was called corned powder, 
 vide pepper-corn J barley-cornj coming-mill. 
 
 Until about the middle of the present century no great 
 improvement*: occurred in gunpowder or in cannon. The 
 reasons for this were the general assumption that gun- 
 powder was instantaneously converted into gas, and the want 
 of any apparatus for measuring pressures. 
 
 Use of Eprouvette. 
 
 Gunpowder was proved by firing it from the Eprouvette, a 
 small mortar with its axis carefully fixed at an elevation of 
 45*. The quality of the gunpowder was determined by the 
 distance to which an accurately fitting ball of a given weight 
 was thrown by a given weight of powder. Although some 
 difference existed in the size of the grain used in different 
 juns, the proof 7'ange increased as the size of the grain dimin- 
 ished; so that for large guns the size of the grain, as meas- 
 ured by our present standard, was exceedingly small. See 
 Chap. XI. 
 
 Rodman's improvements. 
 
 1. Pressure Gauge. 
 
 The late General Rodman, of the United States Ordnance 
 Department, was the first to investigate the properties of 
 gunpowder in the modern method. 
 
3tm.— tttStOkV Of 6tlNl>6Wt)£R. 
 
 His experiments, conducted with the view of increasing 
 the effectiveness of the system of cannon which bears his 
 name, depended primarily upon his employment of the pres- 
 sure gauge. This was a pyramidal indenting tool, previously 
 used by him to test the relative hardness of cannon metals, 
 and applied in the manner indicated for the crusher gauge. 
 
 Although open to many grave objections of detail, this 
 instrument gave useful relative results and served to draw 
 attention to the very erroneous estimates previously made as 
 to the pressure exerted by gunpowder. When fired in its 
 own volume, this had been variously estimated at from 0.7 
 to 700 tons per square inch. 
 
 2. Powder. 
 
 a. Mammoth. 
 
 Rodman's first step was to recommend the use of large 
 charges of "mammoth " powder, which was of about three 
 times the diameter of the largest powder previously used. 
 
 This gave satisfactory velocities and moderate pressures; 
 and, since its manufacture required less granulation than 
 before, it was cheaper, pound for pound. 
 
 b. Perforated. 
 
 About 1860, he improved upon this idea by suggesting 
 the use of perforated powder, made for small cannon in 
 cylindrical cakes, and for larger cannon in hexagonal 
 prisms which could be built up into cartridges. 
 
 Owing to the great cost and novelty of this powder, and 
 to the intervention of the civil war, the perforated powder 
 was used in this country only for experiments ; but the 
 mammoth powder has until lately been exclusively used for 
 heavy guns. 
 
 DERIVATIVES FROM RODMAN's POWDER. 
 
 Russian Powder. 
 
 The perforated prisms were experimented with in Russia, 
 from 1860-1865, being finally made much smaller than 
 
btllt. — kistORY OF GUNPOWDEfe. 
 
 Rodman's, and pierced with seven small holes. The powder 
 was so made in order to adapt it to the muzzle loading guns 
 then used. See Fig. IB, Chap. IV. This is known as 
 /Russian prismatic powder. 
 English Powders. 
 
 The English objected to this powder, saying that, owing 
 to the number of perforations it contained and to its dimin- 
 ished density, it was liable to break up in the gun. 
 
 About 1875, they returned to General Rodman's original 
 idea, adopting the cubical Pebble powder, the cubes, for 
 the largest gun , being about lYz inches on the edge. 
 United States Powders. 
 
 In the United States, the mammoth powder was im- 
 proved upon by the adoption about 1873 of the Du Pont 
 Hexagonal powder. Fig. 12, Chap. IV. 
 
 This and the Sphero-Hexagonal powder, Fig. 12, have 
 the advantage of great uniformity in the size and shape of 
 the grains and in the form of the interstices between the 
 grains. They are also progressive, owing to the diminished 
 density of the interior of each grain. 
 
 This results from the fact that the effect of compression 
 is not transmitted homogeneously throughout the mass 
 compressed. The density is always greatest next to the 
 moving surface. 
 
 For reasons given in the text. Flat powders of the Z. X. 
 type. Fig. 12, are also occasionally used. 
 Italian Powder. 
 
 The Fossano powder, made in Italy, consists of an 
 agglomeration of dense grains of medium size, set in a 
 mass of powder meal and pressed to a density less than 
 that of the individual grains. Its operation is distinctly 
 progressive. 
 
 The principle is applied to other powders, both molded 
 and of irregular granulation. 
 
Xin. — HISTORY OF GUNroWDER 
 
 MODERN POWDERS. 
 
 In order to obtain the most effective combination of gun 
 and powder, each type of gun now requires a special 
 powder, and some cannon, as mortars, require more than 
 one powder for each mortar. This increases greatly the 
 difficulty of supply. 
 
 The kind of powder best suited to each type of gun is 
 still (in 1888) undergoing experimental investigation. 
 
 The advantage of adapting the size of the grain to the 
 size of the gun, upon which for simplicity so much stress 
 has been laid, is becoming of diminished importance, since 
 the effects due to increased size may be attained in many 
 other ways. 
 
 Owing to the great number of conditions which require 
 to be simultaneously satisfied, including the effect of 
 meteorological conditions prevailing during manufacture, 
 the powder makers find it difficult to meet the increasing 
 exactness of the demands made upon them. This applies 
 even to the duplication of satisfactory samples. 
 
 Present Custom. 
 
 All large guns of the present day use hexagonal prisms 
 like the Russian prismatic, but pierced with a single hole. 
 This is easier to make and its ballistic properties are better. 
 
 It is preferably a concrete powder made by consolidating 
 under pressure small grains of powder previously com- 
 pressed in the ordinary manner. Mealed powder is some- 
 times used instead of that which has been grained. 
 
XIV. HIGH EXPLOSIVES. 
 
 CHAPTER XIV. 
 
 HIGH EXPLOSIVES. 
 Classification. 
 
 Except the chlorate mixtures, the high explosives used in 
 warfare are all organic nitro-substitution compounds, gener- 
 ally of the third order, in which 3 atoms of H are replaced 
 by 3 molecules of NOg. 
 
 The most important are Gun-cotton, Nitro-glycerine, 
 and their derivatives. The derivatives of picric acid are 
 growing in importance, and so, for special purposes, are the 
 mono-, di-, and tri-nitro-benzines and naphthalines. 
 
 Those which in their operation resemble the mercuric 
 fulminate are C2i\\t6. fulminating compounds, and include, be- 
 sides their typical salt, the mixtures in which the chlorates 
 are used dry. 
 
 The demands of civil engineering and the hope of success- 
 fully adapting these explosives to warfare are constantly in- 
 creasing the number of those for which both safety and 
 efficiency are claimed. On the other hand, many, once 
 famous, are obsolete, so that the following discussion will 
 relate only to those of which long experience has demon- 
 strated the essential properties, and to the most distinguished 
 of recent competitors for the selection of the engineer, 
 Danger. 
 
 Although their composition and violence render the hand- 
 ling of many as compared with gunpowder, dangerous; yet, 
 a knowledge of their properties is demanded b- the con- 
 ditions of the time; and, as with gunpowder and steam, this 
 knowledge comes principally by experience. 
 
XIV. — HIGH EXPLOSIVES. 
 
 The disasters reported with such apparent frequency are 
 the price of progress toward safety, and point rather to the 
 enormous consumption of these explosives, often by ignorant 
 and reckless persons, than to any necessary peril when proper 
 precautions are observed. 
 Commercial Importance. 
 
 The scale on which these explosives are employed, prob- 
 ably, as with gunpowder, much greater in time of peace 
 than in war, appears from the size of blasts fired almost daily 
 in the Californian mines during the period of their greatest 
 activity. These blasts often contained 50,000 pounds 
 apiece. 
 
 The great blast at Hell Gate, New York Harbor, in 1885, 
 contained but six times as much. 
 
 The economic value of an explosive depends so much upon 
 the net cost of the work performed that it is interesting to 
 note the following relative scale of prices per pound in 1888. 
 
 Explosive, 
 
 Price. 
 
 Proportion. 
 
 Gunpowder, 
 
 20 eta. 
 
 1.0 
 
 Dynamite, 
 
 50 
 
 2.5 
 
 Nitro-glycerine, 
 
 80 
 
 4.0 
 
 Gun-cotton, 
 
 1.00 
 
 5.0 
 
 COMMON PROPERTIES OF GUN-COTTON, NITRO- 
 GLYCERINE, AND THEIR DERIVATIVES.* 
 
 Sensitiveness. 
 
 When not freed from the acids used in their manufacture, 
 these explosives are prone to spontaneous decomposition 
 and tend to form products of a lower order of substitution. 
 
 While undergoing decomposition, their sensitiveness is in- 
 creased, but their efficiency when exploded is diminished. 
 
 When properly prepared, they are not sensitive to moderate 
 
 * Cadets are advised to review the articles in the Chemistry which 
 treat of nitro-glycerine and gun-cotton. 
 
XIV. — HIGH EXPLOSIVES. 
 
 shock; but friction, the impact of a projectile, or the shock 
 
 of discharge may cause their explosion. 
 
 Firing. 
 
 As a rule, they all explode at about 200°. When ignited 
 by a flame and unconfined, they burn more or less quietly. 
 If confined, their explosion is of a low order unless they are 
 detonated. Their behavior in this respect depends much 
 upon their mass and the resistance of the envelope. See 
 Chap. II. 
 
 They possess the remarkable property of exploding vio- 
 lently when gradually heated to about 200°; whereas, if 
 'dropped upon a red hot iron, they may simply deflagrate. 
 Detonation, 
 
 Owing to the variety of the means by which the mercuric 
 fulminate may be ignited and to the nature of its product, 
 it is almost exclusively employed for detonation, preferably 
 alone and pure, and sometimes with a primer of dry gun- 
 cotton. 
 
 The detonators are commercially known as blasting caps^ 
 exploders^ or fuzes of various degrees of "force " according 
 to the quantity of fulminate they contain. The fulminate 
 lies in a thin copper tube, one end of which is closed, and is 
 ignited either by a quick-match or by the heating of a fine 
 platinum wire by the electric current. The detonator is 
 placed in immediate contact with the charge, but should be 
 so disposed that, if the quick-match is used, the charge shall 
 not be prematurely ignited. 
 
 The mass of the fulminate should bear a certain ratio to 
 the mass and condition of the explosive; this may neutralize 
 the advantages on the score of safety which the sluggishness 
 of the explosive confers. 
 
 Long charges may require to have dispersed through them 
 several detonators in order to maintain the energy of the 
 explosive wave. 
 
XIV. — HIGH EXPLOSIVES. 
 
 Products. 
 
 Except Nitro-glycerine all the substitution compounds 
 yield a large amount of CO, and hence, where potential is 
 sought, require the addition of an oxydizing agent. 
 
 Pressures. 
 
 The ordinary gauge being unsuited to measuring the high 
 pressures of detonation, special devices have been contrived. 
 
 General Abbott of the U. S. Engineers, in a series of 
 experiments (which bear to the high explosives the same 
 relation as do Noble and Abel's experiments to gunpowder), 
 suspended in water his gauges at definite distances from 
 the submerged explosive. 
 
 For experiments in air, charges of given weights are 
 detonated either within or upon similar blocks of lead and 
 the resulting deformations compared. Or the exact charges 
 required to burst similar hollow projectiles may be deter- 
 mined. 
 
 Effects. 
 
 General Abbott's experiments give the following scale by 
 which to measure the force^ Chap. II, of explosives. His 
 results apply only to sub-aqueous mining and indicate the 
 paradoxical fact that Dynamite is more powerful than 
 Nitro-glycerine. 
 
 He found that the pressures registered by a crusher gauge 
 varied as the Yi power of the charge and inversely as the 
 1.4 power of the distance. Or calling / the pressure, %v the 
 weight of the charge, d the distance, and k a constant vary- 
 ing for each explosive and for the nadir angle under 
 water. 
 
 3 // kw\* 
 
 These comparative results are expressed by the following 
 table: 
 
XIV.— HtGtt EXPLOSIVES. 
 
 Nitro-glycerine, 81 0.93 
 
 Gun-cotton, 87 1.00 
 
 Dynamite, 100 1.15 
 
 • Explosive Gelatine, 117 1.35 
 
 a result quite different from that of Chap. II. 
 
 On the other hand, extended practice in mining operations 
 under ground confirms the relative useful values of the high 
 explosives as determined by their potentials and stated in 
 Chap. II. 
 
 Three spheres surround the center of the explosion: 
 
 1. The sphere of pulverization. 
 
 2. The sphere of rupture or dislocation. 
 
 3. The sphere of fracture or fissure. 
 
 The relative dimensions of these spheres vary with the 
 force and potential of the explosive. 
 Tamping. 
 
 The great rapidity of the reaction renders special tamping 
 unnecessary, since the pressure of the atmosphere suffices to 
 produce many of the effects desired. This is the origin of 
 the common idea that such explosives act downward. This 
 property is particularly valuable in military operations where 
 time is precious. 
 
 The best results, however, are found when they are 
 tamped. Even a thin layer of earth or water greatly in- 
 creases their effect. For a similar reason the mass of the 
 charge is best placed between the detonator and the object 
 to be destroyed. 
 
 Example. 
 
 Long iron tubes filled with dynamite have been detonated 
 in air without converting all of their contents. When the 
 tubes were submerged, the entire charge was detonated, 
 Chap. II, page 5. The accidental explosion of charges which 
 have been imperfectly detonated leads frequently to disaster, 
 and so, it may be said, does tamping with an iron bar. 
 
XIV.— tttGli eX!>L6S1VES. 
 
 Physical Condition. 
 
 The greater the density of the explosive the smaller the 
 bore hole required to receive it, and hence the greater its 
 economy. 
 
 Plastic explosives are valuable since they may be used in 
 irregular cavities, and in those opening downward; they may 
 also be rammed after loading so as to increase the value of A . 
 
 The advantages in this respect of the liquid state of nitro- 
 glycerine made it very popular at first; but its tendency to 
 leak in transportation and to filter through crevices in the 
 rock is very objectionable, since in a thin film it is easily 
 exploded by impact and especially so by friction. Cans 
 containing it have been exploded by twisting the cork. The 
 granular form is advantageous on account of the ease with 
 which it may be loaded into bottle shaped cavities, as in 
 hollow projectiles and torpedoes. Rigid prisms form con- 
 venient packages for transportation, but require cavities 
 of a special form to develop the best results. 
 Cold. 
 
 When in a liquid or plastic form, the high explosives have 
 their sensitiveness much impaired by freezing. This occurs 
 at a little above 0°. 
 
 The force and sensitiveness of loose dynamite are not im- 
 paired by its freezing. 
 
 Heat. 
 
 In such cases thawing is dangerous unless very gradually 
 performed, as by the heat of the body, of manure, or of luke- 
 warm water. 
 
 The nitro-glycerine in frozen dynamite of the solid form 
 tends to exude on thawing. 
 
 The sensitiveness of an explosive increases with its 
 temperature. 
 Water. 
 
 Nitro-glycerine and gun-cotton are insoluble. Water tends 
 to displace the nitro-glycerine from dynamite' which has been 
 
XTV. — HIGH EXPLOSIVES. 
 
 compressed; but, strangely, has no such effect upon that 
 which is loosely granular. For this reason sub-aqueous 
 torpedoes are charged with loose dynamite. 
 
 Owing to its greater density the displaced nitro-glycerine 
 settles to the bottom of the vessel containing the dynamite, 
 whence it may exude and lead to the consequences noted 
 above. 
 
 When dynamite or gun-cotton is wet, it ignites with great 
 difficulty but may be detonated by a powerful primer. Any 
 soluble addition is of course removed by water. 
 TTse. 
 
 Except gun-cotton and the picrates, all the high explosives 
 have so far been employed only for mining and demolition, 
 and to a limited extent in pyrotechny. 
 
 Efforts are constantly making to adapt them to the burst- 
 ing charges of hollow projectiles, by affecting either their 
 condition, the construction of the projectile, or the source 
 of energy by which it is thrown. 
 
 Such attempts have not yet (1888) wholly passed beyond 
 the stage of experiment and, though occasionally successful, 
 have yet to endure the test of long continued firing. In 
 many cases it appears that failure comes less from explosion 
 under the initial shock than from the friction due to the 
 rotation of the projectile. If the initial shock or acceleration 
 be diminished, flatness of trajectory is sacrificed or the gun 
 is made inconveniently long; if the rotation of the projectile 
 is abandoned, inaccuracy results. 
 
 The sensitiveness of the explosive tends to cause a prema- 
 ture explosion on impact against armor and its force tends 
 to pulverize the envelope into ineffective fragments. 
 
 The sphere of such explosives appears to be confined to 
 the ordinary sub-aqueous mines or to their employment in 
 aerial torpedoes, exploding under water in the vicinity of a 
 vessel, as in the Zalinski system; or against earth works as 
 
XIV. — HIGH EXPLOSIVES. 
 
 in the new gun-cotton shell now employed in Germany. 
 This projectile has been fired with charges as great as 
 110 lbs. Captain Zalinski has fired a mixed charge of high 
 explosives weighing 500 pounds to a distance of one mile. 
 
 Some of the high explosives, notably the gun-cotton class, 
 have been used for fire arms, principally in fowling pieces, 
 for which the reasons assigned, Chap. XI, page 18, particu- 
 larly adapt them. The absence of smoke is a considerable 
 advantage. They have even been employed by the Austrians 
 for field pieces. 
 
 The uncertainty as to the order of the explosion resulting 
 from accidental variations in the value of A , has caused their 
 use in cannon to be abandoned. For the former purpose it 
 is still unfortunately common. 
 
 GUN COTTON. 
 Forms. 
 
 This occurs in three forms; viz.: 
 
 1. In the flocculent or pulverulent form, made from cotton 
 wool as indicated in the chemistry. 
 
 2. Prepared from the first form by pulping and com- 
 pression to a density a little greater than that of water. 
 
 3. In grains, made by disintegrating the second form 
 above. 
 
 Condition. 
 
 The first form is always used dry and is employed only in 
 pyrotechny. The other two are used either wet or dry, and 
 when wet, are sometimes protected by a water-proof coating 
 to retard evaporation. 
 Firing. 
 
 Dry gun-cotton ignites at a lower temperature than any 
 other of the common explosives. Its combustion may be 
 retarded by compression and the addition of a gum. 
 
 When it contains from 20 to 30 per cent of water, it can- 
 
XIV.— HIGH EXPLOSIVES. 
 
 not be ignited until the water has been evaporated by the 
 flame. One ton of loose wet gun-cotton has been burned 
 with safety in a bon-fire 
 Detonation. 
 
 When wet and compressed, it may be detonated by using 
 a sufficiently large primer of dry gun-cotton. Its incorpo- 
 ration in a dry state with paraffine is said to yield the same 
 results as to safety as when it is wet, without diminishing 
 its sensitiveness to detonation. This avoids the difficulty 
 of preventing evaporation. 
 Reaction. 
 
 This varies with the value of A and with other conditions, 
 but may be represented by the following formula, 
 2QH7(N02)3 05=70H2H-3C02 + 9CO + 6N. 
 
 To increase its potential a nitrate or chlorate is often 
 added, the latter being the more energetic. 
 
 Gun-cotton mixed with one third its weight of a nitrate 
 forms Tonite, an explosive much used in the Californian 
 mines. 
 Advantages. 
 
 Compared with gunpowder, its manufacture is less danger- 
 ous and the apparatus can easily be improvised from the 
 paper-mills. 
 
 Since it forms no dust and can be kept wet, it is safe in 
 transportation and in store. 
 
 In mining, as in fire arms, it yields no solid products, and 
 in sub-marine mining it can be used under water; having 
 even been detonated in a net. 
 Disadvantages. 
 
 Besides those which relate to its sensitiveness and vio- 
 lence, the principal objection to its employment in artillery 
 applies to the absence of smoke which serves to mark the 
 bursting point of a distant shell. 
 
10 XIV. — HIGH EXPLOSIVES. 
 
 MANUFACTURE OF GUN-COTTON, 
 
 rormer Method. 
 
 Gun-cotton, like nitro-glycerine, was discovered about 
 1846. It was first made by dipping cotton wool into mixed 
 sulphuric and nitric acid and washing thoroughly the gun- 
 cotton wool so formed. But it was found to be impossible 
 to remove the free acids from the tortuous capillary tubes 
 of which cotton wool is composed, and the resulting product 
 was dangerous in store. 
 Abel's Method. 
 
 The tim? of manufacture has been much reduced and the 
 quality of the product improved by the following method. 
 
 Instead of using raw cotton, often containing impurities 
 which are liable to cause spontaneous decomposition, cotton 
 waste is employed. This has been previously spun mto 
 yarn for cloth and is therefore mechanically clean. 
 Preliminary Operations. 
 
 Its conversion into gun-cotton follows the method previ- 
 ously taught, the essential points being: — 
 
 1. To prevent the continued action of dilute acids and 
 the consequent formation of di-nitro-cellulose (Collodion 
 cotton), by removing the cotton after its first immersion 
 to a fresh mixture of acids in which it is soaked for several 
 hours. After each immersion the excess of acid is removed 
 by wringing. 
 
 3. To prevent an undue rise in temperature, by making 
 the first immersion in small quantities at a time, and sur- 
 rounding the vessels containing the cotton with running 
 water. 
 
 3. To prevent the access of water to these contents. A 
 drop of sweat may cause the acid cotton to ignite. 
 Final Operations. 
 
 After the final wringing, it is washed by plunging small 
 quantities of the cotton into large quantities of water. 
 
XIV. -HIGH EXPLOSIVES. 11 
 
 The cotton is then reduced to a pulp by the rotary knives 
 of the rag engine used in paper making. These operate 
 under water. 
 
 Being now in short tubes, the washing can be thoroughly 
 performed by means of the paper maker's poacher. This is 
 a vertical water wheel working on one side of an oblong 
 trough through which a longitudinal partition extends 
 nearly from end to end. 
 
 After a protracted washing in the poacher, the free acids 
 still remaining are neutralized by some alkali; this having 
 been washed out, the pulp is, after draining, ready for the 
 hydraulic press. 
 
 After pressing the cylinders they are carefully and slowly 
 dried; or, they may be kept wet as previously stated. 
 
 A similar product has been made from bran or straw, and 
 is known djs, fulmi-bran^ etc. 
 
 NITRO-GLYCERINE. 
 
 Manufacture. 
 
 The preparation of this explosive has been sufficiently 
 described in the course of chemistry The principal points 
 to be observed are: — m 
 
 1. To prevent a rise in temperature by pouring the 
 glycerine slowly into the mixed acids, and to preserve a low 
 temperature by a jacket of running water and by agitating 
 the mixture by a current of air. 
 
 2. To wash the product thoroughly with cold water and 
 finally with an alkaline solution. The addition of cold water 
 precipitates that portion of the nitro-glycerine which remains 
 suspended in the heavy acid liquid. 
 
 Too much importance cannot be attached to the entire removal 
 of free acid. The detection of free acid constitutes one of 
 the most important tests of this product. 
 
12 XIV. — HIGH EXPLOSIVES. 
 
 When first made, it is white and opaque; \t soon assumes 
 an oily appearance which, if well made, it retains. Its density 
 is about 1.6. 
 
 Reaction. 
 
 The explosion of nitro-glycerine gives the following 
 reaction, 
 
 2C3H5(NO,)3 03=6CO,+ 6N4-0 + 5 0H«. 
 
 Following a general law, since its composition furnishes 
 an excess of oxygen, the reaction is sensibly constant and is 
 found to agree with that deduced on theoretical grounds. 
 In this respect it differs from most of the explosives. 
 
 Special Properties. 
 
 As ordinarily used, this is the most powerful of the ex- 
 plosives, excelling both in potential and force. 
 
 It was originally thought to be perfectly safe when frozen; 
 but it has since been found that, when in this condition, it 
 can be exploded by a powerful shock if concentrated upon 
 a mass sufficiently small. 
 
 DERIVATIVES OF NITRO-GLYCERINE. 
 
 Owing to the dangerous properties of liquid nitro- 
 glycerine, it is no longer employed except with an absorbent 
 dase or dope which will prevent its exudation. 
 
 The absorbents are of two kinds: — 
 
 I. Those which are chemically inactive, such as kiesel- 
 guhr (also known as " tripoli " and " electro-silicon "), mica- 
 ceous scales, and, for its alkaline properties, magnesium 
 carbonate. 
 
 II. Those which are chemically active. 
 
 These derivatives have a density of about 1.6. They are 
 usually plastic, which gives them great practical utility. 
 
XIV. — HIGH EXPLOSIVES. 13 
 
 I. MECHANICAL ABSORBENTS. 
 
 Dynamites. Giant Powder. 
 
 Of these absorbents the best is kieselgiihr. This consists 
 of microscopic shells, the cavities in which retain the liquid 
 and protect it from ordinary shock. Kieselgiihr has remark- 
 able properties as an absorbent; it can take up three times 
 its weight of nitro-glycerine without exudation, even when 
 under considerable pressure. 
 
 Different grades of dynamite are made depending upon 
 the proportion of nitro-glycerine which they contain. The 
 highest is called No. 1. 
 
 Owing to the knowledge of the properties of this explosive, 
 gained by the torpedo service and by private industry, it 
 may be called the standard high explosive of the United 
 States. For torpedoes its merits consist in: — 
 
 1. Its force. 
 
 2. Its permanency under the varied conditions and 
 accidents of service. 
 
 3. Its safety and convenience in loading. 
 
 4. The readiness with which it may be procured in the 
 market. 
 
 This was true in 1881. Since then several explosives have 
 been invented which threaten its supremacy, 
 Preservation. 
 
 Although used for special purposes in the granular form, 
 in which it resembles brown sugar, it is generally put up 
 compressed in cylinders wrapped tightly with paraffined 
 paper. These are packed in sawdust in wooden boxes, 
 preferably made light, without metallic parts and coated in- 
 side with a water-proof varnish. 
 
 When received, the boxes should be partly opened to 
 facilitate the discovery of the nitrous fumes that accompany 
 the process of spontaneous decomposition. Their contents 
 
14 XIV. — HIGH EXPLOSIVES. 
 
 should be tested for exudation and acidity, and should be 
 carefully kept from water, 
 
 • II. CHEMICAL ABSORBENTS. 
 
 Properties. 
 
 Absorbents of this class reduce the quantity of nitro- 
 glycerine required to produce a given effect and so cheapen 
 the product. 
 
 Their judicious selection adds greatly to the energy 
 developed by the nitro-glycerine alone, so that the economic 
 value of the explosive may increase more rapidly than does 
 'its percentage of nitro-glycerine. 
 
 For sub-aqueous explosions it appears that with any par- 
 ticular base there is an economic gain in increasing the per- 
 centage of nitro-glycerine up to a certain point, but that 
 beyond that point the advantage ceases. There appears to 
 be a decided advantage in gelatinizing the nitro-glycerine 
 before its absorption. 
 
 See Forcite and Explosive Gelatine, /<?j/. 
 
 Classification. 
 
 The chemical absorbents may be conveniently divided 
 into two general groups, according as they are simply com- 
 bustible, or in themselves high explosives. 
 
 Class I. A combustible dope. 
 
 When finely ground cellulose is treated with super-heated 
 steam, it is converted into a jelly capable of absorbing 19 
 times its weight of nitro-glycerine. With or without the 
 addition of nitre, it forms Foi^cite^ a most powerful explosive. 
 
 Gunpowder, preferably made after Col. Wiener's method, 
 Chap. IV, may be coated with nitro-glycerine, the detonation 
 of which detonates powder, Chap. XI, This foruas the 
 Jtidson powder. 
 
Class II, A high explosive as a dope. 
 
 The most famous is known as Explosive Gelatine. This 
 consists of about 93 per cent of nitro-glycerine with 7 per 
 cent of collodion gun-cotton (di-nitro-cellulose). The 
 addition of 3 or 4 per cent of camphor greatly diminishes 
 its sensitiveness and adapts it particularly for warfare. 
 
 It is generally a transparent jelly, but often becomes hard 
 and opaque. The fulmi-bran, page 11, may replace the 
 collodion cotton. 
 
 Although found by General Abbott to be stronger than 
 nitro-glycerine, it is much safer, particularly against shock. 
 It has been found to burn freely without explosion, even 
 when confined, and to resist perfectly the action of water. 
 
 It requires an initial primer for its detonation and the 
 weight of the primer required increases as its sensitiveness 
 diminishes. 
 
 When the collodion cotton is not thoroughly purified, this 
 explosive tends to decompose spontaneously. Otherwise it 
 is quite stable. 
 
 New smokeless powder. 
 
 By reversing the proportions of nitro-glycerine, and col- 
 lodion used in explosive gelatine, and retaining the camphor, 
 the compound becomes plastic when heated. It may then 
 be pressed into sheets or drawn into wires or rods which, on 
 cooling, become horn-like, like the celluloid of commerce. 
 
 The reduction of w and the increase of \i are reported to 
 give in the 6 in. Rifle a value oi %•=. 100 -f-. Its tactical 
 advantages adapt it particularly to rapid firing arms of small 
 caliber. The special difficulties to be overcome refer to the 
 volatiUty of the camphor and to the erosion of the bore re- 
 sulting from the heat of the explosion. See Chap. IX, Notes. 
 
 NITRO-BENZINE OR -BENZOLE. 
 
 The preparation of this resembles that of nitro-glycerine, 
 
16 XIV. HIGH EXPLOSIVES. 
 
 the mono- (liquid), and di-, and tri-nitro benzines, (crystal- 
 line) being formed. (Bloxam, Art. 325.) 
 
 These substitution products are in themselves inexplosive, 
 and show by their composition, C^ H^(N02)g_j, ^^^ necessity 
 for the addition of an oxydizing agent. 
 
 Rack-a-Rock is made at the time of its employment by 
 saturating K CIO3 with crude mono-nitro-benzine, or even 
 with the "dead oil" from the gas works which has been 
 diluted with CSg containing a small proportion of sulphur. 
 By exposure to the air the CSg evaporates, leaving the finely 
 divided sulphur on the salt but protected by the lubricating 
 property of the oil or nitro-benzine against explosion by 
 friction. 
 
 When the dope is finely ground and the charge exploded 
 by a powerful primer it is found to be nearly as powerful 
 as dynamite No. 1. 
 
 This is the only chlorate mixture which has been found 
 safe in practice. 
 
 Helhofite^ as used in Germany for armor piercing pro- 
 jectiles, is another of the Sprengel Safety Mixtures pre- 
 pared as wanted by dissolving di-nitro-benzine in nitric acid. 
 
 Bellite (La.tin: Bel/um — War), is a recent Swedish explosive 
 made of about -J tri-nitro-benzine and | ammpnium nitrate, 
 incorporated together. 
 
 This is distinguished by its great safety under all con- 
 ditions and by its greater potential as compared with 
 dynamite, 
 
 Only dampness affects it. It is almost incombustible, 
 smouldering only by the continued application of flame. 
 It is so insensitive to shock that the detonation of itself upon 
 a box filled with the explosive, or the explosion of gunpowder 
 in its midst fails to explode it. A wad of it has been fired 
 from a fowling piece against a target without injury to either. 
 It gives no injurious gases, nor flame, which properties. 
 
XIV. — HIGH EXPLOSIVES. . 17 
 
 together with its high potential, particularly adapt it for the 
 coal miner. It is also cheap and indifferent to variations in 
 temperature. 
 
 Tamping is necessary to develop its full effect, even when 
 detonated ; but when tamped and detonated, it is about 33 
 per cent stronger than dynamite. 
 
 The crystaline form of the two ingredients of Bellite 
 would appear to insure its stability in store and to make of 
 it one of the best high explosives where potential is required, 
 as in torpedo shells. For sub-aqueous mining, dynamite is 
 probably better suited. 
 
 PICRIC ACID (TRI-NITRO-PHENOL). 
 
 This is made by the action of nitric acid on carbolic acid 
 (phenol). It occurs in slightly soluble plates of a bright 
 yellow and is much used in dyeing. Unconfined, it will not 
 explode by heat, but may be detonated. 
 
 When mixed with gun cotton dissolved in ether, it is said 
 to form the new French explosive, Melinite. 
 
 Emmensite is a recent American explosive, prepared from 
 crystallized Emmens acid and a nitrate. The acid results 
 from the solution of picric in nitric acid. 
 
 The claims made for this explosive resemble those noted 
 under the description of Bellite. It is (1891) under trial in 
 the United States. 
 
 THE PICRATES. 
 
 The potassium and ammonium salts are the only ones 
 employed. 
 
 The former with the addition of nitre and charcoal forms 
 Designolle's powder. This was found too dangerous for 
 use, as it tends to detonate on ignition. 
 
 The ammonium salt is less sensitive to shock and burns 
 in the air like resin. With the addition of a nearly equal 
 
18 XIV. HIGH EXPLOSIVES. 
 
 part of nitre and prepared like ordinary gunpowder, it forms 
 the powder of Briigere. In small arms, a charge less than 
 one half the charge of ordinary gunpowder suffices to pro- 
 duce the same effects. This is of importance since it enables 
 the size and weight of the cartridge used in magazine rifles 
 to be greatly reduced. 
 
 The powder yields no smoke or fouhng but is hygroscopic. 
 
 It is believed that the new powder used in the French 
 Lebel rifle is a variety of Brugere powder. 
 
 THE FULMINATES. 
 
 The mercuric salt is the only one of practical value. Its 
 efficiency depends rather upon its force and the nature of 
 its product than upon the heat evolved by its decomposition. 
 
 This follows from the reaction, 
 
 C2HgN2 0a=:2CO + Hg + 2N. 
 
 Its force is said to be nearly 10 times that of gunpowder. 
 
 When dry it is easily detonated by shock, friction, a tem- 
 perature of about 200°, or by the strong acids. 
 
 Certhelot finds that even so stable a gas as nitric oxide 
 is dissociated by the detonation of mercuric fulminate. 
 While for detonation it is preferably used pure, for igniting 
 the charges of fire arms it is mixed with an oxydizing agent 
 and often a combustible, in order to increase the length of 
 the flame. Powdered glass 's also added v/hen the salt is 
 expiod'^d by percussion. 
 
 Its safety in manufacture depends upon its absolute in- 
 explosiveness when wet. If placed upon a metallic surface, 
 it tends to decompose; hence, percussion caps are varnished 
 before they are primed. 
 
 Under no circumstances should the fulminate be carried or 
 stored near any of the high explosives. 
 
XIV. HIGH EXPLOSIVES. 19 
 
 CHLORATE MIXTURES. 
 
 Since their discovery, a century ago, frequent efforts have 
 been made to utilize the chlorate mixtures in mining and as 
 a substitute for gunpowder. Their extreme sensitiveness 
 to friction has almost uniformly caused their employment 
 for such purposes to result in disaster. 
 
 Mixed with Sbg S3, the potassium chlorate forms the friction 
 composition used in cannon primers. It is also employed in 
 pyrotechny to compensate for the cooling effect of sub- 
 stances employed to give color and brilliancy to the flame. 
 
 GENERAL REMARKS ON THE EMPLOYMENT OF 
 THE HIGH EXPLOSIVES. 
 
 In Guns. 
 
 Their employment has always failed, except for small arms 
 and as noted page 8. 
 
 For Bursting Charges of Hollow Projectiles.* 
 
 Explosive gelatine has been occasionally fired without 
 premature explosion, by the use of diaphragms within the 
 shell. See also gun-cotton, and the experiments with the 
 Zalinslii gun before noted. 
 
 For Demolition of "Walls, etc. 
 
 Unless the wall is very strong, the best results in breach- 
 ing appear to follow the detonation of the explosive at the 
 base of the wall and at a few inches distant. This distrib- 
 utes the effect, and racks and fissures the wall so as to facili- 
 tate its destruction by hand. 
 
 Exploded in immediate contact, a smaller hole is said to 
 be made and the energy to be expended in giving motion 
 
 * The premature explosion of such bursting charges by the shock of 
 discharge is often attributed to the sensitiveness of the fulminate neces- 
 sarily used in the detonating fuze. 
 
20 XIV. — HIGH EXPLOSIVES. 
 
 to but few fragments. About 10 lbs. of dynamite will open 
 a practicable breach in a two foot stone wall. Tamping 
 would reduce the size of the charge required. 
 Houses, Palisades, etc. 
 
 About 5 lbs. of dynamite will wreck a small stone dwelling 
 if exploded near its center, since it tends to overthrow all 
 the walls instead of blowing out through the nearest one. 
 The same quantity suffices for a linear yard of ordinary 
 palisading. A pound of dynamite will shatter a 12 inch 
 bridge timber.* 
 Disabling Cannon. 
 
 When time permits, bring the gun as nearly vertical as 
 possible; fill it with water, plug it, and explode simultane- 
 ously two one pound charges of gun-cotton, one at the 
 bottom of the bore and one in the chase. When time is 
 scant, insert a shot within the bore, and place on top of the 
 chase, between the shot and the muzzle, two pounds of gun- 
 cotton, laying over it a filled sand bag or a sod. Such charges 
 are said in the English Manual to suffice for the lighter 
 natures of sea coast guns. 
 
 It is found to be more advantageous to attack the cannon 
 themselves, than to waste time and explosive material on 
 their carriao:es. 
 
 ♦These directions are intended to apply only to hasty operations. 
 When time permits, the best results will follow from placing the charge 
 under or within the structure to be demolishedo The quantities are 
 approximate. 
 
XV. — M£T ALLURG Y. 
 
 CHAPTER XV. 
 METALLURGY. 
 
 I. TESTING MACHINES. 
 
 Necessity. 
 
 The physical properties of a metal may sometimes be in- 
 ferred from a knowledge of its chemical composition, but so 
 many other causes may contribute to modify these properties 
 that chemical analysis should be depended on, rather to indi- 
 cate the existence of certain limiting or possible conditions 
 than to declare the extent to which these conditions have 
 been approached. Thus, what a metal is becomes subordi- 
 nate to what it can do ; and its proof is more conclusive than 
 even its chemical inspection. 
 
 Requisites. 
 
 A complete testing machine should include means for de- 
 termining the varying strains under tensile, crushing, trans- 
 verse, torsional, and shearing stresses. But for simplicity, 
 and on account of the comparative ease with which all stresses 
 can be referred to that first named, such machines are gen- 
 erally of the tensile type. 
 
 Comparisons. 
 
 For establishing comparisons the stresses are usually meas- 
 ured per unit of minimum area of cross section, and the 
 strains per unit of length between established points on the 
 specimen. But if the form and dimensions of the specimens 
 are constant, absolute measures may be compared. In the 
 following discussion stresses and strains will, unless otherwise 
 stated, be taken per unit of section and of length. 
 
XV. — metallurCV. 
 
 In the United States stresses are given in pounds per square 
 inch; in England in tons of 2240 lbs. per square inch; in 
 France in kilogrammes per square centimetre; in Russia and 
 Germany in atmospheres. 
 
 Form of Specimen. 
 
 Since the deductions from proof are conclusive only as to 
 the actual piece tested and are inferential as to all others, 
 the above precautions for the comparison of properties are 
 not wholly sufficient. The general • rule in experimental 
 comparisons, of dealing with but one variable at a time, 
 should be followed by subjecting specimens as nearly as 
 possible in size and shape lik>e those to be actually employed 
 to the same kind of stress that they will be called on to sustain. 
 
 But the capacity of the machine rarely permits this, and, 
 as its strength limits the maximum cross section, the length 
 of the specimen in units of the corresponding diameter should 
 be approximately proportional to that of the finished piece. 
 The size of the machine and the cost of preparing specimens 
 limit this; so that the length of the specimen is generally 
 about 4, 6, or 8 diameters, with a tendency to increase. 
 
 The specimen is held so that its axis coincides with the 
 action line of the force; otherwise, it will rupture in detail, 
 or tear across. This condition is fulfilled by making the 
 specimens truly cylindrical with enlarged concentric heads, 
 figure 3, by which they may be held in the machine. 
 
 Form of Record. 
 
 This states the strains due to certain stresses. They are 
 functions of each other, and the relation may be expressed 
 
 e —f{w), 
 
 in which e represents the strain, or the change of form pro- 
 duced by applying the stress w. The stress is taken as the 
 independent variable since it can be more readily controlled 
 
XV. — METALLURGY. 
 
 than the strain. Inasmuch as conditions vary too much, and 
 are not yet sufficiently understood to enable the law of this 
 function to be analytically expressed, that which governs any 
 particular case may be best determined empirically: 
 
 1st. By forming successive orders of difference in the 
 observed value of the function for equal increments of the 
 variable w. 
 
 2d. By plotting a line constructed from these co-ordinate 
 values. Such a line is called a strain diagram. 
 
 3d. By constructing a strain diagram automatically during 
 the progress of the test. 
 
 The order of preference is as follows: 
 
 The first method when great accuracy is required and 
 when a micrometer can be used. 
 
 The second and third when general comparisons are to be 
 made. 
 
 The second to the third when the expense of the registering 
 apparatus is objectionable. 
 
 In general, rectilinear strains can be measured more accu- 
 rately than they can be registered by any mechanical apparatus. 
 
 ELASTICITY. 
 
 Elastic Limits 
 
 In operating the machine the stress is very slowly and stead- 
 ily applied, either directly by hydraulic pressure, or indirectly 
 by a screw acting in combination with levers. The stress is 
 relieved at intervals and the specimen permitted to recoil. 
 
 The difference between the strain e and the recoil r is the 
 set s, ov e = r -\- s. The set may diminish in time and be- 
 come the permanent set, but the first temporary set is that 
 generally recorded. Sets probably occur under all stresses, 
 but may be too small for measu^-ement. This may be illus- 
 trated by the curves, figure 1, which are very much exagger- 
 ated. 
 
 Let 00\ 00" represent certain stresses resulting in strains 
 O'p' , 0"p'\ etc. Each of these strains is by definition com- 
 
XV. — METALLURGY. 
 
 posed of the recoil r — r'p' and the set s = O'r' , etc. 
 Starting from 0, as the stresses increase the recoils and sets 
 both increase, but the sets less rapidly than the recoils. 
 
 After a certain stress, Z, the line of sets becomes nearly 
 parallel* to that of strains, so that for a given increment of 
 stress the increments of strain and set are nearly equal. The 
 stress corresponding to L is the superior limit of the stresses 
 for which the sets increase less rapidly than the recoils, and 
 the inferior limit of those for which the sets increase more 
 rapidly than the recoils. This stress is called the Elastic 
 Limit. 
 
 Since below the elastic limit the sets are relatively small, 
 and above it the sets are relatively large, when compared 
 with the recoils, it may be defined as the limit of the stresses 
 within which sets may be neglected and beyond which recoils may 
 he neglected ; or the limit separating the consideration of the 
 elasticity of the metal from that of its ductility. 
 
 It may be determined — 
 
 I. By finding the stress corresponding to the first significant 
 term of the second order of difi"erences of strains or sets. 
 
 II. By inspection of a diagram such as represented in fig- 
 ure 13. 
 
 Coefficient of Elasticity. 
 
 If the strains below the elastic limit be considered directly 
 proportional to the stresses, this portion of the line will be 
 straight, and the tangent of the angle included between it and 
 the axis of E will be proportional to the reciprocal of the 
 rate at which the specimen submits to (i.e., directly to the 
 rate at which it resists) the stress. This is called the coeffi- 
 cient of elasticity, or 
 
 ^ _ r^ _ ^ ^ /Wheeler, \ 
 ^ ~ Z ^ 7 ' V Eq. 1. y 
 
 * As a rule, the recoils increase gradually throughout. 
 
XV.— -METALLURGY. 
 
 Elastic Work, etc. 
 
 The area bounded by the diagram, the axis of E, and a 
 line drawn through any point of this axis parallel to the axis 
 of PFis evidently proportional to the work done by the corre- 
 sponding stress. 
 
 For a given stress O O'", the area, O e r"', is proportional 
 to the work of permanent deformation corresponding to the 
 stress O O'". Similarly the difference between the areas 
 0^'/'"and O^r'" is proportional to the work of restitution, 
 or the elastic work, following the same stress. The term 
 Elastic Work, as a measure of this elastic property, also 
 known as toughness, is properly applied only to the area 
 under the diagram at the elastic limit. 
 
 The total area under the diagram up to the point of rup- 
 ture is proportional to the potential work of deformation. While 
 for mechanical units, such as posts, beams, levers, chains, this 
 property is valuable; in the more complex structures required 
 by the principle of the independence of function, such as 
 wheels, trusses, and built-up guns, the elastic work, which 
 comprises in its measure both the elastic limit and the coeffi- 
 cient of elasticity, is much more important. 
 
 In such structures the permanent change of form of one of 
 the units may derange the rest; and generally the elastic 
 work may be counted on repeatedly, while the work of per- 
 manent deformation can be utilized but once. 
 
 FORMS OF TESTING MACHINES. 
 
 Tensile. 
 
 This is the form most generally used and upon the indica- 
 tions of which modern gun construction is based. 
 
 The sketch, figure 2, shows a simple apparatus extempo- 
 rized for testing the sheet metal from which small-arm car- 
 tridges are made. The strains were taken from the punch- 
 maVks a,b, and plotted. 
 
 For testing the metal of which cannon are made, a form of 
 
XV — METALLURGY. 
 
 tensile machine recently devised in England consists of a 
 hard steel cone, which by a blow from a falling weight is 
 driven through a ring cut concentrically from one of the 
 short cylinders composing the gun. 
 
 Transverse. 
 
 The simplest of all is for transverse stress. The specimen 
 is placed on rollers kept at a constant distance apart. One 
 objection to transverse machines is the difficulty of separating 
 the tensile from compressive strain. 
 
 A valuable modification of this form of machine is that 
 which tests the capacity of the metal to endure extreme bend- 
 ing, even to the extent of working its ends back and forth as 
 long as the tenacity of the specimen permits. The bending 
 angle thus determined is one of the readiest and best tests for 
 ductile material. 
 
 Torsional. 
 
 Although a torsional strain is even more complex than the 
 transverse, yet, owing to the ease with which the power 
 of the lever may be increased; to the simplicity, compact- 
 ness, cheapness and rapidity of operation of machines of this 
 class; and to the ease with which the relative rotary motion of 
 the parts may be made to record the circumstances of the 
 test, this method is very valuable where great accuracy is not 
 required, nor variation in the form of the specimens expected. 
 
 For the machine used in this department of instruction, the 
 specimens are of the standard size shown in figure 3. This 
 requires direct comparison of results. 
 
 Thurston's autographic torsional testing machine, fig- 
 ures 4, 5^ G, 1, 8. 
 
 Description. 
 
 Two similar wrenches with rectangular jaws, facing each 
 other, are carried by the A shaped frames shown in figure 4, 
 and revolve independently about axes which are in the same 
 
XV. — METALLURGY. 
 
 Straight line. The wrenches are not connected except by the 
 interposition of the specimen, which is supported axially by 
 the conical points shown, and kept by folding wedges from 
 revolving in the jaws. The' arm B of one wrench carries a 
 weight W at its lower end. The other wrench is revolved by 
 a worm gear, P. 
 
 To the frame A is secured a guide curve G, of such form 
 that its ordinates are proportional to the successive torsional 
 moments exerted by B during its revolution. 
 
 The pencil-holder/^ is carried on the arm B, to which it 
 is pivoted at a and b so as to oscillate in a plane perpendicu- 
 lar to that in which B rotates. A spring, sp^ keeps the pen- 
 cil-holder in contact with the guide curve. 
 
 Operation. 
 
 As the worm gear revolves it tends to revolved and to raise 
 PTby means of the specimen -S". 
 
 As B revolves, the roller r rides on the edge of G so that 
 the pencil is displaced laterally in a plane perpendicular to 
 that of its rotation; the object being to establish as follows a 
 system of rectangular co-ordinate axes of stresses and strains, 
 to which the position of the pencil may be referred: 
 
 I. To make the lateral displacement of the pencil propor- 
 tional to the stress, W. Since PTis proportional to the mo- 
 ment of ^, which, since the weight of B is constant, is pro- 
 portional to the sine of the vertical angle 0, figure 7, the 
 edge of G is so formed that when B is rotated, the pencil 
 will trace upon the cylinder D a curve the equation of which 
 when developed on a plane surface is _y = ^ sin 0. In 
 this equation J/ is the variable ordinate of the curve measured 
 along that rectilinear element of D upon which the pencil 
 rests when the inclination of ^ = 0, and <2 is a coefficient 
 depending upon the maximum value of _y permitted by the 
 construction of the machine. 
 
 II. To make the peripheral displacement of the pencil 
 
XV. — METALLURGY. 
 
 proportional to the strain, E. Calling ;t: the developed path of 
 the pencil along a circular element of the cylinder, we have 
 
 X '. (p>^ \\%TCr \ 360°, or0 =-— jvand .'.y=^ as'ml- .x\ 
 
 ^ ^ %7tr -^ \Z7tr j 
 
 The circumference of the drum is 36 inches and its length 
 is 5 inches; therefore, taking x in inches. 
 
 jj^ = 5 sin (10 . x). 
 
 Such a curve having been constructed upon paper may be 
 wrapped around D, and the edge of G be adjusted so as to 
 make the point of the pencil follow the curve as B is revolved, 
 D being at rest. 
 
 The strain is evidently proportional to the rotation of D 
 relatively to that of the pencil ; while the stress is proportional 
 to the angular displacement of the pencil. This will be un- 
 derstood by imagining lines traced by specimens which are 
 either perfectly extensible or perfectly inextensible. Such 
 lines are limits for all natural specimens which will cause in- 
 termediate lines to be traced that will express the relation 
 e ^/{w). 
 
 Form of Record. 
 
 The record is made on a piece of cross-section paper ruled 
 in inches and tenths w^rapped tightly around the cylindrical 
 drum D. 
 
 The weight W is so taken that the maximum moment 
 = 500 lbs. ; therefore, since the ruling is 5 inches wide, one 
 division of the paper measured across its width represents a 
 moment of 10 lbs., and, since 2 tt r = 36 inches, one division 
 along the length of the paper = 1° of strain. 
 
 In raising the arm by the specimen, the moment of W is 
 in equilibrio with the torsional stress plus the frictional mo- 
 ment of the journal /; this last is constant and is allowed 
 for in standardizing the machine. 
 
XV. — M£tALLURGY. 
 
 INTERPRETATION- OF THE RECORD. 
 
 For torsional test this is facilitated by considerinij the spe- 
 cimen as consisting of parallel fibres, at first rectilinear, and 
 elongating under stress in a helical form. The general form 
 of strain diagrams, whether made by torsional or tensile test, 
 is so similar, that although the following discussion partic- 
 ularly refers to the results of the torsional test, its application 
 may be considered as general.* 
 
 General Case. 
 
 The combined effect of stress and strain is seen in the 
 typical diagrams, figure 9. 
 
 In curve / the elastic limit is plainly shown at a. The 
 convexity of the first portion is probably due to the prelimi- 
 nary strain of the exterior fibres occurring in soft materials. 
 
 The line then becomes sensibly straight, its inclination 
 
 determining the coefficient of elasticity, -— , or the rigidity 
 
 of the specimen. Beyond the elastic limit it becomes wavy, 
 indicating deficient homogeneity as to structure ; the fibres 
 are then supposed to slip. Having adjusted themselves they 
 
 * The following relation between torsional and tensile stress has been 
 approximately determined by experiment. Let T = tensile stress in 
 lbs. per square inch; Ti = torsional stress in lbs. ; 9 = angle of torsion 
 in degrees. Then, for steel and probably for other ductile metals, 
 
 T= 7\ (300 -^\. 
 For cast iron, 
 
 r=n(soo-^)^|. 
 
 The extension of an external fibre and the reduction in area of cross 
 section corresponding to torsional strain are given in tables furnished 
 with the machine. For ultimate extensions the value of correspond- 
 ing to the maximum and not to the ultimate ordinate is taken. 
 
10 5tV. — METALLURGY. 
 
 work together, as shown by the subsequent regularity of the 
 Hne. 
 
 At some point b the stress is relaxed, and the pencil falls to 
 some point c ; when the stress is re-applied, the pencil rises in 
 the line cb and continues nearly parallel to the straight por- 
 tion of the line Oa until it reaches its former height db. 
 The ordinates then slowly increase until, by the successive 
 rupture of the concentric fibrous layers, the curve terminates 
 at/ 
 
 Note the total work Oabefg 0\ the elastic work OaL; 
 and the recoil dc and set Oc for the stress db. The parallel- 
 ism oi be to O'a shows the practical constancy of the co-- 
 efficient of elasticity under varying stresses provided the total 
 elongation be diminished by the set. By some, this coefficient 
 is considered the most permanent physical characteristic of 
 steel, in various forms of which it has been found to vary less 
 than 8 per cent, in specimens whose elastic limits varied 200 
 per cent. 
 
 The point ^ is a new elastic limit, and the entire line may 
 be termed a locus of elastic limits. Of these the point a is 
 called the primitive elastic limit, and the other points various 
 special elastic limits. Notice that as these successively rise, 
 the potential work diminishes. The special elasticity thus 
 produced by stress, as distinguished from the primitive elas- 
 ticity of the specimen, is treated of in gun construction. 
 
 Some metals give a curve like //, in which it is difficult by 
 either of the methods given, page 3, to determine the elastic 
 limit. In such cases it is generally taken as the stress corre- 
 sponding to the point of tangency of a line inclined at 45°. 
 
 Graphical Representation of Special Physical Properties. 
 
 Considering the diagram, figure 9, to represent that of a 
 tensile instead of a torsional 'test, the principal properties of 
 the specimen are graphically expressed as follows: 
 
 The Tenacity, or the capacity to resist rupture by extension, 
 is measured by the maximum ordinate at e. The correspond- 
 
XV. — METALLURGY. 11 
 
 ing Stress may be greater than that at which fracture finally 
 occurs. In such a case the form of the portion of the dia- 
 gram, ef, indicates probably the progressive rupture of the 
 final layers. 
 
 The Elasticity, or the property of resisting permanent exten- 
 sion or compression, as we have seen may be measured either 
 by an absolute quantity, the elastic limit, or by a rate. When 
 this rate is practically uniform, as in steel, page lo, the elas- 
 tic limit alone may serve to measure the elasticity. 
 
 The Ductility, or the property of submitting to permanent ex- 
 tension, may also be measured by an absolute quantity, O g, 
 or more exactly. Oh, figure 9; or by a rate. This rate- is 
 measured by the cotangent of the angle made by the tangent 
 to the diagram at any point beyond the elastic limit and the 
 axis of strains. This measure, although not generally 
 adopted, io important since it illustrates the phenomenon 
 known as the flow of metals under stress. As seen in the 
 following examples, this rate may vary not only in degree 
 but also in its sign. 
 
 Ductility, though useful in such arts as the drawing of 
 wire and of metallic cups like cartridge cases, is now regarded 
 only a secondary property of cannon metals. Cannon are so 
 proportioned that the elastic limit is the superior limit of the 
 applied forces, but the ductility of the metal is thought to 
 give an additional safeguard against destructive explosion. 
 But safety then depends rather upon the potential work of de- 
 formation of which the metal is capable than upon either its 
 tenacity or its ductility alone. 
 
 Particular Cases. 1. Woods. 
 
 To illustrate these remarks by reference to materials the 
 physical properties of which are more generally known than 
 those of the useful metals, the torsional diagrams of the prin- 
 cipal woods used in ordnance construction are represented 
 in figures 10, 11, 12. 
 
 The woods are arranged from right to left in the order of 
 
12 XV.- METALLURGY. 
 
 their coefficients of elasticity. This brings them approxi- 
 mately in the order of hardness, or stiffness, black walnut 
 leading. 
 
 These qualities fit this wood to resist the abrasion to which 
 gun-stocks are subject, and to give to the easily bent gun- 
 barrel its necessary support. 
 
 The elastic limits of cypress and black walnut are seen to 
 be equal, but the cypress is much the tougher of the two. It 
 appears to be about equal to a poor quality of oak, for which 
 wood, in the construction of gun-carriages, it was formerly 
 used in localities where oak could not be procured. 
 
 The forms of the diagrams after passing the elastic limit 
 •are very characteristic. In some cases, as in ash and white 
 pine, the line continues for some distance parallel to the axis 
 of strains. This would indicate the use of these woods for 
 pieces which being long and slender are apt to be bent. 
 When lightness is an object, as in the former case for wagon 
 poles, sponge and rammer staves, agricultural-tool handles, 
 and in the latter case for building purposes, particularly of 
 railway carriages, the low density of these woods makes them 
 highly esteemed. 
 
 The sudden dip of dog-wood, oak, and hickory occurs in 
 most hard woods. It is supposed to arise from the lateral 
 slipping of the fibres, the cementing substance having given 
 way. When this is brittle, as in the resinous yellow pine, a 
 very sharp depression is sometimes seen. 
 
 In some cases, as in dog-wood, hickory, and notably in 
 elm, the line rises again, sometimes exceeding the elastic 
 limit. The rise is supposed to be due to the retwisting of the 
 fibres, separated at the elastic limit, into a consistent whole. 
 On the other hand, the step-like decline of some of the dia- 
 grams indicates the brittleness of the corresponding woods. 
 
 The surprising qualities of dog-wood show that the small 
 size of this tree is the principal bar to its utility. 
 
 The importance of testing machines is very imperfectly ap- 
 preciated among practical manufacturers. This appears from 
 
XV. — METALLURGY. 13 
 
 one of the oak diagrams which was made by a piece taken 
 from a new gun-carriage the stock of which was broken in 
 two by firing. 
 
 2. Metals. 
 
 The diagrams in figure 13 will be referred to hereafter in 
 discussing the metals represented upon them. To avoid 
 confusion, curves of similar metals are arranged in groups, a 
 new origin for each group being taken along the axis of 
 strains. 
 
 II. ORDNANCE METALS. 
 
 The principal metals used in Ordnance manufactures are. 
 
 Ferreous. - 
 
 Steel I ^'^^' 
 
 ' ( low. Cupreous or 
 
 Wrought Iron, Kalchoids. 
 
 . Cast Iron. 
 
 r Brasses, 
 Bronzes 
 and other alloys 
 of Cu, Sn, Zii. 
 
 Nomenclature. 
 
 For clearness of definition by scientific men, the forgeable 
 ferreous metals are proposed to be classified according to 
 their mode of manufacture and according to their capacity to 
 harden, and are designated as follows: 
 
 1st. Those made from a pasty mass, by the prefix. Weld. 
 
 2d. Those made by fusion, by the prefix, Ingot. 
 
 3d. Those which will harden and temper by the usual 
 treatment of steel, by the suffix, Steel. 
 
 4th. Those which will not sensibly harden, by the suffix, 
 Iron. 
 
 5th. The only unforgeable ferreous cannon metal is cast 
 iron, known in the crude state as pig-iron and after remelt- 
 ing, as castings. 
 
 This classification affords the following scheme; 
 
14 
 
 XV.— METALLURGY. 
 
 
 
 
 
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 cl 
 
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 un-metal = 
 •ass = 
 
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XV. — METALLURGY. 15 
 
 Relative Importance. 
 
 Owing to their peculiar adaptability to the demands of 
 construction, the ferreous ingot metals are gradually super- 
 seding all others, and the time when they will be altogether 
 employed except for subordinate purposes is delayed only by 
 our imperfect knowledge of their properties. These metals, 
 under the common name of steel, already cover in their 
 application the wide range between castings for the frames of 
 iron-clads, weighing many tons, figure 14, and horseshoe 
 nails, the successful making of which was formerly considered 
 the most severe test of the quality of wrought iron. The 
 ages of stone, bronze, cast and wrought iron have been suc- 
 ceeded by the age of steel. 
 
 On this account the following discussion will relate princi- 
 pally to steel. As a cannon metal it has only recently come 
 into favor, having been considered brittle and untrustworthy. 
 It is largely due to the patient genius of Krupp and Whit- 
 worth that this prejudice has been overcome. 
 
 As an example of the quality of modern gun steel may be 
 mentioned the fact that it was found impossible to break a 
 gun hoop under a drop giving a blow of nearly 100 ft.-tons, 
 the arrangement being represented in figure 15. Sixty or 
 seventy blows shortened the vertical diameter only half an 
 inch. 
 
 III. PROPERTIES. 
 
 The useful properties of metals have regard to their 
 
 1, Homogeneity, 
 
 I. Constitution. 
 {Jo be.) 
 
 I. Chemical as to i o' n 
 
 (2, Composition. 
 
 ( 1, Homogeneity, 
 
 II. Physical as to -J 2, Structure, 
 
 ( 3, Strain. 
 
16 XV. — METALLURGY. 
 
 II. Capacity for 
 resisting. 
 {To do.) 
 
 I. Tensile j 1, Tenacity, 
 
 Stress, or ( 2, Ductility. 
 
 II. Compressive j 1, Incompressibility, 
 
 Stress, I 2, Hardness. 
 
 III. Either j 1, Elasticity, 
 
 Stress, or ( 2, Homogeneity. 
 
 III. Facility for being 
 worked. 
 {To suffer.) 
 
 C 1, Fusibility, 
 
 Hot, or \ 2, Weldability. 
 
 ( 3, Malleability (also cold). 
 
 Cold, or 1, Annealability. 
 
 /. CONSTITUTION OF STEEL. 
 Metals should be homogeneous as to composition and struc- 
 ture so as to be homogeneous as to strain. Those which 
 have been fused are the most homogeneous ; but even they 
 may be imperfect, both chemically and physically, as follows : 
 
 I. CHEMICAL CONSTITUTION. 
 
 1. Homogeneity. 
 
 Pure iron can rarely be produced except by the methods 
 of the laboratory, and therefore in exceedingly small quanti- 
 ties. In practice it is combined with the most useful elements 
 by heat, the fusibility of the alloy usually increasing with the 
 number of elements contained. Fused metals in general are 
 imperfect alloys, the constituents of which tend to arrange 
 themselves according to their specific gravities. Due to the 
 property of liquation, certain of the most fusible alloys of 
 steel are found near the core of the ingot in greater propor- 
 tion than elsewhere. Thus, in a steel ingot the parts first 
 solidified represent most nearly its average composition, the 
 centre of the bottom being the softest and that near the top 
 the hardest, since the fusibility and the hardness of the alloy 
 increase with the percentage of C* 
 
 * Order of Oxidation. 
 
 Reactions during fusion depend so much upon the order of oxidation 
 of the constituents of pig-iron that the following approximate relation 
 should be learned: 
 
XV. — METALLURGY. 17 
 
 The segregation of the Kalchoids is very objectionable. 
 
 2. Composition. 
 
 The following elements occur in iron alloys : 
 1. Carbon and iron as the principal constituents make the 
 steel best suited for general purposes. It has often been tried 
 to replace or supplement the action of carbon by other ele- 
 ments such as silicon, tungsten, chromium, nickel, etc., but 
 for general purposes carbon steel is far the most important. 
 
 As a rule, the greater percentage of carbon up to about 
 1.5 (and even 2 5 per cent.), or the higher the grade, 
 
 The more — The less — 
 
 1. hard and elastic ; 1. dense; 
 
 2. tenacious ; 2. ductile ; 
 
 3. brittle ; 3. weldable ; 
 
 4. fusible; 4. forgeable, does steel be- 
 
 5. expansible by heat, does come. 
 
 steel become. 
 
 The terms high and lotv referring to the grade of steel, or 
 per cent, of C contained, are loosely applied, but the tendency 
 is to draw the line at 0.35 per cent., where hardening by heat- 
 ing followed by rapid cooling becomes perceptible. The 
 following table exhibits the classification according to use. 
 So much depends upon the percentage of hardening constitu- 
 ents other than C, and upon the treatment of the steel in 
 manufacture, that the relation expressed is only approximate. 
 
 1. Silicon. 5. Iron. 
 
 2. Manganese. 6. Phosphorus, in presence of an acid 
 
 3. Phosphorus, in presence of slag; i. ^., one containing an 
 
 an oxidizing basic slag. excess of S i O^. 
 
 4. Carbon. 
 
 These and other following relations depend so much upon existing tem- 
 peratures and conditions that they are expressed in the most general terms. 
 
18 
 
 XV. — METALLURGY. 
 
 Grade. 
 
 TABLE IL GRADES OF STEEL. 
 
 Per Cent, of Carbon. Application. 
 
 Low. 
 
 High. 
 
 Mild, 
 
 Hard, 
 
 Extra hard, 
 Tool, 
 
 Extra Tool, 
 Die, 
 
 Extra mild, 0.05 — 0.20 Boiler plates to be flanged, 
 
 bridge material. 
 0.20 — 0.35 Railroad axles, gun bar- 
 rels, etc. 
 
 0.35 — 0.50 Rails, cannon, etc. 
 0.50 — 0.65 Springs, saws, etc. 
 0.75 — 1.00 Chisels, cutters, etc. 
 1.00 — 1.20 Files and very hard tools. 
 2.50 Wire drawing, to resist 
 abrasion. 
 
 Carbon is generally supposed to exist in steel in two princi- 
 pal forms: 1. Cement carbon^ characteristic of annealed or 
 softened steel, and 2. Hardening carbo?i, characteristic of 
 hardened steel. The former is insoluble and the latter is 
 soluble in dilute H^ SO^. See page 48. 
 
 The following elements are admitted, either of necessity or 
 as Si physic ; i. e., replacing something more harmful or pro- 
 ducing a beneficial effect. 
 
 2. Silicon tends to displace C from combination, and to 
 confer its properties, although in a less degree. 
 
 It restores ''burned" or "rotten" steel by forming with 
 the particles of iron oxide, to the dissemination of which 
 this condition is often due, a fusible slag : 
 
 {Fe^ O^ + Siz=zFe Si O^ + Fe), 
 
 As Si increases the solvent power of steel for gases, and, 
 by reducing the iron oxide present in the hquid steel, prevents 
 the formation of CO it also prevents the honeycombing or 
 vesiculation of the metal from the ebullition of the gases 
 while the metal is becoming soUd. 
 
 If uncombined, Si O^ may remain as grit, which is injuri- 
 ous to the strength of the metal and destructive to cutting 
 tools. 
 
XV. — MEtALLtJRGY. 19 
 
 When in excess, Si makes steel brittle. This is generally- 
 true of the non-ferreous ingredients of the alloy. 
 
 3. Manganese, unlike Si, tends to make C combine with 
 iron ; like Si, it tends to replace C functionally, but much less 
 energetically. 
 
 Afn resembles Si as a reducing agent, and forms with it and 
 iron oxide a very fluid, cleansing, slag. 
 
 The physical properties it confers vary with the proportion 
 present. With from 3 to 6 per cent,, the steel becomes very- 
 hard and brittle ; but with from 7 to 20 per cent, the steel 
 becomes very tough and strong. 
 
 Some Mn is necessary to prevent hoi-shortness, or the tend- 
 ency to disintegrate when forged, even when no 6* is present. 
 It also acts as an antidote to S, by forming Mn S, which is 
 insoluble in melted steel. 
 
 4. Phosphorus make steel cold short, or brittle at ordinary 
 temperatures. It can be removed only by some basic process, 
 as follows : Since the ordinary silicious, or acid, lining would 
 prevent the oxidation of P, and, by wasting the iron, would 
 increase the proportion in which P remained ; in the basic 
 process the furnace is lined with dolomite brick. Iron ore 
 and (for economy) limestone are added to the charge, so that 
 the phosphoric slag that is formed may continue basic. 
 
 The presence of Mn and Si in the pig iron from which 
 washed pig is thus formed, protects from oxidation the C that 
 it contains, and therefore maintains the fluidity of the charge, 
 until the Mn and Si are consumed. When this happens and 
 the bath boils with CO, the washed metal is cast into pigs 
 containing only about 0.1 of the original P. 
 
 So much C is retained that (after grading it by analysis) 
 the washed pig is easily remelted in further processes relating 
 to the manufacture of steel. 
 
 These processes permit the use of pig iron, which was 
 formerly too high in P. 
 
20 XV. METALLtfRGV. 
 
 When added to the Kalchoids, P removes their greatest 
 enemy, oxygen. 
 
 5. Sulphur also is very difficult to remove, although the 
 hot-shortness that it produces may be corrected with Mn or 
 eliminated by Ca F^. 
 
 6. Chromium increases the hardness of steel without im- 
 pairing those qualities, such as ductility and malleability, 
 which are incompatible with the hardness resulting from high 
 carbon. 
 
 7. Aluminium is said to increase the fluidity of low steel, 
 and even of weld iron, in a remarkable degree, thus permit- 
 ting the metal to be cast without danger from vesiculation. 
 The fluidity of the metal in the mold permits the escape of 
 the occluded gases. Its action on iron oxide resembles that 
 of Si. 
 
 A new alloy known as Mitis metal, which is thus formed, 
 may be cast into the most complex forms. 
 
 8. Nickel remarkably increases the useful properties of 
 steel ; the result varying with the percentage as in Mn. The 
 armor plates now (1891) preferred are made of nickel steel. 
 
 9. Copper. When thoroughly deoxidized, steel may be 
 improved by the addition of Cu, although it is thought by 
 some that it makes steel hot-short, 
 
 II. PHYSICAL CONSTITUTION. 
 
 1. Homogeneity. 
 
 As in chemical composition, no fused metal is naturally 
 physically homogeneous, either in structure or in strain. 
 These properties may be so modified by after-treatment that 
 the following comparisons apply to non-forgeable metals as 
 ordinarily cooled after fusion ; and to forgeable metals when 
 annealed. This is the standard condition for their comparison* 
 
 2. Structure. 
 
 The structure is juaged of by the appearance of the frac- 
 tures; for exact comparison these should be similarly pro- 
 
XV. — METALLURGY. 21 
 
 duced. By varying the method of breaking it, the fracture 
 of a bar of wrought iron may be made either crystalline or 
 fibrous within a few inches of its length. 
 
 Crystallization. It is assumed that ingot metals are crystal- 
 line, and weld metals fibrous, although the ultimate crystal- 
 line forms are doubtful.* Thus, the former may be supposed 
 to consist of normal crystals, and the latter of distorted crys- 
 tals cemented by a film of slag. 
 
 Normal crystals are supposed to be formed like those of 
 soluble salts ; the more slowly and quietly they are cooled 
 from fusion, the larger and weaker they are, and conversely. 
 (Bioxam, Art. 38.) 
 
 The crystalline axes are found perpendicular to the cooling 
 surfaces, so that surfaces of weakness are formed at the junc- 
 tion of inclined systems. See figures 16, 17. For this reason 
 the corresponding surfaces should be united by gradual curves 
 so as to distribute strains which would otherwise be localized. 
 Sharp re-entrant angles should be avoided in all structural 
 masses, even the non-crystalline. 
 
 Vesiculation. Another structural form arises from the oc- 
 clusion of air and other gases during the casting. This causes 
 ^'' blow -holes,'' which increase with the viscidity of the fluid 
 mass. On the other hand, when the metal is free from blow- 
 holes, an axial cavity is formed, due to internal strain. This 
 is known as 3. pipe. Figure 18. 
 
 3. Strain. 
 
 Differences in the rate of cooling throughout a fluid mass 
 produce internal strain, the parts first solidifying being com- 
 pressed by their adhesion to the layers cooling subsequently, 
 which last are reciprocally extended. Similar effects follow 
 
 * By some the primitive structure of ingot steel is supposed to be that 
 of globules of the alloy imbedded in a mo e highly carbonized cement. 
 This is called the Cellular Theory. 
 
22 XV. — METALLURGY. 
 
 unequal heating. The importance of this principle is fre- 
 quently apparent, particularly in dealing with iron castings. 
 
 //. CAPACITY FOR RESISTING STRESS, 
 
 Properties. 
 
 Owing to the facility of referring other stresses to a tensile 
 stress, this alone is generally considered, the incompressibiuty 
 of cannon metals being sufficiently guaranteed by their com- 
 bined hardness and tenacity. 
 
 The principal properties of 1. tenacity, 2. elasticity, 3. 
 ductility, and 4. toughness, have already been discussed. 
 
 5. Hardness is properly the property of resisting penetra- 
 tion ; combined with tenacity, with which it is almost invari- 
 ably associated, it renders cannon metal incompressible by 
 powder pressure, and in itself resists abrasion, erosion and 
 impact from hostile shot. 
 
 Steel may be artificially hardened by heating it, followed 
 by its rapid cooling. Steel and bronze may also be hardened 
 by their compression in a cold state ; externally by rolling 
 and internally by mandreling, which consists in forcing 
 through a hole conical plugs of slowly increasing diameter. 
 
 It is noteworthy that by heating and rapid cooling, brass, 
 bronze and the high Mn steel, p. 19, are softened, 
 
 III, FACILITY FOR BEING WORKED, 
 
 1. Fusibility. 
 
 This diminishes the number of joints in a given structure, 
 and, other things being equal, increases its cheapness, homo- 
 geneity and strength. Recent advances in mechanical en- 
 gineering have been principally due to the large units of con- 
 struction afforded by the capacity and power of modern 
 furnaces. Thus steel is replacing wrought iron, which is 
 formed by agglutination. 
 
XV. — METALLURGY. 23 
 
 2. Malleability, 
 
 or to the power to endure hammering or roUing, particularly 
 at high temperatures, enables metals to be forged into special 
 shapes, thereby improving the quality of the metal and reduc- 
 ing the labor of finishing. When combined with fusibility, 
 it gives advantages peculiar to steel. 
 
 3. Weldability, 
 
 or the power of adhesion at high temperatures between 
 masses is characteristic of wrought iron and low steel. It is 
 upon this property that the manufacture of wrought iron 
 depends. This property in construction is inferior to fusi- 
 bility and hence is not utilized for steel except in small masses. 
 
 The process of electric welding is now (1891) successfully 
 employed. It consists in sending a powerful low-pressure 
 current through the abutting surfaces of the pieces to be 
 united. The resistance at the points of contact raises the 
 neighboring metal to the temperature of incipient fusion; 
 pressure being then applied, fresh surfaces are successively 
 brought into contact. Owing to the high temperature of the 
 first contacts, the current is mainly conveyed through the new 
 ones and so on until a homogeneous joint is formed. 
 
 Hollow projectiles are thus made from steel tubing welded 
 to a point and a base. It is even proposed to heat finished 
 pieces locally, so as to permit them to be bent or tempered 
 without injury from the hammer or the fire. 
 
 4. Annealability, 
 
 or the power to become soft, facilitates reduction to size by 
 cutting tools. All the cannon metals can be softened by 
 annealing, but to steel only can the necessary hardness be 
 restored, except mechanically. 
 
 Grindi?ig. It fortunately happens that hardened steel, 
 which can cut all the other useful metals, can itself be abraded 
 by grinding almost as easily as when soft. 
 
24 XV. — METALLURGY. 
 
 This permits the change of form which often follows hard- 
 ening to be corrected by the use of either natural or artificial 
 grindstones. See Chapter XVII, page 14 
 CONCLUSION. 
 
 The relative standing of the five cannon metals may be 
 roughly indicated as follows : 
 
 ^STEEL-> , IRON > 
 
 High, Low. Wrought, Cast. Bronze. 
 
 1.1 f?l^„aS'/1 ^ ^ 3 4 5. 
 
 t! 5 -( Homogeneity, I 1 o A. ^ f? 
 
 2 % I Hardness, normal, f ^ ^ ^ d o. 
 
 tn ^ 1^ Ductility, 4 3 15 2. 
 
 f Fusibility, 3 4 — 3 
 
 Malleability, 3 2 1 — 
 
 O cJ 
 cr 
 
 C (U 
 
 •^ § s( Weldability, — 2 1 
 
 Annealability or ^ ^ o q 
 
 variable hardness, f 
 
 This indicates why bronze and the irons, which, owing to 
 their workability, were until recently the only cannon metals, 
 are now obsolete. 
 
 IV. MANUFACTURE of the FERREOUS METALS. 
 
 /. CAST IRON, 
 
 Varieties. 
 
 The gray pig is known diS foundry or 77ielting irow, the white 
 pig as forge iron ; the latter is useful only for conversion 
 into wrought iron. Mottled pig is an intermediate variety. 
 
 Remelting. 
 
 To obtain strong castings, the foundry pig is ordinarily 
 remelted and run into molds of the required shape. 
 
 The specific gravity of pig-iron is about 7.00, and its 
 tenacity about 16,000 pounds to the square inch, but, when 
 remelted, the specific gravity is increased to about 7.25, and 
 the tenacity about doubled. 
 
 The remelting is effected in cupola or reverberatory fur- 
 naces, according to the kind of fuel available and the size 
 and quality of the casting required. It is always necessary 
 
XV. — METALLURGY. 25 
 
 to melt as quickly as possible, and with the least consump- 
 tion of fuel. This usually requires artificial blast. 
 
 In Cupolas. The cupola furnace is generally employed ; 
 its size depends upon the amount of metal to be melted at a 
 time, and upon the kind of fuel. 
 
 A cupola extensively used is of the Mackenzie pattern, fig- 
 ure 19. It consists of the iody B, of elliptical cross section, 
 made of thick sheet-iron lined with fire-brick ; this is sur- 
 mounted by a conical hood H, terminating in the chimney C. 
 The blast is admitted through an annular tuyere extending 
 around the bottom part of the furnace. The charge is intro- 
 duced at the door D, and the molten metal, accumulated in 
 the hearth H, is drawn off at the spout S, and carried to the 
 mold through a channel or by means of ladles. 
 
 The elliptical section of the body in combination with the 
 annular tuyere increases the capacity of the furnace for a 
 given intensity of blast ; the object being to maintain a high 
 temperature in the vertical plane containing the transverse 
 axis of the ellipse, along which, for regularity of feeding, it 
 is desirable to cause the contents of the furnace to descend. I 
 
 The cupola furnace saves fuel, labor and time, and fur- 
 nishes a continuous supply of iron, which, since the carbon 
 in the pig-iron is not diminished by melting, is liquid and 
 therefore of the quality suited to foundry purposes. 
 
 The charge consists of pig-iron and generally scraps of 
 cast iron, a flux, and the fuel ; for the latter, coke and char- 
 coal are best, though anthracite is generally employed. 
 
 In Reverberatory Furnaces. Reverberatory furnaces are 
 principally used for the production of large castings, and are 
 specially adapted to all such as require great strength. Their 
 use is sometimes necessitated if the fuel at disposal contains 
 sulphur. 
 
 The name is derived from the arch which beats back the 
 flame on the metal to be heated. 
 
 The furnace, figure 20, is built of fire-brick bound strongly 
 together by iron bars or plates ; the hearih H is of refractory 
 
S6 XV. — METALLURGY. 
 
 brick covered with a thick layer of Bre-sand ; the grate G is 
 large, that a great volume of flame from the fuel may be 
 drawn over the bridge -5 and through the furnace ; for this 
 purpose the chimney C is made very tall when no artificial 
 blast is used. The metal is introduced at the charging doors 
 D, D\ and, when melted, is drawn off" at the tap-hole (h). 
 
 The dimensions of the furnace depend chiefly on the charge 
 of iron and quality of the fuel. They are of correct propor- 
 tions if a nearly uniform temperature be produced in all parts 
 of the furnace. 
 
 Unlike the cupola, this furnace allows the iron to be kept 
 liquid for any length of time ; and, as the fuel is not in con- 
 tact with the metal, and carbon and silicon are removed by the 
 air, a stronger iron results. On the other hand, it does not 
 admit of constant casting, and involves a great loss of iron 
 by oxidation ; owing to these circumstances and to the greater 
 consumption of fuel, such furnaces are used only in large 
 foundries, and, whenever practicable, are replaced by cupolas 
 of large size. 
 
 Properties of Iron for Castings. 
 
 The color and texture of a casting depend greatly on its 
 size, and on the rapidity with which it has been cooled, and 
 upon its composition. As small castings cool quickly they 
 are almost always white, and the surface of large castings 
 partakes more of the quality of white iron than does the 
 interior. 
 
 When gray iron is melted, the particles of graphite to 
 which its color is due are dissolved by the liquid iron, and if 
 it be poured into a cold iron mold so as to solidify quickly, 
 the exterior of the casting will present much of the hardness 
 and appearance of white iron, the sudden cooling having pre- 
 vented the separation of the graphite. This is particularly 
 apt to follow the presence of manganese in the iron. 
 
 At the instant of solidification gray iron expands more 
 than white, giving a casting with sharp edges and a convex 
 
XV. — METALLURGY. ^? 
 
 surface; and, as it subsequently contracts less, the initial 
 strains due to cooling are less. 
 
 White iron gives a casting with a concave surface, and 
 mottled iron one with a plane surface, the edges slightly 
 rounded. 
 
 SPECIAL CAST IRONS. 
 
 Malleable Cast Iron. 
 
 By extracting a portion of the carbon from cast-iron its 
 composition is assimilated to that of wrought iron and its 
 toughness increased ; the result is known as malleable cast 
 iron. 
 
 The castings to be softened are packed with powdered 
 haematite ore, or scales of oxide of iron, and the temperature 
 raised gradually to a red heat ; this is continued from three to 
 five days according to the thickness of the layer of malleable 
 metal required. 
 
 When withdrawn from the furnace, articles so heated have 
 the appearance of ordinary malleable iron, but are lighter 
 in color ; their fractured surfaces are white and finely granular, 
 occasionally having a silky appearance like that exhibited by 
 soft steel. 
 
 The principal application of this process is to such articles 
 as buckles, bits, stirrups, keys, etc. 
 
 Case-hardening. The stratum of malleable metal on the sur- 
 face may be converted into steel by the process of case-hard- 
 ening, which consists in a similar heating in contact with ani- 
 mal charcoal, after which, while still hot, the casting is plunged 
 into water or oil. This process is applied also to articles of 
 wrought iron, such as the parts of small-arms in which it is 
 desired to have a tough, somewhat soft interior protected 
 from friction or blows by a hard surface. The hammer and 
 breech-block of the Springfield rifle are so treated. 
 
28 XV.— METALLURGY. 
 
 SPECIAL ALLOYS. 
 
 Varieties. 
 
 Spiegeleisen or Spiegel {Sp) and Ferro- Manganese (FM) 
 may be regarded as varieties of white cast iron alloyed with 
 a varying proportion of Mn, That which contains over 20 
 per cent, of Mn is known as FM. When Mn amounts to 
 80 or 90 per cent., it may consume by spontaneous oxidation. 
 
 The price of FM increases with its richness in Mn, for this 
 limits the choice of ores and increases the temperature of 
 reduction and fusion, and the loss by volatilization and oxi- 
 dation. 
 
 Silicon- Spiegel and Ferro-Silican are similar alloys, but con- 
 tain much more Silicon. 
 
 The following table exhibits roughly the ingredients of 
 some of the principal special alloys, and illustrates the state- 
 ments previously made as to the effects of Mn and Si upon 
 the proportion of iron in combination. 
 
 Note the gain in C as Mn increases, and its loss as Si 
 increases. 
 
 TABLE. 
 
 Name. 8% Mn C Fe^ 
 
 (combined.) etc. 
 
 1. Ferro-Manganese, 80 7 13 
 
 2. " '* 60 6 34 
 
 3. Spiegel-Eisen, 1 10 5 84 
 
 4. Silico-Spiegel, 10 20 2 68 
 
 5. Ferro-Sihcon, 10 2 88 
 
 Use. / 
 
 These alloys are manufactured principally for the steel 
 makers, being used by them to improve the quality of steel 
 while in a state of fusion. 
 
 Generally speaking, Ferro-Manganese is used when the 
 quantity of C necessary is small as compared with the Mn 
 required ; and conversely with Spiegel-Eisen, although in the 
 
XV. METALLURGY. 29 
 
 latter case C may be added directly in a pulverulent form, or 
 in a pure pig iron. 
 
 The Silicon irons are principally used to prevent vesicula- 
 tion; No. 4 is preferred to No. 5, as the increase in Mn 
 causes the Si to more thoroughly combine with the steel and 
 improves its structure. 
 
 //. MODERN MANUFACTURE OF WROUGHT IRON. 
 
 Principles. 
 
 The great cost of the hand labor engaged in the ordinary 
 process of puddling has led to the use of mechanical means 
 for accomplishing this result. The two principal processes 
 are those of Danks and Perfiot. Their common feature is 
 the continuous rotation, by mechanical means, of the vessel 
 containing the charge, thus avoiding the loss in time and 
 power due to the reciprocating action of the puddler's rabble ; 
 and diminishing the number of skilled workmen required. 
 
 The principle involved in these processes is that given in 
 Bloxam, Art. 219, viz.: That when cast iron is heated in con- 
 tact with iron oxide, the C and Si in the iron take O mainly 
 from the iron oxide in the fettling of the furnace. The C 
 passes off as CO and CO^, and the Si as an iron silicate or slag. 
 Danks Process. 
 
 The furnace, Figure 22, consists of a horizontal drum, revolv- 
 ing on rollers and lined with 2. fettling of lumps of haematite 
 ore set in a fused paste of the same ore. The flame from a sta- 
 tionary fireplace plays through one end of the drum and passes 
 off through a movable flue at the other end. The removal of 
 the flue permits the drum to be charged and emptied. 
 
 For economy. the furnace maybe charged with melted iron, 
 either directly from a blast furnace or from a cupola. If 
 charged cold the rate of revolution is slow while melting; it 
 is increased while boiling, during which the fettling and the 
 flame rapidly oxidize the C and Si exposed by the rolling of 
 the pasty mass and the adherent film and drip from that 
 
30 XV, — METALLURGY. 
 
 which is melted. The drum is stopped to tap the cinder. It 
 is then revolved more rapidly than before, draining the pasty- 
 mass until it begins to ball. The large lumps, carried around 
 by adhesion, fall on those at the bottom and help to work out 
 the cinder. This is more thoroughly done afterward by the 
 usual methods. 
 
 Pernot Process. 
 
 The pan revolves under a stationary cover, on an axis in- 
 clined about 5° or 6° to the vertical, see figure 85. The fet- 
 tling is thus exposed alternately to the flame and to the metal, 
 the film of oxidized iron thus formed passing under the fluid 
 mass and assisting the reduction. Balling still has to be done 
 by hand ; but the process uses less coal than the ordinary 
 one, and the furnace can be more easily repaired. 
 
 These processes are losing their importance in consequence 
 of the rapidity with which steel of various grades is supplant- 
 ing wrought iron. 
 
 ///. MANUFACTURE OF STEEL. 
 I. IN SMALL MASSES. 
 
 1. Weld Steels. 
 
 Puddled Steel. Puddled steel is made by stopping the pro- 
 cess of puddling when the de-carbonization of the cast iron 
 has sufficiently advanced. It is principally used for conver- 
 sion into other kinds of steel. 
 
 Blister Steel, which is made by cementation, being full of 
 fissures and cavities, is fit only for a few rough purposes, as 
 for facing hammers ; most of that made is used for conversion 
 into other kinds of steel. 
 
 Tilted Steel, When bars of blister steel are heated or 
 hammered into bars under a tilt hammer^ Figure 40, the pro- 
 duct is termed tilted steel ; spring steel is thus prepared. 
 
 Shear Steel. Shear steel is produced by cutting bars of 
 blister steel into convenient lengths, and piling, heating, and 
 welding them under a hammer, whereby is obtained a bar of 
 
XV. METALLURGY. 31 
 
 uniform quality known as single shear steel ; the quality of 
 the metal is still further improved by a repetition of the pro- 
 cess, forming a bar of double shear steel. The oftener the 
 process is repeated, the more uniform is the resulting steel. 
 
 Shear steel is capable of receiving a better edge and a 
 higher polish than blister or spring steel; when well prepared, 
 it is not much inferior to crucible steel. It is very exten- 
 sively used in work where steel and iron have to be united by 
 welding, as in axe-bits and scissors. 
 
 2. Crucible Steel. 
 
 Although blister steel by repeated working under the ham- 
 mer acquires a tolerably homogeneous structure, it is still 
 further improved by fusion. The process, invented a century 
 ago, still remains in principle unaltered. Fragments of blis- 
 ter steel are melted in crucibles, figure 23, covered to exclude 
 the air, and the liquid poured into cast-iron ingot molds of 
 the shape and size required. These ingots usually contain 
 cavities; they are gotten rid of by heating the mass and ham- 
 mering it into coijipact and homogeneous bars. 
 
 Most crucible steel is now made direct from bars of the 
 best wrought iron ; they are broken and placed in the cruci- 
 ble with a small quantity of charcoal or pig iron, the amount 
 varying according to the grade of steel required ; some alloy 
 of manganese is subsequently added. The preliminary frac- 
 ture of the material charged facilitates its classification and 
 increases the uniformity of the product. 
 
 Properties. 
 
 In forging, crucible steel should never be raised beyond 
 a certain temperature, varying inversely with the grade, 
 or it will become brittle. It is difi&cult to weld, as it is usu- 
 ally high in carbon. 
 
 If a small quantity of manganese be added to the molten 
 metal, the steel will be more forgeable and may be welded 
 either to itself or to wrought iron. 
 
32 XV. — METALLURGY. 
 
 Kemarks. 
 
 The manufacture of the weld steels and of crucible steel is 
 losing its importance, and crucibles are now principally used 
 for small masses in which the desired quality of the product 
 can, from the careful supervision exercised, be most easily 
 maintained. 
 
 The size of the crucible charge depends on the strength of 
 the melter and rarely exceeds 80 lbs. ; but with well drilled 
 men large numbers of such crucibles may be poured succes- 
 sively into a common ingot mold of any size. Krupp so casts 
 his large cannon, sometimes employing 1200 crucible bearers. 
 
 II. IN LARGE MASSES. 
 
 Processes. 
 
 The principal processes are the Bessemer and various forms 
 of the Open Hearth. Each of them has its province. The 
 former, owing to its rapidity, excels in cheapness, although 
 there is a loss of about 10 per cent, of iron ; the latter, owing 
 to its controllability, excels in quality. This takes time and 
 increases the cost by about 15 per cent., although there is in- 
 cidentally a slight gain of iron. 
 
 Carbonization and Tests. 
 
 Owing to the loss of iron from oxidation when completely 
 decarbonized, neither process is carried to an extreme, some 
 C being always left in the metal and its final percentage being 
 regulated by adding Sp or FM. 
 
 The percentage of C is judged of by the fracture ; by the 
 appearance of the nick required to produce fracture ; and 
 more carefully by a rapid color test, which consists in compar- 
 ing the color of a solution of the metal in dilute HNOg with 
 that of a standard solution. In the Bessemer process this in- 
 formation is applied to the next succeeding heat ; and in the 
 Open Hearth, as the operation is less hurried, to the heat itself. 
 
 Temperature. 
 
 The high temperature attained permits re-melting on the 
 spot of the scrap accumulating in all steel works, which would 
 
3tV.— MEtALLURGV. 33 
 
 otherwise be of little value. In the Bessemer process this is 
 due to the oxidation of the Si in the pig ; in the Open Hearth 
 to the Siemens regenerator, which increases the temperature 
 cumulatively to a degree limited only by the refractoriness of 
 the furnace linings and the tendency of the gases to disso- 
 ciate. Thus, like many other inventions, the Open Hearth 
 process had to wait for the parallel development of some in- 
 significant art, i. e. that of the brickmaker. 
 
 Cranes. 
 
 The production of metal by both processes depends upon 
 the facility of manoeuvring large masses. Of the various pat- 
 terns of cranes used for this purpose. Sir Wm. Armstrong's 
 hydraulic crane, or some modification of it, is especially valu- 
 able in Bessemer practice. Its efficiency depends upon the 
 arrangement of peculiar valves which unite at a central point 
 called the ** pulpit" and which place the control of the whole 
 plant in the hands of one man. 
 
 For an Open Hearth plant, where frequently very heavy 
 masses must be moved and where the operations need not be 
 so rapidly performed, these cranes may be supplemented by 
 power swinging cranes or replaced by a traveling crane cover- 
 ing the whole building. The traveling crane consists of a 
 horizontal beam the ends of which roll on raised parallel 
 tracks. The weight hangs from a truck rolling on the beam 
 and may thus be transported to any point of the included 
 volume. This crane presents many advantages and is used 
 when the construction of the plant permits. 
 
 Casting Ingots. 
 
 In both processes, the melted steel is run from the furnace 
 into a ladle from which it is distributed by a crane into cast- 
 iron ingot molds. 
 
 Casting is sometimes done through an independent iron 
 gate entering the mold from below (Figure 24). The fluid 
 metal should enter in a quiet, solid stream so as to avoid 
 
84 XV. — METALLURGY. 
 
 entangling air. This is best done by emptying the ladle into 
 the pool, from which it issues, mider a constant head, through 
 a cylindrical nozzle. 
 
 For gun work, the ingots are like Figure 25. The tong- 
 hold serves to attach the porter-bar in forging ; and the drum, 
 being girt with a sHng chain, permits the mass to be moved 
 about and turned axially under the hammer. The dotted 
 lines in Figure 25 indicate the form of the corresponding 
 sections of the ingot. 
 
 Ingots are cast at as low a temperature as possible consist- 
 ent with fluidity in order to diminish internal strain and to 
 save the inner surface of the mold, injuries to which may 
 imprison the ingot. 
 
 In order to fill the voids resulting from the shrinkage due 
 to internal strains, castings of all kinds are generally sur- 
 mounted by a smkifig head. This is a reservoir of the melted 
 metal, the cooling of which is often retarded by containing it 
 in a relatively non-conducting mold. 
 
 For economy of fuel it is generally sought to forge the in- 
 gots as soon as possible after they have solidified throughout ; 
 but, owing to interruptions in the work, the sequence cannot 
 always be maintained. Ingots may thus require re-heating ; 
 this should be gradual so as to avoid internal strain. 
 
 Fluid Compression. 
 
 Whitworth's method of fluid compression tends to obliter- 
 erate cavities by an hydraulic pressure of about 40000 lbs. per 
 square inch. A very strong steel mold provided with a por- 
 ous lining is employed. The pressure crushes down the vesic- 
 ulated shell first formed next to the walls of the mold, and 
 drives the fluid metal throughout the interstices. The lining 
 allows the escape of gas. By this means the ingot is reduced 
 about one eighth in length while cooling after casting. The 
 best results, however, are thought to be obtained by careful 
 melting and after-treatment of the steel while in a fluid state. 
 
XV. — METALLURGY. 35 
 
 Bessemer Process. 
 
 (Figures 27—30.) 
 
 Varieties. 
 
 There are two general processes depending on the nature 
 of the pig-iron converted. If free from P, silicious or acid 
 linings may be used ; but if it contains much P, basic linings 
 are required. The former process, which is the more com- 
 mon, is here described. 
 
 Metal. 
 
 The iron must contain Si as a fuel, and hence gray pig, the 
 color of which is due to the carbon displaced, page 18, is 
 used. It should be free from P and S, as they are not re- 
 moved but, owing to the inevitable loss of iron, their propor- 
 tion is increased. 
 
 Main Operation. 
 
 The pigs are usually melted in a cupola and the fluid 
 charge, after weighing, run into the converter. A blast of 
 air is then blown down through one trunnion and up through 
 the perforated bottom and the fluid metal. The reactions 
 resemble those of puddling* and are principally due to the 
 heat evolved by the burning Si. This burns out the Mn and 
 C in the metal and, by forming ferreous slags, removes part of 
 the iron also. The fluidity of the metal is due to the inten- 
 sity of the heat ; the latter is due to the rapidity of the reac- 
 tion consequent upon the state of subdivision of the mass. 
 The burning Si raises the temperature and promotes the 
 fluidity of the bath more than does the C, because the CO 
 formed absorbs much heat by expansion and carries it off; 
 the slag remains and protects the bath from cooling. The 
 small portion of Mn present also acts as a fuel. 
 
 The basic process requires the blast of the Bessemer blower 
 
 * It has been said as an example of mechanical progress, that we 
 have replaced the laborious operation of the puUdler's rabHc by piercing 
 the iDolten metal by invigjble bars of air. 
 
?56 XV.— METALLURGY. 
 
 to be prolonged after the C and Si in the pig have been re- 
 moved, the burning P maintaining the fluidity of the metal. 
 
 Periods. 
 
 Three periods are recognized, lasting as follows : 
 
 I. Three to five minutes, Si burning. The free C in the 
 pig becomes combined, in which state it is most easily oxi- 
 dized. The flame is feeble, with a hissing noise. 
 
 II. Six to ten minutes. The oxidation of C, principally 
 to CO, makes the mass boil with a thundering noise. A 
 yellow flame of incandescent particles is emitted at the nozzle. 
 
 III. Four to five minutes. The flame, principally of N, is 
 smaller, and of a pale bluish tint. In about 15 or 18 min- 
 utes from the beginning, the flame suddenly drops, showing 
 that the C is almost entirely gone. To save loss of iron by 
 further oxidation, the blow is then stopped as the converter is 
 turned down ; the carbonizer is then added by weight. If 
 Spiegel is used, it is melted in a separate cupola. 
 
 Final Operations. 
 
 The carbonizer preferred for low steel is FM, which, al- 
 though more costly than Sp, contains less C in proportion to 
 the Mn, so that enough Mn may be added to reduce the iron 
 oxide, combine with free O, and impart to the steel its char- 
 acteristic qualities without introducing enough C to make it 
 unduly hard. The production of FM is one of the improve- 
 ments for which this application of the process had to wait. 
 
 After standing for a few minutes, the contents of the con- 
 verter are poured into a ladle, the slag remaining in the vessel; 
 the slag is then emptied and the vessel turned up for a fresh 
 charge. 
 
 Remarks. 
 
 The melted pig may be conveyed directly from the blast fur- 
 nace ; but this is not often done, as it prevents the prelimi- 
 nary grading of the pigs by fracture. 
 
 The process is principally applied to the manufacture of 
 
XV. — METALLURGY. 37 
 
 rails, for which it is sufficiently exact. The quaHty of the 
 product may be improved if time and waste are neglected and 
 the process carefully watched through the spectroscope. 
 
 The steps of the operation in the acid and the basic pro- 
 cesses, showing the rates at which the solid products are 
 oxidized and the proportions of the different gases succes- 
 sively formed, are represented in figures 28, 29, 30. In each 
 figure one scale is that of time in minutes from the beginning 
 of the blow, and the other represents the corresponding per- 
 centage of the special product in question. These diagrams 
 are the result of experiment. 
 
 / Open-Hearth Process. 
 
 Varieties. 
 
 The hearth may be either of the stationary or of the rotary 
 type. In both cases the advantages of the process depend 
 upon the Siemens regenerative apparatus, which requires a 
 gaseous fuel. 
 
 The rotary hearth has the advantage of steam power and 
 of facility in making the repairs which the intense heat due 
 to the regenerative apparatus frequently requires. It is also 
 better able to dephosphorize pig-iron. The principal objec- 
 tion to it is the liability of derangement of the rotating 
 machinery ; but this can be overcome. Its process is here- 
 after described. 
 
 Distinctions were formerly made between the "pig and 
 ore " and the " pig and scrap " processes, depending upon 
 whether the melted pig-iron is decarbonized by the iron oxide 
 or diluted by the addition of scrap steel low in carbon. 
 Such distinctions are no longer important, as the former pro- 
 cess is generally employed. 
 
 The Siemens furnace with either the stationary or the revolv- 
 ing hearth is a mighty instrument for achieving various metal- 
 lurgical ends. Accordingly, many combinations are made in 
 
88 XV. — METALLURGY. 
 
 its employment, pig-iron, washed pig, ore, fluxes, and, par- 
 ticularly for commercial products, scrap being added as 
 required or convenient. 
 Gaseous Fuel. 
 
 Advantages: 1st. Controllability, by which either an oxi- 
 dizing, reducing, or neutral flame can be uniformly obtained. 
 2d. Economy. 3d. Cleanliness. 4th. The accuracy with 
 which the low temperatures used in annealing ovens may be 
 estimated by the eye, the gas having been temporarily cut off 
 so as to obtain a background against which the true color of 
 Uhe heated piece will appear. 
 
 The gas may be natural or artificial. 
 
 Crude petroleum is becoming largely used as a fuel. Being 
 thrown into the furnace as a spray, it has many of the advan- 
 tages of a gas. It is also converted into gas by the action 
 of steam at a high temperature.* 
 
 Siemens Gas Producer. 
 
 This consists of a number of chambers united in groups of 
 four around a common stack E, figure 31. The stacks unite 
 in a common trunk which leads with a slightly downward 
 inclination to the valve box B of the furnace, figures 33, 34. 
 Each chamber is essentially a wedge-shaped funnel with one 
 inclined side terminating at the bottom in a grate B on which 
 the fuel is slowly burned. The CO^ formed, ascending 
 through the incandescent mass, becomes 2C0, and, with 
 other gases due to the partial distillation of the superin- 
 cumbent fuel, passes through the flue D to the stack E and 
 thence to the trunk, having in the trunk a slight excess over 
 atmospheric pressure to prevent leakage inward. The increase 
 
 * The oxygen in the H^ O combines with the carbon in the oil, forming 
 CO, and decomposing the hydro-carbons into new compounds richer in 
 H. The H derived from the steam combines with the new compounds, 
 and makes them still lower in the paraffine series. (Bloxam, Art, 320.) 
 
XV. — METALLURGY. 39 
 
 of density due to cooling causes a gradual flow along the 
 trunk. The same effect can be obtained by using a blast 
 which gives more, better and hotter gas from fewer producers 
 burning poorer fuel than does the natural draft described. 
 
 Almost any kind of fuel from gas coal to sawdust may be 
 used, depending on the purpose in view. 
 
 The charging hopper A and the poker hole Care stopped 
 to prevent the escape of gas. 
 
 . Siemens Stationary Furnace. 
 
 (Figures32, 33, 34.) 
 
 Hearth. 
 
 This rests in a cast-iron basin T, beneath and around which 
 air circulates. It is enclosed in a rectangular box-like fur- 
 nace about 30 feet long, standing above the floor-line W, and 
 provided with the charging door U, and the spout V iox tap- 
 ping out the fluid charge. 
 
 Regenerators. 
 
 These are the essential parts of the apparatus and are 
 applied to many purposes in which high temperatures are 
 required. 
 
 The regenerator consists of four fire-brick chambers of 
 varying section, K; L ; M; iV, arranged in pairs. They 
 are filled with a crib work of loosely stacked fire-brick. From 
 each of the end chambers K^ JV, gas-flues S lead up into the 
 furnace ; and from each chamber Z, M, three air-flues P and 
 R lead up alongside the gas-flues to a point above their exit 
 in the furnace. This arrangement protects the metal from 
 oxidation ; and the roof, made higher than where reverbera- 
 tion is sought, from erosion by the flame. 
 
 Valves, 
 
 The gas, air, and reversing valves are shown in vertical sec- 
 tion (laid over a longitudinal section of the regenerators) in 
 Figure 32 ; in plan (laid over a horizontal section of the main 
 
40 XV. — METALLURGY. 
 
 flues) F, G; Jy H in Figure 34 ; and in cross section in 
 Figure 33. 
 
 Operation. 
 
 Gas from the producers, regulated by the valve B, passes 
 down over the reversing valve C ; this is set so as to direct 
 the gas into the main flue F and the regenerator K, where it 
 percolates through the mass of hot brickwork and thence 
 passes at a high temperature into the furnace. Air is drawn 
 through the regulating valve F over the reversing valve C , 
 through the main flue G into the hot regenerator L and, 
 passing up the flue /*, meets the hot gas as above described, 
 affording progressive combustion with intense heat. 
 
 After burning, the flame passes down the flues R^ S into 
 the other pair of regenerators J/, N^ which absorb most of 
 its heat. It then escapes through the main flues J, H under 
 the two reversing valves, and into the chimney flue AA' . 
 
 After about twenty minutes, K, L becoming cooler and M, 
 N heated, C, C are reversed by the handles D, when the 
 currents of gas and air are also reversed. The efl"ect of 
 reversal is cumulative, since to the heat of combustion is 
 added that which the gases absorb from the brickwork before 
 combustion. As the brickwork becomes progressively hotter, 
 the ultimate temperature attainable is independent of blast or 
 draught and is limited only by the refractoriness of the furnace 
 linings and the tendency of the gas to dissociate at high tem- 
 peratures. 
 
 Advantages. 
 
 The principal advantages are the high and uniform tem- 
 peratures attainable, with the other advantages due to the use 
 of gaseous fuel. 
 
 Employment. 
 
 When the furnace has been brought up to a melting heat, 
 the bottom is repaired with fire-sand and the charge thrown 
 
XV. — METALLURGY. 41 
 
 in by hand. After melting, it is stirred with iron -bars and 
 treated as hereafter described in the Rotary Hearth, 
 
 Pernot Rotary Hearth. 
 
 (Figure 35.) 
 
 Hearth. 
 
 This consists essentially of a circular wrought-iron ' ^ pan " 
 lined with refractory material and mounted on conical rollers. 
 These run on a circular trough-shaped track mounted on a 
 carriage ; the latter rolls on two parallel rails on which it may 
 be run into and out of the stationary furnace chamber. The 
 pan is rotated by a circular-toothed rack beneath it gearing 
 into a toothed wheel or by an endless screw driven by steam 
 power. The pintle, which is hollow and contains a stream 
 of water, is incHned at about 6°, so as to bring the highest 
 portion of the hearth next to the door. In case of accident 
 to the tapping hole, more than one is provided. 
 
 The lining of the pan varies with the kind of work. For 
 ordinary melting it is of refractory siUcious material; but 
 where dephosphorization is sought by the Krupp process, the 
 lining is basic, preferably of lumps of refractory magnetite 
 set in a paste made of powdered haematite and iron scale. 
 The lower courses of the roof are then of dolomite brick. 
 
 Operation 
 
 For steel making, the charge, consisting of about 15 tons 
 of pig-iron free from P and 6", is thrown in through the charg- 
 ing door while the pan is revolving ; this distributes it auto- 
 matically. Further revolution of the pan then causes the 
 unmelted metal to dip into and out of the bath as previously 
 described for wrought iron. When the pig-iron is thoroughly 
 melted, rotation is stopped and ore is added at intervals, 
 each addition being followed by a violent ebullition of the 
 bath. Samples of metal or ''spoon tests'* are taken from 
 time to time and examined by the color test, the fracture, and 
 
42 XV. — METALLURGY. 
 
 by the appearance of the nick made by the chisel at the 
 fracture. When the C in the bath is low enough, Si and Mn 
 are added to prevent vesiculation and to make the steel 
 malleable. The process is continuous, taking about eight 
 hours for a heat, with a variable interval for repairs. 
 
 Bepairs. 
 
 The hearth is repaired between heats by revolving it so as 
 to bring the portions most cut by the flame under a hole in 
 the roof through which material is thrown. The stationary 
 portion is repaired at about every twenty heats, the pan being 
 run out bodily on its carriage. This afl"ords a considerable 
 advantage, since in repairing the stationary furnace, time must 
 be taken to allow the mass of brickwork to cool down to an 
 endurable temperature ; owing to the lack of ventilation this 
 time may be very great. 
 
 V. MECHANICAL TREATMENT OF STEEL. 
 
 CASTING. 
 
 The successful casting of steel into final forms is still un- 
 certain. The principal difficulties arise from vesiculation and 
 internal strain Steel castings frequently replace iron forg- 
 ings of a low grade. 
 
