MEMOIR OF DANIEL TKEADWELL. 405 



" By attention to the preceding statement, we see that two dislhict questions arc brought 

 up for examination. First, Docs the expansive fluid, formed of fired gunpowder, exert an 

 equal force in every direction? and, secondly. Does a cannon, of the usual furui, present in 

 every direction an equal area of metal, acting with an ecpial mechanical advantage, to be 

 torn asunder before the fluid can escape? We may, I think, for all practical purposes, take it 

 as true, that the expansive force of fired gunpowder is equal in all directions, and that, con- 

 sequently, no advantage could be gained by giving any particular direction to the fibres of the 

 wrought iron of which a cannon should be made, depending upon flic force of the fluid being 

 less in one direction than in another. 



" To answer the second question, namely, Does a cannon of the usual foi'm present, in every 

 direction, an equal area of metal, to be torn asunder before the fluid can escape ? we shall 

 find it useful to resort to numbers, and apply them to a form as an example. For this pur- 

 pose, let us suppose that we have a hollow cylinder, say twelve inches long, the calibre being 

 one inch in diameter, and the walls one inch thick, giving an external diameter of three inches. 

 Suppose this cylinder to be perfectly and firmly closed at its ends by screw plugs, or any other 

 sufficient means. Let this be filled with gunpowder and fired. The fluid will exert an equal 

 pressure, in every direction, upon equal surfaces of the sides and ends of the hollow^ cylinder. 

 Let us next examine the resisting power of a portion of this cylinder, say one inch long, 

 situated in the middle, or equally distant from the ends, so that it shall not be strengthened 

 by the iron which is beyond the action of the powder. The fluid, enclosed by this ring of one 

 inch long, contains an area of one square inch, if a section be made through it in the direction 

 of its axis ; and the section of the ring itself, made in the same direction, will measure two 

 square inches. We have then the tenacity or cohesive force of two square inches of iron in 

 opposition to an area of the fluid measuring one square inch ; and if we take the tenacity of 

 the iron at 65,000 pounds, the cylinder will not be burst, in the direction of its length, unless 

 the expansive force of the fluid exceed 130,000 pounds to each inch. Next, let us suppose a 

 section made through the cylinder and fluid transversely. The area of the fluid, equal to the 

 square of the diameter of the hollow cylinder, is one circular inch, and the area of the whole 

 section is, the diameter being three inches, nine inches. Deduct from this the area of the 

 calibre, and we have eight circular inches. That is, the section of the iron is eight times 

 greater than that of the fluid ; whereas in the former case of longitudinal section the iron 

 gave but twice as much surface as the fluid, and if we take, as before, the iron at 65,000 

 pounds per inch cohesive force, it will not be broken unless the force of the fluid exceed 

 520,000 pounds. It will be found, upon a further examination, that the relations of these 

 sections to each other may be varied, as we take the diameter of the calibre to be greater or 

 less, as compared with the thickness of the sides, but their difference can never be made less 

 than as two to one. Here then is a principle, or rather a fact, of the utmost importance in 

 forming cannon of any material, the strength of which is different in different directions ; for as 

 a cannon made in the proportions above specified, if the materials be in all directions of equal 

 strength, will possess four times as much resistance to a cross fracture as it does to resist a 

 longitudinal fracture, it follows that a fibrous material which possesses four times the strength 

 in one direction that it does in another will form a cannon of equal strength if the fibres be 

 directed round the axis of the calibre. It is this fact which gives the great superiority to the 

 various kinds of twist gun-barrels. For in these, although the fibres do not inclose the calibre 

 in circles, yet they pass around it in s[)irals, thus giving their resisting force a diagonal direc- 

 tion, which is vastly superior to the longitudinal direction in which the fibres are arranged 

 in a common musket-barrel. 



