involved in the Construction of Artillery. 181 



residual force of which the tire grips the wheel. A length of time probably 

 elapses before this state becomes perfectly stable, and indeed the gradual 

 loosening of tires, though partly due to the extension of the iron under the 

 continued rolling, out which it sustains against the rails in use, makes it some- 

 what doubtful if stable equilibrium be ever attained. 



89. Assuming, however, the rigidity of the metal perfect, which is in fact ex- 

 tremely great in cast-iron, then in a cylinder, such as a gun, exposed to expan- 

 sion in the inside, the strains are the same as if it were exposed to the normal 

 and tangential strains due to a fluid pressure from within, and as (eq. 1) the 

 equation for equilibrium is — 



.^n^Jl^jn^l^, (4) 



when 



T-t 2 Re 



(5) 



c ~ D" 

 the gun would be burst by the expansion of the interior alone; or if the former 



e 

 be less than the latter member of the equation in the ratio of - then is the w'* 



part of the whole strength of the gun temporarily removed by its internal ex- 

 pansion, or by the reaction of the interior, against the exterior segment of its 

 thickness. 



Applying Professor Hodgkinson's experimental results as to the extensibility 

 of cast-iron under strain, to this reasoning, and taking the coefficient of expan- 

 sion by heat, for cast and wrought-iron as the same for low temperatures (strictly 

 as 1000893 : 1000984 for temperatures under 212°), we have the extension for 

 cast-iron for the square inch of section equal about g-Q^jo of its length for each 

 ton of load, up to 7 or 8 tons, at which its elasticity becomes permanently 

 impaired, that is to say, when it begins to lose its form. An equal change of 

 length is due to eight degrees of Fahr., difference in temperature. (Note K). 



11. — Numerical Example. 



90. Let us now assume a 64 lb. shot, rammed home at 2000° Fahr., which is 

 under a white heat, and that it remains fifty seconds in the gun while the latter 

 is being run out and fired ; that in this interval the shot transmits ^ of its 



VOL. XXIII. 2 B 



