372 Mr. Mallet on the Physical Conditions 



No. 2 can be transmuted to the structure of No. 1 by rolling simply, without any other 

 change, and vice versa, No. 1 may be transformed to the crystalline and comparatively 

 brittle and uneven structure of No. 2, by welding and forging together the most tough and 

 perfectly fibrous bars, provided the mass be large. See Chaps. 22 to 26 of text. 



Note K.— (Sect. 89.) 



This may be put under another form: — If the tension due to the integral or sum of all the 

 partial strains of the exterior of the gun exposed to tension by the variable strain of the 

 expanded interior = ft; 2irR = the length, R being the radius corresponding to ft, and 



/= the extension sustained between t and t', then T = fte - — =, and ifp be the coefficient of 



rupture due to the material. Rupture will occur when 



I 



or, to prevent it, ft must exceed 



^P = ^^2^' 



I 



p-- 



2TrR 



A consideration of these conditions, along with those developed in the latter chapters of 

 the text, will indicate the inutility of construction of guns or mortars of cast-iron of conside- 

 rable thickness, and reinforced with a single ply of heavy wrought-iron hoops, shrunk-on 

 hot, or driven on upon a conic exterior, as originally proposed by M. Thierry, Cap. d'Artil. 

 (" Applic. du Fer au Construe. d'Artillerie," torn, i., p. 153, Paris, 1834), and since attempted 

 in various forms in England, one of the latest being a proposition to strengthen ( ?) the 

 13-inch sea-mortar, of one caliber thick, by one ply of about 3 inches thick of such wrought- 

 iron hoops outside. In all such cases, from the great thickness and rigidity of the interior 

 cylinder of cast-iron, the latter is strained to its utmost limits and split, before any effectual 

 support can be derived from the exterior hoops. They are, therefore, useless in any case, 

 except when, as in the construction proposed in the text, the mutual relations of the interior 

 and exterior of the compound gun, are such as to equalize and make perfectly isochronous 

 the strain upon both. It must be distinctly understood, however, that the constructive 

 references and figures in the text of the subsequent chapter, headed, " Proper Construction of 

 Wrought-iron Guns of the largest class," are not to be viewed as more than indications of 

 the principles of design proposed, and not as conveying detailed instructions as to the prac- 

 tical methods of carrying such out, for which special designs and specifications, fitted to the 

 particular case, would be demanded. I state this, to avoid the possibility of a cavil being 

 raised on any point of practical detail of structure, where none are meant to be given. 



