C E N 



7. In a cone about its axis, D r v -rrp- 



CENTRE of Oscillation. 



1. Let D = distance of the point of suspension from the centre of os- 

 cillation, distance from the centre of gravity, then 



_ A 4- S A2 + B -f S B + C -f S C 2 -f &c. 



(A + B + C + &c.) X S 

 Or if ds be the differential of the body at the distance ,r from the axis r 



" s X $ ' 



2. If S be the point of suspension, G the centre of gravity, O the cen- 

 tre of oscillation, 



G O varies as -^ ;. 



Cor. If O be made the point of suspension, S will be the centre of os- 

 cillation ; or the centre of oscillation and the point of suspension are con- 

 vertible. 



3. If R be the centre of gyration, 



SG : SR :: SR : so. 



2L 



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



2. In an isosceles triangle vibrating flat ways, D ' % alt, 



3. In a circle flat ways, D = r. 



4. In a parabola flat ways, D = alt. 



5. In a sphere, D = a -f- (a = distance of the point of suspension 

 from the centre of the sphere.) 



6. In a cone, D - axis 4- -- - ' - . 



5 5 axis 



7. In a circle vibrating edgeways, D = -- r. 



. ... M-arc X rad, 



. In a sector of a circle edgeways. D = 



4 chord 



9, In a rectangle edgeways, suspended by one angle, D --' % diagoim \ 

 55 D 



