694 Dr. C. Y. Burton on the Kinetic 



(measured downward) on the block C ; then the equations of 

 motion are 



l^ ' • • • (*) 



_ d 



~ dt 



BE 



■a*" 



BE 

 B~ 





= Mz 



'+\z 



2 dM 

 dz 



***** 



U, 2 \s 





,=A/ 



i(i%) s 



(3) 



Now 



«r v ^ CiZ\L 1 / Inconstant 



=-^ 2 S w 



Hence, on the understanding that the differentiation with 

 respect to * is to be performed with 1% constant (that is, 

 with no turning moment applied to the governor, as expressed 

 by (2)) , we may replace (3) by 



Z=Mi'+ii^ +7 ^W). • • • (5) 

 J flte dz 



5. This is precisely the form which the equation of motion 

 corresponding to the r-coordinate would take if the velocity 

 ^ were permanently zero, while the system, in place of the 

 kinetic energy ^T^ 2 , possessed potential energy of like 

 amount. In other words, provided the angular momentum 

 I)£ remains constant, and so long as we confine our attention 

 to the coordinate z, the energy of rotation may be treated as 

 potential. The axial motion of the block C under given 

 axial force (including of course the special case of free 

 oscillations) will be the same as if the rotation were abolished, 

 and suitable springs of negligible mass introduced ; the 

 equilibrium position of the governor under the action of such 

 springs being approximately that shown in fig. 1. 



6. The energy of rotation of the governor considered in 

 the last three paragraphs is more palpably kinetic than 

 anything which we are accustomed to classify as potential 

 energy ; but when we come to consider the dynamical 

 criterion of potential energy, we shall find that, under the 

 limitations above defined, the rotational energy in question is 

 as much entitled to be called potential, as are the forms more 

 commonly included under that designation. 



