10 



ANIMAL MECHANICS. 



The American method of hanging, if properly applied, 

 seems to me to be capable of producing death by shock with 

 even less suffering than the " long drop ;" for, although by the 

 latter method 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 important 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! denote the masses of the two bodies, and let 

 v and v denote their velocities previous to collision or shock, 

 while e denotes the coefficient of elasticity of the rope. 



Let u y u, denote the velocities of the masses m, m\ after 

 the shock ; then it is well known* that 



mv + m'v - em (v - v') , « 



u= ■ — ^ (i) 



m + m 



. mv + m'v - em (v r - v) 



U = ; • 



m + m 



The vis viva lost during the shock is expended upon the 

 neck of the criminal, and is represented by 

 mv 2 + m'v' 2 — mu 2 — m'u' 2 . 

 After some reductions this is found to be 



VYUfl% 



Vis viva lost = T (i - e 2 ) Cv— v'Y. (2) 



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 : — 



* Vide "Manual of Mechanics," p. 156. 



