182 Ml". Mallet on the Physical Conditions 



heat to an equal mass of the cold gun; and that the whole of this is operative in 



expanding a cylindric ring of a determinate thickness around the ball : — then, 



we have 



200° 

 ir=f^^25tons, 



as the mean compressive strain per square inch upon this interior ring. But 

 as the ultimate cohesion of cast-iron does not exceed about 8 tons to the square 

 inch, the actual effect upon the strength of the gun is the same, as if about 

 three inches of its thickness were removed, or that an inch in thickness of its 

 interior metal were removed, and a total strain of 17 tons were at the same 

 time visited upon the remaining section of its thickness. At such a conjuncture, 

 with such a steady strain already on its metal, the gun is fired, and an additional 

 impulsive strain, equal to the work done in giving to the shot its initial velo- 

 city, is suddenly brought upon its material. 



This, even with the regulation reduced charge for hot shot, of f the service 

 charge for cold shot, is seldom less than 2<| tons on the square inch of section, 

 producing, from the impulsive nature of the force, an extension equal to that of 

 a passive strain of 5 tons. The wonder, then, is rather that any gun stands, 

 than that many should burst. 



91. Nor does this statement fully embrace the entire strains visited on cannon 

 by expansion. It is uncertain whether the coefficients of expansion for cast- 

 iron in three rectangular axes are alike. There seems good reason to suppose 

 that iron is a dimorphous body, and that in its rhombohedral form at least 

 they are not so. Its unequal expansion, then, in different directions, probably 

 introduces torsional strains, as well as the normal and tangential ones which we 

 have so far alone considered. We have neglected altogether the longitudinal 

 ones, and this may be safely done, since the pressure required to produce 

 longitudinal rupture is proportionate to 



and that to produce tangential rupture, to 



D' 

 and hence the longitudinal strength of a gun is always greatly in excess 



R^^, 0> 



