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BRINa TBIS OOP7 WITIZ 70U TO THB MEBTINO.

(Subject to Revision.)
DLXXXII.*

NOTES ON THE THEORY OF SHAFT GOVERNORS.

BY ALBEUT K. MANSFIKM), SAI.KM, OHIO.

(Meraber of the Society.)

At our spring meeting of 1890, at Cincinnati, three papers on
shaft governors were presented, which, together with the ex-
tended discussions thereon, make a valuable contribution to the
literature of this subject.

It is the purpose of this p{ per to add something to that dis-
cussion, with the hope of getting a little nearer to a correct
solution of the perplexing proldems surrounding the subject.

The matter ^^^o be discussed will be divided into several topics,
for the sake of clearness.

1. The. path of wi unbaJanccd (jovernor ball of a shaft governor,
isoch ronoushf adjusted.

This problem was proposed by Professor Sweet in one of the
papers referred to, and in an elaborate mathematical analysis
Prof. S. W. Eobinsou seems to prove that the centre of the
approximately circular path is vertically above the centre of
the shaft, and that the distance apart of these centres may be

determined from the formula h —

9.78

h being the distance

sought, in inches, and n being the number of revolutions per
second.

Confirmatory of this result, an experiment was made with an
unbalanced weight, arranged according to the requirements of
the problem. The figure illustrating the experimental appa-
ratus is here reproduced (see Fig. 1).

* Fresieniocl at the Montre il meeting (June, 1894) of the Americiui Society of
M(!chunical Engineers, and forming part of Volume XV. of the Transactions.

2 NOTES ON THE THEORY OF SHAFT QOVERNOIiS.

The spring adjustment was such that this apparatus was
thought to be isochronous at 555 revolutions per minute, and
the experimental determination gave /i=0.l2G inch (mean of
several trials), while by the formula h becomes 0.11-1: inch— a
fairly close agreement.

Following this a table of values of /* was given, derived from
the formula, revolutions per minute being taken at from 1,200
as a maximum down to GO ; h in the former case being by calcula-
tion 0.02 inch, and in the latter 9.78 inches.

Suppose this table to be extended to cover slower speeds
than sixty revolutions per minute, even down to one revolu-

FlG. 1.

tion per minute, /* would be found at this speed to be, by the
formula, 35,200 inches, or 2,933 feet — more than half a mile
above the centre of the shaft.

This extreme result is noted merely as a curious matter of
interest.

The formula is doubtless correct, as deduced from the as-
sumption on which it is based ; but let us examine the assump-
tion.

Eeferring to the figure of Professor Sweet's paper, here repro-
duced (Fig. 2), Professor Kobinson says : '* Suppose, to start
with, that the weight B is at,/, moving along a horizontal por-
tion of arc. The action of gravity tends to deflect it downward

NOTES ON THE THEORY OF SHAFT GOVERNORS.

Fig.

instead of allowing it to move along a circular path concentric
with the shaft, thus giving the mass li an accelerated motion
relative to the wheel A, and along the radius AB, so that by
the time the weight reaches a it will have a considerable
velocity toward the centi o
C. From this point on
gravity counteracts, and on
reaching d will have de-
stroyed the radial velocity
toward C\ when B will
again be moving horizon-
tally, or perpendicular to
the radius, but will be at
a point nearer the centre
C than when at ./. Now,
from this point on a radial
acceleration will occur, so
that at (J the weight will be
moving outward with a
radial velocity which, from
(J on to ./, will again be destroyed by gravity, thus bringing
the weight to rest on the radius at./, though at a greater radial
distance from the centre C than at any point before in the revo-
lution, and putting the weight in the position and condition
supposed at the start, when it will go on in repetition of t^e
curve as the next turn of the shaft is made, and so on, continu-
ously, the curved path described being found to be nearly a
circle, with its centre elevated above that of the shaft."

The questionable part of this reasoning lies in the first sen-
tence : " Suppose, to start with, that the weight B is at^, mov-
ing along a horizontal portion of arc," Under this supposition
what follows is justified ; but the supposition is only one of an
indefinite niimber that may be made with equal correctness, each
leading to a different conclusion.

