50 MEASUREMENT OF COUPLES. 



Solid Cylinder. For a right circular cylinder with parallel bases, 

 of radius a, and of any given length, the radius of gyration in respect 

 of the axis is given by the expression 



In respect of a right line passing through the centre, and 

 perpendicular to the axis, if 2.1 is the length of the cylinder, we 

 have 



79 9 79 / 



/ all 3 



P ~! + ~4 = "3\ 4/ 2 , 



Hollow Cylinder. If a and a' are the radii of two right circular 

 concentric cylinders, the radius of gyration, in respect of the common 

 axis of the volume between them, is given by the formula 



we may write 



p 2 = 



\ 2 



If the thickness a -a = e is very small, we have, disregarding 



terms of - of the second order, 

 a 



Sphere. For a solid sphere of radius a, we have 



702. In accurate experiments, we must employ bodies of easy 

 construction, and the dimensions of which can be precisely measured; 

 it is further preferable, in order to load the oscillating apparatus as 

 little as possible, to choose those which have the greatest moment of 



