involved in the Construction oj" Artillery. 429 



SECTIONS. I'AGI-.. 



122, 123 Three cases of oscillatory movement of elastic bars exposed to extension or com- 

 pression : — 



1°. Where the strain possesses no initial velocity, 199 



124 2°. Where the straining load possesses an initial velocity, .... 200-203 



125 3°. Where a permanent strain being on the bar, it is subjected to that of 



an impulse in addition, 203-205 



126 Conditions of the first oscillation determined, 205 



127 Fundamental equation of motion for velocity V, 206 



128 General conclusions derived for the period and time of oscillation of elastic bars 



exposed to longitudinal extension or compression, assuming the elasticity per- 

 fect, 207 



129 This condition, however, strictly does not exist in nature ; defect of elasticity limits 



the number of oscillations before rupture; these very great when 7", is high 



and surplus strength great, 207 



130 Application of the equations to cannon, 208 



131 As cannon are exposed to impulsive strains, the proper value to be taken for R in 



calculating strength; neglect of this, 208 



132, 133 Precise conditions of impulsive strains of inflamed gunpowder required to be 

 known; rate of its inflammation partially determined by the author; the curve 

 of pressure within the gun, how to be determined, 209 



1 34 The rapid increase of pressure renders necessary the determination of the expres- 



sions for modulus of force trunnion; the moduli for gun-metal, cast-iron, 

 wrought-iron, and steel, 209 



135 Crystalline relations to this, 210 



136, 137 Eelations of ductility and ultimate cohesion; Ardant and Bornet's, and other 



experiments. Tables IV., v., VI., . . . . , 211-213 



138 Diagram expressing geometrically the values of T,&nd T, for the four chief metals 



of ordnance, 213 



139 Comparison of these values for wrought-iron and steel, much in favour of the 



former, 213 



140,141 Comparative values of guns of each of these materials as respects elasticity only, . 214 



142, 143 Resisting powers of German steel compared with the other metals, Table VII., . 215 



144 Cauchy's modulus of torsion ; relation to modulus of elasticity, 216 



145, 146 Diagram giving geometrical expression to the work done in extension up to rupture 



of cast and wrought-iron, 210 



147 Comparative extension per ton of steam-wrought and cast-iron; Hodgkinson's 



experiments. Table VIII., 217 



148 True reasons why the Low Moor and other irons are peculiarly valuable for gun- 



founding, though not having great ultimate cohesion, 2i7 



149 What is to be sought in improving cast-iron for gun-founding; it is not to be 



obtained by using foreign iron only; ultimate cohesion of foreign metals, 

 according to continental experimenters, Table IX., 217,218 



150 General Table of resistant vis viva of elasticity, and of rupture by tension, of the 



metals applicable to the construction of ordnance; for the several metals; 



continental data; Table X., 218, 219 



151, 152 Remarks upon these results; deductions; errors as to assumed comparative ulti- 

 mate resistances of cast and wrought-iron, 219,220 



CHAPTER XIX. — Gun-Metal or Bronze as a Material for Cannon. 



153 Ignorance of the physical and chemical properties of gun-metal; wherefore; the 



knowledge of it little advanced from the earliest times, 220 



154 Four circumstances of chief difficulty and importance in the production of bronze 



guns, 221 



VOL. XXIII. 3 L 



