Mr. J. C. Maxwell oh Governors. 389 



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 be the normal velocity, estimated for the same 



axis, and -jz 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 di- 



(dx \ 

 ~r — V J, then the equa- 

 tion of motion will be 



5( M S)= P : R - F (S- V ) a> 



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

 and 



dt y+ F W 



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

 nently increased. Regulators of this kind, as Mr. Siemens * has ob- 

 served, should be called moderators rather than governors. 



f dx \ 

 In the second kind of regulator, the force F f -j- — V J, instead of 



being applied directly to the machine, is applied to an independent 

 moving piece, B, which continually increases the resistance, or dimi- 

 nishes 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 Bis 



S( B f)= F @- Y > ^ 



and that of M 



!( M £)= p - R - F (S- v W w 



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 



B g=F O-V*) ; (5) 



so that if the governor B has come to rest#=Y£, and not only is the 

 velocity of u the machine equal to the normal velocity, but the posi- 

 tion of the machine is the same as if no disturbance of the driving- 

 power or resistance had taken place. 



Jenkins Governor. — In a governor of this kind, invented by 

 Mr. Fleeming Jenkin, and used in electrical experiments, a centri- 

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



Phil. Mag. S. 4. Vol. 35. No. 238. May 1868. 2 D 