For example, suppose we start the analysis from the point a,
the weight being assumed to have no radial movement at that
point, and the motion to be right-handed. Then, during the
entire first half-revolution, an accelerating force is drawing the
weight away from the centre, always faster, until at g this force
becomes zero, and the velocity outward is uniform. During the
next half-revolution, a force of equaF effect acts to draw the

NOTES ON THE THEORY OF SHAFT (JOVEUNOltS,

weight toward the centre, but this force must 1)e entirely ex-
pended in overcoming the velocity of the weight outward, which
it had when at the point (j, therefore the movement of the weight
is outward during the whole revolution. The same action occurs
in succeeding revolutions, and the Aveight describes a spiral
outward, finally reaching its outer stop.

If we start the analysis from (j, we find by similar reasoning
that the weight describes a spiral inward.

The reasoning in the case of starting from r/ or a, which does
not permit the ball to return to its starting point, is found to be
rational, Avlien compared with the case of any weight moved in
a straight line, with no resistance except that of inertia, by an
accelerating force, and stopped by an equal retarding force. The
weight comes to rest, and no work is gained or lost, yet the
weight is found in a new position.

Again, if we consider the weight to start, with no radial move-
ment, from any other points intermediate between its positions,
CT, g, and./, d, it will be found to describe a spiral outward when
the first position is taken at the right of the axis, and inward
when at the left. These spirals are, as Avill be seen by con-
sideration of the forces of inertia, in no case regular spirals, but
are merely of spiral nature, not re-entering.

The conclusion to be derived from this analysis seems to be
that the problem has no true solution, or if any expression based
on correct reasoning could be found for the curve, it would be
irrational.

Moreover, under the conditions of perfect isochronism
assumed, one would be led to expect the motion of the ball
to be erratic ; as, for instance, it might first move in the outer
spiral, when, reaching the outer stop, it may be compelled to
move horizontally at the point j, which might start it in the
eccentric circle. Slight disturbing influences, as of the atmos-
phere, would probably change it from this to other of its paths.
This expectation seems to be to some extent verified by the
experiment of Professor Robinson, for we find in his table of
results the remarks " spiral inward," " spiral outward,"
" steady," etc.

The practical conclusion to be derived from this analysis is
that an unbalanced weight in an isochronous shaft governor is
not feasible.

NOTES ON THE THEORY OF SHAFT GOVERNORS.

2. Centrifufial moment of a govetmor weMjliK

Theorem : The centrifugal moment about the weiglit pivot,
like the simple weight moment, is the same wherever on the
lino through the centre of gravity of the weight to the centre of
the pivot tlie weight be considered as concentrated.

Let A, Fig. 3, be the centre of the shaft, B the centre of
gravity of the weight, and C the pivot centre or fulcrum.

In considering simple weight leverage about (\ the effective
weight may be assumed to act at any point on the line B C, as at

Fif. 3.

E, in which case the weight at £J is to the actual weight at B as
B C io E C. The centrifugal moment of weight B for any given
number of revolutions is proportional to the radius B A times
the line G C, drawn at right angles to B A through C. The
centrifugal force of the resultant weight E is similarly A E
times D C ; D C being draAvn at right angles to A E prolonged.
According to the theorem,

AB X GCxGE = AExDCxBC,

the lines C E and B C being the relative weights in the two
cases.

Proof: Draw the line FA at right angles to BC. Then we
have the similar triangles AFB ;ind COB; also AFE and
CUE,

NOTES ON THE THEORY OF SHAFT QOVERNOBS.

from which
and

AB: AF= CB\ CO,
CE\ CD.= AE'. AF.

Multiplying tho equations together, and equating product of
means to product of extremes, we have

ABxOCxCIJ=AFkDCxBC

as asserted.

This goes to show that the attempt, which is evident in many
shaft governors, to so design them that tho centre of gravity of
the weight nhall move nearly in a radial lino \h unnoceasary.
Wherever the weight be concentrated on the lino B C, provided
its amount be sufficient, the renult is the same Avhether the arc
described approaches a radial lino or not.

This demonstration leads up to another interesting detail,
which seems to show that shaft governors are not always ar-
ranged for true isochronism.

3. PosUion and tension of spring.

In Fig. 4 let A be the centre of shaft, B the centre of gravity

/T^c

of weight, and 6' the weight pivot, as before. Since the line A B
may be taken as a measure of centrifugal force of B, then a line
from Aio B aX any other position of B in its arc will be, in an

NOTES OS THE THEOIIY OP HIIAFT QOVEUNORS.

i of

any
y of
iiry.
ded
arc

tail,
ar-

vity

AB
line
u an

isoclironons governor, assuming miifoim velocity, a correspond-
ing rnoayuro of the centrifugal force of If in this new position,
as the lino A Ji^ for the ])osition //,. Suppose a pull spring
pivoted HO as to swing about the point A, and to bo j)ivotaliy
attaclied at its outer end to the <!entre of gravity of // ; also,
suppose the spring to be of such tension and strength as to
exactly i*alance the centrifugal force of li. Suppose, also, that
the line A li represents the total extension of the spring — i. e.,
that when the end // of the spring is at .4 the force of the
sprini.i; 's zero — then the spring, from the laws of spring ten-
sion, will just balance the centrifugal force of tno weight B
in other positions, as at Z?,. The arrangement is therefore
isochronous, for centrifugal and centripetal forces are exactly
opposed to each other in direction and amount.

