CHAPTER XV 

 115. The Centre of Gravity or Centroid. 



FIG, 51. 



Let an irregular area (Fig. 51) be so placed with reference to 

 the axes of x and y, that the co-ordinates of its centroid P are 

 x, y. Let this area be divided up into a very large number of 

 small areas, a lt a z , a 3 . . ., situated at the points A, B, C . . . 

 respectively, the co-ordinates of these points being (x-^, /j), 

 (x z , ?/ 2 ), (x 3 , &,)... 



The centroid of the two small areas a^ and a z can be taken 

 to be a point M on the line AB, such that 



a AM = a z BM 



Let the co-ordinates of this point be x v y^. 

 Since the triangles AKM and BLM are similar 



AM KM 

 BM~ ML 



x 



X- 



But 

 Then 



AM 

 BM 



X-, = 



208 