 ROLLING 
 
 Rolling may be intended to produce forms either straight 
 or circular, and may be performed either hot or cold. The 
 latter has the special object of producing hard, polished sur- 
 faces of exact dimensions and is applied to iron or steel of 
 small sections only. The reduction is small. 
 
 Hot Rolling— Straight. 
 
 The following description of the rolHng of armor plate or 
 of structural steel is taken as a type. 
 
 The interior of a newly cast ingot is too liquid for safe 
 
XV. — METALLURGY. 43 
 
 working, and by the time that this has sufficiently cooled in 
 the air, the exterior has become too hard. Consequently, 
 the cooling is often retarded in non-conducting soaking pits, 
 in which the initial heat of the interior and that which be- 
 comes sensible during solidification become uniformly dis- 
 tributed throughout the mass. 
 
 Or, if the ingot has become cold, it is brought slowly to 
 the proper temperature in a heating furnace. If this is done 
 too rapidly, the exterior may be over-heated before the interior 
 is at the proper temperature. The principle involved is of 
 wide application in the treatment of steel. 
 
 The universal mill consists of two pairs of massive rolls at 
 right angles to each other, so that one pair will roll the sides 
 of the ingot while the other pair rolls its top and bottom. 
 Each pair is driven by an independent steam engine. The 
 direction of the rotation may be rapidly reversed, and the 
 space between the members of each pair of rolls be rapidly 
 adjusted to suit the varying dimensions of the work. 
 
 A series of horizontal parallel rollers of small diameter, 
 independently driven, convey the ingot to and from the rolls, 
 and after rolling take it to the shears where it is trimmed and 
 cut into lengths. 
 
 These lengths, or blooms^ are often re-heated and re-rolled 
 by a mill trai?i into various structural shapes. For small work 
 the mill train usually consists of a series of rolls arranged in 
 sets of three, one above the other, or three high. They con- 
 tain grooves of appropriately decreasing section so that suc- 
 cessive /^i^i'<fi' reduce the bloom to the shape required. The 
 rotation of each roll is continuous, so that the piece passes 
 in one direction above the middle roll, and in the opposite 
 direction beneath it. 
 
 In roUing large sections the two-high system is generally 
 employed ; the rotation being reversed and the space adjusted 
 at every pass. 
 
44 5tV.— MEtALLURGY. 
 
 In all large forgings great care is taken to cut out all visible 
 imperfections such as pulls^ which arise from deficient duc- 
 tiHty in the metal, and cold shuts, whicli are due to the folding 
 in of projecting portions at temperatures too low to admit of 
 their union to the mass. 
 
 Hot Rolling — Circular. 
 
 A small cylindrical ingot is flattened out or " upset " into a 
 "cheese" and punched from each side successively with a 
 conical drift. The punchings, or pieces cut out, usually con- 
 tain all the pipe. It is afterward hammered on the horn of 
 an anvil, figure 37, until the approximate forjji is obtained. 
 Then, being hung upon a fixed roller A, figure 38, another 
 roller B, independently driven at a higher rate of speed, is 
 raised by hydraulic pressure to the position shown by the 
 dotted lines. The thickness of the hoop is thus diminished, 
 and its diameter increased, since lateral spread is prevented 
 by the flanges a b which come in contact, each with the end 
 of the other roller. The process is used for making locomo- 
 tive tires and short hoops for guns. It tends to give a fibrous 
 structure to the steel, aff"ording great tangential strength. 
 
 WIRE DRAWING. 
 
 Operation. 
 
 This resembles rolling, except that the conical aperture in 
 the draw plate, figure 39, being stationary, the wire, previously 
 pointed and lubricated, is drawn through it by power, gener- 
 ally by being coiled around a revolving drum. Tubing is 
 similarly made, but large sizes, like gun-barrels, are rolkd as 
 described for rails, the sides being kept apart by an axial 
 mandrel which is stationary. 
 
 Effects. 
 
 The effect of wire drawing at low temperatures resembles 
 that of cold rolling in that it raises the elastic limit and tenacity 
 
XV. — METALLURGY. 45 
 
 and diminishes the ductility of the metal so much that, if the 
 original section is much reduced, frequent annealing is nec- 
 essary. Steel wire has thus been given a tenacity of over 
 333,000 lbs. per square inch with an elastic limit half as high. 
 These qualities are especially adapted to the construction of 
 " wire-wound" cannon. 
 
 FORGING. 
 
 This includes the operations by which hot metal is ham- 
 mered into shape. It therefore requires furnaces, hammers 
 and anvils. 
 
 Furnaces. 
 
 For large masses modifications of the Siemens fupnace 
 called re-heating furnaces are now employed. These furnaces 
 are frequently served by a curved crane of the form shown in 
 figure 42. This increases the elasticity of the crane as against 
 the shocks due to forging. 
 
 Hammers. 
 
 For light work hammers may be of the vibrating class known 
 as //// or helve hammers, figure 40, in which a horizontal beam, 
 working on trunnions, carries at one end a heavy head ; this 
 is caused to rise and fall by the action of projections on a re- 
 volving wheel. Or they may be of the class known as drop 
 hammers, where a weight is raised by hand or by power and 
 allowed to fall upon the work after the manner of a pile 
 driver, figure 41. 
 
 But for heavy work steam hammers are used. They are 
 sometimes of the Single Acting type, figure 42, proposed by 
 Nasmyth in 1833. The inverted cylinder is mounted on legs 
 which spread sufficiently to allow freedom for the workmen. 
 The cylinder is usually traversed vertically by a heavy 
 piston-rod, to the lower end of which, sliding in guides 
 attached to the frame, is fastened a heavy head or tup. 
 Steam being admitted below the piston, it raises the hammer, 
 
46 XV. — METALLURGY. 
 
 which is allowed to fall from any desired height. Its fall may- 
 be arrested by choking the exhaust by the automatic opera- 
 tion of the valves so that rapid rebounding blows may be 
 struck. See figure 43 and page 54. 
 Anvils. 
 
 The anvil with its foundations constitutes one of the most 
 expensive portions of a forge plant. The anvil of the 125- 
 ton hammer at South Bethlehem, Pa., copied from that shown 
 in figure 42, weighs about 1600 tons. 
 
 In order to avoid the effects of vibration, the foundations 
 of the anvil should be independent from those of the hammer. 
 
 The anvil proper, like the tup, is generally flat, but both 
 may be of various forms required by the shape of the work. 
 Small work is thus produced with great exactness by being 
 stamped between dies. The parts of small-arms and of other 
 machines made in great quantities, such as those for sewing 
 and for agricultural purposes, are thus very economically 
 forged into very nearly their finished sizes. When of hori- 
 zontally rectangular section, the anvil is generally set with one 
 of its diagonals in the plane of the legs, so as to give room 
 opposite all its faces for handling long forgings. Figure 43. 
 
 The energy on impact being the same, the action of a heavy 
 weight moving with a low velocity is preferred, as the efi"ect 
 is more penetrating and less local. This principle is utilized 
 in Condies hammer, in which, owing to the fact that the mass 
 of the cylinder is necessarily greater than that of the piston- 
 rod, the cylinder is made movable, the piston-rod being sta- 
 tionary. 
 
 The steam may be admitted above the piston, adding its 
 pressure to the weight of the moving mass. Such hammers 
 are Double Acting. 
 
 For small work a single support, figure 43, gives sufficient 
 steadiness and more room. The valve may then be worked 
 by a treadle under the control of the smith so as to give him 
 the use of both his hands. See figure 41. 
 
XV. METALLURGY. 47 
 
 The local absorption of energy at the point of impact di- 
 minishes the reaction of the anvil, so that, as the thickness 
 of the work increases, the thoroughness of the forging dimin- 
 ishes. This requires frequent rotation of the work so that all 
 sides may be equally extended.* 
 
 For this reason Ramsbottam's duplex hammer is used, the 
 work lying between horizontal hammers moving with equal 
 and reciprocal velocities. 
 
 Anvils for hollow work. In forging hollow work, mandrels, 
 which are heavy solid cylinders passed through the forging, 
 are used in connection with the anvil proper. If supported 
 throughout its length by a V-shaped notch in the anvil, the 
 forging lymg in between, the mandrel is termed _/fj:^^/ if sup- 
 ported only and directly at its ends, the mandrel is called 
 swinging. Figures 44, 45. 
 
 The effect of forging is greatly affected by the way in which 
 the mandrel is used. Forging on a fixed mandrel extends 
 the work in length but does not sensibly affect the internal 
 diameter. Forging on a swinging mandrel increases both 
 internal and external diameters without affecting the length 
 of the work. Hence, the swinging mandrel is used for hoops 
 which are too wide for the tire-rolling machine. 
 
 Forging Press. 
 
 The defects in steam hammers above referred to will prob- 
 ably lead in time to a more general use of the hydraulic forging 
 press designed by Whitworth, Figures 44, 45. Its principal 
 advantage lies in the time during which the work is operated 
 on; this permits the molecular flow desired. t 
 
 * This is also true of rolling and limits the effective thickness of armor 
 plates. 
 
 t Opinions are divided as to the comparative merits of the hammer and 
 the press. The advocates of the hammer prefer it on the following grounds : 
 
 1. In forging solid work the effect of the hammer is greatest on the 
 exterior which is retained; and least on the interior, which for cannon 
 and heavy shafting is subsequently removed. The converse of this is 
 attributed to the press. 
 
48 
 
 XV. METALLURGY. 
 
 VI. MOLECULAR TREATMENT OF STEEL. 
 
 The quality of steel depends upon : 
 
 1. Its composition. 
 
 2. Its structure as modified by heating and cooling. 
 
 1. Composition. 
 
 Pure iron and carbon make a typical steel. But other ele- 
 ments are of necessity present in all the steels met with in 
 practice. 
 
 Pure carbon steel is here discussed. 
 
 2. Structure. 
 
 Changes in structure from the effects of heating and quench- 
 ing steel appear to be associated with changes in its density 
 and also in the state of the contained carbon. What relation 
 exists between the change in state of the carbon and the 
 change in the structure of the steel is still uncertain. 
 
 States of Carbo7i. 
 
 Indeed, the precise nature of the states of the carbon, 
 although much experimented upon and discussed, is not 
 definitely known. As an indication of the uncertainty in 
 this matter, and also of the idea which most theories contain, 
 the following suppositions may be referred to. 
 
 The carbon is supposed by Professor Abel to be either in 
 the condition of an alloy, or of a diffused carbide. Another 
 chemist calls it diamond, or dissolved carbon. Others, and 
 the more recent authorities, waive this issue by calling it 
 ** hardening " or " cement" carbon. See page 18. 
 
 Avoiding any specific hypothesis, we may designate these 
 states respectively as Fixed or Free, The former name, as 
 
 2. The prolonged contact with the dies of the press chills the forging, 
 the initial temperature of which therefore must be excessive ; while the 
 blows of the hammer are heating. 
 
 3. Hammering exposes superficial defects while pressing conceals them. 
 The 1 25-ton hammer, page 46, is intended for forging armor plates, 
 
 the quality of the surface of which is most important. 
 
3tV.— METALLURGY. 49 
 
 the preceding nomenclature would indicate, corresponds to 
 the hard condition of steel, resembling that of white cast iron ; 
 and the latter to its softer condition, resembling gray iron. 
 See Bloxam, middle Art. 220. 
 
 BrinelVs Experiments, 
 Method. 
 
 The accompanying diagrams, Figure 46, are principally 
 based upon a long series of experiments made by a Swedish 
 engineer, J. A. Brinell, upon the changes in the structure of 
 steel due to heating it in diiferent temperatures and cooling it 
 at different rates. His results appear to agree well with those 
 of others. His method was : 
 
 I. To heat separate bars of the same steel, but of varying 
 structure, up to certain temperatures indicated by the color 
 of the hot metal,* and then to cool them in one of two ways : 
 
 1. Slowly in ashes, called herein cooling. 
 
 2. Suddenly in cold water, called herein quenching. 
 
 n. To examine a freshly fractured surface, the fracture 
 being similarly produced in all cases. 
 
 HI. To subject the steel after cooling or quenching to a 
 chemical test as to the state of the carbon contained. 
 
 Classification of Fractures. 
 
 The recognition of fractures, like that of colors due to cer- 
 tain temperatures, requires great experience, but the principal 
 fractures may be designated by symbols, as follows ; 
 
 Structure. Crystalline. Granular. 
 
 i Coarse, A. D. 
 
 Symbols. \ Intermediate, B. E. 
 
 ( Finest, C. F. 
 
 Aspect, glistening, dull. 
 
 The most important is F, which may be called amorphous^ 
 
 *The irisated colors in figure 46 are the chameleon tints of the 
 films of iron oxide of different thickness, which result when a 
 polished steel surface is moderately heated. 
 
50 XV.— METALLURGY. 
 
 the crystals or grains being invisible to the naked eye. The 
 intermediate and various composite fractures described by 
 Brinell are not noted herein. 
 
 Characteristics of Fractures. 
 
 A, B, C, are relatively soft. 
 D, E, F, are relatively hard. 
 A, D, have low density (open grain) and are weak. 
 C, F, have high density (close grain) and are strong. 
 Therefore, C has softness and strength ; it is extensible. 
 This fracture is sought in annealing. 
 
 Therefore, F has hardness and strength ; it is inextensible. 
 This fracture is sought in hardening. 
 F has the maximum density. 
 
 DIAGRAMS. 
 
 Explanation. 
 
 Figure 46 illustrates the changes in structure and state due 
 to heating and either cooling or quenching the steel experi- 
 mented on by Brinell. The axis of each diagram intersects a 
 common scale of temperatures which, for any particular grade 
 of steel, are indicated by the accompanying colors. 
 
 The temperature W is critical in its effects on structure and 
 state : it is the only high temperature at which, without having 
 been exceeded, if steel be que7iched, the resulting fracture will be 
 amorphous, F. The lower the grade of steel, the higher is the 
 temperature corresponding to F, and conversely. The cor- 
 responding color must be determined empirically for each 
 grade, and, for important work, even for each ingot of steel. 
 
 The steel used by Brinell had about 0.50 per cent, carbon, 
 such as is used for cannon. 
 
 Each diagram represents a group of experiments upon bars 
 in which the same structure had been previously produced by 
 the methods indicated above. An ordinate along the axis 
 represents the temperature to which a piece of steel was 
 heated ; the abscissa to the left represents roughly the result- 
 
XV. — METALLURGY. 51 
 
 ing coarseness of structure. The character of the structure is 
 indicated by reference letters. The extremities of abscissae 
 so determined are connected by a line indicating whether, 
 after heating to the desired extent, the bars were quenched or 
 cooled. 
 
 'Quenching is represented by a full line . 
 
 Cooling is represented by a wavy line'-^^_^'^,^_^'^.^^ . 
 
 The dotted line to the right of the axis represents roughly 
 by its abscissae the state of the carbon at different temperatures, 
 its relative freedom being represented by the corresponding 
 abscissae of the dotted hne. 
 
 Interpretation. 
 
 Study of the diagrams will show that — • 
 
 At W quenching always gives F and fixes carbon. 
 
 At W cooling always gives C and frees carbon. 
 
 Below W the crystalline structure does not change. 
 
 Below W the granular structure gradually becomes finer. 
 
 Below W the amorphous structure gradually becomes 
 coarser (the only change possible). 
 
 Above W all structures gradually become coarser, being 
 crystalline if cooled, and granular if quenched. 
 
 The change of carbon from free to fixed is sudden and is 
 called hardening. 
 
 The change of carbon from fixed to free is gradual. If 
 partial, it is called tempering, and if total, it is properly 
 termed annealing. 
 
 Crystalline structure is associated with free carbon. 
 
 Granular structure is associated with fixed carbon. 
 
 Conclusions as to the Treatment of Steel. 
 
 1. After forging a cutting instrument or spring, it must be 
 hardened so as to fix the carbon, as a necessary preliminary 
 to its gradual release by tempering. 
 
 2. In tempering hardened steel, the less it is heated the less 
 
52 XV. — METALLURGY. 
 
 is its structure affected; and the less is the change in the 
 state of the carbon. 
 
 8. The fixed state is the more stable, so that it takes time 
 to change it throughout the mass without exceeding the de- 
 sired temperature externally. Such an excess would affect 
 the structure of the over-heated parts. The metallurgical 
 term soaking aptly illustrates the manner of heating steel 
 from which the best results are obtained. 
 
 The effects due to a given temperature may, however, be 
 produced by exposing the steel to a lower temperature for a 
 longer time than usual. Many of the following apparent 
 exceptions to the general rules appear to depend upon the 
 question of time. 
 
 4. The carbon having been freed by slow heating, the rate 
 of the cooHng below W is indifferent unless the mass of the 
 piece be so great as to cause the structure to change from the 
 prolonged action of its internal heat. 
 
 5. If W be exceeded the effect on structure of hardening is 
 lost, and the steel must be cooled below W and re-heated to 
 W to refine it. 
 
 Use of the Term, Temper. 
 
 Much confusion has followed the loose use of the term 
 temper. Besides being applied to the grade of steel, it is also 
 commonly used to indicate hardening; whereas we see that — 
 
 Hardening is produced by quenching at W and fixing the 
 carbon. 
 
 Tempering is a mitigation of the hardness above produced 
 which follows from subsequently heating steel to some tem- 
 perature below W, the proportion of the carbon thus freed 
 depending on the temperature attained. Whether the steel 
 should then be cooled or quenched depends upon the mass 
 of the piece. It is usually quenched. 
 
 Annealing properly consists in cooling at W so as to free 
 all the carbon possible and to destroy the effects of harden- 
 
X'V. — METALLURGY. 58 
 
 ing. But it is also a term commonly applied to the cooling 
 below W of steel, whether previously fully hardened or not. 
 According to the temperature attained and to the time taken 
 to cool the piece, it is softened and freed from internal 
 strain. 
 
 Bate of Cooling. 
 
 The brittleness and the hardness of steel will be increased 
 by increasing the rate of cooling from W, either by quench- 
 ing in mercury, or in water the conductivity of which has 
 been increased by acidulation or by the solution of a salt. 
 The same effect is obtained by using water at a low temper- 
 ature, or by frequent changes of the particles in contact, by 
 motion either of the metal or of the water. 
 
 By reducing the rate of cooling as by the use of oil or 
 tallow, the effect known as oil hardening is produced. Its 
 effect is intermediate between C and F, and is probably largely 
 mechanical, the sudden cooling of the external layers prevent- 
 ing the expansion of the internal mass during subsequent 
 attempts at crystallization. This limits the size of the crystals 
 formed and increases the strength of the metal; but it pro- 
 duces some internal strain which may be relieved by temper- 
 ing at a low heat. The charred oil next to the surface, like 
 the scale, tends to delay cooling. 
 
 EFFECTS OF FORGING, 
 
 Above W. 
 
 Except when in small masses steel is generally heated above 
 W in order to give it the plasticity required for forging. In 
 this case the crystals are not supposed to be destroyed but to 
 be softened and expanded by the heat. Having been further 
 disturbed by the hammer, they are supposed on cooling to 
 assume the sizes and shapes due to the temperature at which 
 they have been worked, with intervals between the crystals 
 depending on the treatment received. Free crystallization 
 thus implies porosity and a diminished density, which is 
 further diminished by heavy forging at a high heat. 
 
M XV. — METALLURGY. 
 
 Owing to the tendency of the crystals to shde over their ad- 
 jacent surfaces, a heavy blow may cause the fracture of over- 
 heated steel. It may indeed fall to pieces in the fire. But, 
 if such steel be lightly and rapidly hammered over its entire 
 surface, the effect will resemble that due to agitating a crystal- 
 lizing solution (Bloxam, Art. 38), m the reduction of the size 
 of the crystals and in the increased strength of the material. 
 
 This effect having been attained, further forging at a lower 
 temperature tends to form the piece and to distribute locally 
 any cavities which may exist. 
 
 In forging gun work the ingot is reduced in thickness about 
 one-half; the reduction being greatest for those portions of 
 the gun that lie nearest to the bore. 
 
 Wa/er Annealing. Owing to the difficulty of penetrating 
 large masses of metal by the vibrations of the hammer, the 
 greater part of the metal treated as above will be, when cooled, 
 like A or B or a combination of both. When the size of the 
 piece permits, one remedy proposed is to re-heat slowly to W, 
 to quench so as to prevent free crystaUization, and, as soon 
 as the temperature falls sufficiently below W, to remove the 
 steel from the water and allow it to cool slowly in air. See 
 Diagrams IV and V. The internal heat removes internal 
 strain. Railway axles are thus treated, the process being 
 called "water anneaUng." 
 
 The structure of a steel casting may be improved by heat- 
 ing it to W and cooling it slowly. 
 
 Forging Below W. 
 
 When the hammer is of sufficient power, the best effect will 
 be attained by forging just below W. The crystals are sup- 
 posed not to be much expanded by this heat ; but, being 
 softened, they may be compacted so as to destroy the porosity 
 due to free crystallization. This treatment gives the highest 
 density attainable, viz., 8.0; the steel resists the file, has a 
 
XV. — METALLURGY. 6B 
 
 waxy fracture, and yields a beautifully veined surface when 
 etched.* This work requires hammers of great power when 
 large masses are thus forged. 
 
 The experience of all steel makers tends to show the ad- 
 vantage of forging at as low a temperature as possible. Work- 
 men incline to over- heat the steel so as to diminish their labor, 
 — but this should be avoided. 
 
 A very fine quality of steel wire made in England by Stubbs 
 and much used for making drills and fine tools is said to be 
 made by being forged between semi-cylindrical dies by a light 
 "pony" trip-hammer running with very great rapidity. The 
 temperature required is attained by the hammering. 
 
 INTERNAL STRAINS. 
 
 These arise from differences in the rate of cooling through- 
 out the mass, being increased in large masses by the deficient 
 conductivity of hot metals. It thus requires much experience 
 to judge of the internal temperature from the appearance of 
 the outside of the mass. 
 
 These strains increase with the maximum temperature at- 
 tained, being greatest in the ingot. 
 
 They also increase with the area of cross section of the mass, 
 so that it is well to defer the hardening until the pieces are as 
 nearly as possible of their finished dimensions. 
 
 Uneven forging produces "hammer strain" which is re- 
 Heved by annealing. 
 
 Difference in section causes differences in rate of cooling, 
 so that it is well to quench the thicker portions of irregular 
 masses first. 
 
 Other things being equal, internal strain increases with the 
 grade of steel. 
 
 * This is probably the original Damascus steel, which has been imitated 
 by the moderns by twisting together and welding wrought iron and steel 
 as in shot-guns. 
 
56 XV. METALLURGY. 
 
 VII. GUN CONSTRUCTION. 
 
 I. BUILT-UP GUNS. 
 
 The operations are substantially as follows : 
 
 Casting Ingot. 
 
 For forgings such as tubes and jackets the ingot is often 
 cast square, as shown in Figure 25. For short pieces like 
 hoops, it is sometimes cylindrical. In order to obtain solid 
 metal and to free it from slag, sand and other impurities a 
 given amount of the top and bottom of each ingot is cut off 
 and discarded during the process of forging. 
 
 The ingot is sometimes cast hollow. But this is objection- 
 able, for it transfers the unsoundness found in the centre of a 
 solid casting to the middle of the walls of the gun. 
 
 Coring. 
 
 The ingot may then be trepanned by a sort of cylindrical 
 saw by which a solid core is removed. This rapidly removes 
 the more porous portions of the ingot, which are in a more 
 valuable form for minor purposes than the shavings from 
 ordinary boring. This operation sometimes precedes and 
 sometimes follows the forging, depending upon what tools the 
 plant affords and also upon the size of the gun. 
 
 Forging. 
 
 For solid ingots the work is constantly rotated during 
 forging by means of the porter-bar, which is a long handle 
 clamped to the tong-hold. A sling chain around the drum 
 forms a fulcrum. Man or steam power is used according to 
 the size of the work. 
 
 Cored tubes and jackets are forged on a fixed mandrel to 
 approximately their finished dimensions. 
 
 Blanks for hoops are cut off the ingot and upset, or hammered 
 lengthwise into a cheese-like form. After punching they are 
 treated as described page 44, or, instead of rolling, they are 
 
XV. — METALLURGY. 57 
 
 forged on a mandrel. The choice of operations depends on 
 the length of the hoop and the facilities available. 
 
 After every operation the piece is carefully chipped by hand 
 to remove/////?, seams and cold shuts. 
 
 Treatment and Tests. 
 
 The term treatment applies to the methods employed to 
 affect the structure of steel, viz., annealings hardening and 
 re-annealing. The sequence of the tests is important. 
 
 The *' hammer strain" is relieved by annealing. Annealing 
 also facilitates the reduction by cutting tools to the rough- 
 finished sizes required for oil-hardening. 
 
 After annealing, tests of the metal are made to discover its 
 characteristics, and thus, to a certain extent, to regulate its 
 subsequent treatment. 
 
 The pieces are then rough-bored and turned to nearly their 
 finished size. 
 
 They are afterwards oil-hardened (generally called "oil- 
 tempered") by being uniformly heated to W in a furnace 
 constructed with reference to the shape of the heated piece, 
 e.g. tubes in a vertical flue, through many ports in the sides 
 of which flame enters tangentially and hoops in an ordinary 
 low furnace. Each piece is then immersed with its axis 
 vertical in a large tank of oil, holding many tons. 
 
 The tank is surrounded by a jacket through which a stream 
 of water flows with required velocity. The oil is also caused 
 to circulate by suitable arrangements. 
 
 The pieces are re an?tealed * to remove the internal strain 
 due to hardening. For this they are slowly heated to a low, 
 red heat and allowed to cool very slowly. This heat improves 
 the structure, but may slightly reduce the strength of the 
 metal. 
 
 * This is properly tempering. 
 
XV. — metallurgy; 
 
 Tests of the metal are again made to see if it fulfils the 
 necessary requirements. 
 
 Assembling. 
 
 The parts are then turned and bored to finished dimensions 
 and assembled by shrinkage, the interior diameter of the out- 
 side cylinder to be assembled being finish-bored to the diam- 
 eter prescribed for the contact surface, and the exterior diam- 
 eter of the surface upon which it is to be assembled being 
 turned to the excess prescribed for the shrinkage. The eff"ect 
 of the shrinkage, which follows the heating of the outer 
 cylinder so that it may pass over the inner one, is sometimes 
 to bring the surfaces in contact within the range of molecular 
 cohesion. This phenomenon may sometimes be seen even 
 between cold bodies. When the steel plugs, used to gauge 
 the calibre of small-arms, being chemically clean, enter forci- 
 bly a clean bore, they are sometimes lost through ''freezing." 
 
 The hoops are secured by being screwed together, but 
 preferably by interlocking projections that slip by each other 
 when expanded by heat, figure 47. 
 
 The policy of our government with regard to gun con- 
 struction has been to obtain from private manufacturers the 
 forgings rough-bored and turned, and to finish and assemble 
 the various parts in its own shops. 
 
 IL STEEL CAST GUNS. 
 
 Objections. 
 
 The economical advantages of this process, which consists 
 in making the gun of a single steel casting after the manner 
 formerly adopted for cast-iron guns, are off'set by the follow- 
 ing objections: 
 
 I. Mechanical. 
 
 1. The enormous increase of the masses to be handled due 
 to the weight of the sinking head, which, unless its functions 
 can be replaced by other means, may weigh almost as much 
 as the ingot itself. 
 
XV. — METALLURGY. 
 
 A Steel-cast gun weighs, in the rough, about 3 times as 
 much as the heaviest ingot required for a built-up gun of the 
 same calibre. 
 
 2. The difficulty of making molds strong enough to retain 
 the high columns of metal required by modern powder. 
 
 3. The loss in cutting up the sinking head, for re-melting 
 or in disposing of failures. 
 
 II. Constitutional. 
 
 1. The vesiculation, impossible to correct by forging. 
 
 2. The effect on crystallization due to slow cooling, also 
 impossible to correct by forging. 
 
 3. The segregation of elements of different densities in 
 cooling. 
 
 4. The internal strains developed in cooling castings which, 
 for the heaviest guns, cast hollow, would possibly be 60 or 
 80 feet high, with walls 3 or 4 feet thick. If cast solid, this 
 thickness would be increased. 
 
 Remark. This class of objections may possibly be over- 
 come with increased experience in the treatment of the fluid 
 metal, and by annealing the gun after casting. 
 
 Such experience must be costly, for it can be acquired 
 only by dealing with masses approximately as great as those 
 of the guns themselves. 
 
 III. Structural. 
 
 1. The impossibility of making physical or chemical tests 
 of internal specimens. 
 
 2. The impossibility of adapting the composition of con- 
 centric parts to their specific functions by the principle of 
 *' Varying Elasticity," to be hereafter discussed. 
 
 3. The neglect of the principle of "Initial Tension" by 
 which the inner parts may, by preliminary compression, be 
 prepared for the strain of extension on firing. This principle 
 is ilhistrated when a blacksmith shrinks on a tire. 
 
 IV. Historical. 
 
 1. Krupp's original guns, which were massive forgings, 
 
CO XV. — METALLURGY*. 
 
 have been gradually replaced by guns of increasing com- 
 plexity of structure. 
 
 2. The only recorded failures in built-up guns have occurred 
 in the large masses constituting the tube ; sometimes when 
 unsupported, as in the chase; or when imperfectly supported, 
 as when a steel tube was surrounded by a jacket of ductile 
 wrought iron. This, having been expanded beyond its elastic 
 limit, failed to support the tube, which, on further firing, 
 cracked. 
 
XVI. — PROJECTILES. 
 
 CHAPTER XVI. 
 
 PROJECTILES. 
 
 Definition. 
 
 Functionally speaking, a projectile is a vehicle for the 
 transfer of energy to a disconnected object. 
 
 The energy transferred may be wholly kinetic, as when 
 the projectile acts by impact only. It may be wholly potential, 
 as when the kinetic energy of the envelope of the mass may 
 be neglected in comparison with the potential energy of its 
 contents. And it may be of both kinds, as when the kinetic 
 energy of the envelope is considerable. 
 
 SECTIONAL DENSITY. 
 
 On account of the work done on the intervening resist- 
 ances, the energy actually transferred to the object will 
 always be less than that originally imparted to the projectile. 
 
 The resistance to penetration offered by the intervening 
 medium and the object, other things being equal, varies 
 directly with the area of cross-section, a^ at right angles 
 to the trajectory. Let us call, d, the diameter of the circle 
 
 whose area is, «, and F=f—- — the total resistance causing 
 
 retardation. 
 
 The retardation, which for a given projectile is propor- 
 tional to the loss of energy per unit of path, will, for differ- 
 ent projectiles meeting the same resistance, vary inversely 
 with the mass of each projectile; or, calling; 
 
XVI. — PROJECTILES. 
 
 p, the retardation in the direction of the axis of Xj 
 M, the mass of the projectile; 
 E, the energy in the direction of X; 
 we have, neglecting variations in g; — 
 
 _dE \ _gp7t d"^ _ d^ 
 
 ^~"d^"M~ ~T~ 'W^W* (-^^ 
 
 in which k, is some function of the pressure per unit of area, 
 
 /, which pressure will vary with the veloucity, the meridian 
 
 section and the nature of <^he surface of the projectile.* 
 
 d^ 
 The ballistic coefficient^ or coefficient of retardation ^2,^ -— 
 
 is called, may therefore be used to compare the inherent 
 
 capacities of projectiles for retardation; and the reciprocal 
 
 W 
 of this expression, or —-^ which is called the j-^<r//^^/dr/^<?;zj/(>', 
 
 may be used to compare their inherent capacities to over- 
 come resistances. In English measures ^is taken in pounds, 
 and d in inches. 
 
 VARIATIONS IN SECTIONAL DENSITY. 
 
 Causes. 
 
 The sectional density of a projectile may be increased as 
 follows: — 
 
 I. If the dimensions are constant, by increasing the mean 
 density. 
 
 II . If its mean density is constant, by varying its dimen- 
 sions, viz. : — 
 
 * Since the form and dimensions of a projectile are independent of its 
 velocity, and since the effect upon p of variations in the meridian section 
 and the nature of the surface is small compared with those which result 
 from changes in its diameter and weight, and disappears when similar 
 projectiles are compared; we may for the present consider, k, for any pro- 
 jectile as constant, so that the value of p may be considered to vary only 
 With the relation between d^ and W% 
 
XVI. — PROJECTILES. 
 
 1. If its proportions are constant, by increasing its calibre; 
 since w varies as d^^ while a varies only as d}. 
 
 2. If the calibre is constant, by increasing the weight. 
 
 3. If the weight is constant, by decreasing the calibre. 
 All these changes virtually lengthen the projectile. 
 
 Effects on Flight. 
 
 Increasing the sectional density of a projectile which has 
 a given initial velocity increases its range and penetration, 
 since the loss of energy over a given path is diminished. It 
 may also increase its accuracy, since the time of flight over 
 a given path, and therefore the effect of various perturbat- 
 ing causes may be diminished. The penetration is still 
 further increased by increasing the indeformability of the 
 material of which the projectile is composed, so that the 
 work of deformation on impact may be done rather by the 
 projectile, than upon it. 
 
 But, owing to the non-coincidence of the centers of mass 
 and of the area exposed to the resistance of the air, 
 during the flight of an oblong projectile a couple is formed 
 which tends to cause the projectile to tumble or revolve 
 about a transverse axis. This diminishes its sectional den- 
 sity and makes it variable. Such projectiles are therefore 
 given the rifle motion, which impresses upon them sufficient 
 angular velocity about the longer axis to make this a stable 
 axis of rotation, and therefore to make their sectional den- 
 sity constant and a maximum. The same reason applies in 
 a less degree to spherical projectiles, in which the centres 
 of mass and of figure can rarely be made to coincide. 
 
 Effect upon the Gun. 
 
 Increasing the length of an oblong projectile increases 
 its tendency to tumble, and hence requires a greater energy 
 of rotation. This diminishes the kinetic energy of transla- 
 tion due to the conversion of a given charge. In a certain 
 
XVI. — PROJECTILES. 
 
 sea coast rifle the rotary energy amounts to about 0.01 of 
 the total muzzle energy. 
 
 Also, since increasing the sectional density increases the 
 mass to be moved per unit of sectional area, a given accel- 
 eration requires an increase in the intensity of the gaseous 
 pressure per unit of area. Therefore, since V=/adt, to 
 obtain a given initial velocity with a projectile of which the 
 sectional density has been increased, the stress upon the 
 gun must also be increased unless special provision be made 
 by the methods indicated in Chapter XI. 
 
 Owing to the weakness of cannon in use when the rifle 
 principle was first applied, the increase in sectional density 
 required a reduction in the initial velocity; this, although 
 compensated for by greater accuracy and longer ranges, 
 caused the initial portions of the trajectory to be more 
 curved than with the spherical projectiles formerly em- 
 ployed. See Chapter I. Consequently, the general adoption 
 of oblong projectiles was delayed until the necessary im- 
 provements in the gun and its ammunition had been per- 
 fected. See Chapter XIII. 
 
 Comparison of Forms. 
 
 Although the oblong form is universally employed in new 
 constructions, the following comparison illustrates some of 
 the reasons influencing and opposing the change of form. 
 
 Advantages of Oblong Projectiles, 
 
 The form, capacity and sectional density may be altered 
 indefinitely, with the advantages noted in the text. The 
 following incidental advantages also exist: 
 
 Projectiles of the same caliber, but of different natures, 
 or mean densities, may be made of the same weight; so that 
 they may be fired at the same ranges with the same angles 
 of projection. 
 
XVI. — PROJECTILES. 
 
 The oblorg form facilitates the operation of fuzes which 
 act by impact; since the poinf-. and direction of the impact 
 can be predicted. 
 
 Disadvantages of Ohlofig Projectiles. 
 
 The centers of mass and of pressure do not coincide; 
 they are more expensive; the liability to injury of the soft 
 metal device by which they are rotated requires greater 
 care in their transportation and may interfere in their 
 loading; in ricocheting over land or water their rebounds 
 are much less certain and regular, both in altitude and 
 direction. The rotation of rifled projectiles of the explosive 
 class tends, upon bursting, to scatter their fragments unduly 
 beyond the plane of the trajectory. The curvature of the 
 trajectory at short ranges is increased. 
 
 MATERIAL. 
 
 The principle of sectional density mainly determines the 
 selection of the proper material for a projectile, with regard 
 to its behavior in the gun, in the air, and upon the object. 
 
 Its application is so apparent that only a few of the minor 
 properties of the materials employed will be mentioned. 
 
 Stone was employed originally in catapults and continued 
 to be used in cannon by the Turks as late as 1807. 
 
 Lead is suitable for use against animate objects only, since 
 in large cannon it is disfigured and even partially melted. 
 
 Wrought Iron in large masses is expensive, as it requires 
 welding and forging; it is also too soft. 
 
 Cast Iron was until recently exclusively used for artillery 
 projectiles on account of its fusibility and its small original 
 cost. When cast in molds, so that the point cools in con- 
 tact with a cast iron chill, while the body cools more slowly 
 in sand, its local hardness, crushing strength and density 
 are greatly increased, without causing brittleness in that 
 
XVI. — PROJECTILES. 
 
 portion cooled in the sand. Against the wrought iron armor 
 formerly employed, such projectiles are indeformable; but 
 they are pulverized against the steel-faced and chilled iron 
 armor of the present day. For ordinary purposes cast iron 
 is still generally employed. 
 
 Steel possesses all the qualities required in a projectile, 
 but is costly. It is used in two forms, both of which are 
 usually oil-tempered. 
 
 1. Forged; including for special purposes, rolled or drawn 
 steel tubes. This form of steel, especially when alloyed 
 with chromium, is so far the best, but the most costly. A 
 9 inch Whitworth forged steel shell, costing $100, or 12 
 times as much as a similar projectile of chilled cast iron, has 
 been fired three times through wrought iron 12 inches thick. 
 
 2. Steel cast projectiles have, owing to their greater cheap- 
 ness, been much experimented with; but, for the reasons 
 given in Chapter XV, have so far proved inferior to those 
 that are forged. 
 
 SPHERICAL DENSITY. 
 
 W 
 Since the sectional density, -— , of similar projectiles in- 
 creases with the caliber, if we divide the sectional density 
 
 W 
 by the caliber we shall obtain a constant, -73-, which expresses 
 
 the weight per unit of volume of a cube whose weight is 
 equal to that of the projectile and whose height is equal to 
 the diameter of the bore. This is taken as the measure of 
 the spherical density of the projectile. 
 
 Since all spherical solid shot of the same material are simi- 
 lar, their spherical density is constant, and may therefore be 
 taken as the unit by which to measure the spherical density 
 of oblong projectiles of the same material. 
 
 Expressing the spherical density by S^ and the weight in 
 
XVI. — PROJECTILES. 
 
 pounds of a unit of volume of the material by S, we have 
 for a spherical solid shot, of which the volume is F, 
 
 (7)'- 
 
 ci^ d' ~3 \d J ~ 3 8* 
 
 For projectiles made of iron, 6 may be taken as % pound, 
 and 7t may be taken approximately as 3.0; therefore 
 
 ^., _ _ _ c, 
 
 and for an oblong iron projectile in terms of S^^, 
 ^ _W' 1 _ 8 W 
 
 S^i, therefore, expresses the effective increase in density 
 that arises from elongating the projectile. 
 
 We might proceed similarly with other materials having 
 different values of 6; but it is convenient to retain iSg} as a 
 common standard; so that, in general terms, S may be taken 
 to measure the number of times that the mass of the inscribed 
 solid iron sphere is contained in that of the projectile con- 
 sidered. 
 
 Unless the caliber be fixed, the spherical and sectional 
 densities of projectiles vary independently of each other. 
 
 The spherical density of the first oblong projectiles used in 
 cannon in 1859, was about 2.0; but recent improvements in 
 guns, powder and projectiles have increased it from about 3.0 
 m 1880, to about 4.5 in 1887, the muzzle velocity not being 
 correspondingly reduced. 
 
 If all projectiles made of the same material had the same 
 mean density and the same form, their spherical densities 
 would be a function of their lengths. But as such is not the 
 case, their length is independently stated, generally in cali- 
 bers. In fact, the caliber is getting to be taken as the general 
 unit of measure of all the linear dimensions relating to the 
 interior of the piece. 
 
 dim'B.t^' 
 
XVL — l^ROjECTtLEg. 
 
 Corollary, 
 
 Referring to the discussion on page 7, we see that the 
 weight in pounds of a sohd spherical cast iron projectile is 
 very nearly equal to the cube of its radius in inches. This 
 affords an easy method of approximating to the weight of 
 an oblong projectile when the type of gun from which it is 
 to be fired is known. 
 
 RIFLING. 
 
 History. 
 
 The invention of rifling by Gaspard Zoller of Vienna is 
 said to have been made soon after the discovery of America. 
 The first rifle grooves were made straight, and intended only 
 to facilitate the loading of tightly fitting bullets. The advan- 
 tages of the spiral groove, which were accidentally dis- 
 covered, were not applied to oblong projectiles, even in small 
 arms, until about 100 years ago, at which time the subject 
 was thoroughly discussed by the eminent mathematician 
 Eobins. It is worthy of remark that to Robins we owe the 
 first practical apparatus for the measurement of the velocity 
 of projectiles; a pendulum into which the projectile was fired, 
 and from the nwDmentum of which that of the projectile 
 could be computed. 
 
 The general adoption of the rifle principle for small arms 
 was retarded by the difliculty found in loading the rifle: this 
 w^as generally accomiplished by the blows of a mallet on a stout 
 iron ramrod. For cannon, attempts were made at an early 
 date and are frequently renewed, to impart the rifle motion 
 by the action of the gas, or of the air upon spiral grooves 
 or wings formed upon the projectile. Except for low veloci- 
 ties, all such experiments have failed to act with certainty, 
 and the end has been attained only by the positive means 
 mentioned in Chapter I. 
 
XVI. — PROJECTILES. 
 
 Twist. 
 
 The inclination of a rifle groove at any point is determined 
 by the angle which its tangent at that point makes with the 
 axis of the bore. Twist, is the term generally employed to 
 express this inclination. 
 Classification of Twists. 
 
 When the inclination of the groove to the axis of the bore 
 is constant, the twist is called Mniform. When it increases 
 from the breech to the muzzle, the twist is increasing. 
 
 Figure 1 shows the development of the surface of a bore 
 rifled with uniform and increasing twists. Such curves are 
 traced for the construction of templets, by which a combined 
 motion of rotation and translation is given to the cutting tool 
 of the rifling machine. 
 Discussion. 
 
 Let q) be the inclination of the groove at any point; and 
 oa the angular velocity imparted to the projectile from being 
 constrained to follow in the groove while moving in the 
 direction of the axis with a velocity of translation v. Let r 
 be the radius of the projectile. 
 
 We may consider the velocity along the groove to be the 
 resultant of two component velocities at right angles to each 
 other; viz.: z; and f/ tan q). The latter imparts to a point 
 on the surface of the projectile a tangential velocity 
 r Go=^v tan cp. Hence, 
 
 V 
 
 CD =z tan cp • (2) 
 
 That is to say that when the twist is uniform, the angular 
 velocity increases only with the velocity of translation 
 throughout the bore. When the twist is increasing, the 
 angular velocity further increases from this cause; and other 
 things being equal, it increases as the caliber diminishes. 
 
 Since the muzzle velocity of a given projectile is fixed by 
 independent considerations, the angular velocity at the 
 
10 XVT. — PROJECTILES. 
 
 muzzle is measured by the tangent of the angle made at that 
 
 point by the tangent to the groove and the axis. 
 
 If / be the time required to make one revolution, and n 
 
 be the length in calibers over which the projectile must pass 
 
 in order to make one revolution, we have from Eq. (2), 
 
 ODrt ^7tr 7t 
 tan ^ = -— - = --— = -. (3) 
 
 The twist is accordingly generally expressed in terms of n. 
 
 It has been found that for ordinary artillery projectiles, 
 about three calibers long, the requisite steadiness is given 
 by imparting to the surface of the .projectile a tangential 
 velocity of about 200 f. s. at the muzzle of the gun. Hence, 
 
 7t V 
 
 200 = r ci? = tan a>. F= - V .\ n—n — — . (4) 
 n 200 ^ ' 
 
 The value of n at the muzzle of the piece has generally 
 been determined empirically as above indicated; a safe 
 margin being allowed, smce no objection to a moderate in- 
 crease in twist exists but that pertaining to a diminished 
 energy of translation, and to the increased stress upon the 
 piece. 
 
 Recent analysis has determined the minimum twist at the 
 muzzle for projectiles of varying proportions. 
 
 It appears from this analysis that n is constant for similarly 
 proportioned projectiles of the same material, whatever be 
 the caliber; that it increases as the radius of gyration about 
 the axis of revolution and the density of the projectile in- 
 crease, and as the radius of gyration about an equatorial 
 axis diminishes. Also, that the above value for the surface 
 velocity is only approximate, since for the same projectile 
 this may safely diminish as the initial velocity diminishes. 
 Tangential Pressure on the Rotating Device. 
 
 Since, for the same muzzle velocity of translation, the sta- 
 bility of a given projectile depends only on the angular 
 velocity which it has acquired at the muzzle; it appears that 
 
XVI. — PROJECTILES. 11 
 
 SO far as this is concerned, it matters not whether the angular 
 velocity be acquired only through or, the acceleration of 
 translation, or through the combination of this cause with 
 the gradually increasing twist. 
 
 In the first case, the angular acceleration, will be greatest 
 at first, when the gun and the rotating device are under 
 their maximum strain, and will diminish as they become 
 relatively stronger; thus making a disadvantageous distri- 
 bution of the work of rotation, although the quantity of work 
 
 W 
 done will be constant and equal to -^ — /^/ w^ 
 
 2g 
 
 k, is taken as about 0.8 r in the linear units used for V, 
 
 In order to make this stress, particularly that upon the 
 rotating device, constant throughout the bore, so as to avoid 
 either excess or deficiency in strength, the angular acceler- 
 ation must be made constant. Herein lies the value of the 
 increasing twist; since at the breech the diminished value 
 of q) will compensate for the increased value of a\ and con- 
 versely toward the muzzle. 
 
 The determination of the precise form of the developed 
 groove is difficult, both theoretically and practically, since 
 the constancy of a depends upon the properties of the 
 powder employed. 
 
 It was thought for some time that a groove, the twist of 
 which uniformly increased with the length of the bore, and 
 having as its development a parabola, would give the best 
 results. 
 
 Recent practice indicates the advantage of employing a 
 
 semi-cubic parabola, of the form x^—2py, which, in the 
 case illustrated in figure 2, passes from a value of n=50 at 
 the breech, to n=2D at the muzzle. Figure 2 shows how 
 variously may be distributed the tangential pressures. To 
 steady the projectile on leaving the bore, it has been thought 
 
12 XVI. — PROJECTILES. 
 
 advisable to give to a short portion of the rifling neai the 
 muzzle a uniform twist. 
 
 MEANS OF ROTATION. 
 
 I. MUZZLE-LOADERS. 
 
 Classification. 
 
 The first rifled pieces were muzzle-loaders, and hence the 
 projectile was necessarily of smaller diameter than the bore. 
 Rotation was imparted to it in two general ways: 
 
 1. By making the rotating device fit the grooves before 
 firing, by providing the projectile with suitable ribs or 
 flanges. 
 
 2. By making the device fit the grooves after firing by 
 causing it to be expanded by the powder gases, after the 
 manner of the gas check. Chapter VII. 
 
 Operation. 
 
 For this special purpose, and in all cases to avoid abrad- 
 ing the grooves, the rotating device was made of a softer 
 metal than the rest of the projectile; or, if formed on the 
 body of the projectile, had given to it a large area of con- 
 tact so as to accomplish the same result. 
 
 Since the axis of such projectiles did not normally coin- 
 cide with that of the bore, they could be centered^ or made 
 concentric with the bore, only by chamfering the edge of 
 the groove giving rotation, or by some similar device, the 
 operation of which was uncertain. 
 Comparison. 
 
 Examples of the first class are shown in figures 3 and 4. 
 Those with studs were until recently generally employed in 
 Europe. The Whitworth projectile, the surface of which is 
 a twisted prism, is a type of this class. It was once distin- 
 guished, but is no longer employed in new constructions. 
 
 The principal advantage of this class is that the projectiles 
 are certain to take up the rifle motion. 
 
XVI.— PR0JECTIL1E5. 13 
 
 They require special adjustment to the gun, both 
 in manufacture and in loading; the escape through the 
 windage erodes the bore; the stud holes weaken the projec- 
 tile, and their arrangement in tiers, or the use of flanges 
 renders it difficult to adapt these projectiles to the increas- 
 ing twist. 
 
 Examples of the second class are seen in figures 5, 6, 7. 
 
 Their advantages are their adaptation to any gun of the 
 proper caliber and the facility with which they can be load- 
 ed, particularly in action. The former advantage led to 
 their general employment during the Civil War, owing to 
 the elasticity of the conditions then prevailing. Only the 
 weight and the caliber of the projectile were fixed ; so that 
 inventors were free to adopt many ingenious variations of the 
 expanding principle. This is accordingly known as the 
 American system. It answered well the demands of the 
 situation but was uncertain in its operation; the expansion 
 sometimes failing and the entrance of the powder gases be- 
 tween the body of the projectile and the rotating device 
 serving sometimes to tear this from its seat. See figure 7. 
 
 The expanding cup has sometimes been applied to pro- 
 jectiles of the first class so as to prevent the escape of gas 
 above cited. 
 
 Examples of Class II. 
 
 The Butler and Eureka systems are the principal exam- 
 ples of the second class retained for the muzzle-loading 
 cannon still in service. 
 
 The Butler System. Figure 5. 
 The distinctive feature is the double lip formed in the 
 expanding ring. The outside lip is expanded into the 
 grooves, while the inner one is pressed against the tenon 
 on the base of the projectile with an intensity proportional 
 to that of the gaseous pressure. 
 
14 XVI.— PROJECTILES. 
 
 The Eureka Projectile. Figure 6. 
 
 The base of the projectile is a frustum of a cone in which 
 the grooves, «, are cast. The expanding brass cup fits on 
 the frustum and is prevented from turning by correspond- 
 ing projections on its inner surface, and from falling off 
 during transportation by the screw plug, b. 
 
 On firing, the cup is forced forward and expanded into 
 the grooves. 
 
 II. BREECH-LOADERS. 
 
 In breech-loading cannon the chamber is of larger diam- 
 eter than the bore, and permits the use of a projectile pro- 
 vided with a compressible device. 
 
 Beside the advantages named in Chapter XI, the advan- 
 tages of this class are certainty of action, better centering 
 and the absence of windage. These qualities have caused 
 their general- adoption to follow that of the cannon in 
 which they are employed. 
 History. 
 
 Following the analogy of projectiles for small arms, it was 
 at first attempted to coat them with lead, cast over the body 
 of the projectile. But this was weak, the lead fouled the 
 bore, was easily deformed, and added useless weight to the 
 projectile when it was fired against armor. The length of 
 the bearing prevented the use of the increasing twist, and 
 the manner of applying the lead tended to alter the struc- 
 ture of projectiles of hardened steel. Such were the pro- 
 jectiles used by the Germans in the war of 1870. 
 
 To overcome these objections, narrow rings or bands of 
 copper, which is much stronger than lead, were placed in 
 pairs at equal distances from the centre of gravity. Their 
 diameter was equal to the caliber measured between the 
 bottom of the grooves, or slightly greater, while that of the 
 body was a little less than that between the lafids. Such 
 projectiles required the uniform twist. 
 
XVI. — PROJECTILES. 16 
 
 To this class belongs a projectile used in the small 
 Hotchkiss cannon; figure 9. It has a thin sheet brass belt 
 about one caliber wide, compressed radially into a shallow 
 groove of equal width which is symmetrical with the center 
 of gravity. The surface of the groove is circumferentially 
 fluted, as seen in figure 9. When the piece is fired the 
 powder gases press the band into the flutings, forming a 
 series of rings, figure 10, which permit the metal to flow 
 backward as the band takes the rifling. These bands are 
 much cheaper to make and weaken the projectile less than 
 the solid rings formerly employed in these projectiles. 
 This ingenious method is confined to small calibers. 
 Present Practice. 
 
 The increasing twist now used in all large cannon re- 
 quires a narrow bearing, which, to diminish the effect of the 
 oblique action of the powder gases is situated in rear, at 
 such a distance from the base of the projectile as to give 
 sufficient shearing strength to that portion lying in rear of 
 the band. 
 
 To center the projectile a second band was formerly 
 placed in front, but this has been replaced by a very slight 
 enlargement of the body of the projectile near the base of 
 the head. Figure 21. 
 Position of the Eotating Band. 
 
 Although, for ease in loading, the difference of diameter 
 between the front bearing and the lands is made as small as 
 is safe; unless certain precautions are taken, the oblique 
 action of the powder gases — in a manner not thoroughly 
 understood — may set up a nutatory or oscillating motion 
 as the projectile travels through the bore. This leads to 
 inaccuracy, reduces penetration, and may even leave the 
 marks of the rifling on the front portion of the projectile. 
 
 To diminish this effect, the front and rear bearings should 
 be made the loci of conjugate axes of suspension and oscil- 
 
16 XVI. — PROJECTILES. 
 
 lation. When the position of the front bearing is determined 
 by the shape of the projectile, this can be accompHshed by 
 swinging the projectile as a pendulum on a diameter of the 
 front bearing, and ascertaining the time, /, of one vibration. 
 Then the band should be placed at a distance from it, 
 
 I = g l—\ since f=7t\/ — {Michie^ Eq. 404.) 
 
 In order to diminish the effects of the oscillation in pro- 
 jectiles in which, from unavoidable differences in manufac- 
 ture, the method above described does not suffice, the width 
 of the rotating band should be made as great as the nature 
 of the twist permits. It is usually taken as about one-tenth 
 of the caliber. 
 
 LONGITUDINAL SECTION OF THE PROJECTILE 
 
 Profile. 
 
 The value of k in Eq. (1) depends largely upon the profile 
 of the meridian section of the projectile and the nature of 
 the surface. In the last respect breech-loading projectiles 
 of the last class have a decided advantage over those of the 
 first class of muzzle loading projectiles, since the atmocpheric 
 friction is much less. This has required revision of the 
 ballistic tables computed for the non-centered studded pro- 
 jectiles for which these computations were originally made. 
 
 The resistance of the air is not affected by the form of 
 the extreme point, which, even if flat, is supposed to carry 
 along with it a pointed core of compressed air; but the cur- 
 vature of the head of the projectile is of great importance 
 in that it affects the passage of the stream lines of air past 
 the shoulder^ as is called the circle of tangency between the 
 head and the cylindrical portion of the projectile. The cur- 
 vature of the head is expressed by the length of the radius 
 of curvature in calibers. This varies from 1.5 to 2.0 calibers. 
 
XVI. PROJECTILES. 17 
 
 The form of the base is also of importance, in that, if also 
 curved, it facilitates the flowing of the compressed air into 
 the vacuum formed in rear of the projectile and so diminishes 
 the difference of pressure upon the two extremities of the 
 projectile ; to which difference the retardation is principally- 
 due. Examples of this may be seen in the Whit worth pro- 
 jectile and in the Hotchkiss projectile, already described. 
 This advantage is not generally utilized, as it tends to diminish 
 the sectional density, the strength of the base, and the facility 
 of manufacture and of stowage. 
 Mass. 
 
 The mass of the projectile should be distributed so as to 
 bring the center of air pressure as close as possible to the 
 center of mass so as to diminish the overturning moment of 
 the resistance of the air. This is a difficult matter, as the 
 direction of the pressure is constantly changing; it is there- 
 fore adjusted empirically by firing projectiles so weighted 
 that the position of the center of mass may be varied 
 
 INFLUENCE OF THE CALIBER. 
 
 Following the principle of similitude by which cannon of 
 the same class vary their linear dimensions in a given ratio 
 to their calibers, it appears: — 
 
 1. That the muzzle energy varies with the charge of 
 powder, or as the cube of the caliber. 
 
 2. That the capacity to convey this energy to a distance 
 varies as the first power of the caliber. 
 
 3. That the terminal energy varies as a power of the caliber 
 which increases from about 3 at the muzzle to about 4 at the 
 extreme range of the smaller of two pieces considered. 
 
 STRUCTURE AND MODE OF OPERATION. 
 
 Projectiles are classed according to their structure and 
 mode of operation as follows : — 
 
18 
 
 XVI. — PROJECTILES. 
 
 1. Solid shot, or shot, 
 
 2. Shells. 
 
 3. Case shot. 
 
 T. SHOT. 
 
 Shot are used for penetration, generally of armor and in 
 small arms against animate objects. For cannon they are 
 confined almost wholly to the sea coast service. In order 
 to diminish the effects of internal strain due to differences 
 in the rate of cooling, shot are made not wholly solid but 
 with an empty concentric cavity or core, figure 11. In such 
 projectiles the point is carefully preserved. 
 
 II. SHELLS. 
 
 The increase in sectional density resultmg from making 
 spherical projectiles solid, having been attained by a change 
 of form, solid shot are now replaced by those which are 
 hollow and whioh can therefore convey energy in a form 
 unaffected by retardation. 
 
 Shells are hollow projectiles containing an explosive and 
 generally a fuze for its ignition at any desired point of the 
 trajectory, The fuze may operate at a distance which is a 
 function of the time of flight, when it is called a time fuze; 
 or the explosion may result more directly from the arrival 
 of the projectile at the point of impact. Such are called 
 impact fuzes. Each class of fuzes, as will be seen, has its 
 special province. 
 
 The size of the cavity depends upon the specific function 
 of the projectile. If this is intended to convey energy mainly 
 in the kinetdc form, the smaller the cavity, the greater is the 
 sectional density, and the more violent is the explosive 
 required. If the energy is to be mainly potential, the larger 
 the cavity the better the effect, provided that the resistance 
 of the projectile to the shock of discharge is not unduly 
 diminished. 
 
XVI. — PROJECTILES. 19 
 
 The number ot pieces resulting from an explosion, and 
 the facility with which the bursting charge wili" operate, in- 
 crease with the brittleness of the material and with the 
 completeness with which conversion occurs before rupture 
 of the envelope occurs. Since for firing against troops frag- 
 ments below about one ounce in weight are not considered 
 dangerous, it is desirable to increase the number of fragments 
 of about this weight as much as possible and so to compensate 
 for the large, single mass formed by the base of the shell. 
 
 The sectional density of the fragments approaches con- 
 stancy and practically increases as they approach the spher- 
 ical or cubical form ; therefore, many devices have been 
 employed to regulate the rupture of such projectiles, as by 
 making the walls double, figure 12 ; by giving to the cavity 
 a polyhedral form ; or by grooving it spirally so as to dimin- 
 ish the tendency to burst in a meridian plane. 
 
 This appears from the following elementary analysis. 
 
 Tet R and r, be the exterior and interior radii of a shell, 
 the tenacity of which is T, supposed uniform throughout the 
 section. Then, for the meridian rupture of a unit of length 
 the necessary pressure will result from the equation — 
 
 2r/ = 2(i?-r)r.-./=r('^-lY 
 
 for an equatorial or transverse rupture we have 
 
 Operation. 
 
 The rupture of a shell will occur in one of the two ways 
 above indicated only when the material is thin and inelastic, as 
 in some shrapnel to be described. When, as is usually the 
 case, the projectile has thick walls (Chap. V), the inner con- 
 centric layers are more extended than those outside,they are fis- 
 sured until fracture is determined by the line of least resistance, 
 
20 XVI.'— PROJECTILES. 
 
 and the fragments are scattered by the energy remaining in 
 the gases. The resistance of the envelope should therefore 
 be kept within certain Hmits. 
 
 Shells used against armor are pointed, and are filled and 
 fuzed from the rear. They replace shot whenever possible 
 since their penetration can be made almost as great, and 
 their effects after penetrating the sides of a vessel are much 
 more destructive both to men and machinery. 
 
 Against masonry, shell serve a double purpose; first to 
 penetrate the wall and fissure it by their explosion; and 
 second, by throwing out the fragments to present a fresh 
 surface for the next blow. 
 
 Shells used against earthworks should contain the largest 
 possible bursting charges. Such are called torpedo shells. 
 They are sometimes made 6, and even 8 calibers long and, 
 owing to the vertical angle at which they strike, are fired with 
 low velocities from mortars and howitzers. 
 
 A grenade is a form of shell, generally spherical, intended 
 to be thrown by hand or to be rolled down a parapet against 
 masses of troops making an assault. 
 
 BURSTING CHARGES. 
 
 Gnnpowder. 
 
 When powder is used it is preferably of fine grain and of 
 high gravimetric density. Such powder in firing, has a 
 tendency to cake^ or become compressed into a mass of such 
 density that the removal can be accomplished only by the 
 chisel. This increases with the length of the charge and 
 evidently tends to defeat its object. 
 
 The caking, as indicated by the letters a, b, c, in figure 13, 
 results from three causes; viz.: a, from the shock of dis- 
 charge; b, from the rotation of the projectile, and <r, from 
 the shock of impact. 
 
XVI.— PROJECTILES. 21 
 
 The effect is to compress the powder and diminish its 
 inflammability. If the impact be sufficiently resisted, the 
 solidified mass may be thrown forward with such energy as 
 to cause its ignition. To diminish caking, the cavity is 
 often varnished; and to delay the explosion of armor piercing 
 shell, the bursting charge is sometimes enveloped in flannel. 
 On the other hand, where promptness is required, the French 
 place loosely in the cavity a small wooden prism, figure 14, 
 containing on two of its sides a network of oblique grooves 
 through which the gases resulting from ignition may pene- 
 trate the indurated mass. A slip of wood is tied over each 
 grooved surface to prevent the channels from becoming 
 choked. 
 
 The bursting charge has been advantageously made of 
 discs of concrete powder, strong enough to resist the causes 
 leading to a and b, figure 13, but disintegrating under the 
 influence of ignition. Such charges require to be filled 
 through a hole, the size of which is objectionable. 
 High Explosives. 
 
 Gun-cotton is not injured by caking and, when specially 
 prepared, does not readily explode on impact. This, or some 
 equivalent high explosive, appears to be required for shells 
 in which the excessive fragmentation of the envelope is not 
 objectionable. This objection may be removed by using 
 a small charge of dry gun-cotton in a shell filled with water. 
 
 A high explosive is particularly required in armor piercing 
 shells; these, if strong enough to penetrate the armor, may 
 fail to burst with the utmost powder charge whrch they will 
 contain or they may explode harmlessly before penetration 
 is complete. 
 
 The comparative insensibility of explosives of the Bellite 
 class would seem to fit them particularly to this purpose; 
 although the gx&dX force of gun-cotton makes it well adapted 
 for use against earthworks. Its explosion is said to reduce 
 
22 XVI. — PROJECTILES. 
 
 a large spherical zone of earth to a pulverulent form, by 
 which its removal, and the exposure of the masonry which 
 it is intended to protect, are facilitated. 
 
 Sizft of Cavity. 
 
 Great advantage has been found to result from increasing 
 the size of the cavity by making the envelope of the shell 
 of thin steel tubing. A 12 pound shell so made was found 
 more effective against earthworks than a 50 pound shell of 
 cast iron. To produce their full effect, such projectiles 
 require an independent steel base, concave on its interior 
 surface, so that it may be expanded against the walls instead 
 of being driven outward by the explosion before the powder 
 is entirely converted into gas. 
 
 INCENDIARY PROJECTILES, 
 
 Although the explosion of the bursting charge may suffice 
 to ignite the splintered fragments of wooden structures, 
 greater certainty in the effect results from filling the shell 
 with an incendiary composition ignited by the discharge 
 and flaming through specially constructed apertures in its 
 walls. Such projectiles, called carcasses, and also red-hot 
 shot, were formerly employed against wooden vessels. 
 
 To this class may be referred light balls, thrown at short 
 ranges to burn on the ground and illuminate the works of 
 an enemy during a siege. To prevent their extincti*on, they 
 were made to contain a loaded shell or a number of loaded 
 pistol barrels. 
 
 A more recent form consists of a shell containing a para- 
 chute which is distended when the shell explodes, and, 
 when carried over the enemy's works by the wind, illumi- 
 nates them by the light of a mass of incendiary composition 
 suspended beneath it. 
 
 For modern warfare such devices are superseded by the 
 
XVI. PROJECTILES. 23 
 
 electric light, projected from under cover by a reflecting 
 surface. 
 
 III. CASE SHOT. 
 
 Where concentration of energy upon a given point, and, 
 therefore, accuracy is required, shell, or preferably solid 
 shot are used; but where, owing to the dispersion of the ob- 
 jects and their inferior resistance the energy should be 
 distributed, as in fowling pieces, case shot are employed. 
 
 Case shot consist of a number of small projectiles, which 
 we may call the cluster, contained in an envelope; according 
 to the method of their liberation from which they are divided 
 into two classes. 
 
 1. Canister and grape shot, which separate at the muzzle 
 of the piece in consequence of the shock of discharge. The 
 general name, case, is now usually reserved for this variety. 
 
 2. Shrapnel, which separate at a distance in consequence 
 of the explosion of a small bursting charge, contained with- 
 in the envelope. 
 
 These projectiles forcibly illustrate the principle of sec- 
 tional density in regard to the behavior of the projectile as 
 a whole, and to the operation of the component parts, includ- 
 ing the fragments of the envelope. 
 Operation. 
 
 The fragments separate in what is called the sheaf, or cone 
 of dispersion, of which the mean trajectory constitutes the axis. 
 Figure 15 shows a shrapnel provided with a time fuze, burst- 
 ing in air; and figure 16 one with an impact fuze, bursting, 
 as it is called, "on graze." 
 
 The right section of this cone is circular and the horizontal 
 section elliptical. The size and form of the ellipse for any 
 section vary with the energies of the different component 
 parts, horizontally in the plane of the trajectory and normally 
 to that plane; and also with the sectional density of these 
 parts. 
 
24: XVI. PROJECTILES. 
 
 The inevitable lateral dispersion being sufficient for the 
 necessary distribution, it is sought by various means to 
 increase, at the moment of their separation, the component 
 energy of the parts in the direction of the tangent to the 
 trajectory. It is to the success of such efforts that the 
 superiority of shrapnel over case shot of Class I is due. 
 
 Case shot are generally employed against animate objects, 
 a dangerous wound to which is taken to correspond to 
 the energy required to pierce a pine board one inch thick. 
 It is convenient to remember that this requires a velocity 
 of about 500 f. s. in an ounce ball, or to an energy of about 
 one eighth of a foot-ton. A velocity of 500 f. s. is accordingly 
 taken as the limiting velocity for case shot. 
 
 For reasons given, the fragments of the envelope are in- 
 effective as compared with the members of the cluster, which 
 are generally spherical. The envelope is therefore made as 
 light as possible. 
 Structure. 
 
 But for the shock of firing, which deforms the members of 
 the cluster even to the extent of consolidation, and which may 
 even burst the envelope from the dilatation of its contents, the 
 cluster would always be made of lead. But lead is expensive, 
 and requires to be alloyed with tin or antimony; or to be im- 
 bedded in a matrix as of sulphur or rosin; or to be packe'd 
 in coal dust to resist this shock. Consequently, iron is used, 
 except when the conditions require every structural advan- 
 tage to be improved. 
 
 Iron has the further advantage in certain cases of making 
 the mean density of the case shot equal to that of the shell; 
 this permits the firing to be regulated as stated page 4. 
 
 The size of the balls depends upon the facility with which 
 the envelope may be filled, upon the material of which they 
 are made, and upon the distance at which, after separation, 
 they are required to act. 
 
XVI. — PROJECTILES. - 25 
 
 CLASS I. CANISTER AND GRAPE SHOT. 
 
 These are distinguished by the lightness of the envelope, 
 which is designed only for their transportation and loading. 
 The balls, generally of cast iron, are now much smaller 
 than before shrapnel attained its present importance. 
 
 Canister. 
 
 For smooth-bore cannon the envelope consisted of a tin 
 case supported in rear by a disc which was designed to 
 prevent the penetration of the gases into the cluster v^hile 
 within the bore. To avoid the rotation of the projectile 
 in rifled cannon, the envelope is stiffened so as to prevent 
 its upsetting or dilatation into the rifling. In the English 
 service this is done by inserting three trough-shaped pieces 
 of sheet iron around the cluster. In the United States service 
 a thin tube of malleable cast iron, closed at one end, is em- 
 ployed. This is known as Sawyer's patent. The fragment- 
 ation of this tube is assisted by spiral cuts. See figure 17. 
 
 Since canister is retained only for the extreme simplicity 
 of its operation at the short ranges at which it is employed 
 by the defence, the size of the balls has been greatly 
 diminished. 
 
 When, as in the defence of the ditches of permanent works, 
 the desired eflect is not complicated by requiring projectiles 
 of different natures to be fired from the same gun, canister 
 fire is replaced by that from machine guns. This is continu- 
 ous and does not derange the aim so much. 
 
 Grape Shot. 
 
 These were formerly employed in smooth-bore guns 
 against both animate objects and the masts and rigging of 
 vessels. The iron balls were arranged in tiers of three, 
 sustained by a central spindle, a top and bottom plate and 
 two intermediate rings. Figure 18. In former times they 
 were quilted into canvas bags, whence the name. 
 
26 XVI. — PROJECTILES. 
 
 CLASS II. SHRAPNEL. 
 
 Principles of Shrapnel. 
 Notation. 
 
 Let V be the initial velocity and v be the remaining ve- 
 locity of the shrapnel at its explosion. 
 
 Let Vy and v^^ estimated respectively at right angles to, and 
 parallel to the tangent to the trajectory, be the mean veloci- 
 ties of dispersion and of translation of the N balls that form 
 the sheaf, irrespective of the velocities in these directions 
 that are due to the remaining velocity v. 
 
 The velocity v^^ which is taken without regard to its sign, 
 may be due to either or both of two component velocities ; 
 viz. : 1st. The velocity v^^^ due only to the bursting charge; 
 and, 2d. In oblong projectiles, the velocity v^^^ due only to 
 their rotation. 
 
 The velocity v^ , which is an increment of the remaining 
 velocity, is due only to the bursting charge, and its sign de- 
 pends upon the position of the bursting charge within the 
 projectile. 
 
 Tet v' be the resultant velocity of translation due to z^± v^, 
 
 Tet qp be the inclination to the surface of the ground of 
 the tangent to the trajectory (the axis of the cone) at the 
 point of explosion. It is important to remember that, as 
 stated in Chapter I and to be proved in Chapter XX, the 
 curvature of the trajectory, or the value of qp measured from 
 the horizon, is a decreasing function of v. 
 
 Let Q be the angle at the vertex of the cone of dispersion, 
 figure 24. 
 
 We will for simplicity suppose the cone to be composed of 
 rectilinear elements, and the surface of the ground to be 
 horizontal,* so that d will be the angle included between 
 
 * For the effect of varying the inclination of the ground, see Chapter 
 XXX, figure 34. 
 
XVI. — PROJECTILES. 27 
 
 the upper and lower tangents to the sheaf at its vertex, 
 figure 25. 
 
 Distribution, t 
 
 It is evident that the mean density of the sheaf will be a 
 
 decreasing function of ^=2 tan-^ —L Also, from the horizon- 
 
 tal projection in figure 24, that since — balls will be 
 
 found in the area a b o d, the smaller is ^, or the more nearly 
 does the cone approach a cylinder, the more uniformly will 
 the balls be distributed over the entire ellipse a b o d. 
 
 Also, the smaller the angle g), the greater is the eccen- 
 tricity of the ellipse ; or, for a given lateral dispersion, the 
 greater will be the dangerous space in the line of fire. 
 
 N 
 If a be the area of the ellipse, d= — will be the measure 
 
 a 
 
 of the density of the section ; this varies along the ellipse ; see 
 figure 24. 
 
 The shrapnel will be most effective when _ = — is the 
 
 mean area occupied by one man projected on the ground 
 by the elements of the cone. 
 
 Besides ^, g) and N the value of a will depend on the 
 height above the ground, and the distance in front of the 
 target at which explosion occurs, or upon the distance vo=h, 
 
 t Note. The curvature of the axis of the sheaf causes the section to be 
 not truly elliptical, but oval as in figure 25. The ascent of the balls in 
 the upper half of the sheaf, and the curvature of their trajectories due to 
 their small sectional density, reduces their striking energy, so that those 
 that fall near the large end of the oval are comparatively ineffective. 
 This loss will be partly compensated for by the ricochet of balls nearer 
 to the axis, provided they strike ground that is sufficiently hard. For 
 ricochet, the angle of incidence shonld be less than 20° : this establishes 
 
 a limiting value for g} -f" o <C^^°. 
 
 These differences between the actual and the assumed conditions, hav- 
 ing been understood, may, for this discussion, be neglected. 
 
28 XVI. — PROJECTILES. 
 
 Nature of Target. 
 
 The requisites of shrapnel vary somewhat with the dis- 
 position of the troops against which it is to be used. These 
 may be: 
 
 I. Either in columns of manoeuvre, or in deep masses 
 which it is the object of the artillery to force to deploy at 
 long distances. In open ground these distances may uow be 
 as great as two miles. 
 
 II. Deployed in line at shorter ranges. 
 
 In the first case, consistently with the limiting values of 
 
 ^j the values of 6 and /i should be small ; and conversely in 
 
 the second case. In the first case, as the enemy will gene- 
 rally be in motion, and therefore erect, cp also should be small ; 
 and in the second case, as the enemy will generally be lying 
 down and seeking cover, cp also should be large. 
 
 These conflicting considerations require special treatment. 
 In the first case guns with high velocities are needed, and in 
 the second case the limit will probably be found in the use of 
 field mortars. Between these limits guns may be used with 
 reduced charges and at high elevations, and at the closest 
 ranges, say within 300 yards, canister is most effective. 
 
 The two cases correspond to the limiting cases of the cone. 
 First, when = g) r= 0. Second, when 6 :=z cp =z 90"". 
 
 The first case, being that most comprehensive and difficult 
 to satisfy, and since it involves by its opposites the second 
 case, is that herein discussed. 
 
 Choice of Fuze. 
 
 Shrapnel may be exploded in the two ways shown in fig- 
 ure 16, viz., " on graze " by an automatic impact fuze, or in 
 the air by an adjustable time fuze. These have different 
 spheres of action as follows : 
 
 Impact fuzes may be used at short ranges where v is large 
 
XVI. — PROJECTILES. 29 
 
 and and cp are therefore small; and where q' the angle of 
 reflexion (always greater than 9), is also small. Figure 16. 
 
 But they act irregularly when the ground is soft or rolling ; 
 and at long ranges when v is small and 9 is large, the energy 
 lost on impact reduces the already diminished value of v, 
 and consequently increases the value of 6, The time fuze 
 is therefore essential for soft or rolling ground, and for long 
 ranges over any ground. A possible objection to it applies 
 to the risk attending its premature discharge when firing over 
 friendly troops. 
 
 On some accounts the time fuze is less well adapted for use 
 at short ranges than is the impact fuze ; since for a given 
 error in the time of its burning,* the greater is z', the greater 
 will be the resulting variation in h, and therefore, for given 
 values of 6 and qp, the greater will be the variation in a. 
 
 Although this objection is partly neutralized by the small 
 values of 6 and (jp at short ranges, the conditions seem to re- 
 quire the use of two fuzes in each projectile. See the co7n- 
 bination fiize^ Chapter XVIII. Meanwhile the improvement 
 of the time fuze is one of the most important problems in 
 ordnance. 
 
 Computing the Value of d for Rifled Shrapnel. 
 
 Let p be the mean radial distance of the balls. 
 
 This is taken instead of the radial distance of the outer 
 ball, as is generally done, since the distribution of the balls 
 throughout the cross section of the sheaf is more important 
 than their extreme lateral dispersion. 
 
 Let r be the external radius of the shrapnel, taken equal 
 to that of the bore of the gun. 
 
 Although Fwil be reduced during flight, it is assumed, 
 and experiment confirms the assumption, that at ordinary 
 
 * The mean error (Chapter XXX, page 24) in the time of burning may 
 be taken as about 0.05 sec. 
 
80 XVI. — PROJECTILES. 
 
 ranges the angular velocity of the projectile does not sensibly 
 diminish.* 
 
 Under this assumption, from Equations (2) and (3) the tan- 
 gential velocity of the mean ball will be nearly 
 
 P" = ;~^. (5) 
 
 and, since we are considering only the tangential velocity due 
 
 to rotation, we have Vjy = p cj and 
 
 6 p 0) pn F . -. 
 
 tan - = '-J- = "^ ,. (6) 
 
 If we substitute in this equation the empirical value of n in 
 Equation (4) we have, 
 
 tan-=-y--^, (7) 
 
 and for a given shrapnel in which V^ n, and - are known, 
 
 tan|=|; (8) 
 
 an equation easily remembered, and which agrees fairly well 
 with practice. 
 
 History. 
 
 The history of the improvement of shrapnel, which is now 
 the principal field artillery projectile, illustrates many impor- 
 tant principles. As stated, page 24, improvements liave 
 
 tended to reduce the ratio -~- , and to increase the sectional 
 
 7/ 
 
 density of the projectile as a whole, and that of the balls it 
 contains. 
 
 Spherical Shrapnel, 
 
 I. Shrapnel, as invented in 1808, by General Shrapnel of 
 the British service, were simply spherical shell, loaded loosely 
 with musket balls and a bursting charge. 
 
 * Projectiles fired vertically upward have returned to the earth with 
 sufiicient rotation to keep them point foremost. 
 
XVt. — PROJECTILES. SI 
 
 In transportation the powder was triturated by the balls, 
 and on firing the piece the shock might cause a premature 
 explosion, or might conglomerate the balls ; sometimes even 
 .causing the projectile to be ruptured by the resulting dilation 
 of the cluster. The ignition of the bursting charge at the 
 proper time was also uncertain. 
 
 In order to make F large enough to give a large value to 
 Z', the walls of the shell were made thick enough to stand a 
 heavy propelling charge. But this diminished the value of 
 N^ and, since the interstitial volume between the balls was 
 large, 7u had to be made large in order to obtain sufficient 
 pressure to burst the shell. The energy remaining in the 
 powder gases after rupture of the walls being large, the balls 
 were widely scattered, making 7>y large. The resultant value 
 
 of vx was zero. At long ranges, tan - = -^ was there- 
 fore large. 
 
 2. The next step was the invention of spherical case, much 
 used during our civil war. 
 
 By imbedding the balls in melted sulphur and boring out a 
 chamber for the bursting charge, figure 19, the value of iv 
 could be decreased, and the certainty of its ignition at the 
 proper time be increased. The matrix supported the walls in 
 firing, so that their thickness could be decreased and N be 
 increased. But the matrix often retained the balls after ex- 
 plosion, and the value of 7^x was still zero. 
 
 3. Colonel Boxer, of the Enghsh army, devised a shrap- 
 nel, figure 20, in which the balls, hardened by an alloy of 
 antimony, and packed in coal dust, were separated from the 
 bursting charge by a wrought iron diaphragm around which 
 the envelope was cast. The seat of the diaphragm and sev- 
 eral other meridional grooves served to weaken the envelope 
 and to diminish the value of w. 
 
 While the projectile was necessarily fired with the fuze in 
 
32 XVI. — PROJECTILES. 
 
 front, the non-coincidence of the centers of figure and of 
 mass caused the resistance of the air to turn the Hghter 
 portion of the projectile to the rear, so that z^x was always 
 positive. 
 
 This projectile marked the farthest advance of spherical 
 shrapnel. 
 
 Oblong Shrapnel. 
 
 The advantages of the oblong form of shrapnel are as 
 follows : 
 
 It permits the base of the envelope to be strengthened 
 without increasing the thickness of the walls. This, with im- 
 provements in cannon and gunpowder, has increased the 
 value of Vj and since the sectional density has been increased 
 so that at long ranges ^ has been diminished, it has also in- 
 creased the eccentricity of the section of the cone of disper- 
 sion by the ground. By placing the bursting charge in rear, 
 Z'x has become positive, and z'yb has become practically zero. 
 
 An example of such a projectile is seen in figure 21, in 
 which B^ is the cast iron body ; H, the ogival head of wood, 
 covered with a sheet iron cap by which it is riveted to B ; 
 C, the powder chamber, made conical to facilitate unloading; 
 Z>, a disc by which the cluster is swept out to the front; T, a 
 tube to carry the flame from the fuze, 7% to C. A paper lining 
 keeps the rosin matrix from adhering to the walls of the cavity. 
 
 The shght resistance of the attachments of the head makes 
 of this projectile a sort of aerial gun. 
 
 The objections to this projectile indicate the nature of re- 
 cent improvements. The wooden head, the tube, the disc, 
 and the thickness of the walls required by the nature of cast 
 iron, diminish JV so much, that the balls form about one- 
 quarter the weight of the whole projectile. 
 
 The bursting charge is too small to produce sufficient 
 smoke to indicate the explosion at distant ranges, and thereby 
 to assist in correcting the aim. 
 
XVI. PROJECTILES. 
 
 The position of the bursting charge is such that, while 
 acting well in air, when used with an impact fuze the delay- 
 caused by the passage of the flame through the tube causes 
 the projectile to rise too high before bursting. 
 
 Present Practice. 
 
 The most recent ideas on the subject are embodied in 
 figures 22, 23. 
 
 Figure 22 contains a combined time and impact fuze. 
 
 The bursting charge is situated in front, occupying the 
 room which in figure 21 is wasted. It is large enough to 
 give the smallest volume of smoke visible at extreme ranges. 
 
 The envelope consists of a thin drawn steel tube, secured 
 in rear to a separate base, and slit and compressed in front to 
 an ogival form. 
 
 The cluster consists of a column of leaden balls, separated 
 by discs of cast iron. The discs are sunken to fit the balls, 
 and form a skeleton matrix. 
 
 When the bursting charge explodes, the slit ends of the 
 point are thrown back, so as to dirhinish the sectional density 
 of the envelope as compared with that of the cluster. 
 
 The latter moves on with v' z=.v — v^ =v — about 200/. s. 
 
 Figure 23 represents a more recent form, of which in 1891 
 a number are in process of manufacture for experimental trial. 
 
 Its construction is apparent. The tube is of thin brass, 
 enlarging its capacity for powder, and facilitating the passage 
 of the flame from the fuze. The w^alls are weakened by 
 longitudinal grooves. It remains to be seen whether, com- 
 pared with figure 22, the increase in 7'yb resulting from this 
 construction will not neutralize the increase in Vyr^ , 
 
 THE SEGMENT SHELL. 
 
 An attempt was made some years ago to combine the 
 functions of solid shot, shell and shrapnell in the segment 
 shell, in which the cluster was composed of the sectors of 
 
S4 XVI. — PROJECTILES. 
 
 concentric cylinders arranged so as to form a solid mass. 
 But such a violation of the principle of the independe^ice of 
 function^ which requires that where simplicity permits, eacli 
 specific function be separately provided for, necessarily 
 failed. The importance of this principle in the design of 
 machines of all kinds can hardly be too forcibly stated. The 
 opposite of this idea, that of combination, by which more 
 than one office or function is expected of any one member 
 of the machine or organization, is seldom found to be com- 
 patible with the efficiency of the whole, as we shall have 
 many opportunities of seeing during this course. The full 
 development of the principle of the independence of function 
 leads naturally to complication or the multiplication of parts; 
 judgment is therefore required to compromise between sim- 
 plicity and efficiency. The history of invention appears to 
 indicate the pre-eminence of efficiency. 
 
 As a case in point, it is now conceded that three types of 
 the two classes of projectiles are required for field and siege 
 artillery; viz.: shell, to convey kinetic energy for penetration, 
 and potential energy for demolition and moral effect; and 
 case shot for kinetic energy only. Although shrapnel, when 
 reversed in the gun, may in an emergency replace canister; 
 it is better to carry a few rounds of the latter, preferably, 
 as in the British service, on the carriage which supports the 
 piece. 
 
 REGULATING SHRAPNEL FIRE. 
 
 Referring to figure 24 we may consider the horizontal and 
 vertical projections of //, viz., x — h cos cp ; j^ = A sin gi. 
 
 Of these quantities, which are separately discussed in the 
 regulation of fire, x is mainly varied by changing the time of 
 burning ; and y by changing the angle of fire. 
 
 Under given conditions x varies inversely as the range. 
 Its variations, however, are not great, since there are com- 
 pensations that tend to keep it constant. It is found that 
 
XVI. PROJECTILES. 35 
 
 the best results follow a value of j\; = 50 yards for all dis- 
 tances except those very short, for which x may increase up 
 to 100 yards. If x be taken too small, too great a propor- 
 tion of the shrapnel fired will explode beyond the target and 
 be wholly lost. 
 
 In order to utilize the small values of qp in the upper half 
 of the sheaf, it is advisable to make y small. It is found 
 that the best results follow a value of y varying from 2 yards 
 at 500 yards range, to 6 yards at 2,500 yards range. Greater 
 values of y are not used, since they are difficult to observe 
 correctly at long distances. The reason for the increase of ji^ 
 is due to the increase of cp at long ranges, and the consequent 
 decrease in the area of the section cut from the cone by the 
 surface of the ground. 
 
 These rules are in the nature of approximations. In prac- 
 tice the fire is regulated by signals from observers, placed as 
 far as possible to the front and flank. 
 
 EMPLOYMENT OF FIELD PROJECTILES. 
 
 Shells. 
 
 These projectiles when used with a time fuze would follow 
 the principles laid down for shrapnel ; but the large value of 
 6 and the small value of N would make this unprofitable. 
 
 They accordingly use an impact fuze, which makes of them 
 the best means of controlling elevations. See page 4, and 
 Chapter XXX, page 20. 
 
 They are generally used against inanimate objects to be 
 demolished, pierced or set on fire. 
 
 In the following cases they may be used against troops : 
 
 1. At distances too great for the time fuze. 
 
 2. When the enemy is hidden in a village, or in thick 
 woods. 
 
 The violence of their explosion assists their moral effect, 
 particularly against horses and fugitive masses. 
 
36 XVI. PROJECTILES. 
 
 Shrapnel. 
 
 These are exclusively used against animate objects in the 
 open, or in thin cover. They were found very destructive in 
 the Russo-Turkish war. In siege oper ttions they serve to 
 annoy parties working at night to repair the damages done 
 by day. 
 
 PENETRATION OF ARMOR. 
 General Considerations. 
 
 The penetration of armor depends principally — 
 
 I. Upon the nature of the armor. In the order of resist- 
 ance armor may be classed as follows : 
 
 Cast iron with a chilled face, used only for land defenses 
 and not considered herein. 
 
 Steely forged and tempered. 
 
 Compound^ viz., a wrought-iron back with a hard steel 
 face. 
 
 Wrought iron^ now obsolete. 
 
 Roughly speaking, armor yields either by ptinching or 
 racking. In the first case, as in wrought iron, the effect is 
 local. In the second case, the energy of impact is distrib- 
 uted throughout a greater mass of the plate and tends to 
 crack the plate or to wrench it from its fastenings. The effect 
 is mainly to remove an obstacle to further penetration. Cast 
 iron armor yields in this way, and so do steel armor and the 
 face of compound armor if too brittle. 
 
 The object of the artillerist is to concentrate energy on a 
 small area, so as to reach the objects which the armor is in- 
 tended to protect, /. e., to punch. 
 
 The object of ihe armor-maker is to protect these objects, 
 by distributing the energy of impact as much as possible 
 between the projectile and the mass of the plate, so that even 
 at the risk of destroying the plate by racking, the shot must be 
 kept out. 
 
XVI. — Projectiles. 87 
 
 But if racking can be avoided without loss of resistance to 
 punching, the quahty of the plate is improved. In the early- 
 manufacture of armor, racking effects predominated ; these 
 disappeared as its manufacture was improved ; while the resist- 
 ance to punching was maintained or even increased. For ex- 
 ample, the principal objection to steel, for armor as for other 
 purposes, has been its brittleness. But at Annapolis, in 1890, 
 carbon steel armor resisted punching, but was slightly racked. 
 Nickel steel armor resisted both racking and punching. Com- 
 pound armor failed in both respects. 
 
 The nature of the backing or support against which the 
 plate rests, considerably affects its resistance. Except for 
 compound armor, for which the backing cannot be too rigid, 
 the backing should be somewhat elastic, so as to absorb 
 energy, after the manner of a cushion supporting a board in 
 which one seeks to drive a nail. 
 
 As the liability to racking increases, the number of the 
 bolts by which the armor is held in place should also increase, 
 so as to retain those portions which would otherwise be 
 displaced. 
 
 II. As a consequence of the above must be considered 
 the resistance of the projectile to permanent deformation ; 
 page 3. 
 
 III. Upon the striking energy of the projectile, measured 
 in a direction normal to the plate. 
 
 Since the projectile acts after the manner of a punch, 
 shearing its way through the plate, the energy is often 
 estimated per unit of circumference. In earth and masonry, 
 in which the material is soft, the projectile is supposed to 
 compress it to the front, and the energy is taken per unit of 
 area of cross section.^ 
 
 * As experience with plates and projectiles of varying resistance to per- 
 manent deformation, increases, such assumptions are gradually replaced 
 by purel) empirical formulae suited to each special case. 
 
J^8 XVI.— PROJECTILES. 
 
 Whereas in experimental tests normal impact is the rule, in 
 firing at ships it will be the exception. The shape of the 
 point of the projectile also tends to make it glance, so that 
 for these reasons armored ships may be expected to resist 
 more than the formulae predict. 
 
 Haitian d's Formula of 1880.* 
 
 The energy expended in other forms than in perforation, 
 as in heating the plate and projectile, and in deforming the 
 latter, has given rise to many empirical formulae, some of which 
 may be found in the Course of Permanent Fortification. A 
 very successful formula, Froloff''s^ assumes that -the energy so 
 lost is proportional to the striking velocity, so that the pene- 
 tration is proportional to the momentum of the projectile on 
 impact. The following formula, which illustrates a principle 
 already taught, is considered by recent writers to be one of 
 the best Equation (15). 
 
 Let t be the thickness in inches, of wrought iron armor that 
 would just be perforated by a cast iron projectile, whose 
 weight is W^ its normal velocity on impact v^ and its diam- 
 eter d. 
 
 Let e be the normal energy in foot-tons, or ^ = tt— s?r<7r 
 ^^ 2^^ 2240 . 
 
 Let s be the energy in foot-tons per inch of circum- 
 ference, or f = =- . 
 
 TT a 
 
 During a prolonged series of experiments made by Colonel 
 Maitland it was found — 
 
 1st. That / varied directly with £, or 
 
 '=/(■?)■ « 
 
 * It is inferred that the experiments on which Maitland's formula is 
 based were made with ordinary cast iron projectiles, and that the armor 
 was backed. 
 
XVI— I^ROJECTILES. 80 
 
 2nd. It was also observed that when projectiles of different 
 calibers were arranged in classes according to their spherical 
 densities; in each class the penetration measured in calibers 
 was very nearly proportional to the striking velocity. 
 
 For a particular class, known as the standard projectiles, of 
 which the spherical density was 3.0, the penetration was nearly 
 one caliber for every thousand feet of striking velocity. This 
 is known as Captain Orde-Browns *' rule of thumb." 
 
 For purposes of comparison, let us assume a given gun to 
 be fired against a given plate ; d and / will then be constant, 
 and the variation in spherical density will result from varying 
 the weight of the projectile. The variables will then be W 
 and V. For the standard projectiles let these be represented 
 by W, and v^, 
 
 Owing to the number of experiments made with the stand- 
 ard projectiles, special weight is given to the results obtained 
 from them. These results are expressed in the following 
 general formula, differing slightly from Orde-Brown's rule, 
 
 viz. : « = ISOO - *^-^^- (^"> 
 
 To pass from standard projectiles to those not standard, 
 we use Equation (9) in order to ascertain the relation between 
 V, and V, Under the hypothesis that d and / are constant it 
 
 becomes v ^ f y\j ^ ' (11) 
 
 Whence v\v\\ Jw : y/W„ or z; = v \/^. (12) 
 
 In the standard projectiles, J^= 0.375 ^/^ ; whence, from 
 Equation (11) ,, = 1^^^^W^ (13) 
 
 Substituting in Equation (10) we have 
 
40 XVI. — PROJECTILES. 
 
 Y/f__0.14; (14) 
 
 "- 612.4 d 
 Whence, multiplying both members by d^ 
 
 '="'^= ski \/f-- 0.14^. (15) 
 
 The value, /, thus obtained is the thickness of a plate that 
 will just be perforated by a projectile having an ogival head 
 with a radius of curvature of 1.5 calibers. If the radius of 
 curvature is increased to 2 calibers, as is now customary, t 
 will be increased by 5 or 10 per cent, and Orde-Brovvn's rule 
 will increase in exactitude. 
 
 If the plate resists perforation, then the penetration may 
 be taken as about 0.9 of the estimated perforation. 
 
 The Formulae of De Marre. 
 
 The following formulae result from recent experiments in 
 France and, except for Equation (20), cover a great range in 
 
 calibers, and in the ratio - . 
 d 
 
 In the English units previously used we have for modern 
 
 projectiles, viz., chilled iron shot and steel shells. 
 
 I. For the perforation of wooden backing when used as 
 such, i. e., not unprotected 
 
 ^b = 0.1823 / ^-^ ^ ••« (16) 
 
 This is about 70 per cent greater than when the backing is 
 unprotected. 
 
 II. For a wrought iron armor plate that is hacked ; the 
 resistance of the plate alone being considered 
 
 ^j = 5.809 /^-V-^ (17) 
 
 Owing to the improvement of projectiles since 1880 this 
 is less than the value implied by Equation (15). 
 
XVI. — PROJECTILES. 41 
 
 For the entire target consisting ot the plate and backing 
 
 ^i = ^i + ^b. a8) 
 
 III. For the rather soft steel plates^ generally used for heavy- 
 armor, as made at Creusot, when backed 
 
 ^3 = 7.286 Z'-*^'-"* (19) 
 
 See also Equation (18). 
 
 IV. For the thin plates of hard steel, unbacked, used for gun 
 shields, when attacked by the comparatively small cannon 
 known as Rapid- Fire guns and Revolving Cannon 
 
 ^p = 12.86 /'-^^'-^ (20) 
 
 These formulae, while abundantly verified in the French 
 service, must be accepted with caution when the conditions 
 differ from those under which they were deduced. 
 
 Very's Formula. 
 
 Mr. E. W. Very, formerly of the U. S. Navy, has recently 
 proposed a means of comparing the resistance of steel plates 
 that has long been desired, since it eliminates variables 
 relating to the nature of the plate, its thickness and the cali- 
 ber and velocity of the projectile, all of which may differ in 
 experiments made at different times and places. 
 
 It assumes that the projectile is not deformed, and that no 
 other effect is produced but that of punching, which is sup- 
 posed to be complete. The effect is referred to that pro- 
 duced in wrought iron, since withm ordinary limits all such 
 armor is homogeneous, and is therefore, well adapted for use 
 as a standard of comparison. 
 
 Suppose we find by trial that a certain projectile will just 
 perforate a given steel or compound plate with a certain 
 energy e^. Calculate the energy e^ required for the same pro- 
 jectile to perforate a wrought iron plate of the same thickness, 
 
 e 
 and similarly backed. Then -1 z= g), m which qp is a factor 
 
42 XVI. — PROJECTILES. 
 
 expressing the relative per cent of energy required to per- 
 
 2140 
 forate the steel plate, e, g. ^-— — 107 per cent. 
 
 Since 1880 the improvement in projectiles has been so 
 great that e^ has decreased considerably. Improvements in 
 the quality of steel armor have increased e^, so that (p has in- 
 creased from about 125 to over 150. See next topic. 
 
 Weaver's Formula. 
 
 It has long been thought that besides its thickness, the mass 
 of the plate affects its resistance to penetration, and conse- 
 quently the '■^ energy per ton of plate^'' is often recorded in the 
 reports of firing against armor. No use is known to have 
 been made of this knowledge, however, until the following 
 formula, proposed by Lieut. Weaver of the U. S. Artillery. 
 
 • It is probable that the work is practically confined to a 
 mass of some definite volume immediately surrounding the 
 point of impact, and that the volume of this mass is a cylin- 
 der, the diameter of which is n times the diameter, d^ of the 
 projectile, and the height of which is /, the thickness of the 
 plate. 
 
 Experiments show that a notable increase in temperature 
 and the bulge are confined to a tolerably distinct ring, about 
 2 calibers wide, so that n is probably not less than 5. It is 
 probable also that it is safe to allow for an exterior ring which 
 absorbs part of the energy, although the effects in this ring 
 are not apparent. The value of 7i also depends upon the 
 relation between t, the thickness of the plate, and d, the 
 diameter of the projectile. Lieut. Weaver expresses this re- 
 lation for Creusot steel by 
 
 n = 6.25 + 0.22 (/ — d) (21) 
 
 in which / and d are in inches. This value will depend upon 
 the rigidity of the material, and is subject to correction by 
 experiment. 
 
XVI. PROJECTILES. 43 
 
 In wrought iron n will approach unity, as the effect is 
 noticeably local and no great increase of temperature in the 
 adjacent parts is observed. 
 
 From a general consideration of records Lieutenant Weaver 
 finds that about 1828 foot tons of energy per ton of plate is 
 necessary to perforate the entire target, consisting of a steel 
 armor plate and its backing. This assumes the plates to be 
 substantially uniform in resistance, the projectile to be inde- 
 formable, and neglects secondary effects, such as racking. 
 Calling this coefficient, C ; the weiglit in tons of the disc in 
 question, W^\ and the weight in tons of one cubic inch of 
 the plate, w; he writes : 
 
 £.= ff/,C=(«-'^)%/.^C (22) 
 
 Supposing w — log ~^ 4.1028 and substituting for tt, w and 
 C their values, we have the general formula 
 
 A = 0.1828 ie d^ t (23) 
 
 APPLICATION. 
 
 We may now compare the foregoing formulae by reference 
 to the experiments at Annapolis in September, 1890. The 
 plates were 10.5 inches thick, backed by 36 inches of oak, 
 and were fired at by steel shells, as follows : 
 
 No. of fT- ■■ , TT^ Spher. Effect on 
 
 shots. ^^^"^- '^ ^^ Dens. ^ ' Projectiles. 
 
 8 Holtzer Steel, 6 in. 100 lbs. 3.70 2075 2988 6 unbroken. 
 
 2 Firminy " 8 " 210 " 3.28 1850 4988 2 broken. 
 
 Confining our attention to the unbroken 6 inch projectiles, 
 only the points of which perforated the carbon and nickel 
 steel plates, Lieutenant Weaver's formula gives ^g = 362 L 
 If from this we subtract e^ = 77, per Equation (16), we have 
 e^ = 3544, which is 18 per cent more energy than the plates 
 received from any one blow. As the plates were not com ■ 
 plete^ perforated, this would indicate that the value of 
 
44 XVI. — PROJECTILES. 
 
 (p z= 195 from Equations (18, 21) is more nearly correct than 
 that of (p = 158 assigned by Mr. Very's method ; viz., by 
 dividing 2988 X 100 by the vaUie of c, = 1816, given by 
 Equation (18). 
 
 ROCKETS. 
 
 Definition. 
 
 A rocket is a projectile propelled by a source of energy 
 which it contains ; it therefore performs also the functions of 
 a cannon. 
 
 Structure. 
 
 A rocket consists of a cylindrical case of paper or metal, 
 containing a composition formed of the ingredients of gun- 
 powder mixed in suitable proportions. The front end of the 
 case is usually closed, but the other end contains one or more 
 holes or vents for the escape of gas from the ignited compo- 
 sition. Within the rocket is a hollow space called the bore ; 
 this may be formed by driving the composition around a 
 spindle which is afterwards withdrawn ; or by boring out the 
 composition after its compression to a solid state. 
 
 The case is surmounted by a pointed head, which, for 
 signal rockets, consists of a hollow paper cone, and for mil- 
 itary rockets of any suitable projectile Depending upon 
 the particular system of construction, some means is also 
 provided for guiding the rocket in its flight. 
 
 Composition. 
 Since the composition is required to ignite readily, and 
 since the amount of fouling is not objectionable, the pro- 
 portion of sulphur is increased; and, since the gradual 
 evolution of a large volume of gas rather than a large 
 amount of heat is required, the proportion of nitre is dimin- 
 ished, while that of charcoal is increased, so as to yield CO 
 rather than CO,. To further delay the combustion the in- 
 gredients are often mixed, rather than incorporated. 
 
XVI. — PROJECTILES. 45 
 
 Bore. 
 
 The bore is necessary to provide a large surface of initial 
 combustion. In order to maintain a uniform pressure 
 throughout the flight and so avoid either excessive strength 
 and weight of the case when, at first, the pressure is low; 
 or a deficiency of strength when, by the increase of the 
 surface, the pressure increases, the composition should burn 
 on a surface which is nearly uniform. 
 
 To prevent its burning on a decreasing surface, the com- 
 position must be so tightly packed within the case that the 
 flame cannot pass around it. 
 
 The conical form increases the initial surface without 
 increasing either of the above objections. Jt also facilitates 
 the withdrawal of the spindle and increases the strength of 
 the composition at the section corresponding to the immov- 
 able layer in a gun. Chapter VII, page 1. 
 
 Vent. 
 
 The momentum of the rocket is proportional to that of 
 the escaping gas. The velocity of the gas will increase with 
 the pressure, and this will increase as the size of the vent 
 diminishes. The longitudinal and the cross sections of the 
 vent must be so chosen that the gas will escape as fast as it is 
 formed, or nearly so, otherwise the velocity of the rocket 
 will be diminished and it may burst. See Chapter XI, 
 page 8. 
 
 The excess of the total pressure on the head of the bore 
 over that on the base, and the diminishing mass of the 
 composition accelerate the motion of the rocket until the 
 resistance of the air is equal to the propelling pressure: the 
 variation in velocity will then be slight. When the gas 
 ceases to flow the rocket becomes an ordinary projectile. 
 
 Guiding Principle. 
 
 The propelling force of the gas acts always in the direc- 
 tion of the axis of the bore; it follows, therefore, that with- 
 
46 XVI. — PROJECTILES. 
 
 out some means of 'giving stability to this axis, the path 
 described will be very irregular; so much so at times as to 
 fold upon itself. Instances have been known when rockets 
 have returned to the point from which they started. Stead- 
 iness of flight is obtained either by a guide stick, or by 
 rotation. 
 
 The guide stick is used for signal rockets. It consists of 
 a long wooden stick affixed to the case so as to bring the 
 center of atmospheric pressure well in rear of the center 
 of gravity. Any tendency to deflection is resisted by the 
 atmospheric moment. 
 
 The Hale rocket, figure 26, owes its stability to rotation 
 produced by the escaping gas. As this expands on escaping 
 through the vents, it presses against the concentric y^<?;?<r^i-, F^ 
 partly surrounding each of the three vents, and so causes 
 rotation. 
 
 The effect is increased in Macdonald's Hale rocket by a 
 similiar arrangement in front. In this rocket the bore 
 extends throughout the composition. 
 General Remarks. 
 
 The difficulties found in constructing rockets so as to 
 prevent the shrinking of the composition from the walls of 
 its envelope; their inaccuracy, and their low capacity as 
 vehicles of kinetic energy have limited their use m recent 
 times to incendiary purposes, particularly in savage warfare. 
 Where transportation is difficult and the enemy dwells in 
 huts of an inflammable nature, as in Africa, the portability 
 of these weapons causes them still to be retained by the 
 British service. 
 
 Rockets are also much used for transferring life-lines to 
 the crews of wrecked vessels, and may be applied to the 
 movement of floating torpedoes. 
 
 Rockets are fired from inclined troughs or tubes. 
 
 The 12 pounder rockets of the following named varieties, 
 
XVI. — PROJECTILES. 47 
 
 fired at an angle of elevation of 8° 15', gave the following 
 mean ranges and mean lateral errors (for the definition of 
 
 these terms see Chapter XXX, page 24) : 
 
 Range. Mean lat. error. 
 
 Hale rocket 1312 yards. 37 yards. 
 
 McDonald-Hale rocket... 2012 . " " 
 
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 CHAPTER XVII. 
 
 FABRICATION OF ARTILLERY PRO- 
 JECTILES. 
 
 The fabrication of projectiles involves reference to the 
 principles of founding, some knowledge of which is neces- 
 sary to a practical education. 
 
 Founding, or as it is less properly called, castmg, may be 
 divided into three parts, viz.: 
 
 I. Molding : by which a cavity, or ??wldj is formed to re- 
 ceive the molten metal; II. Melting; III. Pouring. 
 
 I. MOLDING. 
 Material of Mold. 
 
 Metallic. 
 
 When the metal to be cast is fusible at a low temperature, 
 so that it will remain liquid for some time after contact with 
 a metallic surface, the mold may be made of a less fusible 
 metal. This permits great exactness in the resulting casting, 
 particularly if the metal does not contract much in cooling, 
 and it allows the mold to be repeatedly employed." For 
 such reasons the molds formerly used for making bullets, 
 and those now employed for making fuze-cases of pewter, 
 and for printing-type, are metallic. 
 
 Metallic molds are also used in casting ingots that are to 
 be forged, and for chill castings, as explained in the Chem- 
 istry and hereafter. 
 
 Non-metallic, 
 
 But when the metal to be cast cools so quickly on contact 
 with a metallic mold that it is apt to set up considerable 
 
2 XVIT. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 internal strain; when it is apt to form blow-holes; and par- 
 ticularly, when its temperature is so high as to be destruc- 
 tive to the mold, this must be made of sand. 
 
 Because of its refractoriness, the sand used is generally 
 silicious; and to increase its porosity to the gases, and its 
 cohesiveness, that which is angular and of moderate size is 
 preferred. Sand also yields slightly to the change in form 
 of a casting while cooling. For example, a dumb-bell, cast 
 in an iron mold would probably pull in two, from longitud- 
 inal strain. 
 
 Sand possessing all the properties to be desired for 
 molding is seldom found in a natural state. Accordingly, 
 artificial molding co77ipositions are made by mixing sand 
 with various proportions of clay or flour to increase its co- 
 hesiveness; or with some combustible material such as coal 
 dust, horse manure or straw, to increase its porosity at a 
 high temperature. 
 
 The addition of water is necessary to give plasticity; but 
 as this causes blcw-holes, and even dangerous explosions to 
 occur, as little of it as possible is employed. In some cases 
 it is removed h^j drying the mold; or, when great strength 
 is required^ by baking it. 
 
 Molding Compositions. 
 
 The presence of water or of a combustible material in the 
 molding composition exercises an important effect upon the 
 casting. In both cases the gases resulting from contact 
 with the molten metal act, as in the familiar example of 
 water in the spheroidal state, to prevent close contact 
 between the fluid metal and the particles of sand. The 
 effect of this contact woujd be to make a rough, gritty 
 surface, destructive to cutting tools. The combustible may 
 be incorporated with the sand or applied upon the surface 
 of the mold. 
 
XVn. — FABRICATION OF ARTILLERY PROJECTILES. 3 
 
 ^lolding compositions are divided into three classes: — 
 
 1. Green Sand, which is wholly or nearly in its natural 
 condition, and slightly damp. This is principally used for 
 low grade castings, often molded in the floor of the foundry 
 so as to avoid the use of flasks. 
 