Take any point h\ as before, on the line />* (', and draw the
line A E; consider A E to represent a spring pivotally sup-
ported at A and pivotally connected at /f, and of such force as to

counterbalance the centrifugal force of B, or of its resultant

weight at E. Then, if the zero of tension of this spring is at yl,
it will counterbalance correctly the centrifugal force of the
weight at all other positions, as at /ii, for the spring lies in the
line of action of centrifugal force, and its leverage I) (■ about
C is the same as that of the centrifugid force. From which it
is clear that a spring pivotally adjusted at A, and pivotally con-
nected to the weight-arm (d <iin/ p<)'>i' n ^e line B (\ is cor-
rectly located to produce exact isoj-
In Fig. 5 let A, li, 7>'„ and C
pivot, as before. Draw lines yl 6* a
C through any point U on the lin>.
From the point E drxw AM,, parallel to ^> ..
to El. The figure ^1, E Ei is exactly similar to the figuv^
A B Bf, and corresponding sides of the figures are parallel to
each other. It will be clear from the foregoing and from inspec-
tion, that if a spring be pivotally connetited from Ai to E, and
has its zero of tension at Ai, and is adjusted to balance the
centrifugal moment of the weiglit, it will balance it in all other
positions, as at Ei. But the arc B Bi need not have been drawn
through the centre of gravity B, for, from the previous demon-
stration (see Fig. 3), it could have been drawn through any
other point of line B C ; therefore, the line B A might have had
any direction between that of the direction of the line A to

> hft, weight, and
'aw an arc from
ing Bi C at El-
and connect Ai

NOTKS ON THE TIIKOltY OF HlIAFl' GOVEIINORS.

tlmt of the (lirnction of a lino A /?.., parallel to />' f. SiK-h un
iudofinito nutnlx^r of coiiHtruetioiiH would brin^' tlio poir' /I, at
any ponition on tho lino A (\ or its eontiuuatioii tlirouj^h A.

It liaH therefore beeTi shown that a spring pivola/ly sicung at
any jxnnt on the line (J A, or it,s nontinnation through A, and pivotally
connected to any point on C B or its continuation throwjh B, arid

Fig. a

\/
ye

having its zero of extension at the first-named point, is correctly
placed to produce exact isochronism.

Referring to Fig. 6, it will be clear without demonstration

NOTEiJ ON THE THLOBY OP 8HAFT QOVERNOHH.

HII

I at

7 at
ally
and

,tly

ion

timt t'lio point of connoction to wei^lit-iirin nned not be ay tlie
lino /> « '. It may bi* anywhoro or the woiglit-arm, as at /
vidnl a now znra lino (I (' bo drawn anguh;;ly tUo same arfiauoe
and (lik'ocrtion from J (' ah tho line /''('from A't'.

it follows that tlu! point of conno(!tion of Hprin*^ to woi^lit-
arm, and tho dinuition of action of H})ring, ininj tk svhvttil cnliirfy
at rdUihnn, or for convenioneo, provided only that tho length
betwaon pivots and tho tension of isprin<^ bo fixed according to
tho principles laid down.

The ctinclusions arrived at by tho preceding reasoning may
be expressed in tho form of a second

Theoreu) : The combined zero and fixed pivotal point of a
spring, anangotl to act isochrononsly on any point of tho line
of weight-arm from weight pivot through centre of gravity of
weight, may be taken at any j)oiut on the line from weight pivot
through centre of shaft. Moreover, the spring force required
will be inversely -s the distance of the fixed pivot from the
weight-arm pivot.

In Fig. 7, ^otters A A^ B C E represent the stn :. parta as in
Drop porpendiculars C G and CD from (J on lines A K

Fi.'. 5

Fig. 7.

and 7s' vl, respectively; also from ^drop the perpendicular EF
on line A C. Then similar triangles yl, EFn,n(\. A^ CD, as well
as A F E and A C (S, are formed, from which proportions may
be made as follows :

A,G

EF.
CD.

