242 Dynamics. 



2 6' dec 



will be the value of the sum of the products of each particle of 

 the body into the square of its distance from the axis AE. 



365. Let us now suppose, by way of illustration, that the 



Fig.176. b jy j n question is a rectangular parallelepiped, turning about 



the axis AB perpendicular to the axis of the parallelepiped, and 



to the side IK. By the nature of this body, the surface tf is con- 



stant ; thus the integral f x 2 6 d x is -, which, when x is equal 

 to the altitude h of the parallelepiped, becomes - . 



In like manner, 6' being a constant quantity,^" x 2 6' dx be- 



comes 



or, MN being represented by ft', which gives x' = \ h', 



and, as the plane which passes through the axis divides the bod}' 

 into two equal parts, the two halves will be 



, h'* 6' h' 3 6' 



therefore the entire sum of the products will be 

 A 3 6 h' 3 & 



35 7t If we would find the centre of percussion or of oscillation, we 



have only to divide this quantity by the product of the mass of 



the parallelepiped into the distance of its centre of gravity ; that 



Geom. is, by h h'f X \ h or h 2 h'f, IM being denoted by/, which gives 



4054 for the distance of the centre of percussion or of oscillation 



2h* 6 h' 9 6' . 2 fc h' 2 



h 6 A* h'f r ~T " 6T } 



since 



<* = # and <f = 



