Pendulum after the String has become slack. 283 



type when the thread becomes slack between the values 

 of a 



90° 



41° 21 



27° 15 



21° 29 



18° 26 



&c, &c. 



These regions become very narrow compared with the spaces 

 separating them and crowd indefinitely close together as 

 a = is approached. 



I -5a 



90° 



and 



76° 21', 



41° 21' 



and 



37° 45', 



27° 15' 



and 



25° 56', 



21° 29' 



and 



20° 50', 



18° 26' 



and 



18° 3', 



(2) From other points on the circle the motion reaches, 

 after a finite number of slackenings and tightenings, the 



