:'.!'. 1 i: .IMSIIIONS RESPECTING ATTRACTION. 



polygon, the axis of a: being perpendicular to a side. I,, t be 

 the (li t' the j)article from the lamina. The resultant 



lit line which jnins tin- particle 

 with the centre of the lamina; and its vain 



tion must extend over the area of the poljgon* 



flfecl the integration it is convenient to transform to 

 polar co-ordinates; thus we obtain 



drdO 



\Ve mu<t integrate with respect to r from r = to r = asec#, 

 and then with respect to 6 from = to 0= - ; and multiply 



the result by 2n. 



rdr I 



No. 



[ 

 / 



taking this between the limits we obtain 



i ooa e 



Hence the required result is 



* 



Jo \C )f& 



that is 



that is 



. 7T 



csm 

 -In p sin"' 