 2. Dry Sand, which is artificially dried after molding. 
 This is used for cylindrical objects, cast vertically, as it per- 
 mits a freer escape of gas than does the green sand. It is 
 also used for castings of copper and brass on account of 
 their greater conductivity, the object being to prevent their 
 iooling as rapidly as in the moist green sand. For cohesion, 
 a certam proportion of clay is mixed with the fresh sand ; 
 and to compensate for the absence of water and the incor- 
 porated carbon, sand which is of a fine grain is employed to 
 give a smooth surface to the casting. 
 
 3. Loam. This consists of a plastic mixture of clay 
 and sand, to which straw, etc., are added for porosity. It 
 is used for forming large volumes of revolution by the 
 operation of sweep moldings to be described. Such objects 
 are cast in pits, and hence the old sand resulting is called 
 pit sand. 
 
 Besides these there are ^v[\^^\o'^Q^^ parting sand 2^x\A facings. 
 The former is lighter in color and of a finer grain than that 
 employed in molding, and particularly free from moisture. 
 Facings are generally composed of carbonaceous material, 
 such as black wash, a mixture of finely ground coal and water, 
 or of dry flour, soot, etc. ; though chalk is sometimes em- 
 ployed on account of the CO^ it gives out when heated. 
 Patterns. 
 
 These are of two classes, according as they have a solid 
 or a hollow form. The former may be called positive, and 
 the latter negative patterns. As each kind of pattern is 
 intended to produce its like in metal, the positive pattern is 
 
4 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 used to form a negative mold, and the negative pattern, or 
 core box^ to form a positive mold or core.^ 
 
 To indicate in the mold the position which is to be occupied 
 by the core, core prints are made on the surface of the pattern. 
 These form cavities in the sand into which fit corresponding 
 projections on the core. 
 
 Positive patterns require to be made somewhat larger than 
 the casting; the difference being determined by the shrinkage 
 of the metal in cooling from the temperature of solidification 
 to that of the atmosphere. 
 
 To facilitate their withdrawal from the sand, patterns are 
 given a smooth taper surface; the difference in diameter is 
 called the draught. This requirement influences the number 
 oi parts in which a pattern shall be made. 
 Parting Plane. 
 
 The parting plane is that in which the main sections or 
 parts of the mold unite. The number of parts depends on 
 the choice of the parting plane. Thus, for a rod of elliptical 
 section, figure 7, if the parting plane contains either of the 
 principal axes, AB, CD, there will be but two parts. But if 
 the parting plane contains an oblique axis, as EF, either the 
 mold or the pattern must be further subdivided. 
 
 The parting plane is accordingly taken so as to include 
 either the maximum or the minimum diameter of the pattern. 
 Long cylindrical pieces are therefore parted on an axial 
 plane, as this direction gives them abundant draught. 
 
 The parting plane is the plane of reference for most of 
 the operations of molding. 
 
 Negative patterns part on an axial plane to facilitate the 
 withdrawal of the core, which is often made truly cylindrical, 
 or of a form not readily admitting ef its withdrawal in the 
 direction of the axis. 
 
 * This distinction is introduced only for purposes of instruction; th« 
 ©rdinary clfissifigation being simply, patterns and corgi. 
 
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 Material. 
 
 The material of which a pattern is made depends upon 
 the number of times which it may be employed, and some- 
 what upon its size. If made of wood, it should be built up 
 of pieces having the grain running in different directions so 
 as to prevent its warping. 
 
 In some cases where large castings are made by sweep 
 moldings the expense of patterns may be spared, and the 
 necessary concave and convex surfaces of revolution formed, 
 by templets revolving about an axial spindle. The differ- 
 ence of radii between the core and the mold so formed 
 determines the thickness of the casting. 
 Flask. 
 
 The sand forming the mold is supported by an outer frame 
 or box, called the flask. As many separate flasks are used 
 as there 2iX& parts in the mold. 
 
 For ordinary molding a two-part flask suffices; the part 
 uppermost in casting being called the cope, and the lower 
 part the drag. 
 
 Lateral motion between the parts of the flask is prevented 
 by dowels, and the cope is prevented from rising under the 
 hydrostatic pressure of the melted metal by weights or 
 clamps, or flanges bolted or keyed to the sides of the drag. 
 
 The flask should conform to the general shape of the 
 casting so as to avoid great differences in the rate of cool- 
 ing and to facilitate the operations of molding. It often 
 contains cross pieces to support the sand. 
 
 For loam castings, the flask may consist of a pit, sunk 
 beneath the surface of the foundry floor. 
 
 Together with the flask is used^ as a temporary bottom, 
 the folloiu board. This may have a plane surface next the 
 flask, or may contain in relief one or more patterns so placed 
 as to determine the proper position of the corresponding 
 molds. 
 
6 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 Molding Tools. 
 
 These consist of shovels, watering pots and sieves for 
 mixing the sand; rammers for packing it around the pattern: 
 trowels of various forms for repairing imperfections, porous 
 bags containing parting sand and facings, and venting wires 
 with which to open an escape for the occluded gases. 
 
 „ , II. MELTING. 
 
 Metal. 
 
 The properties of the metal employed depend on the size 
 of the casting and the nature of the projectile. 
 
 A decided advantage in tenacity follows the use of a large 
 proportion of gun-steel scrap. 
 
 The higher the grade of iron, the stronger it is; but the 
 less fluid it is when melted, and the greater is the shrinkage 
 and the difficulty of subsequently reducing it to finished 
 size. The effects of shrinkage are relatively greatest in 
 small molds. 
 
 Consequently for field projectiles grey iron is used, and 
 for those of larger size that which is more mottled or con- 
 tains a larger proportion of white iron. For chilled shot a 
 mixture is made of charcoal and anthracite pig irons, or of 
 old shot and car wheels in about equal proportions. The 
 components first named in each pair give toughness, and the 
 latter the desired hardness to the casting. Car wheels are 
 cast in chills surrounding the tread, while the centers are 
 cast in sand. The chill gives hardness where abrasion is to 
 be feared, and the sand causes the interior to cool more 
 slowly, thus converting it into grey iron and giving it the 
 softness and toughness required. The same principle is 
 applied in the chill casting shown in figure 6. 
 
 Furnaces. 
 
 The cupola, or the reverberatory furnace is employed 
 according to the quantity and quality of the projectiles;- to 
 be cast. 
 
XVII. — FABRICATION OF ARTILLERY PROJECTILES. ? 
 
 III. POURING. 
 
 To diminish the shrinkage the iron is poured at the lowest 
 temperature consistent with fluidity; and to make the shrink- 
 age uniform, small ladles filled from the furnace are pre- 
 ferred to the large ladles used for great castings. 
 
 The melted metal is skimmed while pouring. 
 
 FABRICATION OF PROJECTILES. 
 
 To apply the preceding principles we will explain the 
 manufacture of the 4.5 inch shot and shell of the Butler 
 pattern, referring to figures 1 to 6. 
 Patterns, 
 
 The parting plane is taken at the junction of the body of 
 the projectile and the tenon for the rotating ring; concen- 
 tricity of these parts being secured by an axial dowel. 
 
 The diameter of the cylindrical portion is enlarged rela- 
 tively to the maximum diameter of the head; so that, during 
 the reduction of the body to its finished size, the curvature 
 of the head near the front bearing shall not be distorted. 
 
 For the shot a teat provides a small surplus of metal near 
 the point and ensures a full casting there. The teat is after- 
 wards turned off to the curvature shown in the dotted lines. 
 
 The shell pattern has a projecting spindle as a core print. 
 This terminates at « in a conical surface, so that in spite of 
 wear and unavoidable variations in manufacture it may be 
 accurately centered in the cross piece,/, of the flask. Such 
 conical bearings are frequently used in construction. 
 
 As it is difficult for the sand to penetrate the small annular 
 cavity above the main portion of the core, this is separately 
 formed in the mold box ^ figure 4, before the spindle is seated 
 in the core box. The mold box represented is of wood, 
 constructed on the same plan as the core box. 
 
 For a double-walled shell the core is covered with a cast 
 iron corrugated sleeve of the form desired. The resistance 
 
8 XVn. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 which this offers to the contraction of the metal about it, 
 explains why this ingenious form of projectile is not more 
 largely employed. 
 
 The patterns for the gate^ by which the melted metal is 
 admitted to the mold, and the riser, by which the air and 
 scoriae escape, are plain conical sticks, sometimes, as in figure 
 6, made in two parts to facilitate their removal. 
 
 Core Box. 
 
 This is of iron, made in halves uniting on an axial plane. 
 It is bored out when bolted together through the four holes 
 shown, and brought into correct opposition by the four 
 conical dowels near the holes. 
 
 To form the core, an iron tube, called the spindle, per- 
 forated with many holes and provided with a conical bear- 
 ing as at a, (all figures,) is wrapped with tow and secured in 
 the core box by a nut, n. Sand is then rammed around the 
 spindle, the final form of the core being given by the cup, ^, 
 so shaped as to strengthen the base of the shell. 
 
 Flask. 
 
 For large projectiles this is cylindrical; but for small ones 
 it may be of rectangular cross section so as to contain several 
 molds. For molding shell or cored shot, a cross piece, /, 
 figures 5 and 6, containing a conical cavity, is so fixed in the 
 flask that the parting plane of the pattern shall fall in the 
 parting plane of the flask. For some projectiles, admitting 
 of complete perforation, two cross pieces are provided. In 
 such cases the conical bearings are not required. 
 
 To give greater strength to the flask and to preserve the 
 concentricity of the projectile the parting plane is one of 
 right section. 
 
 Position of the Pattern in the Flask. 
 
 Shot are cast point down, so as to give density to the 
 point- 
 
XVII. FABFICATION OF ARTILLERY PROJECTILES. 
 
 Casting shell point down leads to porosity and weakness 
 of the base which may cause them to fail in the gun. But 
 when a front fuze is used, as in figure 5, if the shell were 
 cast point up, the feeding of hot metal from the riser against 
 the thinly protected spindle would soften it and cause it to 
 bend. This objection does not apply when the fuze is in the 
 bottom of the shell. 
 
 On account of the difficulty of handling heavy chills^ 
 chilled shot are always cast point down. To prevent the 
 wear of the chill from the hot metal, which limits its life to 
 about 50 casts, removable linings are employed. Following 
 the general principle which requires a symmetrical arrange- 
 ment of the parts of the mold, and to prevent its cracking 
 from unequal expansion, the exterior of the chill should 
 follow the profile of the mold. 
 
 Gate and Eiser. 
 
 For large projectiles, figure 6, the gate enters the mold 
 preferably from below, so as to avoid splashing, and tangen- 
 tially, to give a rotary motion to the ascending column of 
 metal, and so sweep the scoriae away from its axis. 
 
 The riser is intended: — 
 
 1st. To allow free vent to the included air and gases. 
 These are sometimes lighted to assist their dispersion. 
 
 2nd. To allow the melted metal to be stirred during the 
 solidification. This liberates the gases and scoriae; and, 
 since fused metals are poor conductors, it facilitates simul- 
 taneous solidification, and thus diminishes internal strain. 
 
 3rd. To feed the hot metal into, and sometimes to make 
 it flow through the mold. 
 
 By careful stirring and feeding, shot as large as 12-inch 
 have recently been cast solid. 
 
 Small projectiles may be cast in groups with one gate for 
 
10 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 several molds; but each mold should have an independent 
 riser. 
 
 Large spherical projectiles are sometimes cast in strings^ 
 connected by necks which increase in diameter upward. 
 
 OPERATION OF MOLDING. 
 
 Secure the spindle of the shell pattern in its seat in the 
 cross piece by the nut n. Invert the drag so that the shell 
 shall rest upon the follow board on the parting plane. Place 
 the main shot pattern upon the point of the follow board 
 indicated by a dowel. Dust the follow board and the pat- 
 terns with parting sand. Fill the mold, ramming it suffi- 
 ciently to make it solid, but not so much so as to unduly 
 diminish its porosity ; this requires much experience. 
 
 Invert the drag, holding it between the follow board and 
 another board. 
 
 Remove the follow board; place the base patterns on the 
 corresponding bodies and secure the cope by the dowels to 
 the drag. Dust as before, and fill the mold; inserting the 
 patterns for the gate and riser at the proper time. 
 
 Place the follow board on the cope; lift off the cope and 
 reverse it; remove the patterns which it contains: they may 
 require to be slightly jarred, so as to loosen them in the 
 sand. Do the same for the patterns in the drag. 
 
 After repairing, drying, and facing the mold with black 
 wash or its equivalent, place and secure the core which has 
 been similarly treated. 
 
 Replace the cope and secure it to the drag by such means 
 as shown in figure 6. The mold is then ready for pouring. 
 
 FINISHING. 
 
 Preliminary Operations. 
 
 As soon as the metal has become sufficiently solid, and 
 while still hot, and therefore weak, the flask is opened 
 and the excrescences left by the gate and riser broken 
 
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 11 
 
 off. To facilitate contraction about the core the spindle is 
 withdrawn. This may be easily done, since the tow with 
 which it was surrounded has been consumed. To retard 
 the cooling of the casting it is then covered with the 
 loose sand which formed the mold. When cool, the cavity 
 is carefully cleaned from sand. 
 
 The proper cylindrical form is given by the lathe, the 
 most important of all machine tools. 
 Description of the Lathe. 
 
 A lathe is intended to form surfaces of revolution by 
 causing an object to revolve on one of its axes while it 
 is acted on by a cutting tool to which motion either along 
 the axis of revolution, at right angles to it, or in both compo- 
 nent directions may be given, either automatically or 
 by hand. 
 
 Figure 8 shows a lathe, in which A is the frame, the 
 upper surface of which is formed in parallel rectilinear 
 ways or guides. M, is the fixed head stock, in which 
 revolves the cone pulley P. This may be made to carry 
 with it the concentric live spuidlCy S, and the face-plate, 
 F, or may revolve independently of these parts. The 
 spindle is hollow and carries on its interior the conical 
 center, C. Its exterior is threaded for the face-plate. 
 
 T, is the movable tail stock; it contains the dead spindle, 
 S, provided with a conical center like that in the live 
 spindle. The tail stock may be clamped on the ways at 
 any desired distance from Fj a close adjustment of S 
 may be made by the screw Z>, which is clamped by the 
 set screw E. 
 
 The slide rest G, the invention of the great English 
 mechanician. General Samuel Bentham, has been used for 
 only about a century. To its invention is attributed the 
 practical success of the steam engine; it having been pre- 
 viously found impossible to produce truly cylindrical 
 
12 XVII. FABRICATION OF ARTILLERY PROJECTILES. 
 
 surfaces of large diameter. The slide rest, carrying the 
 cutting tool, derives its motion from the rotation of the 
 live spindle by means of a change gear, H, which connects 
 the outer end of the live spindle with the feed screw, J. 
 The feed screw passes through a nut on the lower side 
 of the slide rest, with which it may be thrown into and 
 out of gear. 
 
 Variations in Speed. 
 
 The necessary cutting speed, or the velocity of the surface 
 in contact with the tool, varies with the nature and diameter of 
 the material to be turned. The angular velocity of the work 
 may accordingly be varied by means of the steps on the 
 cone pulley. A similar pulley above the lathe, with its 
 axis reversed, receives the power from the main line of 
 shafting by the driving belt, d, and transmits it to the lathe 
 by means of the working belt, w. The upper pulley is 
 mounted on an axis provided with a fast and a loose 
 pulley, / and /, so that the lathe may be set in motion 
 or stopped by varying the position of the driving belt. 
 This arrangement, which is indispensable to all machine 
 tools, is called a counter-shaft. See figure 9. 
 
 Where great power, and therefore slow speed Is re- 
 quired, the back gear, figure 10, is employed. This consists 
 of two pinions, a and b, mounted on an axis, c, parallel 
 to that of the spindle $, and so placed that when a engages 
 with a toothed wheel, d, which is secured to the spindle, 
 b, shall engage with one of corresponding size, g, upon 
 the cone pulley. 
 
 To use this, the cone pulley is detached from d, and 
 revolves freely upon the spindle. The back gear may 
 then be engaged with g and d. The ratio of the diameters 
 of ^, b, a, d, indicates the resulting gain in power. 
 
 By varying the change gear any desired ratio can be 
 obtained between the angular velocity of the work and that 
 
Xvit. — ^Fabrication Of artillery projectiles. 13 
 
 of the translation of the tool. In this way screws of any 
 desired pitch may be cut. 
 Support of Work. 
 
 The work may be supported by the conical centers form- 
 ing the adjacent ends of the live and dead spindles. For 
 this purpose it is provided with corresponding depressions, 
 which are called center niarks^ at the ends of the axis 
 of revolution. As a rule these center marks are left in 
 finished work, as they permit pieces containing them to be 
 reworked or repaired. The work, in turning between 
 centers, is caused to rotate by means of a dog^ figure 11; 
 the tail of the dog fits in a radial notch in the face plate. 
 
 In certain cases when turning between centers is impracti- 
 cable, one end of the work is secured to the face plate 
 by means of the chuck. This is provided with three radial 
 set screws capable of simultaneous operation. See figure 12. 
 
 In such cases, and to prevent the springing of long pieces 
 in turning betv/een centers, an intermediate back rest^ By 
 figure 8, is sometimes employed. 
 Uses of the Lathe. 
 
 It is evident that the lathe may be used for boring as 
 well as for turning external surfaces, and that by the use 
 of a hook-shaped tool, passed through the fuze hole, 
 such cavities as that of the shell can be turned. 
 
 Also, that plane surfaces can be formed by omitting the 
 longitudinal translation of the tool, or that, preserving this 
 motion and guiding the tool by means of a template, 
 any desired surface of revolution may be exactly repro- 
 duced. 
 
 By replacing the center in the live spindle by a suitable 
 tool, against which the work may be pressed by the back 
 spindle, also without its center, the work may be drilled. 
 
 If the tool be made after the manner of a very thick 
 circular saw, the edge of which may be either cylindrical 
 
14 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 or form almost any surface of revolution, the work may 
 be moved along a plane director at right angles to the 
 plane of rotation, so as to form a new surface composed 
 of parallel rectilinear elements, and having its cross section 
 correspond to the contour of the tool. This operation 
 is called milling; it is of the greatest importance in the 
 manufacture of fire arms, sewing machines and others in 
 which the interchangeability of the parts is required. To 
 the general use of milling machines may be largely attri- 
 buted the eminence of certain American manufactures. 
 
 The principal advantages of machines eniploying the 
 principles of the lathe depend upon the continuity of 
 the motion and the ease with which it may be varied. 
 
 Final Operations. 
 
 Projectiles of soft iron are finished externally on the 
 lathe, or may be forced by an hydrostatic press through 
 a circular steel die. The former method is preferred. The 
 head is not touched, in order that the skin^ which is the 
 hardest part, may remain intact. 
 
 Chilled shot require special treatment by a grindstone 
 or a peculiarly shaped prismatic tool, figure 13. This 
 forms a scraping, instead of the paring edge generally 
 employed; it is less apt to spring away from the work 
 on meeting any portions which are excessively hard, and 
 may be easily and accurately sharpened by a cylindrical 
 grindstone. 
 
 The natural silicious sandstone is frequently replaced 
 by an artificial stone composed of emery concreted by a 
 cement. 
 
 FABRICATION OF STEEL PROJECTILES. 
 
 Those are intended for piercing armor. Either cored 
 shot or shell are employed. They may be either cast or 
 
3tvn. — Fabrication op ARtiLLERY projectiles. 15 
 
 forged, The former are the cheaper; the latter, so far, the 
 
 stronger. 
 
 Steel Cast Projectiles. 
 
 A rather silicious metal is preferred. In order to fix the 
 carbon, both head and body are cast in a chill mold; this is 
 surmounted by a sand mold containing the sinking head. 
 After cutting off the sinking head, the projectile is hardened, 
 the point being heated most. It is cooled by first dipping 
 the point in water and then immersing the whole projectile 
 in oil. In order to further soften the base so as to permit 
 the screw thread in the fuze hole to be cut, the base is an- 
 nealed while the point is kept in running water. To avoid 
 this operation, the base of the projectile may contain a piece 
 of wrought iron pipe, around which it has been cast, as in 
 chilled shot. 
 Forged Steel Projectiles. 
 
 These are hammered into shape from bars of suitable size, 
 turned inside and out, and hardened and tempered as above 
 described. 
 
 Steel shrapnel are now (1891) economically made by elec- 
 tro-welding. Chapter XV, page 23. 
 
 ROTATING BANDS. 
 
 Copper is preferred on account of its softness and strength 
 and its resistance to erosion by the gases. Its uniformity is 
 increased by adding about 5 per cent of zinc. This forms 
 an alloy known 2,% gilding metaiy used in the manufacture 
 of cartridges, cheap jewelry and the bell buttons used in 
 the Cadet uniform. 
 
 The bands are applied in two general ways. 
 
 I. In Casting. 
 
 1. The band may be cast in place on the projectile. This is 
 the simplest plan, but does not always make a good casting. 
 
 2. An annular band, the cross section of which is as shown 
 
16 XVII, — FABRICATION OF ARTILLERY PROJECTILES. 
 
 in figure 14, is placed in the bottom of the mold before the 
 metal composing the body of the projectile is poured. To 
 keep it from melting, it may be surrounded by a much thicker 
 band of the same material, or by a hollow band through 
 which runs a stream of water. 
 
 II. After Casting. 
 
 A seat for the band of the undercut section shown in 
 figure 15, is turned in the body of the projectile and the band 
 forced into this groove by hand or by machine. 
 . 1. By hand. 
 
 In this case the band may be either a straight rolled strip 
 with bevelled ends, as seen in figure 16; or for large pro- 
 jectiles it may be cast in the form of a semi-circular hoop. 
 In both cases the placing of the band is done gradually by 
 the hammer. 
 
 2. By machine. 
 
 The band complete is slipped over the projectile until 
 opposite its seat; it is then set in by powerful presses acting 
 radially. 
 
 INSPECTION AND PROOF OF PROJECTILES. 
 Comparison. 
 
 It can hardly be too strongly insisted upon that the in- 
 spection, not only of projectiles; but of powder and of arms 
 of all kinds is only preparatory for and subordinate to, the 
 proof. The inspection may detect the causes of failure in 
 proof, and often applies to many more articles than can be 
 profitably proved; but that it can not wholly replace it, is 
 proverbially and actually true. 
 
 INSPECTION, 
 
 Object of the Inspection. 
 
 The object of the inspection is to detect defects of work- 
 manship and material which may affect the successful oper- 
 ation of the projectiles. 
 
XVII. — FABRICATION OF ARTILLERY PROJECTILES. 17 
 
 As it is impossible to make all projectiles of exact dimen- 
 sions, certain variations are allowed in manufacture. For 
 sake of economy, the greatest variation or tolerance^ con- 
 sistent with safety and efficiency, should be allowed; both in 
 workmanship, as shown by the gauges, and in the material. 
 This remark is general. 
 Instruments. 
 
 Maximum and minimum ring gauges, see Chapter IV, page 
 11; a hollow cylinder gauge, five calibers long; a profile 
 gauge; a rolling table, and calipers for measuring the 
 thickness of the metal at the sides and bottom of the cavity 
 are the principal instruments required. Besides these there 
 are various gauges to verify the dimensions of the fuze 
 hole, and of the rotating device and its seat. Also various 
 tools for exploring suspicious cavities or defects. 
 
 An easy method of detecting small differences in the 
 diameter of cylindrical holes consists in the use of a 
 slightly conical bar of steel, the diameter of different 
 sections of which is marked upon its length after the 
 manner of a diagonal scale of equal parts. 
 
 Except for the rolling table, the names of these instru- 
 ments and their appearance as represented, figure 17, 
 sufficiently indicate their employment. 
 
 The rolling table is of iron with two parallel ribs at a 
 distance apart slightly less than the length of the cylindrr- 
 cal portion of the projectile. These ribs are brought truly 
 level, so that a concentric projectile will assume a position 
 of equilibrium of indifference. 
 Process. 
 
 The presence of fissures in hollow projectiles may be 
 detected by exposing them to an internal jet of steam, or by 
 observing whether after plunging them in water, notable 
 differences in the rate of drying occur. 
 
 When it is possible, the quality of the material is tested 
 
18 XVII. — FABRICATION OF ARTILLERY PROJECTILES. 
 
 by a specimen cut from the body of a projectile. For 
 chilled shot this is not possible; so that a cast specimen 
 may be tested and compared with those mixtures which 
 have given good results. A certain proportion of such 
 projectiles are also split so as to expose the chill. The 
 homogeneity of such shot is also tested by striking them 
 with a hammer at the junction of the body and head: a 
 clear sound should be produced. In spite of the inspec- 
 tion, such projectiles are liable to split spontaneously from 
 internal strain. 
 
 In order to stimulate the contractor to greater care, 
 projectiles are inspected in lots^ the failure of a certain 
 proportion of which for defects of material suffices to 
 condemn the entire lot. This is then permanently marked 
 so as to prevent its being again presented for inspection. 
 
 This rule is applied also to defects in workmanship when 
 the number of objects is too great to permit of the inspec- 
 tion of every one, as in the ammunition for small arms. 
 
 PROOF OF PROJECTILES. 
 
 Careful inspection generally suffices for all but those in- 
 tended for use against armor. But in all cases it is more 
 conclusive to supplement this by a proof, as by firing for 
 accuracy. 
 
 Armor piercing projectiles are proved by firing about one 
 per cent of a lot against wrought iron armor about one 
 caliber thick ; the chilled iron striking normally and the steel 
 at about 20 degrees to the normal. Upon the performance 
 and endurance of the proof projectiles, fired with penetrating 
 charges, depends the acceptance of the lot. 
 
XVIII. — MEANS OF COMMUNICATING FIRE. 
 
 CHAPTER XVIII. 
 
 MEANS OF COMMUNICATING FIRE. 
 
 These may be divided into two classes, viz.; 
 
 1. Those intended for igniting stationary charges in guns 
 and mines. It includes various forms of matches and 
 primers. 
 
 2. Fuzes, which are intended to be used in moving objects, 
 such as explosive projectiles, torpedoes, etc. 
 
 CLASS I. 
 
 MATCHES AND PRIMERS. 
 
 According to the time elapsing between their own igni- 
 tion and that of the charge, these may be considered as 
 relatively slow or rapid. 
 
 IGNITERS COMPARATIVELY SLOW. 
 
 Slow-Match, 
 
 This was formerly employed for igniting the port-fire, 
 by which the loose gunpowder priming laid around the 
 upper orifice of the vent was fired. It is now employed 
 only for preserving fire. If made of hemp rope, combustion 
 is retarded by saturating it with lead acetate, or the lye 
 of wood ashes. If of cotton it is only necessary that 
 the strands be well twisted. Slow match burns from 4 
 to 5 inches per hour. 
 
 Quick-Match is used to communicate fire, as in fire-works 
 and in experimental work of a dangerous character. It 
 is made of candle wick, steeped in a mixture of mealed 
 
8 XVm. — MEANS OF COMMUNICATING FIRE. 
 
 powder and gummed spirits, wound on a reel, dredged 
 with mealed powder and left to dry. ^t burns at the rate 
 of about 3 inches per second. 
 Varieties of duick-Match. 
 
 The rate of burning may be much increased by enclos- 
 ing the quick-match in a paper tube; see Chapter VIII. 
 
 If, instead of paper, the envelope be made more pliable 
 and strong, as by a spiral wrapping of cloth around a 
 central core of fine powder, the ordinary blastings or Bick- 
 ford fuze results. This inflames at a less rapid rate than 
 the kind just named. 
 
 A tube of lead or one of its alloys may replace the 
 weaker envelopes above described and instead of simply 
 fitting it closely, the tube, enclosing the core, may be 
 drawn as one mass after the manner of wire. 
 
 If gun-cotton be used for the core, a most convenient 
 and rapid form of detonator results. 
 
 IGNITERS COMPARATIVELY RAPID. 
 
 Caps and Detonators. 
 
 These consist of cups or tubes made by means of a 
 double punch, figure 1, the inner member of which, /, 
 passes through a conical hole, h, of somewhat larger diam- 
 eter in a stationary piece, d^ called a die. The outer 
 punch,/', which is concentric with the inner and fits closely 
 to it, as it descends into a shallow cylindrical depression 
 at the mouth of the die, shears from a thin copper ribbon a 
 disc which it holds by the edges while the inner punch forms 
 it into a cup. The elasticity of the cup causes its open end to 
 expand as soon as it has passed through the die : this strips 
 it from the punch as the latter rises for another stroke. The 
 cup is elongated into a tube by the successive operation of a 
 series of single punches and dies of gradually decreasing di- 
 ameter, See plates Chapter XXVII, This operation, which 
 
XVIIl.— MEANS OF COMMUNICATING FIRE. 3 
 
 resembles closely that of rollings in chapter XV, is of great 
 utility in the arts. For military purposes it is principally 
 used in the manufacture of metallic cartridges. 
 
 For percussion caps for small arms, the tube receives 
 a charge of moist fulminating composition. This is pre- 
 vented from falling out, when dry, by a disc of tin foil, 
 held in by varnish. 
 
 The construction of the detonator has already been 
 described in chapter XIV. 
 Cannon Primers. 
 
 These are of two classes, according as they are fired 
 by friction or electricity. 
 I. Friction Primers. 
 
 The friction primer presents the following advantages 
 over the method of firing cannon described, page 1. It 
 is portable, certain and rapid; it affords the means of firing 
 pieces at a distance, and does not attract the attention of 
 the enemy's marksmen at night. 
 
 According to the direction of the vent, friction primers 
 are divided into two classes. 
 
 I. Radial Vent. 
 
 The primer used in the military service of the United 
 States consists of two copper tubes, soldered at right angles 
 to each other, figure 2. 
 
 The short tube contains a charge of friction composition, 
 (Sbg S3 and K CIO3) inserted moist and surrounding the 
 roughened end of a wire, the outer extremity of which 
 forms a loop for the lanyard. The long tube is filled with 
 fine powder, retained by a wad of wax. The nib of the 
 wire is folded over the end of the short tube, so as to 
 prevent its accidental displacement and the firing of the 
 composition in consequence. 
 
 For large guns, the column of fine powder may surmount 
 
4 3^\ltt.--MEAMS OJ* CoMMttNlCATmc MVlU. 
 
 a pellet of compressed powder which will be shot, burning, 
 into the cartridge. 
 
 In some services the cross tube is omitted and the wire, 
 inserted axially, is withdrawn by a motion which causes it to 
 bend continuously around the edge of the vent. See 
 figure 3. 
 
 2. Axial Vent, 
 
 As the discharge serves to expel the empty tube with 
 great velocity, unless it be thrown upward it may injure 
 the bystanders. On this account, and also to prevent the 
 erosion of the vent by the escaping gas, an ohtwating prbner 
 is screwed into a proper seat concentric with the vent. 
 Figure 4 represents an obturating axial friction primer. 
 When the wire is withdrawn, the conical portion, c, finds 
 a corresponding seat at the end of the cavity surrounding 
 the wire. This prevents the escape of gas through the hole, 
 while the escape around the primer is prevented by the 
 radial expansion of the thin edge in which the portion 
 nearest to the charge is formed. 
 
 The stop, ^, prevents the primer from being screwed in 
 too far, and the enlargement, ^, serves a similar purpose for 
 the wire. 
 II. Electric Primers. 
 
 These are used for firing charges at a considerable 
 distance, as in certain cases in modern warfare when the 
 gun is so protected that the object is invisible from its 
 neighborhood; so that the pointing and firing are controlled 
 by a distant observer. By this means also, the simultaneous 
 discharge of several cannon at a common object may 
 greatly increase their effect. A similar advantage follows 
 in mines. 
 
 The primers are of two general classes: 
 
 I. High tension, in which ignition results from the pass- 
 age of the electric spark between the disconnected ends 
 
XVIII. — MEANS OF COMMUNICATING FIRE. 5 
 
 of two insulated conductors. For this class the conductors 
 require careful insulation and to be separated from adjacent 
 circuits, so as to prevent the primers in one circuit from 
 being accidentally exploded by currents induced from the 
 other circuits. 
 
 2. Low tension^ in which ignition results from the heating 
 of a short wire of high resistance which connects the ends 
 of the conductors. Owing to the ease with which the con- 
 dition of the circuit can be tested before firing, and the 
 comparatively low electro-motive force of the currents 
 employed, this is the only class of electric primer used 
 in artillery. 
 
 Figure 5 represents a common electric primer, and figure 
 6 an obturating electric primer. The platinum wire is 
 coiled to facilitate its handling in manufacture. It is sur- 
 rounded by a wisp of gun-cotton. 
 
 The obturating plug,/, of hard rubber seals the channel 
 by being pressed against the sharp ring in rear. In other 
 essentials these primers resemble figures 2 and 4:. 
 
 MEANS OF IGNITING PRIMERS. 
 
 If quick match be used it sufiices to unite the lines so 
 that the distances B C, B C, B C\ etc., in figure 7; or 
 BC^ B D C, figure 8, be equal. If the detonating tubes, 
 page 2 be used, these precautions are unnecessary. 
 
 For electric primers the voltaic battery is generally 
 employed, although for experimental purposes a small 
 portable dynamo or frictional apparatus is very convenient. 
 
 When it is desired to be able to fire without delay, a 
 battery is preferred, which, like the Leclanche, can be kept 
 for a long time in open circuit without sensible change and 
 which only needs the circuit to be closed to produce the 
 effect desired. 
 
 In using the electric current in direct or continuous circuit 
 
6 XVIII — MEANS OF COMMUNICATING FIRE. 
 
 as in figure 9, the number of cells of the battery required 
 increases with the number of primers, /,/',/", and it may 
 happen that the most sensitive of the primers, exploding 
 first, will cause the remainder to fail. 
 
 For the second reason a derived, or parallel circuit, as 
 in figure 10, is preferred. The successive explosion of the 
 more sensitive primers increases the current which passes 
 through each of the remaining primers, since their number 
 is diminished. 
 
 In order to employ a weaker battery, the arrangement 
 shown in figures 11 and 12, serves, by sweeping the key, ky 
 over the ends of the terminals, to produce a practically 
 simultaneous discharge. 
 
 CLASS II. 
 
 FUZES. 
 
 Fuzes are employed to explode the bursting charge of a 
 projectile at any desired point of its trajectory. They may 
 be classified, according to their mode of operation, as timey 
 impact and combination fuzes. 
 
 I. TIME FUZES. 
 
 A time fuze contains a column of com.position, which, 
 having been ignited at the discharge of the piece, after having 
 burned for a definite time, ignites the bursting charge. 
 
 Requisites. 
 
 Such fuzes are principally employed to burst projectiles 
 while in the air; they therefore require that the relation be 
 known between the distance to the point of explosion and 
 the time of flight, and that the column be taken of such a 
 length that it will burn in the time so determined. 
 
 The first of these requisites involves the estimation of the 
 distance by various systems of range finding, and the deter- 
 
XVIII. — MEANS OF COMMUNICATING FIRE. 7 
 
 mination from Ballistics of the required angle of projection 
 and the time of flight to the point desired. The second 
 requirement demands that the rate of burning be known, 
 and, since the time of burning is varied by varying the 
 length of the column, that the rate be uniform throughout 
 its length. Finally, that the column be taken of the exact 
 length required by the rate, and that it both receive and 
 impart fire with certainty. 
 
 The principal points to be considered in the development 
 of time fuzes are, that as we increase the muzzle velocity 
 and sectional density of our projectiles, the longer will be 
 the maximum time of burning required for the fuze. As 
 the remaining velocity increases, the greater will be the error 
 in distance due to a given error in time; and the greater the 
 range, the more difficult will it be to detect the error in 
 distance. Therefore improvements in cannon require corre- 
 sponding improvements in the uniformity of rate and in the 
 exactness of the length of the burning column. The greater 
 the rate of burning, the larger the scale and therefore the 
 smaller the effect of a given error in cutting. 
 
 The rate is so much affected by the conditions relating to 
 the resistance of the air during flight, that, while uniformity 
 of rate may be indicated by the tests of manufacture, the 
 lengths of column for given ranges should be determined by 
 actual trial in the gun. On this account, and to avoid com- 
 putation in the field, when the initial velocity and sectional 
 density are fixed, the scale is preferably one of ranges, in- 
 stead of units of time. 
 
 The great efficiency of projectiles properly exploded in 
 air, as explained in Chapter XVI, and the experience gained 
 with smooth-bore cannon, in which this was the only form 
 of fuze that could be successfully used, account for the pains 
 that have been taken to meet these requirements ever since 
 the early days when the fuze was lighted before loading. 
 
8 XVIII. — MEANS OF COMMUNICATING FIRE. 
 
 Kate of Burning. 
 
 This will depend upon the conditions named Chapter 
 VIII, page 3. 
 
 The rate was formerly varied by varying the composition, 
 but as any departure from the usual proportions is found 
 to diminish the uniformity of the rate, to increase the 
 difjficulty of preservation, and to increase the amount 
 of residue, it is now thought best to vary the rate only 
 by varying the amount of incorporation and the density 
 of the composition. 
 
 When the total time of burning is very great, as in some 
 of the large mortar projectiles, which may be 40 seconds 
 in the air, a return to the variable composition appears 
 necessary. 
 
 Former Practice. 
 
 For spherical projectiles the column was cylindrical and 
 was ordinarily contained in a conical case of paper, wood or 
 metal. This was filled with small successive quantities of 
 mealed gunpowder which were compacted by a drift upon 
 which a given number of blows were struck by a mallet. By a 
 repetition of the process the case was gradually filled. 
 
 The exterior of the case was divided into equal propor- 
 tionate parts by which to regulate the time of burning, 
 either by cutting off the case; or, since the entire column 
 might then be dislodged backward into the cavity of the 
 shell by the shock of discharge, by boring into it with a 
 gimlet. 
 
 The fuze was ignited by a priming of mealed powder 
 placed so as to catch fire from the flame passing through 
 the windage of muzzle-loading guns, both smooth-bore and 
 rifled. 
 
 The method of filling caused variation in fuzes of the same 
 kind, and even between different sections of the same fuze. 
 
\ XVIII. — MEANS OF COMMUNICATING FIRE. 9 
 
 1 ' ~ 
 
 \ 
 
 Exv.mples of Fuzes for Muzzle-loading Projectiles, 
 
 Figures 13 and 14 illustrate two varieties of time fuze, in 
 one of wUch the composition was fixed in the case and in 
 the other v^as movable. 
 
 The Mortar fuze case or plug was made of a close grained 
 wood, like beech, bored out nearly to the bottom. The 
 top of the cavity was enlarged to receive the priming of 
 mealed powder and alcohol. This was covered by a cap 
 of waterproof paper on which was marked the rate of burn- 
 ing. For economy of manufacture the exterior of all 
 mortar fuze plugs was marked in inches and tenths, instead 
 of with reference to the rate of burning of their contents. 
 
 The Sea Coast fuze consisted of a brass plug containing 
 a separate paper case, filled with a composition of variable 
 proportions and bearing on its exterior a scale of times. 
 The mouth of the plug was closed by a water-cap, per- 
 forated by a zig-zag channel. This was also filled with 
 mealed powder for the ignition of the fuze; but was so 
 constructed as to prevent the composition from being 
 extinguished in the ricochet fire over water, largely em- 
 ployed in former times. 
 
 These fuzes answered well for the comparatively low 
 remaining velocities and short ranges usual when spherical 
 projectiles were employed; but they required valuable time 
 for their adjustment and were imperfectly protected from 
 the effects of excessive heat or of moisture while in store. 
 
 The Bormann fuze, figure 15, was invented to overcome 
 these and other objections. The case being of pewter is un- 
 altered in size by meteorological changes, and it contains 
 the composition in a channel, which, though air tight, can 
 be readily cut by a proper tool. The circular form of the 
 column and its diminished section allow the size of the case 
 to be reduced, and the composition to be compressed in the 
 direction of its shortest dimension. The mean density of 
 
10 XV^I. — MEANS OF COMMUNICATING FIRE. 
 
 the succe^ssive layers estimated in the direction of the com- 
 bustion is thereby made uniform. The case is screwed into 
 the fuze hole by a screw driver, the prongs of whxh engage 
 into the recesses a, a. 
 
 The graduated arc lies over the circular column of 
 mealed powder which, after compression, is covered by the 
 tightly fitting wedge shaped ring, b. The only outlet to 
 the channel is under the zero of graduation; this outlet, r, 
 and the magazine^ m, are filled with fine powder which is 
 retained by a disc of tin, e. 
 
 To enable the fy^e to resist the shock of discharge, to 
 which its softness, density and form render it especially 
 weak; and also to increase the effect of a small bursting 
 charge, the lower portion of the fuze hole is closed by a 
 perforated disc,/. 
 
 The objections to the Bormann fuze are the short time 
 of its burning; the uncertainty of its ignition unless it 
 be carefully primed, and that, once set for firing, it is use- 
 less for any greater time of flight. 
 Present Time Fuse. 
 
 The use of breech-loading cannon necessarily prevents 
 the ignition of the fuze through the windage so that a special 
 device called an inertia igniter is employed for that pur- 
 pose. Its operation is illustrated in figures 16 and 24. 
 
 In figure 16 the inertia igniter consists of a mass of lead 
 containing a pellet of fulminate and supported a short dis- 
 tance above the sharp point, /, by some device which, while 
 stable against ordinary shocks, will be surely moved by that 
 of discharge. This device may be either a spiral spring or a 
 transverse pin of brittle material. 
 
 The flame from the fulminate escapes through the holes^ 
 h, into the annular cavity, r, and, by a hole on the inner 
 surface of the ring, r, ignites the circular column of com- 
 position which the rmg contains. 
 
XVIII. — MEANS OF COMMUNICATING FIRE. 11 
 
 The exterior surface of the ring is graduated, as in 
 seconds, and the body of the fuze contains a mark, placed 
 opposite to the entrance to the magazine, w, so that by- 
 setting the ring before firing with any division of its scale 
 opposite to the mark, the length of the burning column is 
 fixed. The cap, k, is used to c^amp the ring in place. 
 
 To prevent the opposing rush of the gases from the two 
 sections of the burning column, it is ignited at one of its 
 ends; this permits a free escape of the gases to the outer 
 air through a hole previously temporarily sealed against 
 moisture. 
 
 Figure 17 shows the course taken by the escaping gases 
 when the burning surface moves, as in the Bormann fuze, 
 in two directions from the hole, ^, to the magazine, m^ 
 Figure 18 shows the improved method. 
 
 For long ranges, since the form of the projectile permits 
 its length to be indefinitely increased, the fuze may contain 
 two or more rings arranged in tiers. 
 
 II. IMPACT FUZES. 
 
 Concussion Fuzes. 
 
 Until the introduction of rifled projectiles many unsuc- 
 cessful attempts were made to combine the time fuze with 
 some device which would be safe when the gun was fired; 
 and yet, if the time fuze failed to act at the proper point, 
 would explode the bursting charge on impact. 
 
 Owing to the uncertainty of the direction of the impact 
 such fuzes are called concussion fuzes to distinguish them 
 from the percussion fuzes now generally employed. 
 Percussion Fuzes. 
 
 Although as stated, Chapter XVI, page 21, the shock of 
 impact may in certain cases suffice to explode the bursting 
 charge, it is much more certain to employ a special appa- 
 ratus for this purpose. 
 
12 XVIII. — MEANS OF COMMUNICATING FIRE. 
 
 Although more complicated in structure than time fuzes, 
 those of the percussion class act with more certainty since 
 the conditions to be fulfilled are more easy of accomplish- 
 ment. They are not as subject to deterioration in store, 
 and, since they are usually entirely automatic, they require 
 no preparation before firing. By the volume of smoke 
 resulting from the explosion of shells containing percussion 
 fuzes, the gunner is afforded one of the readiest means 
 of correcting his aim. 
 
 Percussion fuzes are divided, according to their position 
 on the projectile, into fronts or base fuzes. The former 
 possess the advantage that on impact, the bursting charge is 
 thrown towards the fuze ; the latter class is required for pro- 
 jectiles to be used against armor. 
 Requisites. 
 
 A good percussion fuze requires — 
 
 1. A case to hold and guide the movable parts, and to 
 protect them from being clogged by the dust arising from 
 the bursting charge in transportation, and by the earth 
 against which they may strike. 
 
 2. A plunger, by the motion of which, on impact, the 
 charge is fired. 
 
 3. A fulminating composition, ignited by the plunger. 
 
 4. The priming, a charge of fine powder ignited by the 
 fulminate and serving to increase the certainty of the 
 ignition of the bursting charge. 
 
 5. A safety device, by which the accidental dislodgement 
 of the plunger is prevented; but which will certainly free 
 the plunger when the piece is fired. 
 
 6. A device to prevent the plunger from moving forward 
 in its cavity during flight. This tendency results from the 
 greater retardation of the projectile than of the enclosed 
 plunger by the resistance of the atmosphere. The effect 
 of this relative motion may be to cause a premature explo- 
 
XVllt.— MeA^§ of COMMtJi^lCAftNG FIRE. ' 13 
 
 sion if the fulminate is sensitive; or else on impact to 
 deprive the plunger of sufficient motion to cause the explo- 
 sion of a fulminate, the sensitiveness of which, for the reason 
 above given, has been diminished. 
 
 The most difficult of these requisites to provide is the 
 safety device. In the early percussion fuzes the plunger 
 was a single mass sustained by a transverse pin or by lugs 
 cast upon it. The pin was made strong enough to stand the 
 shocks of transportation; but was shorn off by the shock of 
 discharge. The mass to be given to the plunger was determ- 
 ined by confficting considerations. If made so light as not 
 to be liable to shear its support by accident, it might fail 
 to explode the fulminate when impact occurred at a low 
 velocity. The advantage of a proper distribution of func- 
 tions among the parts of the apparatus appears from the 
 following discussion: 
 Type of Improved Percussion Fuze. 
 
 Let Fhe the initial velocity of the projectile and v, and 
 z;', its velocities on impact, and after impact, as in the 
 ricochet. 
 
 Let m, be the mass of the plunger and p/ that of the 
 safety device: this we will suppose to be a hollow cylinder 
 as in figure 19, surrounding the upper part of the plunger, 
 but kept from moving backward upon it by a suitable pro- 
 jection, as that upon the flat spring, s\ In the type selected 
 the section of the plunger is square and fits the hole in the 
 safety device. 
 
 When the piece is fired, m' moves relatively to the rear 
 
 with an energy which, on account of the large value 
 
 2i 
 of Vj is capable of overcoming a resistance great enough to 
 be absolutely safe against all accidents of transportation. 
 In so doing it becomes solidly united to m, so that when 
 impact occurs, although v—v' may be much less than F", 
 
14 Xvm.— MEANS OF COMMUNICATING FIRE. 
 
 the energy — - — {v—v'Y may easily overcome the resist- 
 
 ance of the spiral springs, and so ignite the fulminate,/, 
 and the priming,/. 
 
 If, during the flight of the projectile m' does not remain 
 relatively at rest its conical form tends to make it roll 
 rather towards the base of the cavity than away from it. It 
 is also urged in this direction by the spring s. 
 
 This fuze, which is of French origin, represents one of 
 the best existing types. It requires a value of V not less 
 than about 1000/. ^., and therefore is somewhat more com- 
 plicated in construction when projectiles containing it are 
 fired with low velocities. 
 
 Percussion Fuzes used in the United States. 
 
 Hotchkiss Front Percussion Fuze. Figure 20. 
 
 A, is the case, closed in front by the screw-cap B, and 
 with a conical hole in rear closed by a lead safety plug C. 
 Dy represents the plunger, composed of lead cast into a 
 brass jacket to prevent its dilatation by shock, 
 
 A continuous brass wire, E, the upper portion of which 
 is bent in a semi-circle concentric with the plunger, is cast 
 into the lead and supports the plunger in the case. The 
 lower ends of the wire are securely held by the friction 
 of the safety plug against the sides of its cavity. At 7% is 
 the fulminate, and at F, the priming. 
 
 When the piece is fired, C, is dislodged backward into 
 the interior of the cavity either by its own inertia or by the 
 blow received from F). The wires spread outward and 
 prevent the plunger from moving forward until the pro- 
 jectile strikes a sufficiently resisting object. 
 
 Hotchkiss Base Percussion Fuze. Figure 21. 
 
 The case. A, carries the fulminate, F, in a large percus- 
 sion cap contained in the perforated screw-box^ which is 
 
XVIII.— MEANS OF COMMUNICATING FIRE. 15 
 
 formed in two sections, G and JI. The base of the case is 
 provided with a projecting flange, /, brought to a thin edge 
 which, when the fuze is screwed home, acts as a gas check. 
 The plunger Z>, is made as in figure 20, but contains a 
 central firing-pin, Z, roughened so that it will hold well 
 in the lead. 
 
 The rear end of the firing-pin projects beyond the bottom 
 of the plunger, while its front end is sunk a little below the 
 surface so that when this compound part {D and L) is in 
 place, it is prevented from moving by the screw-box. 
 
 When the gun is fired the plunger slides back on the 
 firing-pin so that the point projects above the plunger. 
 The lead being soft, and being prevented from expanding 
 by the jacket, it takes a fresh hold on the pin and supports 
 it when it is thrown forward on impact. 
 
 This fuze has certain structural defects which render 
 its operation less certain than that of the front fuze. For 
 its special purpose it is probably one of the best known. 
 Krupp Fuze. 
 
 Figure 22 shows a Krupp fuze in a double walled shell. 
 Safety in loading results from the transverse pin, /, which, 
 with the screw-box containing the fulminate, is inserted just 
 before loading. The rotation of the projectile expels the 
 pin, leaving the longitudinal pin,/, free to be driven inward 
 on impact so as to prevent the entrance of earth into the 
 cavity of the fuze. The nomenclature of figure 22 is the 
 same as that of figures 20 and 21. It is said that this 
 pattern is to be replaced by one containing a safety device 
 which is intended to be unscrewed by the rotation of the 
 projectile. 
 
 III. COMBINATION FUZES. 
 
 These combine the principles of the time and impact fuzes 
 50 as; — 
 
16 XVIII. — MEANS OF COMMUNICATING FIRE. 
 
 1. To increase the probability of explosion; since, if the 
 probability of a failure in each of the two cases be, say, 0.01; 
 that of the combination will be 0.0001. 
 
 2. To permit the character of the firing to be rapidly 
 varied, 
 
 3. To increase the certainty of explosion when the pro- 
 jectile is fired with a low velocity. 
 
 Figure 23 illustrates one of the most recent combination 
 fuzes used in the French service. 
 
 ^ is a leaden fuze tube made as d^escribed page 2. It is 
 wrapped spirally about, and secured to the hollow cone, C; 
 this is held in place by the clamp screw, D. The lower end 
 of the fuze tube communicates through the priming, /*, with 
 the cavity in which lies the percussion fuze described page 13. 
 
 The inertia igniter consists of a loose, pointed piston, ZT, 
 which, until the instant of discharge, is separated from the 
 fulminate, F^ by the spiral springs .S". 
 
 K^ is a conical cap pierced with a series of numbered holes 
 corresponding to the times of burning and provided with a 
 vernier for interpolating a puncture between any two holes. 
 The puncture, owing to the softness of the metal of which (7, 
 is composed, is made entirely through both its walls. 
 
 When the piece is discharged, the washer of compressed 
 powder, W^ is ignited by ZT, and through the puncture the 
 fire extends to the composition in E. At the same time the 
 percussion fuze acts as before described. 
 
 But for the union of the two fuzes in the same case, which 
 the construction of the projectile and the operation of front 
 percussion fuzes requires, this fuze illustrates the principle 
 referred to Chapter XVI, page 34. The simplicity of con- 
 struction, which was formerly considered of prime impor- 
 tance, has been entirely subordinated to efficiency of oper- 
 ation, notwithstanding the greatly increased cost which this 
 involves. 
 
XVIII. — MEANS OF COMMUNICATING FIRE. 17 
 
 The Flagler Combina^tion Fuze. Figure 24. 
 
 This fuze, devised by Colonel Flagler of the Ordnance 
 Department, is now, 1889, undergoing trial. It combines 
 many of the principles just discussed and adds two new 
 features to provide for the requirements numbered 5 and 
 6, page 12. 
 
 The first feature consi^s of a copper wire, d^ screwed from 
 the rear into the open end of the screw-cap^ A. The lower end 
 of this wire is bent at right angles so as to support firmly 
 the leaden time plunger, D. Just below the screw thread 
 by which it is suspended the diameter of the wire is reduced 
 to any desired extent. 
 
 The wire is broken at the neck so formed by the stress 
 due to the acceleration of the projectile, both in translation 
 and in rotation. The latter stress, occurring only when the 
 piece is fired increases the certainty of ignition without 
 diminishing the safety of the apparatus against accidental 
 shock. 
 
 On firing, the mass, Z>, is thrown against the fixed firing 
 pin, F^ and the fulminate ^^, is ignited. The flame from 
 the fulminate escapes through the radial holes and the an- 
 nular channel, ^, b^ to the end of the column of composition 
 projecting into the radial groove, Z, formed on the lower 
 side of the ring, or carcass C. The gas first formed blows 
 off the vent cover, ^, and allows the remaining gases to 
 escape freely. 
 
 When the column has burned to the point, b\ corre- 
 sponding to which there is a fixed mark on that portion 
 of the body next to the graduation on the ring, the priming 
 K^ is ignited and the flame from it passes down the fluted 
 surfaces of the members, G^ H^ 7, of the percussion fuze 
 into the bursting charge. 
 
 The advantage claimed for this safety device over those 
 in which ears projecting from the mass Z>, are shorn off by 
 
IS XVIII. — MEANS OF COMMUNICATING FIRE. 
 
 the shock of discharge, refers to the uniformity of copper 
 wire and to 'the absence of the loose pieces, which, after 
 shearing has occurred, may impede the action of the 
 plunger. 
 
 The percussion fuze resembles the Hotchkiss base fuze, 
 with the following advantages: — 
 
 1. The priming K, which serves for both fuzes of the 
 combination, makes the volume of the flame on impact 
 much greater than when fulminate only is employed. 
 
 2. In order to fulfil requirement 6, page 12, a disc of thin 
 zinc separates the point of the firing pin, h, from the fulmi- 
 nate above it. This presents a positive and uniform 
 resistance to premature explosion; and, since a pressure of 
 6 pounds is required to pierce it, the fulminate may be 
 made as sensitive as may be desired. 
 
 3. On impact the powder is thrown toward the fuze. 
 The fuze works well in practice. The percussion fuze 
 
 was found to operate when the projectile was fired through 
 a 2-inch board, though it failed in penetrating a board one 
 inch thick. It is thought that it will explode on striking 
 animate objects or sandy or marshy ground. 
 
 GENERAL REMARKS. 
 
 Owing to their greater permanency of form in store, and 
 their diminished volume, metallic cases are preferred to the 
 wooden ones formerly employed. 
 
 In order to cheapen the manufacture, which at best is 
 very expensive, the parts are, whenever possible, made of 
 pewter, cast in metallic molds into finished forms. When 
 strength and infusibility are required, brass or bronze are 
 used, cast as described in Chapter XVII. 
 
 To prevent unscrewing during flight, the screw thread of 
 base fuzes should turn in a direction contrary to that of 
 the rifling. 
 
3tvni. — MEANS O^ COMMttNlCATiNG f'lRE. 19 
 
 It takes an appreciable time after impact for tLe explo- 
 sion to occur; so that even when the fulminate was pur- 
 posely ignited by the shock of discharge, the shell did not 
 burst until it had gone several yards beyond the muzzle of 
 the gun. This is of importance in understanding the effect 
 of shrapnel fire with percussion fuzes, and serves to show 
 that explosions within the gun generally result from defects 
 in the construction of the projectile. 
 
 To prevent premature explosion from the plunger's 
 being thrown violently forward by the elasticity of the 
 bottom of the shell, on discharge, a perforated cardboard 
 washer is often required. 
 
 A percussion shell, unexploded in experimental firing 
 should never be tampered with: if possible, it should be 
 exploded on the spot by a dynamite cartridge. 
 
X15t. — GDN CoKstktrcTioN. 
 
 CHAPTER XIX. 
 
 GUN CONSTRUCTION. 
 
 Nomenclature of Stresses. 
 
 The total pressure of the powder gases in a gun may be 
 analyzed as follows with reference to the direction of the 
 resulting strains. 
 
 1. A radial stress, known by the special name of 
 "pressure" (/). 
 
 2. A tangential stress, or hoop tension (/) which tends 
 to split the piece open longitudinally, being similar in its 
 action to the force which bursts the hoops of a barrel. 
 
 3. A longitudinal stress ((/) which tends to pull the piece 
 apart in the direction of its length. 
 
 4. Besides these, which are the principal stresses now 
 considered, was formerly treated the transverse stress which 
 tends to bend outward the staves of which the tube may be 
 supposed to consist. 
 
 Its effects are so closely associated with the strains above 
 named that it is no longer discussed. 
 
 Of the principal stresses named the most important is the 
 tangential, since it is that from which failure most readily 
 occurs. 
 
 BARLOW'S LAW. 
 Limitations. 
 
 This law, which was until recently applied to the con- 
 struction of homogeneous cannon, if confined to stresses 
 beneath the elastic limit, (Chap. XV, p. 11,) under which 
 
XIX. — GUN CONSTRtJCTIOl^. 
 
 limit the stresses are taken to be proportional to the strains, 
 gives results which agree fairly well with those obtained by 
 the more exact methods now generally employed. 
 
 But, when applied to built up guns composed of concentric 
 cylinders assembled by shrinkages as described in Chap. XV, 
 it is no longer generally used because it does not analyze 
 the resultant strain into the component strains occuring in 
 three coordinate directions. For example, if we compress a 
 cube in the direction of the axis of Z, there will be deyeloped 
 along the axes of X and Y component strains correspond- 
 ing to tensile stresses acting in each of these directions and 
 conversely. 
 
 On account of the relative simplicity of Barlow's law it 
 will be employed to illustrate the general principles of gun 
 construction. A more extended discussion of the theory now 
 accepted will be found in the appendix of this chapter. 
 
 DEDUCTION OF BARLOW's LAW. 
 
 Hypotheses. 
 
 Suppose — {a) the piece to be a hollow cylinder of homo- 
 geneous metal, and — {h) that the effect of a central force be 
 transmitted outward in such a manner as to make constant 
 the area of cross-section by a plane perpendicular to the 
 axis. 
 
 {a) The homogeneity of the metal Is required, so that a 
 constant relation may exist between stress and strain ; or that 
 the coefficient of elasticity, known herein as E^ may remain 
 constant. 
 
 {h) The constancy of area or cross-section resembles 
 the assumption that the various stresses, from the effects of 
 which the physical properties of the metal are determined 
 in the testing machine, continue to be applied to the original 
 
XIX. — GUN CONSTRUCTION. 
 
 area of cross-section ; although it is evident that, if the volume 
 of the metal be constant, its area of cross-section must 
 diminish or increase when exposed to tensile or compressive 
 stress respectively.* 
 
 Wertheim's experiments show that the developed strains 
 are each — ^ of the principal strain. 
 Preliminary Statement. 
 
 Suppose that figure 1 represents a section of a homogen- 
 eous gun after firing: the radii R and >^' having been ex- 
 tended to r and J^" so as to maintain the sectional area 
 constant. 
 
 Then, the area whose limiting radii are r and E' being 
 common to both states of the section, we have 
 TT (r^ _ i?^) rr TT {R" » — R' '), or 
 (r J^R){r—R) = {R" + R') {R" — R'), 
 
 But since R" and R' are each greater than either R or r 
 R" + R'y r-\-R 
 
 ,'.r—RyR"^R', or 
 
 2 TT{r—R) __ r—R R" — R' 
 27rie ~". i? -^ R' 
 
 The two members of this inequality measure the strains 
 on the interior and exterior surfaces respectively, so that it 
 appears that the surface of the bore might be strained be- 
 yond its elastic limit before that of the outside layers was 
 reached. 
 
 The resulting set, if slight, might destroy the accuracy of 
 the piece from the dilatation of the bore; and, if consider- 
 able, it might lead to the formation of fissures which would 
 
 *Throughout the following discussion we will consider that we are 
 dealing with a cylinder of but one unit of length, since, as the length of 
 the cylinder varies, both the pressure tending to burst the cylinder and 
 the resistance which it opposes will vary in the same ratio. 
 
XIX. — GUN CONSTRUCTION. 
 
 facilitate the final rupture in detail of the successive cylin- 
 drical layers of which the gun may be supposed to consist* 
 The considerations explain the statement in Chapter V, 
 as to strength vs. weight. 
 
 Analysis. 
 
 To determine the law by which the tangential stresses 
 are distributed throughout the section of a gun: — 
 
 Let J^ and Z be the radius and the circumference of the 
 bore. Let /<, be the radial pressure per unit of area and 
 T the tangential stress on the surface of the bore. Let r, Zy 
 p and / represent the same quantities on any exterior 
 cylindrical surface, the area of cross-section between which 
 and Z is A. Then by assumption, {fi) above 
 
 Tt {f— B}) ::^ A, and .*. rdr = RdR. 
 
 Multiplying the first member of the last equation by -, 
 
 and the second member by -^ we have r^ — = i?^ -^ . 
 
 '' R r R 
 
 I But, since the ratio between the circumference and the 
 
 radius is constant, and since beneath the elastic limit the 
 
 stresses are proportional to the strains 
 
 , dr dz t . dR T 
 
 i - = V = ^ ""^ ■:ff = ■:£ 
 
 Therefore, we have 
 
 tf^ TR^ , TR^ 
 
 _ = — or/=-^ (1) 
 
 Or, since under given conditions of /o? ^ and i?, TR^ 
 will be constant, the tangential stress {or strain) on each sue- 
 
 * This last statement, though generally true, is subject to modification 
 depending on the ductility of the material and the development of special 
 elasticity. See post. 
 
XIX. — GUN CONSTRUCTION. 
 
 cessive concentric elementary cylinder varies inversely with the 
 square of its radius. ' This is Barlow's law. 
 
 This condition may be represented by figure 2, in which 
 the ordinates of the curve T T' represent the tangential 
 stresses on the corresponding circumferences. 
 
 In this figure and in those succeeding it, positive hoop 
 tensions are represented by ordinates laid off above the line 
 representing the trace of the axial plane of least resistance, 
 and negative hoop tensions (compressions) are laid off below 
 this line. See figures 5 and 6. 
 
 RESISTANCE OF THE CYLINDER., 
 
 Bursting Effort. 
 
 Imagine the radial pressure on a unit of area, or /oj to be 
 decomposed into two components/' and/^ figure 3, respect- 
 ively perpendicular and parallel to the axial plane, O R\ 
 along which rupture tends to occur; and consider but one 
 quadrant of the bore at a time. 
 
 Let cp be the variable angle made by the radial pressure 
 with the plane O R', 
 
 Then, /' =/o sin ^, 
 
 and, since, 
 
 d Z'=- R d cp^ 
 J)' dZ=p(iR sm cpdcp = —p^Rd cos cp. 
 
 n R 
 
 Integrating between Z—^ and Z=— -— and the corre- 
 
 <) 
 
 spending values of cp^ viz. and 90°, and calling P^ the 
 total pressure on the inner surface of the quadrant perpen- 
 dicular to the plane of rupture, we have 
 
 =/ 
 
 
 
XIX. — GUN CONSTRUCTION. 
 
 And for the force acting on both quadrants to lift the semi- 
 cylinder from the axial plane, or for the bw'sting effort 
 
 %F=p,%R. (2) 
 
 This might have been inferred from the fact that the burst- 
 ing effort is independent of the configuration of the surface, 
 upon which it acts. 
 Eesistance. 
 
 The bursting effort must be in equilibrium with the sum 
 of the tangential stresses developed in both quadrants, or 
 in figure 2. 
 
 27'=/o2i? = 2^/=2 X areaierr'J?' 
 
 or 
 
 A=2--^-. (3) 
 
 COROLLARIES. I 
 
 1. The maximum permissible value of T\s the elastic limit 
 of the material under tensile stress. Calling this and repre- 
 senting by/g the corresponding powder pressure we have 
 
 }.=e^. (4) 
 
 Equation (4) gives the means of determining the maximum 
 pressure for a gun of which the corresponding section is 
 known, or of determining the thickness of which a gun of a 
 given caliber should be made to resist a given pressure. 
 
 2. If guns be similarly proportioned, R' •=znR^ whence 
 by substitution 
 
 /o=^^- (5) 
 
X13t.— CUJ^ C0N§TRt)Ctl6N. 
 
 Equation (5) shows that all similar guns of the same material 
 can resist the same maximum pressure. 
 
 In the old cast-iron guns, in which for the reinforce, n was 
 generally taken equal to 3, or the walls of the gun made 
 one caliber thick, /o = f ^j i^ the metal be without internal 
 strain. Chapter XV, page 21. 
 
 3. Since < 1, A < 6^ unless i? = or ^' = oo . Or 
 
 n 
 
 the powder pressure must always be less than the elastic 
 limit of the material. 
 
 4. The curves of figure 4 are constructed from equation 1, 
 using a constant value of ^'j= 6 and taking 7"= d and 
 « = 3; 2; f respectively. It is apparent that as n dimin- 
 lishes the curve T t; T^t^; T' t' becomes more nearly 
 parallel to O R\ and the area beneath the curve tends to 
 increase from this cause. On the other hand, this area tends 
 to diminish from the decrease in the thickness of the wall 
 of the gun in consequence of the increase in the radius of 
 the bore: there is consequently some value of n which will 
 make this area a maximum. 
 
 To determine the value of n corresponding to a maximum 
 area or resistance to bursting, denote this resistance by 6", 
 and since it is equal to the maximum bursting effort we have 
 from equations (2) and (4) 
 
 Regarding R' as constant and differentiating we have 
 
 7 C 
 
 Whence, placing — ^ = we find 
 
 R'= %R, or ;? = 2. 
 
XlX. — GUN CONSTRUCTION. 
 
 That is to say, as shown by the following table, that when 
 R' is fixed, if the thickness of the wall is one-half the caliber, 
 the gun can withstand a greater bursting effort than with any 
 other thickness. 
 
 Table for R' = 6. 
 n=S R=2 S' = ^d, 
 n=2 R^S S" = ^ d = i S', 
 « = f R= 4: S'" = id= S\ 
 
 It is to be noted however, that since the bursting effort for 
 one quadrant, or R, is equal to/„ Ry if/„ be kept constant, 
 -P increases with R, so that, under ordinary circumstances, 
 the thicker is the wall exposed to gas pressure, the greater by 
 Equation (4) will be the value of /^. 
 
 In order, as R increases, to diminish the value of the 
 radial stress, we may form the gun of two or more con- 
 centric cylinders. This has been done by boring out old cast- 
 iron guns and lining them with a tube; since, for the same 
 bursting effort, the pressure per unit of area on the cast-iron 
 is diminished because the area pressed is increased. This 
 will occur even if the material of the tube be of copper, the 
 resistance of which may be neglected, and which may there- 
 fore be supposed to act only by transmitting the pressure 
 to the outside walls. 
 
 Within limits the thicker is the tube and the greater its 
 value of jE, the stronger will be the composite gun, since 
 for a given stress on the exterior of the tube the less will 
 be the strain on the adjacent walls, and, therefore, the 
 smaller will be the maximum stress that the exterior wall 
 will be called upon to bear. Conversely the power of such 
 guns may be greatly increased. See /i, Chapter XI, p. 21. 
 
 6. From the preceding corollary it follows that if a gun, 
 the dimensions of which are fixed, be composed of several 
 
XIX. — GUN CONSTRUCTION. 
 
 concentric cylinders, each one will be in the condition of 
 maximum strength if its internal radius is half its external 
 radius, or that the successive radii of contact will be in 
 geometrical progressio7i. This, which is known as Gadolin s 
 law^ is sometimes applied in modern gun construction. 
 
 EQUALIZATION OF STRAINS. 
 
 Preceding considerations show that owing to unequal 
 distribution of the strains in a homogeneous gun, the 
 strength of the gun increases much less rapidly than the 
 thickness of the walls. 
 
 The most favorable case would be when the whole thick- 
 ness of the wall was under a uniform strain, since then the 
 maximum pressure would be 
 
 which would be n times greater than that given by equation 
 (5). This result can be approximated to only by the sepa- 
 rate or combined application of two plans commonly known 
 as the methods of Varying Elasticity and of Initial Tension. 
 These are actually however, but variations of the former 
 principle. 
 
 VARYING ELASTICITY. 
 
 This consists in varying the elasticity of the concentric 
 cylinders as explained in Chap. XV, page 11. The elasticity 
 may be measured either by its coefficient or by its limit. 
 This divides the subject into two heads. 
 
 1. Varying Coefficient, or Rate E. 
 
 Suppose the gun to be composed of two concentric cylin- 
 ders, the tube containing the bore, and the jacket. If these 
 are of the same material the stress transmitted to the jacket 
 
10 XTX. — GUN CONSTRUCTION. 
 
 will follow Barlow's law. But if the jacket be made of a 
 metal with E' > E, then the stress on its inner surface due 
 to the strain arising from a given increase in the external 
 diameter of the tube will be increased. For calling e the 
 common strain, /, /, the corresponding stresses, and E^ E\ 
 the coefficients of elasticity respectively of the tube and 
 the jacket. 
 
 If the value of E increase as r*, then the stress on the inner 
 surface of the wall will he equal to that on the inner surface 
 of the tube. 
 
 For, let us call e^ the strain at the elastic limit of the 
 tube, then 
 
 8 
 '^ = ^ 
 At the outside of the tube the strain will be 
 
 This will cause a stress on the inner wall of the jacket 
 E'e J^ E' jR^ 
 
 If now E : E' :: F? : R'\ E' R^ = ER'^ and t'= d. 
 
 The thinner is the outside wall the less will the stress 
 vary throughout its thickness, so passing to the limit we 
 may say — That to develop an uniform resistance throughout a 
 cylinder the coefficients of elasticity of the eleme7itary concetitric 
 cylifiders must vary as the squares of their radii. 
 
 This principle, though frequently referred to in gun con- 
 struction, is now of little practical importance, since steel, 
 the coefficient of elasticity of which is constant, and is 
 
XIX. — GUN CO^STRUCTION. 11 
 
 greater than that of any other cannon metal, is now gen- 
 erally employed for all portions of the gun. 
 
 2. Varying Limit of Elasticity. 
 
 Equation (1) shows that the stress on any cylinder is 
 always greatest on its inner surface, and Equation (4) that 
 for a given gun the value of p^ is limited by the elastic limit 
 of the tube. 
 
 Consequently, if the value of ^is constant, we may in- 
 crease the strength of the gun by increasing the elastic limit 
 of the tube. 
 
 This may be done in three ways. 
 
 a. By increasing the pt'ifuitive elastic limit hy varying the 
 composition or structure of the tube. This is not practically 
 done. 
 
 b. By giving it a special elastic litnit before the bore is finished, 
 viz. : 1st; by raising the elastic limit itself by preliminary ten- 
 sion, as by mandrehng (Chap. XV, p. 22), or .by firing high 
 proof charges. 2nd ; by lowering the origin of stresses by a 
 preliminary compression, as by temporarily wrapping the tube 
 with successive layers of wire until the surface of the bore 
 receives a permanent set. 
 
 c. The principle of initial tension consists in subjecting the 
 interior cylinders to a stress of compression by the reciprocal 
 extension of the outer cylinders. 
 
 The effect is to increase the work required to deform the 
 inner cylinders, in which the strains due to firing are the 
 greatest, by diminishing the work required to deform the 
 outer cylinders, in which the strains due to firing are the 
 least. 
 
 The foregoing explains the gain in strength by mandrel- 
 ing, and also" why the heat of firing may really tend to 
 strengthen a gun instead of to weaken it as is generally 
 
VZ XIX. — GUN CONSTRUCTION. 
 
 supposed; since in both cases, the inner concentric cylinders 
 being expanded more than those exterior to them, stresses 
 are developed in the exterior cylinders which resist the further 
 extension of the inner portions. 
 
 It also explains the advantage of forming the tubes of more 
 ductile material than the jacket and hoops, since if excessive 
 powder pressure should expand the bore beyond its elastic 
 limit, the initial tension developed outside would tend to 
 prevent its further dilatation. 
 
 It accounts for the former preference for bronze, the duc- 
 tility of which sometimes caused such guns to fissure first 
 on the outside, where it was unsupported, while, on the 
 contrary, cast-iron would crack first on the surface of the 
 bore where the danger would less readily be seen. 
 
 Rodman's process of cooling cast-iron guns from the in- 
 terior by a stream of water, while the exterior of the flask 
 was heated by fires, was intended to utilize this principle 
 and was the first instance of its application on a large scale. 
 (Chap. XV, p. 21.) 
 
 But, while the cooling of the exterior portions of the cast- 
 ing might be retarded relatively to that of the portions next 
 to the bore, it could not be postponed until all the interior 
 portions had solidified. 
 
 Consequently the state of rest of such a gun could be 
 represented by figure 5 in which the dotted lines represent 
 what was desired and the full line what was attained. The 
 process was besides uncertain, since guns have been known 
 to break spontaneously from internal stresses so developed. 
 
 I APPLICATION TO BUILT UP GUNS. 
 
 The results sought by Rodman may be attained much 
 more certainly by the process of building up guns as ex- 
 plained in Chapter XV. In such a gun if the tube be com- 
 
XIX. — GUN CONSTRUCTION. 13 
 
 pressed until, under the law by which the stresses vary, the 
 elastic limit of compression, p, be reached on the surface 
 of the bore, then the effective value of the maximum tan- 
 gential stress to which this surface may be safely exposed 
 on firing will be 6 -\- p and the maximum safe pressure for 
 the tube will approach as a limit 
 
 J. = iS + p)'^. 
 
 The effect of this pressure is shown in figure 6, in which 
 the stress will change from — p to 4- ^ on the surface of 
 the bore. If we take p= 6, as is commonly done, then the 
 stress on the exterior of the tube will change from — ^' 7\ 
 to -^jR^ T^ as shown. 
 
 Now consider the jacket. The negative tension of the 
 tube is due to a positive tension of the jacket resulting from 
 shrinkage. Since the system is in equilibrium, the algebraic 
 sum of the tensions on the tube and the jacket must be equal 
 to 0; and, since from Barlow's law the tension, whether 
 positive or negative, is always numerically greatest on the 
 inner surface of a cylinder, we would have the condition 
 represented by figure 6, in which the area 
 
 RpT^R' = area R' T' T" R" . 
 
 This represents the state of the system at rest. 
 
 It is evident that the configuration of the stress area 
 on the jacket, and therefore the maximum stress, R' T\ 
 which it is called on to sustain from the shrinkage, will 
 depend upon the thickness of the jacket. Also that R' T' 
 must not only not exceed the elastic limit under tension, 6' ^ 
 of the jacket, but must be so far beneath it as to admit of 
 •the increment due to firing. 
 
 Now suppose the system to be placed in action by the 
 powder pressure and for simplicity assume that pz=: =.6', 
 
14 XIX. — GUN CONSTRUCTION. 
 
 As the tension on the surface of the bore changes from 
 — pto -\- 6 the strain on the surfaces of contact will increase 
 the tension there by a quantity. 
 
 For the tube this will simply change the sign of the stress 
 from — to +. 
 
 For the jacket the addition will be positive, the most 
 favorable case being when the dimensions of the jacket are 
 so chosen, as in figure 6, that the tension at rest + the 
 tension in action = 6'. The state of the system in action 
 is shown by the dotted lines of figure 6. 
 
 The tangential resistance of the system will be propor- 
 tional to the sum of the areas p R B T^ R' T^ p {=%s) 
 + R' T/ T,^ R" R' {= s') - R' T' T" R" R' (= s;) or 
 
 :2 
 
 :2 = 2^ + /-^, and/o= ^• 
 
 The dimensions of figure 6 render such a gun about twice 
 as strong as if it were a simple tube of the same size and 
 elasticity. 
 
 It is evident, that if, as on page 9, we suppose the gun 
 to consist of an indefinite number of cylinders in which the 
 initial tensions are properly applied, the thinner the cylinders 
 are made, the less will be the difference of the tensions on 
 their interior and exterior surfaces and the more nearly will 
 the broken line d T, T/ r,, become parallel to O R" , or 
 the more nearly will the resistance of the gun approach the 
 ideal case. 
 
 The difficulties of manufacture have generally limited the 
 number of cylinders to less than 5 but these difficulties can 
 be overcome by making the cylinders of continous wire 
 wrapped around a central tube. 
 
XIX. — GUN CONSTRUCTION. 15 
 
 SHRINKAGE. 
 
 It is seen that the initial tension depends primarily on 
 the shrinkage. In built up guns this may be due to heat- 
 ing the exterior cylinder as described in Chap. XV, or to 
 forcing by hydraulic pressure one cylinder within another, 
 the contact surfaces being reciprocally conical, or by wind- 
 ing wire continuously over a central tube. By whatever 
 method the result may be attained, the stress on the contact 
 surfaces is due to the strain resulting from the compression 
 of the inner cylinder and the extension of the exterior. 
 
 To determine the shrinkage required to produce a given 
 initial compression without exceeding either p in the inner 
 cylinders when the system is at rest or 6 in the exterior 
 when the system is in action, is one of the principal objects 
 of the different theories of gun construction now in vogue. 
 A full discussion of these theories is not possible in this 
 course, but the following treatment of the subject based 
 upon Barlow's law illustrates the methods now employed. 
 
 Let e, e' be the strains on the adjacent surfaces of the 
 tube and jacket, for the corresponding stresses R' T^ = /, 
 and R' T' == /' and let o* = <? + <?' be the shrinkage strain. 
 
 / t' 
 
 Then since e— —=^ and e' = -=r , from note, page 21, 
 jb JtL 
 
 <T=-^ = ^{t+n or AJi'= 5 c+o- 
 
 Consequently, as stated in Chapter XV, the tube would 
 be turned to a diameter 
 
 2R' 
 
 (/ + +2^' 
 
 and the jacket would be bored to its finished size. The 
 effect of shrinkage would be to vary the radii somewhat from 
 
16 . XIX. — GUN CONSTRUCTION. 
 
 those assumed, and to increase the length of the tube. 
 These variations, which, for this discussion are not taken 
 into account, afford one of the best means of testing the 
 accuracy of the hypotheses upon which different theories of 
 gun construction are based. 
 
 LONGITUDINAL STRESS. 
 
 This tends to "unbreech" a gun or to produce what is 
 known as a "ring fracture," the plane of which approaches 
 that of a right section. 
 
 In homogeneous guns it was sufficiently resisted by the 
 sections required to resist the tangential stress; but, in com- 
 posite b. 1. guns, except so far as friction due to shrinkage 
 and powder pressure may assist, that portion which contains 
 the breech block has to support this stress independently of 
 the portions which give tangential strength. 
 
 The bursting effort is tt jR."^ p^. It tends to pull the piece 
 apart, generally in rear of the trunnions to which it trans- 
 mits the pressure causing recoil. Consequently the piece 
 carrying the breech block must be firmly united to the 
 trunnions. When b. 1, guns were first made the block was 
 secured to the tube, but this arrangement, although theo- 
 retically advantageous,* is no longer generally employed. It 
 is thought that the radial expansion of the tube diminishes 
 the bearing of the screw threads of the breech block, and 
 that the tube is inclined to fissure through the screw threads. 
 
 Supposing the longitudinal stress to vary through the 
 cross-section, its resistance may be determined as follows : 
 
 * From the analysis referred to on page 2, it follows that the longitu- 
 dinal stress of the tube should develop a negative radial stress which 
 would neutralize a portion of the powder pressure. This has been con- 
 firmed by experiment on a small scale, and it is said that recent cannon 
 made abroad have the block screwed into the tube. 
 
XIX. — GtJN CONSTRUCTIOK. 17 
 
 The area of cross-section of an elementary cylinder whose 
 radius is r and the thickness of which is dr will be ^Ttrdr. 
 This will receive a variable stress q the intensity of which 
 will vary with its distance from the axis, so that the resistance 
 of the section whose internal and external radii are i?"and R' 
 
 q%7trdr. 
 n 
 
 If we suppose q to vary by Barlow's law, we have 
 
 Substituting this value of q and integrating we have for 
 the total resistance 
 
 ^ J!L=27rie^^Nap.log— . 
 
 Equating this with the bursting effort, we have for the 
 condition of equilibrium 
 
 A = 2 Nap. log ^. (6) 
 
 In modern guns the ordinary values of 0, R' and R are 
 such that the maximum value of /^ allowed by this equation 
 is considerably greater than that allowed by their tangential 
 resistance, so that these guns are abundantly strong against 
 longitudinal stress. 
 
 Equation (6) is useful for computing the pressures 
 necessary to burst spherical shell for which purpose it gives 
 results closely confirmed by practice. In such cases for B 
 should be substituted the tenacity of the material. This is 
 allowable since the ductility of such castings is small. 
 
 WIRE-WOUND GUNS. 
 
 The peculiar properties of cold drawn wire described in 
 Chapter XV; the direction assumed by the fibers in the 
 gun, and the increased facility of construction have for 
 
18 $Ct5t. — GtJN CONSTkUCtlOl^. 
 
 many years made this material a favorite subject of study 
 by gun makers. 
 
 Until recently, however, the difficulty of providing suffi- 
 cient longitudinal strength, and mechanical difficulties con- 
 nected with the attachment of the ends of the wires have 
 caused steel forgings to be preferred. 
 
 The following may be named as devices intended to pro- 
 vide the longitudinal resistance. 
 
 Dr. Woodbridge, of New Jersey, the originator of the 
 idea, proposed, after winding his tube to immerse the entire 
 gun in a bath of melted bronze, so as to braze or solder the 
 spirals and the layers together. This was found mechanic- 
 ally impracticable and the bath, by annealing the wire, 
 de&troyed much of its elasticity. Various experimenters 
 have tried longitudinal bars or staves connecting the trun- 
 nions with the breech, but so far as tried these are not 
 believed to have given satisfaction; the objection appearing 
 to consist in the difficulty of making all the bars resist 
 equally, for otherwise they will tend to rupture in detail. 
 Crozier's Wire Wound Gun. 
 
 This gun, now under construction, is devised by Lieut. 
 Crozier of the Ordnance Department. 
 
 It consists — 
 
 1. Of a thin steel tube forming a core for the winding; 
 to contain the rifling and to prevent the erosion of the wire. 
 It also incidentally gives longitudinal stiffness. 
 
 2. Of wire, to give tangential strength. This is preferably 
 of rectangular cross-section. Relying upon the support of the 
 wire wrapping, it is intended to produce an initial preliminary 
 compression considerably in excess of p. See page 11. For 
 experimental purposes it is assumed that the relatively thin 
 tube will withstand dilatation and contraction through a 
 considerably greater range than 6 -\- p. 
 
XIX. — GUN CONSTRUCTION. 19 
 
 The difficulties in attaching the wires have been success- 
 fully overcome by electro-welding. According to the method 
 proposed by Mr. Longridge of England each coil of wire is 
 wrapped with a tension diminishing from within outwards, so 
 that the tension of the inner layers will be eventually less 
 diminished than if the tension of winding were constant. 
 
 In such a gun, properly constructed, the tangential strain 
 developed by firing will be uniform throughout the entire 
 thickness of the walls. 
 
 3. Of a steel cast jacket carrying the breech block at one 
 end and the trunnions at the other and so furnishing the 
 required longitudinal strength. It also gives longitudinal 
 stiffness and being lightly shrunk on it also affords some 
 tangential resistance. This, the heaviest unit of construc- 
 tion is made, of cast steel on account of its cheapness, its 
 radial distance and its adaptability to the present state of 
 the arts in the United States. 
 
 Practical Corrections. 
 
 WEIGHT OF CANNON. 
 
 The dimensiojis of cannon are sometimes increased be- 
 yond what is required by their elastic strength so as to in- 
 crease their weight and thereby diminish the destructive 
 energy of their recoil; because, calling E this energy, and 
 e that of the projectile at the muzzle, and the corresponding 
 masses and velocities respectively J/, ;//, ?^and v^ we have 
 from the equation of momenta, the general equation, 
 
 8 a m 
 
 M V =^ mv or MV=^mv or E^-^r-pe. (7) 
 
 M ^ ^ 
 
 Equation (7) is an important one to remember, particu- 
 larly for small arms. 
 
20 XIX. — GUN CONSTRUCTION. 
 
 This equation is not exact, since it neglects the momentum 
 of the powder gases, (Chapter XI, page 18), but it is con- 
 venient for general discussions. For a more exact formula 
 see Chapter XXII. 
 
 LINERS. 
 
 In order to provide against the erosion of the bore, large 
 built up cannon are sometimes lined for a short distance in 
 ifront of the chamber with a thin tube which can be replaced 
 with comparative facility. Guns which are properly de- 
 signed appear more likely to fail from this cause than as 
 the result of stress. 
 
 LIMITS. 
 
 It is not considered advisable to work up to the limits p 
 and 6 as, for the sake of illustration, has been supposed. 
 A safe margin is allowed in both cases. Indeed the inverse 
 method is that generally followed, the gun being designed 
 to safely resist a certain value of /<,. 
 
 It can be shown theoretically that no great advantage is 
 gained as to tangential strength by increasing the thickness 
 of the walls over the powder chamber, much beyond one 
 caliber. See General Remarks^ Appendix. 
 
 gadolin's law. 
 
 Owing to the practical difficulty of making perfect forgings 
 of the thickness which this law would require for the exterior 
 layers it is not generally observed. 
 
XTX. — GUN CONSTRUCTION. 21 
 
 Note 1, Page 15. 
 
 Let R^ be the exterior radius of the tube, and R^ the interior radius of 
 the jacket before shrinkage ; and let R/ be their common radius after 
 shrinkage. 
 
 The effect of the shrinkage will be to diminish the radius of the tube 
 
 Similarly, for the jacket e' = • ^ '-^ e, since / <; /''. 
 
 The total shrinkage will be 
 
 R^-R/ R/-R, 
 
 R^ and R^ are so nearly equal to each other, and so large when compared 
 with the numerators of the fractions that either R' or R^ may be used 
 as a common denominator without material error. R' it taken because it 
 pertains to the tube on which the excess is left as described in Chapter XV, 
 The true shrinkage will therefore be slightly greater than 
 
22 XIX. GUN CONSTRUCTION. 
 
 THE ELASTIC STRENGTH OF GUNS. 
 
 By Captain L. L. Bkuff, U. S. Ordnance Department. 
 The object of this discussion is to give a general idea of 
 the methods employed in modern gun construction, for 
 determining the strength of guns, the strains to which they 
 may be safely subjected, and the methods by which the re- 
 quisite strength may be obtained. 
 
 Definitions. 
 
 The elastic limit of a metal is the greatest load in lbs. per 
 square inch of section which the metal will sustain before it 
 acquires a permanent set. 
 
 There are various elastic limits, such as those for tension, 
 compression, torsion, etc., depending on the manner in which 
 the stress is applied but the only ones of practical importance 
 in gun construction are those for tension and compression. 
 
 The modulus of elasticity of a metal (see Michie's Mechanics, 
 art. 22), is the ratio of the load or stress in pounds per square 
 inch, to the elongation or strain per linear inch produced by 
 this load within the elastic limit. It is expressed by dividing 
 the stress by the strain. Since within the elastic limit the 
 strain or elongation is proportional to the stress or load, it is 
 evident that this ratio is constant for the same metal. Its 
 value for all gun steel is taken at 30,000,000 lbs. 
 
 As in the case of the elastic hmit, there are various moduli 
 of elasticity, as for tension, compression, etc., but those for 
 tension and compression, which are the only ones used, agree 
 so nearly, that the uniform value given above is assumed for 
 both. 
 
 Hooke's Law. — This law is expressed above. It is as 
 follows : Within the elastic hmit of a metal, the stress is pro- 
 portional to the strain. 
 
 Stress and Strain. — In the discussion stress will be used to 
 denote the force in pounds per square inch producing a given 
 
^13^. — GUN CONSTRUCTION. 2^ 
 
 extension or compression per linear inch, and strain the corres- 
 ponding elongation or compression produced by the stress. 
 
 General Principles. 
 
 The construction of the modern gun is supposed to be 
 understood. That is, that it is composed of an interior tube, 
 surrounded by a jacket and one or more rows of hoops. 
 That the jacket carries the breech-closing device, and that 
 the jacket and hoops have interior diameters which are less than 
 the exterior diameters of the parts they envelop, by a certain 
 prescribed amount, and that the difference in diameter between 
 the enveloping cylinder and the enveloped cylinder is called 
 the shrinkage. In order to place the smaller or enveloping 
 cylinders over the enveloped cylinders, the former are ex- 
 panded by heat till they will pass over the corresponding sur- 
 faces, when they are cooled in place by the application of 
 water. 
 
 Theory. 
 
 The principle of initial tension is employed in the modern 
 built up gun. The interior layers which are under the greatest 
 strain, due to the action of the powder gas, are compressed 
 by the exterior layers, jacket and hoops. When the pressure 
 of the gas acts upon these interior layers, it has first to over- 
 come this initial compression, and then to extend or compress 
 these layers until they reach their elastic limit for extension or- 
 compression, before the maximum resistance of the gun is 
 reached. The exterior layers are subjected to initial tension, 
 by which their capacity for resisting interior pressure is partly 
 diminished, but owing to the law of its transmission, the strain 
 upon them is so much less per square inch than it is upon the 
 interior layers that they are able to resist it. Thus the interior 
 layers are relieved of a portion of the strain, due to the action 
 of the powder gas, and the strain transmitted to the exterior 
 layers, by the modern process of gun construction. 
 
24 XlX. — GUN CONSTRUCTION. 
 
 The best condition for strength in a gun is when every 
 layer of metal in its cross section is strained equally by a given 
 stress or pressure. 
 
 The foundation of the theory of the built up gun is 
 this. That ifi whatever state the gun may be considered^ 
 whether under the pressure of the powder gas, or free from it, 
 7ione of the fibers of any cylinder in the gim shall be elongated 
 or contracted beyond the elastic lifnit of the metal of that 
 cylinder^ which elastic limit is determined by the test of the 
 metal in a testing machine. 
 
 Two states or conditions of the gun are considered in this 
 discussion ; one, called " the system in action," which means 
 that the gun is subjected to the maximum interior pressure 
 which it can support with safety, and the other, called " the 
 system at rest," that is, when the gun is free from the pressure 
 of the powder gas, although the strains due to the shrinkages 
 still exist. 
 
 Methods of Discussion. 
 
 The general method of discussion is : 
 
 First. To assume a cube of metal the length of whose 
 edges is unity, and which is supposed to be perfectly elastic 
 up to a given limit ; to deduce the equations of equilibrium 
 which show the relations between the forces acting upon this 
 cube in directions at right angles to its faces, and the corres- 
 ponding elongations and contractions produced by them. 
 
 Second. To transform these equations so that they will apply 
 to the elements of a cylinder of metal ; or in other words, to 
 deduce the equations which give the relations between the 
 stresses at different points throughout the right section of a 
 single cylinder. 
 
 Third. To pass from a single cyhnder to a compound 
 cylinder composed of any number of single cylinders, and to 
 deduce for the latter the compressions and extensions pro- 
 
XIX.— GUN CONSTRUCTION. 25 
 
 duced by given pressures, and the shrinkages or differences 
 of diameter which will produce given compressions and 
 pressures. 
 
 FIRST. — EQUATIONS OF EQUILIBRIUM FOR A CUBE OF METAL 
 OF CONSTANT ELASTICITY WHOSE EDGES ARE EQUAL TO 
 UNITY. 
 
 It has been found by experiment, that when a cubical elastic 
 solid is acted upon by a given force of extension or com- 
 pression in a direction perpendicular to two of its opposite 
 faces, this force produces an extension or a compression of 
 the cube in the direction of the force, of a given amount, and 
 a corresponding compression or extension in the two direc- 
 tions at right angles to the given force equal to one-third 
 the first extension or compression. 
 
 The force is supposed to be within the elastic Umit of the 
 solid. 
 
 For example, suppose a force of extension /*, Fig. 7, to act 
 upon the opposite faces of a cube of metal, whose edges are 
 each one inch long. If it extends the edges a a a ^^ of a.n 
 inch it will shorten the edges d I? d and c c c ^ of ^^ :=: ^ oi 
 an inch, and the same for any other force. 
 
 In figure 8 
 Let B = the modulus of elasticity of the cube. 
 
 X, V and Z= three forces acting at right angles to the 
 
 faces of the cube, being tensions in the figure. 
 X; fi; V, =z the extensions produced by the three forces 
 Xy Fand Z, respectively. 
 
 Then the force X, according to the preceding principle, 
 produces an elongation in its own direction equal to 
 
 But the force K diminishes this elongation by the amount 
 
 iZ 
 
26 XIX — GUN CONSTRUCTION. 
 
 and the force Z by the amount 
 
 Hence the total elongation in the direction of X is 
 
 In the same way we have for the total elongations in the 
 directions of Kand Z 
 
 '=4{-f-^) 
 
 These three equations express the relations between the 
 elongations of the faces of an elastic cube whose edges are 
 unity, and the corresponding forces acting on them. 
 
 SECOND. APPLICATION TO AN ELASTIC CYLINDER. 
 
 We have supposed the three forces to be tensions. In the 
 case of a gun cylinder, however^ two of the forces are ten- 
 sions, one acting in the direction of a tangent to the cylinder, 
 and the other parallel to the axis, while the third is a pressure 
 and acts in the direction of the radius. In Figure 9, let / = 
 the radial pressure, / = the tangential tension, ^ the longitu- 
 dinal tension, per unit of area. 
 
 Substitute / for X, — J> for Y since it acts opposite to F, 
 and ^ for Z, and the above equations become 
 
 } 
 
 '--M' + T + l)) W 
 
XIX. — GUN CONSTRUCTION. 27 
 
 The first of these equations expresses the total change per 
 unit of length in the direction of the tangent of the cyhnder ; 
 the second the total compression (being negative) in the 
 direction of the radius ; and the third the total change in the 
 direction of the axis, due to the three forces /, / and q. 
 
 In order to apply these equations in practice the changes of 
 dimensions must be expressed in terms of the radii of the 
 cylinder and of the forces acting upon it. To express the 
 equations in these terms we proceed as follows : 
 
 Equations of Equilibrium in Terms of the Radii of the 
 Cylinder. 
 
 Let Figure 10 represent a section of the cylinder perpen- 
 dicular to the axis. 
 Let R = interior radius. 
 R ' n: exterior radius. 
 r = the radius of any circle of the section. 
 r' = any other radius exterior to r. 
 p zzzthe radial pressure per unit of surface at the distance 
 
 r from the axis. 
 tz=. the tangential stress per unit of surface at r, 
 q = the stress per unit of section parallel to the axis of 
 the cylinder, and supposed uniform throughout the 
 section. 
 /*=the interior radial pressure per unit of surface, 
 
 being the value of / for R. 
 ^'^the exterior radial pressure per unit of surface, 
 
 being the value of / for R' . 
 T and T' = the values of / for r = Rj and r= i?' re- 
 spectively. 
 ^=the modulus of elasticity. 
 The pressure/, whether acting inward or outward, develops 
 in the direction perpendicular to A B, Figure 10, a force 
 equal to 2j>r. 
 
28 XIX. — GUN CONSTRUCTION. 
 
 Increase r to r', and represent by f the new value of/. 
 This develops a force in the direction perpendicular \.q A B 
 equal to 2 p' r* . The algebraic difference between these forces 
 is in equilibrio with the product of twice the thickness of the 
 ring r* — ;' into the mean stress throughout the ring, which 
 represent by r. Hence 
 
 2/ / _ 2 /r = — 2 T (^ — r) 
 
 dividing 
 
 P'r' —pr _ ^ 
 r* — r 
 
 passing to the limit of the ratio in the first member by making 
 
 d{pf) 
 
 ( p' r' —pr \ 
 
 limit of 1 , ^ 
 
 r' ^ 
 
 limit of 
 
 \> 
 Hence 
 
 d (pr) __ 
 
 Taking the last of Equations (8), which expresses the strain 
 in the direction of the axis of the cylinder, and supposing 
 this uniform throughout the cross-section, we have 
 
 P\ 
 
 ^=M' 
 
 i+8 
 
 From this we have 
 
 or t— p=^^{q— V E) (10) 
 
 But the second member of this last equation is constant, 
 since we have supposed v uniform throughout the section ; 
 hence 
 
 / — / = constant. 
 
XIX. GUN CONSTRUCTION. 29 
 
 From which we may unite 
 
 t—p= T—P (A) 
 
 t—p=T' — F' (V) 
 
 From Equation (10) we have 
 
 t=P + i(q-vE) (11) 
 
 Substituting this for / in Equation (9) we have 
 
 performing the differentiation as indicated ; / and r being 
 
 variable, 
 
 pdr + rdp ^ o / Z7\ 
 
 Jr = — / — 3(^— v^) 
 
 reducing 
 
 dr dp 
 
 r ~~ 2 / + 3 (^ — V ^) 
 Integrating 
 
 log= (y) = 4 log. (2/ H- 3 (? - V ^ + log. C 
 
 i- = ^(2/ + 3(?-r^)) 
 Substituting the value of/ + 3 (? — v E) from (11) we have 
 
 ! = .(/+/) 
 
 (/ -j- /) r' = — = constant 
 From which we can write 
 
 {t^- p)r' = {T-^P)R' (Q 
 
 {t-\- p)r' = {T' -\-P<)R''' {D) 
 
 From Equations (A) and (B) we derive the following 
 principle : 
 
 The difference between the tension and the 'Pressure is the 
 same at all points. 
 
30 XIX. — GUN CONSTRUCTION. 
 
 From (C) and {D) we have the following principle : 
 
 At any point whatever^ the sum of the tension in the direction 
 of the circumference, ajid of the pressure in the direction of 
 the radius, varies inversely as the square of the radius. 
 
 This demonstration is given by Captain Crozier, Ordnance 
 Department, in " Notes on the Construction of Ordnance," 
 No. 35. 
 
 Applications. — It has been shown by Captain Birnie, Ord- 
 nance Department, that in considering the radial and tangential 
 strains in a gun cylinder, we may, without appreciable error, 
 omit the longitudinal strain, or the strain parallel to the axis, 
 and afterwards consider this latter strain separately. This 
 conclusion has been proved to be correct, by actual measure- 
 ments of guns during construction. This is equivalent to 
 making in Equation (8) 
 
 q^o, 
 when the equations become 
 
 In the last equation, which gives the change in the longi- 
 tudinal direction, this change will be produced by/ and /only. 
 From Equations (C) and {D) we have 
 
 (5-/ -j- pi) Ri 2 ^ (r-l. p) j^^ 
 
 and from {A) and {B) 
 
 T' — F' = T—F 
 Combining these two equations and ehminating T' we 
 
 have 
 
 ■ F'^ + J^ 2 F' ' F' 
 ^ ^' F'^ — F*" F" — F" 
 
/ = 
 
 XI3^. — GUN CONSTRUCTION. 31 
 
 Substituting this value in (J) and (C), combining the re- 
 sulting equations, and eliminating/ we have 
 
 Ri^ — R' -I- ^,2_^. ^ (13) 
 
 And by combining and eHminating / between the same 
 equations we have. 
 
 _ FJ ^ — P' Ii'\ . J^'^^'iP—P') 1 
 
 Substituting these values of / and / in Equations (12) we 
 have 
 
 2 {PR' — P' R'^) q^R'^ R' i^P— P') 1 
 '^ "" $(R" — R')jS "f" 3{R'' — R')£ r" ^^^ 
 
 _ ^(PR"— P' R'"") 4tR" R' {P—P') 1_ 
 ^— d(R'^ — R')£ ~" S {R' ' — R') E r" (^^^ 
 
 _ ^{PR' — P'R'') 
 ^ — "" 8 (i?"* — R') E vA ') 
 
 These equations give the values of the elongations or con- 
 tractions in terms of the pressures and radii, and the known 
 modulus E^ for any radius r. 
 
 Elastic Strength of a Simple or Single Cylinder. 
 
 Now it may be shown that the greatest elongations and 
 compressions of the fibres of a cyUnder subjected to an interior 
 pressure P, and an exterior pressure P' , take place at the inner 
 surface of the cylinder. (See appendix, Note 35, on the Con- 
 struction of Ordnance.) Assuming this, we recur now to the 
 fundamental principle stated above "that no fibre of any 
 cylinder in the gun shall be elongated or contracted beyond 
 the elastic limit of the metal of that cylinder." 
 
 Let Q = the elastic limit for tension, 
 
 p = the elastic limit for compression in pounds or tons 
 per square inch, of the cylinder. 
 
82 XlX. — GUN CONSTRUCTION. 
 
 Then the extension and compression at the elastic Hmit will 
 be respectively 
 
 and by the above principle these must be equal to the greatest 
 values of /I and [z respectively. 
 
 Since the greatest extensions and compressions will occur 
 at the interior of the cylinder, we have for their greatest 
 values by substituting jR for r in (15) and (16) 
 
 3 (i?' ' — R') E 
 
 (18) 
 
 f^ — — 3 (i?' » — R'YE (^^) 
 
 Placing these equal to -^ and -^ respectively, we have 
 . (4:R" + 2R')P—6R" P' 
 
 d(R'' — R') 
 
 I 2 pt 
 
 ___ (^R'^ — 2R')P—'2R'''P 
 P— 3(R'' — R') 
 
 From which we find two values for P, viz. : 
 ■^ 4 i?' ^ + 2 ^^ 
 
 ^ — 4: R" — '2.R' 
 
 (20) 
 
 (21) 
 
 Equation (20) gives the value for the interior pressure, 
 which will cause the layer of metal on the interior of the 
 cylinder to reach its elastic limit by extension, and Equation 
 (21) the value which will cause the same layer to be com- 
 pressed to its elastic limit ; these pressures being in pounds 
 or tons per square inch according as d and p are expressed in 
 pounds or tons. 
 
XIX. — GUN CONSTRUCTION. 83 
 
 It must be remembered that the less of the two pressures, 
 measures the elastic strength of the cyHnder. 
 
 THIRD. — THE ELASTIC STRENGTH OF A COMPOUND CYLINDER, 
 OR OF A BUILT-UP GUN. 
 
 For the sake of clearness in the nomenclature, and of sim- 
 plicity in discussion, the gun will be supposed to consist of two 
 cylinders only, shrunk one upon the other, and the resistance 
 of this compound cylinder, and the shrinkages to be used in 
 its construction, will be deduced. 
 In figure 11 let 
 
 P^ = the maximum internal pressure to which the 
 
 gun can be subjected. 
 P^ ■=. the normal pressure at the surface of contact 
 
 of the two cylinders. 
 P^ •=. the exterior normal pressure. 
 
 A' Pv P-i ^^ variations in the pressures, P^^ P^ and P^ due 
 
 to any cause whatever. 
 The above pressures and variations of pressure are those 
 which exist with the " system in action," — that is when the 
 maximum gas pressure is acting on the bore. 
 Let 
 
 PI = the normal pressure acting at the surface of 
 
 contact of the two cylinders when the system 
 
 is at rest — that is, when the pressure of the 
 
 gas does not act on the bore. 
 
 // = the variation of P^ due to any cause whatever. 
 
 J?g, i?j, R^ = the radii of bore, of interior of second cylinder, 
 
 and of exterior of second cylinder respectively. 
 
 0„, 0j =: elastic limits of inner and outer cylinders for 
 
 extension. 
 p^, pj = elastic limit of same for compression. 
 E^, E^ = moduli of elasticity of metal of cylinders. 
 
34 XIX. — GUN CONSTRUCTION. 
 
 Writing Equations (20) and (21) we have 
 
 ^ - 4^'^ + 2i?^~ ^^ 
 
 ^ — 4^'" — 2i?^ ^^^ 
 
 Now it will be remembered that in the case of a single 
 cylinder, Equation (20) gives the value of Z*^^^, the interior 
 pressure which will cause the layer of metal on the interior 
 of the cylinder to reach its elastic limit by extension, and 
 Equation (21) the value of P^^ the interior pressure which 
 will cause the same layer to be compressed to its elastic limit. 
 
 Taking the outer or second cylinder of the gun, it is always 
 under a strain of extension both in action and at rest, and 
 hence Equation (21) will not apply to it. 
 
 Equation (20) must therefore be used. To apply it to the 
 present case, R and R' in (20) are the inner and outer radii, 
 which now become R^ and R^ respectively. /*is the interior 
 pressure, and it now becomes P^, P' is the exterior pressure, 
 and it becomes P^. But this exterior pressure on the second 
 cylinder is simply that due to the atmosphere, and it is so 
 small in comparison with the other pressures considered that 
 it may be neglected. Hence 
 
 P. — o. 
 
 Also Q becomes Q^. Making these substitutions in (20) we 
 have 
 
 _ %{R^-R^)Q, 
 ' ~ 4: Rl + 2 R,' 
 
 This gives the value of the interior pressure on the outer 
 cylinder which will cause its inner layer to be strained to the 
 elastic limit for tension, and as this value is expressed in 
 
XIX. — GUN CONSTRUCTION. 85 
 
 known terms, P^ can be readily calculated. The value of 0^ 
 is obtained from test of the metal in a testing machine. 
 
 Now taking the inner cylinder, the pressure P^ just found, acts 
 not only on the interior of the outer cylinder, but also on the 
 exterior of this inner cylinder. Hence one of the normal 
 pressures acting on this inner cylinder is known, and we have 
 to calculate the other. • 
 
 This inner cylinder is not only extended by the action of 
 the powder gas, but it is also compressed radially by this 
 pressure, and it is subjected to a strain of compression by the 
 force P^ which we have just found. In other words the inner 
 cylinder is subjected to both tension and compression, and 
 hence it is necessary to calculate both strains, and to take the 
 smaller as the limit of its elastic resistance. 
 
 Referring to Equations (20) and (21) the following changes 
 must be made to apply them to the inner cylinder — 
 
 P becomes P^ 
 
 P' " P^ 
 
 R " R, 
 
 R' '* R^ 
 
 e - 6^ 
 
 Making these substitutions we can write 
 
 ,, 3{R,^-Rl) e,+ 6R,-'P, 
 V 4:R,' + 2 Rl 
 
 » ~ 4:R,^ ^2Rl 
 
 Substituting in these equations the known values of the 
 radii, and of ^^ and p^ together with the value of P, just cal- 
 culated, we obtain two values for /*„, the smaller of which is 
 the limiting value of the pressure for the compound cylinder 
 under discussion. 
 
86 XIX. — GUN CONSTRUCTION. 
 
 For convenience of reference these equations are collected 
 here — 
 
 p ^ 3 (i?i - R,' ) e, 
 
 4 7?^ + 2 R,' 
 
 ^ (n _ 3(^.'-^a K^ ^^.'P. V (22) 
 
 •^o ~ 4i?,^ + 2J?,1 ^ ^ ^ 
 
 3 {R, - i?^) p„ + 2 i?,' -P. 
 
 p(2) _ 
 
 The values of P, obtained from Equations (22), are the 
 pressures which will cause the interior of each cylinder to 
 reach its elastic limit for extension or compression; and since 
 the greatest strains in a cyHnder occur at its interior surface, 
 and since also no part of any cylinder must be strained be- 
 yond its elastic limit, it is evident that the values of P, thus 
 obtained, represent the greatest strains to which the cylinders 
 can be subjected. It will be seen hereafter, that these values 
 cannot always be used in practice, since the bore in the state 
 of rest, may be compressed beyond its elastic limit, by the use 
 of these values. 
 
