^r4 



Mr. J. C. Maxwell on Governors, [Mar. 5, 



motion 



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 wheelwork 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 dilFereutial system on the governor, 

 or vice versa. When these conditions are fulfilled, the equations of mo- 

 tion 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 re- 

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



V 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 ^^^^ equation of 



will be 



d_ 

 dt 



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

 dt^^ Y ' 



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. 



/'dx \ 



In the second kind of regulator, the force F f ^ — Vj, 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 



|(M|) = P-R-Fg_y) + G,, (4) 



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



space. 



•' Oil Uniform Eotation," Phil. Tmns. 1866, p. 657. 



(MS)=P-K-F(g-y) a) 



