336 APPLIED MECHANICS . 
axis (Figs, 518, 521, 522, 523, and 524), and let the friction be 
neglected. In this case the change in the level of the revolving balls is 
the same as the change in the height & of the governor. If m is the 
- speed of the governor in revolutions per second when the height is h, 
a 
then for the simple governor and also for “se loaded governor h and are 
connected by an equation of the form h=- —,, where c is a constant de- 
pending on the type of governor and “the various weights. Also, 
when friction is considered, c has one value for increasing speeds, and 
another value for decreasing speeds. Let the speed increase from 7 to 
an. (If the increase in speed is 1 per cent.,x=1°01.) The height & 
will decrease to h, 
h 
h_,(@-1 
where y= y=". Hence, h~h, = Ah=h— “= i(@ 57), 
This shows that the sensitivenéss of the governor is directly proportional 
to the height /, and it follows from this investigation that the sensitive- 
ness of the loaded governor is the same as that of the simple governor when 
Friction ts neglected. 
Many writers of note state that, friction being neglected, the loaded 
governor is more sensitive than the unloaded governor, and it is therefore 
necessary that this point should be considered more fully. Take a 
simple governor in which the revolving balls each have a weight w, and 
let this governor be converted into a loaded governor, say of the Porter 
type, by adding a central load of weight W, and for simplicity let 
the factor g (Art. 285) equal 1; then for the unloaded governor 
es: _W+w g : 
h= ine? and for the loaded governor h= mame ra Now if these 
governors are run at the same speed, the height of the loaded governor 
will: bo to” 
WwW 
times the height of the unloaded governor, and under 
Wi+ times as 
these circumstances the loaded governor would be 
sensitive as the unloaded governor; but what really happens in practice 
is that when the simple governor is replaced by a loaded governor the 
height is about the same for both, and consequently the loaded governor 
is run about eA W +1” times as fast as the unloaded governor, and the 
w 
one governor is then no more sensitive than the other when friction is 
neglected. 
Consider now the effect of friction on the sensitiveness of the 
governor. For the Porter governor, in its simplest form, it has been shown 
9 W+R+w g 
that n "eee ae? 
to overcome the friction of the governor and the gear which it has to 
operate. For a given value of h there are evidently two values of n, 
namely, m= fa" Ete, reat and Ny = {oe : rai" 
where R is the force required at the sleeve 
‘Referring to the diagram Ve. 52°, if m, is represented by the point L,, then 
my is represented by the point io If the sleeve is at the level Y, it must 
