RUPTURE OF THE VESSELS WHICH CONTAIN THEM. 119 



es^ 



the cord, equal to \ y. The resistance opposed to the deflecting force is there- 



fore 75-; or ^ must be regarded as constant, and/" as equal to — ; assumptions 

 that reduce the equations (1) and (2) to 



/= 



e 5 \ 



which give b = o' \/4, or the deflection from the initial position to the deflec- 

 tion of load, as vV^ to 1. 



When the deflection, produced in either way, attains the limit of rupture a", 

 we have 5 = 5' = 5"; and denoting by y^ the force that would produce this de- 

 flection when acting from the initial position, and by f the force that would 

 produce the same as a deflection of load, the equation a = ^' gives 



4£=i 

 / 



Qxf= 4/\; or, the force which produces rupture when acting from the position 

 of load, is to the force which produces fracture when acting from the initial posi- 

 tion, as 4 to 1; an imperfection in the elasticity increasing this proportion, as 

 in the former case. 



And observing that when the law of elasticity is as the m*'' power of the de- 

 flection, these equations become 



1 B ff 



' - ^ V — 



/= 



e «' "' 



r 

 1 



v^ = 

 f 



we deduce for the case when m is infinite, the conclusion of the third proposi- 

 tion in regard to that case. 



The application of this theory to the strains occasioned by a column of fluid 

 moving through a pipe, and subject to checks, and separation into distinct co- 

 lumns, will be immediately seen. The most powerful of the interior strains of 

 this class must be due to those blows of the hydraulic ram which occur, both 



