TABLE FOR THE REDUCTION OF PENDULUM VIBRATIONS. 



35 



4oth transit will take place near the time t l + (/j - / ). We get ready 

 for the observation a little beforehand, and note exactly the time / 2 

 of the 4oth transit ; we observe the corresponding amplitude which 

 would give the angle of deflection a. 2 . In like manner we determine 

 the times / 3 , / 4 , / 5 , and the deflections a 3 , a 4 , a 5 , of the 6oth, 8oth, 

 and looth transit. 



From these observations are deduced the values ^ - / , / 2 - /j 



of the period of 20 vibrations during successive series, and the 



. A ~r i CfeTCfa 



corresponding mean angles of deflection , etc. 



If the successive periods do not appreciably differ from each 

 other for large variations in the angles of deflection, we conclude 

 that the directing couple is proportional to the deflection ; the time 



of vibration will then be given by of the total difference. 



100 



691. Most frequently the directing couple is proportional to the 

 sine of the deflection ; the time of vibration varies then with the 

 amplitude, according to the law of pendulum motion, and it is given 

 by formula (8). To simplify the operations, tables have been 

 calculated which give the value in the bracket i 4- /3 for various 

 angles of deflection. The following, for instance, are the values of 

 this angle up to 30 degrees.* 



Table for the Reduction of Pendulum Vibrations to 

 Infinitely Small Angles. 



* DURANDEAU et CHEVALIER. 



Magnetiques, Vol. II., p. 9. 



Voyage de la Bonite. Observations 



D 2 