 It is, therefore, necessary now to consider 
 
 The System at Rest. 
 
 Equations (22) give the pressures acting for the sys- 
 tem when under the maximum pressure of the powder 
 gas. It is evident, however, that when the system is at 
 rest, great pressures will exist at the surface of contact of 
 the two cylinders, due to the shrinkage of one on the other. 
 These pressures generally increase from the exterior to the in- 
 terior, and the interior of the bore is generally compressed 
 from this cause to a greater degree than any other part of the 
 gun. This compression of the bore may be so great as to 
 exceed the elastic limit for compression of the metal of the 
 inner cyHnder, and thus, although the gun is properly calcu- 
 lated for action, the principle upon which the whole structure 
 
XIX. — GUN CONSTRUCTION. 37 
 
 is built may be violated, when the gas pressure is removed. 
 In this case", the elasticity of the tube is destroyed., as effect- 
 ively as if by the powder pressure. 
 
 It is evident, also, that when the powder pressure ceases, 
 the pressure which existed at the surface of contact of the two 
 cyhnders will change, and will assume some other value for 
 the state of rest. The value of this variation of pressure at 
 the surface of contact has been denoted by /, and at the sur- 
 face of the bore by /o- The value of the pressure at the sur- 
 face of contact for the state of rest has been represented 
 by P\ 
 
 Now it is evident that the difference between the pressure 
 in action and at rest for any surface, gives the variation in the 
 pressure at that surface. Hence, since the pressure at the in- 
 terior of the bore, when the system is at rest, is zero, we have 
 
 and also 
 
 When these changes of pressure occur, they are accompanied 
 by corresponding changes of dimensions of the surfaces at 
 which they act, and these changes of dimensions depend 
 directly upon the variations of pressure. The greatest changes 
 of dimensions occur in the direction of the circumference or 
 of the tangent to the surfaces, and Equation (18) gives the 
 value of these changes for the interior surfaces. 
 
 To Calculate these Changes of Dimensions. 
 
 The variation of pressure acting on the outer cylinder .s 
 /,, and the exterior pressure is zero, being that of tlie atmos- 
 phere. Hence, substituting in Equation (18) for P its value 
 
 p^ and making 
 
 /" = o 
 R -^ R, 
 R' ^ R, 
 E =^ E, 
 
38 XIX. — GUN CONSTRUCTION. 
 
 we can write 
 
 ^^(4^^ + 2i?r)A 
 
 3 (J^l — R:^) E, 
 
 This represents the change of dimensions of the interior 
 of the outer cyUnder per unit of length of circumference, 
 under the change of pressure represented by p^. 
 
 To find the change of the exterior of the tube due to the 
 variations of pressures p^ and /, which act on it, we recur to 
 the general Equation (15), which gives the change in the 
 direction of the circumference, or of the tangent, of any 
 cylinder whose exterior and interior radii are R' and R at the 
 distance r from the axis. Replacing r by R' since the change 
 at the exterior of the cyHnder is now required, we have 
 
 _ %R^P-{^R^ + ^R'^)P' 
 ^ - 'i{R''^-R^)E ^^^^ 
 
 To apply this to the inner cylinder now under discussion 
 make 
 
 R' = Ry 
 
 and we write 
 
 6 Rl A. - (4 Rl + 2 R,') A . 
 
 A-= 
 
 3 {R,^ - Rf) E, 
 
 for the value of the change of exterior of inner cylinder or 
 tube. 
 
 Now since the outer surface of the tube, and the inner 
 surface of the outer cylinder are in contact, the same change 
 of dimensions must occur in both, at this surface of contact, 
 and hence the two values of X obtained above are equal. 
 
XIX. — GUN CONSTRUCTION. 89 
 
 We have therefore 
 
 6 RIP, — (4 i?^ + 2 R^)p, (4 i?l + 2 R^) /, 
 
 /i = 
 
 Solving this equation with reference to p, we have 
 QR,E,[Ri-R,']p^ 
 
 E, {R,—Rn (4i^o + ^Rn + E,(J^,^ — J^t) (4^^ + 2 R,') 
 
 (24) 
 Now in this equation /„ is known, since it is equal to — P^ 
 as before shown, and R^ has been already calculated by- 
 Equations (22), hence we can calculate/,. 
 
 Limiting Value for the Exterior Pressure on the Inner Cyl- 
 inder, System at Rest. 
 
 It has been stated that R^, given by Equations (22) represents 
 the maximum stress to which the gun can be subjected in 
 action, the smaller of the two values of P^ being used. It is 
 necessary now to determine what value can be allowed for 
 the exterior pressure upon the inner cylinder at rest, so that 
 the interior surface of the latter will not be compressed by it 
 beyond its elastic hmit. To do this we must find the value 
 of Ri for the state of rest. 
 
 The value of R/ for this state is as has been shown 
 
 R/ =R. + Pi 
 
 Assuming Equation (18) and making P — o^ since the 
 interior pressure at rest is zero, we have 
 
 ~2 R"" P' 
 
 A — 
 
 {R^ — P')E 
 
 which shows since it is negative, that there is tangential com- 
 pression, and as this is generally greater than the radial com- 
 pression. Equation (18) only is used. 
 
 This compression must not exceed that at the elastic hmit 
 
40 XIX. — GUN CONSTRUCTION. 
 
 which is 
 
 P 
 
 E 
 hence we have 
 
 for the limiting value of the compression at the interior of the 
 inner cylinder. Changing the letters to correspond to the 
 case of the tube under discussion ; that is, making 
 
 F' = P/ 
 
 R' ^ R, 
 
 R ^ R, 
 
 E ^E, 
 
 P = Po 
 
 and omitting the negative sign, as that simply indicates com- 
 pression, we write 
 
 2 R,' r/ p. 
 
 or 
 
 but 
 hence 
 
 (y?.' - K) E^ E, 
 
 ^, ^ (i?,' - F?^ p. 
 
 2/C 
 ^ = ^. + A 
 
 />/=/». + /. ^ ^^-'^"5^° (25) 
 
 and this value of P^ must not be exceeded. 
 
 This equation gives the value of /*/ r= P^ -(" A i^^ known 
 terms. 
 
 But we have the value of /i from Equation (24) by substi- 
 tuting for /„ its value — P^. Hence, substituting the value 
 of /i from Equation (24) in (25), we obtain a new value for 
 P^ which will cause the interior of the inner cylinder to be 
 compressed to its elastic limit at rest. The value thus ob- 
 
XIX. — aUN CONStRUCTlOl^. 41 
 
 tained for P^ must be substituted in that one of Equations 
 (22) which gives the least value for P^. The new value thus 
 obtained for P^ will be such that the inner cylinder will not 
 be strained beyond its elastic Hmit either in action or at rest, 
 and it represents the greatest value of the stress to which the 
 gun can be subjected without exceeding the elastic limit of 
 the metal composing it. 
 
 THE SHRINKAGE. 
 
 In Fig. 12, let OA represent the interior, and OB the ex- 
 terior radius of the inner cylinder, and OC and OD the inte- 
 rior and exterior radii of the outer cylinder, before they are 
 assembled to form the gun. Then the length CJS= OB — OC 
 is the shrinkage. As diameters are usually employed instead 
 of radii in tables of shrinkages, a more usual expression for 
 the shrinkage is 
 
 2 C^ = 2 {OB — OC) 
 
 or, in other words, the shrinkage is the difference of diameters 
 of the enveloping and enveloped cylinders. This is called 
 the absolute or actual shrinkage. The relative shrinkage is 
 the shrinkage per unit of diameter, or per unit of radius, and 
 is expressed by dividing the absolute shrinkage by the interior 
 diameter of the outer or enveloping cyUnder. Thus the rela- 
 tive shrinkage in this case is 
 
 2CB ^ '^(OB— OC) CB 
 ^0C~ 2 0C ~ OC 
 
 To determine the shrinkage for the case under discussion. In 
 Fig. 12, let OA, OB, OC and OD represent the same quan- 
 tities as above. 
 
 Now, when the outer cylinder is heated and expanded till 
 its interior radius OC is slightly greater than the exterior ra- 
 dius OB of the inner cylinder, and the exterior cylinder while 
 hot is placed on the interior cylinder, so as to envelop it, and 
 
4^ XIX. — GUN CONSTRUCTlOM. 
 
 is then cooled in this position, it is evident that the outer cyl- 
 inder will compress the exterior of the inner one, and that 
 their surface of contact will assume some such position as 
 K E E''y the outer radius O B oi the tube being compressed 
 to O E^ and the inner radius O C oi the outer cylinder being 
 extended to O E, Hence the radius O B has been compressed 
 by the amount 
 
 OB — OE z= BE 
 
 and the radius OC has been extended by 
 
 OE— 0C=^ CE ' 
 
 and the sum of these two is equal to the original shrinkage, 
 
 BC, or 
 
 BE -^ CE^ BC, 
 
 Hence, if we can find the values of the two quantities BE 
 and CE^ we will have that of the shrinkage. 
 
 Now when the two cylinders are assembled, and the system 
 is at rest, we have found that the pressure P^ acts at the con- 
 tact surface of the cylinders. That is, the exterior cylinder is 
 acted upon by a force represented by P^, and this force pro- 
 duces an extension per unit of radius of 
 
 CE 
 
 OC 
 
 CE being unknown. But Equation (18) gives the value of 
 
 this extension in terms of the radii, pressures and modulus of 
 
 the cylinder. Remembering that 
 
 P' = P^ — o 
 P =P,' 
 R' = R, 
 R = R, 
 E =E, 
 we write 
 
 CE _ (4 ^^ + 2 R,') P! 
 
 OC ~ 3 {Rl ~ R^')E, 
 
 This gives CE, 
 
XIX. GUN CONSTRUCTION. 43 
 
 To find BEy or the compression of the exterior of the tube. 
 The pressure acting is P/, as before, the interior pressure 
 being zero. This change being at the exterior of the cyHnder, 
 we use Equation (23), making the following changes, 
 
 P = o 
 
 P' = P^ 
 
 Hence we have 
 
 E =E, 
 
 oc ~ ■^ - 
 
 (4 iP„ + 2 J?,') P! 
 - 3 {R;- - Rl) E, 
 
 Strictly speaking, the true value is -—- for the change per 
 
 unit of radius, but the difference between OB and OC '\s so 
 small in practice that either may be used without appreciable 
 error. 
 
 Now it will be observed that the value of -^ = A just ob- 
 
 tained, is negative, indicating compression, and this is evi- 
 dently correct. 
 
 But the shrinkage sought is the sum of two positive quan- 
 tities 
 
 BE 4- CE CB 
 'OC ~ ~0C 
 In order to avoid the negative sign, and obtain the quantity 
 
 BE 
 
 j^ under a positive form, we suppose that the exterior cyl- 
 
 inder is removed from the interior cylinder. In this case it 
 is evident that the exterior surface of the inner cylinder will 
 expand and regain its original diameter, and that this expan- 
 sion is exactly the same in amount as the compression BE, 
 which was produced by shrinking on the outer cylinder. 
 This is equivalent to supposing the pressure P^' neutralized 
 
44 XIX. — GUN CONSTRUCTION-. 
 
 by an equal and opposite pressure ; that is, in the value of 
 
 BE 
 
 --T. we make 
 
 P.' = - A' 
 and that value becomes accordingly — 
 
 BE _ (4 R^ + 2 R^) F,' 
 
 a positive quantity. Now denoting by op the shrinkage of 
 the two cylinders, we have 
 
 CE-\.BE (4^/ + 2i?.^)P/ (4.R:-^<2R,^)P' 
 ^ OC ~ ^ (R^' — R:') E,~^S (R,' — R^') E^ ^ ^ 
 
 In using this equation it must be remembered that cp is the 
 relative shrinkage, or the shrinkage per unit of diameter. To 
 obtain the absolute shrinkage, the relative shrinkage must be 
 multiplied by the diameter. That is, if Z> represent the diam- 
 eter and (p the relative shrinkage (both in inches), and *S the 
 absolute shrinkage, then, 
 
 S ^ (j)X z> 
 
 and the exterior diameter of the cylinder must be made 
 E>' = D-{- S 
 Referring to figure 12, 
 
 2 OC^ jD 
 2CR=S=q)XZ> 
 2 0B= D' 
 
 GENERAL REMARKS. 
 
 It can be shown theoretically that the maximum resistance 
 is obtained from a gun cylinder when the radii of the differ- 
 ent cylinders composing it, vary from the interior in geomet- 
 rical progression. 
 
XIX. — GUN CONSTRUCTION. 
 
 45 
 
 This, however, is never adopted in practice for various 
 reasons, one of the principal being the objection to very thick 
 cylinders on account of their being more difficult to forge, 
 less uniform in quality, and more liable to imperfections in 
 the metal. 
 
 It can also be shown that no great advantage is gained as 
 regards tangential strength, by increasing the thickness of the 
 walls of the gun over the powder chamber much beyond one 
 caliber. These considerations combined with the capacity of 
 the forging plant where hoops, tubes and jackets are made, 
 will serve to fix the limits of thickness of the different cylin- 
 ders composing the gun. Examples are given here of three 
 modern guns : 
 
 Gun. 
 
 Diam. of 
 powder 
 chamber. 
 
 Thick- 
 ness of 
 tube. 
 
 Thick- 
 ness of 
 jacket. 
 
 Thick- 
 ness of 
 -Whoops. 
 
 Thick- 
 ness of 
 £ hoops. 
 
 Total 
 thickness 
 of wall. 
 
 Total 
 
 thickness 
 
 of wall. 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Calibers. 
 
 8-in. 
 
 9.50 
 
 2.75 
 
 4.25 
 
 3.30 
 
 
 10.30 
 
 1.0842 
 
 10-in. 
 
 11.80 
 
 3.20 
 
 4.90 
 
 2.525 
 
 3.10 
 
 13.725 
 
 1.1631 
 
 12-in. 
 
 14.20 
 
 3.90 
 
 5.80 
 
 2.90 
 
 3.425 
 
 16.025 
 
 1.1285 
 
 The caliber being the diameter of the powder chamber, 
 the above table shows that the thickness of wall only sHghtly 
 exceeds one calibre. 
 
 Having determined from the above considerations the 
 radii of the different cylinders composing the gun, the values 
 of the pressures which the gun will support in action may 
 be calculated from Equations (22), B and p being known 
 from tests of the metal in a testing machine. 
 
 Having obtained the values of /{ and F^ from Equations 
 (22), the system must be considered at rest, and the values 
 of the pressure P/ deduced which will be safe for that state 
 of the system. This is given by Equation (25). 
 
 Then this value of P^' must be used to deduce a new 
 
46 XIX. — GUN CONSTRUCTION. 
 
 value of Z*! , and this value of P^ must be substituted in that 
 one of Equations (22) which gave the lower value for P^ . 
 The new value of P^ thus deduced will represent the maxi- 
 mum pressure to which the gun can be safely subjected. 
 
 We can now calculate the shrinkage from Equation (26), 
 using the value of P/ already found. 
 
 The same method can be extended to guns composed of 
 any number of cylinders, but the subject becomes more 
 complex as the number of cyhnders increases. 
 
 After calculating the shrinkages, the same fundamental 
 formulas may be used to calculate the compressions of the 
 bore produced by the assembhng of the cylinders. The 
 results of these calculations are then compared with actual 
 measurements of the bore made during the assembling of the 
 gun, and the agreement is in every case found to be 
 remarkably close, and furnishes a proof of the correctness 
 of the theory. 
 
 Thickness of Gun at Different Points. 
 
 The thickness of the gun at the reinforce is determined by 
 the considerations already given, and as stated, rarely 
 exceeds one and a half calibres. To determine its thickness 
 at various points along the chase, it is necessary to have the 
 '* pressure curve " of the powder at different points along the 
 bore. Formulas have been deduced for this curve by various 
 authors, but it is not deemed necessary to give them here. 
 The results obtained from them do not agree, and recent 
 experiments on a small gun show that Noble & Abel's formula, 
 Chapter IX, agrees very well with the results of experiment. 
 Using this formula, the pressure curve can be obtained. 
 
 The elastic resistance of the gun, or the values of P^ for 
 different sections of the gun, are calculated as explamed, and 
 plotted, and the curve of powder pressure for the same gun 
 
XIX.— GUN CONSTRUCTION. 47 
 
 is also plotted to the same scale. The curve of resistance 
 should always He above the curve of pressures. 
 
 Length of Gun. 
 
 This may be determined for a given initial velocity and 
 given conditions of loading, charge of powder, etc., by 
 Sarrau's formulas for velocity, but as a practical rule, it may 
 be stated that at present the total length of modern high 
 power guns varies between 35 and 45 calibres, and that the 
 tendency is toward the higher limit. 
 
XX. — EXTERIOR BALLISTICS. 
 
 CHAPTER XX. 
 
 EXTERIOR BALLISTICS. 
 
 This treats of the motion of the projectile after it has 
 left the gun. 
 Definitions. 
 
 The sights are two projections on the upper surface of 
 the piece, the distance between which parallel to the axis, 
 is called the sight radius^ or sometimes the radius of the 
 gun. 
 
 Each sight contains a definite point called the sight point. 
 That for the front sight, which is fixed, is generally deter- 
 mined by the intersection, at an acute angle, of the faces 
 of a wedge or by the intersection of cross wires as in sur- 
 veying instruments. That for the rear sight consists of a 
 notch in a bar, or a pin hole. 
 
 The rear sight point is movable so as to vary its distance 
 from the axis. 
 
 The difference of the distances of the sight points from 
 the axis of the bore, divided by the radius of the gun, meas- 
 ures the tangent of the angle of elevation^ or of <f, figure I. 
 
 The line of sight is a straight line passing through the two 
 sight points. In the act of aiming it also pierces the target. 
 In this case, therefore, the angle of elevation is the angle 
 included between the line of sight and the axis of the bore. 
 
 The line of departure is the line in which the projectile is 
 moving when it leaves the gun. It is therefore the tangent 
 to the trajectory at the muzzle. Owing to the incipient 
 recoil, due to the conservatism of the system (Chapters VII, 
 
XX. — EXTERIOR BALLISTICS. 
 
 XXI), and to necessary looseness of the joints between the 
 trunnions and the carriage, and between the carriage and the 
 wheels, the piece tends to revolve slightly about some point 
 in rear, so that the projectile does not always leave the piece 
 in the original direction of the axis. The angle included 
 between the axis and the line of departure is called the angle 
 oi ju7np,j\ figure 1. If to attain a given target the jump, 
 which is almost always positive, were neglected, we would 
 find d'> q and the computed value of e would be too great, 
 so that the target would be overshot. 
 
 The angle made by the line of departure with the horizon- 
 tal plane is called the angle of departure, d, figure 1. It is 
 with this angle that we have principally to deal in ballistics, 
 as it is the angle at which the projectile actually begins its 
 flight. 
 
 The angle of projection is the angle included between the 
 line of departure and the line of sight ; it may be thought of 
 as the angle of elevation corrected for jump. 
 
 The quadrant angle is the angle made by the axis of the 
 bore and the horizontal. It is measured by the gunner's 
 quadrant, a form of spirit level, applied to the face of the 
 muzzle or to some cylindrical surface of the gun. Owing to 
 the grooves in rifled guns this is preferably an exterior surface. 
 See q, figure 1. 
 
 The quadrant angle may be measured either above or 
 below the horizontal plane. The term depressed or plunging 
 fire refers to a negative quadrant angle. 
 
 The angle of sight is the angle included between the line 
 of sight and the horizontal plane, or s^ figure 1.* 
 
 * This depends solely upon the altitude of the target in the astronomi- 
 cal sense. It is unfortunate that the term above named should be used 
 to designate this angle, as it has nothing whatever to do with the sights. 
 
 It would be more consistent if the terms angle of sights and of elevation 
 were exchanged. In the P>ench service the angle of sight is called the 
 angle of site. 
 
XX. — EXTERIOR BALLISTICS. 
 
 It is seen from the figure and by definition that 
 
 Of these quantities, s is given by the act of pointing, and 
 e must be computed by the methods hereafter explained. 
 The above equation is principally useful for verifying the 
 elevation given by the sights or for guns which are not pro- 
 vided with sights. 
 
 To determine the Jump, 
 
 Place in front of the gun and at a distance just beyond 
 the reach of the blast a slight screen. Mark upon the screen 
 the point o^ at which it is pierced by the axis of the bore 
 prolonged. In breech-loaders this may be done by means 
 of perforated discs fitting the bore, and in muzzle-loaders 
 by making ^ = and laying off on the screen the coordi- 
 nates of the sight points negatively taken. 
 
 Fire the piece and determine V. 
 
 If then X and y are the horizontal and vertical coordi- 
 nates of the center of the shot hole when referred to ^, and 
 d the distance of the screen from the muzzle we have 
 approximately, from figure 2, 
 
 tan J — 
 
 ._y -Vab 
 
 d 
 
 ^t^ d 
 
 but ad= ^ and t= ~ neartyj 
 
 hence tan /= | + ^^. 
 
 If the shot strikes below the point, then y is measured 
 negatively. 
 
 X 
 
 The lateral jump is evidently tan~^ = —, 
 
 " Cti 
 
XX. — EXTERIOR BALLISTICS. 
 
 A number of such determinations should be made since 
 the method is obviously inaccurate. 
 
 A better plan is to eliminate the effect of the perturba- 
 tions near the muzzle by computing e and determining by 
 experiment the value of p for an extended range of, say 
 600 yards, — then j — p — e 
 
 The jump is usually about 30' which value will be taken 
 in problems in which it is required to be assumed. 
 
 The planes of sight and of departure are vertical planes 
 containing the corresponding lines. 
 
 The computed range is the distance from the gun to the 
 (second) intersection of the trajectory by the line of sight. 
 The term range is also applied according to circumstances 
 to the distance of the target from the gun, and to the hori- 
 zontal distance to the point of impact — in case the target 
 be missed and the projectile strikes some horizontal surface 
 in front or rear of the target — such as water. 
 
 Practically the dimensions of the gun may be neglected 
 so that the front sight point may be considered in the axis 
 of the bore and the range to be measured from either sight 
 indifferently. 
 
 In the following discussions we will also assume that the 
 planes of sight and of departure coincide in the vertical 
 plane containing the axis of the piece, which is called the 
 plane of fire^ and that the projectile travels in the plane 
 of departure. 
 
 This is not actually true, however, for the projectile tends 
 to move sideways out of the plane of departure as shown by 
 the horizontal projection of figure 1. This motion, called 
 the drifts is due to the combined effect of the rotation of the 
 projectile and the resistance of the air ; combined with other 
 causes of inaccuracy it leads at the target to lateral deviation^ 
 which is meaured by the distance of the point of impact from 
 the plane of sight. See Chapter XXX. 
 
XX. EXTERIOR BALLISTICS. 
 
 The deviation in ran^e is similarly measured. 
 
 Classification of Fire, 
 
 In this classification the sights are disregarded and the 
 line of fire is the straight line from the muzzle of the piece 
 to the point aimed at. Similarly for general discussions the 
 quadrant angle is sometimes called the angle of fire. 
 
 Figure 3 illustrates the classification with reference to 
 the vertical plane containing the target, which represents a 
 certain face of a work. 
 
 Figure 4 illustrates the classification with reference to 
 the horizontal plane. The limit for direct fire is imposed 
 by the principle of the rigidity of the trajectory to be here- 
 after explained. 
 
 The classification is also applied, as indicated, to the 
 angles of descent. This is more accurate since it relates to 
 the effect produced rather than to the intention of produc- 
 ing a given effect. 
 
 In figure 1 it is assumed without sensible error, that the lines of 
 sight, departure, etc., intersect at the muzzle, and the drift is very much 
 exaggerated. 
 
XX. — EXTERIOR BALLISTICS. 
 
 Exterior ballistics is usually divided into tw© parts. 1st, 
 in vacuo; 2d, in the air. 
 
 I TRAJECTORY IN VACUO. 
 
 Utility. 
 
 The first of these is sufficiently treated in the course of 
 Mechanics. Its practical utility is confined to two cases. 
 
 1st. That of projectiles of high sectional density moving 
 with comparatively low velocity as in mortars, since in such 
 cases the loss of energy due to the resistance of the air may 
 be neglected where only approximate results are required. 
 Chapter XVI, page 1. 
 
 2d. Cases involving the flight of projectiles in the air, in 
 which some of the data are lacking, or in which the velocity 
 of the projectile in one of its component directions is so 
 low that the consequent retardation may be neglected. 
 
 » USEFUL FORMULAE. 
 
 The principal equations of this kind which are used in 
 this course may be derived from equation (167), Michie, 
 in which we write, as is customary, y for z, 
 
 ^ = Vsme-st; (1) 
 
 whence 
 
 j= Vt sin d- ^r^ (2) 
 
 and by placing -^ =0 
 
 (3) 
 
 for the time to the vertex of the trajectory. 
 
XX. — EXTERIOR BALLISTICS. 
 
 From the symmetry of the trajectory in vacuo, T, the 
 whole time of flight is equal to 2/ or 
 
 and 
 
 Eliminating V by substituting this value in Equation (2), 
 
 y^q.(T-i) (6) 
 
 T s: T^ 
 
 If in this we replace /by — we have F= ^—5 — (7) 
 
 in which jj' now becomes F, the ordinate of the vertex. 
 
 That is, the height of the vertex in feet is nearly four 
 times the square of the time of flight in seconds. 
 
 Equations (6) and (7) are important, and should be re- 
 membered, as they are frequently used in approximate solu- 
 tions in the air. 
 
 If in Equation (169), Michie, rewritten according to the 
 usual nomenclature, or 
 
 y = X tan — -r--- ^-^ (8) 
 
 in which ^is the height through which the projectile must 
 fall to acquire the velocity F, we make j = 6 wq may 
 determine the range X 
 
 2 V sin cos (9 _ V sin 2 d 
 
 X =: (y) 
 
 g g 
 
 Therefore the range will vary less from variations in 0, as 
 d approaches 45°. 
 Also, for the same value of B, as in S. B. mortars, 
 X: X' -.'.V^: V'\ 
 
XX.— EXTERIOR BALLISTICS. 
 
 But, considering the powder as a reservoir of potential 
 energy, frona the equation of energy we have approximately 
 
 And assijming the weight of the projectile, JV, to be con- 
 stant for the same piece 
 
 w: w'v.E'. E'wV^ \ V'^::X: X\ 
 
 Therefore, in a S. B. mortar the charges are proportional 
 to the ranges. This is of importance in regulating charges 
 and works well in practice. 
 
 If in equation (9) we substitute the value of F in equa- 
 tion (5), we find, if we call g=32 approximately and ^=45°, 
 X=16 T' or 
 
 T= ^ (10) 
 
 which gives a rule for timing mortar fuzes. 
 
 RESISTANCE OF THE AIR. 
 
 To give an idea of the pressure exerted on projectiles in 
 the air and consequently of the insufficiency of the preced- 
 ing formulae for practical use, except in the cases cited; it 
 will suffice to say that a velocity of the wind of about 100 
 miles an hour is designated in the Ordnance Manual as a 
 "hurricane that tears up trees, carries buildings before 
 it, etc." 
 
 In projectiles moving with the high velocities now attained 
 the pressure is over 80 times as great as that assigned to 
 the hurricane. 
 
 EXPERIMENTS TO DETERMINE THE RESISTANCE OF THE AIR. 
 
 Experiments have been constantly made since Robins, 
 called the " Father of Gunnery," began to investigate this 
 subject about the middle of the last century. But these 
 
:XX. EXTERIOR BALLISTICS. 
 
 gave untrustworthy results owing to the lack of suitable 
 velocimeters. 
 
 It is upon the investigations of the Reverend Francis 
 Bashforth, conducted under the auspices of the British 
 Government from 1865 to 1880, that our knowledge of the 
 effects of this resistance is based. 
 
 RESULTS OF EXPERIMENTS. 
 
 Resistance. 
 
 Bashforth's experiments demonstrate that the resistance 
 varies with the quantities shown on the following tabular 
 scheme. 
 
 '1. Area of cross-section or ^^, Chap. XVI. 
 
 2. Density of air. 
 
 3. k, Chap. XVI,|l. Meridian section]^ ^^^^^^^» 
 
 Resist- 
 ance 
 
 varies 
 
 with ^ page 2, viz.: |jj Velocity of projectile'. 
 
 1. That the resistance varies with the area is recognized by 
 all experimenters. 
 
 2. The effect of variations in the density of the air, whether 
 due to variations in barometric pressure, in temperature or in 
 humidity, or from the passage of the projectile through strata 
 of varying density, is allowed for m refined computations by 
 suitable coefficients. For this treatise the effects of such 
 variations are neglected. 
 
 3. Variations in k due to slight variations in the meridian 
 section are also neglected, although they may be similarly 
 corrected, see b below. 
 
 1. As to the Meridiafi Section^ viz, : 
 (a) Form of Head. — Bashforth in his experiments used 
 projectiles of the same calibre and weight, and having heads 
 of five different shapes. These were, 1st, hemispherical; 
 2d, hemispheroidal, with axes in the ratio of 1 to 2; 
 3d, ogival, radius of head 1 diameter; 4th, ogival, radius of 
 bead 2 diameters; 5th, fiat. 
 
10 XX. — EXTERIOR BALLISTICS. 
 
 The resistance was greatest on the flat-headed projectile, 
 and least on the hemispheroidal and ogival of two diameters. 
 Rashforth concludes that the resistance offered by the air to 
 the motion of elongated projectiles is but little affected by 
 the more or less pointed apex, but depends chiefly upon 
 the form of the head, near its junction with the cylindrical 
 body of the shot. At this point the forms of the hemisphe- 
 roidal head, and of the ogival head of two diameters radius, 
 are about the same, and their resistances are nearly equal. 
 
 (/^) Form of Body. — Recent experiments by Krupp have 
 shown that the resistance varies also with the shapes of the 
 sides and rear of the projectile, and with the character of its 
 surface. 
 
 2. Retardation and Velocity, 
 
 Rashforth's method was one of interpolation founded on 
 the use of velocimeters of Class II, by which he determined 
 by means of finite differences the retardation of the pro- 
 jectile at certain points of its trajectory at which the velocity 
 was known. 
 
 Everything else being constant, the relation between the 
 retardation and the velocity was known for each of the veloc- 
 ities observed at any one fire. And by varying these veloc- 
 ities as by varying the initial velocity or the distance of the 
 gun from the targets, an indefinite number of velocities could 
 be observed and their corresponding retardations computed. 
 
 Finally, the law connecting the velocity and the retardation 
 could be deduced by analysis, or expressed by plotting a 
 curve of which the retardation and velocities are the coordi- 
 nate axes. 
 
 For the same velocity the retardation was found to vary 
 with (') the sectional density of the projectile, its f ) meridian 
 section and (') surface, and with the (*) density of the air as 
 
XX. — EXTERIOR BALLISTICS. 11 
 
 affected by its temperature, barometric pressure and its 
 humidity. 
 
 Accordingly, such a law must for convenience be reduced 
 to standard conditions, that is, when (i) W (in pounds) = d^ 
 (in inches), i. e., when we have the unit projectile^ and when 
 the (2) proportions and (3) surface of the projectile are well 
 defined, and the (^) density of the air is at a known standard. 
 
 Variations in these four conditions are subsequently 
 allowed for by suitable empirical coefficients of which we 
 shall deal with only that relating to the sectional density. 
 
 It may be stated however that Bashforth used a M. L. R. 
 gun firing studded projectiles^ the points having a radius of 
 IJ calibres. The more recent B. L. projectiles, having 
 sharper points and smoother surfaces, reduce the retardation 
 by 5 or .10 per cent. See page 10. 
 
 bashforth's method. 
 
 , He placed 10 targets at a constant interval of 150 feet=/. 
 This gave such a number of observations at each fire that 
 they served to correct each other by the principle of con- 
 tinuity, so that the final order of differences would be either 
 0, or would change very slowly. Examples of this are seen 
 in the methods used in correcting tables of squares, cubes 
 and of logarithms. 
 
 For this purpose the advantages of instruments of Class 
 II. over those of Class I. are obvious. Such instruments 
 ordinarily give only the velocity at some point between each 
 pair of targets. But Bashforth sought the velocity at the 
 target itself as follows : 
 
 Calling (7;,,) the velocity at the target which is at a distance 
 X from the gun 
 
12 XX. — EXTERIOR BALLISTICS. 
 
 In measuring velocity it is customary to express j as a 
 function of t, in which t (one second) is the constant. 
 But when, as in these experiments, / is constant, it is 
 advisable to express the velocity by varying the value of/. 
 Consequently, calling r^ the retardation at the distance x 
 and observing that, since this is a negative acceleration, we 
 may neglect the minus sign resulting from differentiation, 
 we have "^ 
 
 ~di~~dF 
 
 ^{ij=i^^^ (12) 
 
 The object of presenting the retardation in this form was 
 to make it an explicit function of the cube of the velocity 
 since Bashforth had reason to believe that the retardation 
 followed what is known as the cubic law.^ 
 
 In order to apply equations (U) and (12) practically, it 
 is necessary to find by experiment such finite values for dt 
 and d'^t that, when substituted in the preceding equations 
 they will give proper values for v^ and r,. Or, calling these 
 finite values A/, ^nd AV, 
 
 ^^=^ (11') 
 
 '■.= ~/r^l (13') 
 
 * The simplicity of such a law has always proved attractive to in- 
 vestigators of thir, subject. Sir Isaac Newton took it to vary with the 
 square of the velocity, and others with varying powers of the velocity 
 corresponding to certain limiting velocities. 
 
 Newton's law has recently been proved nearly true for the high veloci- 
 ties and smooth pointed projectiles now employed. It will be seen here- 
 after how Bashforth corrected the cubic law by an empirical coefficient 
 corresponding to the velocity. 
 
XX. — EXTERIOR BALLISTICS. 13 
 
 DETERMINATION OF VELOCITY AND RESISTANCE. 
 
 Referring to Bashforth's experiments, let s denote the 
 distance from any origin to the first target. Then j + / 
 will be the distance from the same origin to the second 
 target and s-\-(n — 1) / the distance to the «'* target at the 
 distance x, and so on. 
 
 Also, let 4 denote the time from any origin until the 
 first target is reached. Then fs+(n-i)i will be the time from 
 the same origin until the n^'^ target is reached and so on. 
 
 Now, let ^1, 4> 4> etc., denote the 1st, 2d, 3d orders of 
 difference and d\ d'\ d"\ the successive terms in these 
 orders of difference so that 4'" will mean the third term 
 in the second order of difference and so on. 
 
 Then 4+i~4=^/> which will be the time of passage of 
 the projectile between the 1st and 2d targets and 
 
 4+21 4+1 = ^1 y 
 
 and d-l*—d^=d^ and so on. 
 
 We may therefore form the following table which may 
 be filled up from experiment as shown below numerically, 
 and graphically by the diagram, figure 5. 
 
 The dotted lines in the diagram serve to indicate the 
 successive orders of difference after the manner of the 
 brackets in the table. 
 
 TABLE. 
 
 No. of -p.. . Time of Orders of difference. 
 
 target. distance. ^^^^^^^ ^^ ^^ d^ . , , d^n-i) 
 
 1. 
 
 s 
 
 ^8 
 
 2. 
 
 s + l 
 
 4-fi 
 
 3. 
 
 j + 2/ 
 
 4+21 
 
 4. 
 
 5 + 3/ 
 
 4+31 
 
 5. 
 
 j + 4/ 
 
 4+41 
 
 [ dJ' etc. 
 
 \d. 
 
 
 
14 :XX. — EXTERIOR BALLISTICS. 
 
 
 NUMERICAL EXAMPLE. 
 
 
 
 
 
 times. 
 
 ^1 
 
 ^. 
 
 ^8 
 
 1. 
 
 S 
 
 3.0526 
 
 .1090 
 
 
 
 2. 
 
 j+150 
 
 3.1616 
 
 .1114 
 
 .0024 
 
 
 
 3. 
 
 J + 300 
 
 3.2730 
 
 .1138 
 
 .0024 
 
 1 
 
 4. 
 
 J + 450 
 
 3.3868 
 
 .1163 
 
 .0025 
 
 
 
 6. 
 
 ^ + 600 
 
 3.5031 
 
 .1188 
 
 .0025 
 
 
 6. .y + 750 3.6219 
 
 From the algebra we have 
 
 ^.+.=4+H' + « ^^/ + «^"~;y3~^^4' + etc. 
 
 Arranging the terms of the second member with refer- 
 ence to n which is arbitrary, we have 
 
 4+ni=4 + « W-i 4' + J 4'-etc.) 
 
 + ^(4'-4' + etc.) (13) 
 
 Now /g^nb being a function of the space (s + nl)^ may be 
 developed by Taylor's formula. Hence we have 
 
 /s+ni=/(^ + «/) =^«+ ^«^+ -^T2- + ^'"- 
 or since, ds=lf 
 
 2 
 
 Equating the coefficients of the first power of n in the 
 second members of the two identical equations (13) and 
 (14), we have 
 
 <^/s=<^i'-J4'+^^3'~etc.=A4 (15) 
 
:XX. — EXTERIOR BALLISTICS. 15 
 
 which is the finite value of dt^ for the constant increment 
 of 5. 
 
 In other words, and as shown by figure 5, if Bashforth 
 had taken d-l to be the increment of time at the first tar- 
 get corresponding to ds^ the velocity computed would have 
 been the mean velocity between the 1st and 2d targets and 
 would have been too small. Consequently this increment 
 is diminished by \ d^ . This makes the velocity too great, 
 so that \ d^ is added, the approximation increasing with. 
 the number of targets employed; since, under the same 
 circumstances, the greater the number of observations, the 
 more truly can the law be determined; or, mathematically 
 speaking, the greater will be the ± correction applied to 
 d^ since the greater will be the number of orders of 
 difference. 
 
 Therefore, for the target at the distance s or the first 
 target, 
 
 _ 2__ 150 ""^^ 
 
 Similarly for the «'* target at the distance x = s-\- (n — 1)/ 
 
 150 / ..„ 
 
 ""- - d^ - i 4° + ^4" - etc.- df, ^ (_,,, ^^^^ 
 
 The number of the targets at which velocities could be 
 obtained is determined by the number of targets employed 
 and by the number of orders of difference which the law of 
 retardation permits. If n' be this number, then velocities 
 may be determined at (n — ;/) points. 
 
 Similarly, we have the coefficients of the second power 
 
 d% = d/—dj + etc. = A V„ (18) 
 
 and for the «** target 
 
 rx = 
 
 -^ AV, = p^.( d^^d,^ + etc. ) (19) 
 
16 .XX. — EXTERIOR BALLISTICS. 
 
 Example. 
 
 The velocity at the 4th target in the preceding table is 
 1304: and the retardation 246.5.* 
 
 RESULTS OF THE EXPERIMENTS. 
 
 If the cubic law had held true for all velocities, the co- 
 efficient k in Equation (1), Chapter XVI, could have been 
 replaced by some explicit function of i^. 
 
 But while this was found to be nearly true for velocities 
 between 1100 and ]350 feet, it failed for velocities above 
 and below these limits, as Bashforth found by increasing 
 his velocities progressively from 100 to 2900 feet. 
 
 He accordingly introduced an empirical constant k* by 
 which to correct the departure from the cubic law so that 
 
 r — — /&' 7/ 
 
 W ' 
 
 and as k' is a very small quantity, he replaced it by 
 
 /ir= (1000)3 >^', 
 so that 
 
 Table I gives the value of K for the velocities named 
 therein and figure 6 is plotted from the indications of 
 Table I. 
 Example. 
 
 A 12.5 inch shell weighing 802.25 lbs. has a velocity of 
 1400. The total air pressure is 1394 lbs. and the retardation 
 is 55.96 at the instant that the velocity is 1400. 
 
 Figure 7 gives the pressure on what is called a circular 
 inch (that is a circle of which ^=1 inch) on spherical pro- 
 jectiles, curve A; on studded oblong projectiles of which 
 
 *Throughout this chapter velocities will be expressed numerically, as 
 the unit of velocity, or foot-second, may be understood. 
 
XX. — EXTERIOR BALLISTICS. 17 
 
 the radius of curvature of the head is | d^ curve B ; and 
 on modern smooth b. 1. projectiles in which the radius = 2 d, 
 curve C, derived from recent experiments by Krupp. 
 
 In curve B two remarkable inflections are observed. One 
 at about 1090, the velocity of sound, and the other at about 
 2413, that of air rushing into a vacuum. 
 
 The first velocity marks the passage of the projectile into 
 a medium undisturbed by the explosion of the gun or by its 
 own passage. The second denotes the formation of a 
 vacuum in rear of the projectile which increases the pressure 
 to ajDout double that of the barometric pressure of the 
 atmosphere. 
 
 In firing at troops, particularly in sieges, it is important 
 to have the terminal velocity exceed that of sound, so that 
 the projectile may precede the warning sound made by its 
 passage through the air. 
 
 The irregularity of curves B and C shows the impossibility 
 of expressing by any simple law the relation between 
 velocity and pressure. 
 
 i 
 Final Velocity. 
 
 Figure 7 enables us to appioximate closely to the final 
 velocity of the projectile. 
 
 This term, which must be carefully distinguished from 
 the ter7ninal velocity (Chap. I), is that velocity which the 
 projectile has acquired in falling when the resistance of the 
 air becomes equal to the accelerating force of gravity. This 
 velocity is necessarily uniform and a maximum. 
 
 For example, a 64 lb. projectile, 6.3 inch in diameter, has 
 a weight per circular inch of 1.613 lbs. If it belongs to the 
 class of projectiles used by Bashforth, an equal and contrary 
 air pressure will result when a velocity of nearly 900 f. s. 
 has been acquired. But for more modern projectiles a 
 higher final velocity will result. 
 
18 XX. — EXTERIOR BALLISTICS. 
 
 This velocity which formerly had only a theoretical signifi- 
 cance, is becoming important in consequence of the great 
 heights and high angles of fire now used in mortar firing. 
 
 The S. C. Mortar has thrown its shell over 3 miles into 
 the air with an angle of fall of about 75°. 
 
 The result can be reached more exactly by a method of 
 approximation based upon the fact that K enters into equa- 
 tion (20) in the first power while v is cubed. Consequently, 
 the first trial values of K will not greatly affect the result, 
 and we may finally find a velocity and corresponding value 
 of K which will satisfy the eqi^-^Hon 
 
 TRAJECTORY IN AIR. 
 
 GENERAL SOLUTION. 
 
 Notation. 
 
 Let O VR = S, figure 8, represent a trajectory. 
 
 Let V be the muzzle velocity in the line of departure. 
 
 ds 
 Let v= —j-he the velocity in the direction of the tangent 
 
 at any point of which the coordinates are x and y. 
 
 Let u be the horizontal component of the velocity v. 
 
 Let 7j\ v'\ u\ 2^", be the corresponding tangential and 
 horizontal velocities at the beginning and end of any arc, 
 the coordinates of the extremities of which are {x*^ y), 
 {x",y"). 
 
 Let (p be the variable inclination to the horizontal of the 
 tangent to the trajectory; then u^v cos (p. 
 
 Let 6 and g9, measured as in the figure, be the particular 
 values of q) for the angles of departure and of fall. 
 
XX. EXTERIOR BALLISTICS. 19 
 
 Let a and /? be the values of q} at the beginning and 
 end of any arc when the velocity is v' and v". 
 
 Then the figure shows that 6 — a — ^ or the angle in- 
 cluded between the tangents is the change in inclination 
 due to a change in velocity from v* to v'\ 
 
 Similarly A=^— (—<») = ^+co is the total change in 
 inclination. 
 
 Let q) (read (p " dash ") be the inclination to the hori- 
 zontal of any chord of the trajectory. 
 
 Let 2/= = = u sec cp be the component velocity of 
 
 cos (p 
 
 V in the direction of the chord, and, as above, let v\ v" be 
 
 the component velocities in the direction of the chord at 
 
 the beginning and end of the arc (^',^')j (^"> ^")- 
 
 Let /,' /" be the times measured from any origin to the 
 
 instants when the velocities are respectively 
 
 ( z/', z/"), P", v^), etc. 
 
 Note that /">/', v''<v'. 
 
 Let t—t"—t' for any arc and r=time to vertex, T\-\- 
 time from the vertex to R^ T^ be the whole time of flight, or 
 
 Similarly, 
 
 Let Jf', y, be the computed coordinates of the vertex 
 measured from 0\ and X^, K^, the computed coordinates 
 of the same point measured from ^, so that the computed 
 range, X=0 R=X' -^-X^. 
 
 The figure shows that the notation of z;', «', cp^ changes 
 from the ascending to the descending branch to z'^, u^^ cp. 
 This distinction will be observed throughout when the 
 branches are separately considered; but, when the trajec- 
 tory is considered as a whole, v\ z;", «&c., refer to the 
 beginning and ending of any arc. 
 
20 XX. — EXTERIOR BALLISTICS. 
 
 Let the ordinate at D represent the height of a target at 
 the distance OD. Then DR is the dangerous space for 
 that target. If we aim at the center of the target this 
 evidently measures nearly twice the ± error permissible 
 in estimating the distance, as a measure preliminary to 
 determining the value of d required to strike the target at 
 some point of its height. See Chap. I., p. 3. 
 
 The dangerous space is known herein as D. S, 
 
 Eesolution of Motion. 
 
 Let AIR, figure 9, be some arc of the trajectory to 
 which //is the tangent at /, p is the radius of curvature, 
 g the acceleration due to gravity, r the retardation due to 
 the resistance of the air. 
 
 Then from the figure, for the horizontal retardation, 
 
 -— - = r cos (p (21) 
 
 and, from Mechanics, for the normal component of the 
 deviating force of gravity ,^^ 
 
 (32) 
 
 
 -=gcos cp 
 
 , 1 dcp . dt 
 
 but - = -/- X -77 
 
 p ds dt 
 
 = — ^ and. therefore, 
 dt.v 
 
 
 dcp 
 
 (23) 
 
 Dividing Equation (23) by (21) member by member, we 
 have, after transposing, 
 
 dq>= 1^ (24) 
 
XX. — 'EXTERIOR BALLISTICS. 
 
 21 
 
 Integrating between the limits (p=^a and ^=/5 and the 
 corresponding values of u^ we have 
 
 /3 y nf' 
 
 or 
 
 A ^g 
 
 du 
 rv' 
 
 From equation (21) we have by similar means, 
 
 du 
 
 r cos q) 
 
 or 
 
 du 
 
 cos q) 
 
 Similarly, from the relations between x,y, t, and Uy 
 
 u dt^=- 
 
 u du 
 r cos q) 
 
 or 
 
 u du 
 rcos (p 
 
 u du 
 
 or 
 
 r cos cp 
 
 u du 
 r cos cp 
 
 tan ^, 
 
 tan ^. 
 
 (25) 
 (25') 
 
 (36) 
 (26') 
 
 (27) 
 
 (27') 
 (28) 
 
 (28') 
 
22 XX. — EXTERIOR BALLISTICS. 
 
 If these general equations (25-28) could be integrated, 
 they would give the change in the coordinates of an arc of 
 the trajector}'- (x^'—x^), (7"— j^') corresponding to a change 
 of horizontal velocity {u^—u")^ the time t required to 
 make this change, and the change of inclination d, corre- 
 sponding to the same change in the velocity. 
 
 But the second members contain three variables, u, cp^ 
 and r, not connected by any law, and hence the integration 
 is impossible. 
 
 Bashforth's experiments, however, give the law connect- 
 ing u and r, and in order to avoid the difficulty arising 
 from the presence of the variable cp we assume for it a 
 constant mean value qy. That is, that on the same princi- 
 ple as that by which we have neglected the small vertical 
 component of the resistance, we now neglect the small 
 component velocity in a direction at right angles to the 
 chord, and suppose the length of the arc to be that of the 
 chord, although its curvature is retained. 
 
 COROLLARIES. 
 
 I. Equation (23) may be written 
 d(p __g cos (p 
 ~dt V ' 
 
 whence, by dividing member by member by 
 cos ^, w 
 dqp __g 
 
 dx 
 
 -—=zv COS cpf we obtain 
 
 sul 
 dcp _W 
 
 Calling esc- -^ — and substituting we have 
 
 dx 'Ze 
 
 (30) 
 
XX. — EXTERIOR BALLISTICS. 23 
 
 Equations (29) and (30) express the rate of change of the 
 direction of the tangent to the trajectory, or the rate at 
 which the trajectory is becoming curved, as a function of 
 the range. Equation (29) ilhistrates the remarks, Chap. I, 
 top page 3, and Equation (30) explains the importance of 
 Chap. XVI, p. 1. These equations set forth a most import- 
 ant property of the trajectory in air. 
 
 Figure 10, >vhich is carefully drawn to a scale, represents 
 in curve A the trajectory in vacuo of a projectile fired with 
 e = 30° and V = about 1700 f. s. 
 
 Curves B and C represent the trajectories m air of spher- 
 ical projectiles as follows : 
 
 B. 15 inch ; W= 450 lbs. d = 14.87 inch. \V= 1700 
 
 C. 24 pdr. ; W = 26.92 lbs. d = 5.9 inch. 5 (9 = 30° 
 Since from Chap. XVI, p. 2, the elements of a trajectory 
 
 ;When 6 and V are given depend on the ballistic coefficient 
 
 ■— r, It appears that the 24 pdr. projectile would describe 
 
 the trajectory B if its weight were increased to 70.86 lbs., 
 the calibre remaining constant; or, by reducing the calibra 
 to 3.637 inches, the weight of the projectile remaining con- 
 stant. The objections to this are given Chap. XVI, p. 4. 
 
 II. If in equation (29) we substitute for 2^ its value 
 \p g cos (pf we find 
 
 dg) 1 J dx 
 
 -~ = or d o) cos (Z) = — 
 
 dx p cos (p ^ ^ p 
 
 Integrating this equation between the limits -(- 6 and — w, 
 figure 8, corresponding to O and X, and assuming some mean 
 value of p = p' by which to measure the flatness of the tra- 
 jectory, we have as a measure of its mean curvature, 
 
 1 _ sin + sin 6> 
 
 7" - X ^^^^ 
 
24 XX. — EXTERIOR BALLISTICS. 
 
 Although from equation (22) and from experience it is 
 evident that, owing to the variable value of g cos cp^ with 
 the sight set for a certain range it is impossible to hit any 
 desired point of a vertical circle described about the gun 
 with the range as a radius; yet, as shown by equation (31) 
 and figure 11, if the altitude of the target or the angle of 
 sight s, be small, the decrease of g>' tends to compensate 
 for the increase of 6', so that sin 6' + sin w' may not differ 
 greatly from sin 6 -\- sin w : OX' = OX cos s will also be very 
 nearly equal to X, Under these circumstances the two values 
 of p' will not differ greatly from each other. 
 
 Under this assumption we may consider the mean curva- 
 ture of the trajectory to be constant or the trajectory to be 
 practically rigid, so that for small altitudes the elements of 
 the trajectory measured along the chord may be safely 
 assumed to be independent of the inclination of the chord 
 to the horizon. 
 
 Equation (30) shows that this assumption will increase 
 in truth when the sectional density and the muzzle velocity 
 increase, which is the present tendency. The principle 
 involved is of especial importance in the rapid fire of 
 modern small arms and field pieces, since it permits the use 
 for inclined ranges of sights graduated for horizontal ranges, 
 when the ± angle of sight is less than about 10°. 
 
 In such cases the change, s' figure 11, in the angle of 
 departure, may for a first approximation be safely taken to 
 be equal to s, and this change is automatically made by the 
 act of pointing. 
 
 Actually however, when s is positive, p' decreases and 
 conversely; so that in firing up hill the projectiles tend to 
 fall short and in firing down hill they tend to pass over the 
 object. 
 
XX. EXTERIOR BALLISTICS. 
 
 NIVEN'S METHOD. 
 
 Various expressions have been deduced for the value of ; 
 that of Mr. W. D. Niven, F.R.S., obtained from an expand- 
 ing series, is one of the most simple and, for illustration, a 
 particular value of 0, deduced for equation (25), is herein 
 applied to all cases indifferendy. 
 
 The appendix to this chapter contains the means of arriv- 
 ing at more exact values of cp. 
 
 Under this hypothesis we shall adopt, as a sufficient approxi- 
 mation for small angles of 8 less than about 3°, 
 
 = ^, (32) 
 
 and for larger angles the approximation 
 
 — tan a -\- tan 6 ^,«„x 
 
 tan = J- -. *(33) 
 
 From the notation we have 
 
 u = V cos ; du =^ dv cos ; v' = u' sec 0, etc. 
 Substituting these values in equation (25), and replacing 
 r by its new value -^ -^r[TK()()] ' ^^ ^^^^ 
 
 S = cos (pg 
 
 * These values of (p give good practical results. 
 
26 XX. — EXTERIOR BALLISTICS. 
 
 In this equation ^ is expressed in circular measure, that is, 
 in terms of the ratio tt = 180°. To reduce it to the corre- 
 sponding number of degrees, d, we have, 
 
 Ttd 
 d:7c::d:180 or ^ = -^^. 
 
 loO 
 
 Substituting this value of S in the above equation, and 
 representing as hereafter the ballistic coefficient ^ by C, we 
 have, after reduction, 
 
 ^ , cos 180^ (1000) 
 
 Ca = 
 
 7t 
 
 
 In this ^ is a function of v, and therefore changes between 
 the limits of integration. Means have, however, been found 
 for determining its mean value for limiting velocities. 
 
 The value so determined is nearly its arithmetical mean. 
 Therefore we have, calling this mean value K\ 
 
 ^^^cos0i8^o_oo): r-s^ 
 
 Similarly, we have 
 
 And representing by s the length of the chord, the co-ordi- 
 nates of the extremities of which are {x' x") (/ y") 
 
 csj^' ry} (36) 
 
 
 We have also 
 
 X 
 
 II 
 
 s cos andji/ = y" — / = s sin (p 
 
XX. EXTERIOR BALLISTICS. 27 
 
 These equations are in a form to be integrated, and Tables 
 II, III, IV have been computed for a projectile in which 
 ^ = 1, as follows : 
 
 Assume any velocity v^ sufficiently low as the origin of in- 
 tegrals, and assigning proper values for K', integrate equa- 
 tions (34, 35, 36) between v^ and successive values of v'. 
 We thus obtain what are called angular /unctions dy> , time 
 functions^ r^> , and space functions, (Ti/ , which may be ex- 
 plained by reference to the time functions in Table II. 
 
 Explanation of the Tables. 
 
 Considering the acceleration to be positive. Table II may 
 be considered to express by its functions the several times 
 r, r', r", etc., required to give to a unit projectile, starting as 
 from rest, the several corresponding velocities under the ac- 
 tion of a variable force equal to the variable resistance of the 
 air. 
 
 Table III may be similarly understood to express the space 
 in feet <t, a', a", etc., over which such a force would have to 
 act in order to increase the velocity from some initial velocity 
 as 0, to the several corresponding velocities given. 
 
 It is evident that each function in each table might be 
 numerically diminished by the first function in its own table 
 without affecting the value of the table or the velocities to 
 which it applies, since it is only the differences between func- 
 tions that are considered. 
 
 Conversely, considering the acceleration as negative, if any 
 time function as r', figure 12, measured from any origin /^ , 
 corresponds to a change v' — v^ in the velocity measured 
 from any origin v^ , and r" similarly corresponds to a change 
 r" — v^ , then r" — r' can correspond only to the particular 
 change &' — v". So that knowing r" — r' ^=^t, and either 
 z/ or v", we may determine the other velocity; and con- 
 
28 XX.' — EXTERIOR BALLISTICS. 
 
 versely as to /, r', or r", without regard to whether the 
 difference is positive or negative. 
 
 Similarly for the angular functions. If any angular func- 
 tion d', figure 13, corresponds to a change v' — v^, and d" 
 to a change jy" — v^ , then 6* — d" = ^ will correspond to a 
 change v' — v". 
 
 In all cases we have two pairs of unknown quantities, of 
 which the difference between one pair and one of the other 
 quantities is needed to determine the remaining quantity. 
 
 These data are given by the conditions of the problem, or 
 are suppHed by certain assumptions to be hereafter explained. 
 
 Example from Table II. 
 
 The change of time (or time required) for a change of 
 velocity of 300 when the greater velocity is 1400 is 231.9883 
 — 230.5314 = 1.4569 sec. When the lesser velocity is 1400 
 it is 0.8697. 
 
 If in the first case the time from some given origin, say the 
 firing of the piece, until the velocity was reduced to 1400 was, 
 say, 2 seconds, then the time measured from the same origin 
 until the velocity fell to 1100, would be 3.4569 sec, and so on. 
 
 PRACTICAL FORMULAE. 
 
 For the ascending branch Equations (34), (35), (36) may be 
 written.* 
 
 Cd — cos (p{di> — 6-^") ; (I) 
 
 a = r-> — T^n ; (II) 
 
 Cs = a^> — <T~v". (Ill) 
 
 Whence from III, 
 
 Cx = Cs cos = cos 0(cr^/ — (Tin); (HI') 
 
 Q/ = Cs sin = sin 0(cr;,/ — (T^"), (HI") 
 
 * Similar equations serve for the descending branch. 
 
XX. EXTERIOR BALLISTICS. S9 
 
 The Greek letters in the second members of the above 
 equations are the corresponding tabular functions found 
 respectively in Tables IV, II, III. 
 
 These tables are arranged like logarithmic tables. Except 
 ■where small changes of the functions are considered, for sec- 
 tion-room work the column of differences need not ordinarily 
 be employed, the nearest function or velocity being taken. 
 
 It is evident that the nearer the chord is to the arc, the less 
 will be the difference v — v, and the more accurate will be 
 the result. In practice, it is considered sufficiently accurate 
 to divide the trajectory into two arcs, at the vertex. 
 
 For simplicity, and by the principle of the rigidity of the 
 trajectory, unless otherwise stated, the chord is taken hori- 
 zontal. 
 
 It is important to note that although ranges are generally 
 given in yards, the chords of trajectories (Chapter I) are ex- 
 pressed in FEET. Neglect of this frequently leads to failure in 
 practical work. 
 
 Example. 
 
 To illustrate the use of the tables in calculating the elements 
 of a trajectory, we will take the 100-ton Armstrong gun and 
 consider figures 8' and 14. 
 
 Data. 
 
 V= 1833; d = ll°50'=ll°.83i; PF=2005 lbs.; ^*=17 in.; 
 
 hence 
 
 C= 0.14414, log-^ = T. 15879, co-log -^ = 10.84121. 
 
 This quantity must always be determined before any other 
 work is attempted. 
 
 *The d above must be distinguished from the angle d elsewhere 
 discussed, 
 
30 XX. — EXTERIOR BALLISTICS. 
 
 Elements required. 
 
 1. The remaining energy at any point or : e, 
 
 2. Height of trajectory at any point ot y. 
 
 3. Total range or X. 
 
 4. Angle of fall at end of range or qd. 
 
 5. The dangerous space, D. S. , for any range. 
 
 6. Time of flight to any distance or /. 
 
 7. Tinxe of flight for the whole range or T. 
 
 8. Inclination of the trajectory at any distance or <p. 
 
 9. Having the initial velocity to find the value of B to at- 
 tain a desired range. 
 
 etc. etc. etc. 
 
 1st. To find the remaining energy, we find the remaining 
 velocity as follows : 
 
 From figure 8 the change of from the origin to the 
 vertex is ^ = « = d. At this point /? = ; therefore, from 
 equation (33), 
 
 - tan Of 4- tan tan 11° 50' 
 
 tan <2!> = — ' — 
 
 2 2 
 
 = tan 5° 58' 50" = tan 5° 58'. 83. 
 
 As we shall have to use the logarithmic functions of 0, we 
 now tabulate them as follows ; 
 
 logs. co-logs, 
 
 sin T. 01783 10.98317 
 
 cos 1.99763 10.00237 = log sec 0. 
 
 To find v' we project V on the horizontal or determine 
 «' = Fcos B\ thence v' = «' sec 0, or «' = 1794, v' = 1803.9. 
 
XX. — EXTERIOR BALLISTICS. 31 
 
 Now to find v'' we transpose equation (I) to read 
 
 COS 
 
 in which 
 
 Oj,' = 1803.9 • 
 
 In Table IV we find 
 
 di803 = 84°.8199 
 p. p. for 0.9 = 21 
 
 84°. 8220 
 
 Consequently, all the quantities in the second member 
 being known, we may write 
 
 14414 
 6-r= 84°.8220 - ll°.83i ^--l-**-^* 
 
 log'-i 1.99763 
 = 84°.8220 - 1°.7149 = 83°.1071. 
 
 From Table IV, again, we have for the velocity correspond- 
 ing to d = 83°.1071, v" = 1318 for the remaining velocity 
 at the vertex, and hence 
 
 «" = 1318 cos = 1310.8. 
 
 The origin is now transferred to the vertex, and we treat 
 the descending branch similarly to the ascending branch. 
 
 The angle a for this arc is evidently 0, and u^ = u" just 
 
 found, but the value of /? = g? required to find is unknown. 
 
 It is therefore necessary to assume a value for it. Equation 
 
 (29) shows that it will be greater than ^, and experience 
 
 4^ 
 proves that it is nearly — or a? = 15°. 77, 
 
3S XX. — EXTERIOR BALLISTICS. 
 
 If we assume an incorrect value, as will generally be the 
 case, the error is corrected by a subsequent operation. So 
 let us assume an incorrect value, or co= 16°, as a first ap- 
 proximation. Thence 
 
 tan 16° oo n/ K 
 
 tan (p = — - — = tan 8 9'. 5 
 — 4 
 
 I 
 and 
 
 v^ = 1310.8 X sec 8° 9'.5 = 1324.1 and (J- == 83°.1406. 
 Using equation (I) again, we have 
 
 *,„ = sr.im - ^-5^-5 16° 
 
 = 83°.1406 - 2°.3298 = 80°.8108; 
 
 and v^^ = 1061, u^^ = 1050, and v^^ , the velocity along the 
 tangent, := u„ sec. w = 1093. The vertical component of v 
 will be = «yy tan w = 301. 
 
 The component energies are generally useful for doing work 
 against targets which are nearly vertical, as the walls of vessels 
 or forts ; or horizontal, as the decks of vessels or the roofs of 
 magazines or casemates. We therefore find that while the 
 projectile started with energy in the direction of the tangent 
 or ^y = 46,700 foot-tons, it now has ^e/,, = 16,604 foot- 
 tons ; only about one third as much as when it started. 
 
 Its component horizontal and vertical energies are 15,320 
 foot-tons and 1260 foot-tons, respectively. 
 
 The steps of the problem can be clearly followed in the first 
 stages of Example I, which is given in the form used for 
 written recitation. 
 
XX. — EXTERIOR BALLISTICS. 
 
 S3 
 
 la. 
 
 Data: F=1833; ^ = 11° 50' ; W=2005; ^=17 in. 
 Required U^,^^. 
 
 Statement of Steps. 
 
 Terms. 
 
 Quantities. 
 
 Functions. 
 
 Logs. 
 
 I- C = ^=0.14414 
 
 c 
 
 T 
 
 17^ 
 2005 
 
 O.14414 
 
 
 2 . 46090 
 3 -30211 
 
 
 1.15879 
 
 
 c 
 
 
 
 IO.8412I 
 
 - tan 9 
 2. tan0= 
 
 
 
 
 
 = tan 5° 58'. 83 
 
 tan B 
 
 tan 11° 50' 
 2 
 
 
 9.32122 
 .30103 
 
 
 tan 
 
 tan 5° 58'.83 
 
 
 9.02019 
 
 
 cos 
 
 I 
 
 cos 
 
 sec " 
 
 
 9-99763 
 
 
 cos 
 
 10.00237 
 
 
 sin 
 
 I 
 
 sin 
 
 cos 6 
 
 sin 
 
 
 9.01782 
 
 
 I ,, 
 sin 
 
 
 10.98317 
 
 3. u'= F'cos = 1794 
 
 cos II 50 
 
 1794 
 
 
 3-26316 
 9.99067 
 
 
 3-25383 
 
 4. v' = u' sec (p = 1803.9 
 
 sec 
 
 v 
 
 1803.9 
 
 
 10.00237 
 
 
 3-25620 
 
 ^■'-^■-'-"-co%-'^^' 
 
 h' 
 
 5l803.9 
 
 84.8220 
 
 
 
 C 
 
 d 
 
 n^83i 
 
 
 1. 15879 
 1.07300 
 
 
 sec 
 
 
 
 10.00237 
 
 
 
 I3I8 
 
 I. 7146 
 
 0.23416 
 
 
 83.1074 
 
 
34 
 
 XX. EXTERIOR BALLISTICS. 
 
 Statement of Steps. 
 
 Terms. 
 
 Quantities. 
 
 Functions. Logs. 
 
 6. u' =: «^ = v" COS 
 
 = I3IO.8 
 
 COS 
 
 1318 
 1310.8 
 
 1 3-II992 
 9.99763 
 
 3.I1755 
 
 7.tan^='^"/ = 8"9'.5 
 
 tan /? 
 
 tan 
 cos 
 sec 
 sin 
 I ~~ 
 
 tan 16° 
 
 tan 8° 9'. 5 
 cos " 
 sec '* 
 sin '* 
 I ., 
 sin 
 
 
 9-45750 
 .30103 
 
 9.15647 
 
 9-99558 
 
 10.00442 
 
 9.15201 
 
 
 sin 
 
 10.84799 
 
 8. vi = u sec = 1324. 1 
 
 sec 
 
 1310.8 
 1324-2 
 
 
 3-11755 
 10.00442 
 
 
 3.12197 
 
 9. d- = (5- — CJ sec 
 
 = 1061 
 
 d 
 sec 
 
 ^1324. a 
 
 16" 
 
 I06I 
 
 83.1411 
 2.3298 
 
 1. 15879 
 
 I. 20412 
 
 10.00442 
 
 The determination of g is 
 omitted. 
 
 0.36733 
 
 80.8113 
 
 
XX. EXTERIOR BALLISTICS. 
 
 35 
 
 lb. 
 
 Data as in la. 
 
 Required » at 1000 yards = 3000 feet. 
 
 Statement of Steps. 
 
 Terms. 
 
 Quantities. 
 
 Functions. 
 
 Logs. 
 
 J. Determine whether to 
 use or by finding 
 whether 3000 is < or > 
 X' .: 
 
 cos 
 
 I 
 C 
 
 X' 
 
 O"i803-9 
 15045 
 
 44456.3 
 42275.8 
 
 9.99763 
 
 jr'=cos0(a--,-o--„)X^ 
 = 15045 ft. =;= 5015 yds. 
 
 .*. use 
 
 2180.5 
 
 3.33856 
 
 IO.84121 
 
 4.17740 
 
 2. 0--,, = (T-, — Cx sec (p 
 v" = 1697 
 
 sec 
 
 3000 
 
 1697 
 
 44456.3 
 434-8 
 
 I. 15879 
 3.47712 
 
 10.00237 
 2.63828 
 
 
 44021.5 
 
 
36 
 
 XX. — EXTERIOR BALLISTICS. 
 
 Data as in la. 
 
 Required V from data of ascending branch. 
 
 Statement of Steps. 
 
 Terms. 
 
 Quantities. 
 
 Functions. 
 
 Logs. 
 
 y:=Y' 
 
 
 
 
 
 = sin 0(o--,-o--„)i 
 
 sin 
 
 
 
 9.01782 
 
 ^1576.1 feet. 
 
 ^i' 
 
 Cri803.9 
 
 44456.3 
 
 
 
 ^-." 
 
 cri3i8 
 
 42275-8 
 2180.5 
 
 3-33856 
 
 
 C 
 
 
 
 IO.84121 
 
 
 v 
 
 1576. I 
 
 
 3-19759 
 
 Similarly we may find from the value of that 
 r, = 1713 feet. 
 
 The difference, 1713 - 1576.1 = 136.9 is evidently due to 
 the error in our assumption of the value of gj, and therefore in 
 our deduced value of ; the effect is to increase the range as 
 shown by figure 14. 
 
 This leads to the means of correcting od to be explained. 
 
 3. To find the range. 
 
 With the assumed value of gd and we find X^ by the 
 method described in lb, or X^ = 11949 feet. 
 Ave also have X' = 15045.4 '' 
 
 Z = Z'-|-X, = 26994.4 '' 
 
 But this range is too great by the distance B^C, figure 14. 
 To find this distance we assume that this short arc coincides 
 with its tangent, which by assumption makes an angle of 16° 
 with the horizon, 
 
XX. — EXTERIOR BALLISTICS. 37 
 
 Therefore 
 
 B'C = -i??^ = 477.4 ft. and X, = 11471.6 ft. 
 tan 16 
 
 and X = 26517. ft. = 8839 yds. = 5 miles + . 
 
 4. To find the incHnation at the end of the range or the 
 angle of fall, oo. 
 
 We can vouch for only the elements of the trajectory in the 
 ascending branch, but if we can determine the range as by 
 firing or by the method just described, we may approximate 
 closely to the angle of fall. 
 
 For 
 
 V tan GD 
 tan0 = ^ = — -; 
 
 . •. tan G? = V and Ce9 = 15° 20' 28". 
 ^/ 
 
 In the example this gives a difference of but 6. 8 feet in the 
 two values of K, which difference can be further reduced to 
 by successively approximating to the true value of oj, or 
 G) = 15° 18' 12" ; and therefore ±^=7° 47' |i and ~v, == 
 1323, z7, = 1067.3, X, = 3840 yds. 
 
 These values will be hereafter employed, since it is most 
 important to have a correct knowledge of the elements of the 
 trajectory at its further end. 
 
 Practical Methods for Detennining w. 
 
 1. Fire through a screen near the point of fall, and note the 
 
 height /if of the hole above the horizontal plane on which 
 
 the projectile strikes, and the distance of its impact, d, beyond 
 
 /i 
 the screen. Then tan w = -— nearly. 
 
38 XX. — EXTERIOR BALLISTICS. 
 
 Or note the inclination of the shot-holes in snow or in 
 horizontal targets composed of double layers of boards. 
 
 2. Determine the range OR, figure 15, for a given value 
 of Q, and then increase ^ by a slight increment AB. This 
 will increase OR by AR = RR\ 
 
 Then assuming HR' to be straight and parallel to the tan- 
 gent at R, 
 
 . RR Rt^nAf) 
 '^'''^ = RR' = -AR~'''^'^y- 
 
 3. Determine the range under two sets of conditions differ- 
 ing only in the height, /i, of the gun above the horizontal 
 plane. Then if this difference be relatively small with regard 
 
 to the range from figure 16, tan go = --t-= . 
 
 4. Figure 17 shows how this would practically be done, 
 since it would be difficult to raise a gun sufficiently without 
 displacing it horizontally : 
 
 tan 6) = 
 
 0' R> — O R. 
 
 Application, 
 
 Range-tables are constructed to give all the principal ele- 
 ments of the piece, charge, and trajectory for different ranges.* 
 
 The following method and figure 18 show how, having a 
 range-table, we may determine the co-ordinates of the vertex. 
 
 Find in the range-table two angles of departure and of fall 
 a and j3, such that their sum =: 6. Then by the principle of 
 rigidity S will be the chord to the vertex, and S cos /? = X', 
 and 5 sin i3 - Y'. 
 
 * See Chapter XXX, pages 9, 52. 
 
XX. EXTERIOR, BALLISTICS. 
 
 5. To find the dangerous space at any range, or the hori- 
 zontal distance over which a target of given height would be 
 struck. 
 
 We have in this case to find the distance at which the height 
 of the trajectory is equal to that of the target. The target will 
 evidently be struck when situated at this point, since the tra- 
 jectory passes through its summit, and it will also be struck 
 if situated at any point intermediate between this and the end 
 of the range. Hence if D, figure 8, be the target the dan- 
 gerous space is DR. 
 
 The simplest way of determining this is as follows. Sup- 
 pose the target to be 30 feet high, then from (HI") 
 
 cr;. = O-1067 3 + -T—r = 40626. 4 + 31.9 = 40658. 3 = (T^^^,^ ; 
 sm 
 
 or z;, = 1070.9. 
 Similarly 
 
 x = DS- 219. 2 ft. = 73 yds. 
 
 If the proper value of w has been found, the same result 
 may be obtained by working downward from the vertex, tak- 
 ing y = 1576.1 — 30 r= 1546.1, and 
 
 Ovn = (^v. ■ — 7 = CT ,070 3 as before.* 
 
 sm 
 
 The accordance of these methods tests the accuracy of the 
 determination of w ; but without exacting the somewhat labo- 
 rious process required for this determination, a check of the 
 accuracy with which the dangerous space has been determined 
 may be had by observing that the angle whose tangent is 
 equal to the height of the target divided by the dangerous 
 space is greater than and less than w. 
 
 * Or taking the trial values assumed for the descending branch , viz^ 
 Vy = 1113 ; J/ ^ = \S24.2'yV yy=z 1061 we have as an approximation 
 ^ = 1683 J v'^^ =5 1064 ',xs=a 202.6 ft. 
 
40 XX. — EXTERIOR BALLISTICS. 
 
 The dangerous space is one of the most important proper- 
 ties of a trajectory, since, Chap. I, it measures the chances of 
 striking an object at a distance which in warfare is only ap- 
 proximately known. 
 
 The flatter the trajectory at its further end the greater is the 
 permissible margin of error in estimating the range before 
 aiming. 
 
 The principles of Chap. XVI and equation (30) illustrate 
 the importance of high velocities and high sectional densities, 
 since if one projectile, a, figure 19, having less sectional den- 
 sity than another, projectile b, be projected with equal ener- 
 gies at the same ranges, although the trajectory of a may be 
 flatter than that of b at the start, yet near the target the D.S. 
 of b will be greater than that of a, if the target lies beyond the 
 intersection of the two trajectories. 
 
 Although the method above described is generally followed, 
 and is best suited to cases where w is accurately known, a 
 simpler and probably a more accurate plan is hereafter given, 
 page 44. 
 
 6. To find the time of flight to any distance. Take the 
 distance as 1000 yards = 3000 feet, as in \b. We have from 
 equation (II) and data previously computed 
 
 / = (r^. — r^//) ^ = (ri803.9 — ^1097) ^ = 1- '^^03 sec. 
 
 7. To find the time of flight for the whole range. 
 
 1st. We proceed as in No. 3, using equation II and the 
 corrected value of v^^ = 1067.3. 
 
 T = (t;/ — r;,//) - = 9.8432 sees, 
 and r, = (r;, - nj i = 9.8569 
 
 r=r + T, =19.7001. 
 
XX. — EXTERIOR BALLISTICS. 41 
 
 2d. Or we may pass directly to the point of fall, as follows: 
 rr=(r;.-r7ji= 19.566, 
 
 which is sufficiently accurate for most purposes. 
 
 3d. If the true value of oo or v^^ is not determined, we may 
 
 still approximate to T^ by finding the time 4 required for the 
 
 projectile to pass over the correction of the range determined 
 
 477 
 in No. 3, with the velocity u^^ or 4 = — — - = 0.454 sec. 
 
 jLUoU 
 
 Therefore having with the assumed value of cl? = 16° found 
 T, = 10.266, its corrected value is 9.812, which added to 7" 
 makes T= 19.6552 sees. 
 
 4th. Or, if we neglect the difference in time of passage 
 over (y, — Y' )j due to the resistance of the air, since 
 
 /, = \/?(n/k_ v'f), we obtain 4= 0.4186 and T, = 
 
 ^ g 
 9.8474 which is a closer approximation than 9.812, since 
 
 T, > T! 
 
 Scholium. 
 Equation (23), which may be written 
 
 cos g 
 
 or 
 
 gj^ COS0 gj^ COS0 
 
 shows that, although for the descending branch the mean 
 value of V is less than that for the ascending branch, the in- 
 crease in the value of shown by equation (29), and the con- 
 sequent decrease in cos (f>, may compensate and keep the ra- 
 
42 XX. — EXTERIOR BALLISTICS. 
 
 tio nearly constant ; so that as far as iifue only is concerned 
 the trajectory may be supposed to be in vacuo. 
 
 That this is practically so appears from the equality of T 
 and T, in the above problem and in those solved by other 
 methods. 
 
 Consequently, and particularly for small values of A, when 
 the vertical component of the velocity is so small that it may 
 be safely neglected, the time to the vertex may be safely taken 
 as half the whole time of flight, and in cases of necessity 
 Equations (6) and (7) may be employed. 
 
 For example, for this case, which is certainly an extreme 
 one, if we substitute the value oi T — 19.70 sec. in the equa- 
 
 tion K = "-^we obtain for Y a value 1561, which is only 
 
 15.2 feet less than that before deduced. When the value of 
 A is large, the equations of the trajectory in vacuo cannot be 
 indiscriminately applied. 
 
 Principle of the Vertex. 
 
 From the above follows this important conclusion : If we 
 represent the time to the vertex by /^ (read / vertex), the ve- 
 locity at the vertex by z^y^, and the corresponding time function 
 
 T 
 
 by r^, then /a = y. 
 
 Then we have from equation (II), generalized as to notation, 
 Ct. — ^ — '^^LZLEul ~ r ' — r . 
 
 and 
 
 
XX. — EXTERIOR BALLISTICS. ^ 43 
 
 Or, the time function of the velocity at the vertex is equal to the 
 arithmetical mean of the time functions of the velocities at each 
 end of the arc. 
 
 This, which may be termed the principle of the vertex, is of 
 great value in approximate solutions. 
 
 If we know the time interval / corresponding to two veloci- 
 ties, of which one is known, then the time function of the ver- 
 tex of any arc may be determined as follows, from the above 
 and Equation (II) : 
 
 Cl , Ct ,^^- 
 
 r A = r^' - Y = -^v" + y . (37) 
 
 8. To find the inclination at the top of the target, which 
 we will now assume to be a rampart 30 ft. high, so that what 
 was before the dangerous space will be the safe space. 
 
 From equation (I), with the corrected values given, page 37, 
 we have 
 
 d=cos(l)iS--6-\l,= -0°, 35674= - 0° 21' 24".*= 
 
 = cos IS 6- \ 77 = 
 
 therefore0 = a7-^ = 15°18'12'"-O°21'24" = 14°56'48". 
 
 Or, working down from the vertex, = 14° 57'. The 
 true safe space will, owing to the increasing curvature, be 
 
 30 
 
 somewhat less than ; ., ,o ^r^, = ^^^ ^t- 
 
 tan 14 57 
 
 The difference between this result and that before reached 
 for the dangerous space shows the limitations of the ordinary 
 method, and is probably due to not having found the correct 
 value of for the function d, as explained page 25 and in 
 the Appendix. 
 
 41 1 
 
 * = cos T 47' ^2 (^1070. 9 — ^1067. 3) ^. 
 
44 XX. EXTERIOR BALLISTICS. 
 
 A closer approximation to the dangerous space would 
 probably be found from the principle of the vertex, as fol- 
 lows: 
 
 Assuming the rigidity of the trajectory, the tangent at the 
 vertex of any elementary arc is parallel to the chord. So that, 
 finding the inclination 0/^, at the vertex of the arc in rear of the 
 target the dangerous space may be found, since 
 
 D.S. = height of target X cot 0/,. 
 
 By using the corrected values pages 37 and 39, 
 
 r -\- T 
 
 w 1070. 8 I 1067. 3 
 
 we find 
 
 V^ = 1069.1, (^,„,,., --(^,„,,.3 = 0°.0260, 
 
 whence 
 
 t/= 0°.1787 and (p^ =15. 30 J - 0.1787 = 15° 7', 47. 
 
 D.S. = 111 feet. 
 
 This method enables us to obtain the dangerous space quite 
 
 closely for an approximate value of v^^ , and to determine an 
 
 important element without requiring the tedious correction 
 
 mentioned, page 37. 
 
 Assuming then v^^ = 1061, the velocity along the tangent is, 
 since u^^ = v^^ cos (f) = v„ cos w. 
 
 V,^ cos 
 
 ^"^■^^^^ = 1^93, 
 
 the vertical component of which is v,, sin w = 1093 sin 16" = 
 301. 
 
 The time of passage over the height of 30 ft. with this ve- 
 locity will be / = 0.09961 sec, though it will actually be a trifle 
 
 less, and -- = 0.0071. 
 
 4 
 
XX. — EXTERIOR BALLISTICS. 45 
 
 Ct 
 
 Now since r^ = 7^./ + - = r,„,, + 0. 0071 = 230. 2330, 
 
 .-. v,^ =: 1061.8. 
 
 Also, since d = cos (c^ioei.e - ^loei)^ = 0.0845, 
 
 30 
 
 d>. = 16° - 0.0845 =15° 54'. 9 and^ = 105 feet. 
 
 ^'^ tan 
 
 This is much nearer the true value than the result given by 
 the method described page 39. 
 
 Very nearly the result arrived at by the method above de- 
 scribed, viz., 105 feet, would be obtained by taking for the time 
 
 of passage / = \J g \ v'1576.2 - |/1546.2l = 0.0947 sec. 
 
 9. Having the initial velocity and the value of C, to find 
 the angle of departure necessary to attain a given range, and 
 other elements. 
 
 The conditions of this problem, which is a frequent one in 
 practice, require (page 6) that the rigidity of the trajectory be 
 assumed and that the principle of the vertex be applied. 
 
 Solution. 
 
 1. The piece is supposed to be fired with its axis horizontal, 
 and we compute the elements of the trajectory as if it were 
 the descending branch of an imaginary trajectory. 
 
 Then we revolve the trajectory upward until the chord 
 becomes horizontal. By the principle of rigidity S is 
 taken = X, which, to test the accuracy of the method, we 
 take = 26517.24 feet, as previously determined. 
 
 -f^'" m THE -)^^:*v 
 
 c 
 
 iiiTh& 
 
46 XX. — EXTERIOR BALLISTICS. 
 
 From equation (III) we have 
 
 (Tj,^^ = (Tv' — Cx, or v^^ = 1081. 
 ^rom equation (II) 
 
 ^A = i (^,833 + ^:o8i) or v^ = 1348. 
 Then from equation (I), since 6 = and cos 0=1, 
 
 d = 1-:^A = 11° 26' 13" = e. 
 
 Compare these results with those previously deduced. 
 2. In such a case, to determine the angle of fall and the 
 dangerous space, we would proceed as follows : 
 
 Find D, in degrees, the total change = 6 -\- go, hy saying 
 
 ■^ = (^:,3. - ^.08:) ^= 26°.29 = 26° 17' 24"; 
 
 then a? = Z> - ^ = 14° 51'. 2 and 
 SO 
 
 It is evident from the above, that, knowing the angle of fall 
 required to strike near its foot a scarp protected by a cover 
 at a known height and separated from it by a ditch of known 
 width, it is only necessary to know the distance of the breach- 
 ing battery from the wall, and the ballistic coefficient of the 
 projectile, to determine approximately the value of 6 and of 
 the initial velocity or charge of powder required to strike the 
 wall at nearly the desired spot, with a required remaining 
 energy. 
 
 It was by some such method that the German artillery 
 breached at hitherto unknown ranges the invisible walls of 
 Strasburg. See problem page 51. 
 
XX. — EXTERIOR BALLISTICS. 4? 
 
 Thus, by the principle of rigidity, 
 
 From CX = ay — c^ determine V and weight of charge. 
 
 ** CD^Sy- d^ *' D. 
 
 *' conditions ** go. 
 
 ** D — GO "6. 
 
 MODIFIED FORMULA. 
 
 For low angles of departure and high velocities and sec- 
 tional densities giving small values of A, the principle of 
 rigidity permits the formulae on page 28 to be written 
 
 Cd •= Sy — 6^ , (A) 
 
 a = Ty — T^; (B) 
 
 0= ay — (7^,. (C) 
 
 In these formulae, since sin = 0, we must resort to Equa- 
 tions (0) and (7) as explained page 7, or 
 
 y=^(T-(): (6) 
 
 y=^^ (7) 
 
 The propriety of this assumption appears from applying it 
 to the case of the 100-ton gun, assuming the velocities to be 
 horizontal and solving without reference to the vertex. Thus, 
 assuming as before (o = 16°, we have from (A), using whole 
 
 numbers, 27°.83 = (6,^ — 6„) ~ .-. 2/,, =1061. 
 
 Similarly we find T= 19.94 sec. and X = 8983 yards, lead- 
 ing, as seen by comparison, to but slight errors providing that 
 0) has been correctly assumed. 
 
 So that we may have confidence in the results obtained by 
 the use of Equations (A), (B), (C), when v does not differ 
 much from u , and, when v sin (p is so small that it may be 
 neglected, we may use Equations (6) and (7). 
 
48 XX. — EXTERIOR BALLISTICS. 
 
 Example. 
 
 The Springfield rifle and ammunition give the following 
 data : 
 
 W= 500 gr. = 0.071428 lbs. ; 
 
 Diameter of projectile = 0.455 inches in flight • 
 
 V= 1300 ft. 
 
 By experiment we find that for a range of 500 yards as 
 measured by the breech sight = 1° 17' 18". 
 
 1. Find GO. 
 
 1st. From (C) determine v^ = 869 
 
 2d. ** (A) " D = 2° 40' 23". 
 
 3d. '* D-d'' fi9 = l°23'05". 
 
 2. Find r. 
 
 1st. From {B) determine T= 1.467 sec. 
 2d. " (7) '' i"=8'.662 feet. 
 
 3. Findj^/ at 400 yards = 1200 ft. 
 
 1st. From (C) determine v at 1200 ft. -= 921. 
 2d. " (B) " / to 1200 ft. = 1.132 sec. 
 
 3d. " (6) and T above determine 7 = 6.105 ft. 
 By this means we may construct a drawing of the tra- 
 jectory. 
 4 Find the 'Dangerous Space at 500 yards. 
 The target is a man 5 ft. 8 in. (5§ ft.) high = y. The gun 
 is supposed to be fired lying down (from the ground) and to 
 be aimed at the feet of the man. 
 
 1st. Reckoning from the summit of the trajectory we have 
 
 ^1 ^ y "~ = 0.4313 for the time from the vertex to 
 
 T 
 
 the top of the man's head, and -^ — /, = time over D. S. = 
 
 0.3022 = f, 
 
 2d From /' and (B) determine v at target = 915. 
 3d. From (C) determine D. S. = 267 ft. = 89 yds. 
 
XX. — EXTERIOR Ballistics. 49 
 
 It is generally 1 etter to work backward from the point of 
 fall than forward from the gun, as the results are more con- 
 sistent if the data are supplied from only one branch of the 
 trajectory. See page 39. 
 
 However, this does not apply in the above case, in which 
 the vertical resistance of the air is wholly neglected, so that 
 the same results would follow from either course of procedure. 
 See page 41. 
 
 Alternate Solution, 
 
 If in Equation (6) we supply the value of T previously 
 deduced, and solve the resulting quadratic equation, we shall 
 have two values of /, one of which gives the time for the 
 projectile to rise to the height of j/, and the other which gives 
 the time for the projectile to rise to the vertex and to fall 
 to this height above the horizontal plane, so that there will 
 be two dangerous spaces, the interval between them being 
 the safe space. 
 
 It is evident that as the range decreases, the other conditions 
 remaining constant, the safe space finally becomes 0. The 
 resulting dangerous space will then be continuous and a 
 maximum. 
 
 The maximum dangerous space for a given small-arm thus 
 depends upon a physical constant, — the height of a man ; 
 and assuming, as above, the mean height of a man to be 5f 
 feet, the maximum dangerous space will be a function of p', 
 page 23, and will be a convenient measure of the joint power 
 of the gun and ammunition. The height i^will = 5f feet. 
 
 5. Find the maximum Dangerous Space for the preceding 
 ballistic condidons. 
 
 Sec. 
 
 1st. From (7) determine T= 1.187. 
 
 2d. '' (B) *' z;=912 
 
 3d. '' (C) ** X= 416.6 + yds. = max. D. S. 
 
50 XX. — EXTERIOR BALLISTICS. 
 
 APPENDIX A. 
 
 The value of was obtained approximately by Mr. Niven 
 from an expanding series. (See Proceedings of the Royal 
 Society of England, 1887; No. 181.) 
 
 The value of to be used with Table IV for changes of 
 inclination is that given in the text for high angles of depart- 
 ure, say ^ > 5°. 
 
 For 6* < 5° may be taken =. ^ ~l -. 
 
 For the other tables he takes 
 
 though, where greater approximation is required, for changes 
 of time he uses 
 
 APPENDIX B. 
 
 Problems. 
 
 The answers given below result from the use of the modi- 
 fied formulae. 
 
 1. The 3.2-inch steel b. 1. rifle. Weight jof shell or shrap- 
 nel = 13 lbs. I. V. = 1634. 
 
 Determine : (1) The distance at which v of shrapnel will be 
 500. 
 
 (2) Time of flight for this distance. 
 
 (3) Angle of departure for this range, supposing 
 
 the shrapnel to explode 40 ft. above the 
 object, or the angle of sight — y'. 
 Answers : (1) 19,106 ft. or 3.62 miles. 
 
 (2) 24.6 sec. 
 
 (3) 24'^ 44'. 
 
XX. — EXTERIOR BALLISTICS. Bl 
 
 2. A target is to be placed on Cro' Nest. The distance 
 from the sea-coast battery to target is 1990 yards ; height of 
 target above battery is 237 feet. . Determine the angle of 
 departure necessary to strike the target, using the 8- inch con- 
 verted rifle. ,/ = 7. 95 inches ; 
 
 Weight of projectile = 180 lbs. ; 
 
 I. V =1414. Answer: 5° 45'. 
 
 3. The 6-inch b. 1. rifle requires according to the range 
 table an elevation of 1° 51' and a muzzle velocity of 1850 f. s. 
 to strike an object at a distance of 2U00 yards. On firing the 
 range obtained was only 1800 yards, and investigation showed 
 that the powder was damp.* What additional elevation would 
 be necessary for a range of 2000 yards ? tV= loo lbs. 
 
 Answer : 0° 28'. 
 
 4. At the siege of Strasbourg in 1870, the Germans wished 
 to breach the scarp wall of an outwork at 2000 yards distance ; 
 the ditch was known to be 50 feet wide, and the shell were 
 to strike 12|- feet below top of counterscarp wall. An 8-inch 
 howitzer firing a projectile weighing 180 lbs. with a muzzle 
 velocity of 700 f. s. was employed. 
 
 Required the striking velocity and the angle of departure 
 
 A i 616 f. s. 
 
 Answer : i 
 
 (11° 47'. 
 
 5. At a range of 1200 yards a 64-lb. shell grazes the top of 
 a traverse 8 feet high. How far beyond the traverse will the 
 shot strike the ground ? 
 
 ^=6.171 inches; 
 
 Weight of projectile = 64 lbs. ; 
 
 I. V. = 1260 f. s. 
 
 Answer : 153 feet or 51 yards. 
 
 6. A Martini-Henry rifle-bullet strikes a vertical target at 
 500 yards at a certain spot when the muzzle velocity is 1353 
 f. s. How much lower on the target will the same projectile 
 
 *See proportion, foot p. 7. 
 
^2 XX. — EXTERIOR BALLISTICS. 
 
 Strike if the muzzle velocity is only 1300 f. s., the elevation 
 and other conditions remaining the same ? 
 
 ^ = 0.45 inch. 
 
 Weight of projectile == 480 grains = 0.06857 lb. 
 
 Answer : 21|^ inches. 
 
 7. Using the Hebler rifle, determine the maximum con- 
 tinuous dangerous space for a man kneeling. 
 
 d =0.296 inch; 
 w - 225 grains = 0.03214 lb.; 
 I. V. =1942f. s.; 
 
 Height of a man kneeling = 42 inches. 
 Compare with Springfield rifle : 
 d =0.45 inch ; 
 w — 500 grains = 0.07142 lb.; 
 I. V. = 1316 f. s. 
 
 Answer: Hebler rifle, 458.0 yards. 
 Springfiold rifle, 340.7 '' 
 
 8. A 3-inch Eureka shell, weight 9 lbs., fired with 2 lbs. of 
 powder, has an I. V. = 1495 f. s. With what charge should 
 a 10-lb. shell be fired to have at 407 yards the same remain- 
 ing velocity that the full charge gives at 2500 yards } 
 
 Answer: 11.5 ounces. 
 
 9. A 3.2-inch shell weighing 13 lbs. is fired with a muzzle 
 velocity = 958 f. s. The target is at a distance of 407 yards, 
 and the angle of sight is 4° 1'. Determine the necessary 
 breech-sight elevation and the quadrant elevation. 
 
 Answer: e = V 19'. 
 q = b° 20'. 
 
 10. A 3.2-inch shell weighing 13 lbs. is fired with I. V. i= 
 986 f- s. How high above the gun should be placed a hori- 
 zontal bar at a distance of 80 feet, so that the shell shall 
 strike the bar and hit a target on the same level as the gun, 
 and at a distance of 1200 yards. Determine also the neces- 
 sary breech-sight elevation. 
 
 Answer: Height = 4 ft. 6.5 ins. 
 ^ = 4° 0' 22'^ 
 
XX.— EXTERIOR feALLlSTlCS. 
 
 BALLISTIC TABLES. 
 
 Table I. 
 
 Value of K for the Cubic Law of Resistance, Ogival-headed 
 Projectiles {1%, diameter heads). 
 
 Velocity. 
 
 Value 
 ofK. 
 
 Velocity. 
 
 Value 
 OfK. 
 
 Velocity. 
 
 Value 
 OfK. 
 
 Velocity. 
 
 Value 
 OfK, 
 
 f.8. 
 
 
 f.s. 
 
 
 f.s. 
 
 
 f.s. 
 
 
 400 .... 
 
 148 
 
 
 
 880 .... 
 
 75 
 
 
 
 1360 . . . . 
 
 106 
 
 7 
 
 1840 .... 
 
 75 
 
 2 
 
 410 . . . . 
 
 145 
 
 2 
 
 890 .... 
 
 75 
 
 
 
 1370 . . . . 
 
 106 
 
 3 
 
 1850 .... 
 
 74 
 
 7 
 
 420 . . . . 
 
 142 
 
 5 
 
 900 .... 
 
 75 
 
 
 
 1380 .... 
 
 105 
 
 8 
 
 1860 .... 
 
 74 
 
 2 
 
 430 . . . . 
 
 139 
 
 8 
 
 910 ..:. 
 
 75 
 
 
 
 1390 . . . . 
 
 105 
 
 3 
 
 1870 .... 
 
 73 
 
 6 
 
 440 .... 
 
 137 
 
 2 
 
 920 .... 
 
 75 
 
 
 
 1400 . . . . 
 
 104 
 
 7 
 
 1880 .... 
 
 73 
 
 1 
 
 4r)0 . . . . 
 
 134 
 
 6 
 
 930 .... 
 
 75 
 
 
 
 1410 . . . . 
 
 104 
 
 1 
 
 1890 .... 
 
 72 
 
 6 
 
 460 .... 
 
 132 
 
 
 
 940 .... 
 
 75 
 
 
 
 1420 . . . . 
 
 103 
 
 5 
 
 1900 .... 
 
 72 
 
 1 
 
 470 . . . . 
 
 129 
 
 4 
 
 950 .... 
 
 75 
 
 
 
 1430 . . . . 
 
 102 
 
 9 
 
 1910 .... 
 
 71 
 
 6 
 
 480 .... 
 
 126 
 
 9 
 
 960 .... 
 
 75 
 
 
 
 1440 . . . . 
 
 102 
 
 3 
 
 1920 .... 
 
 71 
 
 2 
 
 490 .. . 
 
 124 
 
 4 
 
 970 .... 
 
 75 
 
 
 
 1450 . . . . 
 
 101 
 
 6 
 
 1930 .... 
 
 70 
 
 a 
 
 500 . . . . 
 
 121 
 
 9 
 
 980 .... 
 
 75 
 
 
 
 1460 . . . . 
 
 100 
 
 9 
 
 1940 .... 
 
 70 
 
 4 
 
 510 . . . . 
 
 119 
 
 6 
 
 990 .... 
 
 75 
 
 
 
 1470 . . . . 
 
 100 
 
 1 
 
 1950 .... 
 
 70 
 
 
 
 520 . . . . 
 
 117 
 
 3 
 
 1000 .... 
 
 75 
 
 
 
 1480 .... 
 
 99 
 
 4 
 
 1960 .... 
 
 69 
 
 7 
 
 530 .... 
 
 115 
 
 
 
 1010 .... 
 
 75 
 
 1 
 
 1490 . . . . 
 
 98 
 
 6 
 
 1970 .... 
 
 69 
 
 4 
 
 540 . . . . 
 
 112 
 
 8 
 
 1020 .... 
 
 75 
 
 3 
 
 1500 . . . . 
 
 97 
 
 9 
 
 1980 .... 
 
 69 
 
 2 
 
 550 . . . . 
 
 110 
 
 7 
 
 1030 .... 
 
 76 
 
 7 
 
 1510 . . . . 
 
 97 
 
 1 
 
 1990 .... 
 
 69 
 
 
 
 5G0 . . . . 
 
 108 
 
 7 
 
 1040 .... 
 
 80 
 
 8 
 
 1.520 . . . . 
 
 96 
 
 2 
 
 2000 .... 
 
 68 
 
 8 
 
 570 . . . . 
 
 106 
 
 7 
 
 1050 .... 
 
 87 
 
 3 
 
 1530 . . . - 
 
 95 
 
 3 
 
 2010 .... 
 
 68 
 
 6 
 
 580 . . . . 
 
 104 
 
 6 
 
 1060 .... 
 
 94 
 
 
 
 1540 . . . . 
 
 94 
 
 4 
 
 2020 .... 
 
 68 
 
 4 
 
 530 . . . . 
 
 102 
 
 5 
 
 1070 .... 
 
 98 
 
 7 
 
 1550 . . . . 
 
 93 
 
 6 
 
 2030 .... 
 
 68 
 
 3 
 
 600 . . . . 
 
 100 
 
 5 
 
 1080 .... 
 
 102 
 
 2 
 
 1560 . . . . 
 
 92 
 
 8 
 
 2040 .... 
 
 68 
 
 2 
 
 610 . . . . 
 
 98 
 
 6 
 
 1090 .... 
 
 104 
 
 9 
 
 1570 
 
 92 
 
 
 
 2050 .... 
 
 68 
 
 1 
 
 620 .... 
 
 96 
 
 8 
 
 1100 .... 
 
 lOG 
 
 9 
 
 1580 .... 
 
 91 
 
 2 
 
 2060 .... 
 
 68 
 
 
 
 630 . . . . 
 
 95 
 
 1 
 
 1110 .... 
 
 108 
 
 4 
 
 1590 .... 
 
 90 
 
 4 
 
 2070 .... 
 
 67 
 
 9 
 
 640 . . . . 
 
 93 
 
 5 
 
 1120 .... 
 
 109 
 
 2 
 
 1600 .... 
 
 89 
 
 7 
 
 2080 .... 
 
 67 
 
 9 
 
 650 . . . . 
 
 91 
 
 9 
 
 1130 .... 
 
 109 
 
 6 
 
 1610 .... 
 
 89 
 
 
 
 2090 .... 
 
 67 
 
 8 
 
 660 . . . . 
 
 90 
 
 5 
 
 1140 .... 
 
 109 
 
 6 
 
 1620 .... 
 
 88 
 
 3 
 
 2100 . . . 
 
 67 
 
 8 
 
 670 . . . . 
 
 89 
 
 1 
 
 1150 .... 
 
 109 
 
 6 
 
 1630 . . . . 
 
 87 
 
 6 
 
 2110 .... 
 
 67 
 
 7 
 
 630 . . . . 
 
 87 
 
 7 
 
 1160 .. . 
 
 109 
 
 6 
 
 1610 . . . . 
 
 86 
 
 9 
 
 2120 .... 
 
 67 
 
 6 
 
 69S .... 
 
 86 
 
 3 
 
 1170 .... 
 
 109 
 
 6 
 
 1650 . . . . 
 
 86 
 
 2 
 
 2130 .... 
 
 67 
 
 6 
 
 700 .... 
 
 84 
 
 9 
 
 1180 .... 
 
 103 
 
 6 
 
 1660 . . . . 
 
 85 
 
 5 
 
 2140 .... 
 
 67 
 
 5 
 
 710 . . . . 
 
 83 
 
 7 
 
 1190 .... 
 
 109 
 
 6 
 
 1670 . . . . 
 
 84 
 
 8 
 
 2150 .... 
 
 67 
 
 4 
 
 720 .... 
 
 82 
 
 6 
 
 1200 .... 
 
 109 
 
 6 
 
 1680 . . . . 
 
 84 
 
 2 
 
 2160 .... 
 
 67 
 
 3 
 
 730 . . . . 
 
 81 
 
 6 
 
 1210 .... 
 
 109 
 
 6 
 
 1690 . . . . 
 
 83 
 
 6 
 
 2170 .... 
 
 67 
 
 2 
 
 740 .... 
 
 80 
 
 6 
 
 1220 .... 
 
 109 
 
 6 
 
 1700 . . . . 
 
 83 
 
 
 
 2180 .... 
 
 67 
 
 2 
 
 750 .... 
 
 79 
 
 6 
 
 1230 .... 
 
 109 
 
 5 
 
 1710 . . . . 
 
 82 
 
 4 
 
 2190 .... 
 
 67 
 
 1 
 
 760 .... 
 
 78 
 
 7 
 
 1240 . . . 
 
 103 
 
 5 
 
 1720 .... 
 
 81 
 
 8 
 
 2200 .... 
 
 67 
 
 
 
 770 . . . . 
 
 78 
 
 
 
 1250 .... 
 
 109 
 
 4 
 
 1730 . . . . 
 
 81 
 
 2 
 
 2210 .... 
 
 66 
 
 9 
 
 780 .... 
 
 77 
 
 4 
 
 12f30 .... 
 
 103 
 
 3 
 
 1740 . . . . 
 
 80 
 
 6 
 
 2220 ... 
 
 66 
 
 8 
 
 790 ... 
 
 76 
 
 8 
 
 1270 .... 
 
 103 
 
 2 
 
 1750 .... 
 
 80 
 
 
 
 2230 .... 
 
 66 
 
 8 
 
 800 .... 
 
 76 
 
 2 
 
 1280 .... 
 
 103 
 
 
 
 1760 . . . . 
 
 79 
 
 5 
 
 2240 .... 
 
 66 
 
 7 
 
 810 . . . . 
 
 75 
 
 6 
 
 1290 .... 
 
 108 
 
 8 
 
 1770 .... 
 
 78 
 
 9 
 
 22-0 .... 
 
 66 
 
 6 
 
 820 .... 
 
 75 
 
 2 
 
 1300 .... 
 
 108 
 
 6 
 
 1780 .... 
 
 78 
 
 4 
 
 2260 .... 
 
 66 
 
 5 
 
 830 .... 
 
 75 
 
 1 
 
 1310 .... 
 
 lOS 
 
 4 
 
 1700 . . . . 
 
 77 
 
 8 
 
 ' 2270 .. 
 
 66 
 
 4 
 
 840 . . . . 
 
 75 
 
 
 
 1320 .... 
 
 10^. 
 
 1 
 
 noo .... 
 
 77 
 
 3 
 
 , 2280 .... 
 
 66 
 
 2 
 
 850 . . . . 
 
 75 
 
 
 
 1330 .... 
 
 107 
 
 8 
 
 1810 . . . . 
 
 76 
 
 8 
 
 2290 ... 
 
 65 
 
 9 
 
 860 . . . . 
 
 75 
 
 
 
 1340 .... 
 
 107 
 
 5 
 
 1820 . . . . 
 
 76 
 
 2 
 
 2300 .... 
 
 65-5 
 
 870 . . . . 
 
 75 
 
 1350 .... 
 
 1 
 
 107 1 
 
 [ 1830 .... 
 
 75-7 
 
 
 
u 
 
 5C5t. — EXTERIOR BALLISTICS. 
 
 Table II. 
 Time and Velocity Table, Ct = r^, — r^„. 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Difl: 
 
 f.8. 
 40 
 41 
 42 
 
 20 5-0299 
 6-0554 
 7 0276 
 
 sees. 
 5-1349 
 6-1550 
 7-1?,'^0 
 
 sees. 
 6-2393 
 6-2540 
 7-2159 
 
 sees. 
 5-3432 
 6-3525 
 7-3093 
 
 sees. 
 
 5-4466 
 6-4505 
 7-4022 
 
 sees. 
 5-5494 
 6-5480 
 7-4947 
 
 sees. 
 6-6517 
 6 6450 
 7-5867 
 
 sees. 
 5-7534 
 6-7414 
 7-0782 
 
 sees. 
 
 5 8546 
 
 6 8373 
 7-7693 
 
 sees. 
 
