a Mechanical and Physiological point of view. 31 



to me to be capable of producing death by shock with even less 

 suffering than the "long drop;" for although by the latter me- 

 thod death is instantaneous when the shock actually occurs, yet 

 the mental sufferings of the criminal during the second occupied 

 by his fall may be very considerable. This painful interval is 

 altogether avoided in the American method, provided the initial 

 shock be sufficient to destroy the medulla oblongata. This im- 

 portant condition may be effected by the following calculations, 

 which lead to an easy Rule. 



The falling weight, acting through the intervention of the 

 rope, produces its effect in a manner similar to that of the shock 

 or collision of imperfectly elastic bodies. 



Let m and m 1 denote the masses of the two bodies, and let v 

 and 1/ denote their velocities previous to collision or shock, while 

 e denotes the coefficient of elasticity of the rope. 



Let u, u' denote the velocities of the masses m, m! after the 

 shock; then it is well known* that 



mv + mV — em! (v — v f ) 



u = p^ -J 



m -\-m' 



, mv + m!v' — em (v ! — v) 



Uu ^^ • 



m + m! 



(15) 



The vis viva lost during the shock is expended upon the neck of 

 the criminal, and is represented by 



mv 2 - + m l v 12 — mw 2 — mV 2 . 



After some reductions this is found to be 



mm 



vis viva lost = i(l — e 2 )(t> — t/) 2 . . . (16) 



m-\-m! x M ' K ' 



This result may be applied practically to the solution of the 

 American problem of hanging, so as to cause instantaneous 

 death, in the following manner. 



Let P denote the weight employed, and Q, the weight of the 

 criminal ; let e denote the coefficient of elasticity of the rope used, 

 and v the velocity acquired by the weight Q in falling through 

 the height h. 



If we consider the problem of the weight Q moving with the 

 velocity v, and causing the weight P to move through the inter- 

 vention of the rope whose elasticity is e, the shock produced on 

 P at the moment when the " chuck " takes place is similar to 

 that which occurs in the collision of bodies striking each other, 

 and is measured by the vis viva lost during their collision. The 



* Vide * Manual of Mechanics/ p. 156. 



