GOVERNORS. \Q<J 



I shall call all such resistances, if approximately proportional to the velocity, 

 by the name of " viscosity," whatever be their true origin. 



In several contrivances a differential system of wheel-work is introduced 

 between the machine and the governor, so that the driving-power acting on the 

 governor is nearly constant. 



I have pointed out that, under certain conditions, the sudden disturbances 

 of the machine do not act through the differential system on the governor, or 

 vice versa. When these conditions are fulfilled, the equations of motion are not 

 only simple, but the motion itself is not liable to disturbances depending on 

 the mutual action of the machine and the governor. 



Distinction between Moderators and Governors, 



In regulators of the first kind, let P be the driving-power and R the 

 resistance, both estimated as if applied to a given axis of the machine. Let V 



dx 



be the normal velocity, estimated for the same axis, and -*- the actual velocity, 



and let M be the moment of inertia of the whole machine reduced to the 

 given axis. 



Let the governor be so arranged as to increase the resistance or diminish 

 the driving- power by a quantity f \-ji~ V\, then the equation of motion will be 



dt \ dt t 



When the machine has obtained its final rate the first term vanishes, and 



Hence, if P is increased or R diminished, the velocity will be permanently 

 increased. Regulators of this kind, as Mr Siemens* has observed, should be 

 called moderators rather than governors. 



* " On Uniform Rotation," Phil. Trans. 1866, p. 657. 



