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Mr. J. C. Maxwell on Governors, 



[Mar. 5, 



tions of a higher degree than the third ; but I hope that the subject will 

 obtain the attention of mathematicians. 



The actual motions corresponding to these impossible roots are not ge- 

 nerally taken notice of by the inventors of such machines, who naturally 

 confine their attention to the way in which it is designed to act ; and this 

 is generally expressed by the real root of the equation. If, by altering the 

 adjustments of the machine, its governing power is continually increased, 

 there is generally a limit at which the disturbance, instead of subsiding 

 more rapidly, becomes an oscillating and jerking motion, increasing in vio- 

 lence till it reaches the limit of action of the governor. This takes place 

 when the possible part of one of the impossible roots becomes positive. 

 The mathematical 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 adjustments 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 constant 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 disadvantage 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 fur- 

 ther 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 velo- 

 city, 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. 



