Mr. J. C. Maxwell on Governors. 387 



limit of action of the governor. This takes place when the possible 

 part of one of the impossible roots becomes positive. The mathe- 

 matical investigation of the motion may be rendered practically useful 

 by pointing out the remedy for these disturbances. 



This has been actually done in the case of a governor constructed 

 by Mr. Fleeming Jenkin, with adjustments, by which the regulating 

 power of the governor could be altered. By altering these adjust- 

 ments the regulation could be made more and more rapid, till at last 

 a dancing motion of the governor, accompanied with a jerking motion 

 of the main shaft, showed that an alteration had taken place among 

 the impossible roots of the equation. 



I shall consider three kinds of governors, corresponding to the 

 three kinds of moderators already referred to. 



In the first kind, the centrifugal piece has a constant distance 

 from the axis of motion, but its pressure on a surface on which it 

 rubs varies when the velocity varies. In the moderator this friction 

 is itself the retarding force. In the governor this surface is made 

 moveable about the axis, and the friction tends to move it ; and this 

 motion is made to act on a break to retard the machine. A con- 

 stant force acts on the moveable wheel in the opposite direction to 

 that of the friction, which takes off the break when the friction is 

 less than a given quantity. 



Mr. Jenkin's governor is on this principle. It has the advantage 

 that the centrifugal piece does not change its position, and that its 

 pressure is always the same function of the velocity. It has the dis- 

 advantage that the normal velocity depends in some degree on the 

 coefficient of sliding friction between two surfaces which cannot be 

 kept always in the same condition. 



In the second kind of governor, the centrifugal piece is free to 

 move further from the axis, but is restrained by a force the intensity 

 of which varies with the position of the centrifugal piece in such a way 

 that, if the velocity of rotation has the normal value, the centrifugal 

 piece will be in equilibrium in every position. If the velocity is 

 greater or less than the normal velocity, the centrifugal piece will 

 fly out or fall in without any limit except the limits of motion of 

 the piece. But a break is arranged so that it is made more or less 

 powerful according to the distance of the centrifugal piece from the 

 axis, and thus the oscillations of the centrifugal piece are restrained 

 within narrow limits. 



Governors have been constructed on this principle by Sir "W. 

 Thomson and by M. Foucault. In the first, the force restraining the 

 centrifugal piece is that of a spring acting between a point of the 

 centrifugal piece and a fixed point at a considerable distance, and 

 the break is a friction -break worked by the reaction of the spring 

 on the fixed point. 



In M. Foucault' s arrangement, the force acting on the centrifugal 

 piece is the weight of the balls acting downward, and an upward 

 force produced by weights acting on a combination of levers and 

 tending to raise the balls. The resultant vertical force on the balls 

 is proportional to their depth below the centre of motion, which 



