J 10 GOVERNORS. 



In the second kind of regulator, the force F (^ - V\ , instead of being 



applied directly to the machine, is applied to an independent moving piece, B, 

 which continually increases the resistance, or diminishes the driving-power, by 

 a quantity depending on the whole motion of B. 



If y represents the whole motion of B, the equation of motion of B is 



and that of M 



where G is the resistance applied by B when B moves through one unit of space. 

 We can integrate the first of these equations at once, and we find 



(5); 



so that if the governor B has come to rest x= Vt, and not only is the velocity 

 of the machine equal to the normal velocity, but the position of the machine 

 is the same as if no disturbance of the driving-power or resistance had taken 

 place. 



Jenkin's Governor. In a governor of this kind, invented by Mr Fleeming 

 Jenkin, and used in electrical experiments, a centrifugal piece revolves on the 

 principal axis, and is kept always at a constant angle by an appendage which 

 slides on the edge of a loose wheel, B, which works on the same axis. The 

 pressure on the edge of this wheel would be propoi-tional to the square of the 

 velocity ; but a constant portion of this pressure is taken off by a spring which 

 acts on the centrifugal piece. The force acting on B to turn it round is therefore 



jp**"_/7'. 



dt 



and if we remember that the velocity varies within very narrow limits, we may 

 write the expression 



where F is a new constant, and F, is the lowest limit of velocity within which 

 the governor will act. 