 6-9553 
 6-93^7 
 7-8599 
 
 + 
 
 -1028 
 -0975 
 -0925 
 
 43 
 44 
 45 
 
 20 7-9501 
 8-8272 
 9-6622 
 
 8-0398 
 8 9125 
 9-7435 
 
 8-1291 
 8-9974 
 9-8244 
 
 8-2179 
 9-0819 
 9-9050 
 
 8-3063 
 9-1660 
 9-9852 
 
 8-3942 
 9-2497 
 *0-0651 
 
 8-4817 
 9-3330 
 *0 1446 
 
 8-5687 
 
 9 4159 
 
 *0-2237 
 
 8-6553 
 9-4984 
 *0-3025 
 
 8-7415 
 9-5805 
 *0-3809 
 
 -0879 
 -0837 
 •0799 
 
 46 
 47 
 
 48 
 
 21 0-4590 
 1-2205 
 
 1-9487 
 
 0-5367 
 1.2948 
 2-0198 
 
 0-6140 
 1 3687 
 2-0906 
 
 0-6910 
 1-4423 
 2 1611 
 
 0-7677 
 1-5156 
 2-2313 
 
 0-8440 
 1-5886 
 2-3012 
 
 0-9200 
 1 6613 
 2-3708 
 
 0-9956 
 1-7336 
 2-4401 
 
 1-0709 
 1-8056 
 2-5091 
 
 11459 
 
 1-8773 
 2-5779 
 
 -0763 
 •0730 
 -0699 
 
 40 
 60 
 61 
 
 21 2-6464 
 3-3159 
 3-9592 
 
 2-7146 
 3-3814 
 4-0221 
 
 2-7825 
 3-4466 
 4-0848 
 
 2-8501 
 3-5116 
 4 1472 
 
 2-9174 
 3 5763 
 4-2094 
 
 2-9845 
 3-6408 
 4 2713 
 
 3 0513 
 3-7050 
 4-3330 
 
 3-1178 
 3-7689 
 4-3944 
 
 3-1841 
 3 8320 
 4-4556 
 
 3-2501 
 3-8960 
 4-5165 
 
 -0671 
 -0645 
 -0619 
 
 62 
 63 
 64 
 
 21 4-5772 
 5 1719 
 5-7450 
 
 4-6377 
 5-2302 
 5-8012 
 
 4-6979 
 
 5-2882 
 5-8572 
 
 4-7579 
 5-3460 
 5-9130 
 
 4-8177 
 5-4036 
 5-9686 
 
 4-8773 
 5-4610 
 6-0240 
 
 4-9367 
 5-5182 
 6-0792 
 
 4-9958 
 5-5752 
 6-1342 
 
 5-0547 
 5-6320 
 6 1890 
 
 6-1134 
 5-6886 
 6-2436 
 
 -0596 
 -0574 
 -0554 
 
 55 
 66 
 67 
 
 21 6-2980 
 6-8311 
 7-3460 
 
 6-3522 
 6-8834 
 7-3965 
 
 6-4062 
 6 9355 
 7-4469 
 
 6-4600 
 6-9874 
 7-49-71 
 
 6-5136 
 7-0391 
 7-5471 
 
 6-5670 
 7 0907 
 7-5970 
 
 6-6202 
 7-1421 
 7 6467 
 
 6-6732 
 7-1933 
 7-6962 
 
 6-7260 
 7-2444 
 7 7456 
 
 6-7786 
 7-2953 
 7 7948 
 
 0534 
 -0516 
 •0499 
 
 68 
 69 
 60 
 
 21 7-8438 
 8-3271 
 8 7957 
 
 7-8928 
 8 3746 
 8-8417 
 
 7 9417 
 8-4220 
 
 8 8877 
 
 7-9904 
 8-4692 
 8-9334 
 
 8-0389 
 8-5163 
 8-9791 
 
 8-0873 
 8-5632 
 9 0246 
 
 8-1356 
 
 8 6100 
 
 9 0700 
 
 8-1837 
 8-6566 
 9 1152 
 
 8-2316 
 
 8 7031 
 
 9 1603 
 
 8-2793 
 8-7494 
 9 2052 
 
 -0483 
 0468 
 0454 
 
 61 
 62 
 63 
 
 21 9 2501 
 9-6908 
 
 22 0-1183 
 
 9-2947 
 9 7341 
 1604 
 
 9 3393 
 9-7773 
 0-2023 
 
 9 3837 
 9-8204 
 0-2441 
 
 9-4280 
 9-8633 
 0-2858 
 
 9-4721 
 9-9062 
 3273 
 
 9-5161 
 9-9489 
 0-3687 
 
 9-5600 
 9 9914 
 4100 
 
 9-6037 
 *0-0338 
 4512 
 
 9 6473 
 
 *0-0761 
 
 0-4922 
 
 -0441 
 0428 
 0415 
 
 61 
 65 
 66 
 
 22 0-5332 
 0-9359 
 1-3267 
 
 0-5740 
 0-9755 
 1-3651 
 
 6147 
 
 1 0151 
 1-4034 
 
 6552 
 
 1 0544 
 1-4416 
 
 0-6957 
 1-0937 
 1-4797 
 
 0-7360 
 1-1328 
 1-5177 
 
 0-7762 
 1-1718 
 1-5555 
 
 0-8163 
 1-2107 
 1-5933 
 
 0-8563 
 1-2495 
 1 6309 
 
 0-8962 
 1-2881 
 1-6684 
 
 -0403 
 0391 
 ■0379 
 
 67 
 68 
 69 
 
 22 1-7059 
 2 0742 
 2-4322 
 
 1-7432 
 2 1105 
 2-4675 
 
 1-7804 
 2 1466 
 2-5027 
 
 1 8175 
 2-1827 
 2-5377 
 
 1-8545 
 2-2186 
 2-5727 
 
 1-8914 
 2-2545 
 2-6076 
 
 1-9281 
 2-2902 
 2-6424 
 
 1-9648 
 
 2-3259 
 2-6771 
 
 2-0014 
 2-3614 
 2 7117 
 
 2-0378 
 2-3969 
 2-7462 
 
 0368 
 0358 
 0348 
 
 70 
 71 
 
 72 
 
 22 2-7806 
 3-1196 
 3-4492 
 
 2-8150 
 3 1530 
 3-4816 
 
 2-8492 
 3 1863 
 3 5140 
 
 2-8833 
 3-2195 
 3-5462 
 
 2-9174 
 3-2526 
 3-5784 
 
 2-9513 
 3-2856 
 3 6105 
 
 2-9852 
 3-3185 
 3 6424 
 
 3 0189 
 3-3513 
 3-6743 
 
 3 0526 
 3 3840 
 3 7061 
 
 3-0862 
 3-4167 
 3-7378 
 
 0339 
 -0330 
 -0320 
 
 73 
 71 
 75 
 
 22 3 7694 
 4 0804 
 4-3828 
 
 3-8009 
 4-1110 
 4 4125 
 
 3-8323 
 4 1416 
 4-4422 
 
 3-8636 
 4 1720 
 4-4719 
 
 3-8949 
 4-2024 
 4-5014 
 
 3-9260 
 4-2326 
 4-5308 
 
 3-9571 
 
 4-2628 
 4-5602 
 
 3-9881 
 4-2929 
 4-5895 
 
 4-0189 
 4 3230 
 4 6187 
 
 4-0497 
 4-3529 
 4-6478 
 
 0311 
 -0302 
 -0294 
 
 76 
 77 
 78 
 
 22 4-6769 
 
 1 4-9624 
 
 5-2394 
 
 4-7058 
 4-9905 
 6-2666 
 
 4-7347 
 5-0185 
 5-2937 
 
 4-7635 
 5 0464 
 5 3208 
 
 4-7922 
 5-0742 
 5-3478 
 
 4-8208 
 5-1020 
 5-3747 
 
 4-8493 
 5 ■ 129G 
 5-4015 
 
 4-8777 
 5 • 1572 
 5-4282 
 
 4-9060 
 5 1847 
 5-4549 
 
 4 9343 
 5-2121 
 
 5 4814 
 
 -0286 
 •0277 
 -0268 
 
 79 
 80 
 81 
 
 22 5-5079 
 5-7685 
 6 0214 
 
 5-5343 
 5 7941 
 6-0463 
 
 5-5606 
 
 5-8197 
 6 0711 
 
 5-5869 
 5 - 8452 
 6-0959 
 
 5-6130 
 5-8706 
 6-1205 
 
 6-6391 
 5-8959 
 6-1451 
 
 5-6652 
 5-9212 
 6-1696 
 
 5-6911 
 5-9463 
 6-1941 
 
 5-7170 
 5-9714 
 6-2184 
 
 5-7428 
 5-9965 
 6-2427 
 
 -0261 
 -0253 
 -0245 
 
 82 
 83 
 84 
 
 22 6-2669 
 6-5044 
 6-7337 
 
 6-2910 
 6-5277 
 6-7562 
 
 6 3151 
 6-5509 
 6-7786 
 
 6-3390 
 6 5740 
 6-8009 
 
 6-3629 
 
 6-5971 
 6-8232 
 
 6-3867 
 6 6201 
 6-8454 
 
 6-4104 
 6 6430 
 6-8675 
 
 6-4340 
 6 6658 
 6-8895 
 
 6-4576 
 6-6885 
 6-9114 
 
 6 4810 
 6-7111 
 6 9333 
 
 0237 
 0229 
 -0221 
 
 85 
 86 
 
 22 6-9551 
 
 ■7- 1688 
 7-3752 
 
 6-9768 
 
 7-1898 
 7-3954 
 
 6-9984 
 
 7-2107 
 7 -U5G 
 
 7 0200 
 
 7 ■ 2:315 
 7-43J7 
 
 7 -0415 
 
 7-2522 
 7-4358 
 
 7-0629 
 7-2729 
 
 7-4757 
 
 7 -0842 
 7-2935 
 7-4956 
 
 7-1055 
 7 3140 
 7-5155 
 
 7 -1267 
 7-3345 
 7 5353 
 
 7-1478 
 7-3549 
 
 -0214 
 -0206 
 0199 
 
XX. — EXTERIOR BALLISTICS. 
 
 55 
 
 Table II. — Continued. 
 Time and Velocity Table, Gt — r^, 
 
 22 7 
 7 
 7 
 
 22 8 
 
 22 8 
 
 22 9 
 9 
 9 
 
 22 9 
 
 22 9 
 
 23 
 
 
 23 
 
 
 
 23 
 
 
 
 23 
 
 
 
 23 
 
 
 
 23 1 
 •1 
 
 1 
 
 23 1 
 
 1 
 1 
 
 23 1 
 
 1 
 1 
 
 23 1 
 
 1 
 1 
 
 23 1 
 1 
 
 1 
 
 5746 
 7677 
 9544 
 
 1346 
 3090 
 4778 
 
 6411 
 7994 
 9528 
 
 1014 
 2454 
 3851 
 
 5207 
 6522 
 7796 
 
 9024 
 0177 
 1226 
 
 2170 
 3031 
 3835 
 
 4593 
 5314 
 
 6668 
 7311 
 
 8545 
 9142 
 9720 
 
 0283 
 0832 
 1367 
 
 3381 
 3855 
 4318 
 
 4771 
 5214 
 5647 
 
 6071 
 6486 
 6893 
 
 23 1 7291 
 1-7682 
 1-8066 
 
 5942 
 7866 
 9727 
 
 1523 
 3261 
 4943 
 
 6572 
 8150 
 9678 
 
 1160 
 2596 
 
 5340 
 6651 
 7921 
 
 9144 
 0287 
 1325 
 
 3114 
 3913 
 
 4667 
 5384 
 6071 
 
 6733 
 
 7374 
 7997 
 
 8605 
 9200 
 9777 
 
 0338 
 0886 
 1420 
 
 1941 
 2449 
 2945 
 
 3429 
 3902 
 4364 
 
 4816 
 5257 
 5690 
 
 6113 
 6527 
 6933 
 
 7331 
 7721 
 8104 
 
 6137 
 8055 
 
 1699 
 3432 
 5109 
 
 6732 
 8305 
 
 1306 
 
 2737 
 4126 
 
 5473 
 6780 
 8046 
 
 9262 
 0396 
 1423 
 
 4740 
 5454 
 6139 
 
 6798 
 7437 
 8059 
 
 8665 
 9259 
 
 0394 
 0940 
 1473 
 
 1992 
 2499 
 2994 
 
 3477 
 3948 
 4410 
 
 4860 
 5301 
 5732 
 
 6155 
 6568 
 
 7370 
 7760 
 8142 
 
 2347 
 3196 
 
 
 6332 
 8244 
 0091 
 
 1875 
 3602 
 5273 
 
 8459 
 9978 
 
 1451 
 
 2878 
 4262 
 
 5606 
 6C08 
 8170 
 
 0504 
 1520 
 
 2435 
 3278 
 4067 
 
 4813 
 5524 
 6206 
 
 6863 
 7500 
 8120 
 
 8726 
 9317 
 
 0449 
 0934 
 1525 
 
 2549 
 3043 
 
 3524 
 3995 
 4455 
 
 4905 
 5345 
 5775 
 
 6196 
 6609 
 7013 
 
 7410 
 
 7798 
 8179 
 
 6526 
 8431 
 0272 
 
 2050 
 3772 
 5437 
 
 7051 
 8613 
 0128 
 
 1595 
 3018 
 4398 
 
 5738 
 7036 
 8294 
 
 9496 
 0610 
 1615 
 
 2522 
 3359 
 4143 
 
 4885 
 5593 
 
 7563 
 8181 
 
 8787 
 9375 
 9947 
 
 0504 
 
 1048 
 1578 
 
 1-2095 
 1-2599 
 1 3091 
 
 3572 
 4041 
 4501 
 
 4949 
 5388 
 5818 
 
 7449 
 7837 
 8217 
 
 6719 
 
 sees. 
 
 7- 
 
 0452 j 8 
 
 2225 ! 8 
 
 3941 8 
 5601 
 
 7209 
 8767 
 0276 
 
 1740 ' 9 
 3158 ! 9 
 4534 9 
 
 7164 
 8417 
 
 9612 
 071G 
 1710 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 1 
 1 
 
 1 
 1 
 1 
 
 1 
 
 1 
 1 
 
 1 
 1 
 1 
 
 1 
 1 
 
 1 
 
 1 
 1 
 1 
 
 3439 
 4219 
 
 4958 
 5662 
 6339 
 
 7625 
 8242 
 
 8847 
 9433 
 0003 
 
 0559 
 1101 
 1630 
 
 2146 
 2649 
 3140 
 
 3619 
 4088 
 4546 
 
 7875 
 8255 
 
 6912 
 
 0632 
 
 4109 
 5764 
 
 7367 
 8920 
 0425 
 
 1884 
 3298 
 4670 
 
 6001 
 
 7291 
 8540 
 
 9727 
 0820 
 1804 
 
 2694 
 3520 
 4295 
 
 5731 
 6405 
 
 7056 
 
 7688 
 
 9490 
 0059 
 
 0614 
 1154 
 1682 
 
 2196 
 2698 
 
 4134 
 4591 
 
 5475 
 5902 
 
 6321 
 6731 
 7133 
 
 7527 
 7913 
 8292 
 
 7 
 
 9 
 
 9 
 
 sees. 
 7-7104 
 7-8991 
 8-0812 
 
 sees. 
 7 7295 
 7 9176 
 8-0990 
 
 sees. 
 7 7486 
 
 7 9360 
 
 8 1168 
 
 8-2573 
 8 4277 
 8 5927 
 
 8 2746 
 8-4445 
 8-6089 
 
 8-2918 
 8-4611 
 8 6250 
 
 8-7525 
 8 9073 
 9-0573 
 
 8-7682 
 8-9225 
 9 0720 
 
 8-7838 
 
 8 9376 
 
 9 0867 
 
 9 2027 
 9-3437 
 9-4805 
 
 9-2170 
 9 3575 
 9-4939 
 
 9 2312 
 9 3713 
 9 5073 
 
 9-6132 
 9-7418 
 9-8662 
 
 9-6262 
 9-7544 
 9-8783 
 
 9-6392 
 9 7670 
 9 8904 
 
 9-9841 
 0923 
 0-1897 
 
 9-9954 
 1025 
 1988 
 
 *0 0066 
 1126 
 0-2079 
 
 0-2780 
 3599 
 4370 
 
 0-2864 
 0-3678 
 0-4445 
 
 2948 
 3757 
 4519 
 
 0-5101 
 5800 
 6471 
 
 0-5172 
 0-5868 
 6537 
 
 0-5243 
 5936 
 6603 
 
 0-7120 
 7750 
 0-8364 
 
 0-7184 
 7812 
 8424 
 
 0-7248 
 0-7874 
 0-8484 
 
 0-8965 
 0-9648 
 1-0115 
 
 9024 
 9605 
 1-0171 
 
 9083 
 
 9663 
 
 1 0227 
 
 10669 
 1-1208 
 11734 
 
 1 0723 
 1-1261 
 1 1786 
 
 10778 
 1-1314 
 1-1838 
 
 1-2247 
 1-2748 
 1 3237 
 
 1-2298 
 1 2797 
 1-3285 
 
 1-2348 
 1-2847 
 1 3333 
 
 1 3714 
 1-4180 
 1-4636 
 
 1-3761 
 1 4226 
 1-4681 
 
 1-3808 
 1-4272 
 1-4726 
 
 1-6082 
 1-5518 
 1-5945 
 
 1-5126 
 1-5561 
 1-5987 
 
 1 5170 
 1 5604 
 1-6029 
 
 1-6362 
 1-6772 
 1-7173 
 
 1 6404 
 1-6812 
 1 7212 
 
 1 6445 
 1-6852 
 1 7252 
 
 1 7566 
 1-7952 
 1 8330 
 
 1 7605 
 1-7990 
 1-8367 
 
 1-7644 
 1-8028 
 1-8405 
 
m 
 
 X5t. — EXTERIOR BALLISTICS. 
 
 Table II. — Continued. 
 Time and Velocity Table, Ct = r 
 
 23 1 
 
 1 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 2 
 2 
 
 23 2 
 
 23 2 
 2 
 2 
 
 23 2 
 
 23 3 
 3 
 3 
 
 23 
 
 8442 
 8812 
 9175 
 
 9532 
 9883 
 0228 
 
 0569 
 0904 
 1234 
 
 2197 
 
 2509 
 2818 
 3123 
 
 3424 
 3722 
 4016 
 
 4308 
 
 4597 
 4882 
 
 5165 
 5444 
 5721 
 
 5994 
 62G5 
 6533 
 
 6798 
 7061 
 7320 
 
 7577 
 7832 
 8084 
 
 8333 
 
 8580 
 8824 
 
 9065 
 9304 
 9541 
 
 9776 
 0008 
 0237 
 
 0465 
 0690 
 0913 
 
 1134 
 1353 
 1569 
 
 •8479 
 •8848 
 •9211 
 
 !•{ 
 1^{ 
 1 < 
 
 •9567 
 •9918 
 •0263 
 
 1^{ 
 !•' 
 2 ( 
 
 0602 
 •0937 
 •1267 
 
 2 ( 
 2( 
 2 ] 
 
 •1591 
 •1912 
 •2228 
 
 2 ] 
 2 ] 
 2 5 
 
 •2540 
 •2849 
 •3153 
 
 2-' 
 2' 
 2- 
 
 •3454 
 •3751 
 •4046 
 
 2- 
 2- 
 2 
 
 •4337 
 ■4625 
 •4911 
 
 2- 
 
 2- 
 2- 
 
 •5193 
 •5472 
 •5748 
 
 2- 
 2- 
 2- 
 
 •6022 
 •6292 
 •6560 
 
 2- 
 2- 
 2 
 
 •6825 
 •7087 
 7346 
 
 2- 
 2- 
 2- 
 
 •7603 
 
 •7857 
 •8109 
 
 2 
 2- 
 2- 
 
 •8358 
 •8604 
 •8848 
 
 2 
 2- 
 2- 
 
 •9089 
 •9328 
 •9565 
 
 2- 
 2- 
 2- 
 
 •9799 
 J 0031 
 5 0260 
 
 2- 
 3- 
 3- 
 
 r0488 
 J 0713 
 {•0935 
 
 3 
 3^ 
 3- 
 
 $1156 
 $1375 
 J 1591 
 
 3 
 3 
 3- 
 
 •8517 
 •8885 
 •9247 
 
 •9602 
 •9952 
 •0297 
 
 •0636 
 •0970 
 •1299 
 
 •1624 
 •1944 
 •2260 
 
 •2571 
 
 ■2879 
 
 •3484 
 •3781 
 •4075 
 
 •4366 
 •4654 
 •4939 
 
 •5221 
 •5500 
 •5776 
 
 •6049 
 •6319 
 
 •6851 
 •7113 
 •7372 
 
 •7628 
 •7882 
 •8134 
 
 •8629 
 •8872 
 
 •9113 
 •9352 
 
 •9822 
 0054 
 
 0510 
 •0735 
 ■0958 
 
 1178 
 1396 
 •1613 
 
 8554 
 8921 
 9282 
 
 9638 
 9987 
 0331 
 
 0670 
 1003 
 1332 
 
 1656 
 1975 
 2291 
 
 2602 
 2910 
 3214 
 
 3514 
 3810 
 4104 
 
 4395 
 4683 
 4967 
 
 5249 
 5528 
 
 6076 
 6346 
 
 6877 
 7139 
 7398 
 
 7654 
 7908 
 8159 
 
 8407 
 8653 
 
 2 9137 
 2 
 
 2 9612 
 
 2-9845 
 
 3 0077 
 3 0306 
 
 3 0533 
 3 0757 
 
 3 1200 
 3 1418 
 3 1634 
 
 8591 
 8958 
 9318 
 
 9673 
 0022 
 0365 
 
 0703 
 1036 
 1364 
 
 1688 
 2007 
 2322 
 
 2633 
 2940 
 3244 
 
 3543 
 3840 
 4133 
 
 4424 
 4711 
 4996 
 
 5277 
 5555 
 5831 
 
 6373 
 6640 
 
 7165 
 7423 
 
 7679 
 7933 
 8184 
 
 8432 
 8678 
 8921 
 
 9161 
 9399 
 9635 
 
 0100 
 0329 
 
 0555 
 0780 
 1002 
 
 1222 
 1440 
 1656 
 
 8628 
 8994 
 9354 
 
 9708 
 0056 
 0399 
 
 0737 
 1069 
 1397 
 
 1720 
 2039 
 2354 
 
 2664 
 2971 
 3274 
 
 3573 
 3869 
 4162 
 
 4453 
 4740 
 5024 
 
 5305 
 
 5583 
 5858 
 
 6130 
 6400 
 6666 
 
 7191 
 7449 
 
 7705 
 7958 
 8209 
 
 8457 
 8702 
 
 9185 
 9423 
 9659 
 
 9892 
 0123 
 0351 
 
 0578 
 0802 
 1024 
 
 1244 
 1461 
 1677 
 
 8665 
 9030 
 
 9743 
 0091 
 0433 
 
 0770 
 1102 
 1430 
 
 1752 
 2071 
 2385 
 
 2695 
 3001 
 3304 
 
 3899 
 4192 
 
 4481 
 4768 
 5052 
 
 5333 
 5611 
 
 6157 
 6426 
 
 6956 
 7217 
 
 7475 
 
 7730 
 7983 
 8234 
 
 8481 
 8726 
 
 9209 
 9447 
 9682 
 
 9915 
 0146 
 0374 
 
 0600 
 0824 
 1045 
 
 1266 
 1483 
 1698 
 
 8702 
 9067 
 9425 
 
 9778 
 0125 
 0467 
 
 1135 
 1462 
 
 1784 
 2102 
 2416 
 
 2726 
 3032 
 
 3928 
 4221 
 
 4510 
 
 4797 
 5080 
 
 5361 
 5638 
 5913 
 
 6184 
 6453 
 6719 
 
 6982 
 7243 
 7500 
 
 7756 
 8008 
 8258 
 
 8506 
 
 8751 
 
 9470 
 9705 
 
 9938 
 0169 
 0397 
 
 0623 
 0847 
 1068 
 
 1287 
 1505 
 1720 
 
 8738 
 9103 
 9461 
 
 9813 
 0160 
 0501 
 
 1168 
 1494 
 
 1816 
 2134 
 2447 
 
 2757 
 3062 
 
 3958 
 4250 
 
 4539 
 
 4825 
 5108 
 
 5666 
 5940 
 
 6211 
 6480 
 6745 
 
 7008 
 7268 
 7526 
 
 7781 
 8034 
 8283 
 
 8531 
 
 8775 
 9017 
 
 9257 
 9494 
 9729 
 
 9961 
 0192 
 0420 
 
 0645 
 0869 
 1090 
 
 1309 
 1526 
 1741 
 
 8775 
 9139 
 
 •9848 
 0194 
 0535 
 
 0870 
 1201 
 1527 
 
 1848 
 2165 
 2478 
 
 2787 
 3093 
 3394 
 
 3692 
 3987 
 4279 
 
 4568 
 4854 
 5137 
 
 5416 
 5693 
 5967 
 
 6238 
 6506 
 6772 
 
 7034 
 7294 
 7552 
 
 7806 
 8059 
 8308 
 
 8555 
 8799 
 9041 
 
 •9281 
 •9518 
 •9752 
 
 0215 
 0442 
 
 0668 
 0891 
 1112 
 
XX. — EXTERIOR BALLISTICS. 
 
 57 
 
 Table II. — Continued. 
 Time and Velocity Table, Ct = r^, — r^„ 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 f.R. 
 184 
 
 185 
 18G 
 
 sees. 
 23 3 1784 
 3 1997 
 3 2207 
 
 Bees. 
 3 1805 
 3-2018 
 3-2228 
 
 sees. 
 3 ■ 1827 
 3 2039 
 3-2249 
 
 g 
 3 
 3 
 3 
 
 ecs. 
 1848 
 2060 
 2270 
 
 sees. 
 3-1869 
 3-2081 
 3-2291 
 
 s 
 3 
 3 
 3 
 
 eca. 
 
 1891 
 2102 
 2312 
 
 sees. 
 3-1012 
 3-2123 
 3-2333 
 
 sees. 
 
 3 1033 
 3-2144 
 3-2353 
 
 8 
 3 
 3 
 3 
 
 ecs. 
 1954 
 2165 
 2374 
 
 sees. 
 3-1975 
 3-2186 
 3-2395 
 
 + 
 
 •0021 
 -C021 
 
 0021 
 
 187 
 188 
 139 
 
 23 3 2416 
 3-2623 
 3-2828 
 
 3-2437 
 3-2643 
 3-2848 
 
 3 2457 
 3-2664 
 3-2869 
 
 3 
 3 
 3 
 
 2478 
 2683 
 2889 
 
 3-2499 
 3-2705 
 3-2909 
 
 3 
 
 3 
 3 
 
 2520 
 
 2726 
 2930 
 
 3 2540 
 3-2746 
 3-2950 
 
 3-2561 
 3 2767 
 3-2970 
 
 3 
 3 
 3 
 
 2582 
 2787 
 2091 
 
 3-2602 
 3-2803 
 3-3011 
 
 -0021 
 -0021 
 0020 
 
 100 
 191 
 102 
 
 23 3-3031 
 3-3233 
 3-3432 
 
 3-3051 
 3-3253 
 3-3452 
 
 3-3072 
 3-3273 
 3 3472 
 
 3 
 3 
 3 
 
 3092 
 3293 
 3492 
 
 3-3112 
 3-3313 
 3-3511 
 
 3 
 3 
 3 
 
 3132 
 
 3333 
 3531 
 
 3-3152 
 3-3353 
 3-3551 
 
 3-3172 
 3 3372 
 3-3571 
 
 8 
 
 3 
 3 
 
 3102 
 3302 
 3500 
 
 3-3212 
 3-3412 
 3-3G10 
 
 -0020 
 -0020 
 -0020 
 
 193 
 104 
 105 
 
 23 3-3630 
 3-3825 
 3 4019 
 
 3-3649 
 3 3845 
 3 4038 
 
 3-3669 
 3-3864 
 3-4057 
 
 3 
 3 
 3 
 
 3689 
 3884 
 4077 
 
 3-3708 
 3 3903 
 3 4096 
 
 3 
 3 
 3 
 
 3728 
 3922 
 4115 
 
 3-3747 
 3-3942 
 3 4134 
 
 3-3767 
 3-3061 
 3 4153 
 
 3 
 3 
 3 
 
 3786 
 3080 
 4172 
 
 3-3806 
 3 4000 
 3-4192 
 
 -0020 
 0019 
 0019 
 
 IOC 
 
 107 
 108 
 
 23 3 4211 
 3 4400 
 3-4588 
 
 3-4230 
 3-4419 
 3 4606 
 
 3-4240 
 3-4438 
 3-4625 
 
 3 
 3 
 3 
 
 4268 
 4457 
 4644 
 
 3-4287 
 3 4476 
 3-4662 
 
 3 
 3 
 3 
 
 4306 
 4494 
 4681 
 
 3-4325 
 3-4513 
 3-4699 
 
 3 4344 
 3-4532 
 3-4718 
 
 3 
 3 
 3 
 
 4362 
 4550 
 4736 
 
 8-4381 
 3-45C9 
 3-4755 
 
 0019 
 0019 
 0019 
 
 100 
 200 
 201 
 
 23 3 4773 
 3-4956 
 3-5137 
 
 3 4791 
 3-4074 
 3 5155 
 
 3-4810 
 3-4002 
 3-5172 
 
 3 
 3 
 3 
 
 4828 
 5010 
 5190 
 
 3-4846 
 3-5028 
 3 5208 
 
 3 
 3 
 3 
 
 4865 
 5047 
 5226 
 
 3-4883 
 3-5065 
 3 5244 
 
 3-4901 
 8-5083 
 3-5262 
 
 3 
 3 
 3 
 
 4920 
 5101 
 5280 
 
 3-4938 
 3-5119 
 3-5297 
 
 -0018 
 0018 
 0018 
 
 202 
 
 203 
 204 
 
 23 3-5315 
 3-5402 
 3-5666 
 
 3-5333 
 3-5500 
 3-5683 
 
 3-5351 
 3-5527 
 3-5700 
 
 3 
 3 
 3 
 
 5368 
 5544 
 5717 
 
 3-5386 
 3-5561 
 3 5735 
 
 3 
 3 
 3 
 
 5404 
 5579 
 5752 
 
 3-5421 
 3-5596 
 3-5769 
 
 3-5439 
 3-5614 
 3-5786 
 
 3 
 3 
 3 
 
 5456 
 5631 
 5803 
 
 8-5474 
 3-5648 
 3 5820 
 
 0018 
 •0017 
 0017 
 
 205 
 208 
 207 
 
 23 3-5837 
 3 6007 
 3-6174 
 
 3-5854 
 3-6024 
 3 6191 
 
 3-5871 
 3-6040 
 3-6207 
 
 3 
 3 
 3 
 
 5888 
 6057 
 6224 
 
 3 5905 
 3-6074 
 3 6240 
 
 3 
 3 
 3 
 
 5922 
 6091 
 6257 
 
 3-5939 
 3-6107 
 3-6273 
 
 3 5956 
 3-6124 
 3-6290 
 
 8 
 3 
 3 
 
 5973 
 6141 
 6306 
 
 3-5990 
 3-6157 
 3 6323 
 
 0017 
 -0017 
 -0016 
 
 203 
 
 2O0 
 210 
 
 23 3 6339 
 3 6502 
 3-6662 
 
 3-6355 
 
 3-6518 
 3 -6078 
 
 3-6372 
 3-6534 
 3-6694 
 
 3 
 3 
 3 
 
 6388 
 6550 
 6710 
 
 3 6404 
 3-6566 
 3-6726 
 
 3 
 3 
 3 
 
 6420 
 6582 
 6741 
 
 3-6437 
 3-6598 
 3-6757 
 
 3-6453 
 3-6614 
 3-6773 
 
 3 
 
 3 
 3 
 
 6469 
 6630 
 6789 
 
 8 6485 
 3-6646 
 3 6805 
 
 -0016 
 0016 
 0016 
 
 211 
 
 212 
 213 
 
 23 3-6820 
 3-6977 
 3-7131 
 
 3 6836 
 3-6902 
 3-7146 
 
 3-6852 
 3-7008 
 3-7162 
 
 3 
 3 
 3 
 
 6867 
 7023 
 7177 
 
 3-6883 
 3-7039 
 3-7192 
 
 3 
 3 
 3 
 
 6899 
 7054 
 7207 
 
 3-6914 
 3 7070 
 3 7223 
 
 3-6930 
 
 3-7085 
 3-7238 
 
 3 
 3 
 3 
 
 6946 
 7100 
 7253 
 
 8-6961 
 3-7116 
 3-7268 
 
 0016 
 •0015 
 0015 
 
 214 
 215 
 216 
 
 23 3-7283 
 3-7434 
 3-7582 
 
 3-7298 
 3 7448 
 3-7597 
 
 3 7313 
 
 3 -7463 
 3 7612 
 
 3 
 3 
 3 
 
 7329 
 
 7478 
 7626 
 
 3 7344 
 3-7493 
 3 7641 
 
 3 
 3 
 3 
 
 7359 
 7508 
 7656 
 
 3-7374 
 3-7523 
 3 7670 
 
 3-7389 
 3-7538 
 3-7685 
 
 3 
 3 
 3 
 
 7404 
 
 7552 
 7700 
 
 3-7419 
 3-7567 
 3-7714 
 
 0015 
 0015 
 -0015 
 
 217 
 218 
 210 
 
 23 3 7729 
 3-7874 
 3-8016 
 
 3 7743 
 
 3 7888 
 3 8031 
 
 3-7758 
 3 7002 
 3 8045 
 
 3 
 3 
 3 
 
 7772 
 7917 
 8059 
 
 3-7787 
 3-7931 
 3 8073 
 
 3 
 3 
 3 
 
 7801 
 7945 
 8087 
 
 3-7816 
 3-79G0 
 3-8101 
 
 3-7830 
 3-7974 
 3 8115 
 
 3 
 3 
 3 
 
 7845 
 7988 
 8129 
 
 3-7859 
 3 8002 
 3-8144 
 
 0014 
 OOU 
 0014 
 
 220 
 221 
 222 
 
 23 3-8158 
 3-8297 
 3 8435 
 
 3-8372 
 3 8311 
 3 8448 
 
 3 8186 
 3-8325 
 3 8462 
 
 3 
 3 
 3 
 
 8200 
 
 8338 
 8476 
 
 8-8214 
 3 8352 
 3 8489 
 
 3 
 3 
 3 
 
 8227 
 8366 
 8503 
 
 3-8241 
 3-8380 
 3 8517 
 
 3-8255 
 3 8394 
 3 8530 
 
 3 
 3 
 
 8269 
 8407 
 8544 
 
 8 8283 
 3-8421 
 3-8557 
 
 0014 
 0014 
 0014 
 
 223 
 224 
 
 225 
 
 23 3-8571 
 3-8705 
 
 3-8838 
 
 3-8584 
 3-8718 
 3-8851 
 
 3 8508 
 3-8732 
 3-8864 
 
 3 
 3 
 3 
 
 8611 
 8745 
 8877 
 
 3-8625 
 3-8758 
 3-8890 
 
 3 
 3 
 3 
 
 8638 
 8772 
 8903 
 
 3-8651 
 
 3-8785 
 3 8916 
 
 3-8665 
 3-8798 
 3-8930 
 
 3 
 3 
 3 
 
 8678 
 8811 
 8943 
 
 8-8692 
 3 8824 
 3-8956 
 
 i ooia 
 
 0013 
 -0013 
 
 226 
 227 
 228 
 
 23 3 8969 
 3 00'^« 
 3-922G 
 
 3-8982 
 3-9111 
 3 92u9 
 
 3-8995 
 3 9124 
 3-9252 
 
 3 
 3 
 
 3 
 
 -9008 
 -9137 
 9264 
 
 3-9021 
 3-9150 
 
 3-9277 
 
 3 
 3 
 
 3 
 
 9034 
 9162 
 9290 
 
 3-9047 
 3-9175 
 3 y..03 
 
 3-9059 
 3-91R8 
 3 9315 
 
 3 
 3 
 3 
 
 9072 
 9201 
 -9323 
 
 3-9085 
 3-9214 
 3 9341 
 
 001& 
 0013 
 •0013 
 
 229 
 230 
 
 23 3-9353 
 3 9470 
 
 3-9366 
 3-9i92 
 
 3-937S 
 
 3- 0:01 
 
 3 
 
 -9301 
 -9517 
 
 3 9401 
 3 -2029 
 
 3 
 
 9*15 
 
 ' 3-9429 
 3-9554 
 
 3-9441 
 3-9507 
 
 8 
 3 
 
 -9454 
 9579 
 
 3-9467 
 3-9592 
 
 0013 
 0013 
 
58 
 
 XX. EXTERIOR BALLISTICS. 
 
 Table III 
 
 Distance and Velocity Table, Cs = c^ — (7^/,. 
 
 feet. 
 
 2 5008 
 
 5424 
 
 5827 
 
 2 6219 
 6601 
 6972 
 
 2 7335 
 7688 
 8034 
 
 2 8373 
 8704 
 9029 
 
 2 9347 
 9659 
 9966 
 
 3 0267 
 0.563 
 
 . 0854 
 
 3 1140 
 1423 
 1701 
 
 3 1076 
 
 2247 
 
 - 2514 
 
 3 2777 
 3037 
 3292 
 
 3 3544 
 3793 
 4038 
 
 3 4280 
 4519 
 4754 
 
 3 4986 
 5215 
 5440 
 
 3 5662 
 5S80 
 6094 
 
 3 6305 
 6512 
 6716 
 
 3 6916 
 7111 
 7303 
 
 3 74nO 
 
 7672 
 7850 
 
 feet. 
 5050 2 
 5464-9 
 5867-3 
 
 6258 
 6638 
 7009 
 
 7370 
 7723 
 8068 
 
 8406 
 8737 
 9061 
 
 9690 
 
 0297 
 0592 
 
 1169 
 1451 
 1729 
 
 7 
 
 2274 
 2540 8 
 
 3318 
 
 3569 
 3818 
 4062 
 
 4304 
 4543 
 
 4777 
 
 5009 
 5237 
 5462 
 
 5684 
 5902 
 6116 
 
 6326 
 6533 
 
 7 
 5 
 
 1 
 
 1 
 
 4 
 1 
 6736 3 
 
 6935 7 
 7131 
 7322 
 
 7^0'^ -5 
 7690-5 
 7868-2 
 
 feet. 
 5092 
 5505 
 5903 
 
 6296 
 6676 
 7046 
 
 7406 
 7758 
 8103 
 
 8439 
 8769 
 9093 
 
 9410 
 9721 
 0027 
 
 0327 
 0622 
 0912 
 
 1197 
 1479 
 1757 
 
 2031 
 2301 
 
 2567 
 
 2829 
 3038 
 3343 
 
 3594 
 
 3842 
 4087 
 
 4328 
 4566 
 4801 
 
 5032 
 52G0 
 5484 
 
 5706 
 5923 
 6137 
 
 6347 
 6553 
 6756 
 
 6955 
 7150 
 7340 
 
 7526 
 7708 
 7885 
 
 feet. 
 5134 
 5546 
 5946 
 
 6335 
 6713 
 7082 
 
 7442 
 7793 
 8137 
 
 8473 
 8802 
 9125 
 
 9441 
 9752 
 ^0057 
 
 0357 
 0651 
 0940 
 
 1226 
 1507 
 
 1784 
 
 2058 
 2327 
 
 2855 
 3114 
 
 3619 
 3867 
 4111 
 
 4352 
 4590 
 
 5055 
 5282 
 5507 
 
 5728 
 5945 
 6158 
 
 6368 
 6574 
 6776 
 
 6975 
 7169 
 7359 
 
 7.^45 
 7726 
 7903 
 
 feet. 
 
 5176 
 5586 
 5985 
 
 ' 6373 
 6751 
 
 I 7118 
 
 I 
 
 : 7477 
 7828 
 
 1 8170 
 
 8835 
 9157 
 
 6 9472 
 
 2 9783 
 
 3 *0087 
 
 0386 
 0680 
 
 9 , 0969 
 
 1254 
 1535 
 1812 
 
 2354 
 2020 
 
 28S1 
 3139 
 3394 
 
 3644 
 3891 
 4135 
 
 4376 
 4613 
 
 4847 
 
 5078 
 5305 
 5529 
 
 5749 
 5966 
 6179 
 
 6594 
 6796 
 
 6994 
 
 7188 
 7378 
 
 3 7563 
 
 4 7744 
 3 ' 7920 
 
 I 
 
 feet. 
 
 5217 
 5627 
 6025 
 
 6411 
 
 6788 
 7155 
 
 7513 
 7862 
 8204 
 
 8539 
 
 8867 
 9189 
 
 9504 
 9813 
 mi7 
 
 0416 
 0709 
 0998 
 
 1282 
 1563 
 1839 
 
 2112 
 
 2381 
 2646 
 
 2907 
 3165 
 3419 
 
 3669 
 3916 
 4159 
 
 4400 
 4637 
 4871 
 
 5101 
 
 5328 
 5551 
 
 5771 
 5988 
 6200 
 
 6409 
 6614 
 6816 
 
 7014 
 7207 
 7397 
 
 7581 
 7762 
 7938 
 
 feet. 
 
 5259 
 5667 
 6064 
 
 6449 
 6825 
 7191 
 
 7548 
 7897 
 
 8572 
 8900 
 9220 
 
 9535 
 9844 
 "^0147 
 
 0445 
 0738 
 1026 
 
 1310 
 1590 
 
 1867 
 
 2139 
 2407 
 2672 
 
 2933 
 3191 
 3444 
 
 3694 
 3940 
 4184 
 
 4424 
 4660 
 4894 
 
 5124 
 5350 
 5573 
 
 5793 
 6009 
 6221 
 
 6430 
 6635 
 
 7033 
 7227 
 7415 
 
 7600 
 7779 
 7955 
 
 feet. 
 
 5300 
 5707 
 6103 
 
 6487 
 6862 
 7227 
 
 7583 
 7931 
 8272 
 
 8932 
 9252 
 
 9566 
 9874 
 '^0177 
 
 0475 
 0767 
 1055 
 
 1339 
 
 1618 
 1894 
 
 2166 
 2434 
 
 2959 
 3216 
 3469 
 
 3719 
 3965 
 4208 
 
 5815 
 6030 
 6242 
 
 64.50 
 6655 
 6856 
 
 7053 
 
 7246 
 7434 
 
 7618 
 7797 
 7973 
 
 4448 -0 
 4684-4 
 
 4917-4 
 
 5146 9 
 5373 
 5595 
 
 feet. 
 5341 
 5747 
 6142 
 
 6525 
 6899 
 7263 
 
 7618 
 7966 
 8305 
 
 8964 
 9284 
 
 9597 
 9905 
 '0207 
 
 0504 
 0796 
 
 1367 
 1646 
 1921 
 
 2193 
 2461 
 2725 
 
 2985-4 
 3242 
 3494 7 
 
 3743 
 3989 
 4232 
 
 4471 
 4707 
 4940 
 
 5169 
 5395 
 5617 
 
 5837 
 6052 
 6263 
 
 6471 
 
 6675 
 6876 
 
 7072 
 
 7265 
 7453 
 
 7636 
 7815 
 7990 
 
 feet. 
 
 5383 
 5787 8 
 6181 
 
 6563-6 
 6936 1 
 7299-2 
 
 7653-9 
 
 8000 
 
 8671 
 8996 
 9315 
 
 9628 
 9935 
 ^0237 
 
 0534 
 0825 
 1112 
 
 1395 
 
 1674 
 1949 
 
 2220 
 2487 
 2751 
 
 3011 
 
 3267 
 3519 
 
 3768 
 4014 
 4256 
 
 4495 
 4731 
 4963 
 
 , 5192 
 
 ! 5417 
 
 5640 
 
 5858-7 
 6073-6 
 6284 6 
 
 6492 
 
 7092 
 
 7284 
 7471 
 
 76.54 
 7833 
 8007 
 
XX — EXTERIOR BALLISTICS. 
 
 Table III. — Continued. 
 Distance and Velocity Table, Cs = o-^, — cr^,,. 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Dim 
 
 88 
 89 
 90 
 
 feet. 
 3 8024-8 
 8195 
 8361-5 
 
 feet. 
 8042 
 8211-9 
 8377-9 
 
 feet. 
 
 8059 2 
 8228-6 
 8394-3 
 
 feet. 
 8076.3 
 8245 4 
 8410-7 
 
 feet. 
 8093-4 
 8262-1 
 8427-0 
 
 feet. 
 8110-4 
 8278-7 
 8443-3 
 
 feet. 
 
 8127-4 
 8295-4 
 8459-6 
 
 feet. 
 8144-4 
 8312-0 
 8475-8 
 
 feet. 
 8161 3 
 8328-5 
 8492-0 
 
 feet. 
 8178-2 
 8345-0 
 8508-2 
 
 + 
 
 17-0 
 16 6 
 16-3 
 
 91 
 92 
 93 
 
 3 8524-3 
 8683-5 
 8839-4 
 
 8540 4 
 8699-3 
 8854-8 
 
 8556-4 
 8715-0 
 8870-2 
 
 8572-4 
 8730-7 
 8885-5 
 
 8588-4 
 8746-3 
 8900-8 
 
 8604-3 
 8761-9 
 8916-1 
 
 8620-3 
 8777-5 
 8931-3 
 
 8636-1 
 8793-0 
 8946-5 
 
 8652-0 
 8808-5 
 8961-7 
 
 8667-8 
 8824-0 
 8976-8 
 
 15 9 
 15-6 
 15 3 
 
 94 
 95 
 96 
 
 3 8991-9 
 9141 2 
 9287 4 
 
 9007-0 
 9156 
 9301-9 
 
 9022-0 
 9170-7 
 9316 3 
 
 9037-0 
 9185-4 
 9330-7 
 
 9052-0 
 9200 1 
 9345 
 
 9066-9 
 9214-7 
 9359-4 
 
 9081-9 
 9229-3 
 9373-7 
 
 9096-7 
 9243-9 
 9387-9 
 
 9111-6 
 9258 4 
 9402-2 
 
 9126-4 
 9272-9 
 9416-4 
 
 15 
 14-6 
 14-3 
 
 97 
 98 
 99 
 
 3 9430 6 
 9570 8 
 9708-3 
 
 9444-7 
 9584-7 
 9721-9 
 
 9458 9 
 9598-6 
 9735-4 
 
 9473-0 
 9612-4 
 9749-0 
 
 9487-0 
 9626 1 
 9762-5 
 
 9.501-1 
 9639-9 
 9775-9 
 
 9.515-1 
 96.53-6 
 9789-4 
 
 9529 1 
 9667-3 
 9802-8 
 
 9543-0 
 9681-0 
 9816-2 
 
 9557-0 
 9604-6 
 9829-6 
 
 14 
 13-7 
 13-5 
 
 100 
 101 
 102 
 
 3 9842 9 
 9975 
 
 4 0104 3 
 
 9856 3 
 9988 1 
 0117 1 
 
 9869-6 
 *0001-1 
 0129 8 
 
 9882-9 
 *()014-1 
 0142-5 
 
 9896-1 
 *0027-l 
 0155-2 
 
 9909-3 
 
 :*0040-0 
 
 0167-8 
 
 9922-5 
 *00.52-9 
 0180-4 
 
 9935-3 
 
 *0065-8 
 0192 9 
 
 9948 8 
 *0078-7 
 0-205 4 
 
 9961-9 
 *009l-5 
 0217-8 
 
 13-2 
 12-9 
 12-6 
 
 103 
 104 
 105 
 
 4 0230-1 
 0349 4 
 0459-2 
 
 0242 4 
 0360-8 
 0469 6 
 
 0254-6 
 0372-2 
 0479-9 
 
 0266-8 
 0383-4 
 0490-0 
 
 0278-8 
 0394-5 
 0500-1 
 
 0290-8 
 0405-6 
 0510 1 
 
 0302-7 
 0416-5 
 0520 
 
 0314 5 
 0427-3 
 0529-8 
 
 0326-2 
 0438-1 
 0539 5 
 
 0337-8 
 0448-7 
 0549-2 
 
 11 9 
 11-0 
 9-9 
 
 106 
 107 
 108 
 
 4 0558 7 
 0650 5 
 0736-8 
 
 0568-2 
 0659-3 
 0745 2 
 
 0577 6 
 0668 1 
 0753 6 
 
 0.586-9 
 0676-9 
 0761-9 
 
 0596 2 
 0685-6 
 0770-2 
 
 0605-4 
 0G94-2 
 0778-4 
 
 0614-5 
 0702-8 
 0786-6 
 
 0623-6 
 0711-4 
 0794-8 
 
 0632-6 
 0719-9 
 0802-9 
 
 0641-6 
 0728-4 
 0811-0 
 
 9 2 
 8 6 
 8-2 
 
 109 ' 
 
 110 
 
 111 
 
 4 0819 
 0897-9 
 0974-2 
 
 0827-1 
 0905 7 
 0981 6 
 
 0835 
 0913-4 
 0989 1 
 
 0843-0 
 0921-1 
 0996 6 
 
 0850-9 
 0928-7 
 1004-0 
 
 0858-9 
 0936-4 
 1011-4 
 
 0866-7 
 0944-0 
 1018-8 
 
 0874-6 
 09.51-5 
 1026 2 
 
 0882-4 
 0959 1 
 1033-5 
 
 089(r 
 0966 
 1040 
 
 2 
 6 
 9 
 
 7-9 
 
 7-6 
 
 7-4 
 
 112 
 113 
 lU 
 
 4 1048 2 
 1120 5 
 1191 4 
 
 1055-5 
 1127-6 
 1198-4 
 
 1062-8 
 1134-8 
 1205-4 
 
 1070 
 1141 9 
 1212 4 
 
 1077-3 
 1149-0 
 1219-4 
 
 1084-5 
 1156-1 
 1226-4 
 
 1091-7 
 1163 2 
 1233 3 
 
 1099 
 1170 2 
 1240 3 
 
 1106-1 
 1177-3 
 1247-2 
 
 1113 
 1184 
 1254 
 
 3 
 
 4 
 
 1 
 
 7-2 
 71 
 6 9 
 
 115 
 116 
 
 117 1 
 
 4 1261 
 1329-5 
 1396 8 
 
 1267-9 
 1336 3 
 1403-5 
 
 1274-8 
 1343-1 
 1410 1 
 
 1281-7 
 1349 8 
 1416-8 
 
 1288-6 
 1356 6 
 1423-4 
 
 1295-4 
 1363-3 
 1430 
 
 1302-3 
 1370 
 1436-6 
 
 1309 1 
 1376-7 
 1443-2 
 
 1315-9 
 
 1383-4 
 1449-8 
 
 1322 
 1390 
 1456 
 
 7 
 1 
 4 
 
 6 8 
 6 7 
 66 
 
 118 
 119 i 
 120 
 
 4 1462 9 
 1528-0 
 1591 9 
 
 1469 5 
 1534-4 
 1598-3 
 
 1476-0 
 1540 9 
 1604-6 
 
 1482 6 
 1547-3 
 1610-9 
 
 1489-1 
 1553-7 
 1617-2 
 
 1495-6 
 1.560-1 
 1623-5 
 
 1502 1 
 1566-5 
 1629-8 
 
 1508 6 
 1572-9 
 1636-1 
 
 1515-1 
 1,579-2 
 1642-3 
 
 1521 
 1585 
 1648 
 
 5 
 6 
 6 
 
 6 5 
 6-4 
 6 3 
 
 121 
 122 
 123 
 
 4 1654-8 
 1716 7 
 1777-5 
 
 1661 1 
 
 1722-8 
 1783 6 
 
 l«67-3 
 1728-8 
 1789-6 
 
 1673-5 
 1735 
 1795-6 
 
 1679-7 
 1741 1 
 1801 6 
 
 1685-9 
 
 1747-2 
 1807-6 
 
 1692-1 
 1753 3 
 1813-6 
 
 1698-2 
 1759-4 
 1819-6 
 
 1704-4 
 1765 4 
 1825 6 
 
 1710 
 
 1771 
 1831 
 
 5 
 5 
 5 
 
 6-2 
 6-1 
 6 
 
 124 
 
 125 1 
 126 
 
 4 1837 5 
 1896 5 
 1954-6 
 
 1843 4 
 1902 3 
 1960 4 
 
 1849-4 
 1908-2 
 1966-1 
 
 1855-3 
 1914 
 1971-9 
 
 1861-2 
 1919-8 
 1977 6 
 
 1867-1 
 1925-6 
 1983 3 
 
 1873-0 
 1931-5 
 1989-0 
 
 1878-9 
 1937-3 
 1994-8 
 
 1884-8 
 1943 
 2000 5 
 
 1890 
 1948 
 2006 
 
 6 
 8 
 2 
 
 5 9 
 
 5 8 
 
 5-7 
 
 127 
 128 
 129 
 
 4 2011-8 
 2068-3 
 21-23-9 
 
 2017-5 
 2073-9 
 2129-4 
 
 2023-2 
 2079 5 
 2135 
 
 2028-9 
 2085-0 
 2140 5 
 
 2034-5 
 2090-6 
 2146-0 
 
 2040-2 
 2096-2 
 2151-5 
 
 2045-8 
 2101 8 
 2157-0 
 
 2051-4 
 2107-3 
 2162-4 
 
 2057 
 2112-9 
 2167-9 
 
 2062 
 2118 
 2173 
 
 7 
 4 
 4 
 
 5-6 
 5-6 
 5-5 
 
 130 
 131 
 132 
 
 4 2178-8 
 2233 
 2286 4 
 
 2184-3 
 2238-4 
 2291-8 
 
 2189-7 
 2243-7 
 2297-1 
 
 2195-1 
 2249-1 
 2302-4 
 
 2200-6 
 2254-5 
 2307-6 
 
 2206 
 
 22.59-8 
 2312 9 
 
 2211-4 
 2265-1 
 2318-2 
 
 2216-8 
 2270-5 
 2323 5 
 
 2222-2 
 2275-8 
 2328-7 
 
 2227 
 2281 
 2334 
 
 6 
 1 
 
 
 5-4 
 5 3 
 53 
 
 133 
 134 
 135 
 
 4 2339-2 
 2391-4 
 2443 
 
 2344-5 
 2396 6 
 2448-1 
 
 2349-7 
 2401 8 
 2453-2 
 
 2355 
 2406 9 
 2458-3 
 
 2360 2 
 2412 1 
 2463 4 
 
 2365-4 
 2417-3 
 2468-5 
 
 2370-6 
 2422-4 
 2473-6 
 
 2375-8 
 2427-6 
 2478-7 
 
 2381-0 
 2432-7 
 2483-8 
 
 2386 
 2437 
 2488 
 
 2 
 8 
 9 
 
 6-2 
 5-2 
 5-1 
 
60 
 
 XX. — EXTERIOR BALLISTICS. 
 
 Table III. — Continued. 
 Distance and Yelocity Table, Gs = cr^, 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diff. 
 
 f.s. 
 136 
 137 
 138 
 
 feet. 
 4 2493-9 
 2544 4 
 2594-3 
 
 feet. 
 2499 
 2549-4 
 2599-2 
 
 feet. 
 2504 1 
 2554-4 
 2604-2 
 
 feet. 
 2509-1 
 2559-4 
 2609 1 
 
 feet. 
 2514-2 
 2564-4 
 2614-1 
 
 feet. 
 
 2519-2 
 2569-4 
 2619 
 
 feet 
 2524- 
 2574- 
 2624- 
 
 3 
 
 4 
 
 
 feet. 
 2529-3 
 2579 4 
 2628-9 
 
 feet. 
 2534-3 
 2584-3 
 2633-8 
 
 feet. 
 2539-4 
 2589-3 
 2638-8 
 
 + 
 5 
 5 
 4 9 
 
 139 
 110 
 141 
 
 4 2643-7 
 2692-6 
 2741-2 
 
 2648-6 
 2697-5 
 2746-0 
 
 2653-5 
 2702-4 
 2750-8 
 
 2658-4 
 2707-2 
 2755-7 
 
 2663-3 
 2712-1 
 2760-5 
 
 2668-2 
 2717 
 2765-3 
 
 2673 
 
 2721 
 2770 
 
 1 
 8 
 1 
 
 2678-0 
 2726-7 
 2774-9 
 
 2682-9 
 2731-5 
 2779-7 
 
 2687-8 
 2736-3 
 2784-5 
 
 4-9 
 4-9 
 4-8 
 
 142 
 143 
 144 
 
 4 2789-3 
 2837-1 
 2884-4 
 
 2794 1 
 2841-8 
 2889 1 
 
 2798-9 
 2846-6 
 2893-8 
 
 2803-7 
 2851-3 
 2898-6 
 
 2808-5 
 2856-0 
 2903-3 
 
 2813-2 
 2860-8 
 2908-0 
 
 2818 
 2865 
 2912 
 
 
 
 5 
 
 7 
 
 2822-8 
 2870-2 
 2917-4 
 
 2827-5 
 2875-0 
 2922-1 
 
 2832-3 
 2879-7 
 2926-7 
 
 4-8 
 
 4-7 
 4-7 
 
 145 
 146 
 147 
 
 4 2931-4 
 2978-1 
 3024-5 
 
 2936 1 
 2982-8 
 3029 1 
 
 2940-8 
 2987-4 
 3033-7 
 
 2945-5 
 2992-1 
 3038-4 
 
 2950 1 
 
 2996-7 
 3043-0 
 
 2954-8 
 3001-3 
 3047 6 
 
 2959 
 3006 
 3052 
 
 5 
 
 2 
 
 2964-1 
 3010-6 
 3056-8 
 
 2968-8 
 3015-2 
 3061-4 
 
 2973-5 
 3019-9 
 3066-0 
 
 4 7 
 4 6 
 4-6 
 
 148 
 149 
 150 
 
 4 3070-6 
 3116 4 
 3162-0 
 
 3075-2 
 3121 
 3166 5 
 
 3079 8 
 3125-6 
 3171 
 
 3084-4 
 3130 1 
 3175 6 
 
 3089 
 3134-7 
 3180 1 
 
 3093-5 
 3139-2 
 8184-6 
 
 3098 
 3143 
 3189 
 
 1 
 8 
 2 
 
 3102-7 
 3148-3 
 3193-7 
 
 3107-3 
 3152-9 
 3198-2 
 
 3111-8 
 3157-4 
 3202-7 
 
 4-6 
 4 6 
 
 4-5 
 
 151 
 152 
 153 
 
 i 3207 2 
 3252 3 
 3297-2 
 
 3211 • 8 
 3256-8 
 3301-7 
 
 3216-3 
 3261-3 
 3306-2 
 
 3220-8 
 3265-8 
 3310-6 
 
 3225-3 
 3270-3 
 3315 1 
 
 3229-8 
 3274-8 
 3319-6 
 
 3234 
 3279 
 3324 
 
 3 
 3 
 1 
 
 3238-8 
 3283-8 
 3328-5 
 
 3243-3 
 3288-3 
 3333-0 
 
 3247-8 
 3292-8 
 3337-5 
 
 4-5 
 4 5 
 4 5 
 
 154 
 155 
 156 
 
 4 3342-0 
 3386-5 
 3430 9 
 
 3346-4 
 3391-0 
 3435-3 
 
 3350 9 
 3395-4 
 3439-8 
 
 3355-3 
 3399-9 
 3444-2 
 
 3359-8 
 3404 3 
 3448-6 
 
 3364-3 
 3408-7 
 3453 
 
 3368 
 3413 
 3457 
 
 7 
 2 
 4 
 
 3373-2 
 3417-6 
 3461-9 
 
 3377 6 
 3422 
 3466-3 
 
 3382-1 
 3426-5 
 3470-7 
 
 4-5 
 
 4-4 
 4-4 
 
 157 
 158 
 159 
 
 4 3475-1 
 3519-1 
 3563-0 
 
 3479-5 
 3523-5 
 3567-3 
 
 3483-9 
 3527-9 
 3571-7 
 
 3488-3 
 3532 3 
 3576-1 
 
 3492-7 
 3536-7 
 3580-4 
 
 3497 1 
 3541 1 
 3584-8 
 
 3501 
 3545 
 3589 
 
 5 
 4 
 1 
 
 3505-9 
 3549-8 
 3593-5 
 
 3510 3 
 3554 2 
 3597-9 
 
 3514-7 
 3558-6 
 3602 2 
 
 4-4 
 4-4 
 4-4 
 
 160 
 
 161 
 162 
 
 4 3606 6 
 3650-0 
 3693-3 
 
 3610-9 
 3654-3 
 3697 6 
 
 3615-3 
 3G58-7 
 3701-9 
 
 3619-6 
 3663 
 3706-1 
 
 3624-0 
 3667-3 
 3710-5 
 
 3628-3 
 3671-6 
 3714 8 
 
 3632 
 3676 
 3719 
 
 6 
 
 
 1 
 
 3637 
 3680-3 
 3723-4 
 
 3641-3 
 3684-6 
 3727-7 
 
 3645-7 
 3688-9 
 3732-0 
 
 4-3 
 4-3 
 4-3 
 
 163 
 164 
 165 
 
 4 3736-3 
 3779-2 
 3821-9 
 
 3740-6 
 3783-5 
 3826-2 
 
 3744-9 
 3787-8 
 3830-4 
 
 3749 2 
 3792 
 3834-7 
 
 3753-5 
 3796-3 
 3838-9 
 
 3757-8 
 3800-6 
 3843-2 
 
 3762 
 3804 
 3847 
 
 1 
 9 
 4 
 
 3766-4 
 3809-1 
 3851-7 
 
 3770 6 
 3813-4 
 3855-9 
 
 3774-9 
 3817-6 
 3860-2 
 
 4 3 
 4-3 
 4-3 
 
 166 
 167 
 168 
 
 4 3864-4 
 3906-8 
 3949 
 
 3868-7 
 3911-0 
 3953 2 
 
 3872-9 
 3915-2 
 3957-4 
 
 3877-2 
 3919-5 
 3961-6 
 
 3881-4 
 3923-7 
 3965-8 
 
 3885-6 
 3927-9 
 3970-0 
 
 3889 
 3932 
 3974 
 
 9 
 1 
 2 
 
 3894-1 
 3936 3 
 
 3978-4 
 
 3898-3 
 3940 5 
 3982-6 
 
 3902-5 
 3944-7 
 3986-7 
 
 4-2 
 4-2 
 4 2 
 
 169 
 
 170 
 171 
 
 4 3990-9 
 4032-7 
 407i 3 
 
 3995-1 
 4036 9 
 4078-5 
 
 3999 3 
 40111 
 4082-6 
 
 4003-5 
 4045-2 
 4086-8 
 
 4007-7 
 4049-4 
 4090-9 
 
 4011-9 
 4053-6 
 4095-1 
 
 4016 
 4057 
 4099 
 
 
 7 
 2 
 
 4020-2 
 4061-9 
 4103 3 
 
 4024-4 
 4066-0 
 4107-5 
 
 4028-6 
 4070-2 
 4111-6 
 
 4-2 
 4 2 
 4 1 
 
 172 
 173 
 174 
 
 4 4115-7 
 4157 
 4198 
 
 4119-9 
 4161-1 
 4202 1 
 
 4124-0 
 4165-2 
 4206-2 
 
 4128-1 
 4169-3 
 4210 3 
 
 4132-3 
 
 4173-4 
 4214-4 
 
 4136-4 
 
 4177-5 
 4218-5 
 
 4140 
 
 4181 
 4222 
 
 5 
 6 
 6 
 
 4144-6 
 
 4185-7 
 4226-7 
 
 4148-7 
 4189-8 
 4230-8 
 
 4152-9 
 4193-9 
 4234-8 
 
 4-1 
 4 1 
 4 1 
 
 175 
 176 
 
 177 
 
 4 4238 9 
 4279 6 
 4320 2 
 
 4243 
 4283-7 
 4324-2 
 
 4247-1 
 4287-8 
 4328-3 
 
 4251-2 
 4291-8 
 4332 -3 
 
 4255-3 
 4295-9 
 4336-4 
 
 4259-3 
 4300-0 
 4340-4 
 
 4263 
 4304 
 4344 
 
 -4 
 
 -4 
 
 4267-5 
 4308-8 
 4348 5 
 
 4271-5 
 4312-1 
 4352-5 
 
 4275-6 
 4316 1 
 4356-5 
 
 4-1 
 41 
 4-0 
 
 178 
 179 
 180 
 
 4 4360-5 
 4100 7 
 4440-8 
 
 4364-6 
 4404-7 
 4444-7 
 
 4368-6 
 4408 8 
 4448-7 
 
 4372-0 
 4412-8 
 4452-7 
 
 4376-6 
 4416 8 
 4456-7 
 
 4380-7 
 4420-8 
 4460-7 
 
 4384 
 4424 
 4464 
 
 -7 
 -8 
 7 
 
 4388-7 
 4428-8 
 4468-7 
 
 4392 7 
 4432 8 
 4472-6 
 
 4396-7 
 4436-8 
 4476-6 
 
 40 
 4 
 40 
 
 181 
 182 
 183 
 
 4 4480 6 
 4520-3 
 4559-8 
 
 4484-6 
 4524-2 
 4563-7 
 
 4488 5 
 4528-2 
 4567-7 
 
 4492 5 
 4532-2 
 4571-6 
 
 4496-5 
 4536 1 
 4575-6 
 
 4500 5 
 4540-1 
 4579-5 
 
 4501 
 4544 
 4583 
 
 •4 
 
 4 
 
 4. '08 -4 
 4518 
 4587-4 
 
 4512-4 
 4551-9 
 4591-3 
 
 4516-3 
 4555 9 
 4595-2 
 
 4-0 
 40 
 3-9 
 
XX. — EXTERIOR BALLISTICS. 
 
 61 
 
 Table III . — Continued. 
 Distance and Velocity Table, Cs — a^' — cr^„. 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Diffi 
 
 f.s. 
 
 184 
 185 ! 
 186 
 
 feet. 
 
 4 4599-2 
 4638-4 
 4677-4 
 
 feet. 
 4603-1 
 4642-3 
 4681-3 
 
 feel 
 4607 
 4646 
 4685 
 
 
 
 2 
 2 
 
 feet 
 4610 
 4650 
 4689 
 
 9 
 
 feet. 
 4614-9 
 4654 
 4693-0 
 
 feel 
 
 4618 
 4657 
 4696 
 
 8 
 9 
 9 
 
 feet. 
 
 4622-7 
 4661-8 
 4700 8 
 
 feel 
 
 4626 
 4665 
 4704 
 
 6 
 
 7 
 6 
 
 feet. 
 
 4630-5 
 4669-6 
 4708-5 
 
 feet. 
 4634-4 
 4673 5 
 4712-4 
 
 + 
 3-9 
 3-9 
 3-9 
 
 187 
 188 ' 
 189 
 
 4 4716 3 
 4755 
 4793 7 
 
 4720-2 
 4758-9 
 4797-5 
 
 4724 
 4762 
 4801 
 
 1 
 
 8 
 4 
 
 4727 
 4766 
 4805 
 
 
 4731-8 
 4770 5 
 4809-1 
 
 4735 
 
 4774 
 4812 
 
 7 
 4 
 9 
 
 4739-6 
 4778-2 
 4816-8 
 
 4743 
 4782 
 4820 
 
 4 
 
 1 
 6 
 
 4747-3 
 4786-0 
 4824-5 
 
 4751-2 
 4789-8 
 4828-3 
 
 3 9 
 3 9 
 3 8 
 
 190 
 
 191 i 
 
 192 j 
 
 4 4832-2 
 4870-5 
 4908-7 
 
 4836 
 
 4874-3 
 4912 5 
 
 4839 
 4878 
 4916 
 
 8 
 1 
 3 
 
 4843 
 
 4882 
 4920 
 
 
 4847-5 
 4885-8 
 4923-9 
 
 4861 
 4889 
 4927 
 
 4 
 6 
 
 7 
 
 4855-2 
 4893 4 
 4931-5 
 
 4859 
 4897 
 4935 
 
 
 3 
 3 
 
 4862-8 
 4901-1 
 4939-1 
 
 4866-7 
 4904-9 
 4942-9 
 
 3 8 
 3 8 
 3 8 
 
 193 i 
 
 194 
 
 195 
 
 4 4946-7 
 4984-5 
 5022 2 
 
 4950-5 
 4988-3 
 5025 9 
 
 4954 
 4992 
 5029 
 
 3 
 
 1 
 7 
 
 4958 
 4995 
 5033 
 
 
 4961-9 
 4999 6 
 6037-2 
 
 4965 
 5003 
 5040 
 
 7 
 4 
 9 
 
 4969-4 
 5007-1 
 5044-7 
 
 4973 
 5010 
 
 5048 
 
 2 
 9 
 4 
 
 4977-0 
 5014 7 
 5052-1 
 
 4980-7 
 5018-4 
 5055-9 
 
 3-8 
 3-8 
 3 7 
 
 196 
 197 
 
 198 , 
 
 4 5059-6 
 5096-9 
 5133-9 
 
 5063-4 
 5100 6 
 6137-5 
 
 5067 
 5104 
 6141 
 
 1 
 3 
 2 
 
 5070 
 5108 
 5144 
 
 8 
 
 9 
 
 5074-6 
 5111-7 
 5148 6 
 
 5078 
 5115 
 5152 
 
 3 
 
 4 
 3 
 
 5082-0 
 5119 1 
 5150-0 
 
 5085 
 5122 
 5159 
 
 7 
 8 
 6 
 
 6089-4 
 5126-5 
 5163-3 
 
 5093 1 
 5130 2 
 6166 9 
 
 3-7 
 3-7 
 3 7 
 
 199 
 200 
 201 
 
 4 5170-6 
 5207-1 
 5243-3 
 
 5174-3 
 5210-7 
 6246-9 
 
 5177 
 5214 
 5250 
 
 9 
 3 
 5 
 
 5181 
 5218 
 5254 
 
 6 
 
 
 1 
 
 5185-2 
 5221-6 
 
 5257-7 
 
 5188 
 5225 
 5261 
 
 9 
 2 
 3 
 
 5192-5 
 5228-8 
 6264-9 
 
 5196 
 5232 
 5268 
 
 2 
 5 
 5 
 
 5199-8 
 5236-1 
 5272-1 
 
 5203-4 
 5239-7 
 5275 7 
 
 3 6 
 
 3 6 
 3 6 
 
 202 
 
 203 
 204 
 
 4 5279 2 
 631 i 9 
 6360-3 
 
 5282 8 
 6318-5 
 5353-8 
 
 5286 
 5322 
 5357 
 
 4 
 
 3 
 
 5290 
 5325 
 5360 
 
 
 6 
 9 
 
 5293-0 
 5329-1 
 6364-4 
 
 5297 
 5332 
 5367 
 
 2 
 
 7 
 9 
 
 5300-7 
 5336 2 
 6371-4 
 
 5304 
 5339 
 5374 
 
 3 
 
 7 
 9 
 
 5307-8 
 5343-3 
 5378-4 
 
 5311 4 
 5346 8 
 5391 9 
 
 3 6 
 3 5 
 3-5 
 
 205 
 206 
 207 
 
 4 5385-4 
 6420-2 
 5454-7 
 
 5388 9 
 5423-7 
 6458-1 
 
 5392 
 5427 
 5461 
 
 4 
 
 1 
 6 
 
 5395 
 5430 
 5465 
 
 9 
 6 
 
 
 5399-4 
 5434-1 
 6468-4 
 
 5402 
 
 5437 
 5471 
 
 9 
 5 
 9 
 
 5406-3 
 5441 
 5475-3 
 
 5409 
 5444 
 5478 
 
 8 
 4 
 
 7 
 
 5413-3 
 5447-8 
 5482-1 
 
 5416-7 
 5451-3 
 5485-6 
 
 3 5 
 3 5 
 3 4 
 
 208 
 
 209 ! 
 
 210 ' 
 
 4 5488-9 
 5522-8 
 5556 4 
 
 5492-3 
 5526 2 
 5559-8 
 
 6495 
 5529 
 6563 
 
 7 
 6 
 1 
 
 5499 
 5532 
 6566 
 
 1 
 9 
 4 
 
 5502-5 
 5536-3 
 5569 8 
 
 5505 
 5539 
 6573 
 
 9 
 
 7 
 1 
 
 5509 3 
 5543 
 6576 5 
 
 5512 
 5546 
 5579 
 
 7 
 4 
 8 
 
 5516-1 
 5549-7 
 5583-1 
 
 6519-4 
 5553-1 
 6586-4 
 
 3 4 
 3 4 
 3-3 
 
 211 
 212 
 213 
 
 4 5589-7 
 6622-8 
 5655-5 
 
 5593 
 6626-1 
 6658-8 
 
 5596 
 5029 
 5662 
 
 4 
 
 3 
 
 
 5599 
 5632 
 5665 
 
 7 
 6 
 3 
 
 5603-0 
 5635-9 
 5668-6 
 
 5606 
 5639 
 5671 
 
 3 
 
 2 
 8 
 
 5609-6 
 5642-5 
 6675 - 1 
 
 5612 
 5645 
 5678 
 
 9 
 
 7 
 3 
 
 5616-2 
 5649-0 
 5681-5 
 
 5619-5 
 5652-3 
 5684-8 
 
 3 3 
 3-3 
 3-2 
 
 214 ' 
 
 215 ! 
 216 
 
 4 5688 
 6/20-2 
 6752-2 
 
 5691 2 
 5723-4 
 5755-4 
 
 5694 
 
 5726 
 5758 
 
 5 
 6 
 6 
 
 5697 
 5729 
 5761 
 
 7 
 9 
 8 
 
 5700-9 
 5733-1 
 6764 9 
 
 5704 
 5736 
 5768 
 
 2 
 3 
 
 1 
 
 5707-4 
 5739-5 
 6771-3 
 
 5710 
 
 5742 
 
 5774 
 
 6 
 
 6 
 4 
 
 5713-8 
 5745-8 
 5777-6 
 
 5717-0 
 6749-0 
 6780 8 
 
 3 2 
 3 2 
 3 2 
 
 217 ' 
 
 218 
 
 219 
 
 4 5783 9 
 5815-4 
 5846 6 
 
 5787-1 
 5818-5 
 5849 7 
 
 6790 
 5821 
 6852 
 
 2 
 6 
 8 
 
 5793 
 5824 
 5855 
 
 4 
 8 
 9 
 
 5796-6 
 5827-9 
 5859 
 
 5799 
 5831 
 5862 
 
 7 
 
 1 
 
 5802-9 
 6834 1 
 5865-2 
 
 5806 
 5837 
 5868 
 
 
 3 
 3 
 
 5809-1 
 5840-4 
 5871-4 
 
 5812-2 
 6843 5 
 5874-4 
 
 3 1 
 3 1 
 3 1 
 
 220 
 221 
 222 
 
 4 5877-5 
 5908 3 
 5938-7 
 
 5880-6 
 5911 3 
 5941-8 
 
 «883 
 5914 
 6944 
 
 7 
 4 
 8 
 
 5886 
 5917 
 5947 
 
 8 
 4 
 8 
 
 6889-9 
 5920-5 
 5950-9 
 
 5893 
 6923 
 5963 
 
 
 6 
 9 
 
 5896-0 
 5926-6 
 5956-9 
 
 5899 
 5929 
 5959 
 
 1 
 6 
 9 
 
 5902-1 
 5932-7 
 6963-0 
 
 5905 2 
 5935-7 
 5966-0 
 
 3 1 
 3 
 3 
 
 223 
 224 : 
 225 
 
 4 5969-0 
 5999 
 6028 7 
 
 5972-0 
 6002 
 6031 7 
 
 5975 
 6004 
 6034 
 
 
 
 9 
 6 
 
 6978 
 6007 
 6037 
 
 
 9 
 6 
 
 5981 
 6010 9 
 6040-5 
 
 5984 
 6013 
 6043 
 
 
 
 9 
 5 
 
 5987-0 
 6016 9 
 6046 5 
 
 5990 
 6019 
 6049 
 
 
 
 8 
 4 
 
 5993-0 
 60-22 8 
 6052 4 
 
 5996-0 
 6025-8 1 
 6055 3 j 
 
 6084 7 ' 
 
 6113-8 
 
 6142-8 
 
 30 
 3 
 3 
 
 226 
 
 227 j 
 
 228 
 
 4 0058-3 
 6087-6 
 6116-7 
 
 6061-2 
 6090 5 
 6119 6 
 
 6064 
 6093 
 6122 
 
 1 
 4 
 5 
 
 0067-1 
 C0'.)6 3 
 6125 4 
 
 0070-0 
 6099-3 
 6128 3 
 
 6072 
 6102 
 6131 
 
 9 
 2 
 
 -2 
 
 6075-9 
 6105 1 
 6134 1 
 
 6078 
 6108 
 6137 
 
 8 
 
 
 
 6081-7 
 6110 9 
 0139-9 
 
 2 9 
 2 9 
 29 
 
 2^-0 ^ 
 
 4 6145 -7 
 6174-6 
 
 6148-6 
 6177-5 
 
 6151 5 
 6180-4 
 
 6154-4 
 6183-3 
 
 6157 3 
 6186-2 
 
 6160 
 6189 
 
 1 
 
 4 
 
 6163 1 
 6191-9 
 
 6166 
 6194 
 
 
 
 8 
 
 6168 8 
 6197-7 
 
 6171 7 
 6200-6 
 
 2-9 
 2 9 
 
 
 
62 
 
 XX. — EXTERIOR BALLISTICS. 
 
 Table IV.* 
 Inclination and Velocity Table, Cd — d^, — S^„. 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 f.8. 
 
 40 
 41 
 42 
 
 d( 
 
 4 
 9 
 
 ?g8. 
 
 
 6757 
 0056 
 
 Cl( 
 
 5 
 9 
 
 3g8. 
 4838 
 1240 
 4207 
 
 d 
 
 5 
 9 
 
 9640 
 5688 
 8327 
 
 d( 
 
 1 
 
 6 
 
 10 
 
 4407 
 0101 
 2410 
 
 d( 
 
 1 
 
 6 
 
 10 
 
 3ff8. 
 9137 
 4482 
 6467 
 
 d 
 
 2 
 
 6 
 
 11 
 
 3^8. 
 3830 
 8828 
 0496 
 
 d 
 
 2 
 
 7 
 
 11 
 
 3S8. 
 8488 
 3141 
 4494 
 
 d 
 
 3 
 
 7 
 
 11 
 
 3110 
 
 7421 
 8462 
 
 d 
 
 8 
 12 
 
 3^8. 
 7689 
 1660 
 2397 
 
 degs. 
 
 4-2240 
 
 8-5874 
 
 12-6306 
 
 43 
 
 13 
 16 
 20 
 
 0187 
 7450 
 2125 
 
 13 
 17 
 20 
 
 4039 
 1030 
 5460 
 
 13 
 17 
 20 
 
 7862 
 4585 
 8772 
 
 14 
 17 
 21 
 
 1652 
 8110 
 2054 
 
 14 
 18 
 21 
 
 5419 
 1614 
 5320 
 
 14 
 18 
 21 
 
 9159 
 
 5094 
 8565 
 
 15 
 
 18 
 22 
 
 2872 
 8549 
 1788 
 
 15 
 19 
 22 
 
 6557 
 1980 
 4989 
 
 16 
 19 
 22 
 
 0211 
 5383 
 8169 
 
 16-3843 
 19.8766 
 23 1327 
 
 46 
 47 
 
 48 
 
 23 
 26 
 29 
 
 4463 
 4691 
 3006 
 
 23 
 26 
 29 
 
 7578 
 7607 
 5739 
 
 24 
 27 
 29 
 
 0671 
 0503 
 8455 
 
 24 
 
 27 
 30 
 
 3736 
 3376 
 1151 
 
 24 
 
 27 
 30 
 
 6788 
 6234 
 3833 
 
 24 
 27 
 30 
 
 9821 
 9075 
 6498 
 
 25 
 28 
 30 
 
 2C34 
 1897 
 9147 
 
 25 
 28 
 31 
 
 5927 
 4702 
 1779 
 
 25 
 28 
 31 
 
 8801 
 7486 
 4393 
 
 26 1756 
 29-0254 
 31-6993 
 
 49 
 60 
 
 ei 
 
 31 
 34 
 36 
 
 9576 
 
 4557 
 8073 
 
 32 
 34 
 37 
 
 2143 
 6973 
 0349 
 
 32 
 34 
 37 
 
 4695 
 9375 
 2613 
 
 32 
 35 
 37 
 
 7227 
 1761 
 4862 
 
 32 
 35 
 37 
 
 9747 
 4134 
 7099 
 
 33 
 
 35 
 37 
 
 2253 
 6493 
 9323 
 
 33 
 
 35 
 38 
 
 4743 
 8837 
 1534 
 
 33 
 36 
 38 
 
 7219 
 1167 
 3731 
 
 33 
 
 36 
 38 
 
 9679 
 3480 
 5914 
 
 34 2125 
 36-5783 
 38-8086 
 
 52 
 53 
 
 54 
 
 39 
 41 
 43 
 
 0246 
 1175 
 0967 
 
 39 
 41 
 43 
 
 2394 
 3204 
 
 2887 
 
 39 
 41 
 43 
 
 4529 
 5221 
 4795 
 
 39 
 41 
 43 
 
 6651 
 7225 
 6690 
 
 39 
 41 
 43 
 
 8762 
 9221 
 8578 
 
 40 
 
 42 
 44 
 
 0860 
 1205 
 0456 
 
 40 
 
 42 
 44 
 
 2947 
 3179 
 2324 
 
 40 
 42 
 44 
 
 5022 
 5142 
 4182 
 
 40 
 42 
 44 
 
 7083 
 7095 
 6031 
 
 40-9135 
 42-9037 
 
 44-7870 
 
 55 
 56 
 57 
 
 44 
 46 
 48 
 
 9698 
 7437 
 4270 
 
 45 
 46 
 48 
 
 1510 
 9160 
 5906 
 
 45 
 
 47 
 48 
 
 3325 
 0874 
 7534 
 
 45 
 
 47 
 48 
 
 5122 
 2581 
 9153 
 
 45 
 47 
 49 
 
 6910 
 4277 
 0764 
 
 45 
 47 
 49 
 
 8689 
 5965 
 2368 
 
 46 
 
 47 
 49 
 
 0457 
 7644 
 3963 
 
 46 
 
 47 
 49 
 
 2217 
 9314 
 5551 
 
 46 
 48 
 49 
 
 3964 
 0973 
 7130 
 
 46-5705 
 48-2625 
 49-8701 
 
 58 
 59 
 60 
 
 50 
 51 
 53 
 
 0265 
 5492 
 0003 
 
 50 
 51 
 53 
 
 1822 
 6975 
 1417 
 
 50 
 51 
 53 
 
 3370 
 
 8451 
 2825 
 
 50 
 51 
 53 
 
 4909 
 9917 
 4224 
 
 50 
 52 
 53 
 
 6442 
 
 1378 
 5618 
 
 50 
 52 
 53 
 
 7968 
 2832 
 7005 
 
 50 
 52 
 53 
 
 9487 
 4280 
 8386 
 
 51 
 52 
 53 
 
 0999 
 5721 
 9761 
 
 51 
 52 
 54 
 
 2505 
 7155 
 1130 
 
 51-4002 
 
 52-8583 
 54-2492 
 
 61 
 62 
 63 
 
 54 
 55 
 56 
 
 3847 
 7054 
 9663 
 
 54 
 55 
 
 57 
 
 5196 
 8342 
 0891 
 
 54 
 55 
 57 
 
 6539 
 9623 
 2114 
 
 54 
 56 
 
 57 
 
 7875 
 0899 
 3330 
 
 54 
 56 
 57 
 
 9205 
 2169 
 4542 
 
 55 
 56 
 
 57 
 
 0529 
 3433 
 5749 
 
 55 
 56 
 57 
 
 1846 
 4690 
 6950 
 
 55 
 56 
 
 57 
 
 3158 
 5942 
 8146 
 
 55 
 56 
 
 57 
 
 4462 
 7188 
 9338 
 
 55-5761 
 56-8428 
 58-0523 
 
 64 
 65 
 
 66 
 
 58 
 59 
 60 
 
 1703 
 3209 
 4207 
 
 58 
 59 
 60 
 
 2878 
 4332 
 5280 
 
 58 
 59 
 60 
 
 4046 
 5449 
 6348 
 
 58 
 59 
 60 
 
 5209 
 6562 
 7411 
 
 58 
 59 
 60 
 
 6367 
 7669 
 8470 
 
 58 
 59 
 60 
 
 7521 
 8772 
 9523 
 
 58 
 59 
 61 
 
 8669 
 9869 
 0572 
 
 58 
 60 
 61 
 
 9832 
 0961 
 1616 
 
 59 
 60 
 61 
 
 0949 
 2047 
 2654 
 
 59-2081 
 60 3130 
 61-3688 
 
 67 
 68 
 69 
 
 61 
 62 
 63 
 
 4719 
 4779 
 4414 
 
 61 
 
 62 
 63 
 
 5744 
 5761 
 5356 
 
 61 
 62 
 63 
 
 6766 
 6739 
 6294 
 
 61 
 62 
 63 
 
 7783 
 7711 
 
 7227 
 
 61 
 62 
 63 
 
 8796 
 8680 
 8157 
 
 61 
 62 
 63 
 
 9804 
 9646 
 9084 
 
 62 
 63 
 64 
 
 0808 
 0607 
 0006 
 
 62 
 63 
 
 64 
 
 1807 
 1565 
 0924 
 
 62 
 63 
 64 
 
 2802 
 2519 
 1838 
 
 62 3793 
 63-3468 
 64 2749 
 
 70 
 71 
 
 72 
 
 64 
 65 
 66 
 
 3656 
 2522 
 1015 
 
 64 
 65 
 66 
 
 4559 
 3388 
 1845 
 
 64 
 65 
 66 
 
 5459 
 4250 
 2671 
 
 64 
 65 
 66 
 
 6356 
 5107 
 3494 
 
 64 
 65 
 66 
 
 7249 
 5962 
 4313 
 
 64 
 65 
 66 
 
 8137 
 6813 
 5128 
 
 64 
 65 
 66 
 
 9022 
 7660 
 5940 
 
 64 
 65 
 66 
 
 9903 
 8504 
 6749 
 
 65 
 65 
 66 
 
 0779 
 9345 
 7553 
 
 65-1652 
 66-0182 
 66-8355 
 
 73 
 74 
 75 
 
 66 
 67 
 68 
 
 9153 
 6955 
 4436 
 
 66 
 
 67 
 68 
 
 9949 
 7717 
 5168 
 
 67 
 67 
 68 
 
 0740 
 8476 
 5896 
 
 67 
 67 
 68 
 
 1529 
 9231 
 6620 
 
 67 
 67 
 68 
 
 2314 
 9983 
 7342 
 
 67 
 68 
 68 
 
 3096 
 0733 
 8062 
 
 67 
 68 
 68 
 
 3875 
 1479 
 8778 
 
 67 
 68 
 68 
 
 4649 
 2223 
 9492 
 
 67 
 68 
 69 
 
 5422 
 2964 
 0204 
 
 67-6190 
 68-3702 
 69 0912 
 
 76 
 
 77 
 78 
 
 69 
 69 
 70 
 
 1617 
 8497 
 5082 
 
 69 
 69 
 70 
 
 2318 
 9169 
 5725 
 
 69 
 69 
 70 
 
 3017 
 9838 
 6365 
 
 69 
 70 
 70 
 
 3712 
 0503 
 7004 
 
 69 
 70 
 70 
 
 4404 
 1166 
 7639 
 
 69 
 70 
 70 
 
 5094 
 1826 
 8271 
 
 69 
 70 
 70 
 
 5780 
 2483 
 8901 
 
 69 
 70 
 70 
 
 6464 
 3137 
 9527 
 
 69 
 70 
 71 
 
 7145 
 3787 
 0149 
 
 69-7823 
 70-4436 
 71-0770 
 
 79 
 80 
 81 
 
 71 
 71 
 72 
 
 1388 
 7432 
 3225 
 
 71 
 71 
 
 72 
 
 2004 
 8023 
 3791 
 
 71 
 71 
 
 72 
 
 2617 
 8611 
 4354 
 
 71 
 
 71 
 
 72 
 
 3228 
 9196 
 4915 
 
 71 
 71 
 
 72 
 
 3837 
 9779 
 5473 
 
 71 
 
 72 
 72 
 
 4442 
 0359 
 6030 
 
 71 
 
 72 
 72 
 
 5045 
 0937 
 6584 
 
 71 
 
 72 
 72 
 
 5646 
 1513 
 7135 
 
 71 
 
 72 
 72 
 
 6244 
 2086 
 7685 
 
 71-6839 
 72 2656 
 72-8232 
 
 82 
 83 
 
 84 
 
 72 
 73 
 73 
 
 8776 
 4079 
 9143 
 
 72 
 73 
 73 
 
 9317 
 4596 
 9636 
 
 72 
 73 
 74 
 
 9856 
 5111 
 0127 
 
 73 
 
 73 
 74 
 
 0393 
 
 5622 
 0615 
 
 73 
 73 
 
 74 
 
 0927 
 6132 
 1101 
 
 73 
 73 
 74 
 
 1458 
 6639 
 1585 
 
 73 
 73 
 
 74 
 
 1988 
 7145 
 2067 
 
 73 
 73 
 
 74 
 
 2514 
 7648 
 2546 
 
 73 
 
 73 
 
 74 
 
 3038 
 8149 
 3023 
 
 73-3560 
 73-8647 
 74-3498 
 
 85 
 86 
 87 
 
 74 
 74 
 75 
 
 3971 
 8573 
 2966 
 
 74 
 74 
 75 
 
 4441 
 9022 
 3395 
 
 74 
 74 
 75 
 
 4910 
 9468 
 3821 
 
 74 
 74 
 75 
 
 5376 
 9912 
 4246 
 
 74 
 75 
 75 
 
 5839 
 0355 
 4668 
 
 74 
 75 
 75 
 
 6301 
 0795 
 5089 
 
 74 
 75 
 75 
 
 6760 
 1233 
 5507 
 
 74 
 75 
 75 
 
 7217 
 1669 
 5924 
 
 74 
 75 
 75 
 
 7670 
 2104 
 6339 
 
 74-8123 
 75-2536 
 75-6752 
 
 By W. D. Kiven, Esq., M. A., F. S. S. 
 
XX. EXTERIOR BALLISTICS. 
 
 Table lY .—Continued. 
 Inclination and Velocity Table, Cd = 8^ — S^„ 
 
 V. 
 
 
 
 1 
 
 !3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 f.8. 
 
 88 
 
 89 1 
 90 
 
 degs. 
 
 75 7163 
 
 76 1171 
 76-5005 
 
 degs. 
 75-7572 
 76-1562 
 76-5379 
 
 degs. 
 75-7980 
 76-1952 
 76-5751 
 
 degs. 
 
 75 8385 
 76-2339 
 
 76 6121 
 
 degs. 
 
 75-8788 
 76-2725 
 76-6490 
 
 degs. 
 
 75-9190 
 
 i 76-3109 
 
 76-6857 
 
 degs. 
 75 9590 
 76-3492 
 76-7223 
 
 degs. 
 75-9988 
 76-3873 
 76-7588 
 
 d 
 
 76 
 76 
 76 
 
 4252 
 7951 
 
 degs. 
 76-0778 
 76-4629 
 76 8312 
 
 91 
 92 
 93 
 
 76-8671 
 77-2179 
 77-5540 
 
 76-9029 
 77-2522 
 77-5868 
 
 76-9385 
 77-2863 
 77-6195 
 
 76-9739 
 77-3203 
 77-6520 
 
 77-0092 
 77-3541 
 77-6844 
 
 77-0444 
 
 77-3878 
 77-7167 
 
 77 0794 
 77 4213 
 
 77-7488 
 
 77-1142 
 
 77-4547 
 77-7807 
 
 77 
 77 
 77 
 
 1489 
 4879 
 81-25 
 
 77-1835 
 77-5210 
 77 8442 
 
 94 
 
 95 
 96 
 
 77-8757 
 78 1841 
 78-4798 
 
 77 9071 
 78-2142 
 
 78 5087 
 
 77-9384 
 78-2442 
 78-5375 
 
 77-9695 
 78-2741 
 78-5622 
 
 78-0005 
 78 3039 
 78-5947 
 
 78-0314 
 78-3335 
 78-6231 
 
 78 0622 
 78-3630 
 78-6514 
 
 78-0929 
 78-3924 
 78-6796 
 
 78 
 78 
 78 
 
 1234 
 4216 
 7076 
 
 78 1538 
 78 4508 
 78 7356 
 
 97 
 98 
 99 
 
 78-7634 
 79-0354 
 79-2968 
 
 78-7911 
 79 0621 
 79-3224 
 
 78-8188 
 79-0886 
 79-3478 
 
 78 8463 
 
 79 1150 
 79-3731 
 
 78-8736 
 79 1413 
 79-3983 
 
 78-9009 
 79 1675 
 79-4234 
 
 78-9280 
 79 1936 
 79-4484 
 
 78-9551 
 79-2195 
 79-4734 
 
 78 
 79 
 79 
 
 9819 
 2454 
 4982 
 
 79-0087 
 79-2712 
 79 5230 
 
 100 
 101 1 
 102 
 
 79-5476 
 79-7889 
 80-0203 
 
 79-5722 
 79-8124 
 80 0430 
 
 79-5966 
 79-8359 
 80-0655 
 
 79-6210 
 79-8593 
 80-0879 
 
 79-6453 
 79-8826 
 80 1102 
 
 79 6695 
 79-9058 
 
 80 1324 
 
 79-6935 
 79 9289 
 80-1544 
 
 79-7175 
 79-9519 
 80-1763 
 
 79 
 79 
 80 
 
 7414 
 9748 
 1981 
 
 79 7652 
 79-9976 
 80-2197 
 
 103 
 104 
 
 105 
 
 80-2412 
 80-4466 
 80-6321 
 
 80-2625 
 80-4661 
 80-6495 
 
 80-2837 
 80-4854 
 80-6667 
 
 80-3408 
 80-5045 
 80-6835 
 
 80-3256 
 80 5234 
 80 7003 
 
 80-3462 
 80 5420 
 80 7169 
 
 80 3667 
 80 5605 
 80 7333 
 
 80-3869 
 80-5787 
 80-7495 
 
 80 
 80 
 80 
 
 4071 
 
 5967 
 7654 
 
 80-4270 
 80 6145 
 80 7813 
 
 106 
 
 107 ' 
 
 108 1 
 
 80 7970 
 80-9463 
 81-0841 
 
 80-8126 
 80-9606 
 81-0973 
 
 80-8280 
 80-9747 
 81 1105 
 
 80-8432 
 80-9886 
 81 1236 
 
 80-8583 
 81 0026 
 81 1366 
 
 80-8733 
 
 I 81 0164 
 
 81 1495 
 
 80-8882 
 81-0301 
 81 1624 
 
 80 9029 
 
 81 0437 
 81 1751 
 
 80 
 81 
 81 
 
 9175 
 0573 
 1877 
 
 80-?319 
 81 0707 
 81 2003 
 
 109 
 110 
 lllj 
 
 81-2129 
 81-3342 
 81-4495 
 
 81-2253 
 81-3460 
 81-4607 
 
 81-2377 
 81-3578 
 81-4719 
 
 81 2501 
 81 3695 
 81 4829 
 
 81-2623 
 81-3811 
 81 4939 
 
 81-2745 
 81-3927 
 81 5049 
 
 81-2866 
 81-4042 
 81-5159 
 
 81-2986 
 81-4156 
 81-5268 
 
 81 
 81 
 81 
 
 3105 
 4269 
 5377 
 
 81-3224 
 81 4382 
 81 5486 
 
 112 
 113 
 114 ! 
 
 81-5593 
 81-6647 
 81 7662 
 
 81-5700 
 81-6750 
 81-7761 
 
 81-5807 
 81-6853 
 81-7861 
 
 81-5913 
 81-6955 
 81-7960 
 
 81-6019 
 81-7057 
 81-8058 
 
 81-6124 
 81 7159 
 81-8156 
 
 81-6230 
 81-7260 
 81-8254 
 
 81-6334 
 81-7361 
 81-8351 
 
 81 
 81 
 81 
 
 6439 
 
 7462 
 8448 
 
 81-6543 
 81-7662 
 81 •8545 
 
 115 
 116 
 117 
 
 81-8641 
 81-9588 
 82-0503 
 
 81-8737 
 81-9681 
 82-0592 
 
 81-8833 
 81-9774 
 82-0682 
 
 81-8929 
 81-9866 
 82 0771 
 
 81-9024 
 81-9958 
 82-0860 
 
 81-9119 
 82-0049 
 82 0948 
 
 81-9213 
 82 0141 
 82 1036 
 
 81-9307 
 82-0232 
 82 1124 
 
 81 
 82 
 82 
 
 9401 
 0322 
 1212 
 
 81-9496 
 82 0413 
 82-1299 
 
 118 
 119 
 120 
 
 82 1386 
 82-2241 
 82-3066 
 
 82-1473 
 82-2325 
 82-3147 
 
 82 1559 
 82-2408 
 82-3228 
 
 82 1645 
 82-2492 
 82 3309 
 
 82 1731 
 82-2575 
 82-3389 
 
 82-1817 
 82-2657 
 82-3469 
 
 82-1902 
 82-2Y40 
 82-3549 
 
 82-1988 
 82-2822 
 82-3629 
 
 82 
 82 
 82 
 
 2073 
 2903 
 3708 
 
 82-2157 
 82-2985 
 82-3787 
 
 121 
 122 
 123 
 
 82-3865 
 82-4639 
 82 5386 
 
 82-3944 
 82-4715 
 82-5459 
 
 82-4022 
 82-4790 
 82 5533 
 
 82-4100 
 82-4865 
 82-5606 
 
 82-4178 
 82-4940 
 82-5679 
 
 82-4255 
 82 5015 
 82-5751 
 
 82-4333 
 82-5090 
 82-5824 
 
 82-4410 
 82-5164 
 82-5896 
 
 82 
 82 
 82 
 
 4486 
 5238 
 5968 
 
 82-4563 
 82-5312 
 82 6040 
 
 124 
 125 
 126 
 
 82-6112 
 82-6814 
 82-7494 
 
 82-6183 
 82-6883 
 82-7561 
 
 82-6254 
 82-6951 
 82-7627 
 
 82 6324 
 82-7019 
 82 7694 
 
 82-6395 
 82-7088 
 82 7760 
 
 82-6465 
 82-7156 
 82-7826 
 
 82-6535 
 
 82-7224 
 82-7892 
 
 82-6605 
 82-7291 
 82-7957 
 
 82 
 
 82 
 82 
 
 6675 
 7359 
 8023 
 
 82-6744 
 82-7427 
 82-8088 
 
 127 
 128 
 129 
 
 82-8153 
 82-8794 
 82-9415 
 
 82-8218 
 82-8857 
 82-9477 
 
 82-8283 
 82-8920 
 82-9538 
 
 82-8348 
 82-8983 
 82-9599 
 
 82-8412 
 82-9045 
 82-9660 
 
 82-8477 
 82-9107 
 82-9720 
 
 82-8541 
 82-9169 
 82-9780 
 
 82-8604 
 82-9231 
 82-9840 
 
 82 
 82 
 82 
 
 8668 
 9292 
 9900 
 
 82-8731 
 82-9354 
 82-9900 
 
 130 
 131 
 132 
 
 83-0019 
 83 0606 
 83 1176 
 
 83-0079 
 83-0664 
 83 1232 
 
 83-0138 
 83-0721 
 83-1288 
 
 83 0197 
 83-0779 
 83-1344 
 
 83-0256 
 83-0836 
 83-1400 
 
 83 0315 
 83-0893 
 83 1455 
 
 83-0373 
 83 0950 
 83 1511 
 
 83-0432 
 83-1007 
 83 1566 
 
 83 
 83 
 83 
 
 0490 
 10^3 
 1621 
 
 83 0548 
 83-1119 
 83-1676 
 
 133 
 184 
 136 
 
 83-1730 
 83-2271 
 83-2797 
 
 83-1785 
 83-2324 
 83-2849 
 
 83 1840 
 83-2377 
 83-2900 
 
 83-1894 
 83-2430 
 83-2951 
 
 83 1949 
 83-2483 
 83-3003 
 
 83-2003 
 83-2536 
 83-3054 
 
 83-2057 
 83-2588 
 83-3105 
 
 83 2110 
 83-2641 
 83-3156 
 
 83 
 83 
 83 
 
 2164 
 2693 
 3207 
 
 83 2217 
 83 2745 
 83-3257 
 
64 
 
 XX. — EXTERIOR BALLISTICS. 
 
 Table lY .—Continued. 
 Inclination and Velocity Table, Cd = d^, 
 
 .. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 " 
 
 f.s. 
 
 136 
 137 
 138 
 
 degs. 
 83-3308 
 83-3808 
 83-4295 
 
 d( 
 
 83 
 83 
 83 
 
 5gS. 
 3359 
 3857 
 4343 
 
 degs. 
 83-3409 
 83-3906 
 83-4391 
 
 degs. 
 
 83-3459 
 83-3955 
 83-4438 
 
 d( 
 
 83 
 83 
 83 
 
 3509 
 4004 
 4486 
 
 d( 
 
 83 
 83 
 83 
 
 3560 
 4053 
 4533 
 
 d< 
 
 83 
 83 
 83 
 
 3g8. 
 3609 
 4101 
 
 4581 
 
 d( 
 
 83 
 83 
 
 83 
 
 5g8. 
 3659 
 4150 
 4628 
 
 d( 
 
 83 
 
 83 
 83 
 
 3g8. 
 3709 
 4198 
 4676 
 
 degs. 
 83-3759 
 83-4247 
 83-4723 
 
 139 
 140 ' 
 141 
 
 83 
 83 
 83 
 
 4770 
 5233 
 5687 
 
 83 
 83 
 83 
 
 4817 
 5279 
 5732 
 
 83-4863 
 83-5325 
 83-5777 
 
 83-4910 
 83-5371 
 83-5821 
 
 83 
 83 
 83 
 
 4956 
 5417 
 5866 
 
 83 
 83 
 83 
 
 5003 
 
 5402 
 5910 
 
 83 
 83 
 83 
 
 5049 
 5507 
 5954 
 
 83 
 83 
 83 
 
 5095 
 5553 
 5999 
 
 83 
 83 
 83 
 
 5141 
 5598 
 6043 
 
 83-5187 
 83-5642 
 83-6087 
 
 142 
 143 
 144 
 
 83 
 83 
 83 
 
 6130 
 6565 
 6988 
 
 83 
 83 
 83 
 
 6174 
 6607 
 7030 
 
 83-6218 
 83 - 0650 
 83-7072 
 
 83-6261 
 83-6693 
 83-7114 
 
 83 
 83 
 83 
 
 6305 
 6735 
 7156 
 
 83 
 83 
 83 
 
 6348 
 6778 
 7197 
 
 83 
 83 
 83 
 
 6392 
 6820 
 7239 
 
 83 
 83 
 83 
 
 6435 
 
 6862 
 7280 
 
 83 
 83 
 83 
 
 6478 
 6904 
 7321 
 
 83-6522 
 83-6946 
 83-7362 
 
 145 \ 
 
 146 i 
 147 
 
 83 
 83 
 83 
 
 7403 
 7810 
 8209 
 
 83 
 83 
 83 
 
 7444 
 7850 
 8249 
 
 83-7485 
 8.3-7891 
 83-8-288 
 
 83-7526 
 83-7930 
 83 8327 
 
 83 
 83 
 
 7567 
 7970 
 8366 
 
 83 
 83 
 83 
 
 7608 
 8010 
 8406 
 
 83 
 
 83 
 83 
 
 7649 
 8050 
 8445 
 
 83 
 83 
 83 
 
 7689 
 8090 
 8484 
 
 83 
 83 
 83 
 
 7730 
 8130 
 8522 
 
 83-7770 
 83 '8170 
 83-8561 
 
 148 
 149 
 150 
 
 83 
 83 
 83 
 
 8600 
 8983 
 9359 
 
 83 
 83 
 83 
 
 8639 
 9021 
 9396 
 
 83-8677 
 83-9059 
 83-9433 
 
 83-8715 
 83 9096 
 83-9470 
 
 83 
 83 
 
 83 
 
 8754 
 9134 
 9507 
 
 83 
 83 
 83 
 
 8792 
 9172 
 9544 
 
 83 
 83 
 83 
 
 8830 
 9209 
 9581 
 
 83 
 83 
 83 
 
 8869 
 9247 
 9617 
 
 83 
 83 
 83 
 
 8907 
 9285 
 9654 
 
 83-8945 
 83-9322 
 83-9691 
 
 151 ' 
 
 152 
 
 153 
 
 83 
 84 
 84 
 
 9727 
 0090 
 0446 
 
 83 
 84 
 84 
 
 9764 
 0126 
 0481 
 
 83-9800 
 84-0161 
 84-0516 
 
 83-9837 
 84-0197 
 84-0551 
 
 83 
 84 
 84 
 
 9873 
 0233 
 0587 
 
 83 
 84 
 84 
 
 9909 
 0269 
 0622 
 
 83 
 84 
 84 
 
 9946 
 0304 
 
 0657 
 
 83 
 84 
 84 
 
 9982 
 0340 
 0692 
 
 84 
 84 
 84 
 
 0018 
 0375 
 0727 
 
 84-0054 
 84-0410 
 84-0762 
 
 15. 
 155 
 
 156 
 
 84 
 84 
 84 
 
 0796 
 1140 
 1479 
 
 84 
 84 
 84 
 
 0831 
 1174 
 1513 
 
 84-0866 
 84 1208 
 84-1546 
 
 84-0900 
 84-1242 
 84-1579 
 
 84 
 84 
 84 
 
 0935 
 1276 
 1613 
 
 84 
 84 
 
 84 
 
 0969 
 1310 
 1646 
 
 84 
 84 
 84 
 
 1004 
 1344 
 1679 
 
 84 
 84 
 84 
 
 1038 
 1378 
 1713 
 
 84 
 84 
 84 
 
 1072 
 1412 
 1746 
 
 84-1106 
 84 1445 
 84-1779 
 
 157 
 158 
 159 
 
 84 
 84 
 84 
 
 1812 
 2139 
 2461 
 
 84 
 84 
 84 
 
 1845 
 2172 
 2493 
 
 84-1878 
 84-2204 
 84-2525 
 
 84-1911 
 84-2237 
 84-2557 
 
 84 
 84 
 84 
 
 1943 
 2269 
 2588 
 
 84 
 84 
 84 
 
 1976 
 2301 
 2620 
 
 84 
 84 
 84 
 
 2009 
 2333 
 2652 
 
 84 
 84 
 84 
 
 2041 
 2366 
 2683 
 
 84 
 84 
 84 
 
 2074 
 2398 
 2715 
 
 84-2107 
 84-2430 
 84-2746 
 
 160 ' 
 
 161 
 
 162 
 
 84 
 84 
 84 
 
 2778 
 3088 
 3394 
 
 84 
 84 
 84 
 
 2809 
 3119 
 3424 
 
 84-2840 
 84-3150 
 84-3454 
 
 84-2871 
 84-3180 
 84-3484 
 
 84 
 84 
 84 
 
 2902 
 3210 
 3514 
 
 84 
 
 84 
 
 ,84 
 
 2933 
 3242 
 3544 
 
 84 
 
 84 
 84 
 
 2965 
 3272 
 3574 
 
 84 
 84 
 
 84 
 
 2996 
 3302 
 3604 
 
 84 
 81 
 84 
 
 3027 
 3333 
 3634 
 
 84-3058 
 84-3363 
 84-3664 
 
 163 
 164 
 165 
 
 84 
 84 
 84 
 
 3694 
 3990 
 4281 
 
 84 
 84 
 84 
 
 3724 
 4019 
 4310 
 
 84-3753 
 84-4018 
 84-4339 
 
 84-3783 
 84-4078 
 84-4367 
 
 84 
 84 
 84 
 
 3813 
 4107 
 4396 
 
 84 
 81 
 84 
 
 3843 
 
 41S6 
 4425 
 
 84 
 84 
 84 
 
 3872 
 4105 
 4453 
 
 84 
 84 
 84 
 
 3902 
 4194 
 
 4482 
 
 84 
 84 
 84 
 
 3931 
 4223 
 4510 
 
 84-3960 
 84-4252 
 84-4539 
 
 166 
 137 
 168 
 
 84 
 84 
 84 
 
 4567 
 4849 
 5127 
 
 84 
 84 
 84 
 
 4595 
 4877 
 5154 
 
 84-4624 
 84-4905 
 84-5181 
 
 84-4652 
 84-4933 
 84-5209 
 
 84 
 84 
 84 
 
 4680 
 4961 
 5236 
 
 84 
 84 
 84 
 
 4709 
 4988 
 5263 
 
 84 
 84 
 84 
 
 4737 
 5016 
 5291 
 
 84 
 84 
 84 
 
 4765 
 5044 
 5318 
 
 84 
 84 
 84 
 
 4793 
 5070 
 5345 
 
 84-4821 
 84-5099 
 84-5372 
 
 169 
 170 
 171 
 
 84 
 84 
 84 
 
 5399 
 5668 
 5933 
 
 84 
 84 
 84 
 
 5426 
 5695 
 5959 
 
 84-5453 
 84-5721 
 84-5985 
 
 84-5480 
 84-5748 
 84-6012 
 
 84 
 84 
 84 
 
 5508 
 
 5775 
 6038 
 
 84 
 84 
 84 
 
 5534 
 6801 
 6064 
 
 84 
 84 
 84 
 
 5561 
 5828 
 6090 
 
 84 
 84 
 84 
 
 5588 
 5854 
 6116 
 
 84 
 
 84 
 84 
 
 5615 
 5880 
 6142 
 
 84-5641 
 84-5907 
 84 0168 
 
 172 
 173 
 174 
 
 84 
 84 
 
 84 
 
 6193 
 6449 
 6701 
 
 84 
 84 
 84 
 
 6219 
 6475 
 6726 
 
 84-6245 
 84-6500 
 84-6750 
 
 84-6271 
 84-6525 
 84-6776 
 
 84 
 84 
 84 
 
 6297 
 6550 
 6800 
 
 84 
 84 
 84 
 
 6322 
 6575 
 6825 
 
 84 
 84 
 84 
 
 6348 
 6001 
 6850 
 
 84 
 
 84 
 84 
 
 6373 
 6626 
 6875 
 
 84 
 84 
 84 
 
 6399 
 6651 
 6899 
 
 84-6424 
 84-6676 
 84-6924 
 
 175 
 176 
 
 177 
 
 84 
 84 
 84 
 
 6948 
 7192 
 7432 
 
 84 
 84 
 84 
 
 6973 
 7216 
 7455 
 
 84-6997 
 84-7240 
 84-7479 
 
 84-7022 
 84-7264 
 84-7503 
 
 84 
 84 
 84 
 
 7046 
 7288 
 7526 
 
 84 
 84 
 84 
 
 7071 
 7312 
 7550 
 
 84 
 84 
 84 
 
 7095 
 7336 
 7574 
 
 84 
 84 
 84 
 
 7119 
 7360 
 7597 
 
 84 
 84 
 84 
 
 7144 
 7384 
 7621 
 
 84-7168 
 84-7408 
 84-7645 
 
 178 
 179 
 180 
 
 81 
 84 
 84 
 
 7608 
 7P02 
 8131 
 
 84 
 81 
 84 
 
 7692 
 •7925 
 8154 
 
 81 -771 5 
 84-7918 
 84-8177 
 
 84-7739 
 81-7972 
 8i-8199 
 
 84 
 
 81 
 84 
 
 7762. 
 7904 
 8222 
 
 •84 
 81 
 81 
 
 7785 
 
 roi7 
 
 8214 
 
 84 
 84 
 84 
 
 7809 
 
 80 :o 
 
 82u7 
 
 84 
 84 
 84 
 
 7832 
 803 
 8289 
 
 84 
 84 
 84 
 
 7855 
 80SG 
 8312 
 
 84-7878 
 81-8109 
 84-8334 
 
 181 
 
 182 
 183 
 
 84 
 84 
 84 
 
 83R7 
 8579 
 8798 
 
 81 
 
 84 
 84 
 
 8379 
 8601 
 8819 
 
 84-8-101 
 84-8623 
 84-8841 
 
 81 ■ 8424 
 84-8645 
 84-8863 
 
 84 
 84 
 
 84 
 
 8446 
 8667 
 8884 
 
 84 
 i ^* 
 
 8168 
 8689 
 8906 
 
 84 
 84 
 
 84 
 
 81 PO 
 
 8711 
 8927 
 
 84 
 84 
 84 
 
 8513 
 
 8732 
 8949 
 
 84 
 84 
 84 
 
 8535 
 8754 
 8970 
 
 84-8557 
 84-8776 
 84-8992 
 
XX. — EXTERIOR BALLIStlCS. 
 
 Table IV.— Continued. 
 Inclination and Velocity Table, Cd = S^, — S^„. 
 
