involved in the Construction of Artillery. 199 



Te = ¥^, (18) 



indicating that the work done by any strain in extension or compression of an 

 elastic bar varies directly as the square of the strain, times its length, and in- 

 versely as its cross section, times the modulus of elasticity of its material. 

 (Moseley.) 



122. Poncelet has investigated, with his usual adroitness, a number of ques- 

 tions relating to the oscillatory, movement of bars subjected to constant strain 

 and to impulses, separately or together, which are of the highest interest in rela- 

 tion to the peculiar class of strains brought upon "artillery at the moment of 

 discharge. There are three principal cases : — 



1°. Where strain possesses no initial velocity, as in that just considered. 

 2°. Where the strain does possess an initial velocity — impulse. 

 3°. Where a permanent strain being on the bar, it is subjected to that 

 of an impulse in addition. 



123. Case I. — As has been already stated, the maximum extension or 

 compression, 2i, is double that duo to the statical extension or compression, i; 

 while the extension or compression at the point of maximum velocity of oscil- 

 lation, is one-half the maximum, or equal to the static = i. 



Let 21 = I' the maximum, and I be the extension or compression due to some 

 intermediate point in the range of oscillation of the strain P and of the ad- 

 jacent extremity of the bar; then the velocity due to any extension or compres- 

 sion, I, is 



I' 



or, more simply, since P = eAi = eA-=r, suppressing the common factors, 



V' = f,(2l'-i]l, (20) 



and extracting the square root, and making [j)= lipj ) = ^j 9 being the 



coefficient of gravity, — 32^^ feet, 



V^ky\{2l'-l)l\ (21) 



2 d2 



±-r'^2{Pl-i~P] = i2P -'-^1)1; (19) 



