NATURAL PHILOSOPHY. 171 



The diameter of the bore being 14 inches, we have-^~- = 63,960 pounds, 

 as the resistance to oppose to each square inch of the fluid from the powder. 

 The gun will bear, then, a pressure of 4,264 atmospheres. 



The resistance to cross fracture at the part nearest to the breech will be, 

 from the cast iron 28 2 14 - = 784 196 circular inches, equal to 460 

 square inches. Cohesive force, unreduced, 30,000 pounds, and 30,000 x 460 =. 

 13,800,000 pounds, the whole strength. The bore contains 153 square inches, 

 and - -"f^j - = 90,196 pounds to resist each square inch of the fluid, or 

 26.236 pounds to each square inch more than is provided to resist the longitu- 

 dinal fracture, and this excess will be further reinforced by the wrought iron 

 rings, which being screwed upon the casting, and the outer layer breaking 

 joint over the inner, will add to the resistance to a great amount, which how- 

 ever need' not be computed. 



Let us now examine a gun made of a single casting of the dimensions that 

 are given above ; that is, of 14 inches bore, and sides 14 inches thick. 

 Taking the normal strength of cast iron as before at 30,000 pounds per inch, 

 we must reduce it, according to the laws before explained, to one third, or a 

 mean of 10.000 pounds per inch; and the thickness of both sides being 28 

 inches, we have 10.000 x 28 = 280,000 pounds for the whole strength, and 

 = 20,000 pounds to each inch of the fluid pressure, or 1,333 atrno- 



14 



20000 



spheres, or , or less than one third of the first example. Against a cross 



A 6 > 9 ti * 



fracture the cast gun will possess a great excess of strength, which I do not 

 like to call useless, although I do not perceive how it can be of any essential 

 practical advantage. 



Let us next inquire what force is required to give a ball of 14 inches 

 diameter a velocity of 1,600 feet a second ? "We shah 1 obtain a better concep- 

 tion of this force by estimating it in the height required by a fluid column to 

 produce it. Suppose the ball impelled by the pressure of a column of the 

 same substance, which would be in this case a column of fluid iron. Then 



1600 2 2560000 

 (from the formula v = \' 2gh) we obtain = = 40,000 feet, for 



the height of the column. But this would produce a jet forming a continuous 

 stream. Suppose this stream to be 14 inches in diameter, and divided into a 

 series of short cylinders, each of which, to equal a bah 1 of 14 inches diameter, 

 must be 9 inches long. Now in giving 1,600 feet velocity to this series of 

 cylinders by a superincumbent column, the force will act upon each cylinder 

 only through a space equal to its length. But in a cannon the powder acts, 

 though with a variable force, through the whole bore of the gun. The vari- 

 ation of this force must depend, in every case, upon the quickness of the 

 powder, arising from its composition, fineness of grain, dryness, and the heat 

 received from the gun from previous firings ; and most essentially from the 

 amount of the charge ; and we dp not know the exact law of the variation 

 for any one case or condition. Our best judgment, therefore, must be but an 

 approximation to the truth, entirely empirical. But if we cannot determine 

 the truth with exactness, we can at least assign limits within which it must 

 be contained, and upon a comparison of the velocities produced by different 



