38 MEASUREMENT OF OSCILLATIONS. 



and the whole time 0, 



Putting 



we get 

 (32) 



The correction - being of the order of thousandths, we have, 

 n 



with sufficient approximation, 



. 



The term is the correction of time for the total duration of 

 n 



n oscillations ; ~ is the correction for the mean time - of a 

 if 1 n 



vibration. 



The logarithmic decrement A only depends on the extreme 

 deflections a and a n , or on the corresponding values /3 l and /J n . We 

 have 



n-i a n n-i 

 and may put 



7 



When the logarithmic decrement is also very small, of the order 

 of thousandths, so that its square may be neglected, the develop- 

 ment of <? 2A - in series gives simply 



