METHOD OF RECOIL. 269 



As those free oscillations are repeated in pairs, they enable us to 

 follow variations of zero throughout the duration of the experiment. 



When the damping is not very small, a permanent regime is soon 

 established, the period of which comprises four oscillations with two 

 kinds of elongation, one set greater a and the other less <, the values 

 of a and b being moreover given as the semi-distance of the elonga- 

 tions of the same order A and A', B and B'. We have then 



If a is the angle which corresponds to the displacement =r- , 

 and observing that 



7T 7T X 



arc tan - = arc tan - , 



A 2 7T 



equation (39) becomes 



\ \ 



HI \ 9 " " 



T I A z arc tan - 



(40) m = a 



888. The method of recoil is not convenient when the damping 

 is feeble. Weber and Zollner* employed in this case a mixed 

 method. At the passage of the needle through zero, successive 

 swings are given in alternately opposite directions, as in the pre- 

 ceding cases; but these swings are sometimes in accordance with, 

 and are sometimes in opposition to, the actual velocity. 



At the end of a great elongation A (Fig. 170) on the positive 

 side, the needle, as it passes through zero, receives a positive swing 

 which reduces the following elongation at C'; at the second passage 

 a negative swing gives an elongation B' of mean magnitude, and the 

 next oscillation BB' is free ; at the fourth passage a positive swing 

 gives a small elongation C ; then a negative swing at the fifth 

 passage reproduces a large elongation A'. The vibration A'A X is 

 still free, and the same series recommences. 



* W. WEBER and ZOLLNER. Berichte der Konigl. Sachs. Gesellschaft. 

 Leipzig, 1880. 



