Motion of Oscillation. 217 



whence, 



_. <? (BM) 



h 

 Substituting this value in the expression for d f, we have 



and by integrating, 



We have therefore only to determine the constant quantity C; 

 and it will be seen, that when t = 0, that is, when the body sets 

 out from the point A, the arc BM' becomes the semicircumfer- 

 ence BM'Z-, accordingly, 



We have thus an expression for the time employed in describing 

 any arc AM, the time being supposed to be reckoned in seconds. 

 But when the arc AM becomes &B, that is, at the end of a semi- 

 oscillation, the arc ZM' becomes ZM'B ; consequently, by call- 

 ing the duration of a semioscillation J /', we shall have 



Meek. 38 



-JF 



o^ ZJkPB 



