GENERAL PROPERTIED 101 



Hie volume (I") of * portion of a cylin . 

 I between two planet, one of < perpendicular to 



oxidoft .ic equation 



P.JH 



e plane of (x % y) is supposed perpendicular to tlui 



H the ordmatc of a point in the other plane. 



< of the integrations depend on the curve in which 



lane of (JT, y) cuu the surface. This follows from the 



Integral Calculus. 



denote the angle between the two planes; the 

 area of an clement of the other section of which 



tion on the plane of (, v) is AxAjr sec . Let A 

 denote the area of the sect .. cylin'i plane of 



. and consequently A sec the area of the other set 

 let s denote the ordinate of the centre of gravity of the plane 

 are* formed by the intersection of the cylinder with the 

 second plane; then 



A sec .i //* sec <f> dxdy, 

 or A*-ffMdxd>/, 



fore V-A*. 



The volume is therefore equal to the area of the base tnulti- 

 ular upon it from the centre of gravity 

 the other acct 



centres of gravity of the two plane sections are on 

 irae straight line parallel to the generating lines. For 

 the co-ordinates of the centre of gravity of the section by 

 lane of (x, y) are 



A A 



and those of the upper section are 



Jfrsec <f> dxdy , 

 c* 



agree with the former values. 



