1868.] 



Mr. J. C. Maxwell on Governors. 



271 



Most governors depend on the centrifugal force of a piece connected 

 with a shaft of the machine. When the velocity increases, this force in- 

 creases, and either increases the pressure of the piece against a surface or 

 moves the piece, and so acts on a break or a valve. 



In one class of regulators of machinery, which we may call moderators 

 the resistance is increased by a quantity depending on the velocity. Thus 

 in some pieces of clockwork the moderator consists of a conical pendulum 

 revolving within a circular case. When the velocity increases, the ball of 

 the pendulum presses against the inside of the case, and the friction checks 

 the increase of velocity. 



In Watt's governor for steam-engines the arms open outwards, and so 

 contract the aperture of the steam-valve. 



In a water-break invented by Professor J. Thomson, when the velocity 

 is increased, water is centrifugally pumped up, and overflows with a great 

 velocity, and the work is spent in lifting and communicating this velocity 

 to the water. 



In all these contrivances an increase of driving-power produces an increase 

 of velocity, though a much smaller increase than would be produced with- 

 out the moderator. 



But if the part acted on by centrifugal force, instead of acting directly 

 on the machine, sets in motion a contrivance which continually increases 

 the resistance as long as the velocity is above its normal value, and reverses 

 its action when the velocity is below that value, the governor will bring 

 the velocity to the same normal value whatever variation (within the 

 working limits of the machine) be made in the driving-power or the re- 

 sistance. 



I propose at present, without entering into any details of mechanism, to 

 direct the attention of engineers and mathematicians to the dynamical 

 theory of such governors. 



It will be seen that the motion of a machine with its governor consists 

 in general of a uniform motion, combined with a disturbance which may 

 be expressed as the sum of several component motions. These components 

 may be of four different kinds :~ 



1 . The disturbance may continually increase. 



2. It may continually diminish. 



3. It may be an oscillation of continually increasing amplitude. 



4. It may be an oscillation of continually decreasing amphtude. 



The first and third cases are evidently inconsistent with the stability of 

 the motion ; and the second and fourth alone are admissible in a good go- 

 vernor. This condition is mathematically equivalent to the condition that 

 all the possible roots, and all the possible parts of the impossible roots, of 

 a certain equation shall be negative. 



I have not been able completely to determine these conditions for equa- 



See Mr. C. W. Siemens On Uniform Rotation," Phil. Trans. 1866, p. 657. 



2 c 2 



