1 -1C} i 1:1: Of BBAJ 



.vill now give polar formula* involving double. 

 >n. 



Let a series of straight lines be drawn from a pole 0, also a 



- of circles be described from as a centre. Let at be one 



of the elements formed l>y this mode of dividing a plane an a; 



let r and be the polar co-ordinates of , r + Ar and 6 -f A0 the 



co-ordinates of t; then the area of the element at will l>c ulti- 



mately rA0Ar, and the abscissa and ordinate of its centre of 

 gravity will be rcos0 and rsin0 respectively. Hence we 

 obtain 



- _ ffr cos Or d6dr _ ("Jr* cos OdQdr 

 JfrdBdr ffrdOdr ' 



_ ffr*sm0d0dr 



Supopse the area bounded by the curves BPQE, bpqc, and 

 the raaii ObB, OeE. Let r <f>(0) be the equation to the 

 first curve, r ^(6) that to the second; and let a and @ be 

 the angles which OB and OE make respectively with Ox. 



The sum of the values of r 2 cos 6 Ar A# for all the elements 

 comprised in the strip PQqp, will be found by multiplying 

 the sum of the values of r*Ar by cos #A0; the former sum 

 is ultimately 





