1868.] 



Mr. J. C. IMaxwell on Governors. 



275 



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



^f=¥{x-\H); (5) 



SO that if the governor B has come to rest x=^t, and not only is the velo- 

 city of 'Ihe machine equal to the normal velocity, hut 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 propor- 

 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 



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

 may write the expression 



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

 which the governor will act. 



Since this force necessarily acts on B in the positive direction, and since 

 _it is necessary that the break should be taken off as well as put on, a weight 

 W is applied to B, tending to turn it in the negative direction ; and, for 

 a reason to be afterwards explained, this weight is made to hang in a 

 viscous liquid, so as to bring it to rest quickly. 



The equation of motion of B may then be written 



^ ^=^(5^-^)-^%-^; ■ ■ ■ ■ ■ ■ («) 



where Y is a coefficient depending on the viscosity of the liquid and 

 on other resistances varying with the velocity, andW is the constant weight. 

 Integrating this equation with respect to we find 



B^ = F(x-V/)-Yj,-W< (7) 



If B has come to rest, we have 



(8) 



or the position of the machine is affected by that of the governor, but the 

 final velocity is constant, and 

 W 



V>+F=V, (9) 



where V is the normal velocity. 



