C E N 



2. In parabola, D = -~ altitude. 



3. In a J4 circle distance from centre = - 



J !f 



4. In a cycloid, D ~T5~- 



5. In a sector of a circle, distance from centre = % - ' -- . 



arc 



rad. x chord 



6. In a circular arc, custance from cent. re - - - . 



arc 



7. In cones and all regular pyramids, D % altitude. 



8. In a paraboloid, D = % altitude. 



9. In % sphere and % spheroid D = ~a~* 



10. In the surface of a V 2 sphere, D = . 



CENTRE of Gyration. 



Let A, B, C, &c. be the bodies, or the particles of which the body is 

 composed, S the point round which the particles revolve, D = distance 

 of the centre of gyration from the axis, then 



_ 

 - 



+ cxscs-i&c N 



A + B + c x &e. 



Or if d s be the differential of the body at the distance x from the axis, 



Ex. 1. In a straight line, D = Len th .. 



Vs 



2. In a circle revolving in its own plane, round its centre, or in a cy- 



Under, D=-T=. J r J,V 



3. In the periphery of a circle revolving about its diameter, D = rr 



Va 

 r 



4. In the plane^of a circle revolving round its diameter, D = ~%. 



i- 



5. In a sphere revolving round its diameter D r */&, ~ 



6. In the surface of a sphere, D r s /jL 



*- v 



