involved in the Construction of Artillery. 285 



e = -^ X hyp. log. 



e = -^ X hyp. log. 2, 



Each on a different assumption as to the nature of the molecular forces under 

 strain, and the mode in which fracture occurs. 



e = n ' , Barlow. (5) 



R—p ^ ' 



e being the thickness of metal, D" the internal diameter, or the caliber, R the 

 coefficient of rupture of the metal, and j^ the maximum pressure on the unit of 

 interior surface in each case ; a in equation 2 being the fraction of D" that 

 determines the point in the radius, round which the motion at rupture is 

 supposed to rotate. 



275. Professor Barlow, who was the first to point this out, in his paper on the 

 strength of hydraulic press cylinders (Trans. Ins. Civ. Eng., vol. i.), remarks 

 that the result is apparently paradoxical. He has, however, himself produced 

 the apparent paradox, by not drawing quite the correct conclusion from his 

 own investigation, for it is not true to say, that no addition of thickness 

 adds anything to the strength of the cylinder, but that no addition of thick- 

 ness will prevent the rupture of the interior, as soon as the pressure per 

 square inch reaches the point of final estensibihty of the metal at the internal 

 surface. 



276. If D" and p be given, the value of e for different materials depends both 

 upon the absolute tenacity of the particular metal and upon its extensibility. 

 The thickness at which rupture internally will commence, is as the final tenacity 

 directly, and as the final extensibility inversely ; the limit of thickness, therefore, 



is m proportion to „ for each material, from which it follows that, the thickness 



VOL. XXIII. 2 p 