 V. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 
 f.s. 
 
 184 
 185 
 186 
 
 d 
 
 84 
 84 
 84 
 
 9013 
 9226 
 9435 
 
 d 
 
 84 
 84 
 84 
 
 egs. 
 9035 
 9247 
 9456 
 
 d 
 
 84 
 84 
 84 
 
 9056 
 9268 
 
 9476 
 
 d 
 84 
 84 
 84 
 
 egs. 
 
 9077 
 •9289 
 
 9497 
 
 d 
 
 84 
 84 
 84 
 
 egs. 
 •9099 
 •9310 
 9518 
 
 d 
 
 84 
 34 
 84 
 
 9120 
 9331 
 •9538 
 
 d 
 
 84 
 84 
 84 
 
 egs. 
 9141 
 9351 
 
 •9559 
 
 degs. 
 84-9162 
 84 9372 
 84-9580 
 
 d 
 
 84 
 84 
 84 
 
 egs. 
 ■9184 
 ■9393 
 -9600 
 
 degs. 
 
 84-9205 
 84 9414 
 84-9621 
 
 1?7 
 188 
 189 
 
 84 
 84 
 85 
 
 9C41 
 •9845 
 0045 
 
 84 
 84 
 86 
 
 9C62 
 9865 
 0065 
 
 84 
 84 
 85 
 
 9682 
 9885 
 0085 
 
 84 
 84 
 85 
 
 9702 
 9905 
 0105 
 
 84 
 84 
 85 
 
 9723 
 9925 
 0125 
 
 84 
 84 
 85 
 
 •9743 
 •9946 
 •0145 
 
 84 
 84 
 85 
 
 9763 
 •9966 
 0165 
 
 84 • 9784 
 84-9986 
 85 0185 
 
 84 
 85 
 85 
 
 9804 
 0006 
 0204 
 
 84-9820 
 86-0026 
 85-0224 
 
 190 
 191 
 192 
 
 85 
 
 85 
 85 
 
 0244 
 0438 
 0630 
 
 85 
 85 
 85 
 
 0263 
 0458 
 0650 
 
 85 
 85 
 85 
 
 0283 
 0477 
 0669 
 
 85 
 85 
 85 
 
 0303 
 0496 
 0687 
 
 85 
 85 
 85 
 
 0322 
 0515 
 0706 
 
 85 
 85 
 85 
 
 0342 
 0535 
 0725 
 
 85 
 85 
 85 
 
 •0361 
 0554 
 0744 
 
 85 0380 
 
 86 0573 
 85 0763 
 
 85 
 85 
 85 
 
 0400 
 0592 
 0782 
 
 8.'5 0419 
 85-0611 
 85-0801 
 
 193 
 194 
 195 
 
 85 
 85 
 85 
 
 0820 
 1006 
 1190 
 
 85 
 85 
 
 85 
 
 0838 
 1025 
 1208 
 
 85 
 85 
 85 
 
 0857 
 1043 
 1227 
 
 86 
 86 
 85 
 
 0876 
 10C2 
 1245 
 
 85 
 85 
 85 
 
 0895 
 1080 
 1263 
 
 85 
 85 
 85 
 
 0913 
 1099 
 1281 
 
 85 
 85 
 85 
 
 •0932 
 1117 
 1299 
 
 85 0951 
 85 1136 
 85 1317 
 
 85 
 85 
 85 
 
 0969 
 1154 
 1335 
 
 85-0988 
 86 1172 
 85 -136a 
 
 196 
 197 
 198 
 
 85 
 85 
 85 
 
 1371 
 1549 
 1724 
 
 85 
 86 
 85 
 
 1389 
 1567 
 1741 
 
 85 
 85 
 
 85 
 
 1407 
 1584 
 1759 
 
 85 
 85 
 85 
 
 1425 
 1602 
 1776 
 
 85 
 85 
 85 
 
 1443 
 1619 
 1793 
 
 85 
 85 
 85 
 
 1460 
 1637 
 1810 
 
 85 
 85 
 85 
 
 1478 
 1654 
 
 1827 
 
 85 1496 
 85-1672 
 
 85 1844 
 
 85 
 85 
 85 
 
 1514 
 1689 
 1862 
 
 86-1531 
 85 1707 
 86-1879 
 
 199 
 200 
 201 
 
 85 
 85 
 85 
 
 1896 
 2065 
 2231 
 
 85 
 85 
 85 
 
 1913 
 2081 
 2247 
 
 85 
 85 
 85 
 
 1930 ' 
 
 2098 
 
 2264 
 
 86 
 85 
 85 
 
 1947 
 2115 
 2280 
 
 85 
 85 
 85 
 
 1964 
 2131 
 2290 
 
 84 
 85 
 85 
 
 1981 
 2148 
 2313 
 
 85 
 85 
 85 
 
 1998 
 2165 
 2329 
 
 85 2014 
 85-2181 
 85-2346 
 
 85 
 85 
 85 
 
 2031 
 2198 
 2362 
 
 86-2043 
 85-2214 
 85-2378 
 
 202 
 203 
 204 
 
 85 
 85 
 85 
 
 2394 
 
 2556* 
 
 2714 
 
 85 
 85 
 85 
 
 2411 
 
 2572 
 2729 
 
 85 
 
 85 
 85 
 
 2427 
 2588 
 2745 
 
 85 
 85 
 86 
 
 2443 
 2604 
 2760 
 
 86 
 85 
 85 
 
 2459 
 
 2620 
 2776 
 
 85 
 
 85 
 85 
 
 2476 
 2635 
 2791 
 
 85 
 85 
 86 
 
 2492 
 2651 
 2807 
 
 85 2507 
 85-2667 
 85-2822 
 
 85 
 
 85 
 86 
 
 2524 
 2682 
 2838 
 
 85-2540 
 85-2698 
 85-2863 
 
 205 
 206 
 207 
 
 85 
 85 
 85 
 
 2868 
 3020 
 3170 
 
 85 
 86 
 85 
 
 2884 
 3035 
 3184 
 
 86 
 85 
 85 
 
 2899 
 3061 
 3199 
 
 86 
 85 
 85 
 
 2915 
 3066 
 3214 
 
 85 
 85 
 85 
 
 293C 
 3081 
 3229 
 
 86 
 85 
 
 2945 
 3095 
 3244 
 
 85 
 85 
 86 
 
 2960 
 3110 
 3258 
 
 85 2975 
 85-3125 
 85-3273 
 
 85 
 
 85 
 85 
 
 2990 
 3140 
 
 3287 
 
 85-3005 
 85 3165 
 85-330a 
 
 208 
 209 
 210 
 
 85 
 85 
 85 
 
 3316 
 3460 
 3601 
 
 85 
 85 
 85 
 
 3331 
 3474 
 3615 
 
 85 
 85 
 85 
 
 3345 
 3488 
 3629 
 
 85 
 85 
 86 
 
 3360 
 3503 
 3643 
 
 85 
 85 
 
 85 
 
 3373 
 3517 
 3657 
 
 85 
 85 
 85 
 
 3388 
 3531 
 3671 
 
 86 
 85 
 
 85 
 
 3403 
 3546 
 3685 
 
 86 3417 
 85-3559 
 85-3698 
 
 85 
 85 
 85 
 
 3431 
 3573 
 3712 
 
 85-3446 
 85-3581 
 85 3726 
 
 211 
 212 
 213 
 
 85 
 85 
 85 
 
 3740 
 3876 
 4010 
 
 85 
 
 85 
 88 
 
 3754 
 3890 
 4023 
 
 85 
 85 
 85 
 
 3767 
 3903 
 4036 
 
 85 
 85 
 85 
 
 3781 
 3917 
 •4049 
 
 85 
 
 85 
 85 
 
 3795 
 3930 
 4063 
 
 85 
 
 85 
 85 
 
 3808 
 3943 
 4076 
 
 85 
 85 
 85 
 
 3822 
 3957 
 4089 
 
 85 3836 
 85 3970 
 85-4102 
 
 85 
 
 85 
 86 
 
 3849 
 3983 
 4115 
 
 85-3863 
 85-3996 
 85 4128 
 
 21^ 
 215 
 216 
 
 85 
 85 
 85 
 
 4141 
 
 4271 
 4398 
 
 85 
 85 
 85 
 
 4154 
 4284 
 4411 
 
 85 
 86 
 85 
 
 4167 
 4297 
 4423 
 
 85 
 86 
 85 
 
 4180 
 4309 
 4436 
 
 85 
 85 
 85 
 
 4193 
 4322 
 4448 
 
 85 
 85 
 85 
 
 4206 
 4335 
 4461 
 
 85 
 85 
 86 
 
 4219 
 4348 
 4473 
 
 85-4232 
 85-4360 
 85-4485 
 
 86 
 85 
 85 
 
 4245 
 4373 
 
 4498 
 
 85-4258 
 85-4385 
 86-4510 
 
 217 
 218 
 219 
 
 85 
 85 
 85 
 
 4523 
 4645 
 4766 
 
 85 
 85 
 
 85 
 
 4535 
 
 4658 
 4778 
 
 85 
 85 
 85 
 
 4547 
 4670 
 4790 
 
 85 
 85 
 85 
 
 4560 
 4682 
 4802 
 
 85 
 85 
 86 
 
 4572 
 4694 
 4814 
 
 85 
 85 
 85 
 
 4584 
 4706 
 4825 
 
 85 
 85 
 85 
 
 4597 
 4718 
 4837 
 
 85-4609 
 85-4730 
 85-4849 
 
 85 
 85 
 86 
 
 4621 
 4742 
 4861 
 
 86-4633 
 86-4754 
 86-4873 
 
 220 
 221 
 222 
 
 85 
 85 
 85 
 
 4885 
 5001 
 5116 
 
 85 
 85 
 85 
 
 4896 
 5013 
 5128 
 
 86 
 85 
 85 
 
 4908 
 5024 
 5139 
 
 85 
 86 
 86 
 
 4920 
 6036 
 6150 
 
 85 
 85 
 85 
 
 4932 
 5047 
 5162 
 
 86 
 85 
 85 
 
 4943 
 5059 
 5173 
 
 85 
 85 
 85 
 
 4965 
 6070 
 6184 
 
 85-4967 
 85-5082 
 85 5195 
 
 86 
 85 
 86 
 
 4978 
 5093 
 5207 
 
 85-4990 
 85-6105 
 85-5218 
 
 223 
 224 
 225 
 
 85 
 85 
 85 
 
 5229 
 5340 
 5449 
 
 85 
 85 
 85 
 
 5240 
 5351 
 5460 
 
 85 
 85 
 85 
 
 5251 
 5362 
 5470 
 
 85 
 85 
 85 
 
 5262 
 5373 
 6481 
 
 85 
 85 
 85 
 
 5273 
 5384 
 5492 
 
 85 
 85 
 86 
 
 5285 
 5394 
 5502 
 
 85 
 85 
 85 
 
 5296 
 5405 
 5513 
 
 85-5307 
 85-5416 
 86-5624 
 
 86 
 85 
 85 
 
 5318 
 5427 
 5534 
 
 85-5329 
 86-5438 
 86-6545 
 
 226 
 227 
 228 
 
 85 
 85 
 85 
 
 5556 
 5661 
 5765 
 
 85 
 85 
 85 
 
 5566 
 5672 
 6775 
 
 85 
 85 
 85 
 
 5577 
 5682 
 5785 
 
 85 
 85 
 85 
 
 5688 
 6693 
 5796 
 
 86 
 85 
 85 
 
 6598 
 5703 
 5806 
 
 86 
 85 
 85 
 
 5609 
 5713 
 5816 
 
 85 
 86 
 86 
 
 5619 
 5724 
 5826 
 
 85-5630 
 85-5734 
 85-5836 
 
 85 
 85 
 85 
 
 5640 
 
 5744 
 5846 
 
 85-5651 
 85-5755 
 85-5856 
 
 229 
 230 
 
 85 
 85 
 
 5866 
 5966 
 
 85 
 85 
 
 5876 
 5976 
 
 85 
 85 
 
 5886 
 5986 
 
 85 
 85 
 
 5896 
 5996 
 
 85 
 85 
 
 5906 
 6006 
 
 85 
 85 
 
 5916 
 6015 
 
 85 
 85 
 
 6926 
 6025 
 
 85 5936 
 85-6035 
 
 85 
 85- 
 
 5946 
 6045 
 
 85-5956 
 85-6055 
 
XXI. — VARIETIES OF CANNON. 
 
 CHAPTER XXI. 
 
 VARIETIES OF CANNON. 
 
 CLASSIFICATION. 
 
 The numerous ways in which cannon may be classified 
 have been simpHfied by the almost universal adoption of 
 those which are breech-loading rifies^ built up of steel. 
 
 For convenience of treatment we may consider them ac- 
 cording to t\\Q\v proportions, construction and service, 
 
 1. Proportions. 
 
 The facility with which breech-loading cannon of all 
 lengths may be loaded has practically abolished the distinc- 
 tion between mortars and howitzers, although both terms are 
 still used for pieces which do not differ materially in their 
 proportions. 
 
 It has become customary to distinguish guns (Chapter I) 
 from howitzers by calling the first named rifles, although all 
 new howitzers are also rifled. 
 
 2. Construction. 
 
 As to construction, cannon are divided into muzzle-loaders 
 and breech-loaders; some of the former class being still re- 
 tained in service pending the preparation of those of the better 
 type and also for subordinate purposes. 
 
 Breech-loaders may be divided into those having but one 
 barrel, or single fire pieces, which are loaded by hand, and 
 into machine guns, in which the loading is automatically per- 
 formed by machinery. The former may be either the com- 
 paratively slow fire cannon, in which the cartridge and 
 projectile are loaded separately, or the rapid fire in which 
 
XXI. VARIETIES OF CANNON. 
 
 the ammunition makes but one package, as in small arms, 
 and the recoil of which does not derange the aim. 
 
 Machine guns generally consist of a number of barrels so 
 disposed, that while one is firing, the remainder may be 
 loaded and prepared for loading. Like the rapid fire cannon 
 these require metallic ammunition, and unlike them their size 
 is imited by the weight of the required number of cartridges 
 which can be conveniently kept in motion by the machinery ; 
 the latter is generally operated by hand. 
 
 3. Service. 
 
 According to their employment, cannon are divided into 
 those for the mountain, field, siege and sea coast services. 
 
 The principal distinction here refers to the difficulties of 
 transportation, for the rule is general that the most power- 
 ful cannon that can be efficiently transported should always 
 be employed. 
 
 For field artillery especially, the principle of independence 
 of function requires a very exact adaptation of the weight of 
 the arm to the service required of it. Thus, we have, 1st, 
 Horse Artillery, which, the cannoneers being mounted on 
 horses, may accompany the Cavalry ; 2nd, Light Field Ar- 
 tillery, which manoeuvres with Infantry ; and 3rd, Heaiy Field 
 Artillery, which forms batteries of position at important tacti- 
 cal points, and is intended to engage at long ranges. 
 
 This affords the following table : 
 
 CLASSIFICATION OF ARTILLERY ACCORDING TO 
 
 1 P.-r,^^rt;r.nc S Guiis, for direct fire. 
 
 1. rioporuons ^ Howitzers, or Mortars for curved fire. 
 
 r Muz de loading ^Smoothbore. 
 
 I (obselete, retained) \ Rifled. 
 
 2. Construction \ ' i c- „, <-_ ( slow. 
 
 ' * ( ■ ( slow, 
 
 j Breech loading rifles ) ^'"^le fire | ^.^p- j^ 
 ( Machine guns, 
 
XXI. — VARIETIES OF CANNON. 
 
 3. Service. 
 
 Mountain. 
 
 i Horse Artillery, very light. 
 Field < Light Field Artillery, medium. 
 
 f Heavy Field Artillery. 
 Siege. 
 Sea Coast. 
 
 SYSTEM OF ARTILLERY. 
 
 This term refers to the character and arrangement of the 
 materiel* as adopted by a nation at any particular epoch. 
 
 The principal requisites of a system of artillery are sim- 
 plicity^ mobility and power. To these the enormous arma- 
 ments of the present day may add economy. 
 
 The improvements of the last four hundred years have had 
 these qualities in view, the compromises between simplicity 
 and mechanical efficiency, noted Chapter XVI, causing 
 sometimes one, and sometimes another of these qualities to 
 pieponderate. 
 
 As in other nations the system of artillery in the United 
 States service is still in an experimental state. 
 
 For lack of funds, withheld largely because of uncertainty 
 regarding the direction of improvement, many obsolete 
 weapons have been retained by us either unchanged, or 
 converted so as to increase their power at a moderate expense. 
 
 The following description is therefore partly historical, and 
 contains incidental reference to methods adopted in other 
 countries whose political situation has made their immediate 
 armament urgent. It is confined to slow fire guns, since 
 other types of breech-loaders depend for their efficiency 
 almost wholly upon the control of their recoil and upon the 
 use of metaUic ammunition; subjects not yet discussed. See 
 Chapter XXIX. 
 
 * See Webster, 
 
XXr. — VARIETIES OF CANNON. 
 
 CONSTRUCTION. 
 
 I. MUZZLE LOADING CANNON. 
 
 United States. 
 
 The field guns used during the Civil War were of two 
 kinds. 
 
 1. The 3 ijich wrought iron (10 pdr^ rifle. 
 
 This was made by wrapping boiler plate around a wrought 
 iron bar to form a rough cyUnder, which was welded 
 together under the rolls and finished in the usual manner. 
 
 It made a very strong, light gun well adapted to the 
 Horse Artillery. 
 
 2. The 12 pdr. Napoleon Gun^ S7nooth bore. 
 
 This was of bronze, cast solid. Its value depended upon 
 the topography of the seat of war. 
 
 The broken surface of the Appalachian system and the 
 heavy woods with which much of the country was covered 
 restricted the fighting to ranges which, compared to those 
 obtainable on the broad plains of Europe, are very moderate. 
 For such ranges its heavy shell and well filled shrapnel were 
 more efiective than those of the rifle, and the initial velocity 
 was so great that for ranges of about 1000 yards the trajectory 
 of the smooth bore was flatter than that of the rifle. 
 
 The siege gims, in which mobility was less important, were 
 of cast iron. Owing to the length of the bore and its rela- 
 tively small diameter these guns were cast solid. The pro- 
 jectile weighed about 30 pounds. 
 
 One of these pieces, the Parrott, was strengthened by a 
 wrought iron cylinder shrunk over the breech and reinforce. 
 
 In order to prepare so massive a forging a hot iron bar was 
 coiled helically around a mandrel, brought to a welding heat 
 and forged by axial blows of the hammer. To prevent 
 
XXr. — VARIETIES OF CANNON. 
 
 distortion during welding, the coil was held in a hollow cyl- 
 inder. Several coils would be similarly welded end to end. 
 The direction of the fibers gave great tangential tenacity, but 
 for reasons given in Chapters XV, page 60, and XIX, page 
 12, the construction was faulty. 
 
 Sea coast guns were generally of cast iron, cast hollow on 
 the Rodman principle. To some the Parrott construction 
 was applied. 
 
 Since 1875 many Rodman guns have been converted on 
 the Palliser (English) plan by reaming out the bores to receive 
 a thick, wrought-iron tube, which was then rifled. Chapter 
 XIX. 
 
 These tubes, first made by coiling as above described, were 
 ultimately replaced by those of solid steel, the intrinsic 
 strength of which was almost sufficient. 
 
 The wrought-iron tube was at fiist inserted from the muzzle ; 
 but, as it was liable to be carried out with the projectile, a 
 stronger but much more costly breech insertion was employed. 
 
 With steel, which presented no false welds for the action 
 of the powder gases, the muzzle insertion was resumed. 
 
 In this way many 10 inch smooth-bore Rodman guns were 
 altered to 8 inch rifles. The 15 inch Rodman guns are re- 
 tained unchanged for subordinate purposes. 
 
 Foreign Services. 
 
 Abroad a similar course was followed. In France^ the old 
 cast-iron guns were hooped with puddled steel, originally to 
 retain the fragments on explosion. The bores were lined 
 with a short steel tube. This method is now followed for 
 subordinate pieces of large caliber. 
 
 Engla7id tried the Palliser plan of conversion for her old 
 guns. For new guns wrought iron was at first exclusively 
 employed ; then wrought iron coils on a steel tube were used, 
 
XXI. — VARIETIES OF CANNON. 
 
 and finally with breech loaders steel throughout. The fear 
 of the brittleness of steel, the consequent preference for the 
 weaker though more ductile wrought iron, and the indiffer- 
 ence to the molecular treatment of steel as practiced by their 
 more exact neighbors, the French, have cost the English 
 Government much loss in time and money. 
 
 To Krupp, in Germany, belongs the credit of first using 
 steel in large masses. The weight of his ingots has increased 
 since 1851 from two tons to seventy. 
 
 The construction of his cannon now requires relatively 
 large units of construction. The tendency elsewhere is to 
 reduce the weight of the maximum unit so as to avoid the 
 large outlay for plant required only for its manufacture and 
 handling. For it must be remembered that although cannon 
 comprise the heaviest masses now made, yet their commercial 
 importance is relatively small. Chapter XIV, page 2. 
 
 II. BREECH LOADING CANNON. 
 
 These may be classified according to the means by which 
 the breech is closed ; but, as this depends largely upon the 
 form of gas check employed, this will be first discussed. 
 
 1. Gas Checks. 
 
 Many early efforts were made to prevent the escape of gas 
 by some rigid fastening after the manner of a plug ; but, owing 
 to the erosion through the slightest crevice caused by dust, 
 rust or fouling, the efficiency of these devices was short-lived. 
 
 The self-sealing gas check alone made breech loading prac- 
 ticable. Gas checks may be classified according as they are 
 attached to or detached from the breech block. 
 
 Detached Gas Checks. 
 The ordinary metallic cartridge case is the best example of 
 this class. The flexibility of its walls and its renewal at every 
 fire peculiarly adapt it for this purpose. 
 
XXI, — VARIETIES OF CANNON^ 
 
 But, since it would be impracticable to use cartridges of 
 the size required for heavy cannon, the cartridge case may be 
 replaced by a short permanent ring as shown in figure 1. 
 
 This represents one form of an American invention, the 
 Broadwell ring, r, with its obturator plate, /. 
 
 The gaseous pressure expands the thin edge laterally 
 against the seat in the tube and also presses the ring bodily 
 backward against the plate. The annular grooves, g, in the 
 base of the ring serve as air packing ; they also increase the 
 intensity of the pressure on a vital surface, and, with the hol- 
 low, h, collect any fouUng, which might otherwise occur on 
 this surface. 
 
 The surface^ s, is spherical so as to adjust itself easily to he 
 spherical seat of the ring around the mouth of the chamber, 
 past which the obturator plate is caused to slide by the motion 
 of the breech block to which it is attached. 
 
 This form of gas check is difficult to maintain, as it is diffi- 
 cult to prevent entirely the escape of gas between the ring 
 and the plate. 
 
 Attached Gas Checks, 
 
 These necessarily require some motion of the block in the 
 direction of the axis of the piece and across the joint to be 
 sealed. 
 
 Figure 2 represents the Freyre gas check of Spanish origin. 
 It consists of a steel ring, r, of triangular cross-section sur- 
 rounding a conical wedge, w. This last is formed with a 
 spindle, 5, passing axially through the breech block, B, The 
 stem is surrounded by a spiral spring against which it acts by 
 a shoulder. The thickness of the wedge is slightly less than 
 that of the ring. 
 
 The gases press the wedge backward and thus expand the 
 ring ; when they cease to act the spring moves the wedge 
 forward and thus prevents the ring from sticking in its seat. 
 
 Figure 3 represents the De Bange (French) gas check, de- 
 
XXI. — VARIETIES OF CANNON 
 
 rived from that used in the Chassepot b 1, rifle, a small arm 
 firing a non-metallic cartridge The steel ring of figure 2 is 
 replaced by a plastic ring, r, composed of a mixture of asbes- 
 tos and tallow enclosed in canvass and having the joints 
 through which the composition might extrude protected by- 
 metallic rings. When the mushroom head, h, is compressed 
 axially the ring, r, expands laterally, giving a pressure per 
 
 unit of area against the surface of its seat nearly equal to ^^-i- ; 
 
 in which R is the common external radius of the head and 
 ring, and / is the length of its bearing. 
 
 A nut on the rear end of the spindle regulates the initial 
 compression required for efficiency. A spring beneath the 
 nut relieves it from shock as the head is thrown forward after 
 firing by the elasticity of the tallow. 
 
 ^ Comparison. 
 
 The Broadwell ring has to seal four surfaces not protected 
 from dirt instead of but two, and the joint, most difficult to 
 seal, is that which is most exposed to dirt. 
 
 Of the attached gas checks, the Freyre, being inorganic, is 
 less subject to extreme variations of temperature ; it also takes 
 up less room in the thickest part of the gun. It is open to 
 objection that a sHght nick on the edge of the ring might 
 render the entire apparatus worthless. 
 
 To the last consideration is due the almost universal 
 employment of the De Bange gas check, since this has been 
 found almost indestructible by the accidents of service and to 
 resume its shape when deformed in firing. 
 
 2. Fermeture. 
 
 The fermeture (French, fermer to close) is the device by 
 which the breech is opened and closed. Its principal requi- 
 sites are safety and convenience. The form of fermeture 
 depends largely upon the kind of gas check employed. 
 
XXI. — VARIETIES OF CANNON. 
 
 Two principal varieties exist, the Krupp and the French 
 systems. 
 
 1. The Krupp or wedge system, figure 4. 
 
 Description. 
 
 The breech block, B^ moves transversely through a hori- 
 zontal slot in rear of the chamber. The front face of the 
 block is flat, and the rear surface a convex semi-cylinder whose 
 axis is slightly inclined to the plane of the face. This avoids 
 the sharp reentrant angles noted. Chapter XV, page 21. It 
 has been found expedient also to round the angles in front 
 of the slot. 
 
 The upper and lower surfaces of the slot contain guides, ^, 
 which are parallel to the elements of the cylindrical surface 
 and enter corresponding grooves in the block. The block 
 thus receives a component longitudinal motion in the direc- 
 tion of the axis of the bore which prevents friction between 
 the ring and the obturator plate, and also assists somewhat in 
 pressing the cartridge home. 
 
 A hole, h, through the block permits the gun to be loaded 
 when the block is withdrawn to the proper position. It is 
 prevented from passing this point by a stop bolt, screwed 
 through the body of the gun and having a blank end pro- 
 jecting into a groove on the upper surface of the block. 
 
 Locking. 
 
 To secure the fermeture a revolving latch^ /, is employed. 
 For small cannon using metallic ammunition this may be a 
 simple turn-button operated by an exterior handle, (9, and 
 entering a recess in one of the faces of the slot. 
 
 With a less perfect gas check, means must be provided for 
 pressing the obturator plate, /, against the ring, r, so that 
 for larger guns the latch consists of a screw. In order to 
 faciUtate the operation of the fermeture, the fillets on one 
 
10 XXI. — VARIETIES OF CANNON. 
 
 side of the newel of the screw are removed so that a half- 
 turn of the screw may engage or disengage the remaining 
 fillets. 
 
 Translation. 
 
 For field pieces the block is withdrawn directly by hand, 
 but heavy pieces are provided with a long screw, S^ con- 
 tained in a groove in the upper part of the block, and turn- 
 ing in two cylindrical collars, one at each end. The rotation 
 of this screw in a half nut which is attached to the gun, 
 causes relative motion to occur between the block and the 
 gun. 
 
 Since for this motion speed is required, the screw is cut 
 with a considerable pitch. As this causes a loss of the power 
 required to start the block from its seat and to close it firmly, 
 there is supplied an auxiliary locking screw, d^ which passes 
 through the latch, /. By a peculiar arrangement illustrated 
 in a model in the Ordnance Museum, in closing the breech 
 this screw first turns the latch and then by its slow pitch 
 supplies the power required, and conversely in opening. 
 
 Both screws are operated by a T wrench, G, which is 
 detached. 
 
 2. The interrupted screw fermeture is commonly 
 known as the French system, although its origin is probably 
 American. 
 
 Description. 
 
 A cylindrical block fills the breech in the prolongation of 
 the bore and in rear of the tube. 
 
 The block is held by a screw thread which engages with 
 the base ring ; this in turn is screwed to the jacket by a 
 ratchet screw thread, Chapter XV, figure 47, and figures 2, 3 
 and 10, Chapter XXI. 
 
 To facilitate its operation, alternate sections, ordinarily of 
 
XXI. — VARIETIES OF CANNON. 11 
 
 60", are removed from the adjacent surfaces of the block and 
 base ring, so that after sUding the block nearly into place it 
 may be easily locked. 
 
 Some device is required to support the block when with- 
 drawn. For small pieces this is supplied by the carrier ring. 
 
 This ring is provided with two lugs forming, with corre- 
 sponding cavities in the jacket and a vertical pin, a hinge on 
 which it swings to the left and rear in opening. 
 
 A stop^ a b^ Chapter XV, figure 47, screwed to the carrier 
 ring, enters a groove formed in one of the smooth sectors of 
 the block. This groove terminates in front at a short dis- 
 tance from the face of the block, and in rear makes a return 
 of 60° parallel to the screw thread. 
 
 The carrier ring also contains a shallow groove, c d, for 
 the head of the lever, and the latch, /, the action of which is 
 important. See figure 10. 
 
 The latch is pressed by a spiral spring radially inward 
 against the block, so that its inner extremity describes on the 
 smooth sector on which it rests a path parallel to the groove 
 in which travels the stop. We will designate the rearmost 
 end of this path by r, and the front end by /. At r and / 
 are formed cavities into which the inner end of the latch may 
 enter sufficiently to sink its outer end to the level of the outer 
 edge of the carrier ring. Each cavity is connected with the 
 intervening path by an inclined plane ; the cavity at / is prac- 
 tically a cylinder. 
 
 On the rear face of the base ring is a conical dowel, the 
 point of which, when the carrier ring is closed, enters a corre- 
 sponding cavity in the adjacent face of the carrier ring. 
 After passing this cavity, the point of the dowel enters a 
 conical hole in the front surface of the latch, and thus serves 
 to press it radially outward, so that when the carrier ring has 
 been completely closed, the inner end of the latch will have 
 been raised so far out of the cavity / that the block may slide 
 
12 XXI. VARIETIES OF CANNON. 
 
 freely through the carrier ring. As it slides it forces the 
 outer end of the latch into its seat in the jacket. 
 
 There are three concentric pieces, the block, the carrier 
 ring and the jacket. The latch unites these alternately in 
 pairs. 
 
 Operation. 
 
 Suppose the block to be closed and locked. Raise the 
 lever and turn the block to the left until the stop prevents 
 further rotation. 
 
 In so doing, the inner end of the latch rides up the inclined 
 plane leading from r, and the outer end enters the jacket as 
 shown in the end view of figure 47, Chapter XV. This pre- 
 vents the obstruction to the withdrawal of the block caused 
 by the simultaneous swinging of the ring which would other- 
 wise occur. 
 
 The block can now ordinarily be freely withdrawn ; but if, 
 from the expansion of the gas check, it should not move 
 freely, an eccentric projection on the head of the lever acts 
 as a cam''^ and starts the block from its seat. 
 
 It is well to observe that the rotation of the block being 
 independent of that of the gas check, the binding of the 
 latter does not 'resist the initial rotation above described. 
 
 On withdrawing the block to the extent allowed by the 
 stop grove, the inner end of the latch drops into the cavity 
 f ; the carrier ring is then free to swing in continuation of 
 the motion of withdrawal. 
 
 After loading, these motions are reversed. In closing the 
 breech the latch locks the block and carrier ring together, 
 since any slippipg of the block through the ring would cause 
 the edge of the gas check to strike against the base ring. 
 This would be particulariy objectionable in the Freyre check. 
 
 When the carrier ring comes against the rear face of the 
 
 * See Webster. 
 
XXI. — VARIETIES OF CANNON. IB 
 
 base ring the conical pin described lifts the pin from the hole, 
 /, and permits the block to slide forward until ready to en- 
 gage with the threads in the base ring. 
 
 After closing the breech the eccentric head of the lever 
 enters the groove, c d ; this prevents the unscrewing of the 
 block by the tangential component of the pressure on the 
 screw threads. This pressure is so great that it has been 
 found necessary to protect the bearing surface of the groove, 
 ^^, by a plate of hardened steel.* 
 
 Variations, 
 
 For large pieces a more stable support than that offered by 
 the thin carrier ring is required during the withdrawal of the 
 block. 
 
 This is furnished by a tray which supports it for its whole 
 length. 
 
 This tray is supported by a hinge bracket, called the coit- 
 sole, which, being fastened to the face of the breech, allows 
 the block and tray to be swung aside. 
 
 For such pieces the simple lever used in the field piece 
 affords insufficient power. 
 
 It is accordingly replaced by more or less complicated 
 machinery which, for the largest calibers, may be operated by 
 steam, hydraulic or electrical power. 
 
 One of the most ingenious devices is that of the French 
 engineer, Canet, who has an apparatus in which the contin- 
 uous rotation of a crank performs all the varied operations 
 of unlocking, withdrawing and swinging the block. 
 
 Vent. 
 The system adapts itself to the use of an axial vent which 
 facilitates ignition. To permit renewal, the vent piece is 
 
 * The latest model (1890) exhibits slight changes in the details of the 
 construction shown in figure 47, Chapter XV. 
 
14 XXI. — VARIETIES OF CANNON. 
 
 made removable ; and to avoid erosion, its front portion is 
 of copper. 
 
 To avoid the danger of a premature discharge, the vent is 
 preferably protected by a sliding shutter, a projection from 
 which travels in a concentric groove in the rear face of the 
 piece which is so formed that the primer cannot be inserted 
 until the block is securely locked in place. 
 
 The complication attending the operation of an axial vent, 
 the likelihood of accident to the gunners from the projection 
 of the fragments of the ordinary primer and the necessary 
 delicacy of the safety shutter when made on the small scale 
 required for the field gun have so far caused these guns to be 
 provided with a radial vent piece of copper leading to the top 
 of the charge at about half its length. 
 
 Base Ring. 
 
 The seat of the block is of somewhat greater diameter than 
 that required for loading in order to give a large bearing sur- 
 face to the threads of the screw. 
 
 Under Barlow's law, this surface is less dilated by the gas 
 pressure than one nearer to the axis ; and, since from a simi- 
 lar reason the greatest stress is borne by the foremost fillets, 
 these do not approach as closely to the end of the tube as 
 the construction might otherwise permit. 
 
 All exposed screw threads have their angles rounded, to 
 avoid fracture and to resist deformation by the projectile in 
 loading. For heavy pieces a loading tray is slipped into the 
 opening so as to cover the thread in the base screw while the 
 projectile is being pressed home. 
 
 The operation of the gun is very much facilitated by de- 
 vices which avoid the translation of the breech block. One 
 of these consists in giving the breech block a general conical 
 shape so that it will swing directly into the position for 
 locking. 
 
XXI. — VARIETIES OF CANNON. 16 
 
 The same end is accomplished in the Gerdon fermeture, 
 figure 13, now on trial in the United States. After revolving 
 the block through 90° so as to clear the two threaded sectors, 
 it is swung to one side through a slot cut in the jacket. A 
 radial slide on the rear face of the block acts both as a latch 
 and as a shutter to the axial vent. 
 
 The parts are remarkably few and simple. 
 
 Comparison of the Two Systems. 
 
 1. Except where metallic ammunition is employed the 
 French system permits the use of the best gas check. 
 
 2. It diminishes the weight of the gun for a given value 
 of u and d. Chapter XII. 
 
 3. It serves to press the cartridge into place instead of 
 guillotining it as in the Krupp. 
 
 4. The fermeture, when open, is less exposed to injury 
 from a front fire. 
 
 5. It may be worked by power. 
 
 The Krupp system in its conception is of almost rustic 
 simplicity. 
 
 This advantage is counterbalanced by the inferior gas 
 check which is required when non-metallic ammunition is 
 employed ; also by the thickness and mass of the forging 
 containing the slot, the presence of which must cause inju- 
 rious internal strain in oil hardening. 
 
 The jar in opening it suddenly may deform and even bend 
 the stop bolt. The parts are less securely protected in travell- 
 ing. It has also the comparative disadvantages named in the 
 discussion of the French system. The danger of premature 
 discharge, though not so great as in the French system, is still 
 said to exist. 
 
16 XXI. — VARIETIES OF CANNON. 
 
 U. S. SYSTEM OF ARTILLERY. 
 
 MOUNTAIN SERVICE. 
 
 The Hotchkiss 1.65-inch Rifle. 
 
 This gun weight but a Httle over 100 pounds and its car- 
 riage about twice as much, so that either makes but a fair load 
 for a mule. Metallic ammunition is employed > The gun is 
 a single piece of steel provided with the simplest form of 
 Krupp fermeture as shown in figure 5 The operation of the 
 fermeture can be readily seen from the figure and from pre- 
 vious discussions. 
 
 Its special feature is the extractor, x. This is a prismatic 
 bolt, a hook on the front end of which engages with the 
 flange of the cartridge (Chapter XVI, figures 8 and 9) as this 
 is loaded 
 
 The extractor slides in a longitudinal groove, g, on the 
 upper surface of the slot On its lower face is a tenon which 
 enters a transverse groove, g' , in the upper face of the block. 
 
 The groove, g' ^ near the handle is straight and slightly 
 inclined to the rear face, so as to give power in wedging the 
 cartridge case from its seat. The screw thread on the latch 
 also assists. At the other end it is so curved that when, in 
 opening the breech, the loading hole comes opposite to the 
 chamber the extractor will be suddenly drawn backwards, 
 throwing the free cartridge case clear of the gun. The first 
 of these operations is called the extraction, and the second 
 the ejection 
 
 For simplicity this piece is fired with the ordinary friction 
 primer. The blast from this raises the central portion of a 
 thin, cup-shaped gas check within the cartridge, and the 
 flame passes through the three holes shown in figure 8, Chap- 
 ter XVI. As soon as the charge is ignited the back pres- 
 sure of the gases closes the vent by reversing the action of 
 the gas check, 
 
XXI. — VARIETIES OF CANNON. 17 
 
 Hotchkiss 3-Inch Mountain Rifle. 
 
 In order to permit the use of shrapnel a heavier mountain 
 gun of 3-inch caUber has been recently produced. Figure 11. 
 
 Foreign Variations, 
 In order to increase both the power and portability of 
 mountain cannon they are frequently made abroad in sections 
 which are screwed together before firing. " Screw-guns " of 
 8-inch caliber have been successfully fired . 
 
 FIELD SERVICE. 
 
 The 3.2 B. L. Rifle shown in Chapter XV, figure 47, is 
 the only new field piece now issued. (1891.) It is eventu- 
 ally intended for use as a Horse Artillery gun, and to be 
 replaced for Field Service proper by a similar gun of 3.6 
 in caliber, firing a 20-pound shell. A 3.6 B. L. Mortar, 
 figure 12, firing the same projectile, is also contemplated for 
 delivering vertical fire against troops sheltered by temporary 
 defences. It has a range of nearly two miles. 
 
 Foreign Variations. 
 It is proposed in France to have but one caliber, about 
 3 in. for all mountain and field service, viz., short, light, 
 long and heavy pieces. 
 
 SIEGE SERVICE. 
 
 Siege cannon are intended for attacking and defending 
 inland fortifications and the land fronts of sea- coast fortifi- 
 cations. 
 
 The term is usually applied to pieces which, although too 
 heavy for field operations, are yet light enough to be trans- 
 ported over common roads upon the carriages from which 
 they are fired. 
 
 This limits the weight of the gun and carriage together to 
 that which may safely be transported across a pontoon bridge. 
 
18 XXI. VARIETIES OF CANNON. 
 
 Siege Gun. 
 
 The 5-inch siege rifle, figure 6, resembles in its construction 
 the field gun described. 
 
 Siege Howitzer. 
 
 Principles of Design, 
 
 Defences of masonry have been largely replaced by those 
 which are armored, or, particularly for the besieging party, 
 of earth. 
 
 While armor requires for its penetration the concentration 
 of kinetic energy found in a projectile of relatively small 
 diameter fired from a gun, the demolition of earth works 
 demands rather the transfer of energy in the potential form. 
 Such defences should therefore be attacked by cannon of 
 the largest caliber consistent with portability. 
 
 If the maximum weight of the piece is fixed by the con- 
 siderations previously named, then by the definition of 
 Chapter I, a howitzer results. 
 
 The proportions of this piece are also demanded by the 
 advantages pertaining to vertical fire againt the large and 
 well defined area occupied by the besieged, against com- 
 munications of the besieger which are screened from view, 
 and against the roofs of turrets. The shorter the piece is 
 in rear of the trunnions the more easily may high angles 
 of fire from a given carriage provided with the ordinary 
 elevating screw be attained.* The avoidance of preponder- 
 ance and the requisite strength of the chase demand that 
 the length in front of the trunnions be also reduced. 
 
 Such considerations have fixed the value of u at about 
 12 times the caliber, which is 7 inches. 
 
 It is intended to throw a projectile weighing about 100 
 pounds to a distance of about 3 miles. 
 
 *A new German howitzer has the trunnions placed ahuost at the breech. 
 In this carriage the elevating screw is under the chase, as the arrange- 
 ment adopted gives a considerable muzzle preponderance. See also Car- 
 riage for 7-inch Howitzer, Chapter XXIII, figure 6. 
 
XXK — VARIETIES OF CANNON. 19 
 
 Owing to the strength of the construction a larger cahber 
 might have been employed for the given weight, but in such 
 a case the energy. of recoil, (Equation 7, Chapter XIX,) 
 would have been excessive. 
 
 Since with the value of /„ usual in built up steel guns, the 
 short length of bore reduces the value of e^ it is proposed to 
 utilize the value of E permitted by the strength of the car- 
 riage by increasing the value of ;//. 
 
 This will permit the use of very long torpedo shells 
 (Chapter XVI, page 20). The limit of E for the wheeled 
 carriage having thus been reached, for high angles of fire 
 which increase the stress upon the axle, E may be further 
 increased by dismounting the wheels and laying the stock of 
 the carriage on a platform It is now (1891) proposed to use 
 in the field service a 6 inch B. L mortar throwing a 70 
 pound shell, to be mounted as above described 
 
 It is probable that in the future the obstruction to effi- 
 ciency which is due to the requirement that the piece be 
 transported on the carriage from which it is to be fired, will 
 disappear before the adoption of special carriages designed 
 with the view of efficiently satisfying their independent 
 requirements. 
 
 Charges. 
 
 In order to vary the angle of fall* to suit the range and 
 the kind of fire employed, the howitzer is fired with varying 
 charges of powder as well as with varying angles of fire. In 
 this it differs from the gun in which the charge is usually a 
 constant and a maximum. See Chapter XXX, page 9. 
 
 7-Iiich B. L Howitzer 
 
 The construction, figure 8, resembles that of the field piece, 
 the principal difference being in the construction of the key 
 ring. This consists of two semi-circular segments of rect- 
 
 *The angle with the horizontal made by the tangent to the trajectory 
 on impact. 
 
20 XXI. — VARIETIES OF CANNON. 
 
 angular cross-section which are laid in a shallow groove in 
 the tube so as to project above its exterior and to bear 
 against the front face of the trunnion hoop. They are kept 
 in place by the lap of the sleeve. 
 
 The friction developed by shrinkage between the jacket 
 and the tube throws part of the longitudinal stress upon the 
 tube from which the key ring transfers this stress to the 
 trunnions. 
 
 A shoulder formed on the tube in rear prevents the for- 
 ward motion of the tube from the friction between it and the 
 projectile. See page 5. This feature is general, 
 
 The cavities in the ends of the trunnions are for the points 
 of the bailm which the piece is slung in mounting. 
 
 SEA COAST CANNON. 
 
 These comprise rifles of and above 8-inch caliber, and 
 12-inch rifled mortars, 
 Eifles. 
 
 Figure 7 shows the 8-inch b 1. steel gun with which most 
 of the recent experiments have been made. 
 
 The construction resembles that heretofore discussed, 
 except that the jacket is strengthened by two rows of hoops, 
 which since the original design, have been extended to the 
 muzzle. (Chapter XI, page 18, paragraph 4.) 
 
 Other S. C, Rifles. 
 
 The guns so far designed are of 8, 10, 12 and 16-inch 
 caliber. Being intended for use with the largest charges of 
 slow burning powder, they are made very long, the values of 
 u ranging from about 24 to 27 calibers. 
 
 For the largest calibers it is proposed to dispense with 
 trunnions which are to be replaced by several rows of cir- 
 cumferential ribs, by which, as in cannon of the very earliest 
 iimeSy the pieces are to be secured to their support. The 
 necessary alterations in elevation will be given by varying the 
 
XXI. — VARIETIES OF CANNON. 21 
 
 inclination of the chassis, to which by this arrangement the 
 recoil is always parallel. 
 
 Mortars. 
 
 The importance of nearly vertical impact against the 
 decks of vessels at short ranges requires the mortars to fire 
 with angles of elevation as great as 75°. 
 
 It is proposed to group them in sunken batteries of 12 or 
 16 mortars, united under the control of one officer. He will 
 occupy a detached position free from smoke, and will be pro- 
 vided with an accurate range finder, and with means of com- 
 municating to the chiefs of pieces the direction and elevation 
 required. A simultaneous volley from the battery will prob- 
 ably drive from its anchorage any vessel within range. This 
 will be an important aid to the defense, since, as the bom- 
 bardment of Alexandria in 1882 clearly showed, the accuracy 
 of fire from a vessel is much diminished when the vessel is 
 under way. 
 
 V2,-inch B. L. Mortar. {Figure 9.) 
 
 The immediate supply of these cannon demanded by our 
 present necessities (1891) and the relatively low energies 
 required to penetrate armored decks by vertical fire have so 
 far permitted the body of these pieces to be made of iron 
 cast on the Rodman principle and strengthened by two rows 
 of steel hoops as shown in figure 9. 
 
 The recent failure at a pressure of less than 20,000 pounds 
 of an unhooped 12-inch cast iron mortar would indicate the 
 future use of steel throughout the piece as soon as the steel 
 works and the gun factory shall have become able to supply 
 a sufficient numl)er of heavy steel guns. 
 
 The growing importance of vertical fire has caused the 
 employment of mortars, even upon ship board, to be seriously 
 considered. 
 
 The value of u in this piece is about 6 calibers. 
 
22 
 
 XXI. — VARIETIES OF CANNON. 
 
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XXII. — ARTILLERY CARRIAGES. 
 
 CHAPTER XXII. 
 
 ARTILLERY CARRIAGES. 
 
 PRINCIPLES OF CONSTRUCTION. 
 
 Classification. 
 
 Artillery carriages may be classified according as they are 
 intended to support the piece when fired, to transport it, and 
 to supply it with ammunition and accessories. These func- 
 tions are sometimes combined. 
 
 They may also be classified according to the service in 
 which they are employed. 
 Requisites. 
 
 1. Strength to resist permanent deformation from the shock 
 of recoil. 
 
 2. Stability in firing and on the march. 
 
 3. Mobility as regards the ease of service in battery, and 
 of transportation when required. 
 
 4. Only a moderate recoil in firing, so as to facilitate the 
 service of the piece and to avoid the exposure of the gunners 
 when sheltered by defences. A compromise between these 
 properties is often necessary. 
 
 I. CARRIAGES WHICH SUPPORT THE PIECE. 
 
 GENERAL DESCRIPTION. 
 
 These are called gun carriages. They may be either sta- 
 tionary or wheeled. 
 
 Stationary Carriages. 
 
 The simplest form exists in the iron mortar bed used for the 
 old S. B. Mortars. 
 
X3tll. — ARTILLERY CARRIAGES. 
 
 This consists of trapezoidal plates forming the cheeks^ which 
 support the trunnions of the piece at such a height as to per- 
 mit it to receive the elevation required. The cheeks are con- 
 nected by transverse diaphragms called transoms and bolts in 
 order to form a strong frame. For heavy pieces each cheek 
 may consist of two plates united to a T shaped bar as shown 
 in figure 1. The cheeks may be stiffened in the direction of 
 compressive stresses by bars included between the plates. 
 
 The bearings of the trunnions may be widened by trunnion 
 bed plates^ so as to diminish the pressure per unit of area 
 which they are called upon to support. The mortar bed is 
 made low for ease of loading and for stability. The prin- 
 ciples of construction above noted are of general application. 
 
 Sea coast gun carriages are intended to be used in firing 
 over a parapet or through an embrasure. In the first case 
 they are called barbette carriages, and in the second, casemate 
 carriages. Owing to the height of the piece above the 
 ground and the low angles of fire employed, the stability of 
 the system generally requires the support of the piece to be 
 divided into the gun carriage proper, constructed like the 
 mortar bed, and tlie chassis, which is a moveable railway 
 capable of directing the piece in its recoil and of being trav- 
 ersed in azimuth. 
 
 Non-recoil carriages are separately treated hereafter. 
 
 Wheeled Carriages. 
 
 In the mountain, field and siege services, the gun carriage 
 must also be adapted to transportation. This involves the 
 use of wheels, which complicate the problem of controlling 
 the recoil. 
 
 Parts. 
 
 Their essential parts are : — 
 
 1, The stock. This is a prolongation of the cheeks which, 
 with the wheels, forms the three points necessary for stability. 
 
XXII. — ARTILLERY CARRIAGES, 
 
 A greater number of supports might affect the stability on 
 uneven ground. 
 
 The stock serves also to point the piece, since it sustains 
 the elevating screw, and with the aid of the handspike gives 
 the necessary changes in azimuth 
 
 It also connects the front and rear wheels in transporta- 
 tion. 
 
 For modern carriages the stock consists of two sheet 
 steel flasks or brackets which rest at the head of the stock 
 upon the axle, and are united at the further end by the trail 
 plate or shoe, 
 
 2. The wheels and the axle replace the continuous support 
 afforded in stationary carriages by the cheeks. 
 
 PERIODS OF THE RECOIL. 
 
 The recoil may be separated into two periods : 
 
 1, That during which the projectile is acquiring energy in 
 the piece. 
 
 2. That comprising the subsequent recoil. Since the 
 carriage is found not to move materially until the projectile 
 has reached the muzzle, and since the system is not rigid, 
 the corresponding phenomena may be taken to be : 
 
 1. A series of shocks between the trunnions and their 
 beds transmitted through the axles to the wheels and through 
 the stock to the trail. The system is finally set in motion by 
 these shocks. 
 
 2. The resulting motion of the system accelerated by the 
 remaining gaseous pressure and retarded by friction and 
 various artificial resistances. 
 
 Energy of Recoil. 
 
 The nature of the recoil is preferably studied by veloci- 
 meters of Class III. But, as this is difficult and requires the 
 previous construction of the carriage, it is customary for 
 theoretical discussions of a general nature to ignore the first 
 
XXII — ARTILLERY CARRIAGES. 
 
 period, and to assume that the system is rigid and that the 
 acceleration to the system during the second period is com- 
 pensated for by the acceleration of the projectile noted in 
 Chapter XI, page 18.* 
 
 We may therefore change Equation (7), Chapter XIX, 
 to read 
 
 in which the subscript s refers to the entire system recoiling. 
 For greater accuracy, when the mass of the powder, or 
 m'^ bears a considerable ratio to that of the projectile, we 
 may use the following formula in which v' represents the 
 mean velocity of the products of combustion, found by 
 experiment to be about 3,000 /. s. 
 
 _ m V + m' v' 
 
 Distribution of "Work of Eecoil. 
 
 Since this work is distributed between the two periods, 
 and since it is necessary to restrict the exent of the recoil, it 
 becomes necessary, as in Chapter V, to determine the 
 maximum stress which the system can safely endure and to 
 maintain this stress as nearly constant as possible over the 
 path of the recoil. 
 
 This principle, which underlies all recent improvements, in 
 gun carriages, owes its importance to the recent increase of 
 m and e and the decrease m M (Equation 7, Chapter XIX), 
 due to the general use of built up rifled cannon firing large 
 charges o^ progressive powder In fact, it may be said that 
 the limit of the power of cannon, or h, page 21, Chapter XI, 
 is fixed by the difficulty of controlling their recoil, 
 
 If we assume that the mobility of the system fixes the sum 
 of the masses, M and J/', composing the gun and carriage, 
 
 This assumption will be corrected as occasion arises hereafter. 
 
XXII. ARTILLERY CARRIAGES. 
 
 the following discussion explains the prevailing practice of 
 making M' approximately equal to M. 
 
 For, if we assume the carriage to be properly proportioned, 
 general experience shows that its permanent deformation, Q, 
 may be considered inversely proportional to its mass and 
 directly proportional to the energy which it receives. So that 
 
 liM-{- M' =z C, Q will be least when M — M'. 
 
 The assumption on which this deduction is based, although 
 confirmed by experience in the construction of carriages, an- 
 vils and armor, is not conclusive ; since mechanical ingenuity 
 may compensate for the loss of strength resulting irom a 
 diminution of M' . 
 
 REMARKS. 
 
 It is found that with quick powders the velocity of recoil 
 during the first period is greater than with slow powders, the 
 maximum momentum of the projectile being the same. 
 
 With slow powders the velocity during the second period 
 is increased to such an extent by the high pressure as the 
 projectile leaves the gun (Chapter XI, page 18), that special 
 devices have become necessary to diminish the increased 
 extent of the recoil. 
 
 The problem is so complicated that computations, princi- 
 pally by graphical methods, are mainly resorted to in order 
 to determine the direction of the stresses, the corresponding 
 dimensions being found empirically. It is highly probable 
 that the gun carriages of the future, like many other construc- 
 tions, will be the outgrowth of practical experience. 
 
 FORCES ACTING ON A GUN CARRIAGE. 
 
 Velocity of Translation. 
 
 If the axis of the bore intersects the axis of the trunnions 
 at the centre of gravity of the piece, the force producing re- 
 
XXII. ARTILLERY CARRIAGES. 
 
 coil is communicated to the carriage at the trunnion beds. 
 The carriage being constructed symmetrically with regard to 
 the axis of the piece, we may suppose that the wheels, trun- 
 nion beds and trail are all situated in the same plane and that 
 the force producing recoil is applied at the point where the 
 axis of the trunnions pierces this plane. 
 
 The direction in which this force acts will be that given by 
 the angle of fire or the inclination to the horizontal of the axis 
 of the piece. 
 
 Let V figure 2, be the position of the axis of the trunnions, 
 and mv-=.I,^ represent the intensity and direction of the 
 force, and Q the angle of fire. Let Z'be the point of contact 
 of the trail and ground, / the distance of this point from the 
 trunnions, and a the angle made by the line Tv, with the 
 horizontal. Let W^ be the weight of the system acting 
 through the center of gravity G at the horizontal distance b 
 from the point T. Let/ be the coefficient of friction between 
 the carriage and the horizontal platform on which it rests. 
 
 The vertical component of /, , and W^ will cause friction 
 between the carriage and the platform. The force of friction 
 or/(^g 4" '^^ ^ s^'^ ^)' wil^ oppose motion. So that, repre- 
 senting by Fthe horizontal velocity of recoil, we have 
 
 y. m V cos 6 — / ( ^8 4~ ^^^ ^ sin B) 
 m V (cos — / sin 0) 
 
 in which g f may be neglected. 
 
 The vertical component will be distributed along the sup- 
 ports in a manner determined by the construction of the car- 
 riage and the values of Q. For wheeled carriages /will have 
 separate values for the wheels and the trail. 
 
 If, in Equation 4, we neglect the weight of the system in 
 comparison with the vertical component of 7, , (or g /), we 
 
XXII. — ARTILLERY CARRIAGES. 
 
 find that V will reduce to 0, or that recoil will cease for a 
 value of 0, such that, calling this angle 0, 
 
 tan e, = y (5) 
 
 This is called the angle of no recoil. 
 
 Extent of Recoil. 
 
 The extent of the recoil will be 
 
 
 s=^-^.' (6) 
 
 If, as is usual, the platform be inclined at an angle, /3, with 
 the horizon so as to check the recoil, then for 6 in the above 
 equations should be written 
 
 d + (3; and for F, Tcos 3. 
 
 In this case, since the energy of the recoil is absorbed not 
 only by friction but by the work done in lifting JV^ through 
 a height = s sin (3, we have 
 
 Fcosfi' 
 
 2 g (sin (3 + / cos (i) 
 
 (J) 
 
 These equations are said to give correct values for stationary 
 carriages, but do not apply very exactly to those which are 
 wheeled. 
 
 Angpilar Velocity. 
 
 The force, /, , also acts to rotate the carriage around 
 the point T with a moment proportional to its lever arm, 
 / sin (a — 6), so that the moment of this force will be 
 m V Isin (a — 6). 
 
 This is opposed by the moment of the weight, or JV^ b. 
 Then, since the angular velocity of the system is equal to 
 the resultant moment of the impressed forces divided by the 
 moment of inertia of the system, we have, representing the 
 
XXII. — ARTILLERY CARRIAGES. 
 
 angular velocity, about T by o) and the corresponding radius 
 
 of gyration by k. 
 
 mvl sin (a — Q\ — W^ b 
 --S '-j^J •- (8) 
 
 With this relation we may discuss in an elementary manner 
 the stability of the system. For example, in the old S. B. 
 Mortars, since W^ is small, a is made less than 0, so as to 
 make w negative. 
 
 Phenomena of Recoil. 
 
 Practically the phenomena are much more complex, since 
 the rotation of the system is not immediate. 
 
 Wheeled Carriages. 
 
 In these the wheels tend to slide or rise to an extent 
 determined by the resistance to sliding at T. Since T is 
 not necessarily on a reciprocal axis of spontaneous rotation, 
 the stock is subjected to a transverse stress. When, after 
 rotation, the wheels fall, the axle receives a shock, and the 
 trail being thrown up, the system recoils by roUing, and so 
 on until the system comes to rest. 
 
 Rotation during the first period tends to derange the aim 
 by what is called the angle of jump^ See Chapter XX. 
 
 During the first period, since the trunnions fit rather 
 loosely in their beds, a frictional moment is developed on 
 the under side of the trunnions This causes abnormal 
 pressure on the head of the elevating screw, which, owing 
 to the elasticity of the system, subsequently receives one or 
 more severe blows from the breech. The effect is destructive, 
 since the bearing of this screw upon its nut is restricted, and 
 the necessary play between the screw and nut increases the 
 striking velocity of the parts. 
 
 The objections may be mitigated by making the piece 
 without preponderance, and by arranging the elevating screw 
 so that its axis will be always normal to the surface which it 
 
XXII. — ARTILLERY CARRIAGES. 
 
 supports, since this will avoid the tendency to bend under 
 pressure. 
 
 Other phenomena also occur. 
 
 The inertia of the wheels develops in the axle a consider- 
 able transverse stress. 
 
 In rifled pieces a rotary moment is developed which tends 
 to raise from its bed the trunnion toward which the top of the 
 projectile is revolving, and thus to raise one wheel higher 
 than the other as the system jumps. The effect will be to 
 concentrate most of the shock of the fall upon the lower 
 wheel. 
 
 Stationary Carriages. 
 
 The chassis of stationary carriages revolves around a massive 
 vertical pintle which may be placed in front of the chassis or 
 at its middle. 
 
 While the former position is necessary for pieces firing 
 through embrasures, in other cases the center pintle chassis 
 is preferred, since a given change in azimuth covers less 
 ground. 
 
 The tendency of the top carriage to jump is restrained by 
 projections which engage under the chassis, but tend to lift 
 the pintle from its socket. The pintle is also exposed to a 
 horizontal stress nearly equal to the normal pressure between 
 the carriage and the chassis multiplied by the sine of the 
 inclination of the chassis to the horizon. 
 
 The strength of the pintle and its fastenings is therefore an 
 important subject of consideration. 
 
 Angle of Greatest Recoil. 
 
 Since the energy of recoil is distributed between the 
 motions of rotation and translation, the maximum velocity 
 of recoil will follow from an angle of fire such that w = 0. 
 Equation (8) does not contain all the data necessary for a 
 
10 XXIi. — ARTILLERY CARRIAGES. 
 
 full discussion ; but it may be shown that, if the weight of 
 the system be neglected, and the notation of figure 2 be 
 adopted, if we call the angle of greatest recoil, 6^, then 
 
 Since A'^/i, this value of B^ is always positive, or the 
 maximum velocity of recoil will follow the use of an angle 
 of fire ]>0. This value of 6 should therefore be employed 
 in all calculations relating to limiting the extent of recoil. 
 
 The angle 6^, may also be called the ang/e of no rotation^ 
 i. e. the angle for which all the energy of recoil is expended 
 in translation only. It may be taken to measure the exposure 
 of the system to the injurious shocks resulting from rotation, 
 since, in ordin-ary firing, Q is less than Q^^ and therefore rota- 
 tion is ordinarily produced. 
 
 Equation 9 shows that d^ may be diminished by the fol- 
 lowing means : 
 
 1. By making h' — h as small as possible. Owing to the 
 length of a in stationary carriages this correction is princi- 
 pally confined to those that are wheeled. In these h' is 
 made as small as facility of loading and the protection of the 
 gunners by the parapet will permit, and h is increased by 
 bringing the axle as near to the trunnions as the size, strength 
 and weight of the wheel will allow. 
 
 2. By making a as long as conditions relating to mobility 
 in transportation will permit. , 
 
 3. By making /small. 
 
 In stationary carriages / is normally great, and, as here- 
 after seen, the resistance to sliding is generally artificially in- 
 creased. For these carriages it is especially necessary that a 
 be made large. 
 
 The stresses developed in field carriages by a large value 
 of/, as when the site is sandy or the trail is rested against a 
 
XXII. — ARTILLERY CARRIAGES. 11 
 
 rock, are evidently prejudicial. They may sometimes be in- 
 evitable, as when firing across a valley at a high mark, since 
 in such a case the trail may require sinking into a hole. 
 
 DEVICES TO CONTROL RECOIL. 
 
 These may be considered according to the end in view, 
 as they seek, I, merely to limit the path; or, II, to regulate 
 the resistance. 
 
 It is generally advisable to store up enough of the work of 
 recoil to assist in bringing the piece back into battery. The 
 return may be facilitated by the use of eccentric rollers. 
 
 These devices ar-e often combined in the same carriage. 
 
 Class I. To the first class of devices belong those in which 
 the energy is absorbed by friction or in which a weight is 
 raised. 
 
 Stationary Carriages. 
 Friction Checks. 
 
 This variety is least valuable since it stores up no useful 
 work. In the best types the friction, due to the normal com- 
 ponent of the weight, is increased by the artificial pressure 
 of a screw clamp. 
 
 The effect of a given pressure on the screw may be in- 
 creased by increasing the number of surfaces upon which it 
 acts. Thus, in Ericcson*s compressor we have 7i parallel plates 
 attached to the chassis and alternating between n -\-l pieces 
 so attached to the carriage that while they recoil with it, a 
 sHght initial play is allowed. Suppose this play to be de- 
 stroyed by a normal pressure P. We shall then have for the 
 friction of the compressor P =: P/ {2 n) and from Equa- 
 tion (7) 
 
 (v cos 13 y 
 
 2g(s[nf5+/cos(3+-^j 
 
 (10) 
 
12 XXII. — ARTILLERY CARRIAGES. 
 
 The main objection to this system is the variable value of 
 F^ since this depends upon the judgment of the operator, and 
 upon the state of the surfaces, and is greater for static friction, 
 when the acceleration is greatest, than afterwards. 
 
 This arrangement is modified in the Sinclair check used 
 with some converted U. S. Sea Coast guns. 
 
 This consists essentially of a clamp embracing a plate in- 
 creasing slightly in thickness from front to rear. To prevent 
 the plate from buckling in consequence of the counter recoil 
 produced by the elasticity of the parts, the front end of the 
 plate is free to move forward through its attachment to the 
 chassis. 
 
 Wheeled Carriages. 
 
 These may be braked by various means. Among these is 
 the Hotchkiss brake which consists of nuts threaded upon the 
 axles between the wheels and serving, by friction produced 
 against the hubs of the wheels, to keep the wheels from 
 turning. 
 
 This brake is an example of the friction clutch often em- 
 ployed in the transfer of energy. When the tangential com- 
 ponent of the force producing rotation exceeds that of fric- 
 tion, sliding takes place and the destruction of the resisting 
 parts is averted. 
 
 This principle is sometimes applied to the elevating screw, 
 since the clutch, which is required to vary d only, will 
 yield under the shocks of recoil and save the deformation 
 of the parts. 
 
 A simple brake may be extemporized by lashing the 
 wheels to the trail by a rope ; but, as this strains the wheel, 
 a better way, often used, is to rest the wheels on shoes 
 attached by tension to the trail, as in wagons of commerce. 
 
 The latest patterns of brake admit of a partial distribution 
 of the pressure, as explained later and in Chapter XXIII. 
 
XXII. ARTILLERY CARRIAGES. 13 
 
 They may also be used in transportation without necessarily 
 stopping the carriage, as is required when the shoe is used. 
 
 Raising a Weight. 
 
 If the piece raise its own weight, its exposure is increased ; 
 while, if it raise a counterpoise, it may itself descend. Such 
 carriages are called disappeari7ig carriages, 
 
 Moncrieff Carriage. — Figure 3 
 
 In this the flasks rock on the chassis so that the counter- 
 poise, Wy which was at first beneath the gun, has finally 
 a considerable moment of restitution. By varying the 
 curvature of the flasks this moment may be made to vary 
 inversely with the acceleration of the recoil so that the 
 stresses between the piece and the counterpoise may be 
 nearly constant. Conversely, the return to battery will be 
 gentle. The rack and pinion serve to retain the piece for 
 loading, and to control its return to battery. 
 
 Kings Carriage. 
 
 The chassis is steeply inclined to the rear, and the coun- 
 terpoise, which is in a well, is lifted by a rope passing 
 through the pintle. 
 
 This carriage, invented by Major King of the Engineers, 
 is cheaper than the Moncrieff", and has been successfully 
 tried in the United States. 
 
 In both carriages exposure may be minimized by aiming 
 with mirrors, and by firing by an electrical contact automat- 
 ically made when the piece comes into battery. 
 
 • 
 Regulation of Stress. 
 
 1. BY FLUID PRESSURE. 
 
 The method now generally adopted is the use of hydraulic 
 or pneumatic buffers. 
 
14 XXII. — ARTILLERY CARRIAGES. 
 
 These consist essentially of a cylinder and a piston, rela- 
 tive motion between which results from the recoil. The 
 effect is to force the fluid contained in the cylinder through 
 orifices or ports which may be either constant or variable 
 in size 
 
 In the pneumatic buffer the ports are in the cylinder heads ; 
 in the hydraulic buffer, as the liquid is to be used again, they 
 are in the piston. 
 
 Pneumatic Buffer, 
 
 This, although simpler and requiring less attention than 
 the hydraulic buffer, is more bulky, can be less easily regu- 
 lated, and gives an injurious counter recoil. 
 
 Hydraulic Buffer, 
 
 Description. Let the arrangement be in principle such 
 as shown in figure 4. C is the cyUnder filled with a non- 
 freezing mixture of glycerine and water ; it is attached to the 
 carriage P is the piston fixed on the rod R^ which is secured 
 to the chassis. 
 
 Many alternative arrangements are made. 
 
 By placing it under tensile stress during the recoil, the 
 bending of the rod may be avoided. 
 
 The size of the ports in the piston may be varied by the 
 profile of the ribs, r, which are fixed to the interior of the 
 cylinder, or by a notched disc revolving on the piston and 
 provided with projections which enter rifle grooves in the 
 cyhnder. 
 
 We will consider only the second period of recoil, and will 
 neglect the friction of the liquid and that of the rod in its 
 stuffing box, so that the pressure considered "^ill be that 
 required to give a constant acceleration to the fluid. 
 
 The value of this method appears from the fact that it may 
 safely restrict the most powerful cannon to a recoil of about 
 3 calibers. 
 
 \ 
 
XXn. — ARTILLERY CARRIAGES. 15 
 
 Notation, , 
 
 Let: 
 
 A be the area of cross-section of the bore of the cylinder 
 diminished by that of the piston rod and ribs. 
 
 a^ the total initial area of the ports. 
 
 a this area at the end of the time, /, or after a displace- 
 ment, X. 
 
 v' the corresponding velocity of the liquid current. 
 
 11 the corresponding velocity of recoil. 
 
 Vq the initial velocity of recoil, obtained either by meas- 
 urement or by means of the formula 
 
 ("'+?) 
 
 .„- ^_ r;[cos(e, + /3)-/sin(9, + /3)] (11) 
 
 derived from Equation (9), Chapter VII, and the remarks 
 noted on pages 7 and 10 herein. 
 
 6 the density of Uquid, or the ttiass of one unit of its 
 volume. 
 
 P the pressure on the piston at any moment. 
 
 a the corresponding acceleration. 
 
 Extent of recoil. If the cylinder is full, the volume a v', 
 of liquid which in a unit of time passes from in front of the 
 piston to the rear must be equal to the volume, A u caused 
 by the translation of the cylinder, whence 
 
 
 
 Au 
 
 
 
 
 (12) 
 
 The 
 
 mass of the 
 
 liquid 
 
 escaping in 
 
 the 
 
 time 
 
 A/ 
 
 is then 
 
 
 ;;/ = 
 
 8av' 
 
 A/= 6 A u 
 
 A/ 
 
 
 
 (13) 
 
 and its 
 
 energy 
 
 mv"' 
 
 6 A' u'/\ t 
 
 - 
 
 
 
 a4) 
 
 
 2 
 
 - 2d' 
 
16 XXII. — ARTILLERY CARRIAGES. 
 
 This is equal to the work done by P over the path u A /, 
 and therefore 
 
 „ d A" u^ 
 
 Since P is constant, Equation (15) must be true, for the 
 initial values of u and a, and therefore 
 
 From this, by equating the initial energy of the system, 
 with the work of the resistances, including the lifting of the 
 weight of the system, and the work of friction over the path 
 iS", we have 
 
 ~\^^^\_~2^' +^-^s(sin/3+/cos/?)J, (17) 
 
 from which S can be determined when A and a^ are known, 
 or from which a^ can be determined when *S and A are 
 known. 
 
 Profile oj the ribs. From the theory of energy we have 
 
 or 
 
 u=K^l-^-^ (19) 
 
 Also, since the recoil is uniformly retarded if we consider 
 the resistance of the liquid only, we have 
 
 Fl = 2a S 
 which value of VI in Equation (19) gives 
 
 «=K\/i-i- 
 
 which from Equations (15.16) may be written 
 
 -V^ 
 
 (20) 
 
 (21) 
 
XXII. — ARTILLERY CARRIAGES. 17 
 
 a 
 If there are n similar ports, the area of each one is - -. If 
 
 n 
 
 each notch in the piston has a breadth, b^ and a depth, d^ 
 
 and the rib has the same breadth and, as shown by figure 4, 
 
 a variable depth, j, then 
 
 a = nb {d — y) (22) 
 
 Which value of a substituted in Equation (21) and solved 
 with respect to y gives 
 
 This is the equation of a parabola. 
 
 At the end of the recoil, when x = S, y =z d, or the ports 
 are completely closed 
 
 This formula applies only to the path of the recoil after 
 the system has acquired its maximum velocity or during the 
 second period. 
 
 While the projectile is in the gun the piece recoils from one 
 to two inches and continues to gain velocity for four to six 
 inches more so that the maximum velocity is not attained 
 until after a recoil of five to eight inches 
 
 Figure 11 shows these phenomena and the effects of a 
 suitable control, based largely upon the analysis of velocity 
 curves obtained during the practically free recoil of the ])iece. 
 The data were as follows : Weight of piece, about 100000 
 lbs. ; of projectile, 754 lbs. ; of powder, 244 lbs. ; initial 
 velocity, 1857 f. s. 
 
 Cylinder, The thickness of the walls of the cylinder may 
 be determined from Equation (4), Chapter XIX, by placing 
 
 
 The area A will be determined practically by the construc- 
 tion of the chassis. As the depth of the chassis limits the 
 
18 XXII. — ARTILLERY CARRIAGES. 
 
 diameter, it is customary to have two cylinders connected by 
 a tube so as to equalize the resistances and prevent slueing. 
 
 Counter RecoiL Owing to the incompressibility of most 
 liquids the tendency to counter recoil is slight ; and, as the 
 velocity of return is small, the weight of the system generally 
 suffices to return it to battery. 
 
 Or the hquid may be forced into another vessel or a set of 
 stationary vessels containing air or powerful springs, which 
 store up energy to return the piece to battery when a valve 
 or latch is opened. Figure 5 illustrates the operation of such 
 a carriage. When air is compressed by the liquid, the variety 
 is known as the hydro-pneumatic 
 
 Regulation of Stress. 
 
 2 BY THE ELASTICITY OF SOLIDS. 
 
 The weight of the cylinder, and the difficulty of prevent- 
 ing leaks in the preceding apparatus, renders it objectionable 
 in wheeled carriages, and more so for those used in the field 
 service than for those in the siege service 
 
 A compromise has therefore been sought by the inter- 
 position of an elastic solid, the work done upon which in the 
 first period will reduce the shock felt by the system. The 
 restoration of this work is not essential, although it tends to 
 distribute the stresses over the path. 
 
 Such an arrangement is shown in the Engelhardt (Russian) 
 carriage, figure 6. 
 
 Engelhardt Buffer. The flasks are notched so as to allow 
 the axle, a^ a limited play. They are also similarly pierced 
 for the cross-bar, ^, each end of which is united to the outer 
 end of «, by a brace, k. This keeps the axle from bending 
 easily since the force of recoil is applied close to the wheels. 
 
 The transom, c^ separates e from an elastic buffer, K The 
 buffer consists of layers of cork, rubber, or of Belleville 
 
XXII. — ARTILLERY CARRIAGES. 19 
 
 Springs {post ), assembled on a bolt, /, the front end of which 
 is secured to e, and the rear end of which is provided with a 
 nut, d. 
 
 When discharged, the piece, with its flasks and c and b, 
 slides back relatively to the wheels and / and ^, so that b is 
 compressed. A considerable proportion of the energy of re- 
 coil is thus absorbed before the wheels begin sensibly to move. 
 
 After recoil, the elasticity of b restores the parts. 
 
 Belleville Springs, These are saucer shaped discs of sheet 
 steel, pierced by an axial hole by which they are united in 
 pairs on a spindle, base to base. They are now much used 
 under compression where space is limited. 
 
 Lejnoine Brake. The French artillery have borrowed from 
 the omnibus of Paris a more perfect but more complex brake, 
 figure 12. On the march it may be set against the tire, by 
 hand, as in the wagons of commerce. When the piece is 
 fired, the relative motion of a mass, w, throws forward the 
 elastic cross-bar, b^ to each end of which is attached a taper- 
 ing cord, c. Each cord after making several loose turns 
 around the nave is secured to the brake beam, B. When m 
 is thrown forward it is held in place by the serrated edge of 
 an axial bar, b', to which it is secured. The motion of b 
 stretches the cords and tightens them around the naves so 
 that they are further wound up by the revolution of the 
 wheel in recoiling. 
 
 The greater the extent of the recoil at any instant, and 
 therefore the less the velocity of recoil, the thicker will be 
 the cord and therefore the greater will be the increment of 
 the pressure of the brake upon the tire. 
 
 See also the U. S. Buffington brake in the next chapter. 
 
 PLATFORMS. 
 
 To insure continued accuracy of fire from the same site, 
 it is absolutely necessary that the carriage should rest upon 
 a solid and substantial platform, 
 
20 XXII. ARTILLERY CARRIAGES. 
 
 The mobility of field pieces restricts this necessity to the 
 sea coast and siege services. 
 
 In the sea coast service the platforms are constructed by 
 the Engineer Department with the works which the cannon 
 defend. 
 
 Wooden platforms are employed for siege pieces, in which 
 long continued firing at one object as in breaching, would 
 cut into the unprotected soil deep ruts, which would increase 
 the difficulty of serving the piece and restrict both its 
 horizontal and vertical field of fire. 
 
 The construction of the platform should be such that it 
 may be taken up without injury for removal to another site. 
 
 Siege platforms consist of a certain number of pieces of 
 wood ; and in order that these pieces may be carried on the 
 backs of soldiers from the depot to the battery, the weight 
 of the heaviest piece should not exceed fifty pounds. Siege- 
 platforms consist of sleepers (i), (fig. 7), and deck platik (2). 
 The general direction of the sleepers is parallel to the axis 
 of the piece, and the deck-plank at right angles to it ; this 
 disposition of the parts offers the greatest resistance to the 
 recoil of the carriage. The deck-planks are fastened together 
 at their edges by dowels ; the outer planks are secured by 
 iron eye-pins, one at each end of a sleeper. The platform is 
 secured in its place by driving stakes around the edges. 
 
 There are two principal platforms for the siege-service, viz., 
 the ^2^;z-platform and the mortar-'^XdXioxm. The former is 
 composed of twelve sleepers and thirty-six deck-planks; the 
 mortar-platform of six sleepers and eighteen deck-planks. 
 
 A simple and strong mortar-platform, called the rail- 
 platform may be used where trees or timber can be easily 
 procured. This is composed of three sleepers and two rails, 
 secured by driving stakes at the angles and at the rear ends 
 of the rails. The rails are placed at the proper distance 
 apart to support the cheeks of the bed. 
 
XXII. — ARTILLERY CARRIAGES. 21 
 
 II. TRANSPORTATION. 
 
 For certain light pieces, as machine guns, a two-wheeled 
 vehicle is used. Where the weight of the load requires its 
 distribution on several supports, the gun carriage is converted 
 into a four-wheeled carriage by attaching it to another two- 
 wheeled carriage, called the limber. 
 
 PRINCIPLES OF THE WHEEL. 
 
 In transportation the wheel is intended to transfer sliding 
 friction from between the surfaces of the tire and the ground, 
 where the coefficient of friction is large and variable, to the 
 lubricated surfaces of an axle and its bearing, where the 
 coefficient is small and nearly constant. 
 
 In this respect its value as a mechanical power varies 
 directly with the radius of the wheel and inversely with that 
 of the bearing. 
 
 The wheel, as shown by figure 8, increases also the lever 
 arm, /, of the power, P, with respect to that, q, of the weight, 
 W^ to be raised over the obstacle, h. 
 
 On these accounts, since the diameter of the bearing, 
 which is generally equal to that of the axle arm, is fixed by 
 the maximum stress which the axle arm has to support, the 
 mechanical advantage of the wheel increases with its diameter. 
 
 An increase in diameter as well as in the width of the tire, 
 diminishes the pressure per unit of area between the tire and 
 the ground, and therefore diminishes the rolling friction, or 
 the work lost in permanently deforming the ground on which 
 it travels. The elasticity of the wheel also favors this reduc- 
 tion ; hence the use for railways of iron wheels on iron 
 tracks. 
 
 The increase in size is limited by the weight of the wheel, 
 the stability of the system on the march and in firing, and the 
 convenience of loading. The mobility of transportation 
 also limits the size, for all wheels in the same service being 
 
22 XXII. — ARTILLERY CARRIAGES. 
 
 interchangeable, the facility of turning depends upon their 
 diameter, as will be shown. 
 
 As shown by figure 8, an advantage also follows from 
 inclining the direction of the draught, particularly for the 
 front wheels, which do most of the work of rolling friction 
 and which therefore are designed to carry only about J of 
 the total load. Since the point at which the horse exerts his 
 power is fixed by his conformation, it is evident that this 
 advantage will be diminished with the increase of diameter of 
 the wheel. 
 
 These considerations have generally fixed the diameter of 
 all field artillery wheels at about 5 feet, and their weight at 
 about 200 pounds. 
 
 Siege wheels are made heavier and larger. 
 
 CONSTRUCTION OF THE WHEEL, 
 
 The requisites of size, weight, elasticity and facility o. re- 
 pair demand a more general use of wood in the wheel than in 
 other parts of the carriage, and involve a marked application 
 of the principle of independence of function. This will ap- 
 pear by comparing the rudimentary wheel, still used in remote 
 districts, consisting of a disc cut from the trunk of a tree, with 
 the complex elastic structure employed in the bicycle. 
 
 The Archibald wheel, figure 9, now much used in the U. S., 
 resembles that now generally employed in other services, 
 although it applies less fully the principle above named. 
 
 Starting from the center, which is the best way of consid- 
 ering any circular structure, we find : — N^ N\ the 7iave or 
 hub. This receives the pressure of the axle arm on a lubricated 
 surface, and distributes the pressure to the spokes. The nave 
 is made in two parts, to facilitate repairing the spokes. The 
 portion of the nave in contact with the axle, or the axle box, 
 is so shaped as to receive the lubricant in the cavity, O, 
 
XXII. ARTILLERY CARRIAGES. 23 
 
 In some foreign wheels and in the ordinary wooden wheel 
 the axle box consists of a separate piece, so that it may be 
 replaced when worn. Since friction is less between dissimilar 
 metals than between surfaces of the same metal, and in order 
 to cause the wear to take place most on the part which can 
 be most easily replaced,* the axle box, when separate, is pref- 
 erably made of phosphor-bronze, while the nave, as in the 
 Archibald wheel, may be made of malleable cast iron. The 
 metal nave marks a great improvement over the wooden nave 
 formerly employed. The cross section of this piece made it 
 difficult to season, its softness caused it to wear from the 
 alternate compression of the vertical and extension of the 
 horizontal spokes, and it was especially exposed to decay 
 from moisture lodging in the angles between the spokes. 
 
 6", 6", are the spokes, which transmit the weight to the rim. 
 For elasticity and facility of repair they are made of oak or 
 hickory. Their inner extremities are shaped like voussoirs, 
 which abut closely upon the box to avoid destructive play. 
 In the Archibald wheel the voussoirs are made a trifle large 
 and simultaneously set together by a powerful radial press 
 which subjects them to a stress many times greater than they 
 are likely to receive in service. 
 
 R is the rmi which distributes the weight over the ground. 
 For the same reasons as the spokes, and because mud adheres 
 less to wood than to iron, the rim is made of oak. In order 
 to avoid cutting too much across the grain the rim consists 
 of a number of segments called felloes or fellies. 
 
 T is the tire, shrunk on to bind the parts together and to 
 protect the rim from wear. As it may require shortening in 
 order to produce the necessary compression on parts which 
 have become loose from wear, it is usually made of wrought 
 iron or of low steel. 
 
 *This is an important principle in machine design. 
 
24 XXII. — ARTILLKRY CARRIAGES. 
 
 The figure shows also various bolts and clips and the 
 line h pin and ivasher, the functions of which are evident. 
 
 Dish. 
 
 The spokes are so arranged as to form a conical surface 
 which is called ih^dish. The principal object of the dish is 
 to give stiffness to the wheel, since (figure 13) on a trans- 
 verse slope or on uneven ground, the lower wheel, which 
 bears the greatest share of the weight, will resist the lateral 
 thrust of the axle by a compressive stress upon the spoke. 
 If the spokes lay in the plane of the rim, there would be an 
 alternating transverse stress on the ends of the spokes ; this 
 stress would make them work loose in their sockets and accel- 
 erate the destruction of the entire machine. 
 
 Axle. 
 
 T\ie axle or axle tree consists of the body and the arms. 
 The arms are conical so as to give the greatest strength with 
 the least mean diameter. In some vehicles, the wear between 
 the arm and box is taken up by means of washers of varying 
 thickness. 
 
 The axis of the arm is inclined slightly downward, forming 
 the hollow^ and to the front, forming the lead. Both together 
 constitute the set of the arm. 
 
 In a dished wheel the hollow frees from transverse stress 
 the *' working spoke," which is that which bears the greatest 
 load ; it also relieves the linch pin from thrust. For a given 
 width of carriage body it allows the axle body to be made 
 shorter and therefore stronger ; and, from the inclination of 
 the plane of the rim, it tends to throw the mud clear of the 
 carriage. 
 
 The efiect of the lead is to diminish the transverse stress 
 upon the front spoke in meeting obstacles. 
 
XXII. — ARTILLERY CARRIAGES. 25 
 
 Axle Body. 
 Although the interval between the cheeks transfers the 
 transverse stress upon the axle to points near the wheels, it 
 was found necessary in former carriages to reinforce the axe 
 with a wooden body. In modern carriages this is sometimes' 
 replaced with two grooved plates which clamp the cylindrical 
 axle between them and are extended to the front and rear so 
 as to stiffen the axle in recoihng. They also serve to fasten 
 the axle to the cheeks. The axle may, without sensible loss 
 of strength, be made hollow, and three-fourths of its weight 
 when solid. 
 
 THE STOCK. 
 
 The prolongation of the cheeks is called the stock. The 
 use of metal instead of wood, has permitted a return to the 
 construction of the great French designer. General Gribeau- 
 valy in whose gun carriages the flasks were parallel extensions 
 of the cheeks. 
 
 The metallic flasks now used converge to the trail. 
 
 In the stock trail syste?n, recently in use, the cheeks con- 
 tained between them a single piece of wood called the stock. 
 
 Besides its functions under fire the stock of the gun carriage 
 unites the two axles of the four-wheeled vehicle, as does the 
 reach or perch of the ordinary vehicle. For artillery carriages 
 used simply for transportation, such as the caisson and the 
 forge, the stock is a single piece of wood joining the body to 
 the limber. 
 
 Tiirnmg A?igle. 
 
 The dimensions of the stock affect the mobility in turning. 
 This is often measured by the tiirfiing angle, which is half the 
 horizontal angle through which the pole can revolve when 
 the carriage is at rest. Practically, the space required to turn 
 the carriage will vary with : 
 
 1. The length and width of the line of horses and their 
 gait. 
 
26 XXII. — ARTILLERY CARRIAGES. 
 
 2. The distance of the pintle from the vertical plane tan- 
 
 gent to the rear face of the front wheels. 
 
 3, The thickness of the stock at the point rubbed b" the 
 
 wheels in turning. 
 • 4. The length of the stock. 
 
 Owing to the first condition above named a turning angle 
 of 60° is generally considered as sufficient. This may be 
 increased by increasing the distance of the pintle from the 
 front axle, but this is apt to cause the pole to *' thrash." 
 
 Pintle. 
 
 The distance of the pintle in rear of the axle in connection 
 with the moment of the trail, afiects also the pressure on the 
 necks of the wheel horses caused by the moment of the pole. 
 
 In siege carriages and in those used only for draught, the 
 pintle is placed at some distance to the rear ; or a similarly 
 placed transverse sweep bar is used, which supports the 
 weight of the stock. 
 
 But, in field carriages for which flexibility of attachment 
 and mobility are essential, the pintle is placed more to the 
 front and the evil corrected as far as possible by distributing 
 the load or by various mechanical means. 
 
 In this arrangement the preponderance of the system com- 
 posed of the gun and its carriage is an important factor. If 
 the trunnion beds are moved towards the Hmber the pole is 
 lifted, but the labor of Hmbering is increased, and the sta- 
 bility of the carriage in firing is diminished. (Eq. 9.) 
 
 To diminish the labor of limbering, the pintle is placed as 
 low as permitted by the requirement that as much free space 
 as possible should be left beneath the axles for mobility on 
 ground covered with large stones, stumps, etc. 
 
 In the siege service, as the piece does not require to be 
 brought into action rapidly, and as the limber carries no 
 extra load, the piece may be shifted to the traveling trunnion 
 
XXII. — ARTILLERY CARRIAGES. 27 
 
 beds which, on the march, are in front of those from which 
 the piece is fired. 
 
 THE LIMBER. 
 
 Nomenclature. 
 
 The wooden field Umber, figure 10, is composed of an 
 axle tree (1) ; a fork (2) ; two hounds (3, 3) ; a splinter bar 
 (4) ; two foot boards (5, 5) ; a pole (6) ; the pintle hook and 
 key (7); two pole yokes (8, 8); and pole pad {^). 
 
 Ahhough destined to be soon replaced by one composed 
 more largely of steel, it is here discussed as it illustrates some 
 valuable principles- 
 
 The hounds serve to support the ends of the limber chest 
 and the foot boards, and also to transmit the draught of the 
 horses from the splinter bar to the axle. 
 
 The pole or totigue is employed to stop the carriage and to 
 give it direction. As it is liable to be broken, it is practically 
 made in two pieces, of which the fork, which is least exposed 
 to accident, forms one. The fork then is a socket for the 
 pole, and braces the entire frame by its attachment to the 
 axle body and the parts in front. 
 
 The pole should be so attached to the fork that it may be 
 readily replaced when broken. 
 
 The pole yokes transfer the weight of the free end of the 
 pole to the necks of the wheel horses and the soft pad pro- 
 tects the leading horses from harm. 
 
 Attachments, 
 
 The metaUic limber body consists of channel irons and T 
 angle irons united in various ingenious ways. The rigid 
 splinter bar may be replaced by the ordinary jointed double 
 tree and si?tgle trees. These permit the horses to work more 
 independently of each other than the splinter bar does, but 
 are probably not so strong. A joint is always a cause of 
 expense and generally a source of weakness. 
 
28 XXII. — ARTILLERY CARRIAGES. 
 
 In the British service the pole is replaced by shafts. 
 Since the pace of the team is regulated by that of the slowest 
 horse, this arrangement, while more manageable than the 
 pole, and therefore better fitted for the showy evolutions of a 
 drill, is objectionable for the march, since the work which 
 devolves on the shaft horse diminishes his endurance. 
 
 The Limber Chest 
 
 This serves to carry ammunition, and also furnishes a seat 
 for some of the cannoneers. The gun carriage is often 
 arranged to carry two cannoneers on side seats, in order to 
 diminish the time required for coming into action, a matter 
 which, owing to the precision, rapidity and range of infantry 
 fire, is becoming of vital importance. The carriage also 
 often carries two rounds of canister for use at close quarters. 
 
 The principal distinction between limber chests depends 
 upon how the lids are placed. 
 
 If on top, the chest may easily be made waterproof in 
 fording streams ; but the contents are less accessible. If 
 behind, the lid may form a convenient tray for preparing 
 fuzes, &c. This arrangement is more liable to accidental 
 opening than the former, and waterproof packages for the 
 cartridges may be necessary. 
 
 The ammunition chests in the U. S. Service are still con- 
 structed of wood. In other countries sheet steel is generally 
 used. For what reason is unknown ; since, if not unduly 
 heavy, they are not proof against infantry fire. 
 
 THE MORTAR WAGON. 
 
 This is used for transporting siege projectiles, mortars and 
 their beds, and spare guns. 
 
 The body consists of a strong, rectangular frame provided 
 with a stock by which it is attached to the siege limber. At 
 the rear of the body is placed a windlass which aids in loading 
 
XXII. ^ARTILLERY CARRIAGES. 29 
 
 heavy weights. Stakes may be placed around the sides to 
 sustain boards used in retaining loose objects. 
 
 Since rifle projectiles are always issued boxed instead of 
 loose, as was the former custom, the necessity of the mortar 
 wagon for their transportation no longer exists; but its 
 general utility is great. It will .probably be used hereafter 
 for transporting siege guns for considerable distances, since 
 the height of the carriage from which they are now fired 
 renders them unstable on rough roads. 
 
 A special wagon with a crank axle, so arranged as to carry 
 the load close to the ground without diminishing the height 
 of the wheels would appear to offer special advantages. 
 
 III. CARRIAGES FOR SUPPLY. 
 
 New U. S. System. 
 
 These include, 1st, the caisson^ for carrying a larger quan- 
 tity of ammunition than can be carried by the limber, and 
 also a spare pole, wheel, handspikes, buckets and tools ; 
 2nd, the forge and battery wagon, containing a larger assort- 
 ment of tools and material for repairs ; 3rd, the artillery 
 store wagon, an ordinary four-horse wagon, containing extra 
 small arms and ammunition and the men's knapsacks, etc., 
 so as to confine the load of the fighting teams to the neces- 
 sities of action. 
 
 REMARK. 
 
 The increased weight of each round of modern ammuni- 
 tion and the necessity for an even greater number of rounds 
 than formerly sufficed, increases the difficulty of supply. 
 
 It is proposed abroad to increase the number of caissons 
 per piece and to retain the supply in the limber for extreme 
 emergencies. 
 
XXtil. — VARIOUS AkTiLLEkY CaRria6E§. 
 
 CHAPTER XXIII. 
 VARIOUS ARTILLERY CARRIAGES. 
 
 The U. S. Field Carriage. Figures 1-4. 
 
 Constmction, 
 
 This carriage, designed by Colonel Buffington of the Ord- 
 nance Department, is made of steel, since, owing to the large 
 value Qii h of this gun (Chapter XI, page 21), wooden car- 
 riages, and even some differently constructed of steel, were 
 found insufficiently strong. 
 
 The principal features relate to the construction of the axle 
 body, of the stock and to the operation of the brake. The 
 hollow cylindrical axle is strengthened by axle plates, figure 
 2, which stiffen it in the direction of the recoil. The stock 
 consists of two brackets, each of which is made of two nearly 
 symmetrical sheets of steel stamped hot between dies so as to 
 give the corrugated cross section indicated in figure 3. When 
 riveted through the webs, each bracket forms a strong, light 
 truss, resisting stress both in its own plane and transversely. 
 
 The lower flanges of the outer plates project inwardly and 
 serve to unite the brackets to the axle plates. The brackets 
 are further united by transoms, three of which with a hinged 
 lid form the trail box for the oil can and tools which have 
 become a necessary portion of the equipment. 
 
 The carriage is provided with two axle seats for cannoneers. 
 
 The wooden handspike is permanently hinged to the trail. 
 
 Elevating Screw, 
 
 The space between the brackets allows the breech to 
 descend sufficiently for the high angles of fire used with low 
 
XXIII. — VARIOUS ARTILLERY CARRIAGES. 
 
 charges against troops sheltered, from view, and the crank 
 which operates the elevating screw is placed at the side, so 
 that under these conditions it will be readily accessible. 
 
 The nut of the elevating screw oscillates slightly on trun- 
 nions, and the head of the screw is connected by a fork to 
 an axis parallel to and beneath the trunnions, so that, as the 
 angle of fire changes, the axis of the screw will be nearly 
 normal to that of the gun. 
 
 Brake. 
 
 The great strength of this carriage has permitted the 
 employment of Colonel Buffington's brake, figure 4. 
 
 This consists of an [_ shaped rod, the stem of which is 
 surrounded by a spiral spring contained within a tube ; the 
 rod swings freely from a loose joint situated eccentrically 
 above the axle. 
 
 The length of the brake is such that when held vertically 
 the hook will pass over the wheel ; and, being allowed to fall 
 to the rear, it will engage with the tire at some point as a. 
 
 When the wheel revolves in the recoil, the friction at a 
 tends to extend the rod. But this compresses the spring and 
 increases friction, so that as the velocity of recoil decreases, 
 the resistance to rolling increases, and the retardation 
 a])proaches constancy, at least during the critical period 
 preceding sliding. 
 
 The recoil has thus been reduced from 26 feet to 8 feet, 
 without injury to the carriage. 
 
 In transportation the brake is secured vertically to one of 
 the seat arms. It may also be used as a traveUng brake. 
 
 Limber and Caisson. 
 These carriages are constructed substantially on the lines 
 previously named. Steel angle irons are largely used for the 
 frame. 
 
XXIII. — VARI6US ARTILLERY CARRIAGES. 3 
 
 The chests, which are of wood, open on top and are only 
 high enough to receive the projectile standing ; this brings 
 the center of gravity very low. 
 
 The cartridges lie in a compartment between the two end 
 compartments reserved for the projectiles, which thus serve 
 to protect the powder from hostile fire. 
 
 For safety, no friction primers are carried with the powder, 
 as was formerly done. Unbroken packages are placed in 
 outside cases, and loose primers are carried with the tube 
 pouch in the trail box. 
 
 The four chests per piece can carry 42 projectiles each, 
 with a greater number of cartridges for curved fire. 
 
 The Siege Carriage. Figure 5. 
 
 The principal feature of this carriage is its height. For 
 the protection of the gunners the axis of the trunnions is 
 placed 6 feet above the ground. 
 
 In order to prevent the system from tipping forward in 
 limbering, the trunnions are so placed that when limbered 
 the center of gravity of the system will fall between the axles. 
 
 The wheels, axle plates and brakes are such as just 
 described. 
 
 The carriage is intended to transport the piece only for 
 short distances about the work which it defends. 
 
 REMARK. 
 
 A small hydraulic buffer connecting the stock with a pintle 
 sunk into the platform between the wheels, and two movable 
 chocks, assist in controling the recoil. The chocks rotate 
 around the pintle with the gun and serve to return the piece 
 into battery. 
 
 The Siege Howitzer Carriage. Figure 6. 
 
 The piece is mounted in two trunnion carriages, a, upon 
 the inclined slides, '^, upon which it is allowed a recoil of six 
 
4 XXIII. — VARIOUS ARTILLERY CARRIAGES. 
 
 inches. The recoil upon the shdes is checked by the 
 hydrauhc cyUnders, r, and the courses of Belleville springs, 
 d. The latter serve to return the piece to the firing position. 
 They rest against the traveling trunnion beds, e^ and the rods 
 upon which they are strung pass through holes in these beds. 
 
 The flasks, /, are of rolled steel plate \ inch thick, and are 
 flanged inward except on their upper edges. From each 
 flask is cut a large triangular piece in order to diminish its 
 weight ; the edges of the apertures being flanged inward as 
 above. The flasks are xmited by three transoms, ^, and the 
 double transom, //, to which is fastened the piston rod of the 
 hydraulic brake. 
 
 The flasks rest upon the axle through two iron forgings, /, 
 and are strengthened by two supporting plates,/. 
 
 In order to facilitate the elevation of the piece a pecuhar 
 arrangement is employed. This consists of the elevating 
 rack, /, which is attached to the piece, and the worm, m ; the 
 shaft, ;/, and the hand-wheel, o. The worm is attached to 
 the right trunnion carriage, and in recoihng slides along the 
 shaft, n. A spline (see AVebster) on the shaft permits the 
 worm to shde along the shaft, and yet constrains it to follow 
 in any position the rotation given to the hand-wheel, o. 
 
 The advantage claimed from this design is that the recoil 
 of the piece upon the carriage so diminishes the maximum 
 stress upon the flasks and trail that their weight may be 
 greatly reduced. A portion of the weight so saved is used 
 to strengthen the axle and the wheels. 
 
 Weight of wheels, 375 pounds, each. 
 Weight of carriage, complete, 3200 pounds. 
 Pressure of trail on platform, 13(K) pounds. 
 Height of trunnions, 6 feet. 
 
XXIII. — VARIOUS ARTILLERY CARRIAGES. 5 
 
 Barbette Sea Coast Carriage.* 
 
 The principal feature of the gun carriage is borrowed from 
 the old *' flank-defense howitzer" carriage. 
 
 Its object is to return the piece to battery and by diminish- 
 ing the variable work of sliding friction to increase that of 
 the hydraulic buffer, which can be made constant. 
 
 Each cheek carries two rollers ; that in rear is on an 
 eccentric axle and that in front is on a concentric axle. 
 When the piece is in battery the front rollers are nearly in 
 contact with the chassis rail ; while those in rear are usually 
 raised from it, but may be thrown in contact by means of the 
 eccentric. The lower front angles of the cheeks are trun- 
 cated, so that, when the carriage is thus tilted to the front, all 
 the rollers come into play and the piece may be moved from 
 battery with comparative ease. 
 
 In firing, the rear rollers are out of gear so that the vertical 
 thrust of recoil is borne by the lower face of the cheek and 
 the axles are not endangered. 
 
 As the carriage recoils the rear rollers strike inclined planes 
 bolted to the upper surface of the chassis rails and tilt the 
 carriage sufficiently to cause it to move by rolling until it 
 returns again to battery. 
 
 Muzzle-loading guns are retained from battery by means of 
 an automatic latch. 
 
 MODERN TYPES OF SEA COAST CARRIAGES. 
 
 Owing to our deficiency in modern cannon the U. S. have 
 not yet (1891) decided on any special pattern of sea coast 
 carriage; but the following examples, derived from the 
 French service, probably contain the essential features of the 
 system to be adopted for the barbette carriages, as soon as 
 the new cannon shall have been supplied. 
 
 * The Sea Coast Battery at West Point contains several specimens of 
 this type. 
 
O XXIII. — VARIOUS ARTILLERY CARRIAGES. 
 
 The types of disappearing carriages and those designed 
 for turrets are too numerous for description here. They 
 generally apply the principles previously discussed with those 
 treated in the course of Military Engineering. 
 
 Gun Carriage. 
 
 Figures 7, 8 represent the elements of a modern sea coast 
 barbette gun carriage. It consists of three main parts : 1st, 
 the top carriage, T^ consisting essentially of the buffer; 2nd, 
 the chassis, C, the lower part of which is circular ; by means of 
 a great number of loose conical rollers, it revolves upon the 
 circular pintle platform, P. This platform, cast in a single 
 piece, rests upon a proper foundation. 
 
 To avoid the complications due to sliding friction during 
 recoil, the top carriage also moves on rollers recessed in the 
 chassis rail. 
 
 Pointing in azimuth is performed by an endless chain 
 engaging in a sprocket* bed around the platform. The chain 
 passes over a windlass, W, which is rotated by the crank, K, 
 
 The loading scoop, s, is on a lever, L, which is rotated by 
 a geared crank so as to bring both the charge and the pro- 
 jectile into the position of loading. 
 
 In order to minimize the number of men required for 
 loading, the act of lowering the scoop stores up energy in 
 certain springs so that the maximum pressure which can be 
 counted on shall be continuously apphed, as in the hydraulic 
 buffer. 
 
 The steel shield, /, protects the gunners from light pro- 
 jectiles. 
 
 Advantages, The carriage is low, stable, and as seen in 
 figure 9, very compact. The use of rollers increases its 
 mobility and their number distributes the thrust over a large 
 area. All wheels are protected and the traversing chain is of 
 
 * See Webster. 
 
XXIII. — VARIOUS ARTILLERY CARRIAGES. 7 
 
 rustic simplicity and easy of repair, even in action. The 
 arrangement of the scoop facilitates loading since its load 
 may be placed by simply tilting the hand truck on which it 
 is brought from the magazine. 
 
 Sea Coast Mortar Carriages. Figures 10, 11. 
 
 Although of an entirely novel design, the carriage in figure 
 10 resembles essentially the gun carriage just described. The 
 nomenclature is the same in both figures. 
 
 The chassis is divided into two portions, Ci, C^ ; the sur- 
 face of contact being cylindrical about the axis of the trun- 
 nions. By this arrangement fon all angles of fire the axis of 
 the gun is always in the plane of the axes of the hydraulic 
 cylinders, so that the friction in starting is not increased by 
 the pressure causing recoil. 
 
 Rotation from recoil is prevented by the clips, c, c, etc. 
 
 The diminished intensity of the maximum vertical pressure 
 has caused this carriage to be adopted in the French Navy; 
 for ships now, as well as forts, are beginning to utilize the 
 advantages of vertical fire. 
 
 In another type of mortar carriage, shown in figure 11, also 
 under trial in the U. S., the chassis is made in one piece, the 
 direction of the recoil being downward at a constant angle of 
 60° This is a mean between the limiting angles of 6 for 
 mortar fire, viz. : 45" and 75°. The mortar is returned to 
 battery by springs that are compressed during the recoil. 
 
 Another form of loading scoop is also shown. 
 
 This is known as the Easton- Anderson carriage, of Eng- 
 lish design. 
 
XXIV. — H0RS£ AND HARNESS. 
 
 CHAPTER XXIV. 
 
 HORSE AND HARNESS. 
 
 The horse transports his load in two ways. 1st, as a pack 
 horse ; 2nd, as a draught horse. 
 
