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334 APPLIED MECHANICS 
More frequently the central load is suspended from the pendulum 
weights by links, as in Fig. 522, which shows the Porter governor, 
so called from the name of its inventor. The particular governor shown 
- in Fig. 522 is one made by Messrs. Tangyes of Birmingham. : 
To determine the relation between the height and speed in the Porter 
governor, consider the diagram Fig. 523. Let W 
equal the total weight of the central load, and w the B 
weight of each revolving ball. The central load will 
cause a tension in each suspension link equal to 
W 
2 cos 0° 
of each ball into a vertical component uf and a 
aaa 
This tension may be resolved at the centre 
horizontal component Q equal to - tan 0. Taking 
moments about B, the point of suspension of the 
pendulum arms, 
(z aa w)r + W,, tan 0=Fh= wow?rh ; 
2 2 y Fia. 523. 
Let tan 0 =3 = t, then (¥ + w)r Li wn 
and therefore h= {at +o)t "| 5 ; B 
w 
Ifr,=7, theng=1, and h= W46. ‘ : 
When the pendulum arms and the e 
suspension links are of equal length, and 
the axes of the joints at B and C either Fria. 524. Fig. 525. 
intersect the main axis (Fig. 524) or are at 
equal distances from that axis (Fig. 525), then g is equal to 1. In other 
cases, the value of g is best found by measuring r and r, on a diagram 
to scale. It should be noted that when g is not equal to 1, its value 
alters as the height h changes. 
286. Effect of Friction on Governors.—The frictional resistances 
of the various joints of the governor itself, and of the gear which the 
governor has to operate, may be reduced to a single force R acting on the 
sleeve in a direction opposite to that of its motion. When the sleeve is 
rising, and the speed of the governor therefore increasing, R will act 
downwards, and in a loaded governor this will be equivalent to altering 
the central load from W to W+R. Again, when the sleeve is descending 
R will act upwards, and this will be equivalent to altering the central 
load from W to W—R. Hence for a loaded governor of the type shown 
in Fig. 521, copes sa ©, the plus (+) sign being used for 
increasing speed, and the minus (—) sign for decreasing speed. 
--3 K--- 
