involved in the Construction of Artillery. 275 



end of a spiral spring; the elongation traversing the whole length of the gun, 

 and arriving at the muzzle, leaves it at its original length, assuming the elon- 

 gation to have been far within the elastic limits. In its rapid progress, however, 

 it has produced a strain in succession in the line of the axis upon every part of 

 the gun. 



2.58. If the gun have no trunnions, but, resting without friction, abut firmly 

 against a fixed obstacle against the breech at x, then the segment in rear of the 

 cartridge will be compressed by a force equal to the whole recoil in the direc- 

 tion yx, while the remaining parts of the gun will be extended by a force in 

 the direction yz, which, at the transverse section ?/, is equal' to the recoil, and 

 at the muzzle is = 0. If F, then, be the work done to tear the gun in two at 

 the section y, and t — the momentary time of the traject of the shot along the 

 chase until leaving the muzzle, 



'^t = Ft (62) 



will be the longitudinal strain upon the gun. 



259. If the breech be imsupported at x, the strain tending to tear it off at 



M'v'^ 

 the section y is = — -— t, diminished only by the inertia due to its small mass 



between y and x, or, 



Ft = ('-^-'^V ■ -(63) 



260. If the gun be fixed rigidly on trunnions placed in the usual position at 

 t, the strain tending to tear or break them oif is equal to the whole work done 

 by the recoil. The bearings always yield something, however. 



The tendency to tear the gun in two at the trunnions, if 3L" be the mass 

 between x and t, is 



*^"-i^>. (64) 



This extension in the section at t at the first moment is, on the principle already 

 stated, followed by a compression in the direction zt, of equal amount, and so 

 for any other position of the trunnions. 



261. The amount of extension or compression, assuming the gun of equal 



