120 IKE OF < 



. It is sometimes convenient to use polar formula. 



Let DE be the arc of a curve; and supnos inin 



tbe centre of gravity of the area comprised (between tl. 

 DE and the- radii OD, OE drawn from the pole 0. 



Divide the angle DOE into a number of angles, of which 

 POQ represents one; let OP=r, P0x = 6, POQ = &0. The 

 area POQ = $r'M ultimately (Diff. Cak., Art. :il.r>. Also 

 the centre of "gravity of the figure POQ will be ultimately, 

 like that of a triangle, on a straight line drawn from bi- 

 secting the chord PQ, and at a distance of two-thirds of this 

 straight line from 0. Hence the abscissa and ordinate of the 

 centre of gravity of POQ will be ultimately 



jr cos 0, and $r s ' m O respectively. 





*- 



,ie_ 



In these formulae we must put for r its value in terms of 6 

 given by the equation to the curve; we must then intc^rat<- 

 Q = a to 6 = fi, suptwsing a and /9 the angles which OD 

 and OE respectively make with the fixed straight line Ox. 



