MOMENTS OF INERTIA. 49 



The radius of gyration of a body in reference to an axis is 

 the distance to which the entire mass of the body must be trans- 

 ported, so that its moment of inertia in reference to this axis is not 

 modified. If p is the radius of gyration measured in centimetres, the 

 moment of inertia is expressed in C.G.S. units by 



and, with the gramme as unit of force, 



We may here mention a theorem very useful in practice. 



The moment of inertia K' of a body in respect to a given axis, is 

 equal to the moment of inertia K of the body referred to an axis 

 parallel to the first, and passing through the centre of gravity, plus the 

 product of the mass by the square of the distance r of the two axes. 



The radius of gyration p in respect of the new axis satisfies the 

 equation 



701. We shall give the value of the radius of gyration of a certain 

 number of homogeneous bodies of simple form. 



Rectangular Parallelopipedon. If the dimensions of the parallelo- 

 pipedon are 2a, zb, 2C, we have for an axis passing through the centre 

 parallel to the dimension c, 



The expression *Ja 2 + ft represents half the diagonal of the face 

 perpendicular to the axis. When one of the transverse dimensions, 

 b for instance, is very small, as in the case of a thin plate, this 

 expression, put in the form 



shows that we may take as the value of p, the approximate value 



a ffi 



=, when is a negligable quantity. 



VOL. II. E 



r ./ 



