whence 



FIRST AND SECOND MOMENTS 

 AX A-.XI 



23 



Now let c denote the length of the chord CD and a the length of the 

 arc CBD. Then, from the results of this and the preceding articles, 



_ 2 re 



and also, from geometry, 



7 2 



Inserting these values in the expression for # o , the result is 



do * = ir; 



~2 



For a semicircle, A Q = and c = 2 r. Therefore, in this case, as 

 also shown above, 



17. Centroid of para- 

 bolic segment. For a 



parabolic segment with _Y_ 



vertex at A (Fig. 16) 

 the position of the cen- 

 troid G is given by 



FIG. 16 



(18) 



3 



where a and b denote the sides of the circumscribing rectangle. Also, 



(19) 



Area^LBC = - ab. 

 3 



For the external segment ABD (Fig. 16) the centroid is given by 



3 _3 & 



and the area of the external segment is 



(21) 



Area ABD = - ab. 

 3 



