GOVERNORS 337 
have reached that level either by falling from a higher level, or by rising 
from a lower level. Suppose that the sleeve reached the level Y by 
falling from a higher level, due to a diminution in speed, then its speed 
must be m,. Now suppose that the speed diminishes still further, the 
sleeve will again fall, but the friction will not affect the sensitiveness of 
the governor ; the sensitiveness will be simply proportional to h, as has 
already been shown. Next, suppose that instead of the speed diminish- 
ing to less than m, it begins to increase after coming down to m,, then 
there can be no change in the level of the sleeve until the speed has 
increased to n,. If after the speed has increased to m, it goes on 
increasing, the sleeve will continue to rise, and the sens¢tiveness will again 
be unaffected by the friction. 
If n is the mean speed = }(n,+,), and represented by the point L 
(Fig. 527), then “2 — is the coefficient of fluctuation of speed of the 
governor when the direction of the motion of the sieeve is reversed, and 
the smaller this coefficient is, the more sensitive is the governor. 
The value of the expression a for a Porter governor of the 
simplest form is found as follows :— 
— /W+Rtw g & -R+w g 
My Ae. hrs cy re ob Agi 
W+w 9 i 
n al ree. Se (see footnote), hence 
ma—m  J/W+R+w- LOR f+ to a 
n J/W+w Wtw W+w 
If W be increased, the term al 1 a decreases, and the term 
—<$<$—$—$—$ ____—_—— 
al 1- R increases, therefore the value of “2—™! decreases as W 
W+w n 
increases. Hence, considering the effect of friction on a loaded governor, 
the sensitiveness is greater the heavier the central load, and consequently 
the loaded governor is more sensitive than the unloaded governor when 
the pendulum weights are the same in both. But the unloaded governor 
may be made as sensitive as the loaded governor by increasing the 
pendulum weights. Let w,= weight of each ball of a simple or unloaded 
governor, 7 = weight of each ball of a loaded governor, and W = weight 
of central load. Then for the unloaded governor W =0, and 
For the loaded governor ae lt a, _ ‘emit. Te 
Hence if = is the same for both governors, w,=W +t. 
Note.—The mean of the rising and falling speeds for a given level of sleeve, 
and for a given value of R, is not quite the same as the speed for the same level 
when R=0, but as R is generally small compared with W +, the error intro- 
duced by taking n as above may be neglected. 
Y 
