298 Vi Mil MOSELEY, ON THE 



Now, 



BP' - Pm _ BP - DG 

 PP' ~ GP' ' 



2a — (mn) _ 2 (a — i) _ 

 ' ■ ^sec7 ~" ^ ' 



/ V « 2 (« - A) . 



.'. (mn) = 2a —r — - secy . A; 



.-. area (BAnm) = ^ {{AB) + {mn)\ . (P'P) . sin (PP'A) 



= sin {(3 +y) secy {2a A- ^-^ .secy .A"}; 



d\aYea(BAnm)} - /o , \ ia 2(a — b) 

 .'. -^ V^ ^ = 8111 (/3 + 7) sec 7 {2a ^ , ^ sec7 . A\. 



- Now each element of the area has its centre of gravity in P'G ; 

 ,-, moment of area = 2^sin (/3 + 7) sec 7 ^{a^ ^— sec7^'} 



=^sin(/3 + 7)sec7{«^* ^"7 ^ sec7^H. 



Now, 

 iVs = moment of p + moment of area (BAmn) 



2 (a — b) 

 = PffK sin (0 + /3) + ^sin (/3 + 7) sec7 {aA^ ^ , ' sec 7 A""). 



Also, 

 Mx — pg cos (p, Mz = 0, 



M^ =pgsm(j> - g sin (/3 + 7) sec 7 {2a^ ^ sec 7 ^^}, 



iv, = 0, iV3 = o. 



Calling therefore x and » the co-ordinates of any point in the re- 

 sultant of the forces applied to the area (ABmn), we have for the 

 equation to that resultant. 



