700 



Dr. C. V. Burton on the Kinetic 



energy of rotation may property be treated as potential 

 energy. In fig. 2 let B be a rigid frame, and let there be 



Fig. 2. 



two equal and similar governors journalled in this frame, so 

 as to be capable of rotation about a common (geometrical) 

 The construction of the governors ACEFGrH, 



axis. 



A'C'E'F'G'H' is essentially similar to that of the governor 

 shown in fig. 1, like letters indicating like parts. Each 

 governor, however, has four arms (instead of only two), 

 each carrying a ball, and all symmetrically arranged about 

 the axis A A. The rotatable system which constitutes the 

 governor proper has of course moments of inertia which vary 

 according to the inclination of tbe arms E PI ; but the axis 

 A A is always a principal axis of inertia, and the moment of 

 inertia is the same about all axes which intersect A A perpen- 

 dicularly at a given point. This condition has to be fulfilled 

 in order that the angular coordinates ^, %f (defining the 

 integral angular rotations of the governors relatively to the 

 frame) may not appear in the coefficients of the expression 

 for the kinetic energy of the system. 



