214 ^Ii'. Mallet on the Physical Conditions 



respective curve. It is obvious, then, to the eye, that although the strength of 

 cast-steel (its ultimate cohesion) is enormously greater than that of the very 

 ductile iron, still, from the greater range of extension, of the latter, in the 

 abscissa d'z, the " work done" in producing its extension to final rupture, or 

 even its extension within the elastic limit, is enormously in excess of tliat 

 required to bring the cast-steel up to its point of rupture. In fact, in round 

 numbers, it loill require of any foixe' in motion^ above fifty times the effort to rupture 

 a given section and length of ductile wrought-iron, that will rupture the best and 

 toughest cast-steel; while again, for the very ductile wrought-iron, its value for 

 Tr is nearly six hundred and fifty times that for J^, so great is the range or limit 

 of work to be done, between the elastic (safe) limit and that of rupture. 



140. Hence it follows, that a gun formed of cast-steel, or of harsh strong 

 wrought-iron, provided it have an enormous surplus of strength above the 

 highest strain to which it is to be exposed, will be very safe ; but if its pro- 

 portions be reduced within a narrower limit of balancing the final resistances 

 with the bursting strain, or if the latter be brought up, accidentally or other- 

 wise, so as to approach sucli balance, the cast-steel or the harsh wrought-iron ivill 

 be the most unsafe gun possible, ivliile in all cases the gun of ductile iron will be the 

 safest. This might be popularly illustrated by saying that the former gun 

 approximates to one of enormous strength, but made of glass, while the latter 

 approximates to a gun made of sufficient strength, if conceivable, of leather or 

 of India-rubber, or to the silk- wrapped guns of the Chinese. 



141. The highest possible ultimate cohesion is, no doubt, most desirable; 

 but this quality alone will not answer for ordnance (or for any other purpose in 

 which impulsive strains are concerned) : it must be united with the largest pos- 

 sible amount of ductility within the elastic range, to give security, or otherwise 

 security must be purchased by the accumulation of an immense overplus of 

 material. Were it possible to procure some variety of wrought-iron or of steel 

 that should possess the great ultimate cohesion of the latter, united with the 

 long range of extension of soft ductile, such wrought-iron as is used for making 

 chains or rivets of, we should obtain tlie ne plus ultra of a material for the 

 fabrication of artillery ; but the latter indispensable quality appears, in tiie 

 present state of metallurgic science, incompatible with tlie nature of steel in 

 any form. The attempts, therefore, recently made, at great expense, to fabri- 



