216 



Mr. Mallet 07i the Physical Conditions 



mottled and nearly white iron, of very coarse grain, as the angle of torsion is so 

 small, 12° ; indeed the Eeport states, rather oddly, that it yielded " without ex- 

 tension" in the experiments of direct tension. This produces a value of Tr too 

 small to truly represent cast-iron. 



144. It might appear doubtful, how far values for the coefficient JV, can be 

 properly deduced from experiments on torsion. The proportionality of the 

 numbers, however, is certain, as Cauchyhas shown (Exerc. de Math., 4^ anne) 

 that in prisms exposed to torsion the constant G, or modulus of torsion, bears 

 a constant relation to that of elasticity for any given material, or 



145. Habit, and an uninstructed mode of viewing such questions, have pro- 

 duced the prevalent notion, of the brittleness of cas^iron, as contradistinguished 

 from the toughness oi wrought-ivon. The fact is, cast-iron, within the range of 

 four or five tons tension per square inch, is a much more ductile material than 

 wrought-iron ; its total extension per ton per unit of section, is far greater, 

 and the "work done" in producing the extension for the first few tons (up, in 

 fact, to the very limited strain, about 7 tons, at which rupture occurs), is much 

 greater than in wrought-iron ; and were it not that, the ultimate safe strain upon 

 wrought-iron, is so much higher, cast-iron 

 would be the better material for ordnance. 

 But wrought-iron has a far greater ultimate 

 cohesion — in about the ratio of 20 to 6 — 

 than cast-iron, and its softer varieties, a 

 long and uniform range of extension ; it is, 

 therefore, in the exact sense of the word, 

 the toiu/hestmatenal we are asyet acquainted 

 with, and therefore the best, for artillery. 



146. This peculiar property of cast- 

 iron is evident from the accompanying 

 diagram ; in which, from the origin d', the ordinate d'y is that of strain, and 

 the abscissa d'z that of extension ; the curve a, that for wrought-iron, and b 

 that for cast-iron ; half the quadratures of the curves, d'aa', d'bb' being the 

 work done to produce them in each case, the latter being obviously greatly in 

 excess of the former. 



df a' 



