THE GOVERNOR.] 



APPLIED MECHANICS. 



863 



seconds, or half seconds, or any other intervals that may 



be required ; so in the conical pendulum or governor, 



Fig. 191. 



the length of the arms that carry the balls must be 

 Dialed by the speed at which they revolve. In 

 discussing this question, we need only consider one ball, 

 a* each is regulated by the same law, and they are 

 rally made in duplicate for the sake of balancing the 

 api watus, and to give it symmetry. The force which 

 teuds to throw the ball outwards from the vertical 

 spindle, is the centrifugal force of its revolution, or its 

 tendency in obedience to the first law of motion to 

 proceed in the straight line E F (Fig. 1.92), touching the 



Fig. 192. 



H 



circle in which it revolves, rather than to be continually 

 diverted from its straight to a circular path. The force 

 which opposes the centrifugal force, and causes the ball 

 to be continually deflected from the straight line, is the 

 weight of the ball tending to push it close home to the 

 vertical spindle. If we take any position of the ball, 

 such as D, A B being the vertical spindle, and complete 

 the parallelogram of forces A B D H, while the line 

 D H or A B represents in quantity and direction the 

 weight of the ball, drawing it down, and D B or AH 

 the centrifugal force pushing it outwards, A D represents 

 the resultant of those two forces as a tension on the rod 

 by which the ball is suspended. If we know the velocity 

 with which the ball moves in its path, and the radius of 

 that path, we can estimate its centrifugal force in com- 

 parison with its weight, and can make the limb A D of 

 such a length that these two forces shall be properly 

 proportioned for a certain velocity.* 



* E G being part of the circular path, which may 

 be taken as small as we please, and E K perpen- 

 dicular on C F, F K is nearly bisected in G, and E K 

 is nearly equal to E F, and K F nearly parallel to C E. 



AlaoCE : EF :: EK : KF = 



EK-EF 



. 

 or nearly 



EF* 



A body projected from Ewi-.i such a velocity as would 



The length of the arm of the governor, measured from 

 the point of suspension to the centre of the ball, may be 

 found from the following rule : 



Divide 200 by the number of revolutions per minute, 

 and multiply the quotient by itself for the length in 

 inches. 



Example. Required the length of a governor arm 

 suited to 50 revolutions per minute : 



-gQ- = 4, and 4 X 4 = 16 inches. 



To find the speed suited to a governor of a given 

 length of arm. 



Divide 200 by the square root of the length (in inches), 

 and the quotient will be the number of revolutions per 

 minute. 



Example. Required the proper speed for a governor 

 having an arm 16 inches long. 



200 

 The square root of 1C is 4, and -j- = 50 revolutions 



per minute. 



The rods and levers connecting the governor with the 

 throttle-valve should be capable of adjustment, and it is 

 useful to have an adjusting counterbalance to the centri- 

 fugal force of the balls, by changing which, the regulated 

 speed of the engine can be varied at pleasure. Although 

 the governor we have described is a most valuable ac- 

 cession to an engine, yet it is not a perfect regulator ; 

 for its very mode of action implies that the velocity of 

 the engine must have undergone a change, before the 

 governor can have begun to act on the throttle- valve. But 

 within certain limits, the variation in speed of an engine 

 thus regulated is inconsiderable, and there is no appa- 



in a small period A' cause it to describe EF, if 

 acted on during that period by a constant deflecting force 

 parallel to CE, giving it during A* a velocity which 

 would cause it to describe uniformly F K in the time 

 A<, would be deflected through F G, the half of F K in 

 the time A<- 



If/= the deflecting force (measured by the velocity 

 acquired in one second), /A< 2 is the space traversed 

 during A' at the velocity acquired during A<^> and if 

 be the velocity per second of the body in E F, and 

 therefore E F = v A<, and r = C E, the radius (measured 

 in inches), 



. :,-? 



Taking n = the number of revolutions per minute, 



- 



number per second, and 2 irr the circumference 



traversed in each revolution, .'. v = 



_ . i*n* rn* 



Hence, /= ,-5^^ - 91 -lie. 



GO 

 very nearly. 



_rn_ 

 9-545 



The force of gravity is measured by a velocity 

 feet or 385 inches acquired per second, and taking w 



the weight of the body, / : w 



91 



wrn* w rv? 



* 91-1 in. X 385 = 35344 



385 



very nearly. 



Now, as / is represented by B D, while w is measured 

 by A B, and as B D = r 



or 



35344 B D _ 35344 _ ,188\* 

 AB n' BD~ n 3 "k"S"' 



It is convenient in practice to make the angle BAD 

 about 3V when the governor is at its average speed, 

 when AD = 2DB;andas A D 2 = AB' + DB 2 , we find 



188\ J /200\ 2 

 -)-() very nearly. 