 PACK HORSE. 
 
 The daily work of a pack horse is about equal to that of 
 five men similarly employed ; or, if he moves at a walk, he 
 may carry a load of 200 pounds 25 miles a day, or 5000 mile- 
 pounds. 
 
 If he trots, the increased expenditure of muscular energy 
 reduces his daily work about one-third.* 
 
 In the above the weight of the horse is neglected, and it is 
 assumed that, though this daily work may be temporarily ex- 
 ceeded, the excess cannot be long continued without injury. 
 
 The mule, owing to his build, carries more than the horse ; 
 he eats less and is surer of foot. He is therefore generally 
 used in the mountain service. 
 
 DRAUGHT HORSE. 
 
 Load. 
 
 Although a horse can pull much less than he can carry, 
 the advantages of the wheel enable him to draw over ordinary 
 roads a load weighing about seven times as much as his pack. 
 With a pull of 80 pounds the daily work of a draught horse 
 
 * It has been found that for any animal the maximum rate of work per 
 unit of time (or/ z/, Chapter XI, page 4) is attained when the velocity is 
 about I of the maximum velocity unloaded, and the load about g of the 
 maximum load at the lowest positive velocity. 
 
XXIV. — HORSE AND HARNESS. 
 
 is generally given as 1600 pounds X 23 miles, or 36800 mile- 
 pounds of load, or 1840 mile-pounds of actual work. 
 
 Owing to their interference with each other's motions, the 
 maximum load drawn by teams of horses increases less rapidly 
 than does the number of horses in draught. Thus, when the 
 teams comprise respectively 2, 4, 6, 8 horses, the maximum 
 loads which they can continuously draw are in the relation 
 per team, of the numbers 9, 8, 7, 6. 
 
 These considerations, the mobility of the system (Chapter 
 XXII, page 1), the increased weight of forage and length of 
 column required, have generally fixed the limit of efficiency 
 at the six-horse team. 
 
 It is estimated that when a draught horse carries a rider, 
 his efficiency is diminished J at a walk and § at a trot. Con- 
 sequently, supplying the data given, the maximum load for a 
 team of 6 horses moving at a trot will be about 
 
 near files. off files. 
 
 3 X 1600 3 X 1600 
 + ^ 
 
 ^1 = 3733 pounds; 
 
 or 622 pounds per horse. 
 
 This may be considered 2i physical constant^ the best method 
 of distributing which between the objects transported and the 
 means of transportation is still open to inquiry. 
 
 Various conditions must be allowed for : On one hand are 
 bad roads, insufficient food, rapid movements for short times, 
 and forced marches. On the other hand, the reduction in 
 the load caused by the expenditure of ammunition, the dis- 
 mounting of the cannoneers, and the infrequency of the trot. 
 
 Upon these considerations are based the following approx- 
 imate loads per horse. 
 
 Horse artillery, 650 pounds. 
 
 Light field artillery, 700 pounds. 
 
 Heavy field artillery, 850 pounds. 
 
 Siege artillery, 1000 pounds. 
 
XXIV. — HORSE AND HARNESS. 
 
 REMARK. 
 
 The 12 pdr. Napoleon gun, which was the heaviest field 
 gun used in our civil war, and which traveled over roads quite 
 as bad as any used in foreign wars, gave a load of 645 pounds 
 per horse, and was found amply mobile. The load per horse 
 for the 3.2 inch B. L. R., field, is 632 pounds. 
 
 Angle of Draught. 
 
 The power of an animal in draught may be supposed to 
 consist in his ability to maintain himself rigidly in a position 
 such that the moment of his weight may be increased without 
 increasing the lever arm of the resistance. 
 
 Thus in figure 1, let / be the position on the ground line, 
 / g, of the hind feet of the horse in draught. Let s be the 
 shoulder of the horse or the point at which he applies his 
 power to the trace, s c, which is attached to the carriage at 
 the point c. Let W be the weight of the horse, and / be 
 the distance from / on the line / s, of the vertical passing 
 through his center of gravity. Let r be the tension on the 
 trace, the length of which s c ■=. t^ and let R be the horizontal 
 component of r, producing uniform motion of the point c in 
 a horizontal plane. 
 
 Let / be the variable angle with the ground line of the line 
 s /, and g} be the variable angle between s f and s c. Let 
 ^, drawn from /, perpendicular to s c, be the lever arm of 
 the resistance. Let the same symbols ** primed " represent a 
 new position of the system caused by the horse bending his 
 knees in pulling. For simplicity, we will suppose that his 
 fore feet are otf the ground and that his hind legs are not 
 extended so as to increase /, as these suppositions tend to 
 neutralize each other. Also that the center of gravity is on 
 the line f s. 
 
 The construction of the figure shows that, as the point s 
 moves to s', c will move to c\ and that R will increase until 
 
XXIV. — HORSE AND HARNESS. 
 
 the compression along s f causes the horse to bend so that / 
 will shorten. 
 
 The stress R may under these circumstances be deduced as 
 follows : 
 
 From the equaHty of moments we have W I cos i-=.r h, 
 
 and from the figure 
 
 . W I cos i cos ii — (p) 
 i? = r cos (? — g)) = ^^ ^ 
 
 Graphical construction shows that, as i diminishes, h and 
 qp will diminish slowly, and / — qp will rapidly approach zero. 
 
 R will have its maximum value when s falls on the line c p^ 
 either from raising the point of attachment to the load at c or 
 from the descent of the point of appHcation of the power at s. 
 This value is not realized in practice, since, in addition to the 
 effect noted above, as i decreases the force of friction at / 
 decreases and the feet tend to slip. 
 
 A proper inclination of the trace is therefore valuable since 
 it enables R to be increased according to the ability and 
 willingness of the horse, and also that it enables him to draw 
 by increasing the friction between his feet and the ground. 
 
 By experiment it was found that when the horse is free, 
 the maximum practical value of R^ or about 0.6 W^ was 
 attained for a value of i — 9 = 12°. When the horse had 
 a rider, i — 9 could profitably be reduced to 7°. From 
 these data it is estimated that, since tan 12°= 0.2, a draught 
 horse should carry \ of his load on his back. 
 
 The preceding general considerations apply to the case of 
 men pulling on ropes or pushing on capstan bars, etc. They 
 partly explain also that, while for the horse the maximum 
 value of i?=0.6 W^ for man, it is found practic ''" that 
 R^W, 
 
 Arrangement of the Horses. 
 
 Owing to the difficulty of coordinating the movement of 
 the horses the single file is used only when the gait is slow 
 
XXIV. — HORSE AND HARNESS. 
 
 and the road smooth, so that the shaft horse will not be un- 
 duly fatigued by frequent changes of direction. 
 
 When the double file is used, the control of the direction 
 is shared by the horses of the wheel team, provided the car- 
 riage have a pole. 
 
 This team is preferably attached to a movable double tree^ 
 Chapter XXI F, page 28, since this shows by its inclination 
 whether the horses are pulling evenly, and also transfers the 
 draught to the axis of the carriage. For these reasons it is 
 often called the evener. 
 
 By attaching the traces to the single trees hooked on to 
 each end of the double tree, greater flexibiHty is attained; 
 and, since the shoulders of the horse are naturally brought 
 into bearing alternately, he is less apt to be chafed by the 
 sliding of the collar. 
 
 He may also, when harnessed, be more readily hitched 
 and unhitched. 
 
 In commerce the leading team is generally attached to 
 an evener fastened to the front end of the pole. This is 
 objectionable since it confuses the functions of the pole. 
 A better method, sometimes followed, is to support the 
 evener by the pole, and to connect it with the axle by an 
 independent tensile member, as by a chain. 
 
 In the present arrangement, the objections to supporting 
 the weight of the evener on the end of the pole, and here- 
 fore on the necks of the wheel team, are avoided, and the 
 traces of each team are connected with those in rear by an 
 arrangement which permits continuous draught without caus- 
 ing the effort of wiUing horses to be neutralized by the 
 laggards. 
 
 The team between the leaders and the wheelers is called 
 the swing team. The horse on the left of each team is 
 called the near horse and that on the right the off horse. 
 
XXIV. — HORSE AND HARNESS. 
 
 Requirements, 
 
 The preceding considerations illustrate the application of 
 the principle of independence of function to meet the require- 
 ments of artillery harness which, as stated by another writer, 
 may be thus abridged. 
 
 " No horse should be restrained by the efforts of another, 
 and the direction of the traces should be most favorable for 
 draught. The drivers should be able to harness and unhar- 
 ness promptly, by night as well as by day, when benumbed 
 by cold and when excited by danger. The fall or loss of a 
 horse should not be a permanent obstacle to the advance, 
 and disabled horses should be easily replaced. ' 
 
 U. S. Artillery Harness. Figure 2. 
 
 WHEEL HARNESS. 
 
 This is composed of four essential systems, three of which 
 occur in all harnesses except for horses in the lead. The 
 systems are : 
 
 1st. The head gear to guide and hold the horse. 
 
 2nd. The saddle to transport the driver, who, for the 
 independent control of his team, is mounted. 
 
 3rd. The draicght harness which enables the horse to move 
 the carriage forward. 
 
 4th. The breeching for moving it backward. 
 
 1. The head gear consists of the bridle and halter. To 
 the bit of the off horse is attached the lead rein, one end of 
 which is held by the driver. 
 
 2. All horses are saddled, the off horse carrying the driver's 
 valise, and, when necessary, an extra cannoneer. 
 
 3. The draught harness and the breeching constitute two 
 independent systems symmetrically arranged. 
 
 The former is composed of the following parts. 
 The hameSj h, figure 2, are two curved irons shaped like 
 the signs ( ). They are connected together below by an 
 
XXIV. — HORSE AND HARNESS. 
 
 iron clasp, and adjusted at the top by a leather strap so as to 
 embrace the neck and form a rigid frame against which the 
 horse may thrust. To diminish the pressure per unit of area 
 on the horse's shoulder* the hames rest on a similarly 
 shaped cushion, the collar. To each hame is attached by a 
 flexible hinge a stout leather tug^ t. This terminates in an 
 iron ring through which passes the trace chain, c^ terminated 
 by the toggle^ t' . The latter connects the front trace chain 
 of the wheel horse with the rear trace chain of his leader, 
 and so on throughout the column. When in motion, the tug 
 ring plays on the trace chain and thus makes the leading 
 horses independent of those in rear. 
 
 The length of the rear trace chain may be varied by a 
 toggle to suit the conformation of the horse. 
 
 The safe, s, protects the shoulder from chafing. 
 
 The loin strap, /, sustains the trace when relaxed, and the 
 belly band beneath the saddle keeps it from rising over the 
 back in turning. 
 
 4. The breeching is composed of the broad breech strap, 
 b, figure 3, corresponding to the collar ; it is supported by 
 the hip straps h. Corresponding to the traces is a Y-shaped 
 system consisting : — 1st. Of the continuous breast strap, bs, 
 which, passing around the breast, is united at each end to the 
 breech strap. It is supported in front by iron Hnks hanging 
 from the hames. 2nd. The stem of the Y is formed by the 
 pole strap, p, connected at one end to the breast strap by an 
 iron double-loop, shaped like a figure 8, and leading obliquely 
 downward and inward to the end of the pole. The functions 
 of the pole thus correspond to those of the splinter bar 
 in rear. 
 
 * This end is served in modern practice by using hames of sheet steel 
 formed to fit the shoulder. The same principle is applied in the cavalry 
 saddle. 
 
XXIV. — HORSE AND HARNESS. 
 
 Pole Yoke, 
 
 The weight of the pole is supported by the pole yoke, 
 which is connected by a short chain to the clasp of the 
 hames. The branches of the yoke are so hinged to a collar 
 revolving loosely around the pole that they can play only in 
 a plane passing through the axis of the pole. 
 
 This allows the horses to travel freely at different levels 
 and prevents the lateral thrashifig of the pole. 
 
 LEAD HARNESS. 
 
 The leading horses have longer traces than the wheelers 
 and have no breeching; otherwise their harness is identical. 
 
 Improved Harness. Figure 4. 
 
 The harness devised by Major Williston of the Artillery, 
 which is now undergoing trial, resembles that above described 
 except in the following principal points. 
 
 1st. For interchangeability, the saddles and bridles are 
 the same as those used by the cavalry, and saddle bags 
 replace the valise. 
 
 2nd. The wheel traces are attached to single trees which 
 may be hooked to the saddle when not in use. 
 
 3rd. The breeching is that used in commerce. The stem 
 of the Y passes under the horse to a transverse bar in front, 
 which corresponds to the evener, and is called the neck yoke. 
 
 This is the most important change from the regulation 
 harness. It prevents the breech strap from slipping upward 
 in stopping suddenly, and also avoids the oblique thrust on 
 the horse's neck which tends to make him fall. 
 
 The neck yoke also controls the pole better than the hinged 
 pole yoke. 
 
 4th. The bridle rein of the off horse passes through a 
 pulley on his saddle, so that, in holding him back, the 
 oblique stress above mentioned is further avoided. 
 
XXIV. — HORSE AND HARNESS. 
 
 5th. The collar, instead of being continuous, is hinged 
 above and is provided with a fastening below in easy reach. 
 
 6th. The horse of the chief of piece is provided with a 
 light draught harness, consisting of a breast collar and traces, 
 with which in an emergency the other horses may be assisted. 
 When not in use the traces are folded across the horse's 
 withers. 
 
 This harness is distinguished for the ease with which the 
 horses may be detached from the carriage in all conditions of 
 service. 
 
 LEATHER. 
 
 That used in harness is classified according to its thickness, 
 into harness," bridle and collar leather. 
 
 The leather from the necks, shanks, flanks and bellies, or 
 the offal, figure 5, is rejected as too spongy for use, so that 
 only about one-half of the hide is employed. Of this, the 
 butt is the best portion. 
 
 The lighter hides are slit axially into sides. 
 
XXV. — ARTILLERY MACHINES. 
 
 CHAPTER XXV. 
 
 ARTILLERY MACHINES. 
 Object- 
 
 Artillery machines are employed to mount and dismount 
 cannon and to transport artillery material from one part of a 
 work to another. They comprise the gin, the gun lift and 
 Jacks of various forms; and wheeled vehicles such as the sling 
 cart, the truck, etc. 
 
 Machines Used in Mounting Cannon. 
 
 The gin consists of a tripod composed of two legs which 
 form a shear or derrick, and a pry pole by which the legs 
 are lifted and braced. 
 
 The hoisting apparatus consists of a block and fall sus- 
 pended from the apex and operated by a windlass supported 
 by the legs in a position convenient for the use of handspikes. 
 
 The use of the gin is confined to relatively light weights. 
 Heavy weights are preferably lifted by the hydraulic jack and 
 loose blocking. 
 
 The hydraulic jack is a compact form of the hydraulic 
 press, which contains within itself the reservoir of liquid 
 required. It is provided with valves by which the direction 
 of the motion of the ram may be varied. 
 
 Other jacks apply the principles of the lever and the screw, 
 and are correspondingly named. 
 
 The gun lift consists of two massive trestles so framed that 
 they may be easily dismounted for transportation. 
 
 Each trestle carries on its beam a hydraulic jack ; the latter 
 by means of a lever raises a bar of iron which passes verti- 
 cally through the beam and the lever, between the jack and 
 the fulcrum of the lever. This bar is pierced at short inter- 
 vals by holes, and its lower end is formed into a hook. 
 
XXV. — ARTILLERY MACHINES. 
 
 Both bars having been attached to the weight, and a pin 
 having been passed through the hole in the bar next above 
 the lever, the ram of the jack is raised to its full extent. A 
 pin is then inserted through the hole next above the beam 
 and the ram is lowered. The upper pin is then shifted down- 
 ward and the operation continued. 
 
 For comparatively light weights a single trestle may be 
 employed like a gin. 
 
 Machines Used in Transportation. 
 
 Heavy weights are usually transported by the aid of cap- 
 stans and rollers. 
 
 When space permits, cannon may be rolled bodily by par- 
 buckling. In such cases a muzzle collar of the maximum 
 diameter of the piece corrects the circular path which the 
 conical mass tends to describe. 
 
 Heavy weights may also be rolled through the narrow 
 passages of forts on a low framework called the cradle. 
 
 The wheels of sling carts are large and have but little dish. 
 Since, hke the gin, they suspend the load, they are relatively 
 weak, and hence are used for lighter weights than the cradle. 
 
 By mechanical appliances mounted on the axle, the weight 
 may be lifted from the ground, and during transportation 
 may be permanently secured to the axle by hooks which 
 relieve the more delicate mechanism from shocks. 
 
 The means of lifting are the screw, and the hydraulic jack 
 which works on the principle explained for the gun lift. 
 
 For light weights the eccentric position of the hooks may 
 enable the weight to be raised by lifting the pole before the 
 weight is attached and afterwards by depressing it. This 
 means of lifting is applied to the iron sling cart. The field 
 limber may be similarly used to carry a piece, the carriage of 
 which is disabled. 
 
 In transportation the pole of the sling cart is supported by 
 the limber. 
 
XXVI. — HAND ARMS. 
 
 CHAPTER XXVI. 
 
 HAND ARMS. 
 
 The weapons carried by the soldier, or portable arms may 
 be divided into hand arms and small arms. 
 
 The former class is known in French as '^armes blanches ; " 
 the latter requires, as in cannon, a preliminary study of the 
 ammunition employed. See Chapter XXVII. 
 
 Classification. 
 
 Hand arms are divided into 
 
 1st. Thrusting arms which act by the point. 
 
 2nd. Cutting arms which act by the edge. 
 
 These functions may be combined in the same weapon, 
 though at some sacrifice of efficiency. 
 
 Thrusting Arms. 
 
 The body of a thrusting weapon should be straight so as 
 to avoid a rotary moment on impact, and the center of gravity 
 should be placed near the handle. This may be attained by 
 fluting the blade, or by suitably weighting the handle. 
 
 The principal thru^sting weapons are the straight sword, the 
 lance and the bayonet. 
 
 The sword is composed of the blade, the hilt by which it 
 is held, and the guard. A knob sometimes acts to counter- 
 poise the blade as in the foil. 
 
 The lance is composed of a short steel blade fixed to the 
 end of a wooden handle about 10 to 16 feet in length. The 
 handle is furnished with a leather arm-loop placed over the 
 center of gravity. 
 
XXVI. — HAND ARMS. 
 
 After a long period of comparative disuse, in spite of the 
 greatly increased efficiency of small arms, its use abroad is 
 now becoming more general. In this country it has never 
 been successfully employed. 
 
 The bayonet is useful principally for guard duty and for 
 its moral effect. Like other hand arms, it has the merit of 
 "never missing fire." 
 
 The objections attending its weight and that of its scab- 
 bard, and its eccentric position in firing may be partly over- 
 come by combining its functions with those of the ramrod. 
 Attempts have also been made to turn it into an intrenching 
 trowel. The tendency is now to shorten it to the proportions 
 of a dirk, which may form a useful knife. 
 
 Cutting Arms. 
 
 The efficiency of these arms is promoted by increasing the 
 distance of the center of gravity from the handle, and by giv- 
 ing a curvature to the cutting edge so as to develop on impact 
 a tangential or slicing component which will call into play 
 the serrated edge possessed by even the sharpest knife. This 
 enables the weapon to rupture in detail the muscular fibers 
 on which it acts. 
 
 Description. 
 
 The principal cutting weapon is the saber. Sabers are 
 classified according to their use. In the U. S. service there 
 are two kinds, viz. : the cavalry saber and that for the light 
 artillery. 
 
 The cavalry saber, being used on horseback for thrusting as 
 well as for cutting, has but a slight curvature, a long blade, 
 and a basket hilt (properly a guard) which carries the center 
 of gravity toward the handle. 
 
 The light artillery saber being intended for hand to hand 
 conflict by troops, who for the service of their batteries are 
 
XXVI. — HAND ARMS. 
 
 dismounted, is shorter than the cavalry saber, is more curved, 
 and has a guard composed of a single scroll of brass. 
 
 Remarks. 
 
 The present tendency is to make the artilleryman depend 
 for his personal defence upon the gun which his duty to the 
 other troops compels him to serve to the very last extremity. 
 He should therefore be free from any incumbrance which 
 will distract him from his proper functions. 
 
 In order to avoid the exposure of the person in cutting, 
 many cavalry officers are in favor of avoiding the objections 
 to the combined functions of the cavalry saber by using it 
 solely for thrusting. 
 
 On the other hand the swordsmen of East India, than 
 whom there are few more expert, prefer blades which are 
 greariy curved, the radius of curvature of some being about 
 18 inches. 
 
 The following discussion illustrates the effect of curvature, 
 frequently utilized in the useful arts. 
 
 ^ "-V s' ^'"' 
 
 Let O S Ph^ the edge of a curved blade rotated around 
 O and striking at P with a blow, P F, at right angles to 
 OP, ThenP T=PPcQS(p =PF cos i^ Z' r is the tan- 
 gential component, and this will be measured by P P cos 
 C P Oj which gives an easy method of discussing the effect 
 of curvature. If, as in the artillery saber, S', the radius of 
 
XXVI. — HAND ARMS. 
 
 curvature, be shortened by placing the center at C ; or, if 
 as in some Eastern blades which have a tangential handle and 
 also in the common scythe, the center of rotation be placed 
 above the line P O, the value of cos (p will be increased and 
 so will the proportionate value of the tangential component. 
 On the other hand if, as in the cavalry saber, the handle 
 be lowered as to O, in order to increase the tangential com- 
 ponent in thrusting, the slicing component will decrease. 
 
XXVII. — SMALL ARM AMMUNITION. 
 
 CHAPTER XXVII. 
 
 SMALL ARM AMMUNITION. 
 
 The Eelation between Arms and Ammunition. 
 
 As seen in Chapter V, the efficiency of all fire arms has 
 been dependent principally upon the nature of their ammu- 
 nition. 
 
 This may be called the food of the gun as the means of 
 conveying it to the chamber is actually called the feed. As 
 a rule the gun must be made to fit the ammunition as a shoe 
 should be made to fit the foot. 
 
 MUZZLE LOADING AMMUNITION. 
 
 Powder and ball were originally carried loose; but for 
 some time the greater rapidity of fire with arrows at the 
 ranges common to both weapons, caused the latter to be 
 preferred. 
 
 Gustavus Adolphus made important improvements in the 
 ammunition. 
 
 He first provided separate receptacles for each powder 
 charge ; these were called cartridges from their paper 
 envelopes. (Latin charfa, paper.) 
 
 He subsequently combined the powder with the projectile 
 in the paper wrapper, which, until about 1865, formed the 
 principal ammunition for small arms. See Figure 1. 
 
 In addition to the comparative disadvantages of muzzle 
 loading arms cited in Chapter XI, may be named the vari- 
 able amount and condition of the powder in the chamber, 
 since the powder was but imperfectly protected from moist- 
 ure and was hable to be wasted in loadmg. There was also 
 
XXVII. — SMALL ARM AMMUNITION. 
 
 the danger of inadvertently loading tlie piece with more 
 than one cartridge at a time. Nearly one-half of the 
 muskets abandoned at the battle of Gettysburg were found 
 to contain more than one cartridge. 
 
 In spite of the theories of those who feared that increased 
 rapidity of fire would lead to a disastrous expenditure of 
 ammunition, there has always been the feeling expressed by 
 Frederick the Great in saying, that other things being equal, 
 " He who fires fastest hits most." 
 
 BREECH LOADING AMMUNITION. 
 
 Non-metallic Ammunition. 
 
 The state of the arts required the first breech loading 
 ammunition to be formed after the manner of that just 
 described ; and, as it was impossible to permanently prevent 
 the escape of gas by the close fitting of the parts of the 
 breech, the joint required for rapid loading was generally 
 placed in front of the chamber, from which position the 
 soldier would suffer least from the discharge. 
 
 To facilitate loading the section of the barrel containing 
 the chamber was caused to oscillate about an axis in rear; 
 so that, the paper cartridge having been broken for loading, 
 the bullet acted as a stopper to prevent the exposure of the 
 loose powder before the piece was closed. 
 
 This structure distinguishes a large class of arms, now 
 obsolete, which are known as having 7novable chambers. 
 This includes the Hall rifle, used in this country in the early 
 part of the century. It is believed to be the first breech 
 loading small arm used by troops. 
 
 The operation of such guns was necessarily slow and 
 defective. 
 
 METALLIC AMMUNITION. 
 
 Origin. 
 
 The primed metallic cartridge case, invented in France, 
 was first used by troops during our Civil War. It contained 
 
XXVlt. — SMALL ARM AMMUNITION. 
 
 all the components of the ammunition, under invariable con- 
 ditions, in an envelope which formed a gas check, and was 
 therefore adapted to arms in which the chamber was fixed. 
 
 Being rigid and of exact dimensions it could be and was 
 at first most extensively used in magazine arms, in which 
 the operations of loading are automatically performed. 
 
 Rim Fire. 
 
 In order to support it against the blow which exploded the 
 fulminating priming, and to extract the empty case, it was 
 provided with a rim. For simplicity of manufacture, and 
 because the arms in which it was principally employed con- 
 tained the cartridges in tubular magazines and were carried 
 by mounted troops, the fulminate,/, was placed within the rim, 
 as shown in figure 2. 
 
 This construction, although confusing the functions of the 
 rim and the primer, was intended to prevent accidental ex- 
 plosions in the magazine. 
 
 For the small charges of powder then used, the metal could 
 be made thin enough for certainty of fire, since it was com- 
 posed of soft copper. 
 
 Figure 2 shows that such a cartridge, having what is termed 
 a folded head, is necessarily unsupported by the walls of the 
 chamber for a length at least equal to the thickness of the 
 metal forming the rim. Consequently, as charges and pres- 
 sures were increased, the rim fire cartridges were found to 
 shear across the edge of the chamber ; and the copper was so 
 deficient in elasticity that they would resist extraction. 
 
 The quantity of fulminate contained in the rim was much 
 greater than was required for ignition at any one point, and 
 further tended to destroy the fold. The distribution was im- 
 perfect and misfires were frequent. 
 
 The cartridge could not be reloaded. 
 
XXVII. — SMALL ARM AMMUNITION. 
 
 Central Fire. 
 
 As metallic ammunition became more generally employed 
 in all arms, these objections led to the use of the center fire 
 cartridge, now universally employed ; these objections led 
 also for a time to the disuse of magazine arms. 
 
 The adoption of central fire permits the case to be strength- 
 ened indefinitely in the shearing plane ^ and to be made of 
 an elastic material like brass, the special elasticity of which, 
 developed by its manufacture, facilitates its extraction. It 
 also permits the reloading required by the great expenditure 
 of ammunition m target practice. 
 
 Folded Head. 
 
 The first center fire cartridges were made with folded heads, 
 as the arts then furnished no other method of forming the rim. 
 To avoid shearing, a thin, cup-shaped, gas check, as shown in 
 figure 3, was, and is still employed. This contains a central 
 hole to allow the flame from the fulminate, /, to pass through 
 the vents, vv^ in the anvil, a. 
 
 The Ordnance Department for several years made the copper 
 cup-anvil cartridge shown in figure 4. In this it was attempt- 
 ed to combine in one piece the functions of the gas check 
 and of the anvil. But these were inconsistent, and the cart- 
 ridge, although avoiding objections urged against a per- 
 forated head which contained a loose primer, was abandoned. 
 
 The limit of resistance to shearing was soon reached, 
 because, owing to the manufacture, the maximum thickness of 
 metal is that of the head. So that if a thicker or more elastic 
 metal was used misfires would result, unless the energy of the 
 blow required for ignition was so much increased that the 
 rapidity of fire was diminished. 
 
 The flat anvil, figure 5, demanded by the obhque firing 
 pin of the Springfield rifle, requires a more powerful blov/ 
 than does that shown in figure 3, and the thickness of metal 
 
XXVII. SMALL ARM AMMUNITION. 
 
 requires the firing pin to be sharp. On the other hand, the 
 anvil of figure 3 is well adapted to the axial blow of a flat 
 pointed pin. This requires less work in cocking and is less 
 apt to pierce the cap. 
 
 Solid Heads. 
 
 The state of the arts now permits the U. S. cartridge to be 
 made with a solid head, as in figure 5. The shearing plane 
 lies in front of the edge of the chamber even when, owing to 
 the yielding of its support, the case may be forced backward 
 in firing. 
 
 Certainty of ignition now requires that the anvil shall be 
 renewed at every fire. Consequently the primer is assembled 
 before issue with its anvil and fulminate complete. The 
 resulting variation in figure 3 is shown in figure 6. 
 
 An objection to the solid head cartridge arises from its un- 
 equal expansion when fired. The mouth, being thin, is more 
 firmly held by friction against the walls of the chamber than 
 is the thicker portion in rear, so that the latter may slide 
 backward to the extent permitted by its support. Cases 
 which have been often reloaded are found to tear across by 
 longitudinal stress. 
 
 The Morse cartridge, figure 7, provides for this by making 
 the head entirely separate from the body of the case. 
 
 Remark, 
 The influence of improvements in metallic ammunition has 
 probably reached its limit in the cartridge employed in rapid 
 firing cannon, Chapter XXIX, page 18. The size of the 
 cartridges which these employ is limited by the weight which 
 one man can conveniently handle. 
 
 METALS USED FOR CARTRIDGE CASES. 
 
 Copper was first employed on account of the ease with 
 which it could be worked. When alloyed with a small pro- 
 
XXVn. — SMALL ARM AMMUNITION. 
 
 portion of zinc it was until recently preferred by the U. S. to 
 brass, which, when in contact with gun powder, undergoes in 
 time a molecular change that renders it as brittle as baked 
 clay. It is said that the discovery of this defect in the 
 Russian ammunition postponed the war of 1877. 
 
 The deficient elasticity of copper accounts for the preva- 
 lence of the lever used for extraction in early breech loading 
 arms, and for their comparative slowness of fire. 
 
 Brass is cheap and so elastic that guns in which it is used 
 may be opened by the direct action of an axial bolt. For 
 the reasons given, Chapter XXVIII, page 6, the rapidity of 
 fire of such arms is increased. This is the metal now 
 generally employed. In order to protect it from the powder 
 the cavity may be varnished or tinned. 
 
 The elasticity of brass adapts it to reloading since resizing 
 is less necessary than with copper. 
 
 The operation of resizing is required by unavoidable dif- 
 ferences in the chambers of different guns. The brass cart- 
 ridges used in the rifle, Cal. 0.45 may often be reloaded for 
 use in the same gun without resizing them ; but owing to the 
 greater pressures found in the new Cal. 0.30 rifle, firing smoke- 
 less powder, resizing is always required for this arm. See 
 Chapter XXVIII, page 3. 
 
 Low steely when protected from oxidation, is proposed as a 
 cartridge metal, on account of its strength elasticity and 
 freedom from structural change. 
 
 MANUFACTURE OF METALLIC AMMUNITION. 
 
 The cartridge case may be made in two general ways, 
 viz. : 1st, by coiling by hand a thin sheet of metal into a 
 tube ; 2nd, by drawing the tube from a thicker disc as de- 
 scribed in Chapter XVIII, page 2. 
 
XXVII.— SMALL ARM AMMUNITION. 
 
 1. Wrapped Metallic Cartridges. Chap. XVI, figure 8 
 
 The metallic sheet is trapezoidal so as to increase the 
 thickness of the walls near the head. This gives the ex- 
 terior the conical form required for extraction, while the 
 interior being cylindrical retains its hold on the bullet. It 
 also increases the thickness of the flange by which the 
 case is riveted to Ihe separate disc that forms the head. 
 
 This method, the origin of which is evident, avoids the 
 use of the expensive machinery used in the second process, 
 so that in an emergency the manufacture could be easily 
 improvised. 
 
 The cartridge is serviceable, but neither waterproof, rigid, 
 nor exact enough in its dimensions, for all the requirements 
 of service. 
 
 2. Drawn Cartridges. 
 
 The operation of drawing necessarily leaves the exterior 
 of the tube cylindrical, so that the required variation in 
 thickness is obtained by varying the diameter of the 
 punch. 
 
 The primary draws are facilitated by removing by an- 
 nealing, (/. ^., heating followed by quenching), the special 
 elasticity developed by the previous operations. Chapter 
 XV, page 22. 
 
 After having been drawn to a length slightly in excess of 
 that required, the tubes are trimmed to an exact length to 
 prepare them for the operations of heading. 
 
 The mandrel, figure 8, supports the trimmed case in a 
 closely fitting die. A hunter of the proper dimensions first 
 forms the pocket for the primer, and a second operation with 
 a bunter, such as shown, causes the metal to flow into the 
 annular space provided for the rim. The pocket is then 
 vented. 
 
XXVII. — SMALL ARM AMMUNITION. 
 
 To facilitate extraction the case is tapered by forcing over 
 it a conical die. The cylindrical seat for the bullet is 
 simultaneously formed. 
 
 Components 
 
 The U, S. atwil is made from a copper wire of rectangular 
 cross section containing on one side a continuous groove. 
 From this are punched a series ot circular discs which form 
 the anvils, The edges of the discs are notched so as to 
 form a passage way for the flame of the fulminate,/, through 
 the notches, into the groove which bridges over the vent, z/, in 
 the head of the cartridge. 
 
 The bullet is composed of an alloy ot lead and tin ; the 
 latter metal, although it increases the difhculty of manufac- 
 ture, gives the hardness required to resist deformation in 
 the gun. Chapter XXVIII, page 3. 
 
 The bullet is made by compression between dies which 
 part on an axial plane. See figure 9. The cavity in the 
 base of the bullet may be varied to bring the bullets to an 
 exact weight. 
 
 The bullet is lubricated by being forced through a vege- 
 table wax so as to fill the cannelures, or grooves. This is 
 preferred to a fat, as it does not corrode the metals in store. 
 
 Common Operations 
 
 In the loading machine a measured charge of powder is 
 first deposited in the case and slightly compressed so as to 
 increase the density of loading. The bullet is next inserted 
 and secured by crimping the case upon it. 
 
 The finished cartridges are all inspected for weight and 
 dimensions. 
 
 The first is accomplished by a weighing machine which 
 rejects all that weigh less than a prescribed minimum. The 
 principal object of this operation is to detect charges in- 
 
XXVII. — SMALL ARM AMMUNITION. 
 
 sufficient to expel a projectile which might cause a subse- 
 quent discharge to burst the gun. 
 
 The gauging machine makes sure that every cartridge 
 will enter the gun. The gauging die, which is sUghtly 
 smaller than the minimum chamber, verifies the length of 
 the cartridge to the rear from the circle of contact between 
 the bullet and the rifling, the profile between these planes, 
 and the maximun radius of the rim. 
 
 For safety the primer is sunken below the plane of the 
 head. 
 
 The automatic operation of the machinery has greatly 
 reduced the cost of manufacture, and has thus removed one 
 of the principal objections to metallic ammunition. 
 
 The inspection merely precedes the proof. Chapter 
 XVII, page 18. This consists in firing a portion of the 
 daily product to verify the certainty of fire, the strength of 
 the case, to determine the volume of the charge, the com- 
 pression required for the standard velocity and above all to 
 test the accuracy of fire. 
 
 U. S. SMALL ARM AMMUNITION. 
 
 The following varieties are now made (1891) : 
 
 1. The rifle ball cartridge, /^^q, or about 70 grains of 
 powder and a 500 grain bullet. / V= 1280 / s. 
 
 2. The carbine ball cartridge, /o\- ^ ^-= 1150 / s, 
 
 3. The revolver ball cartridge, f^^. I V= 730 /j-. 
 
 4. The rifle and carbine blank cartridge, filled with com- 
 pressed powder that is protected by a varnished paper cup, 
 and retained by crimping the case so as to facilitate loading. 
 
 5. The revolver blank cartridge as in 4. 
 
 Important changes in this ammunition are now pending. 
 Their principles will be hereafter discussed in connection 
 with the arm. It is significant to observe that now, as here- 
 tofore, the adoption of the new arm awaits the perfection of 
 its ammunition. Chapter XXVIII, page 19. 
 
XXVIII. — SMALL ARMS. 
 
 CHAPTER XXVIII. 
 
 SMALL ARMS. 
 Classification. 
 
 Small arms may be classified according to the service in 
 which they are employed, as this determines the maximum 
 length of barrel, given to the rifle^ i\\Q carbine^ and W^q pistol. 
 
 Muzzle-loading arms, and breech-loaders having movable 
 chambers being now obsolete, breech-loading small arms 
 with fixed chambers may be classified into single loading and 
 magazine arms. 
 
 The latter class is now supplanting the former, because of 
 the moral and physical advantage of being able at will to 
 increase the rapidity of musketry fire. 
 
 Historical Sketch. 
 
 Some of the objections formerly made against the breech- 
 loader have been discussed in Chapter XXVII. To these may 
 be added the former fear that the mechanism might not endure 
 the accidents of service. 
 
 But the Prussian wars of 1864 and 1866, and the more 
 extended campaigns of 1870, proved that after a victory 
 there is generally time enough for repairs. 
 
 During the siege of Plevna in 1877, these conclusions 
 were emphasized by the use by the Turks, for the first time 
 in Europe, of the American Winchester repeater. 
 
 Although of a model now considered imperfect, its success 
 was conclusive. 
 
 It is now realized that the change from muzzle-loading to 
 breech-loading having established the advantages of rapidity, 
 the choice of a magazine arm is a detail to be determined by 
 
XXVIII. — SMALL ARMS. 
 
 independent considerations. The selection is attended with 
 many complications which, as in the past, relate principally 
 to the ammunition. Some of these will be hereafter dis- 
 cussed in detail » but it may be premised that, while the 
 power ol the weapon depends principally upon the abiUty of 
 its (human) carriage to resist recoil ; its continued operation 
 depends upon the number of cartridges which this carriage 
 can conveniently transport. 
 
 The development is thus limited by a physical constant. 
 
 COMPONENT PARTS OF B. L. SMALL ARMS. 
 
 I. THE BARREL. 
 
 Weight. 
 
 Except for considerations relating to the recoil and the 
 practical necessities of service, the general use of steel would 
 permit the barrel to be considerably reduced in weight. 
 
 Caliber. 
 
 Although the best results follow from adapting to each arm 
 its own ammunition, yet in order to meet emergencies the 
 cartridges for the rifle and the carbine may be interchanged. 
 These arms are therefore of the same caliber. 
 
 For the reasons stated in Chapter XVI, since the adoption 
 of the rifle principle the tendency has been to reduce the 
 caliber. The limit is fixed by questions of internal ballistics, 
 and also by the nervous shock communicated to the animal 
 struck. Upon the shock is thought to depend the " stopping 
 power " of a bullet that does not kill. 
 
 Until lately the limit was generally taken at about 0.45 
 inch, but recent experiments have induced many countries to 
 reduce it still further to about 0.30 inch. 
 
 The propriety of the change is still debated, and like many 
 others requires the test of war. The advantage may consist 
 in this : that a shock which might be insufficient to stop a 
 
XXVIII. — SMALL ARMS. 
 
 man in the heat of a close action may, at the long ranges 
 which the reduced caliber provides, be severe enough to cause 
 him to withdraw. But this would not apply to horses. 
 
 Rifling. 
 
 The cross-section of the rifling depends principally on the 
 nature of the bullet. If this be of a soft material, like lead, 
 the lands may be broad as in the Springfield rifle and con 
 versely, figure 15, if the metal be hard. The grooves should 
 be shallow and so formed as to be readily cleaned. 
 
 The increase of spherical density, which results from 
 reducing the diameter of a projectile of which the length, 
 and therefore the sectional density, is kept nearly constant, 
 has required a considerable increase in the twist, so that 
 special precautions have been required to prevent the pro- 
 jectile from shearing. Chapter XVI, page 10. 
 
 In the caliber 0.45 bullet this was done by alloying the lead 
 with tin, Chapter XXVII, page 8 ; the new bullet is more- 
 over coated with a thin jacket of a harder metal. Chapter 
 XXVII; Plates. 
 
 II. THE STOCK. 
 
 This forms the handle by which the barrel is directed. It 
 is made of wood on account of its lightness and strength and 
 its deficient conductivity of heat. 
 
 The form of the stock depends on the conformation of the 
 average man. 
 
 The butt is widened and curved so as to diminish the 
 pressure per unit of area due to the recoil. It is bent for 
 convenience in aiming. A rotary component of recoil is 
 thereby developed, which, if the crook be excessive, may 
 cause inconvenience to the firer. 
 
 The stock is necessarily weakened by being cut across the 
 grain to form a grasp, and more so by the present develop. 
 
XXVIII. — SMALL ARMS. 
 
 ment in the volume of the parts about the breech It is 
 consequently frequently made in two pieces, the /// stock 
 being of a rigid material, such as black walnut, and the butt 
 itoik preferably tough, as of elm. Chapter XV, page 12. 
 
 The support m rear of the barrel should be of sufficient 
 area to avoid permanent deformation; and that beneath the 
 barrel should not be unduly rigid, since otherwise the barrel 
 may be distorted by the effects of moisture upon the wood. 
 
 Ill THE SIGHTS. 
 
 The position of the rear sight is determined by the limit of 
 distinct vision, and is so taken that the two sights and the 
 object shall collectively be most plainly seen. 
 
 The sights are separated as far as convenience permits, so 
 as to rectify their ahgnment with the object. See Chapter 
 XXX, page 7. They admit of a permanent correction for 
 jump and a variable correction for range, drift and the effects 
 of wind. 
 
 The increasing flatness of the trajectory and the growing 
 rapidity of fire will, except for sharpshooters, probably 
 diminish the number of adjustments now given to the rear 
 sight. 
 
 It is probable also, that instead of providing an extension 
 to the slide for use at extreme ranges, a separate pair of sights 
 will be placed on the side of the arm. The ordinary func- 
 tions of the members of this pair will be reversed; that is, the 
 rear sight will be fixed and the front sight movable down- 
 ward, so that a considerable elevation may be attained with- 
 out great variation in the relative positions of the eye of the 
 marksman and the point of his body which receives the recoil. 
 
 It may be remarked that the requirements of sights for war 
 service and for target practice at kiiowti distafices are in many 
 essentials incompatible. 
 
XXVIII. — SMALL ARMS. 
 
 [V. THE MOUNTINGS. 
 
 The bands, screws, pins, etc., are intended to connect the 
 parts ; and the butt plate, tip and the extension of the guard 
 beneath the small of the stock are intended to protect from 
 wear and to strengthen the relatively perishable wood. 
 
 Functions. 
 
 V. THE BREECH MECHANISM. 
 
 The functions of the breech mechanism are five, viz. : to 
 open, load and lock the breech, to fire the charge, and to 
 remove the empty shell. 
 
 The manner in which these functions are performed 
 depends primarily upon the manner of opening and closing 
 the breech, as is shown by the following scheme : 
 
 Classification of B. L. Small Arms.* 
 
 o 2 
 
 a> ? 
 
 u ^ 
 
 ■5 « 
 
 as 
 
 Barrel, 
 which 
 
 slides 
 
 b 
 
 ...2. 
 ...3. 
 
 Breech 
 
 block 
 
 which 
 
 rotates 
 
 about J JUo axis of gnn. 
 an axis 1 Lto axis of gun. 
 which is [ 
 
 slides I Jltoaxis of gun 4. 
 
 ^^'"^^ 1 Lto axis of gun 5. 
 
 f 1 1 to axis of gun 6. 
 
 fin front of block 7. 
 
 L to axis . 
 of gun. 1 
 
 not in front of 1 
 block. I 
 
 No. Examples. 
 (Rare). 
 
 Revolvers t 
 Shot guns. 
 
 Bolt guns. 
 Sharps, (Krupp). 
 
 Joslyn, Warner. 
 ( Springfield, 
 I Remington. 
 
 Martini. 
 
 , movable chambers (obsolete) 9. Hall, Burnside. 
 
 Discussion of Table. 
 
 The mass of the barrel renders the classes, 1, 2, 3, unsuit- 
 able for the military service except when, as in revolvers, the 
 mass is greatly reduced. 
 
 * For a fuller discussion, see Report Chief of Ordnance, 1873. 
 
 t The classification ot these is difficult. For some reasons they may 
 be considered as movable chambers, and in other respects they may be 
 considered as an aggregation of barrels of reduced length. 
 
XXVIII. — SMALL ARMS. 
 
 Classes 5, 6, 8, are objectionable, as their operation does 
 not assist in loading the cartridge, but rather, as the French 
 say, to guillotine it. 
 
 They possess, however, the advantage of naturally resisting 
 the pressure which tends to blow open the breech or to 
 " unlock'' it. 
 
 Class 7 naturally forms a lever, formerly useful in forcing 
 into the chamber a deformed cartridge or in extracting one 
 that stuck. Arms of classes 4, 5 and 8 were frequently pro- 
 vided with levers. 
 
 Bolt System. 
 
 But, as the quality of the ammunition has improved, the 
 arms of class 4 7vithout levers^ have grown mto general use. 
 
 The following are the principal objections which have 
 hitherto prevented the more general adoption of the bolt gun, 
 although its advantages were recognized by the Prussians as 
 early as 1847. 
 
 1. The risk of premature discharge from striking an over- 
 sensitive cartridge in loading. 
 
 This was long considered an insuperable objection, but, as 
 will be seen, has been overcome by very simple means. 
 
 2. The danger resulting from the necessity of loading the 
 piece at a full cock. 
 
 This objection neglected the supreme advantage of the 
 rapidity of fire which results from suppressing a discontinuous 
 motion,* and which is further increased by the facihty with 
 which the reciprocating motion of the bolt adapts itself to 
 the demands of magazine arms. 
 
 To illustrate the latest type of this arm, the American 
 Lee system is described, as it contains in probably the best 
 
 *The word is used as in the drill book. 
 
XXVIII. — SMALL ARMS. 
 
 and simplest form the elements of the mechanism required 
 for performing the functions above named.* 
 
 Lee System (as single loader) Figures 1 and 2. 
 
 Descripiion, 
 
 The receiver, of approximately cylindrical form, is screwed 
 to the breech and receives the mechanism. It is bored out 
 and slotted to permit the axial motion of the bolt. The slot is 
 widened to the front to form the well of the receiver, through 
 which the operations of loading and ejection are performed. 
 
 The rectangular shoulder at a forms a support for the locking 
 mass, a\ of the bolt in firing, and the oblique edge at b gives a 
 short, spiral motion to the bolt as the locking mass is ap- 
 proaching or leaving its support. 
 
 The system is mortised vertically through the well to receive 
 the magazine. As this is a special feature of the arm, its 
 consideration is deferred until the features common to the 
 best bolt guns have been discussed. 
 
 The reciprocating motion of the bolt sets the whole 
 mechanism in motion. 
 
 The /ia7idle is placed in rear and is curved downward so 
 that the hand need not leave it in firing. 
 
 A lug diametrically opposite to the locking mass engages 
 with a corresponding recess in the bore of the receiver, so 
 
 *The Prussian Needle Gun used a combustible cartridge case, the 
 fouling from which tended to obstruct the chamber ; the joint was most 
 imperfectly sealed, the flames escaping not only around the end of the 
 bolt, but into the channel traversed by the firing needle. The tactical ad- 
 vantages of the arm, however, offset these very serious objections, so 
 that it was retained unchanged until adapted to metallic ammunition 
 after the war of 1870. 
 
 Its opponent in this war, the Chassepot, was of similar construction, 
 but possessed for the end of the bolt a gas check, from which that of 
 Colonel De Bange is derived. 
 
XXVIII. — SMALL ARMS. 
 
 that, by making the support symmetrical, certain objectionable 
 vibrations of the barrel may be avoided. 
 
 The bolt contains an axial firing pin which is surrounded 
 by a spiral main spring and secured to the hammer. 
 
 The bolt carries in front and to the right a hook shaped 
 extractor^ which, like the hammer, is so disposed as to share 
 only in the motion of translation which the bolt receives. 
 The extractor is retained by a flat spring which serves also to 
 key the system together. 
 
 Operation. 
 
 To open the piece, raise the handle so that the locking 
 mass may lie in the prolongation of the slot, and withdraw 
 the bolt. 
 
 The incipient rotation of the bolt is ingeniously commuted 
 into one of translation at each of its ends ; as follows : — 
 
 In rear, a radial projection on the bolt strikes an oblique 
 surface on the hammer and forces it back relatively to the 
 bolt until the point of the firing pin is retracted, or withdrawn 
 behind the plane surface in contact with the cartridge. To 
 avoid premature explosion the point of the firing pin is kept 
 back until the desired moment of discharge. 
 
 In front, the spiral motion due to the surface, b, forces the 
 bolt slowly back from the barrel so that power is obtained to 
 start the fired cartridge case from its seat. This slow and 
 therefore powerful motion of extractiofi is commonly used. 
 A rapid motion might cut through the cartridge rim and dis- 
 able the rifle. 
 
 As the bolt is withdrawn, the extracted case foflows until it 
 passes from the chamber. The rim then strikes the ejector 
 stud, a projection on the bore of the receiver opposite to the 
 path of the extractor. The case is thereby rapidly revolved 
 about the hook and ejected, or thrown clear of the gun. 
 
 A cartridge may then be dropped into the well, the bottom 
 
XXVltl. — SMALL ARMS. 
 
 of which is nearly continuous with the lower element of the 
 chamber. A reversal of the motions forces the cartridge into 
 ,<lace and locks the breech. 
 
 The surface, ^, now serves to prevent the shock referred to 
 on page 6, and also to make the motion of the hand con- 
 tinuous. 
 
 In the final motion of closing, the mainspring is fully com 
 pressed, or the piece is cocked, by the interposition of the 
 sear, the nose of which arrests the forward motion of the 
 hammer while the bolt moves on. 
 
 The U shaped sear spring acts against the trigger through 
 the sear; so, that when the trigger is drawn, the sear spring 
 is compressed, the sear is lowered -and the hammer allowed 
 to fall. 
 
 Remarks. 
 
 Opening^ closing and loading. These operations are safely 
 and rapidly performed. 
 
 Locking, The method is of great simplicity and affords a 
 sohd support. Jointed surfaces, however well made, permit 
 an objectionable displacement under the stress of firing. 
 
 Firing. The coiled spring is admirably adapted to the 
 purpose, since, owing to its developed length, the stress on 
 any of its spires is slight ; and, owing to its position on the 
 pin, it will continue to work, even if broken. 
 
 Extraction and ejection. These are readily performed, 
 Vven with inferior ammunition. 
 
 Assembling. The parts are few in number, strong and simple. 
 They are arranged so as to avoid the effects of rust and dust, 
 and are so connected as to be readily dismounted for cleaning 
 without the use of special tools. 
 
 MAGAZINE ARMS. 
 
 If by any means a succession of cartridges can be auto- 
 matically placed in front of the bolt as it is closing, a mag- 
 azine gun will result. 
 
10 JCXVIIl.— SMALt ARM§ 
 
 This has been accomplished in many ways which may be 
 classified. 1st. According as the niagazmes are tubular, or 
 box shaped, 2nd. According as they are permanently fixed 
 to the gun, or are detachable. The tubular magazines are 
 always fixed. 
 
 TUBULAR MAGAZINES. 
 
 These may lie either, 1st, in front, as beneath the barrel, 
 or 2nd, in the cylindrical volume lorming the small of the 
 stock and its prolongation in rear. 
 
 A spiral spring forces the contents of the tube toward the 
 receiver, and a valve regulates their entrance. 
 
 In the first class a carrier, operated by the withdrawal of 
 the bolt, raises the cartridges successively from the mouth of 
 the tube to the mouth of the chamber. See figure 3 for one 
 form of carrier. 
 
 The operation is that of the bell crank. Chapter XXIX, 
 figure 7^ 
 
 Advantages. 
 This form of magazine, used in the French Lebel Rifle, 
 adapts itself to the profile of the gun. When in front, the 
 capacity is large for cartridges which are short and thick, and 
 a simple trap door on the side permits the magazine to be 
 filled without opening the breech, /. e., luithout unloading the 
 gun. 
 
 Disadvafitages. 
 
 The cartridges lie end to end, and in firing are exposed to 
 shocks which may explode them or deform them sufficiently 
 to interfere with the regularity of the feed. 
 
 The feed acts in the direction of the longest dimension of 
 the cartridge. 
 
 For the front magazine the weight is not well distributed ; 
 and for that in the butt the capacity is smal^, and the filling 
 
XXVIII. — SMALL ARMS. 11 
 
 of the magazine is complicated with the unloading of the 
 gun. 
 
 The operation of filling is slow, since the cartridges are 
 passed in singly ; and, since nothing external indicates the 
 state of the supply, the control of the fire by the soldier, and 
 of the soldier by the ofticer is impaired. 
 
 The "Cut-off." 
 
 By a device which may limit the withdrawal of the bolt, 
 the magazine may be 'Wut-ojf and its contents reserved for 
 a suitable necessity. The piece meanwhile is used as a single 
 louder. 
 
 Such attachments are fragile and in moments of excitement 
 are confusing. When tried under such circumstances, they 
 have been found unsuited to the conditions of service. 
 
 BOX MAGAZINES. 
 
 By placing the cartridges side by side in a box, many of 
 the objections urged against the tube disappear. The 
 principal point to be decided relates to whether the box 
 shall be detachable or fix 
 
 1. Detachable Box- 
 
 An example of this type is seen in the Lee magazine, 
 figure 2, which consists of a box of sheet steel, in which the 
 cartridges lie over the feed spring, N. 
 
 The box is readily inserted through the mortise in the well 
 of the receiver into the position shown. 
 
 The operation of the bolt passes the cartridges in succes- 
 sion into the chamber, and acts as a valve to regulate the 
 ascent of those lemainmg to be fired. 
 
 A number of these magazines are carried by the soldier, 
 who IS expected to use his arm as a single loader until he 
 receives the order to fix magazines. 
 
12 XXVIII. SMALL ARMS. 
 
 This facilitates control by the officer, but the uncertainty 
 of the soldier as to the state of the supply may lead him to 
 go through the motions of firing with an empty arm. 
 
 The principal objection to the system applies to the ex- 
 cessive weight and cost of the box as a package, if many 
 magazines are carried; and, if but few, to the probabiHty of 
 losing so important a component in the act of replacing it 
 under fire. 
 
 2. Fixed Box. 
 
 I. A prominent arm of this type is the Austrian Mannlicher 
 rifle, figure 4. 
 
 The cartridges are held by their bases in a sheet metal 
 frame, the whole package being bodily inserted into the 
 magazine through the well of the receiver, where it is retained 
 by a spring latch, r, A follower^ /, impelled by a strong 
 spring, ^, lifts the column so that the top cartridges are suc- 
 cessively shoved into the chamber by the bolt. The fall of 
 the empty case through the bottom of the magazine warns 
 the soldier that the magazine is exhausted. 
 
 In a recent model the heads of the cartridges are so held 
 by the frame that they lie in the same plane. With this 
 model no special care is needed in inserting the frame into 
 the magazine; while in that shown, the obliquity of the frame, 
 caused by the step-like arrangement of the heads, may cause 
 confusion. 
 
 The device for locking the arm consists of a brace, b^ 
 attached to the bolt. It is forced downward in front of a 
 shoulder, t", in the receiver, by a wedge-shaped projection 
 below an axial stem to which the knob, k^ is attached. By 
 simply pulling on the knob, the brace is lifted from its seat 
 by the wedge, and the brace, knob and bolt slide out together. 
 
 This arrangement avoids the rotation of the bolt required 
 in the Lee and in almost every other bolt gun. 
 
XXVIII. — SMALL ARMS. 13 
 
 This arm cannot be used as a single loader. 
 
 2\ The Schulhojf magazine rifle, figure 5, may be used as 
 such or as a single loader. 
 
 The cartridges are carried in an annular box, beneath the 
 receiver. 
 
 The axial shaft, s, carries a radial plate, ox follower, f, that 
 ia turned m one direction by the act of opening the lid, /, 
 figure 6, and m the other direction by a spiral spring (not 
 shown) surrounding the shatt, which is twisted in the act of 
 opening. 
 
 The cartridges may be thrown in loosely, or may be loaded 
 in mass from the quick loader shown in figure 7. 
 
 A circumferential slide, <:, operated by the thumb piece /, 
 forms a very simple cut-off. 
 
 The strength and solidity of the magazine enables it to be 
 slit, so that the state of the supply may be seen at a glance. 
 
 The position of the box enables it to be filled without 
 unloading the arm. 
 
 Quick Loader. 
 
 A cheap quick loader, figure 7, containing the supply of 
 cartridges for one magazine enables them to be transferred 
 to it in mass when rapid recharging is required. For this 
 purpose the lower end of the quick loader being placed over 
 the mouth of the magazine the pressure of the thumb of the 
 operator on top of the column of cartridges forces them 
 down into the magazine against the resistance of the 
 magazine spring. 
 
 They are retained by a valve at the mouth of the magazine, 
 and the quick loader is then thrown away. The valve serves 
 to retain successive cartridges singly loaded. 
 Form Proposed. 
 
 The eventual preference of the fixed or the detachable 
 box magazine will probably be largely determined by moral 
 considerations. 
 
14 I XXVIII. SMALL ARMS. 
 
 The dispersed formations of future wars will probably 
 require a more extended exercise of discretion in the lower 
 grades than has hitherto been customary. The question 
 arises, how far down will the discretionary control of fire 
 extend ? 
 
 It is now proposed to attach the box magazine perma- 
 nently to the receiver, and ordinarily to load the arm con- 
 tinuously through the magazine, so that the cartridge last 
 inserted shall be the first to be fired and that the number 
 remaining shall be automatically held in reserve. 
 
 It is possible that the time gained by making the opera- 
 tion of the piece simple and invariable, as in the type pro- 
 posed, may be so utilized in the general instruction of the 
 troops that it will not be considered necessary to burden 
 them with an inferior weapon in order to control their fire. 
 
 REQUISITES OF A MAGAZINE ARM. 
 
 The preceding considerations enable us to name the fol- 
 lowing necessities : 
 
 1. The best ballistic conditions attainable. These may 
 modify the size and proportions of the cartridges, and so 
 affect the capacity of the magazine. 
 
 2. Consecutive rapidity of fire as a single loader as great 
 as that of any other arm, and the greatest possible inter- 
 mittent rapidity when the magazine is employed. 
 
 3. The possibility of filling the magazine with single car- 
 tridges, or " in mass," without unloading the piece. 
 
 4. A maximum capacity which is yet to be determined 
 by experience. It will probably be about 5 shots in the 
 magazine. 
 
 5. A ready view of the state of the supply. 
 
 6. The most simple construction compatible with the 
 maximum efficiency under the conditions of service. 
 
 Beyond a certain point objections to complexity become 
 
Xxviii. — Small arms. 18 
 
 pedantic, since experience shows that the instinct of self- 
 preservation may be counted on for the care necessary to 
 maintain an efficient arm. 
 
 THE SPRINGFIELD RIFLE. 
 
 History. 
 
 This arm, although originally intended as a means of 
 utilizing the large supply of muzzle loading muskets left by 
 the Civil War, has acquired a standing which, in 1886, 
 caused its preference by 73 per cent of the officers to whom 
 were submitted, for comparative trial in service, three of the 
 best magazine arms. 
 
 Apart from the excellence of its manufacture and the ease 
 with which it may be operated with but one hand, this pre- 
 ference may be attributed to the independent action of a 
 form of lock, the outgrowth of centuries of experience ; and 
 the perfection of the apparatus for extraction and ejection. 
 
 The design of the cam latch and of the firing pin are 
 exposed to criticism. 
 
 As a reserve supply of this arm is likely to be retained for 
 many years after the adoption of a magazine gun, a few of 
 its principles are described. The nomenclature is supposed 
 to be known. 
 
 Operation. Figure 8. 
 
 Locking. 
 
 When the piece is fired the tendency of the block to swing 
 upward out of the receiver, A^ is corrected by the loose fit 
 of the hinge pin, E^ in its hole. The block, therefore, sHdes 
 bodily to the~rear until stopped by the interposition of the 
 body of the cam latch F, between the block and the breech 
 screw, C. The journals of the cam latch are loose in their 
 bearings so that they may be free from strain. 
 
 The centre of pressure on the breech screw is brought 
 
16 XXVIII. — SMALL ARMS. 
 
 as nearly as possible in the prolongation of the axis of 
 the bore so as to diminish the tangential component of the 
 pressure, which tends to revolve the cam latch and tlirow 
 open the block. This is imperfectly resisted by the friction 
 developed by the normal pressure between the surfaces in 
 contact, and also by the combined action of the thumb piece 
 and the hammer, the functions of which are thereby perverted. 
 
 Extraction. 
 The power needed for extraction results from the compound 
 lever formed by the breech block and the extractor, J, 
 
 Ejection. 
 
 In opening the block the revolution of the extractor com- 
 presses the coiled ejector spring, K, until the action line of 
 this spring passes from above the axis of rotation to below it. 
 
 The expansion of the spring then rapidly revolves the ex- 
 tractor. This impels the cartridge case against the ejector 
 stud Z, which deflects it upward and throws it clear of the gun. 
 
 Firing Mechanism. 
 
 The lock, figures 9, 10, 11, consists of the lock plate, to 
 which the parts are attached and by which the mechanism is 
 secured to the stock by the side screws. 
 
 The hammer, A^ outside the lock plate, and the tumbler, B^ 
 inside of it form mechanically but one piece, the arrangement 
 adopted being required for the protection of mechanism from 
 dirt. 
 
 The tumbler, B, is connected with the mainspring by a 
 swivel, y, so disposed that the resistance to cocking the piece 
 shall be nearly constant. This is accomplished by the varia- 
 tion in the lever arm of the mainspring ; as the resistance of 
 the mainspring due to its compression increases, the action 
 line of the resistance passes nearer to the axis of the tumbler, 
 
kXVlIt. — SMALL ARMS. 17 
 
 while the lever arm of the power, the thumb, is constant. 
 The tumbler is thrice notched to receive the nose of the sear, 
 E. This, under the action of the sear spring, G^ maintains 
 the hammer at the distances from the head of the firing pin 
 required for convenience of transportation, safety of loading, 
 and certainty of fire, respectively. 
 
 The bridle, C, holds the parts together. 
 
 The oblique blow of the firing pin is objectionable. Chap- 
 ter XXVII, page 5. 
 
 RECENT DEVELOPMENT OF SMALL ARMS. 
 
 PHYSICAL CONSTANTS. 
 
 Owing to the mechanical improvements in the construction 
 of arms and ammunition the ballistic development of the small 
 arm is now limited by the soldier's endurance of its recoil. 
 Similarly its tactical employment is limited by his ability to 
 transport the burden of its ammunition ; for the maintenance 
 of the rapid fire of the extended lines now rendered possible 
 is a problem which increases in difficulty as the fire increases 
 in rapidity and range. 
 
 L Recoil. 
 
 These constants are influenced by racial peculiarities, and 
 may be considerably modified by training ; but the proper 
 training of large armies in the endurance of recoil implies so 
 great a cost, that the present tendency is to render the recoil 
 supportable by inexperienced troops, so that the accuracy of 
 their fire may not be impaired by their apprehension of its 
 effects.* 
 
 *Tlie effect of racial peculiarities, and incidentally of training, is shown 
 by the following data which relate to arms of caliber about 0.45 in. 
 
 In the relatively small armies of Great Britain and the U. S. the energy 
 of recoil IS about 14 ft. pounds. 
 
 The low average stature of the French fixes a limit of about 11 ft. 
 
18 XXVIII. — SMALL ARMS. 
 
 2. Burden. 
 
 Training in weight-carrying is not expensive, and its im- 
 portance is becoming recognized by the frequency with which 
 practice marches are made. As in the artillery service 
 Chapter XXIV, page 2, a judicious distribution of the bur- 
 den between the arm and its ammunition depends greatly 
 upon the former's recoil. 
 
 MODIFICATIONS OF THE RECOIL. 
 
 The recoil may be reduced by modifying the arm or the 
 ammunition. 
 
 1. Modifications in the Arm. 
 
 If the ballistic conditions are kept constant, the weight of 
 the arm may be reduced, and a greater number of cartridges 
 be carried, by : — 
 , 1. The use of an elastic cushion attached either to the gun 
 or to the clothing. 
 
 These plans are found impracticable. 
 
 2. Increasing the mass of the gun in firing by adding to it 
 that of a portion of the ammunition, as in magazine guns. 
 
 The correction is variable and sometimes injurious to 
 accuracy. 
 
 3. Storing up the energy of recoil as by the compression of 
 a spring, which, by its resihence may operate the piece. 
 
 pounds. But in Germany, although the ballistic conditions are nearly 
 identical with the French, the desire for durability has developed the 
 heaviest small arm known. Notwithstanding the strength of the Ger- 
 mans the recoil is only 10 ft. pounds. 
 
 In Italy, as in our service during the Civil War, about 7 ft. pounds is 
 allowed. 
 
 This IS the limit reached by the present reduction in caliber. The re- 
 turn to the former standard, page 23, is significant of its practical con- 
 stancy. 
 
XXVIII. — SMALL ARMS. 19 
 
 This has been tried, but so far without success, owing to the 
 complicated nature of the mechanism required. 
 
 4. The pressure due to the recoil may be distributed over 
 an increased area of the person by the proper use of the gun 
 sling. By lying down to fire, the path of the recoil is 
 shortened and the pressure on the body increased. 
 
 General consent seems to have established the weight of 
 the rifle at between 8.5 and 9.5 pounds. 
 
 2. Modifications in the Ammunition. 
 
 1. Caliber and Recoil Constant, 
 
 The advantages of any particular cahber being general, 
 that of all military rifles at any epoch is approximately con- 
 stant. It has recently been about 0.45 inch. See figure 12. 
 
 When the caliber and the weight of the arm are constant, 
 
 the recoil can be reduced only at the expense of the ballistic 
 
 properties of the arm. But these being maintained at the 
 
 highest value consistent with the recoil endurable in any 
 
 i 7n v V 
 particular case, the Equation M E ■=. C ^ - — - — - shows 
 
 that modifications in the ammunition must be confined to 
 factoring the momentum of the projectile. The following 
 considerations illustrate the effect of variations in m and z', 
 their product in any one case being constant. 
 
 a. If we increase w at the expense of z/, we lose in danger- 
 ous space at short and decisive ranges but conversely at long 
 distances. Chapter XX, page 40. 
 
 b. During the wars of 1870 and 1877 it was found advis- 
 able to deliver at extreme ranges an almost vertical fire 
 against masses of troops. 
 
 It has since been found that the extreme range increases 
 more rapidly with the sectional density of the bullet than 
 with its initial velocity. The present U. S. bullet was accord- 
 
20 XXVIII. — SMALL ARMS. 
 
 ingly increased in weight from 405 to 500 grains, and an 
 extreme range of two miles was attained. 
 
 c. It is found that the accuracy of fire at moderate known 
 distances is incompatible with tlie high velocities required in 
 actual service. This is probably due to the vibration of the 
 barrel. Page 4. 
 
 Conclusion. 
 
 Owing to the impossibility of simultaneously satisfying the 
 requirements of the different ranges, it is considered that 
 efficiency at long ranges should be sought by the use of special 
 means, such as machine guns firing heavy projectiles. For 
 small arms it is considered that accuracy should become sub- 
 ordmate to flatness of trajectory for ranges exceeding 600 
 yards, at which individuals cease to be distinguished by the 
 unaided eye ; and that the trajectory should be so flat that 
 but one height of the rear sight would be required within that 
 distance, and the smallest number of changes beyond it. 
 
 Differences of elevation within the limits of graduation 
 would be adjusted by varying the coarseness of the front 
 sight. Chapter XXX, page 2. 
 
 2. Caliber Variable. 
 These conditions can be attained, and the number of cart- 
 ridges in a given burden increased, by reducing the caliber. 
 Under the conditions named on page 2, the limit of reduc- 
 tion has been fixed by the difficulties of manufacture and by 
 those relating to the cleaning of the bore. 
 
 Small Caliber Rifle. 
 
 The following general principles govern the changes in 
 ammunition resulting from the reduction in caliber. For 
 simpHcity of treatment we will first assume the muzzle velocity 
 unchanged from the larger caliber. 
 
 Bullet, The sectional density, and therefore the length of 
 
XXVIII. — SMALL ARMS. 21 
 
 the bullet, has remained approximately constant ; since, as 
 shown in Chapter XVI, page 4, an increase in the sectional 
 density would increase the value of /„, unless the muzzle 
 velocity were reduced. 
 
 The strength of the barrel is not materially greater than 
 that of the caliber 0.45, and, owing to the reduction in the 
 area corresponding to the bottom of the bore, the increase 
 in the strength of the fermeture is only relative ; therefore, 
 the maximum value of p^ formerly allowed cannot be greatly 
 exceeded. 
 
 The sectional density being constant, the reduction in 
 caliber reduces the mass of the bullet, and therefore, although 
 the ballistic properties of the arm (being dependent only 
 upon the sectional density or C, Chapter XX, and the muzzle 
 velocity) would not be affected, the recoil would be reduced 
 
 (m' \ "^ 
 — ). With the weights of bullet given in the 
 
 following table, this would reduce the recoil from about 14 
 foot-pounds to about 3 foot-pounds. 
 
 Powder, This reduction being excessive, the normal 
 endurance of the soldier against recoil is utilized by increas- 
 ing the weight of the charge, and therefore the muzzle 
 velocity. 
 
 The baUistic properties of the arm are therefore improved, 
 figure 12, but the internal pressure* would be excessive unless 
 
 * If in Equation (D), Chapter XII, we place K^a^ /\=z C, and repre- 
 
 IV , . w 
 
 sent by (J = -jj the sectional density of the projectile, and by « = — 
 
 the ratio between the weight of the powder and that of the projectile, we 
 have, after reduction. 
 
 But if, as in the case considered, 6 is constant, /„ will vary with nj^. 
 
 From this it follows that if the same charge of the same kind of powder 
 were used in the Hebler rifle as in the Springfield, the pressure would be 
 nearly doubled. 
 
22 XXVIII. — SMALL ARMS. 
 
 the powder were made specially progressive. The value of 
 
 J for the cartridge shown in figure 14 is 11.43. See Table I, 
 
 Chapter XII. 
 
 In spite of these precautions the main difficulty in the new 
 small caliber high-powered guns is due to the excessive pres- 
 sures developed. 
 
 Powder. 
 
 The principal difficulties found in realizing the advantages 
 of a reduction in caliber exist in the powder. 
 
 It was thought by Professor Hebler, of Germany, to whom 
 much of the credit of the proposed change is due, that these 
 difficulties could be overcome by compressing the powder as 
 in a rocket, in a cartridge case like the Morse. Figs. 13, 14. 
 
 The objections to this method noted, Chapters XII, page 
 
 21 ; XVI, page 45, and the large volume of smoke resulting 
 
 from rapid fire, cause many to prefer a high explosive, such 
 
 as described, Chapter XIV, page 15 ; in spite of its recognized 
 
 objections. The complete solution of the problem is still 
 
 deferred. 
 
 Projectile, 
 
 The projectile proposed is distinguished by its penetration, 
 its cleanliness as regards the bore, and the nature of the 
 wounds which it inflicts, page 2. When they are flesh wounds 
 they are punctured rather than lacerated; but when they 
 involve the bones these are shattered. 
 
 Cartridge Case. 
 
 In order to avoid the increase in the length and weight 
 of the breech mechanism, resulting from the relative increase 
 in the length of the cartridge case, this is made bottle-shaped, 
 as in figure 14. 
 
 This unfits it for reloading with compressed powder, unless 
 the Morse cartridge be used ; the latter has been found too 
 delicate to endure reloading by troops. 
 
XXVIII. — SMALL ARMS. SS 
 
 In some cases the volume of the magazine has been 
 diminished by eliminating the rim and replacing it by a V 
 shaped groove, in which the hook of the extractor may 
 engage, figure 16. In order to faciUtate reloading with per- 
 forated cyhnders of powder, previously compressed, such as 
 c, the cavity is cylindrical ; the reduction in diameter being 
 made by a brass ring, r. The blow of the hammer is sup- 
 ported by XhQ front of the cartridge case. 
 
 Comparison. 
 
 The following table illustrates the advantages of the 
 reduced cahber, since it compares the present Springfield 
 rifle, which is one of the best of the arms recently used, 
 with the Hebler, which is a fair type of the arms proposed : 
 
 
 Springfleld. 
 
 Hebler. 
 
 Caliber, inches 
 
 0.450 
 
 0.296 
 
 Bullet, wt. grains, 
 
 500 
 
 225 
 
 Powder, wt. grains. 
 
 70 
 
 83 
 
 Sectional density, 
 
 0.353 
 
 0.367 
 
 Spherical density. 
 
 3.6 
 
 5.6 
 
 Twist in inches, 
 
 22 
 
 4.58 
 
 Twist in calibers, ratio about, 
 
 3 
 
 1 
 
 Initial velocity, f. s., 
 
 1280 
 
 1942 
 
 Cartridges, ratio of weights, 
 
 100 
 
 85. 
 
 Arm, weights pounds. 
 
 9.3 
 
 9.9 
 
 Maximum dangerous space, yds.. 
 
 880 
 
 440 
 
 Accuracy at 440 yds., ratio 
 
 1 
 
 3 
 
 Muzzle energy, foot-pounds. 
 
 1818 
 
 1882 
 
 Recoil energy, foot-pounds. 
 
 13.95 
 
 6.11 
 
 REVOLVERS, 
 
 As a military weapon the revolver is useful principally in 
 enabling a horseman to use but one hand in delivering a 
 rapid fire. In closed masses its employment is dangerous, 
 
24 XXVlll. — SMALL ARMS. 
 
 since it is difficult to fire to the front without striking the 
 horse or the leading files, and the shortness of. the piece 
 leads to accidents to those alongside. 
 
 It is therefore considered generally an inferior arm, and one 
 to be used only for personal defence and in maintaining dis- 
 cipline upon the field. Its ballistic properties need not be 
 greater than necessary to stop a man at 50 or 60 yards. 
 
 The revolver is one of the oldest forms of magazine arms. 
 Its present perfection is due to the invention of Col. Colt of 
 Hartford, who combined the cocking of the hammer with 
 the revolution of the cylinder. 
 
 Owing to the considerable moment of inertia of the loaded 
 cylinder, this tends when rapidly revolved to pass the position 
 in which the axis of the chamber next to be fired coincides 
 with that of the barrel. This is the principal difficulty found 
 in the construction of these arms. 
 
 To facihtate their operation, revolvers are sometimes made. 
 self'Cockifig, the action of the trigger causing all the motions 
 to be performed. For greater continuous rapidity of fire, in 
 which these arms, like many magazine rifles, are deficient, 
 the cartridges may be simultaneously extracted by sliding or 
 swinging the barrel and cylinder away from the breech. The 
 chambers may then be simultaneously reloaded by using 
 ammunition packed in clusters. 
 
 The complexity of these refinements and the limited scope 
 of the revolver generally cause simpler patterns to be pre- 
 ferred. 
 
 MANUPACTURE OF SMALL ARMS. 
 
 Where Made. 
 
 The service rifle and carbine are made by the Ordnance 
 Department at the National Armory. Pistols and such other 
 special arms as may from time to time be needed are bought 
 from private estabUshments. 
 
XXVIII. — SMALL ARMS. 25 
 
 How Made. 
 
 Efficiency in service and ultimate economy in manufacture 
 require that the similar parts of arms of the same model shall 
 be interchangeable. This is secured by the principle of 
 gauging, noted in Chapters IV and XVII. 
 
 Gauging. 
 
 The general design of a gun having been perfected, an 
 exact working model is carefully prepared. The component 
 parts are so formed as to be as far as possible adapted to the 
 operation of the varieties of the lathe. Chapter XVII, 
 page 13. 
 
 Each of the components is then examined with reference 
 to its gauging points. These are the surfaces between which 
 the most exact relations are required. 
 
 For surfaces of revolution like the barrel, or parts intended 
 to revolve like the Springfield breech block and the tumbler, 
 the gauging points are established with reference to the axis 
 of rotation. 
 
 For pieces subject to compression, like the bolt of the Lee 
 rifle, the greatest pains would be taken with the distance from 
 the rear face of the locking mass, a', to the front face of the 
 bolt ; and, in the receiver, with the distance from the shoulder, 
 a, to the plane containing the mouth of the chamber, since 
 the difference of these distance must be kept invariable in 
 order to insure the proper working of the ammunition. 
 
 While the first of these is readily gauged, the second in- 
 volves the relations between the barrel and the receiver ; 
 each of which must be similarly watched with reference to 
 their abutting surfaces. 
 
 When the number of such surfaces is considerable, as in 
 the Springfield mechanism, the sum of their possible errors 
 requires the closest gauging of each link of the chain of parts. 
 
 Many forms of gauges are employed. They may be 
 
26 XXVIII. — SMALL ARMS. 
 
 classified like patterns as positive or negative gauges, the 
 latter being sometimes simple notches, and sometimes mat- 
 rices so formed as to contain exactly pieces of an irregular 
 shape. 
 
 To retard their wear, the working surfaces of gauges are 
 made of hardened steel ; and, as steel tends in hardening 
 to change its form, these surfaces are finished in the hardened 
 state. 
 
 The number of gauges required not only for the finished 
 parts but for the intermediate stages demand that, before the 
 first arm of a series be produced, many thousand dollars shall 
 be expended in preparation. 
 
 When tlie gauges and the corresponding tools and fixtures 
 are made, the work goes on rapidly ; for the functions of each 
 workman are independent, and no time is wasted in fitting 
 the product of different hands. 
 
 In illustration: The model may cost $600 — the first hun- 
 dred guns made from the gauges $100 each, and the first ten 
 thousand, all equal in quality to the model, $15 each. 
 
 The sense of feeling is so much more acute than that of 
 sight, that by the use of guages differences far within the 
 limits of ordinary measurement may be detected. The thou- 
 sandth part of an inch is the customary unit, and this may 
 be subdivided practically according to the requirements of 
 the work. 
 
 The system more than anything else promotes the "division 
 of labor," upon which industrial prosperity depends ; and, by 
 substituting an absolute for a discretionary standard, it edu- 
 cates in a remarkable manner the workman upon whose skill 
 the value of the product is practically based. 
 
 OPERATIONS OF MANUFACTURE, 
 
 Barrels. 
 
 The principal operations are rolling, boring, turning, 
 straightening and rifling. The rolling is done as previously 
 
XXVIII. — SMALL ARMS. 27 
 
 described, Chapter XV, page 44. While hot the rough ends 
 of the tube are sawed off and it is straightened under a drop 
 hammer, after which it is annealed by the residual heat. 
 When cold the hard scale is removed by pickling in diluted 
 acid. 
 
 In the preliminary borings the revolving auger is drawn 
 through the barrel instead of being pushed, so as to keep the 
 hole straight.* The bore is then enlarged by rapidly re- 
 volving reamers whose cross sections are square. 
 
 In turnhig the slide rest is guided by a template so as to 
 produce a conical surface, and the barrel is kept from 
 springing by the back rest. 
 
 Straightenifig is performed by light blows of the hand 
 hammer appHed at points which are indicated by the shadow 
 of a straight edge reflected from the walls of the bore. This 
 operation requires a peculiar knack which very few can 
 acquire. 
 
 In order to secure uniformity in the rifling^ a number of 
 cutters equal to that of the grooves is provided and these 
 are transferred automatically between adjoining grooves at 
 the end of each stroke of the axial rifling rod. 
 
 This rod receives a combined motion of translation and 
 rotation, by which, as in rifled cannon, the spiral motion is 
 produced. 
 
 While in an intermediate stage, the barrel is proved by fir- 
 ing a very large charge of both powder and lead. 
 
 The final proof of the efficiency of the mechanism and 
 of the accuracy of the arm is made with service ammunition. 
 
 MANUFACTURE OF THE MINOR PARTS. » 
 
 The form is defined roughly by Gorging between dies. 
 
 *The adoption of the 0.30 caliber will increase the difficulty of boring 
 since the barrel may require to be rolled solid and bored under 
 compression. 
 
28 XXVIII. — SMALL ARMS. 
 
 The slow operation of a very powerful press permits many 
 parts to be reduced to nearly their finished dimensions 
 when cold. 
 
 The principles of milling, Chapter XVII, are used when- 
 ever practicable. The most complicated arms have thus 
 been made without requiring the use of the file. 
 
 The most interesting operations are those required to pro- 
 duce irregular forms. 
 
 Profiling. 
 
 The profiler is a sort of milling machine in which relative 
 motion in three coordinate directions can be produced between 
 the revolving mill and the work. To limit the relative dis- 
 placements the following arrangement is provided. See 
 figure 17. 
 
 To a table moving in a horizontal plane the work, W, is 
 clamped at a fixed distance from a hardened steel model, M, 
 of the finished part. 
 
 At the same distance from the mill, m, and with its axis 
 vertical, is a blank pin, /, of corresponding dimensions. We 
 thus have two pairs of parts ; one pair consistmg of the 
 model and the work and the other of the pin and the mill, 
 with relative motion between the pairs. When the mill begins 
 to cut it is necessary only to cause the pin to follow the pro- 
 file of the model in order to reproduce it in the work. 
 
 The intricate l^ed or matrix of the lock is thus formed with 
 the greatest accuracy in about one mmute. 
 
 Eccentric Turning. 
 
 This operation was devised by Thomas Blanchard, an em- 
 ployee of the National Armory, for the purpose of forming 
 the gun stock. It has been applied to many other useful 
 purposes, as in the manufacture of shoe lasts, spokes, and 
 even of statuary. Its principle is as follows: See figure 18. 
 
 In ordinary turning the cutter does not sensibly change its 
 
XXVIII. — SMALL ARMS. 29 
 
 distance from the axis during one revolution of the work and 
 therefore leaves behind it a partically concentric surface. 
 
 But in eccentric turning the cutter, C, which revolves after 
 the manner of a mill about an independent axis parallel to that 
 of the work, is caused to oscillate slowly in a plane normal 
 to the axis of rotation during each revolution of the work, JV. 
 This oscillation is produced by an iron model, J/, revolving 
 with and parallel to the work and resting against a blank 
 wheel, B, attached to the oscillating frame which supports 
 the cutter. 
 
 In concentric turning the cutting speed is due to the tan- 
 gential velocity of the work, and in eccentric turning the 
 high speed required in wood working is due to that of the 
 cutter. The motion of translation is similarly performed in 
 both cases. 
 
 The cutting edges are placed at progressively increasing 
 radial distances, so as to cut to different depths during each 
 revolution of the cutter. This principle is frequently applied 
 in revolving tools. 
 
 The developed length of the cuts required to turn a gun- 
 stock is 13 miles ; the operation takes about 8 minutes. 
 
 Blacking and Browning. 
 
 To protect the parts from rust and to prevent them from 
 flashing in the sun, small pieces are blackened by heating 
 them until they will ignite the oil with which they are covered. 
 
 The outside of the barrel is oxidized by coating it with a 
 dilute acid mixture and exposing it in a warm, damp place. 
 The loose coating of red oxide having been brushed off, a 
 permanent layer of black rust remains. Some parts are 
 rapidly oxidized by immersing them in fused nitre. 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 CHAPTER XXIX. 
 
 CANNON WITHOUT RECOIL. 
 
 The advantages of rapid fire from cannon would be 
 neutralized by the time required to readjust the aim, were 
 it not that means have been found to so control the recoil 
 that the piece may return, between shots, to its original 
 position and direction. Such systems may be said to be 
 practically without recoil. 
 
 They may be divided into two general classes. 1st. Those 
 in which the mass of the system is so great in proportion to 
 the momentum of the projectile that the velocity of recoil 
 may be neglected. 2nd. Those in which so much of the 
 energy of recoil of the piece is absorbed by an elastic resist- 
 ance that the piece will be automatically returned to battery 
 in time for reloading. 
 
 The former class contains the systems for which mobility 
 is essential, and the latter contains those that are stationary. 
 Some systems may ^be placed in an intermediate class, 
 requiring mobility and permitting recoil of the piece rela- 
 tively to its support. 
 
 FIRST CLASS. MACHINE GUNS. 
 
 Owing to the desire to simplify the supply of ammunition, 
 these pieces are frequently fitted to the cartridge used by 
 infantry. The conditions of transportation furnish the 
 mass required. Their ballistic properties restrict their 
 scope to the zone of infantry fire, within which their value 
 consists in the small number of men required for their service 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 and the consequent possibility of selecting the coolest 
 and most skillful men and of protecting them from the 
 enemy's fire. 
 
 The difficulties of transportation on land appear to assign 
 this class to the defence, for which service the concentra- 
 tion of its fire upon objects hidden by its own smoke, 
 renders it most valuable. 
 
 To this class in the present U. S. Service belong the 
 Gatling and the Gardner machine guns, which use the same 
 ammunition as the service rifle, and the Hotchkiss Revolving 
 Cannon, firing an explosive projectile such as described 
 Chapter XVI. 
 
 THE GATLING GUN. 
 
 Construction. 
 
 This gun consists essentially of a cluster of parallel mag- 
 azine bolt guns grouped cylindrically about an axial shaft 
 to which they are attached by circular diaphragms called 
 barrel plates. Each member of the combination is inde- 
 pendent of the others except that the magazine is common 
 to them all. 
 
 The rotation of a hand crank attached to the shaft brings 
 each member in succession opposite to the mouth of the 
 magazine where it is loaded, and operates the bolts so that 
 they progressively perform the functions noted in Chapter 
 XXVIII. 
 
 The manner in which this is accomplished is as follows; 
 see figures 1, 2. 
 
 ' Fixed upon the shaft, 6*, in rear of the barrels is a com- 
 posite fluted cylinder, C, each flute in which corresponds 
 to the well of tiliej receiver. Each flute carries a bolt, 
 Z, containing the essentials of the lock for a bolt gun. The 
 firing pin is peculiar in that it passes through the bolt and 
 terminates in a knob in rear. 
 
XXIX.— CANKON WITHOUT kECOlL. 
 
 From the rear of each bolt projects a radial lug. corre- 
 sponding to the handle of the ordinary rifle. These lugs 
 enter a cam groove fixed within the casing that surrounds the 
 fluted cylinder. This groove is essentially an oblique section 
 of the casing, the highest point of the section being in rear. 
 
 The constraint of the flutes and of the groove commutes 
 the continuous rotation of the cluster of bolts with respect 
 to the axis, into intermittent reciprocating motion with 
 respect to the barrel to which each bolt belongs.* 
 
 The upper and lower segments of the cam groove have 
 their planes at right angles to the axis of revolution so that 
 the developed groove is of the form shown in figure 3. The 
 resulting arcs may be termed the advancing and retiring seg- 
 mentSy a and r, and the loading and firing flats^ I and f. 
 The flats give the intermittent motion desired by interrupt- 
 ing the reciprocating motion cf the bolts; in the first case 
 to allow the cartridge time to fall before the bolt, and in 
 the second case to allow for the event of a cartridge ** hang- 
 ing fire." Such concentric surfaces are frequently found in 
 the cams used in machine guns. 
 
 The firing flat is at a distance in rear of the barrels exactly 
 equal to the length of the bolt; the loading flat is in rear of 
 the firing flat at a distance a little greater than that of the 
 cartridge. See figure 2. 
 
 The exterior casing, which supports the ends of the shaft, 
 the crank and the trunnions, is pierced above the front end 
 of the cylinder to admit cartridges from a detachable maga- 
 zine for which the casing provides a seat. 
 
 The sear is replaced by a grooved cocking rib, R, figure 3, 
 into which the knob passes as the bolt advances along the 
 
 * The principle has already been seen in the guide curve of the 
 torsional testing machine, Chapter XV. 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 segment, a. Just as the coiled mainspring attains its maximum 
 compression the lug on the bolt enters the firing flat, and 
 the termination of the cocking groove allows the firing pin 
 to fall. 
 
 The retraction of the firing pin and the extraction and 
 ejection of the empty shell are effected by means similar to 
 those already described for the small arm. 
 
 It is significant to observe how closely the latest type of 
 the magazine arm approaches the principles of the Gatling 
 gun, the essential features of which have not been changed 
 since its appearance in 1865. 
 
 Eemarks. 
 
 Each member is thus fired only once In each revolution, 
 but the number of members (5 or 10) is such that while the 
 individual feed is deliberate, the collective fire is rapid. 
 
 The bolts are interchangeable and can be readily removed 
 and replaced. Being independent of each other, the removal 
 of a disabled bolt affects only the intensity of the fire. 
 
 The crank handle may be attached directly to the shaft, 
 or, when power rather than rapidity is required, to a worm 
 gear on a shaft at right angles to the main shaft, as shown 
 in figure 1. In the latter case each revolution of the crank 
 causes one member to fire, whereas in the former case the 
 number of shots fired in each revolution of the crank is equal 
 to the number of the barrels. 
 
 Mounts. 
 
 The gun is mounted on a universal joint so that it may 
 be trained i. e. moved in azimuth, without disturbing the 
 position of the trail. 
 
 Instead of the wheeled carriage a tripod is sometimes 
 used, as in mountain warfare; but, though light, its want of 
 mobility is objectionable. 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 The Magazine. 
 
 With good ammunition the efficiency of the arm depends 
 largely upon the efficiency of the feed, and this upon the 
 form of magazine employed. 
 
 X. THE FEED CASE, 
 
 In the earlier models the magazine, or feed case, consisted 
 of a tin prism of trapezoidal cross section containing 40 
 cartridges lying horizontally one above the other, as in the 
 Lee magazine, inverted. These were surmounted by a 
 weight provided with a projecting thumb-piece to which an 
 assistant could apply the pressure necessary to prevent the 
 dislocation of the column from the shock of falling and of 
 firing. 
 
 In practice it was found difficult to prevent a cartridge 
 from occasionally entering the flutes obliquely and thus 
 jamming the gun; also, the longitudinal component of the 
 weight varied with the inclination of the gun. The risli of 
 jamming tended to retard the firing, which was further 
 delayed by the time required to refill the empty feed cases. 
 
 2. THE BRUCE FEED. FIGURE 4 
 
 This consists of two parts. 
 
 First, a coarsely toothed wheel revolving loosely in the 
 hopper just below the mouth of the magazine. This guides 
 the cartridges from the magazine to the fluted cylinder and 
 keeps their axes parallel to that of the shaft. It may be 
 used with all magazines. 
 
 Second, the detachable feed case is replaced by a semi- 
 permanent bronze standard, figure 5. The front face of this 
 contains two T sliaped grooves so arranged as to hold two 
 parallel columns of cartridges horizontally by the flanges 
 
XXIX. CANNON WITHOUT RECOIL. 
 
 around the heads of the cartridges. The grooves are readily 
 filled by entering into them the heads of the cartridges con- 
 tained in the pasteboard boxes in which they are issued to 
 the troops. 
 
 By pulling off the box at right angles to the grooves the 
 cartridges are left hanging in the position desired. Under 
 pressure from above, the grooved piece swings aside as each 
 groove is alternately emptied and directs the remaining column 
 into the hopper. 
 
 This arrangement enables the fire to be maintained as long 
 as the general supply of ammunition for the troops is available. 
 
 3. THE ACCLES' FEED DRUM. FIGURE 5. 
 
 This consists of a cylinder having two heads which are 
 at a distance apart about equal to the length of a cartridge. 
 On the inside of each head is a spiral groove * the pole of 
 which is in the axis of the drum, and the radial interval 
 between the spires is equal to the diameter of that end of 
 the cartridge in contact with the head. 
 
 Around the axis of the drum lie the radial arms of the 
 propeller. These divide the interior of the drum into sectors, 
 each of which contains a number of cartridges equal to the 
 number of intersected spires. The ends of the arms project 
 beyond the outer groove suflnciently to engage with the 
 flutes of the cylinder, so that when this cylinder revolves 
 the spiral groove is emptied from the outer end. 
 
 Thefeedisthusindependentof gravity, and the connection 
 between the fluted cylinder and the propeller arms is such 
 that each cartridge as it emerges from the drum is carried 
 parallel to itself and tangentially into the corresponding 
 flute. The synchronism thus attained permits the gun to 
 
 * The spiral is not truly geometrical, as seen by the figure. 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 be fired with certainty at any angle of elevation, and at a 
 speed that is limited only by the rapidity with which the 
 crank can be turned. It has been fired at the rate of 2000 
 rounds per minute and also at a elevation of 87 degrees. 
 
 The objections to the drum refer to its bulk and to the 
 (time lost in refilling it. It contains 104 cartridges. 
 
 THE GARDNER GUN. FIGURES 6, 7. 
 
 This consists essentially of two or more bolt guns placed 
 side by side, and surmounted by a magazine resembling the 
 Bruce feed guide, but without the valve. 
 
 The bolts are operated by a transverse crank shaft, or lock 
 cam, turned by a handle outside. The cranks are at 180 
 degrees from each other, and their crank pins, figure 7, ^, 
 work in vertical U shaped pieces in which the base of the 
 bolts are formed. 
 
 The contact surfaces of the notches are partly concentric 
 and partly eccentric with respect to the crank shaft; just 
 as the cam groove of the Gatling is partly at right angles, 
 and partly oblique to the axis of revolution. So long as the 
 contact surfaces are eccentric the rotation of the crank will 
 cause one bolt to advance and the other to retire. 
 
 When the crank pins are approaching the axis of the bore 
 the contact surfaces become concentric; the bolts then be- 
 come stationary; on one side to allow the cartridge to be 
 fired, and on the other side to allow the next cartridge to fall 
 into the well. 
 
 The reciprocating motion of the bolts operates a valve 
 that allows the cartridges to descend in alternate succession 
 from the grooves in the magazine. The valve swings hori- 
 zontally under the lid. See figure 7. 
 
 The advantages of the arm are its lightness, and the sim- 
 plicity and accessibility of the mechanism; as the lid cover- 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 ing the Interior can be readily raised. On the other hand 
 the rapidity of fire is much less than that of the Gatling, 
 since the number of barrels is less; and the dependence of 
 the feed upon the operation of both the bolts causes the 
 gun to be disabled by accidents to its ammunition. 
 
 THE NORDENFELT MACHINE GUN. 
 
 This arm, principally used in the British Navy, has 2, 4, 
 or more barrels arranged in a horizontal plane. In rear is 
 a corresponding row of bolts moved back and forth together 
 by a horizontal hand lever. The feed is by gravity through 
 a series of hoppers, one of these standing over the well of 
 each receiver. 
 
 The firing is practically by volley, although the interval 
 between the discharges may be varied by the rapidity with 
 which the lever is worked. 
 
 Accidents are said to have occurred from the explosion of 
 the magazine by the flame escaping from defective cartridges, 
 and igniting the ammunition in the adjacent magazine. 
 
 THE MAXIM AUTOMATIC MACHINE GUN. FIGURES 8, 9, 10, 11. 
 
 The distinguishing feature of this arm is its continuous 
 operation by the force of the discharge, and the necessarily 
 continuous supply of the ammunition afforded by the nature 
 of the magazine. 
 Peed. 
 
 The magazine consists of a series of belts, made of two 
 long strips of tape riveted together at intervals sufficient to 
 hold single cartridges between them. Each belt contains 
 334 cartridges, and, as they may be linked together, the 
 supply is continuous. The belt is fed transversely through 
 the gun so that the cartridges occupy successively a fixed 
 
XXIX. — CANNON WITHOUT RECOIL. 
 
 position over the chamber. From this position they are 
 automatically transferred to the chamber from which they 
 are fired. 
 
 Immediately 'beneath the chamber is the ejecting tube 
 through which the empty shells are successively passed for- 
 ward and dropped to the ground. 
 
 Construction and Operation. 
 
 Omitting many important particulars, the operation of the 
 arm is as follows: — 
 
 Construction. — The barrel is secured to a frame that has a 
 slight sliding motion from front to rear in the exterior casing. 
 In the rear end of this frame is journalled a double crank, 
 figure 8. The crank pin is connected by a connecting rod 
 with the breech-block in front. The breech-block slides 
 longitudinally within the frame to a greater extent than the 
 frame slides within the casing. 
 
 The ends of the crank shaft project through the casing 
 and are utilized as follows: — 
 
 On one end is an arm, d^ pointing downward and attached 
 at its lower end by a short chain, ^, to a powerful spiral 
 spring,/, the front end of which is fixed to the casing. 
 
 On the other end is a curved arm, /, pointing upward 
 and lying in front of a stop, g^ rigidly fixed to the casing. 
 On the same end of the crank shaft, but outside of / is a 
 handle, h. This handle receives from the crank a recipro- 
 cating motion of nearly 180 degrees, being limited on one 
 side by the flat spring, b, and on the other by the latch, / 
 The space, o^ shows the distance to which the frame can 
 recoil. 
 
 Before firing, the tension of the spring,/, brings the breech- 
 block in contact with the barrel and forces the latter to its 
 foremost position. The crank, crank pin and the connect- 
 
10 5txtx.— cannom without recoil. 
 
 ing rod are then in the horizontal plane containing the axis 
 of the barrel. 
 
 Operation. — When the piece is fired (by pressing with the 
 thumb on the trigger, /, meanwhile directing the aim with 
 the handles, m^ the barrel and frame with the included 
 parts begin to recoil together. 
 
 This motion brings the curved arm, /, against the stop, ^, 
 and rotates the crank downward with a motion which is 
 accelerated by the curvature of /. In so doing the connection 
 between the crank and the breech-block draws back the latter 
 faster and further than the barrel moves, and thus leaves room 
 for the cartridge to be loaded. At the same time the arm, d^ 
 winds up on itself the chain and puts on the spring, /, a 
 tension that tends to restore the parts to their original 
 position. 
 
 Ako the handle, h^ strikes the spring, b, which throws it 
 back to the latch,/, thereby assisting the restoration of the 
 parts by the spring, /. The cycle is now complete, as far as 
 regards the parts named. 
 
 Feeding. — The feeding ofthe ammunition, which, from what 
 precedes, is seen to be the motive power, is accomplished by 
 a peculiar extractor, x. This slides up and down in front of 
 the breech-block and, in an undercut groove on its front 
 surface, holds two cartridges by their flanges. One cartridge 
 is that last fired, and the other is that next to be fired. 
 
 When the block recoils the extractor pulls out these car- 
 tridges from the chamber and the belt respectively: and just 
 before the block advances the extractor drops, so as to bring 
 the fired case opposite to the ejector tube and the full car- 
 tridge opposite to the chamber. 
 
 After their entrance into their respective cavities the ex- 
 tractor rises, leaving the flange of the fired case unsupported, 
 (as the undercut groove extends only over the upper portion 
 
XXIX. — CANNON WITHOUT RECOIL. 11 
 
 of the face of the extractor) and embraces another cartridge 
 from the belt. The latter has meanwhile been moved along 
 one interval by a pawl actuated by the preceding machinery. 
 
 If, as is usual, the pressure on the trigger be maintained 
 during these motions another shot will be fired and the 
 motions will be repeated as long as the ammunition is 
 supplied. 
 
 Under these circumstances the rapidity of fire is 11 shots 
 per second. 
 
 The operation of the lock may be understood from an in- 
 spection of figure 11. The cocking power is applied to the 
 tumbler through a forked lever by which the connecting rod 
 is attached to the block. 
 
 The handle, //, is used to start the gun firing or to over- 
 come the stoppage resulting from a misfire. 
 
 As there is but one barrel, which in continuous firing might 
 become heated to excess, it is surrounded with a water jacket. 
 The recoil pumps a small quantity of water into this at every 
 fire; it is provided with holes for the escape of the steam 
 generated. 
 Advantages. 
 
 The principal advantages of this arm depend upon the 
 absorption of so much of the energy of recoil by the work- 
 ing of the parts that the weight of the carriage may be 
 greatly reduced without affecting its stability. The most 
 important results from this principle will be found in its 
 application to the field cannon hereafter described. 
 
 Another advantage results from the greatly increased 
 dirigibility of the arm, since it may be pointed like a hose 
 by the one man required for its service. 
 
 Considering the variety of the functions to be performed, 
 the rapid motion of the parts and their restricted space, the 
 construction cannot be called complicated. In such matters 
 
13 XXIX. — CANNON WITHOUT RECOIL. 
 
 it is better to seek simplicity of service tlian excessive sim- 
 plicity of construction. 
 
 GENERAL REMARKS ON MACHINE GUNS. 
 
 Owing to the excitement prevailing during the few 
 moments when rapidity of fire is of the greatest importance 
 the efficiency depends mainly upon: — 
 
 1. The quality of the ammunition, the food. 
 
 2. The certainty of its supply, the feed. 
 
 3. The facility with which the aim may be changed, or 
 the dirigibility of its fire. 
 
 1. The Food. 
 
 When compared with ordinary field artillery the range 
 and power of the infantry ammunition is so limited, the 
 correction of the aim so difficult, and the moral effect of 
 solid projectiles so small that machine guns of small caliber, 
 although rendered popular by their great mechanical effi- 
 ciency, will probably in service be relegated to the subordi- 
 nate purposes of the defense, and for use against an enemy 
 unprovided with artillery. 
 
 When compared with infantry operating in broken or 
 wooded ground their deficient mobility would often render 
 them an obstruction rather than a help; since only under 
 exceptional circumstances can they maintain their own 
 defense. 
 
 Owing to the suddenness with which, in order to produce 
 a decisive effect, their services are required it has been pro- 
 posed to attach them to small tactical units of infantry and 
 cavalry; but the objections above cited and the evident 
 difficulty of administering such scattered commands would 
 probably cause this plan to fail, as did the system of 
 battalion guns, which, after trial in the Seven Years War, was 
 abandoned. 
 
XXIX. — CANNON WITHOUT RECOIL. 13 
 
 The transport of the large amount of ammunition that 
 machine guns require compels the use of wheeled draught 
 (except in the mountain service) and therefore assigns them 
 to the artillery. The question then arises, whether, having 
 a given supply of men, horses and money, these means may 
 not be better utilized in the legitimate sphere of the artillery 
 rather than in providing a defensive arm of only occasional 
 utility. The preponderance of opinion seems to be adverse 
 to the general employment of machine guns of small caliber, 
 and shows that mechanical perfection must be subordinated 
 to tactical utility. 
 
 In the war of 1870 they were speedily silenced by the 
 German artillery and have not since been organized for 
 service in any European army. For naval purposes, where 
 the difficulties of supply hardly exist, and where the deploy-. 
 ment of a firing line is impossible, their value is greater, 
 although here they are giving way to the rapid firing guns 
 to be described. 
 
 2. The Feed. 
 
 The great rapidity with which the gun is operated is apt 
 to lead to "jamming" in case a cartridge should from any 
 cause fail to enter its proper chamber. The injury will be 
 aggravated from the natural tendency in moments of excite- 
 ment to overcome the obstruction by force. To this cause 
 may be attributed grave complaints made against these guns 
 during the recent fighting in the Soudan. 
 
 3. Dirigibility. 
 
 The dirigibility of these guns, except the Maxim, is im- 
 paired by the necessity of temporarily clamping them to resist 
 the deflection due to the operation of the crank. The accu- 
 racy is also impaired by vibrations due to firing. 
 
 The fire may be distributed by oscillating the piece ui a 
 
14 XXIX. — CANNON WITHOUT RECOIL. 
 
 plane parallel to the axle; but, if the line fired at be oblique 
 to this plane it will be cut at but one point. The difficulty of 
 sweeping a curved or oblique line is increased by the screen 
 of smoke and by the uncertainty of the point of nnpact. 
 
 In the Maxim gun these objections only partly apply, 
 since the pointing of the gunner is not interfered with by 
 the motions of the men at the magazine and at the crank. 
 
 THE HOTCHKISS REVOLVING CANNON. FIGURES 12, 13. 
 
 In its mechanical construction this resembles the Gatling 
 gun, but, as it fires an explosive projectile, it occupies a place 
 intermediate between the machine guns proper and the rapid 
 fifing guns to be described. 
 
 It uses primed metallic ammunition of a caliber the in- 
 ferior limit of which for explosive projectiles was, from 
 reasons of humanity, fixed by International Convention at 
 about one pound, and the superior limit of which is deter- 
 mined by the difficulties of the feed. 
 Operation. 
 
 The continuous revolution of the transverse crank shaft 
 causes the cluster of five barrels to revolve intermittently in 
 one direction. The interruption in the rotation enables the 
 single breech mechanism, whose motion is continuous, to 
 serve each barrel in succession, by simultaneously firing one 
 barrel, loading another and extracting the empty cartridge 
 case from a third, while the cluster is at rest. These oper- 
 ations are performed at every rotation of the crank, during 
 half of which period the cluster is at rest. 
 
 The cartridge is supported by a r.tationary breech, in front 
 of which the cartridges circulate an i through which the firing 
 pin passes at the lowest point. 
 
 The feed is by gravity through a trap door, which, being 
 raised by the advance of the loading bolt, admits but one 
 
XXIX. — CANNON WITHOUT RECOIL. 15 
 
 cartridge at a time. The rapidity of fire is from 30 to 60 
 
 per minute. 
 
 Remarks. 
 
 The gun compensates for the relative infrequency of its 
 fire by the use of an explosive projectile, each fragment of 
 which may cause a hit. This permits the aim, which is 
 normally deliberate, to be further corrected by ob.erving 
 the point at which the projectile explodes. A percussion 
 fuze is used. 
 
 The strength of the parts of the breech mechanism and 
 their accessibility compensate for the dependence of the 
 performance of the gun as a whole upon that of each of its 
 constituent parts. 
 Employment. 
 
 The Revolving Cannon was originally devised to defend 
 vessels from the attacks of swift torpedo boats, the time 
 allowed for firing at which, between their discovery and the 
 impact of their torpedoes, might not exceed two minutes. 
 
 It has been attempted to introduce it into the field service; 
 but the relation between the caliber and the weight of the 
 piece and carriage has so far prevented its systematic adop- 
 tion. For, while in the naval service perforation is of the 
 utmost importance, and the operation of the percussion fuze 
 is rendered certain by the nature of the object first struck; 
 in the field the use of shrapnel ignited by an adjustable time 
 fuze against animate objects is more important, since against 
 defenses the Hotchkiss shell is powerless. Against field 
 defenses indeed, it is curved fire with reduced charges and 
 large projectiles that is required, rather than the flat trajectory 
 needed for penetration. 
 
 For these reasons the Revolving Cannon has been princi- 
 pally confined to the naval service, in which during the war 
 between France and China, in 1881, it was most effective. 
 
16 XXIX. — CANNON WITHOUT RECOIL. 
 
 An exception may be made as to its use in defending capon- 
 nieres, for which purpose, as the range is constant and mo- 
 bility IS not necessary, the gun is well adapted. In this 
 service canister is employed, and the barrels have each a 
 different twist so as to distribute their fire with uniformity 
 over the area to be swept. 
 
 SECOND CLASS. RAPID FIRING GUNS. 
 
