“a a ee 
’ 
; 
GOVERNORS 339 
For the direct loaded governor (Fig. 521), P= 4(W + 2w) (x - 1), 
dn=(“5*)h=k U=Pk= MW + 2u)( =*Yn, 
For the simple governor, (Fig. 526), except that B and C’ are on the 
| : l x? —1 a x? — 1\ha 
main axis, P= }u(x*—1)-, Ah= A ye b= 20ng = (==), 
x 
2_\2 
For a change in speed of 1 per cent. (==) = 0°0004. 
2_]\2 
For a change in speed of 10 per cent. ——) = 0°0364. 
290. Diagrams of Governor Effort and Power.—The formule 
obtained in the two preceding Articles will perhaps be better under- 
stood by reference to the 
diagrams of effort and F, 
power now to be de- : 
scribed. Taking first the © Fa 
simplest form of governor, 
namely, the simple conical F3 4 
ulum, OA, (Fig. 528) YA 
is one position of the pen- Fy 
dulum, and OA, is a higher 7 
position. Let N, denote es 
the normal speed of the ae: 
governor in revolutions ¥ 
per minute for the position f 
OA,, and N, the normal | K,~4 Hy 
te for the position \ 
. Let H,A, =”, and 
=r,, and let w= es H 
HA of one ball. bo Ky -4- A ! 
Make the vertical line Fig. 528. 
a¥, =centrifugal force of 
ball when its speed is N, and position Aj. aF,=cwNjr,, where c 
is a constant. . 
Make A,F,=centrifugal force of ball when its speed is N, and posi- 
tion A,. A,F,=cwNjr,. Let also the centrifugal force for intermediate 
positions be plotted in the same way, and a fair curve F,F, drawn 
through the points thus obtained. 
The work done by the centrifugal force while the ball moves from 
A, to A, is evidently represented by the area of the figure aF,F,A,. But 
as the speed has been assumed to be normal for each position of the ball, 
‘all the work done by the centrifugal force must have been spent in rais- 
ing the ball against gravity. Draw the horizontal line H,K, to represent 
w to the same scale as was used in representing the centrifugal force. 
Complete the rectangle H,K,K,H,. The area of this rectangle will 
represent the work done in raising the ball through the height H,H,. 
oF u 
+. 
