involved in the Construction of Artillery. 197 



P = eAi 

 A = I, I = L, and i = 1; so that when (14) 



then e is the modulus of elasticity, or the force that for a given material on 

 the unit of section (= 1 square inch) should be equal to compress or extend 

 the bar its own length ; a purely arbitrary constant, which may be conveniently 

 expressed in terms of the length of the bar ; for if 8 = its specific gravity, and 

 E = the breaking weight, or force, for unit of cross section, L the length 



jO p 



= — or modulus of cohesion, and X^ = - or — the modulus of elasticity, and as 







here i = 1, if i' be such a fraction of the extension or compression as belongs to 

 the point at which the elasticity is crippled, - i' may be used to express the 



modulus of elastic limit. 



118. The property of elastic, or rather of imperfectly elastic bodies, as we find 

 them in nature, is that at a certain limit of force, their elastic resistance gives 

 way altogether, and the body, whether by extension or compression, becomes 

 crippled, when after a certain range, greater or less, a new equilibrium is estab- 

 lished, and so on until at length, by a further application of force, it becomes 

 ruptured or crushed. "When the actual strain bears a large proportion to that of 

 rupture, the element of the duration of its application can never be in strictness 

 neglected. Vicat showed, by experiments made before 1833 (" Ann. de Chem. 

 et Phys.," t. liv. p. 38), that when the actual strain did not exceed one-fourth that 

 of rupture, the extension of wrought- iron which took place almost immediately, 

 did not increase by time, but that with strains above this proportion, the exten- 

 sions slowly increased, in a ratio which was directly as the time, and for equal 

 times, was directly as the tension or strain. Thus, also, a strain almost, or per- 

 haps altogether, capable, after some time, of producing rupture, may be borne 

 ■with impunity for a very brief interval ; so that a gun may sustain, without injury, 

 during the momentary expulsion of the shot, a pressure that, continued for some 

 longer time, would burst it. 



Vicat's brief but conclusive experiments, made about five years anterior 

 to the publication of Mr. FaLrbairn's, on cast-iron, seem to have been quite 

 unknown to that gentleman, as well as the elaborate experiments of the 



VOL. XXIII. 2 D 



