30 ELECTRICAL MEASUREMENTS 



kT 

 Logarithmic Decrement. Let X = jp, then (18) and (19) 



become 



' - ,.,,_,,*:. -(f^dnl^ + tan-'?! (18a) 

 and 



The utility of this substitution lies in the fact that X is much 

 more easily determined than its components k and P. 



X is called the Napierian logarithmic decrement; it is a quantity 

 of importance in the theory of damped vibrations. 



The first elongation after the circuit is broken occurs when 



t = 2 : Substituting this value in (19a) and using (21) gives 



cos TT 



The nth elongation, when t = n, is 



2 



T . 

 -, 



n = B F e~ nx cos mr. 



' e~ n = X(T 



and 



(20) 



The method of determining X is obvious: To obtain the neces- 

 ry data one has only to set the movable system in motion 



e CaUed ' and ' a 

 ir damping X is sli 



and ' after 



of elongations read n . 



From the 



27T <> 



JL k2 ' fc?~*& 

 VP 4P 2 VTV ~ ^2 



