290 Mr. Mallet on the Physical Conditions 



value of 2, for often repeated, impulsive strains, as derived from sect. 110; the 

 strain upon the internal longitudinal bars will be derived from equations 

 6 and 7, sect. 91, and from the principles enunciated in chapters 18 and 31 ; 

 and hence the total transverse section of these bars, all of which are strained 

 alike. 



284. The relation between the longitudinal and the tangential strains, for a 

 given internal maximum pressure, depends upon the thickness of the portion 

 of the gun resisting the latter, and upon the caliber. 



D' — D" 

 From equations 1 and 2, e = , (65) 



If we assume such a length of the gun in the line of the axis J, that 



i>'7 = 



7rO"= 



4 



■kD" 



and hence I = —r—. (66) 



The strains, both longitudinal and tangential, upon this segment of the length 

 of gun shall be equal in amount. 



But the forces to resist these separately, are proportional to the total section 

 of metal in the transverse section of the gun, and in its longitudinal section 

 due to the length I; and these are 



^ (i)'2 - D"') = Tre (D" + e), and (67) 



2fe = '^, (68) 



which bear to each other the ratio of 



D" f e 



i»" + e:i^orof2(^l+ -^ 



or of 2 + — jy, — : 1; 



and this is the proportion that the total resisting power of the external rings 

 must bear to that of the internal longitudinal bars at a minimum ; but, for the 

 purposes of reducing the maximum strain upon the former, by removing them 

 further from the axis, it will often be convenient and advantageous to give a 