 These are single barreled and may be classified according 
 to the means by which they are loaded as: — 
 
 1. Hand served, or non-automatic. 
 
 2. Automatic, in varying degrees. 
 Object. 
 
 These arms may be said to have been developed from the 
 later type of machine guns by the improvements in the 
 offensive and defensive power of torpedo boats. Their 
 proper employment on shore has yet to be determined; but 
 in the naval service, in which their development is limited 
 only by the weight of the ammunition to be handled, they 
 have rapidly increased from the comparatively recent 1 pdr. 
 and 6 pdr. to the 6 in. 100 pdr., and have made great 
 changes necessary in the armament of vessels.* 
 
 * As the power of the gun Jincreased, the weight of the armor in- 
 creased so that but few vessels are able to carry enough armor to protect 
 the entire surface exposed to fire. The armor is therefore often concen- 
 trated over the vital portions, and the ends left with little or no protection. 
 Against the light armor required by these conditions, and now generally 
 used, the rapid fire of guns small enough to be easily directed and large 
 enough to carry an effective bursting charge, would be very destructive. 
 Compared with a heavier caliber, the aim could be more easily corrected, 
 the number of rounds for a given stowage capacity be increased, and the 
 striking energy of the shell being sufficient to penetrate the target, their 
 explosion would riddle it sufficiently to endanger the stability of the vessel. 
 The effect would be increased by repeated impact in the same spot so that, 
 
XXIX. — CANNON WITHOUT RECOIL. 17 
 
 The Italian ironclad "Piemonte" built in England in 
 1889, is the most striking illustration of the principle in- 
 volved. In a given time she can fire more than twice as 
 great a weight of metal as any vessel afloat, including those 
 costing five or six times as much. The 33 pounder with 
 which she is largely armed has hit a target 6 feet square 
 five times in succession in 81 seconds at a range of 1300 
 yards. Suppose the target to be a torpedo boat, advancing 
 to attack the vessel carrying the gun at a speed of 20 knots 
 per hour, (35 f. s.) and capable of effectively discharging 
 its torpedo at a distance of 300 yards; she would be under 
 fire for 86 seconds, during which time 20 shots might be 
 fired, as against 2 or 3 shots from an ordinary breech load- 
 ing cannon. A similar advantage would follow great rapidity 
 of fire at the ports of an armored structure during the short 
 time that they would be exposed to fire. There would be 
 not only the chance of entering the port with shell, but that 
 of disabling the gun, as it has been found that the chase of 
 
 principally on account of their accuracy, the aggregate effect in a given 
 time produced by a given weight of rapid fire guns would be greater than 
 that of a smaller number of heavy cannon. The question involves the 
 determination of the best utilization of that fraction of the entire displace- 
 ment of the vessel that is allowed for its offensive power. This is small, 
 being in the neighbourhood of 7 per cent. 
 
 For the reasons given Chapter XVI, page 21, armor piercing pro- 
 jectiles are becoming more and more restricted in their "mining power." 
 It is thought that a 4 inch plate of the best quality will explode any high 
 explosive fired against it as a bursting charge, before penetration is 
 effected. 
 
 From what precedes it will appear that the present state of the question 
 is that of a reaction from the idea which considers the ship as but a float- 
 ing carriage for the heaviest gun that it can carry. 
 
 When tested in battle the truth will probably be found to lie between 
 the two extremes, and the best results to be obtained by a proper appli- 
 cation of the principle of the independence of function. 
 
18 XXIX.— CANNON WITHOUT RECOIL. 
 
 a modern gun can be penetrated by the armor-piercing pro- 
 jectiles fired from R. F. guns. 
 
 One great advantage of these guns would be, that as the 
 attacking vessel approached and as therefore the flatness of 
 the trajectory increased, the elevation would not require 
 sensible adjustment between shots, and the target could be 
 "followed" by the gunner; his eye being on the sights, his 
 finger on the trigger, and the piece being directed by the 
 motions of the body as hereafter described. 
 
 GENERAL PRINCIPLES. 
 
 The development of R. F. guns has followed improve- 
 ments in the ammunition and in the 7tiounts, as are called 
 the means of supporting and directing the gun. 
 Ammunition. 
 
 Rapidity of fire results from the use of a simple fermeture 
 in connection with self primed metallic ammunition con- 
 structed on the same principle as that used in small arms. 
 
 The size of the cartridges is now limited only by the diffi- 
 culty of expeditiously handling tl m. That for the 33 pdr., 
 containing about 12J lb. of powc jr and weighing complete 
 about 50 lbs., is as heavy as one man can load with ease. 
 That for the 70 pdr. requires the united efforts of two men, 
 the greatest number that can be employed about the breech 
 without interfering with the gunner. For large calibers the 
 projectile is sometimes loaded separately; in this case rapid- 
 ity of fire depends solely on the mount. 
 Mounts. 
 
 The mounts are of two classes, depending upon the rela- 
 tion between the energy of the recoil and the character of 
 the emplacement. When the latter is relatively strong 
 Non-Recoil Mounts may be used, as in firing light guns from 
 
XXIX. — CANNON WITHOUT RECOIL. 19 
 
 ships and heavier guns from masonry emplacements. The 
 structural elasticity of these mounts absorbs the recoil and 
 returns the piece to battery. 
 
 When the emplacement is not rigid enough to resist the 
 recoil, Recoil Mounts must be used, as in the field service. 
 In these springs or hydraulic buffers distribute the pressure 
 over a longer path than in the former case. 
 
 In all cases the aim is corrected by a crutch shaped stock 
 which the gunner holds against his shoulder with one hand, 
 while the other hand rests on the trigger. 
 
 The piece thus becomes almost as dirigible as a small 
 arm, and is particularly adapted for firing from an oscillat- 
 ing platform at objects with relative motion, as in naval 
 combats. In non-recoil mounts the stock may be faster.jd 
 to the gun, but in the other class it must be fastened to the 
 mount. 
 
 Figure 14 shows a crinoline or cone non-recoil mount; and 
 figure 15 a type of the recoil mount. In this figure, b, is 
 the buffer and, j-, s^ springs intended to return the piece to 
 battery by their action on the bent levers, /, /. 
 Hotchkiss Mountain Carriage. 
 
 Figure 16 shows a non-recoil mount for a mountain car- 
 riage. The carriage as a whole is kept from sliding by the 
 brake and by a transverse plate under the trail plate called 
 the spade. The spade may be sunk into the ground by the 
 weight of a man standing on the wifigs of the trail plate, 
 and by that of the gunner on the seat. 
 
 The cheeks are unusually high, permitting the gun to be 
 fought without wheels in exposed positions. A slight play 
 in azimuth is allowed, since this greatly facilitates aiming, 
 and the lateral component of the recoil is insufficient to 
 affect the stability of the piece. 
 
 To facilitate transportation the stock is in two pieces. 
 
20 XXIX. — CANNON WITHOUT RECOIL. 
 
 The elevating gear is detachable; when used without it. 
 the system resembles a large pistol on wheels. 
 Hotchkiss Field Carriage. 
 
 Figure 17 shows a recoil mount; the carnage consisting 
 of three main parts and the wheels. 
 
 These parts are: — 
 
 1. The stock, s, secured to the axle. 
 
 2. The chassis, ^, which has a limited motion in azimuth 
 by means of the training screw^ T. 
 
 The top carriage, t c^ to which is attached the ele- 
 vating screw, e. 
 The top carriage is allowed considerable recoil on the 
 chassis; being limited by the buffer^ b, and restrained by three 
 oblique spiral springs on each side. These are fastened at one 
 end to the top carriage and at the other end to the chassis. 
 Powerful brakes, B^ B, lock the wheels and are assisted 
 by the spade. The brakes are connected by the brake bar., 
 This is slung from the axle by two rods, so that in march- 
 ing it may be hooked up under the trail. 
 
 CONSTRUCTION OF THE AMMUNITION. 
 
 Cartridge Case. 
 
 This may be either solid drawn as in small arms, or built 
 up. In the latter case, for economy, the tube forming the 
 body is bent in at the base and riveted between two cups 
 by a wrought iron disc that forms the head, as shown in 
 figure 18.* For greater certainty of fire the primer is renewed 
 at every reloading. 
 Drill Cartridge. 
 
 That shown in figure 19 is of soft material formed to the 
 full size of the cartridge about a section of the service musket 
 
 * It is now proposed (1890) to electro-weld the head to the bottom of 
 the tube. 
 
XXIX. — CANNON WITHOUT RECOIL. 21 
 
 barrel. From this barrel the service cartridge may be fired 
 at drill. This familiarizes the gunners with the service of 
 the piece in action without requiring the great expense 
 attending the use of the regular ammunition. 
 Projectiles. 
 
 Shell and shrapnel are provided. The former'use a base 
 percussion fuze and are either of cast iron or of forged and 
 tempered steel according to the use required of them. 
 
 CONSTUCTION OF THE GUN AND FERMETURE. ^ 
 
 Gun. 
 
 Except for the smallest calibers, this is a built up steel 
 gun, the type of which for medium calibers is represented in 
 figure 20. 
 
 The jacket carries both breech-block and trunnions so as 
 to relieve the tube from longitudinal stress. The enlargement 
 of the jacket in rear increases the bearing surface of the 
 breech-block. 
 Fermeture. Figures 21, 22, 23, 24, 25. 
 
 This resembles that of the mountain gun already described; 
 but it differs from it in that the motion of the block being 
 vertical, its own weight helps to open it. The mechanism is 
 contained in and about the block, and is situated so as to be 
 most easily accessible for repairs. 
 
 It consists of the following parts : 
 
 B, the block, the left side of which contains three shallow 
 grooves, viz.: 
 
 g g — the guide groove. 
 
 s g — the s/op groove. 
 
 X g — the extractor groove. 
 
 Note. — To the late B. B. Hotchkiss, an American whose works were 
 in France, is due the first practical application of the principle of rapid 
 fire guns. His system is that generally used in this work to illustrate 
 these principles. Many variations of his methods have arisen, some of 
 the more important of which will be discussed. 
 
22 XXIX. — CANNON WITHOUT RECOIL. 
 
 On the right side is another guide groove, g' g' j and s w, 
 the stud ivay; beneath which is a wide triangular recess, 
 c w, the crank way. 
 
 The double lever, L, is secured to the crank shaft, c s, 
 which passes through the side of the breech, and terminates 
 inside in the crank, c, on the upper end of which is the 
 stud, s. 
 
 The hub of the double lever is formed into the cocking 
 toe, c t. 
 
 The hanifner, h, is secured to the rocking shaft, r j, by a 
 spline (see Webster), so that it may be assembled with the 
 rocking shaft and yet revolve certainly with it. The rock- 
 ing shaft traverses the lower front quarter of the block. 
 Its right hand extremity forms the cocking arfn, c a, project- 
 ing so as to revolve in the same plane as the cocking toe 
 above it. 
 
 The double-leaved 7nain spring, in s, presses up the rear 
 end of the hammer, and pulls it down in front through the 
 swivel, s V, thus diminishing the friction of the rocking shaft 
 in bearings. The main spring is kept from moving as a 
 whole, by engaging its folded end in a notch in the rear 
 portion of the block. 
 
 The sear, s', is pivoted to the block just below the rocking 
 shaft, and is constantly pressed up by the sear spring, s s. 
 
 When the block is in place, the extremity of the sear 
 comes in contact with the front end of a bent lever forming 
 the trigger, T. This trigger plays in the pistol grip which 
 is rigidly connected with the breech. 
 
 Stock. Figure 14. 
 
 To the left side of the piece in non-recoil guns; or, in 
 recoil guns, to that portion of the carriage which does not 
 recoil, is fastened the stock. 
 
XXIX. — CANNON WITHOUT RECOIL. 23 
 
 A rubber tube forms a cushion for the gunner's left 
 shoulder. 
 
 The handles beneath serve for grasping with the left 
 hand at different elevations. The right hand then holding 
 the pistol grip, the piece may be aimed by the motions of 
 the body, and fired at the exact moment that the object is 
 pierced by the line of sight. 
 
 OPERATION OF THE FERMETURE. 
 
 To open the Piece. 
 
 Turn the most convenient handle to the rear. In the first 
 portion of its motion the crank stud travels in the concentric 
 portion of the stud-way so that the block does not move; 
 the direction of the stud-way then changing, further rotation 
 causes the block to fall until it is arrested by the stop screw. 
 The crank finally becomes nearly horizontal. 
 
 During the first portion of the rotation of the lever the 
 cocking toe presses upon the cocking arm and revolves it, 
 and with it the rocking shaft and hammer, until a notch 
 upon the rocking shaft has engaged with the sear. At this 
 moment the whole block, including the hammer, begins to 
 fall. 
 
 The extractor operates as in the mountain gun already 
 studied. Owing to the slight inclination of the groove x g 
 to g g, the first movements of the extractor are relatively 
 slow, developing great power. Ejection follows when the 
 abrupt change in the inclination oi x g reaches the stud on 
 the extractor. 
 
 To close the Piece. 
 
 The rotation of the levers is reversed. The beveling of 
 the front face of the block facilitates the insertion of the 
 cartridge, as in the mountain gun. 
 
24 XXIX. — CANNON WITHOUT RECOIL. 
 
 To lock the Breech. 
 
 The weight of the block tends to keep the piece closed, 
 since the vertical through s passes in front of the center of 
 the crank shaft. 
 
 In recoil, the moment of the upper lever also tends to 
 tighten the joint 
 
 THE NORDENFELT R. F. GUN. FIGURES 26, 27, 28. 
 
 This is principally intended to overcome an objection to 
 the Hotchkiss system, that is based upon the guillotining 
 action of its block, in case the cartridge is not fully inserted 
 into the chamber before the breech is closed. 
 
 Its operation resembles that of the Hotchkiss, but in its 
 construction the breech-block is divided by a plane of right 
 section into the block proper, B, in front; and the wedge, 
 W, in rear. 
 
 The upper rear porti6n of the wedge forms a convex 
 cylindrical surface with its elements at right angles to the 
 axis of the bore. 
 
 The first motion in opening the breech gives a downward 
 movement to the wedge, the block remaining at rest. As the 
 hand lever continues to move, the block and wedge revolve 
 downward and backward together, so that when, as in clos- 
 ing, these motions are reversed, the cartridge is pressed 
 home. This arrangement permits the cartridge to be actually 
 
 Note: — Observe \h^ face plate, fp, and the detachable hammer point 
 both good examples of independence of function. 
 
 The breech-block may be dismounted by opening the gun after 
 removing the stop-screw. In this case the crank is revolved downward 
 into a cavity formed for this purpose on the right face of the breech-block. 
 The crank may be turned so as to emerge to the front from the groove; 
 the block, being no longer supported on the stud, will then drop. 
 
XXIX. — CANNON WITHOUT RECOIL. 25 
 
 thrown into place, as its base may rebound several inches 
 without affecting the rapidity of fire. 
 
 MAXIM R. F. GUN. FIGURES 29, 30, 31, 32. 
 
 Nomenclature. 
 
 The breech-block C, slides vertically in the barrel, A^ and 
 not in the jacket, as is usually the case. 
 
 The barrel slides back and forth for about six inches in the 
 relatively thin jacket, £. 
 
 The jacket carries the trunnions, and beneath it is attached 
 the cylinder of the hydraulic buffer, Z>. The piston rod of 
 the buffer is attached to the barrel in rear, and is surrounded 
 by a powerful helical spring lying within the cylinder. This 
 spring gives the counter-recoil as in the smaller model. 
 
 Beneath the mouth of the chamber the barrel is traversed 
 by the rocking shafts K^ to which are rigidly attached two 
 curved arms of which but one, y, is shown. The arms are 
 united in rear by a cross pin, J/", that plays in a slot, iV, 
 passing through the block. 
 
 The extractor, in one piece, is composed of the upper 
 claw, X, which engages with the rim of the cartridge, and 
 of the tail^ H. The extractor revolves about the horizontal 
 axis, Z, lying between X, and H. Its upper portion, seen 
 from the rear, is crescent shaped so as to engage both 
 sides of the rim of the cartridge. Each of the arms of the 
 crescent carries a projection, F, that may engage in a corre- 
 sponding depression in the upper front edge of the block. 
 Operation. 
 
 When the gun is fired the barrel and block recoil together, 
 with no relative motion between them. The hydraulic buffer 
 acts as usual, and the counter-recoil spring is compressed. 
 
 As the spring draws the burel forward, by means of some 
 
26 XXIX. — CANNON WITHOUT RECOIL. 
 
 mechanism in the side box, hereafter explained, the rocking 
 shaft is given a small left handed rotation that causes M to 
 slide through N and so depress the block. As the block 
 passes H ii presses it to the front, first extracting and then 
 ejecting the cartridge by means of the gradually increasing 
 curvature of H. 
 
 At the same time the hammer within the block is cocked, 
 and other necessary functions are performed by means not 
 herein described. 
 
 As soon as the cartridge has been ejected, the block is 
 raised by the action of a spring which the act of recoil has 
 compressed until it is caught by the projection V, V. 
 
 The entrance to the chamber being then clear, (or the door 
 held open by the latch, AT,) if a cartridge be inserted, X is 
 pressed forward by the rim of the cartridge and F released. 
 The spring before mentioned then fully closes the block. 
 
 By pulling the trigger, T, the piece may then be fired and 
 the cycle be repeated. Or if, during the closing, the trigger 
 be kept drawn back, the piece will be fired at the instant 
 that the breech is closed. Under these circumstances the 
 operation is completely automatic except as concerns the 
 loading; the weight of the ammunition requires this to be 
 done by hand. 
 
 A rapidity of 80 rounds per minute has been attained with 
 the 3 pdrs., and guns have been designed up to a 40 pdr. 
 caliber. 
 
 In commencing the firing, the rocking shaft may be 
 revolved enough to open the breech by means of an in- 
 dependent handle outside. This may be also used when a 
 cartridge misses fire. 
 Advantages. 
 
 A reduction of the work done on the carriage by the gun. 
 A diminution of the jump, and of the vibrations, caused by 
 
XXIX. — CANNON WITHOUT RECOIL. 27 
 
 operating a hand lever. The reduction of the number of 
 gunners required. One man can fire ten aimed rounds per 
 minute, and can deliver unaimed fire as rapidly as he can 
 throw the cartridges into the chamber. 
 
 The increase in efficiency of service due to the greater safety 
 and certainty of operation, and the increased accuracy of 
 this arm, compensate for its slightly greater complexity of 
 structure as compared with other hand loaded Rapid Fire 
 Guub. 
 
 Side Box. 
 
 As the barrel recoils, the shaft, K^ figure 31, goes with it, 
 carrying the triangular piece shown, upon the lower corner 
 of which is the friction roller e. 
 
 The upper end at a slides under the lever, <:, which is kept 
 in close contact with a by the spring d. 
 
 When the counter recoil spring in D draws K forward, the 
 notch in a engages with the rear end of c. This tilts the 
 triangular piece into the position shown in figure 82 ; the 
 spring, b^ being compressed by the rising of the roller, e. 
 
 The partial rotation thus given to K causes the breech- 
 block to descend as before explained. 
 
 The block is kept from rising under the pressure of b^ 
 until the projections F", F, figure 29, are unlatched. When this 
 occurs the side mechanism resumes the position of figure 31. 
 
 Lock, etc. 
 
 As y, figure 29, swings downward, a cross pin, J/", carries 
 the swinging lever, 6^, to the rear. In the first part of the 
 motion of M (the slot, N^ being for a short distance con- 
 centric with K,^) the block does not descend. It is during 
 this time that G withdraws the hammer, E^ through which it 
 
 * See page 3. 
 
28 XXIX. — CA^fNON WITHOUT kECOlL. 
 
 passes, sufficiently to allow a spiral spring surrounding the 
 firing pin, R^ to retract its point sufficiently to clear the front 
 face of the mortise in which works the block. 
 
 The continued motion of G compresses the mainspring, Z, 
 until the lower end of G engages with the hook on the end 
 of the firing sear /. A projection, O^ on G^ also engages 
 with the notch, P^ in rear of the safety sear, F. During the 
 closing of the block the lever, G, is thus held back by two 
 sears : figure 30. 
 
 When the block is fully closed M strikes the front end of 
 F from below, and releases O from P. By pulling the 
 trigger, g^ figure 30, /is depressed and the gun is fired. 
 
 The safety sear is intended to prevent a premature discharge 
 when the trigger is kept drawn back during loading. See 
 page 26. 
 
XXX. — ACCURACY OF FIRE. 
 
 CHAPTER XXX. 
 ACCURACY OF FIRE 
 
 INCLUDING pointing; ACCURACY; PROBABILITY AND 
 MANAGEMENT OF FIRE. 
 
 I I. POINTING. 
 
 To point a gun is to give it such direction and elevation 
 that when fired the projectile shall strike a given target. 
 The target may, or may not be seen, and the subject there- 
 fore divides itself into direct^ and indirect pointing. 
 
 DIRECT POINTING. 
 
 Principles. 
 
 Remembering that the line of sight is fixed by the position 
 of the target and the eye, and includes the front sight point, 
 the object of the rear sight is to determine the extent to 
 which the breech must be depressed below the line of sight 
 so as to give the angle of elevation required. 
 
 The rear sight is then a tangent scale, that may be gradu- 
 ated in ranges or in degrees according as the conditions of 
 loading are, or are not, fixed. 
 
 The graduated portion, or standard^ is parallel to, and 
 generally out of the plane of fire at a distance from the axis 
 determined by the position of the front sight. 
 
XXX. — ACCURACY OF FIRE. 
 
 Upon the standard moves the slide; this carries the rear 
 sight point to which lateral motion in both directions may 
 be given. 
 
 It is well to bear in mind that the deviation follows the 
 motion of the rear sight .point; thus, if we move it up further 
 than is required, the projectile will strike high; if we move 
 it too far to the right, the projectile will go to the same side 
 of the plane of sight. 
 Horizontal Inclination. 
 
 Since the piece is elevated to correct for the action of 
 gravity, the elevation must be taken in a vertical plane; so 
 that if the trunnions be not horizontal the rear sight standard 
 must be capable of being revolved to a vertical position. 
 
 It is also necessary that the axis about which the rear 
 sight revolves shall be the nahiral line of sight, or that for 
 which the elevation is 0. For then, since the natural line 
 of sight is parallel to the axis of the piece, the inclination 
 of the trunnions will cause it to describe a cylindrical sur- 
 face, the inclination of any one of the elements of which is 
 that of the axis. With a rear sight so arranged we may 
 measure the vertical angle included between the natural line 
 of sight and the actual or artificial line of sight, which is the 
 angle required. Thus ni figure 1, if the trunnions are 
 inclined at the angle (]p, the construction shows that if the 
 front and rear sight points are / and r, the plane of sight, S^3^^ 
 will be inclined to the plane of fire at the angle p f r' : and 
 therefore, since the direction given to the gun is fixed by the 
 line of sight, the gun will shoot to the left of the target. 
 Also, when the rear sight is used, if h be the height of the 
 slide, the vertical angle of elevation will be that subtended 
 by only h cos qp, or the gun will shoot low. 
 
 But if the height of the front sight =/, ^/, or the dispart, 
 (Chapter I) the planes of sight and of fire will become 
 
XXX. — ACCURACY OF FIRE. 
 
 parallel ; and if the standard be revolved to a vertical posi- 
 tion the adjustment will be complete. 
 
 Field Sight. 
 
 As a type of this class of sights, that adopted for the 3.2 
 inch field gun is here described. 
 
 The tangent scale, A, figure 2 is divided into degrees and 
 ten minute intervals; and, by means of the attached vernier, 
 Vj it may be read to minutes. The vernier slide, S, carrying 
 Xhtpeep sight, is moved to the desired elevation by the screw, 
 E. The tangent scale admits of rotation about C, and may 
 be placed in a vertical plane by observing the small spirit 
 level Z. It may also be moved laterally, by means of the 
 screw, W, the scale, D, indicating the distance to the right 
 or left of the natural line of sight passing through C. 
 Sights for Heavy Guns. 
 
 When the axis of the trunnions is maintained horizontal, 
 as in the Siege and Sea Coast services, the operation of ele- 
 vating the piece carries the natural line of sight in a plane 
 parallel to the plane of fire, and the device described is not 
 required. 
 
 For such pieces the standard may be replaced by gradu- 
 ated arcs and pointers for giving direction in both elevation 
 and azimuth. For the former purpose the arc may be on 
 the breech of the piece or on the cheek; and for the latter 
 it may be concentric with the pintle. The horizontal arc is 
 used for firing at objects not seen from the battery; but the 
 bearing of which with reference to some meridian is known 
 to an observer outside. 
 Ilelinemeiits. 
 
 Accuracy of pointing may be increased by the use of tele* 
 
XXX. — ACCURACY OF FIRE. 
 
 scopes or of combined ''peep sights" and cross wires. To 
 avoid the delay in pointing resulting from the limited field 
 of view a preliminary adjustment with the ordinary form of 
 open sight is required. 
 
 Telescopic Sight. — This consists essentially of a small 
 transit which for heavy cannon is mounted on a shelf fixed 
 to one of the trunnions so that its upper plane shall be paral- 
 lel to that made by the axis of the bore and that of the 
 trunnions. The telescope is removed before firing. For 
 field guns various models have been tried experimentally; 
 but so far none has been found sufficiently simple for general 
 adoption.* 
 
 Peep Sight. — In the 3.2 field rifle the front sight is as 
 shown in figure 3, and the slide of the rear sight as in figure 2. 
 The distance a a' is equal to bb\ so that, having found the 
 object by the sights a b, the aim may be corrected by the 
 line passing through the peep hole b' and the cross wires a' 
 contained in the cylindrical housing C. 
 
 INDIRECT POINTING. 
 
 This term applies to the method followed when the target 
 cannot be seen from the piece. An example occurs in mortar 
 practice. 
 
 I. The general practice consists in establishing an auxil- 
 iary mark (in mortar practice this is the front plummet) to- 
 wards which the piece is pointed. The elevation is subse- 
 
 * A simple form of telescopic sight for the field gun is now, 1890, 
 under trial. 
 
 The vernier slide, S, is extended to the left as shown in figure 2, so 
 as to form one support for a telescope, the other end of which rests on a 
 similar crutch near the right trunnion. 
 
 When detached, the telescope may be used for watching the effect of 
 the fire. 
 
XXX. — ACCURACY OF FIRK. 
 
 quently given by the level and corrected by an observer so 
 situated as to see the effect of the fire. 
 
 II. Or else, the proper elevation of the piece having been 
 determined by trial, a distant mark may be selected (or 
 placed) in the plane of sight; the slide of the rear sight may 
 then be moved until the rear sight point is on the prolon- 
 gation of the line joining the mark and the front sight point. 
 Whenever then, after firing, the new line of sight passes 
 through the mark, the piece will have its primitive direction 
 and elevajtion, provided that its new position does not differ 
 materially from its primitive position. This method is service- 
 able in small arm firing. 
 
 ' III. In some cases it may not be possible to find a suitable 
 mark. Under such circumstances the following method may 
 be employed with cannon mounted on permanent platforms. 
 Establish nearly parallel to the axis of the piece, when in its 
 normal position, a vertical plane director. Establish by trial 
 the piece in its proper direction and measure the shortest 
 distance; 1st, from the plane director to the end of the 
 axle arm; and 2nd, from the plane director to some definite 
 point on the trail. When, after firing, these distances are 
 restored, the piece is in its primitive direction. 
 
 By establishing the inclination of the plane directoE with 
 reference to some common meridian, this method enables 
 any piece of a battery to be oriented on the target by a 
 distant observer in the manner indicated page 3. 
 
 Tables provided for this purpose give the difference of 
 distance from the plane director for all inclinations to the 
 common meridian likely to occur in practice. 
 
 II. ACCURACY OF FIRE. 
 Definitions. 
 
 The plane curve discussed in Chapter XX is called the 
 normal trajectory. In practice the trajectory is a curve of 
 
XXX. — ACCURACY OF FIRE. 
 
 double curvature. The conditions of firing vary so greatly 
 that it is impossible to secure the coincidence of two con- 
 secutive trajectories, so that, however constant these con- 
 ditions may be made, the trajectories of any series of shots 
 group themselves in the sheaf of trajectories^ a sort of bent 
 cone, the apex of which is at the muzzle and the axis of 
 which is the inean trajectory. Figure 34, 
 
 Owing to the tendency of the individual trajectories to 
 approach the mean trajectory, the density of the sheaf in- 
 creases toward its axis, like the stream from a hose. Figure 
 33 shows approximately the manner in which the sheaf is 
 subdivided: the nucleus v.ox\\.2^\n'i the half lying nearest to the 
 axis; the ejivelope surrounds the nucleus and contains 40 per 
 cent of the whole, and the remaining 10 per cent constitute 
 lh£ tailings. 
 
 In order to hit the target we must know its position with 
 reference to the mean trajectory, or the deviation of the gun 
 at the range in question, and also the distribution of the 
 trajectories throughout the sheaf, or the errors. We may 
 accordingly study 1st, the causes of deviation and the cor- 
 rections required to make the mean trajectory pass through 
 the target; and 2nd, the measurement of the errors of the 
 systenj comprising the gun, ammunition, carriage, gunner, 
 etc., with a view of estimating the probability of striking a 
 target of known dimensions at a given range. 
 
 I. CAUSES OF DEVIATION. 
 
 These may be either internal or external, as follows: — 
 
 Internal. 
 
 These are variations in the conditions of loading, in the 
 temperature of the bore and in meteorological conditions. 
 They affect the Initial Velocity, and for practical purposes 
 
XXX. — ACCURACY OF FIRE. 
 
 may be neglected, since the variations in velocity may be 
 
 made less than 1 per cent. 
 
 External. 
 
 Among the external causes leading to deviation are: — 
 
 I. The error of the eye. 
 
 II. The drift, due to the rotation of the projectile. See 
 Chapter XX. 
 
 III. The wind and weather. 
 
 IV. The inclination of the trunnions to the horizon, and 
 the jump. 
 
 V. Errors in estimating the distance to the target, and 
 also those due to variations in the angle of sight, or in the 
 difference of level between the gun and the object. 
 
 VI. The rotation of the earth. This has no practical 
 importance and may be neglected. In the northern hemis- 
 phere it carries the projectile to the right of the object. 
 
 These causes and their corrections are discussed as 
 follows: — 
 
 I. The Error of the Eye. 
 
 The average error of the eye among a number of selected 
 marksmen, determined by the method jLised in the prelimi- 
 nary instruction in small arms firing, is such that only about 
 one half can be depended on to direct the line of sight in- 
 variably upon a 2 foot target at 1000 yards. 
 
 This error arises principally from variations in the height 
 at which the line of sight pierces the front sight of the piece. 
 It may be diminished by increasmg the sight radios, by the 
 use of telescopes and cross hairs, and by allowing for vari- 
 ations in the illumination of the front sight. When the front 
 sight is obscured, too much of it will be taken, and when 
 one side is brighter than the other the deviation will be from 
 the light. 
 
XXX. — ACCURACY OF FIRE. 
 
 The nearer is the eye to the rear sight, the better will the 
 front sight be seen, and the ^ner can the sight be taken. 
 
 The permissible error of the eye will depend upon the 
 semi-height of the target and its distance; or, calling e the 
 error, / the sig/i^ radius of the gun, R the range, and h the 
 height of the target, we have, assuming from the principle 
 of rigidity of the trajectory that it is a straight line, and 
 from the similarity of the triangles in figure 4, 
 h ^ hi 
 
 :/::- \ R oi e 
 
 2 ' 2R' 
 
 II. Drift. 
 
 As the elevation increases, the deviation due to drift 
 increases more rapidly than the range, so that the horizontal 
 projection of the mean trajectory is convex toward the plane 
 of fire. 
 
 Drift may be approximately compensated by giving to the 
 rear sight leaf a permanent inclination to the plane of fire 
 in the direction opposed to the drift. The angle of incli- 
 nation is called the J^ermanent angle. It may be shown that 
 
 D 
 
 tan t = -^—. — . 
 R sm g 
 
 in which i h the permanent angle; Z>, the deviation due to 
 drift; R, the range, and e the angle of elevation. 
 
 Sin e increases more rapidly than the range, so that if D 
 varied as R sin e, i would be constant. 
 
 Drift at ordinary ranges may be sufficiently compensated 
 for by the permanent angle, and at long ranges a further 
 correction may be given by the lateral motion of the rear 
 sight slide. 
 
 With pointed projectiles the drift is in the direction of the 
 rifling. In the U. S. service this is to the right. 
 
 Range tables, giving the ballistic properties of the gun as 
 determined by experiment, furnish the angles of elevation 
 
XXX. — ACCURACY OF FIRE. 
 
 and the drift for the different ranges as well as the perma- 
 nent angle. 
 
 RANGE TABLE FROM EXPERIMENT. 
 
 English 8 in. M. L. R. Howitzer (»)— («^=180 lbs.), w of R. L. G3. 
 
 
 
 
 
 
 1 
 
 is 
 
 
 5' chanj^e of 
 
 e or d 
 changes. (») 
 
 50 per cent. 
 zonesi=2/'.(^) 
 
 
 
 
 
 /. F. 
 
 X 
 
 e. 
 
 drift 
 
 1.^ 
 
 GO. 
 
 
 
 V. 
 
 T. 
 
 !» 
 
 w 
 
 X, 
 
 F.orZ, 
 
 x{*) 
 
 y- 
 
 Z. 
 
 1 
 
 lbs. 
 
 f.s. 
 
 yds. 
 
 0/ 
 
 yds. 
 
 0/ 
 
 0/ 
 
 yds. 
 
 yds. 
 
 yds. 
 
 yds.' yds. 
 
 f.s. 
 
 sec. 
 
 
 
 1 
 
 1200 
 
 2.44 
 
 1.9 
 
 0.06 
 
 4.00 
 
 25.0 
 
 1.74 
 
 16.4 
 
 0.40 1.21 
 
 876 
 
 4.0 
 
 
 
 
 1600 
 
 5.06 
 
 3.8 
 
 0.09 
 
 5.36 
 
 23.8 
 
 2.32 
 
 21.3 
 
 0.56 i 2.14 
 
 852 
 
 5.4 
 
 
 11.5 
 
 956 [ 
 
 2300 
 
 7.3;^ 
 
 8.7 
 
 0.13 
 
 8.42 
 
 23.8 
 
 3.34 
 
 29.7 
 
 0.87 i 4.64 
 
 814 
 
 7.9 
 
 
 
 
 3400 
 
 7.54 
 
 9.5 
 
 0.13 
 
 9.12 
 
 22.7 
 
 3.49 
 
 30.9 
 
 0.92! 5.07 
 
 809 
 
 8.2 
 
 
 
 J 
 
 2600 
 
 8.16 
 
 10.4 
 
 0.14 
 
 9.42 
 
 22.7 
 
 3.63 
 
 32.1 
 
 0.98| 5.50 
 
 804 
 
 8.6 
 
 
 
 1 
 
 1200 
 
 4.12 
 
 2.3 
 
 0.07 
 
 4.36 
 
 20.8 
 
 1.74 
 
 15.5 
 
 0.45 1.31 
 
 845 
 
 4.1 
 
 
 
 
 1600 
 
 5.4K 
 
 4.5 
 
 0.10 
 
 6.21 
 
 20.8 
 
 2.32 
 
 20.3 
 
 0.62' 2.31 
 
 823 
 
 5.6 
 
 
 10.5 
 
 920 I 
 
 2300 
 
 8.36 
 
 10.5 
 
 0.16 
 
 9..51 
 
 20.8 
 
 3.34 
 
 28.3 
 
 0.99 4.99 
 
 787 
 
 8.3 
 
 
 
 
 2400 
 
 9.00 
 
 11.5 
 
 0.17 
 
 10.24 
 
 20.8 
 
 3.49 
 
 29.4 
 
 1.05 1 5.44 
 
 782 
 
 8.7 
 
 
 
 J 
 
 2500 
 
 9.24 
 
 12.7 
 
 0.18 
 
 10.57 
 
 20.2 
 
 3.63 
 
 30.5 
 
 1.12 5.90 
 
 777 
 
 9.1 
 
 
 
 473} 
 
 1200 
 
 ifi.as 
 
 11.4 
 
 0.33 
 
 17.30 
 
 4.6 
 
 1.74 
 
 21.7 
 
 1.50 6.9 
 
 438 
 
 8.4 
 
 
 3.5 
 
 1600 
 
 24.21 
 
 22.3 
 
 0.48 
 
 26.00 
 
 3.6 
 
 2.32 
 
 30.4 
 
 2.18 14.9 
 
 433 
 
 11.8 
 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 
 III. The Wind. 
 
 For any range the deviation of a projectile caused by a 
 wind of which the velocity is one mile per hour, acting at 
 
 (1) The rear sight of this piece is not set at the permanent angle. 
 (») The actual time of burning varies in flight from that at rest. See Chapter 
 XVm, page 7. 
 
 (3) Eange tables for guns assume a constant value of w. They give in addition 
 
 to the above, the jump, the inclination of qo as —, and the penetration in wrought 
 iron at the different ranges. 
 
 (*) For guns this is much more uniform. See page 52. 
 
 (■) See post. 
 
10 XXX. ACCURACY OF FIRE. 
 
 right angles to the plane of fire, is called the coefficient of 
 the deviation for that range. So that, calling u the velocity 
 of the wind in miles per hour as shown by the anenometer, 
 ^ the inclination of the wind to the plane of fire as shown 
 by the wind vane, and k the coefficient above defined, we 
 have 
 
 D ^ku sin ^. 
 The relation between k and R may be recorded by an em- 
 pirical curve, from the indications of which the rear sight 
 may be set to the right or left of its normal position when 
 the force and the direction of the wind are known. 
 The Weather. 
 
 The relative effect of varying meteorological conditions 
 is provided for by the coefficients explained in Chapter XX, 
 pp. 9, 11. 
 IV. Inclination of the Trunnions. 
 
 This has been explained page 2. 
 
 V. ESTIMATION OF DISTANCES.* 
 
 The importance of this correction varies inversely with 
 the height of the target and the flatness of the trajectory. 
 Chapter XX, Eq. (30). 
 
 The distance of the target may be ascertained: — 
 
 1st. By the eye. 
 
 Constant practice is necessary, even at short ranges, and 
 the results are much affected by varying atmospheric con- 
 ditions and by the nature of the intervening ground. At 
 long ranges it even requires experience to determine whether 
 a shell bursts short or beyond the target. 
 
 2nd. By rapid measurements with different range finder s.\ 
 
 * The extent of this sub-head requires a variation in the method of 
 using type. The subject extends to page 22. 
 \ For 3rd see page 21. 
 
XXX. — ACCURACY OF FIRE. 11 
 
 RANGE FINDERS OR TELEMETERS. 
 
 These may be divided into two general classes, the acoustic 
 and the optical instruments. The former depend upon the 
 assumed constancy of the velocity of sound, and the latter 
 upon the rapid solution of plane triangles. 
 
 1. ACOUSTIC TELEMETERS. 
 
 These measure the time elapsing between the flash of an 
 enemy's gun and the arrival of the report. Then, taking 
 tiie velocity of sound at 1100 f. s. we have R=.vt, The 
 following methods are in use. 
 
 1. The Le Boulenge Telemeter. 
 
 This consists of a graduated glass tube filled with some 
 non-freezing transparent liquid, through which, when the 
 tube is vertical, a metallic index falls with a slow uniform 
 motion. 
 
 To use the instrument, hold it horizontally with the index 
 at 0: the instant that the flash or smoke is seen turn it ver- 
 tical; when the sound is heard return the tube to a hori- 
 zontal position and take the reading in meters. 
 
 2. A simple method is to count the number, «, of cadenced 
 
 steps made during this interval. If these are at the rate of 
 
 110 per minute, then 
 
 1100x60 ^_^ 
 R in yards = n -— — — -r- = 200 n. 
 
 o X ilU 
 2. OPTICAL TELEMETERS. 
 
 General Principles. 
 
 If we consider the distant object as a point, its parallax 
 is the apparent difference of direction of the object as seen 
 from two different points of view; and conversely, if the 
 dimensions of the object are considerable, its parallax may 
 
12 XXX. — ACCURACY OF FIRE. 
 
 be measured by the angle that it subtends from a single 
 point of view. 
 
 The triangle formed in the first instance by the object 
 and the two points of view, and in the second case by the 
 point of view and the observed extremities of the object is 
 the triangle to be solved. Its solution is facilitated and 
 sufficient accuracy for first approximations attained by con- 
 sidering it either a right angled triangle or an isoceles 
 triangle, of which, in the first case the distance between the 
 two points of view, and in the second case the known or 
 assumed dimensions of the object forms the base. The base 
 or the point of view should evidently be selected so as to 
 diminish the error of this assumption. 
 
 If the triangle to be solved is a right angled triangle, 
 figure 5, we may measure ^ C by multiplying the length of 
 the base ^^ by the reciprocal of the sine of the parallax 
 at C when this is found; or, as the parallax is generally 
 small, the reciprocal of the tangent may be used, giving CB 
 practically equal to A C, figure 6. 
 
 If the triangle is isoceles the length of a side will be given 
 
 A B ] 
 
 by X —. — ;;. Some instruments use a fixed parallax 
 
 •' 2 sm I" 
 
 and vary the position of the observer at the extremities of 
 the base until the desired triangle is formed. As the paral- 
 lax is so chosen that -: — r is a whole number, say 20, it is 
 sm§ 
 
 only necessary to multiply the length of the base by 10 to 
 obtain the range. This can easily be done mentally. 
 Classiiication. 
 
 Accordingly instruments may be classified as follows;-— 
 
 I. Fixed base, variable parallax. 
 
 II. Fixed parallax, variable base. 
 
 III. Variable parallax, variable base. 
 
XXX. — ACCURACY OF FIRE. Vd 
 
 The same instrument may sometimes be used in more 
 than one method, and the parallax may be either vertical or 
 horizontal. 
 
 In Older to diminish their size and to permit the simulta- 
 neous observation of two distant points from an unsteady 
 support, many instruments employ the principle of the sex- 
 tant by using two reflecting surfaces, the angle between 
 which is one half of that between the incident and the second 
 reflected ray, figure 7. The relative inclination of the 
 reflecting surfaces m^ m^ may be fixed, or, as in the sextant, 
 variable. 
 
 The conflicting claims of portability, rapidity of operation 
 and accuracy have caused many forms of range finders to 
 be devised. No one kind has yet been generally adopted. 
 
 The ingenuity of inventors has been principally exercised 
 in increasing the scale on which the parallax is measured 
 and in avoiding all but the simplest computations in the field. 
 Vertical Parallax. 
 
 These instruments require the vertical base to be known. 
 The base may be, 1, either the height of the object, as the 
 average height of a man, or that of the mast or funnel of an 
 enemy's vessel, or, 2, the height of the instrument above the 
 horizontal plane on which the object is situated, as in coast 
 batteries having considerable command. 
 1. Stadfa. Figure 8. 
 
 This instrument was formerly used when the ranges of 
 small arms were so short that the parallax for an object the 
 height of a man was of appreciable magnitude. 
 
 The button b is held between the teeth, and the Stadia S 
 is held at a distance from the eye regulated by the cord c. 
 The head and feet of the man whose distance is to be 
 measured are brought tangent to the lines oh^ ot, and the 
 slide *S' brought to the corresponding position along the 
 
14 XXX. — ACCURACY OF FIRE. 
 
 scale. The average height of a man in this service is taken 
 at 5 ft. 8 in. 
 
 The objections to this particular instrument are evident, 
 but the principle is applicable against vessels. A very con- 
 venient surveying instrument of this nature uses fixed paral- 
 lel horizontal wires inside a telescope, and a graduated staff, 
 from which the distance to the staff may be read off directly. 
 2. The Depression Range Finder. 
 
 This consists of a telescope, the height of which above 
 the water level is known. The distance and direction of the 
 object can be read directly from scales; so that, if the ob- 
 server be remote from the smoke of the battery, and be 
 screened by natural objects from the enemy's view, he may 
 safely direct the continuous firing of pieces provided with 
 the pointing apparatus described page 3. 
 
 The instrument admits of a correction for the stage of 
 tide, etc. 
 
 HORIZONTAL PARALLAX. 
 
 CLASS I. FIXED base; VARIABLE PARALLAX. 
 
 1. The Plane Table. 
 
 This is used in plotting the effects of fire over water, and 
 the principle is applicable in warfare. 
 
 For target practice the base is established so that straight 
 lines drawn from its extremities to the point of impact shall 
 intersect as nearly as possible at right angles. The position 
 of the base with reference to the piece having been estab- 
 lished on a chart, the various points of fall can be plotted 
 in their relative positions and the ranges and deviations 
 determined by a scale. In this practice the base may be 
 established parallel to the plane of fire and near the target; 
 but as in war this would not be possible, the equivalent of 
 
XXX. — ACCURACY OF FIRE. 15 
 
 the plane table is established so near the piece that the 
 difference of its distance from the object may be neglected. 
 In such cases the length of the base should increase with 
 the range, so as to neutralize errors in observing the paral- 
 lax; but since in practice a base of suitable length cannot 
 always be obtained, the errors due to the use of a short base 
 may be corrected by refinements in the construction of the 
 instrument, as in the following cases. 
 
 2. Berdan Range Finder. Figure 9. 
 
 In this instrument we find a fixed base only 6 feet long, 
 so that it is contained within .the limits of the vehicle on 
 which the whole apparatus is carried. At one end is the 
 fixed telescope B with its line of collimation exactly at 
 right angles to the base A B. The inclination of the mova- 
 ble telescope A to the axis of B^ or the parallax of the ob- 
 ject C, can be read off from a scale giving A C directly. 
 This instrument is rapid and accurate; but is necessarily 
 confined to the Artillery. 
 
 3. The Fiske Range Finder. Figure 10. 
 
 This is intended to be used on naval vessels in which the 
 length of the base is necessarily restricted. It operates on 
 the same general principle as the Berdan; but permits the 
 solution of oblique angled triangles. In order to magnify 
 the scale it employs the principle of the Wheatstone Bridge. 
 
 Let A B \>& the base, at each end of which is a telescope 
 pivoted at A and B^ which are the centers of the graduated 
 arcs, G H I, J K L. Let C be the object. Draw A E 
 parallel to B C, Then 
 
 sm C 
 The angle at B can be easily measured, and the angle 
 
16 XXX. — ACCURACY OF FIRE. 
 
 IfAI=d.^L /K—2iXC 6^ ZT, is determined substantially as 
 follows. 
 
 Let C, figure 11, be the target and A and B the metallic 
 pivots of the two telescopes connected with the battery at L, 
 and through the telescopes and their graduated traverse 
 circles JDEFG, H I J, with the galvanometer K. The 
 letters a, b, c, d^ refer to the usual nomenclature of the arms 
 of the Wheatstone Bridge. 
 
 The angle ABC can be read off directly from the trav- 
 erse circle H I J^ and the angle E A /^=the parallax may 
 be measured in two ways. 
 
 First; Supposing the galvanometer to be under the eye 
 of the observer at A^ he has merely to swing his telescope 
 until the galvanometer balances. Then, since a \ b \\ c \ d 
 the change in the angle at A will be the parallax, the range 
 for which, corresponding to an angle A B €•=■ 90°, can be 
 read off directly from the traverse circle and then be corrected 
 by multiplying by sin B, This correction is mechanically 
 performed in the act of sighting from A, 
 
 Second; Suppose the galvanometer to be under the eye 
 of a distant observer, as at the gun, and let him be provided 
 with means for determining with sufficient exactness the 
 angle A B C, ox sin B. The observers at the telescopes 
 may then simply follow the object with their instruments and 
 the observer at the gun may determine the range by intro- 
 ducing into the circuit a rheostat graduated for ranges.* 
 
 CLASS II. FIXED PARALLAX ; VARIABLE BASE. 
 
 1. The Weldon Range Finder. Figure 7. 
 
 This uses two small, thin, triangular prisms having one side 
 silvered and the angles between two of the reflecting surfaces 
 = 44° 17'. 
 
 * This description is much abbreviated and omits many interesting 
 details, 
 
XXX. — ACCURACY OF FIRE. 17 
 
 C 1 
 
 Therefore, in figure 6, ^ = ^ = 88** 34' and tangent -- = — 
 
 The instrument requires two observers, each of whom holds 
 the prism so as to see C by double reflection, and simulta- 
 neously the eye of the other observer by direct vision over 
 the prism. 
 
 A single observer may use the instrument by establishing 
 the direction of the base line from A; marking the spot 
 and finding some spot B upon the base line from which C 
 can be seen by double reflection and A by direct vision. 
 Then 
 
 2. The Pratt Range Finder. Figure 12. 
 
 Each instrument contains two pairs of mirrors, called the 
 upper and the lower pair. The upper pair are inclined at 
 45° to each other, and the lower pair at an angle of less than 
 45°. Suppose this angle to be fixed, as in the Weldon at 
 44° 17', although it may be set at various other angles. 
 
 1. Suppose the distance B C, figure 13, is to be measured. 
 Standing at B, with the upper mirrors and by direct vision 
 establish some distant and well defined mark D, so taken 
 that CB D=i 90°, and mark the point B. 
 
 Move in the prolongation oi D B till A is reached, from 
 which point D seen by direct vision coincides with the image 
 of C reflected in the lower pair of mirrors. Then 
 
 AB^M<i-BC. 
 
 2. The operation may be reversed by moving from A to 
 B. In this case, as the observer's back will be turned to- 
 wards A while changing his station, the direction AD should 
 be preserved by selecting an auxiliary mark d' between Z> 
 and B, 
 
18 XXX. — ACCURACY OF FIRE. 
 
 3. It is evident that the instrument may be used for solv 
 ing isoceles triangles in the same manner as the Weldon. 
 
 4. The instrument may be used to measure the distance 
 between two objects, both of which are inaccessible, as in 
 determining on shore, the distance between a friendly vessel 
 and an enemy's. To illustrate, let B C, figure 14, be the 
 distance to be measured and let the obsejrver be at A. Es- 
 tablish ^ Z> at right angles \.o A B and with the lower pair 
 
 A B 
 of mirrors determine the point D so that A D = -j~- . The 
 
 distance A B need not be measured. 
 
 A C 
 
 Similarly, determine the point E so that A E= -j— , 
 
 Then, since A D E and ABC are similar triangles, 
 BC^A:^ ED. 
 Remark. 
 
 Instruments of Class II are simple, portable and fairly 
 accurate; but in broken or wooded country time may be 
 lost in finding a base suited to the parallax. 
 
 CLASS III. VARIABLE BASE; VARIABLE PARALLAX, 
 
 1. Gautier's Telemeter. 
 
 This is one of the earliest and best forms of this class. 
 Its essential principles may be illustrated as follows. 
 
 Suppose we have a form of protractor such as the dividers 
 shown in figure 15, and provided with sight points at ^, b, c. 
 Let it be required to find the distance A C, figure 16. 
 
 Select some distant point Z>, such that CB £)=cab=z^O^, 
 Then advance to A on the line BD and sight along ab 
 at Cj d c will then point to X>' . If now we move a c ^o 
 that while a b still points \.o C^ ac will point to Z>, the change 
 
 cac' will be the parallax and AC= ABy. -. j . 
 
 sm cac' 
 
XXX. — ACCURACY OE FIRE. 19 
 
 In practice c ab = A B C may vary 8° from 90° without 
 
 A C 
 causing the resulting error in range to exceed—— . This 
 
 permits slight modifications in the length of the base to allow 
 for the nature of the ground. 
 
 Construction. 
 
 The instrument resembles in appearance a telescope, the 
 object glass being replaced by a glass prism, the angle of 
 which is 6°. This is set in a graduated ring that may be 
 turned axially about the line of collimation of the eye piece E. 
 
 The prism causes rays entering from the front to be devi- 
 ated by an amount / T I\ equal to half the angle of the 
 prism, or 3°. So that by turning the graduated ring the 
 refracted ray will describe a cone, the angle of which is 6°. 
 The ring is graduated for the reciprocal of the sines of the 
 intermediate angles corresponding to whole numbers vary- 
 ing by 10, 20, etc. 
 
 Operation. Figure 16. 
 
 The variable inclination of the mirrors permits the points 
 B and Z>Z^ to be selected according to the ground. Hav- 
 ing caused the image of C in the mirror M to come just 
 below some well defined point of D seen through the prism 
 
 when set at "Infinity" or-^— - , we may then advance along 
 
 B Z> to A and restore coincidence by turning the graduated 
 ring, the reading of which will give the multiplier for the 
 base. 
 
 Or else, we may set the ring to some simple factor as 20, 
 and advance until coincidence is made. 
 
 Like the other instruments, the Gautier admits of a 
 variety of applications. 
 
20 XXX. — ACCURACY OF FIRE. 
 
 2. The Gordon Range Finder. Figure 18. 
 
 This resembles in principle the Gautier. It consists of an 
 opera glass in front of which is mounted a frame containing 
 two plane mirrors, MM', M lying just below the line of 
 collimation. 
 
 M may be turned by a thumb screw to an extent measured 
 by an enlarged scale, the of graduation of which corre- 
 sponds to an inclination of the mirrors of 45°. 
 
 Having established a right angle at J3, figure 16, we 
 restore coincidence at A, and pass from the reading to a 
 table of factors. The telescope aids in defining distant ob- 
 jects and is useful in watching the effects of the fire, by 
 which after all the elevation is mainly regulated. 
 
 3. The Nolan Range Finder. Figure 19. 
 
 This consists of a pair of instruments, each of which com- 
 prises a tripod upon which are mounted two telescopes of 
 different lengths and powers and placed one above the other 
 with their lines of collimation set at about 90°. This angle 
 may be varied and the difference from 90° read from a 
 decimal scale. 
 
 Having established a base that will form with the object 
 nearly an isoceles triangle, we direct the short telescopes, 
 s and /, on each other, and the long telescopes, /, /', on the 
 same point of C. The sum of the displacements of A and B 
 is the parallax, and considering the triangle isoceles, 
 
 log I A C= B C= -y X gjj^ J )= log —^ + colog sin |^ 
 
 To avoid calculation by ordinary methods a reckoning 
 
 cylifider, consisting of a series of concentric discs, is used. 
 
 This applies the principle of the slide rule ; since of two suc- 
 
 ,, A B 
 cessive nngs, one is graduated in terms of log— ^, ana 
 
XXX. — ACCURACY OF FIRE. 21 
 
 the other in terms of colog sin — -. • By setting the of the 
 
 scale of sines to the reading of the scale of bases, if we take 
 the point on the scale of bases corresponding to the reading 
 of the scale of sines (or for simplicity, to the sum of the 
 readings on the two decimal scales) we have the range at 
 once.* 
 
 To avoid having the tripods to transport, the instruments 
 may be mounted on the cheeks of the flank pieces of a 
 battery. 
 
 Returning to the Estimation of Distances page 10, we 
 have as the next method — 
 
 3rd.f By trial with smaller pieces, using percussion shell, 
 as described Chapter XVIII, page 12. The sights for these 
 guns should be graduated in yards. 
 
 4th. By establishing a /(?r^ by changing the elevation until 
 about one half of the projectiles fall short. There are two 
 methods of doing this. 
 
 1st. Tht progressive method^ or feeling the way from the 
 first range by ± increments until the target is en- 
 closed in the fork. 
 2nd. The method of successive means. Having established 
 a large fork by throwing one shot short and one be- 
 yond the target, we take the mean of the two ranges 
 for the next range; and, according as this is beyond 
 or short of the target, take the mean of it and 
 that one of the first two that was short or beyond, 
 
 * The simplicity of this principle will become apparent by taking two 
 scales of equal parts 'held in the same plane and sliding one along the 
 other, 
 t This article follows 2nd, page 10, 
 
22 XXX. — ACCURACY OF FIRE. 
 
 and so on, continually narrowing the fork. This 
 method is preferred when time permits its employ- 
 ment. 
 In some services the number of turns of the elevating 
 screw required to change the range by a nearly constant in- 
 crement at the different ranges is known. This number 
 varies less rapidly than the range. 
 
 Variations in the Angle of Sight.* 
 
 As seen in Chapter XX, page 24, for the same elevation 
 the range varies somewhat with the angle of sight. The 
 correction for this with the flat trajectories now common 
 may be included with that for deviations in range. 
 
 II. ERRORS. 
 
 CAUSES OF ERROR. 
 
 It is usual to consider in gunnery practice that there are 
 two main causes of error, one tending to increase or diminish 
 the range, or, what is the same thing, tending to raise or 
 lower the trajectory, and producing range errors; and the 
 other tending to move the trajectory to the right or left, 
 producing lateral errors. 
 
 Lateral errors evidently follow the same laws as range 
 errors, 
 
 MEASUREMENT OF ERRORS. 
 
 The errors of a piece f at a given range are determined 
 by firing the piece under as constant conditions as possible. 
 
 For small arms the gun is clamped in a fixed rest, and 
 the shots received on an iron target, the image of which is 
 
 * See page 7. 
 
 f This will be considered to include the errors due to the carriage, 
 ammunition, and to other causes of deviation that cannot be controlled. 
 
XXX. — ACCURACY OF FIRE. 23 
 
 projected by a camera on a sheet of paper ruled to scale. 
 The target may then be computed as hereafter described. 
 
 The resulting accuracy is compared with that of alternate 
 targets made with a standard arm, and with ammunition 
 carefully prepared in such large quantities that its uniformity 
 from, day to day may be considered as constant. 
 
 We may thus eliminate all variables but the particular one 
 under consideration. 
 
 For cannon, however, for which it is often impracticable 
 to procure vertical targets of sufficient size, the firing is often 
 conducted over water and its results plotted with a plane 
 table. 
 
 COMPUTATION. 
 
 Definitions. 
 
 Let n be the number of shots fired. Let X Y Z h^ the 
 
 axes of coordinates, drawn through the point aimed at ; }t 
 
 being taken parallel to the plane of fire, Y at right angles 
 
 thereto, and Z vertical. Let x' , x" ; y', y" ; z', z" ; etc., 
 
 be the coordinates of the shot marks taken with their proper 
 
 signs, and r' , r" their radial distances from the origin. Let 
 
 2" be the distance to the target. Then we have 
 
 it x' d: x" it etc. 
 Mean deviatio?i in range, X, = '-, 
 
 Mean lateral deviation 
 
 Mea?t vertical deviation Z, z= 
 
 ± y ± y" ± etc. 
 
 71 
 
 ± z' ± z" ± etc. 
 
 Mea7i range R z=. T± X , 
 
 ^ \ yji \ r^"-L. etc. 
 
 Mean radial deviation or " string'^ S z=z -L- — -* 
 
 ?i 
 
 Mean point of impact^ or center of impact. This is the 
 
 point of which the coordinates are (X, FJ or ( Y, Z). This 
 
 point determines the nieaji trajectory^ mean line of fire and 
 
M XXX. — ACCURACY OF FIRE. 
 
 mean plane of fire. It is the center of the group of shot 
 marks, and the origin for the measurement of errorsJ^ 
 
 Range error for a single shot v^ = X, '^ x' . + 
 
 Lateral error for a single shot v^ = Y, -*' y'. 
 
 Vertical error for a single shot z^g = Z, ^ z'» 
 
 Mean error in range. 
 
 Mean lateral error. 
 
 Mean vertical error. 
 
 Mean absolute error, 
 
 n 
 
 In which r^, r^^, etc., are measured radially from the mean 
 point of impact^ so that 
 
 ^1 
 
 
 V 
 
 ' + 
 
 V' + etc. 
 
 
 
 n 
 
 ^2 
 
 — 
 
 v^ 
 
 4- 
 
 V + etc. 
 
 
 
 n 
 
 ^3 
 
 = 
 
 V,' 
 
 + 
 
 V + etc. 
 
 
 
 ?i 
 
 
 
 ^/ 
 
 + : 
 
 0/ + ^// + etc. 
 
 r^= y v^ + z/j, or = yv.^ + v^ 
 
 according to the position of the target. 
 
 Of these mean errors the first three are used to analyze 
 the causes of error. Thus if e^ or fg should be found to 
 greatly exceed fg it would be assumed that either the powder, 
 or the weight of the projectile had varied, or that there had 
 been an irregular wind in the direction of the plane of fire. 
 On the other hand, if £, should greatly exceed e^ or fg, it 
 
 * While deviations are measured from the point aimed at, errors are 
 measured from the mean point of impact. 
 
 t The sign, '"^, means that the coordinate distance between the mean 
 point of impact and the shot mark is taken. The confusion arising when 
 these lie on opposite sides of an axis may be avoided by selecting, instead 
 of the target, an arbitrary origin outside the group; so that all deviations 
 shall be -j-. 
 
XXX. — ACCURACY OF FIRE. 25 
 
 would be likely that there had been an irregular wind across 
 the plane ot fire. 
 
 The mean absolute error is principally employed to 
 measure the accuracy of fire arms when tested under the 
 conditions given, page 23. 
 
 Vertical Projections. 
 
 In firing over water, z', z" are unknown or not observed. 
 Therefore, in order to determine where the projectile would 
 have passed through a vertical target in the plane KZ, it is 
 necessary to assume that the angle of fall, w, is constant 
 for the particular range under consideration. Therefore if, 
 as in Chapter XX, we assume that the trajectory for the 
 small distance involved is a straight line, we may write 
 
 s = X X tan c», etc. 
 
 Similarly if we assume that the mean trajectory passes 
 through the mean point of impact in both the vertical and 
 the horizontal planes, we may write e^ = e^ tan go. 
 
 The following system is evidently applicable to computing 
 the results of firing against either horizontal or vertical 
 planes. 
 
 EXAMPLE. 
 
 Suppose we fire 10 shots over water with the sight fixed 
 at the estimated distance of the target, or 1000 yards. The 
 first shot falls 50 yards beyond and 10 yards to the left, and 
 so on as shown in the following table. Shots falling beyond 
 the origin and those going to the right of it are estimated 
 positively. Suppose that we obtain the following record. 
 
26 
 
 XXX. — ACCURACY OF FIRE. 
 
 COMPUTATION. 
 
 
 DEVIATIONS. 
 
 EKRORS. 
 
 SQUARES OP 
 
 
 
 
 
 
 ERRORS. 
 
 
 No. 
 
 
 
 
 
 
 
 r, etc. = 
 
 of 
 Fire 
 
 In Range. 
 
 Lateral. 
 
 In Range. 
 
 Lateral. 
 
 In Range. 
 
 Lateral. 
 
 (^+<)' 
 
 
 
 
 
 
 
 
 
 + 
 
 - 
 
 + 
 
 - 
 
 + 
 
 - 
 
 + 
 
 
 '! 
 
 1 
 
 1. 
 
 50 
 
 
 
 10 
 
 25 
 
 
 
 8 
 
 625 
 
 64 
 
 26 
 
 2. 
 
 
 30 
 
 5 
 
 
 
 55 
 
 7 
 
 
 3025 
 
 49 
 
 55 
 
 3. 
 
 20 
 
 
 15 
 
 
 
 5 
 
 17 
 
 
 25 
 
 289 
 
 18 
 
 4. 
 
 100 
 
 
 
 6 
 
 75 
 
 
 
 4 
 
 5G25 
 
 16 
 
 ■(5 
 
 5. 
 
 
 70 
 
 
 4 
 
 
 95 
 
 
 2 
 
 90i5 
 
 4 
 
 95 
 
 6. 
 
 150 
 
 
 
 20 
 
 125 
 
 
 
 18 
 
 15625 
 
 324 
 
 126 
 
 7. 
 
 
 60 
 
 
 
 
 
 
 85 
 
 2 
 
 
 7225 
 
 4 
 
 85 
 
 8. 
 
 
 
 
 10 
 
 
 
 25 
 
 12 
 
 
 625 
 
 144 
 
 2S 
 
 9. 
 
 90 
 
 
 
 10 
 
 65 
 
 
 
 8 
 
 4225 
 
 64 
 
 66 
 
 10. 
 
 
 — 
 
 — 
 
 
 
 25 
 
 2 
 
 
 625 
 
 4 
 
 25 
 
 Total 410 
 —160 
 
 160 
 
 30 
 
 50 
 -30 
 
 290 
 
 +290 
 
 290 
 
 40 
 
 +40 
 
 40 
 
 ^V 1=46650 
 
 ^17, =962 
 
 10)600 
 £ —00 
 
 10)250 
 
 
 
 10)20 
 
 10)580 
 
 
 10)80 
 
 
 
 
 
 + 25.0 
 
 
 
 —2.0 
 
 £,=58.0 
 
 
 £2=8.0 
 
 
 
 
 
 Mean deviation in range = 
 
 Mean error 
 
 in range 
 
 
 + 25.0 yds. 
 
 = 58.0 yd 
 
 3. 
 
 
 
 
 Mean lateral deviation = 
 
 Mean latera 
 
 1 error = 
 
 
 
 
 -2.0 yds. 
 
 =8.0 yds. 
 
 
 
 
 
 From the above computation and figure 20 it appears 
 that the mean range is 1025 yards, so that if the elevation 
 had been taken for 975 yards the target would have been 
 more probably hit. 
 
 The shaded rectangle of figure 20 represents the plan of 
 a vessel: it applies to the subject of Probability of Fire yet 
 to be discussed. 
 
 Note. — When the mean range is correctly found the + errors are 
 equal to the — errors of the same kind. This tests the accuracy of the 
 work. It is not necessary however that fractional parts of yards should 
 enter into the value of the mean range. 
 
XXX. — ACCURACY OF FIRE. 27 
 
 Swiss Method. 
 
 When the number of shot marks is very great, as in 
 volley firing with small arms, it may be very difficult to 
 measure all the individual shot marks without error. The 
 following method may then be employed. See figure 20'. 
 
 Count the total number of shot marks = n. Then hold- 
 ing a straight edge horizontally slide it over the face of the 
 
 fi 
 target until - marks lie above it; indicate this by a hori- 
 zontal line. Draw similar lines for-— and — -, and repeat the 
 
 process with the straight edge vertical. 
 
 We may thus approximate closely to the measurement of 
 all the elements of the computation; but we must assume 
 that all the shots strike the target. 
 
 III. PROBABILITY. 
 
 By the probability of hitting a target under certain circum- 
 stances is meant the ratio of the number of times that the 
 target would be hit to the whole number of shots fired, sup- 
 posing the number of shots fired under these circumstances 
 to be infinite. 
 
 Here unity is the mathematical symbol for certainty, so 
 that a probability of \ or 25 per cent, signifies that one hit 
 may reasonably be expected from four independent shots 
 fired under the same circumstances. 
 
 If the same ratio held with a finite number of shots we 
 could calculate with certainty beforehand the number of shots 
 necessary to yield a certain number of hits. But in practice 
 the ratio is not certain, but only approximate ; the approxi- 
 mation increasing with the number of shots upon which the 
 calculations are based. 
 
28 XXX. — ACCURACY OF FIRE. 
 
 Probability Curve. 
 
 Suppose we take as an origin a point at a distance from 
 the gun equal to the mean range, and lay off the errors to 
 the right and left of this point according as they are pos- 
 itive or negative. If then, corresponding to each error in 
 range as an abscissa we draw an ordinate of a length pro- 
 portionate to the probability of that error, the coordinates 
 so obtained will be those of the points of a curve known as 
 Probability Curve, figure 21. 
 
 The general form of this curve will appear from consid- 
 ering; 
 
 1. That small errors are more probable than large ones, 
 and therefore that the ordinates will be greatest for the 
 smallest errors.* 
 
 2. That postive and negative errors are equally probable, 
 and therefore that the probability curve will be symmetrical 
 about the axis of S. 
 
 3. That large errors are not practically to be expected; 
 since such errors would come under the head of avoidable 
 mistakes. 
 
 4. That the curve will have the axis of X as an asymp- 
 tote; since, theoretically, the only error that can never be 
 committed is one that is infinitely great. 
 
 The equation of the probability curve is 
 
 in which s is the probability of an error of the magnitude 
 x; e is the base of the Napierian system of logarithms, a:id 
 h is the measure of precision, the value of which is found 
 to be 
 
 ^ = \/^> (3) 
 
 * See remark as to the density of the sheaf of trajectories, page 6. 
 
XXX.— ACCURACY OE FIRE. 29 
 
 in which n is the number of shots fired, and ^z;^ is the 
 sum of the squares of the errors in the direction in which 
 these are estimated. 
 
 By multiplying both members of Eq. (1) by dx and inte- 
 grating between limits x^ = OM and x^^ON we may 
 obtain the probability of committing an error in range 
 between the two errors x^ and ^„, or 
 
 h /• /jv-2 2 
 
 P=—^f^-e dx= 2iVQ2i RMNL. (3) 
 
 The total area between the curve and the axis of X is 
 unity, so that, for a particular curve in which range errors 
 only are considered, if the area R M N L = ^, the mean- 
 ing of the case would be, that when the center of the 
 group of shot marks was at O, a target, the length of 
 which measured in the plane of fire is MN, and the width 
 of which at right angles to the plane of fire is infinite, and 
 which is situated at the distance O M from the center of 
 the group could reasonably be expected to be struck by 
 one tenth the number of shots fired at it; the certainty of 
 prevision increasing with the accuracy with which h is 
 known, or with n, Eq. (2). 
 
 It is evident that the above discussion applies as well to 
 lateral errors as to errors in range, and that for each gun 
 and range an infinite number of probability curves exists, 
 depending upon the directions assumed fo^ the axes. Of 
 these we shall consider but two, but it is well to remember 
 that the others together form the surface of probability j\ 
 
 Note. — For the deduction of these equations and for the fuller treat- 
 ment of the subjects herein discussed see the work on " The Accuracy 
 and Probability of Fire " by Ensign J. H. Glennon, U. S. N. The sub- 
 ject is treated in other works on Probability, and Least Squares. 
 
 f Consider an infinite number of shots fired against a target. Im- 
 agine that after firing all the projectiles are arranged upon the points on 
 
30 XXX. — ACCURACY OP FIRE. 
 
 figure 22, the volume between which and that portion of the 
 plane of reference bounded by any plane figure is propor- 
 tional to the probability of striking an object of the 
 dimensions and position of the figure at the range and 
 under the circumstances in question. 
 
 Since, from the symmetry of the probability curve the 
 integral between the limits — x and + x Eq. (3) is twice 
 the integral from — ^ to O, or from O to -\-x, we have 
 
 as the probability that a it error in range taken without 
 regard to its sign is numerically less than x. 
 
 Taking /ix as one variable, the values of I* correspond- 
 ing to its different numerical values have been calculated 
 and are arranged in the following Table I. 
 
 Example. — Suppose it be desired to compute the chance of 
 hitting the deck of a ship 300 feet long and 36 feet wide 
 (100 yds by 12 yds.), the keel of the ship being in the plane 
 of fire and the center of the ship being at the mean point 
 of impact. The circumstances being those given in the 
 preceding example. 
 
 We have h^ = \/ -^r^^r-^ " \/ 93300 ^ ~M "^ ().^(^^^. 
 
 Therefore, supposing for the present that the ship is of 
 indefinite width or that we are firing at a belt or zone at 
 right angles to the plane of fire and limited by parallel 
 lines at 50 yards on each side of the mean point of impact; 
 
 which they struck, being superposed one upon the other upon the ele- 
 mentary surfaces upon which they fell. The mass of projectiles will thus 
 form a volume bounded by the surface of probability and the target. 
 
XXX. — ACCURACY OF FIRE. 
 
 31 
 
 P^ 
 
 TABLE I. 
 
 PROBABILITY OF ERRORS, 
 2 ^.^ —h^x^ 
 
 S'Tt J 
 
 d {hx), 
 
 hx 
 
 P 
 
 hx 
 
 P 
 
 hx 
 
 P ' 
 
 hx 
 
 1 
 
 P 
 
 hx 
 
 P 
 
 0.00 
 
 0.00000 
 
 0.40 
 
 0.42839 
 
 0.80 
 
 0.74210 
 
 1.20 
 
 0.91031 
 
 1.60 
 
 0.97635 
 
 .02 
 
 .02256 
 
 .42 
 
 .44747 
 
 .82 
 
 .75381 
 
 1.22 
 
 .91553 
 
 1.62 
 
 .97804 
 
 .04 
 
 .04511 
 
 .44 
 
 .46622 
 
 .84 
 
 .76514 
 
 1.24 
 
 .92050 
 
 1.64 
 
 .97962 
 
 .06 
 
 .06762 
 
 .46 
 
 .48465 
 
 .86 
 
 .77610 
 
 1.26 
 
 .92523 
 
 1.66 
 
 .98110 
 
 .08 
 
 .09008 
 
 .48 
 
 .50275 
 
 .88 
 
 .78669 
 
 1.28 
 
 .92973 
 
 1.68 
 
 .98249 
 
 .10 
 
 .11246 
 
 .50 
 
 .52050 
 
 .90 
 
 .79691 
 
 1.30 
 
 .93401 
 
 1.70 
 
 .98379 
 
 .12 
 
 .13476 
 
 .52 
 
 .53790 
 
 .92 
 
 .80677 
 
 1.32 
 
 .93806 
 
 1.72 
 
 .98500 
 
 .14 
 
 .15695 
 
 .54 
 
 .55494 
 
 .94 
 
 .81627 
 
 1.34 
 
 .94191 
 
 1.74 
 
 .98613 
 
 .16 
 
 .17901 
 
 .56 
 
 .57161 
 
 .96 
 
 .82542 
 
 1.36 
 
 .94556 
 
 1.76 
 
 .98719 
 
 .18 
 
 .20093 
 
 .58 
 
 .58792 
 
 .98 
 
 .83423 
 
 1.38 
 
 .94902 
 
 1.78 
 
 .98817 
 
 .20 
 
 .22270 
 
 .60 
 
 .60386 
 
 1.00 
 
 .84270 
 
 1.40 
 
 .95228 
 
 1.80 
 
 .98909 
 
 .22 
 
 .24429 
 
 .62 
 
 .61941 
 
 1.02 
 
 .85084 
 
 1.42 
 
 .95537 
 
 1.82 
 
 .98994 
 
 .24 
 
 .26570 
 
 .64 
 
 .63458 
 
 1.04 
 
 .85865 
 
 1.44 
 
 .95830 
 
 1.84 
 
 .99073 
 
 .26 
 
 .28690 
 
 .66 
 
 .64938 
 
 1.06 
 
 .86614 
 
 1.46 
 
 .96105 
 
 1.86 
 
 .99147 
 
 .28 
 
 .30788 
 
 .68 
 
 .66378 
 
 1.08 
 
 .87333 
 
 1.48 
 
 .96365 
 
 1.88 
 
 .99216 
 
 .30 
 
 .32863 
 
 .70 
 
 .67780 
 
 1.10 
 
 .88020 
 
 1.50 
 
 .96610 
 
 1.90 
 
 .99279 
 
 .32 
 
 .34912 
 
 .72 
 
 .69143 
 
 1.12 
 
 .88679 
 
 1.52 
 
 .96841 
 
 1.93 
 
 .99338 
 
 .34 
 
 .36936 
 
 .74 
 
 .70468 
 
 1.14 
 
 .89308 
 
 1.54 
 
 .97058 
 
 1.94 
 
 .99392 
 
 .36 
 
 .38933 
 
 .76 
 
 .71754 
 
 1.16 
 
 .89910 
 
 1.56 
 
 .97263 
 
 1.96 
 
 .99443 
 
 .88 
 
 .40901 
 
 .78 
 
 .73001 
 
 1.18 
 
 .90484 
 
 1.58 
 
 .97455 
 
 1.98 
 2.0 
 3.0 
 
 00 
 
 .99489 
 
 .99532 
 
 .99998 
 
 1.00000 
 
32 XXX. — ACCURACY OF FIRE. 
 
 the permissible error is ± 50 yds =::v .*. >^^ = 0. 49 and 
 /i* from the table is about 0.51. 
 
 Similarly for the lateral precision; — 
 
 ^2 = i / ^ = 0.0684 and h^x-= 0.41, 
 y 1924 
 
 and p^ from the Table is about 0.43. 
 
 That is, that about 43 per cent of the shots will fall with- 
 in a belt 6 yds. wide on each side of the plane of fire. 
 
 Now, from the theory of probabilities, the probability of 
 the concurrence of two events is the product of the proba- 
 bility of each of the two events when considered separately; 
 the probability that a shot will fall within both belts is 
 /o = 0.51 X 0.43 = 0.22 
 
 OTHER MEASURES OF INACCURACY. 
 
 Probable Error. 
 
 In case that hx is so chosen that P in Eq. (4) is equal 
 to J, the probability of committing an error numerically less 
 than X is equal to that of committing an error numerically 
 greater than x. Such a value of x is called the probable 
 error, or r. By interpolating in Table I it is found that 
 for P = \,hx = hr — 0.4769, or 
 
 r = -^iZ^ = 0.4769 yi / ^^^^^^ = 0.6745 
 
 /4^i 
 
 The term probable error is a misnomer. Its true mean- 
 ing may be illustrated by reference to figure 21 in which if 
 x = r=OM be so taken that O SMR = J then, from the 
 symmetry of the curve 2 0SMP = ^; or 2r will be the 
 width of the space, measured equally in both directions 
 from the mean point of impact, within which the shots are 
 
 * The symbols /i /g /a correspond to the nomenclature page 24. 
 
XXX. — ACCURACY OF FIRE. 33 
 
 as likely to fall as not, or within which there is an even 
 chance of striking. The accuracy varies inversely with the 
 magnitude of this error. 
 
 True Mean Error. 
 
 The probable error must not be confused with the 
 mean error already found. In the example the probable 
 error in range is r = 48.5 yds. and the mean error is 58 
 yds. The latter value is only an approximation to the 
 true mean error^ for which the symbol is x. From the 
 equation of the probability curve this has been found 
 
 -__ 1 
 
 or in the example, ^ = 57 yards: very nearly the mean 
 error. 
 
 By combining the expressions for x and r we find the 
 ratio 
 
 -^ = 0.8453. (6) 
 
 X 
 
 Probable Zones and Rectangles. 
 
 From the foregoing example we see that the true mean 
 error does not differ materially from the computed mean 
 error obtained with a fair number of shots. 
 
 Also, that since the positive and negative errors are equal, 
 if r be the probable error in either direction from the mean 
 point of impact, 2r = 1.69 x will be the width of a zone 
 measured at right angles to the direction of the error that 
 will contain half the number of shot marks. 
 
 This measure is much used in the British service in 
 which the mean error in range X 1.69 gives very nearly 
 
 * In the mathematical course this is called the mean error. 
 
34 XXX. ACCURACY OF FIRE. 
 
 the width (in the plane of fire) of the length zone, figure 23. 
 See page 38. 
 
 Similarly, the mean lateral error x 1.69 gives the width 
 (at right angles to the plane of fire) of the breadth zone^ 
 figure 24. 
 
 The mean vertical error x 1.69 — the mean error in 
 range xtano? x 1.69, gives the width (vertically) of the 
 height zone. 
 
 Referring to the horizontal plane, the intersection of the 
 length and breadth zones gives a rectangle probably con- 
 taining \ of ^, or \ of the whole number of shots. See 
 pages 27 and 32. This is called the ^h per cent rectangle. 
 
 The Probable Rectangle is the 50 per cent rectangle, or 
 is the rectangle of which (the center being at the mean 
 point of impact, and the sides being parallel to the directions 
 in which the errors are measured) the sides are respectively 
 proportional to the probable errors in the same directions, 
 and the probability of hitting within it in either direction is 
 
 = ^"1=0.7071.1 
 
 By reference to Table I, we find that for /'^z: 0.7071, 
 hx = 0.7438. 
 
 By substituting the value of h (Eq. 2) we have for the sides 
 of the probable rectangle — 
 
 length = 2 X, = 2.104 \J ^ (6) 
 
 breadth = 2 ^, := 2.104 y ~i (7) 
 
 Remark. 
 
 The probable rectangle is seen to be useful in comparing 
 the accuracy of two guns by comparing the magnitudes of 
 the errors which they will make with equal facility. 
 
XXX. ACCURACY OF FIRE. 35 
 
 Its determination is based on the Theory of Probabilities, 
 but is only indirectly connected with the probability of 
 hitting at a single shot a target the dimensions and position 
 of which are known. 
 
 Accuracy of a Gun. 
 
 The probable rectangle in the horizontal plane will vary 
 in dimensions for different guns and different mean ranges, 
 and its size will be an inverse measure of the accuracy of 
 the gun for the mean range for which it is calculate<i. 
 
 Unless the angle of fall is the same for the different 
 guns in question, the relative accuracy as determined by 
 the size of the i)robable rectangle in the vertical plane will 
 be very different from that determined in the horizontal 
 plane. A gun having a very flat trajectory is placed at a 
 disadvantage when its accuracy is measured by the size of 
 its probable rectangle in the horizontal plane; and, in gen- 
 eral, the more nearly the plane of the target coincides with 
 direction of the fall of the projectiles, the greater is this 
 disadvantage. On the other hand, guns are placed on the 
 sam«=» footing, and each shows best its accuracy when the 
 target plane for each gun is chosen perpendicular to 
 the trajectory at the mean point of impact. Against 
 vulnerable horizontal targets, as the decks of ships, better 
 results may therefore be expected with rifled mortars than 
 with high powered guns; unless these latter are mounted 
 in a commanding position, or the muzzle velocity is so re- 
 duced, as to give a large angle of fall on the horizontal 
 plane in question. 
 
 Probability of Hitting an Object of any Form. 
 
 Table I may be used for finding the probability of hitting 
 a target. As, however, the probable errors, laterally and 
 in range, would usually be given, a more convenient table 
 
S6 
 
 XXX. — ACCURACY OF FIRE. 
 
 X. 
 
 IS one in which the argument is -* This is readily formed 
 from Table I by remembering the relation between /i and 
 r, or - = ____- whence, 
 
 0.4769 
 
 ^x 
 
 r ~~ 0.4769 ^^ 
 
 Table II, known as Chauvenet's table, is to be used after 
 the manner of a table of logarithms. Thus for a value of 
 
 X 
 
 -=0.40 the corresponding probability is 0.21: Con- 
 versely, a probability of 0.535, or 53^ per cent, corresponds 
 
 X 
 
 to a value of — = 1.08. 
 r 
 
 In figure 25 is plotted the curve expressing the relation 
 
 between — and F, 
 r 
 
 F = 
 
 TABLE II. 
 
 PROBABILITY OF ERRORS, 
 
 2 .* —t^ 
 
 
 dt, t 
 
 X 
 
 >^jt: = 0.4769 - 
 r 
 
 P. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.0 
 
 
 
 .02 
 
 .04 
 
 .06 
 
 .07 
 
 .09 
 
 .11 
 
 .13 
 
 .15 
 
 .17 
 
 .1 
 
 .18 
 
 .20 
 
 .22 
 
 .24 
 
 .26 
 
 .28 
 
 .30 
 
 .32 
 
 .34 
 
 .36 
 
 .2 
 
 .38 
 
 .40 
 
 .41 
 
 .43 
 
 .45 
 
 .47 
 
 .49 
 
 .51 
 
 .53 
 
 .55 
 
 .3 
 
 .57 
 
 .59 
 
 .61 
 
 .63 
 
 .65 
 
 .67 
 
 .70 
 
 .72 
 
 .74 
 
 .76 
 
 .4 
 
 .78 
 
 .80 
 
 .82 
 
 .84 
 
 .86 
 
 .89 
 
 .91 
 
 .93 
 
 .95 
 
 .98 
 
 .5 
 
 1.00 
 
 1.02 
 
 1.04 
 
 1.07 
 
 1.09 
 
 1.12 
 
 1.14 
 
 1.17 
 
 1.19 
 
 1.22 
 
 .6 
 
 1.25 
 
 1.27 
 
 1.30 
 
 1.33 
 
 1.36 
 
 1.39 
 
 1.42 
 
 1.45 
 
 1.48 
 
 1.51 
 
 .7 
 
 1.54 
 
 1.57 
 
 1.60 
 
 1.64 
 
 1.67 
 
 1.71 
 
 1.74 
 
 1.78 
 
 1.82 
 
 1.86 
 
 .8 
 
 1.90 
 
 1.94 
 
 1.98 
 
 2.03 
 
 2.08 
 
 2.13 
 
 2.18 
 
 2.24 
 
 2.30 
 
 2.37 
 
 .9 
 
 2.44 
 
 2.52 
 
 2.60 
 
 2.69 
 
 2.78 
 
 2.91 
 
 3.04 
 
 3.22 
 
 3.45 
 
 3.82 
 
XXX. — ACCURACY OF FIRE. 
 
 RECTANGULAR OBJECT. 
 
 In figure 26 suppose O is the mean point of impact of a 
 number of shots in the horizontal plane, OX the direction 
 in which range errors are measured, and (9 F perpendicular 
 to OX, the direction in which lateral errors are measured. 
 Required the probability of hitting the rectangle A B CD, 
 of which O is the center, A B and B C being parallel to 
 OX and O Y, 
 
 Let ri and r^ be the probable errors of the gun in range 
 and laterally under the circumstances. 
 
 The probability of committing an error in range less 
 numerically than OE is, found in the table for 
 x__ O E 
 
 The probability of committing a lateral error less num- 
 erically than OF IS found likewise in the same table 
 
 OF 
 
 for ■. The probability of the concurrence of these 
 
 two events is the probability of hitting inside the rectangle 
 A BCD, which is therefore the product of the two prob- 
 abilities found. 
 
 The probability of hitting inside the rectangle O F B E 
 is \ the probability of hitting inside the rectangle A BCD; 
 since numerically equal positive and negative errors are 
 equally probable, and the probability of hitting A BCD is 
 the sum of the probabilities of hitting the four smaller 
 rectangles into which it is divided. 
 
 The probability of hitting inside the rectangles OFM N 
 and O LRE is found in the same way as that of hitting 
 inside OFBE. 
 
 The probability of hitting inside NM B E is that of 
 hitting inside OFBE minus that of hitting inside OFMN, 
 Similarly for LFBR, LFMK and NKRE. 
 
38 XXX. — ACCURACY OF FIRE. 
 
 The probability of hitting KMB R is that of hitting 
 NMBE minus that of hitting N K R E. 
 
 ANY PLANE FIGURE. 
 
 Any plane figure may be divided (approximately) into 
 small rectangles and the probability of hitting each rec- 
 tangle found. The sum of the separate probabilities may 
 then be found, and this will be the probability of hitting 
 the figure. 
 
 In what has preceded we have used horizontal targets. 
 There is nothing in the method, however, that will not 
 apply equally well to vertical targets if we substitute ver- 
 tical for range errors. 
 
 EXAMPLES IN THE PROBABILITY OF FIRE. 
 
 Although the value of the probable error may be ascer- 
 tained, the computation may be abbreviated by assuming 
 that the true mean error, x^ does not differ materially from 
 the mean error f, determined as shown on page 24. 
 
 So that in Table II the ratio — may be taken as equal to 
 2^ 2j\? 2x 
 
 2^ 2 x0.845 a: 1.69 e* 
 
 from which the corresponding probability may be found. 
 
 The same results are obtained by the English method of 
 using the 50 per cent zones, as follows: 
 
 This considers that the width of the 50 per cent zone is 
 unity, see Table II, and therefore, (the probable error of the 
 gun being constant for the same range and circumstances) 
 that the width of other zones containing a per cent of shots 
 greater or less than 50 per cent is proportional to the cor- 
 
XXX. — ACCURACY OF FIRE. 39 
 
 2x 
 responding value of — ; 2r representing the width of 
 2r 
 
 the 50 per cent zone. And conversely, that when the 
 
 ratio - is known, the probability of striking within the given 
 r 
 
 zone is that given by the corresponding value of /'in Table II. 
 
 Data. 
 
 For a given gun under given conditions we have— 
 E = 4945 yds.; cj = 7° 25': e, =19.4 yds.; e,= 1.8 yds.; 
 ^3 = 19.4 X tan 7° 25' = 2.5 yds. 
 
 Suppose that unless otherwise stated the mean point of 
 impact is at the center of the target. 
 
 1. Determine the probability of striking a raft 12 yds. 
 square at the range R, 
 
 9y- 19 
 
 ri!= — = 4 . •. A. = 1, or practical cer- 
 
 2/2 1.8 X 1.69 
 
 tainty ; and about 1 out of 5 shots may be expected to 
 strike the raft. 
 
 2. Suppose the target to be of the same dimensions and 
 vertical : we have /^ = 1 ; /3 = 0.945 =/o- See page 85. 
 
 3. If a zone of a certain width catches 20 per cent of the 
 shots fired, how much wider must another zone be to catch 
 80 per cent? 
 
 From Table II we have for / = 20 per cent, — = 0.38 
 
 x' 
 and for / = 80 per cent, — =1.90, and smce r is constant 
 
 — : - :: 1.90 : 0.38 or ^' = 5 x. 
 r r 
 
40 XXX. — ACCURACY OF FIRE. 
 
 4. Suppose that the mean point of impact is at the middle 
 of the lower edge of a target 8 feet square. (The case cor- 
 responds to firing at the water line of a vessel.) 
 
 We suppose the target to be extended downward by an 
 amount equal to its height, and take for p^ half the prob- 
 ability of striking the whole target: we have 
 
 /2 = 0.45; A = -^ ••• A = 0.135. 
 
 5. What would be the effect of raising the mean point of 
 impact 2 feet on the above target? 
 
 Suppose that target to be extended downward 4 feet, as 
 in figure 27. Then the target may be supposed to be com- 
 posed of two portions a and b, the former of which is half 
 the height of a target 12 feet high, and the other portion 
 half the height of a target 4 feet high. 
 
 We find for a p^ = ^^ = 0.24 
 
 2 
 
 and for ^ p/ = ^ = 0.085 
 
 .-. /3= 0.325 
 
 and /o== 0.146. 
 
 6. Suppose, as in figure 28, that there are two targets 8 
 feet square and 8 feet apart fired at from the above gun and 
 at the above range. Which plan would give the greater 
 number of hits in the two targets collectively : 
 1st. To aim at the center (a) of one ? 
 2nd. To aim at the center ^^) of the space between 
 the two ? 
 We will suppose the mean point of impact will fall on the 
 point aimed at, and, as the mean vertical error will be con- 
 stant, we may neglect it in making the comparison desired. 
 
XXX. — ACCURACY OF FIRE. 41 
 
 First Case. 
 
 For the target aimed at we have // = 0.45. 
 
 Now, consider the target (4 + 8 + 8) x 2 = 40 feet wide, 
 and take one half the resulting value of p^ or p^' = 0.50. 
 
 Similarly consider the target (4 + 8) x 2 = 24 feet wide 
 and find //" = 0.47. 
 
 Then, /a" — //" = 0.03 is the probability of hitting the 
 target not aimed at, and p^ =// + (//' — //" ) = 0.48 will 
 be the probability for both targets. 
 
 Second Case. 
 
 Considering the target 24 feet wide p^ = 0.947 
 and for the middle space A"== ^-^^ 
 
 A = 0.497. 
 
 RIGHT LINE METHOD. 
 
 The abscissa of the center of gravity of the area included 
 between the axes OX and OS and the probability curve 
 A B Cf figure 29, is evidently the frue mean error, x, or the 
 arithmetical mean of an infinite number of errors. 
 
 If we draw D E so that the centers of gravity oi D O E 
 and O A B C a:^ O shall coincide, and call O E — m, then 
 
 D O E = O A B 'C ^ O = h 2cci^ D O = -' 
 
 m 
 
 From the properties of the triangle the abscissa of the 
 
 171 
 
 center of gravity oiDOE^ — =E\ and if the probability 
 
 o 
 
 curve were considered to be a right line we would have x = e. 
 Given then the mean error, e, the line D E would be deter- 
 mined. 
 
 In case the right line method were strictly accurate, 
 
42 XXX. — ACCURACY OF FIRE. 
 
 there would be no possibility of committing an error greater 
 them m^ which would therefore be an extreme error. 
 
 Let us see from the probability curve what would be the 
 probabiHty of committing an error less than in. We have, 
 assuming e = x. See page 33. 
 
 3 
 
 h 
 
 ^Jn' 
 
 m = 3x mean error = 
 
 3 
 
 whence /im= — ; — = 1.6925. 
 
 Referring to Table I, we find the corresponding proba- 
 bility 0.983; that is, 98 per cent of the shots will make an 
 error less than three times the mean error: a close approxi- 
 mation. 
 
 Also making x= 0, in Equation (1.) 
 
 we have the value of the maximum ordinate of the proba- 
 bility curve. It is 
 
 L=^V^ = ___J___ 
 
 •^0 ~ ^^ ^r~ 7t X mean error ' 
 
 Similarly the corresponding ordinate in the case of the 
 right line is 
 
 3 X mean error* 
 or slightly greater than the probability curve. 
 
 These differences are not material. The approximation in 
 other cases is shown by figure 29; the probability of com- 
 mitting an error between O and -{- x {= O J*') being, ac- 
 cording to the probability curve, the area O A B F^ and 
 according to the right line the area ODGF. Experience 
 also shows that, in firing projectiles, the extreme error is 
 a little more than three times the mean error, but this is not 
 of great importance; all that is necessary is that the proba- 
 
XXX. — ACCURACY OF FIRE. 43 
 
 bility of exceeding this error should be small enough to 
 be neglected, and we cannot have any doubt in this respect. 
 
 Equation of the Eight Line. 
 
 In the two triangles ODE and FGE, tan DEO=^ 
 
 CE DO 
 
 -j^-pr^ = -TTTF-or Substituting for G E, EE, DO 2ind OE 
 EE OE ^ ' ' 
 
 their values, s, m — x^ — and m, respectively, we have 
 
 (9) 
 
 m — X 
 
 m 
 
 
 1 
 
 m — X 
 
 m"' 
 
 °' ^- m' ' 
 
 as the equation of the line D E. 
 
 The probability of hitting within a small length dx, at x 
 is then 
 
 pz=zs dx — ^ dx. (10) 
 
 Probability of Hitting any Plane Figure. 
 
 Suppose positive errors in range are measured in the 
 direction OX figure 32, from the mean point of impact O^ 
 O M being equal to m^ the extreme error in range. 
 
 Following out the supposition of the two causes of error, 
 
 suppose positive lateral errors are measured in the direction 
 
 of the axis O Y, (9 iV being equal to «, the extreme lateral 
 
 error. 
 
 w ~~ X 
 li D C represent dx, p^ = g— dx, is the probability 
 
 of hitting somewhere between the lines AD and B C, dis- 
 tant -\- x\w range from the mean point of impact. 
 
 n — y 
 If KR represent dy, p^ = — g— dy, is the probability 
 
 of hitting between the lines ET and -^^S", distant + y lat- 
 erally from the mean point of impact. 
 
44 XXX. — ACCURACY OF FIRE. 
 
 The small area A' B' C D' fulfills both these conditions 
 and the probability of hitting it is therefore 
 
 m—x. n—y , 
 pxy = «- dx — /- dy. 
 
 If we denote by Z>" D and A" D, figure 32, by y^ and y^ 
 respectively, the probability of hitting between two lines 
 drawn through the points £>" and A'^ parallel to O X is 
 
 PJ=/:^^y. 
 
 If however, we limit the target in the direction of the 
 range errors to the length dx at + x, the probability of 
 hitting the target, which is represented by A'' B" C" D" is 
 
 If y^-=f^{x) and jJ^2=/2 (^) are the equations of two 
 curves H D" G and E A'* F we can write 
 
 = ^Z^^. /•/«(-) ^li:^dy^F(x)dx, 
 
 as the probability of hitting any elementary area 
 A'' B'' C B>'\ 
 Calling O Z. a^, and O K^ a^^ the probability of hitting 
 the figure E F G If is 
 
XXX. — ACCURACY OF FIRE. 45 
 
 Remark. 
 
 Caution is necessary in using the right Hne method. The 
 ordinates of the prolonged hne D E^ figure 29, to the right 
 of E do not represent probabihties, nor do they to the left 
 of D. As a consequence, in the figure, first ^i, a^^ yi^y^ 
 must be positive ; second, when either of these exceeds the 
 extreme error in its direction, it must be placed equal to 
 that extreme error. The probability of hitting a figure, part 
 of which is in each of the quarters of the extreme rectangle 
 surrounding the mean point of impact, is obtained by ad- 
 ding together the probability of hitting the parts, calculated 
 separately. Distances measured along the axes OX and 
 O Y from the mean point of impact are regarded as pos- 
 itive in each quarter. 
 
 It will be noted that this method dispenses with the use 
 of the tables. 
 Abbreviation of the Right Line Method. 
 
 In figure 30 the probability of an error less than x will 
 be the quotient of the area of the trapezoid above x by the 
 area of the triangle above m. Call these areas T and A 
 and let e be the abscissa of the center of gravity of the 
 triangle, then 3 e = m. 
 
 We have 
 
 -•v'>- 
 
 
 From the similarity of the triangles 
 
 
 m 
 
 ■6e 
 
 -(-0 
 
 
 30 sm 3 s s 
 
 
 or 
 
46 XXX. — ACCURACY OF FIRE. 
 
 Therefore 
 
 Jy _ T _% X 1 [X\^ 
 
 This gives a formula that can be very easily memorized. 
 See below. 
 Application to Different Figures. 
 
 Rectangle. — In figure 31, denotin-g O F hj a, and O E 
 by b, the probability of hitting the rectangle E A F O is 
 
 ^mn\ m J \ nj 
 
 The probability of hitting the rectangle D A B C of 
 which the center is at the mean point of impact, is four 
 times the probability for E A F 0; or 
 
 ° m n \ in J \ nj 
 
 '%a 
 m 
 or, since m = Z e^ and n = ^ e^, 
 
 ^»- [si - 9 J "" [37, 9" (1;) J • 
 
 Applying this method to example page 30, we have, 
 since w = 58 x 3 = 174 and ;? = 8 x 3 = 24 
 
 rioo / 50 \n ri2 /6 \n 
 ^-[m-(m;J"L24-(24)J 
 
 = 0.4922 X 0.4375 = 21.54 per cent, 
 a close approximation to the longer method. 
 
XXX. — ACCURACY OF FIRE. * 47 
 
 Other Figures. 
 
 Similar applications are given in the work of Ensign 
 Glennon, for triangles, trapezoids and rhombs, so that such 
 apparently difficult problems as the probability of hitting 
 the gable end of a house may be computed. These meth- 
 ods are too elaborate for this course; but the following 
 formula may be used for small arm firing, the targets in 
 which are ellipses whose axes are determined by the rela- 
 tion between the mean vertical and lateral errors of the arm 
 and ammunition. 
 
 Ellipse: — Calling a and b the semi-axes of the ellipses 
 corresponding in direction to m and «, we find in Glennon 
 
 p^-2ab fn 2a 2b ab \ 
 \ mn \2 3m 3?i 4= m n J' 
 
 (13) 
 
 Circle. — If we make b = a — r the ellipse 
 
 becomes a 
 
 circle, and 
 
 ^ _2r'' f n 2r 2r r^ \ 
 
 ^"^ mfi\2 3m 3n^ 4.mn) ' 
 
 (14) 
 
 Remarks. 
 
 
 These methods have a practical application in determin- 
 ing the supply of ammunition necessary to produce a given 
 result. Also, when time is limited, as in the attack of tor- 
 pedo boats, and the rate of fire of the guns is known, the 
 number of guns to be mounted on a certain front may be 
 calculated. 
 
 In solving problems for ranges at which the mean erroi's 
 are not given, these may be taken as proportional to the 
 squares of the nearest ranges for which the errors are given. 
 Animate Objects. 
 
 The following table may be used in connection with 
 problems in the probability of small arm fire. It is derived 
 from the measurement of photographs of a number of Ital- 
 ian soldiers, of average size and build, taken naked. 
 
48 
 
 XXX. — ACCURACY OF FIRE. 
 
 TABLE III. 
 
 
 Mean 
 h't, ft. 
 
 Mean 
 
 Vertical 
 
 OBJECT. 
 
 width, 
 ft. 
 
 Area 
 sq. ft. 
 
 Foot soldier, standing, front. 
 
 5.3 
 
 0.95 
 
 5.0 
 
 Foot soldier, standing, side. 
 
 5.3 
 
 0.57 
 
 3.0 
 
 Foot soldier, kneeling and firing, front. 
 
 3.4 
 
 1.00 
 
 3.4 
 
 Foot soldier, lying down and firing, front. 
 
 1.4 
 
 1.18 
 
 1.7 
 
 Foot soldier, lying down close. 
 
 0.7 
 
 1.64 
 
 1.8 
 
 Horseman and horse, front. 
 
 8.0 
 
 1.52 
 
 12.2 
 
 Horseman and horse, side. 
 
 8.0 
 
 2.4 
 
 19.4 
 
 Horse, front. 
 
 — 
 
 — 
 
 9.0 
 
 Horse, side. 
 
 — 
 
 — 
 
 17.0 
 
 IV. MANAGEMENT OF FIRE. 
 
 THE COLLECTIVE FIRE OF SMALL ARMS. 
 
 Advantages. 
 
 The need of reserving fire for the critical moments of an 
 action, and the difficulty of controlling the fire of troops in 
 dispersed order have led to the use of collective fire from 
 groups of men under the direction of subordinate officers. 
 
 Careful experiments have shown that the superiority of 
 very good individual marksmen over ordinary marksmen 
 diminishes rapidly as the range increases; while skill in 
 collective fire maintains it superiority at all ranges. This 
 skill depends less upon natural aptitude than upon practice 
 under the disturbing circumstances of collective fire, and 
 thus demands "fire discipline". This is even more impor- 
 tant for troops armed with magazine arms than for those 
 armed with single breech loaders. 
 
 Collective fire is regulated by watching the dust thrown 
 up by the hits, at least one half of which should fall short. 
 
XXX. — ACCURACY OF FIRE. 49 
 
 The ricochet at low elevations considerably increases the 
 efficiency of the fire. 
 
 Definitions. 
 
 The intersection of the nucleus and envelope of the sheaf 
 of trajectories by the horizontal plane through the line of 
 sight forms the beaten zone: the grazed zone corresponds to 
 the dangerous space for the lower element of the envelope 
 and is taken to be equal to that of the mean trajectory: the 
 sum of the beaten and grazed zones forms the dangerous 
 zone, as seen in figure 33. 
 
 This figure represents the projection of the sheaf and the 
 zones on the plane of sight. The line of sight is supposed 
 to coincide with the surface of the ground; the firer lying 
 down and aiming at the enemy's feet. He was formerly 
 supposed to stand up and aim at the waist. 
 
 Constancy of the Beaten Zone. 
 
 It has been observed that as the range increases the increase 
 in longitudinal diviation resulting from accidental differences 
 in the angles of departure, is approximately compensated for 
 by the diminished obliquity of the horizontal section of the 
 sheaf resulting from the increased angle of fall. See lines 
 b' z' = b" z"y figure 34. Consequently the depth of the beaten 
 zone is approximately constant at all ranges, although the 
 width of the beaten zone, is, except at extreme ranges, ap- 
 proximately y^f, of the range. With arms and ammunition 
 of the type of the service rifle, cal. 0.45, it is about 100 yards 
 for the nucleus, and about 300 yards for both the nucleus and 
 envelope, as shown in the figure. See extract from Range 
 Table, page 52. 
 
 Eemarks. 
 
 These data are derived from target firing ; in battle the 
 deviations may be eight times as great. 
 
50 XXX. — ACCURACY OV FIRE. 
 
 The depth of the beaten zone may be advantageously 
 increased by varying the elevation of the pieces in a group. 
 Variations in Dangerous Zone. Vulnerability. 
 
 The depth of the dangerous zone varies with; — 
 
 1. The flatness of the trajectory. 
 
 2. The height of the target. 
 
 3. The range. 
 
 4. The inclination of the ground to the line of sight. 
 
 1. FLATNESS OF TRAJECTORY. 
 
 This principally affects the grazed zone. The maximum 
 grazed zone for a man kneeling is in round numbers as 
 follows, Springfield 350 yds., new Hebler 550 yds. See 
 example 7; Chapter XX. The maximum grazed zone is a 
 convenient measure of the power of the arm and ammu- 
 nition. Within this zone adjustment of the rear sight is 
 unnecessary, 
 
 2. HEIGHT OF THE TARGET. 
 
 The maximum grazed zone for a man standing is, Spring- 
 field 420 yds., Hebler 450 yds. In connection with the 
 effect of change of position upon the probability of being 
 struck it may be stated that at medium ranges the vulner- 
 ability^ or chance of being hit with a given expenditure of 
 ammunition, is as follows: Lying down : kneeling : stand- 
 ing :: 1 ; 2 : 3. See ratio of areas in Table III. 
 
 Owing to the increase in the angle of fall at long ranges 
 these differences disappear. 
 
 3. RANGE. ' 
 
 Beyond the maximum grazed zone, the depth of the 
 dangerous zone diminishes as the range increases; and so 
 does the vulnerability, which is approximately diminished 
 one half for every increase in range of 250 yards. 
 
XXX. — ACCURACY OF FIRE. 51 
 
 4. INCLINATION OF THE GROUND TO THE LINE OF SIGHT. 
 
 The effect of variations in the slope of the ground is 
 shown by figure 34 which represents, but not to scale, 
 the nucleus of a 1000 yard trajectory. 
 
 The beaten zones B Z dX different ranges are practically 
 100 yards in depth, if measured on the line of sight. See 
 page 49. 
 
 The included figures show the variations in the beaten 
 zone arising from varying the inclination of the ground 
 respectively -j^; ^; ^ above and below the line of sight.* 
 
 The limit of efficiency is reached when the ground is par- 
 allel to the tangent at and beyond the object aimed at, B. In 
 this case we shall have the largest grazed zone and a large 
 beaten zone making together a deep dangerous zone. Be- 
 yond B there will be one or two grazed zones, depending 
 on, the height of the target T. 
 
 For a given slope the safe zoiie^ x x\ will increase as the 
 enemy approaches from O to B and as his trajectory con- 
 sequently becomes flatter. Troops behind cover will there- 
 fore be better protected by advancing toward the cover as 
 the enemy approaches. 
 
 This explains the vulnerability of deep columns on de- 
 scending slopes and the insecurity of apparently good cover in 
 rear of the point at which the enemy is directing his fire. 
 This was noticed at the battle of Inkerman, in which great 
 destruction was wrought among the horses of an English 
 battery which were out of sight of the enemy, but in rear 
 
 * These slopes arc found about West Point as follows : j 
 y*^ Road to Post-office, near its intersection by the Dragoon path. 
 ^^ From S. W. corner of Academic Building, for a short distance to the 
 
 west. 
 ^ From crosswalk in front of sally port of Academic Building to the 
 north. 
 
52 XXX. — ACCURACY OF FIRE. 
 
 of the guns and on the reverse slope of a hill, the slope of 
 the hill being nearly tangent to the enemy's trajectory. 
 
 Effect of Increasing the Rapidity of Fire of Small Arms. 
 
 Owing to the diminished accuracy of rapid fire, its effect 
 in a given time increases less rapidly than does its rate. It 
 appears from experiment that doubling the rate increases 
 the efficiency about IJ times; viz — 
 
 Kind of Fire. Kate per Min. Kelative Eflaciency 
 
 Common 6 1.0 
 
 Rapid 12 1.5 
 
 Magazine 24 2.25 
 
 The factor of efficiency may be determined from the fol- 
 lowing equation in which e is the factor; n is the number 
 of shots fired at a given target and range, h is the number 
 of hits, and t is the time in minutes required to fire the 
 shots, n. 
 
 Then since the efficiency is directly proportional to h^ and 
 inversely proportional to ?t and to /, we have 
 
 h h h' 
 e = - x- = ■ . (15) 
 
 n i ny^t 
 
 Range Table. Extract. 
 
 Hotchkiss 6 pdr. R. F. Gun. See page 49. I V = 1818, 
 a/ = 2 lbs., W= 6 lbs. 
 
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