AC
A,E

CG,
EF.

NOTES ON THE THEORY OF SHAFT GOVERNORS.

Multiplying together, equating products of extremes and
means, and canceling K F, we Lave

AEx CGy. A,C=AyE^ CD -K A(\

AE^ CG^AE-x CI) x~

AiC

If we consider A C to be the unit of force oi the spring when
the fixed pivot is at A^, and J, the unit of force when the
pivot is at A, then this becomes intelligible.

It shows that the linear extensions of the springs A E and
AJ^., multiplied by their leverages G C ■axiOi CD and by the
units of force of the springs, are equal. The points A' and A^
were taken at random, which makes the demonstration general.

A further consideration of Fig. 3 Avill show tliat when A is the
fixed pivot the unit of spring force is inversely as the distance
of the point of connection on line B C from C.

If, therefore, we have computed the centrifugal force of the
weight />*, we have merely to multiply this centrifugal force by the

^. B C A C r T^' r , ■■,.

ratio j^ X -^— ^ (see b ig. 5 for illustration) to find the corre-
sponding balancing spring force ; or to multiply the centrifugal
force per inch of radius by this ratio to find the correspond-
ing spring force per inch of extension. The linear extension
of the spring was before shown to be EAi.

4. Af proximate isochronism.

In Fig. 8 let AD C be the centres t.i shaft, of gravity of
weight, and of pivot, as before. Draw a line from B through
A to any point O. Let C be the fixed point of a spring pivotally
attached to //, and having its zero of extension at A.

It is clear that the arrangement may be made isochronous for
the two positions A and B. For the moment consider O to be
infinitely removed from A, and investigate the mid-position of
B at />'i. Draw />', O^ parallel to B O, and A A^ parallel to
i?i C; also A B^, and B C at right angles to A B^ through C.

Lat A C be represented by 11 and the angle A C By by a.
Then the spring moment at By is R- sin. a, and the centrifugal

moment is 2 /?'sin. - x cosin. ^, which expressions are equal to

each other, by trigonometry. Therefore, wiuh a spring so located

NOTES ON THE THEORY OF SHAFT GOVERNORS.

and adjusted, a third point, i?i, is isochronous. If the point O
is a finite distance from A, as shown, it will be found that there
will still be a point Bx, near the middle of the arc A B, which
will be isochronously balanced ; other points, however, between
A and Z?i will have their spring moment too small, and points
between B^ and B will have their spring moment too large.

Suppose the spring to be arranged as in Fig. 9, the point B^
being the inner or initial position of the weight B ; then clearly,
from previous demonstrations — being the pivotal jooint of the
spring — to produce isochronism at points Z>\ and B, A^ must be
the zero point of the spring. It will be found as before that a
point nearly midway between B and B^ is also isochronous ;
also, if the angle B C By is not large, the approach to complete
isochronism is very close.

This corresponds to the arrangement commonly used in prac-
tice. Clearly, the arc Ji By may be drawn in any other place

NOTES ON THE THEORY OP SHAFT GOVERNOES.

from C as a centre, as at D D„ the line of the spring being made
to pass through these two points, and their angular distance
apart being the same as that of U and /?,.

5. Influence of the weight of the spring.

Let the spring be applied, as in Fig. 10, and let G be its centre
of gravity. Determine its moment m of centrifugal force about
its pivot 0, and divide bj the length of the spring I), O, which
we will call I. Owing to the weight G being constant, and the

direction of / practically always the same, — is very nearly con-
stant— ^/i being the moment of centrifugal force and I tlie length
of the spring— for any degree of extension between I)^ and 1),

and the quantity -^ is the tangential force at /), due to the cen-
trifugal force of the spring. Extend the arc D Z>, across the
line A C, and lay off each side of the line to F and J'\ one-half
the arc JJ D,. Draw radial lines from ^'to 7'\and /;. Draw a
circle through O whose diameter is the cho-d I) />,. From A

NOTES ON THE THEORY OF SHAFT GOVERNORS.

made
tance

draw lines tangent to this circle, crossing the radial lines C F
and CFi at K and J\\. Let d represent the distance A K.

Then, since j is the force, . is the weight, which, concen-
trated at Kov /ri— according to the position of the weiglit-arm
/> ("— Avill produce a centrifugal moment about 6' almost exactly
equivalent, at the three points K, K^, and (">,, to the centrifugal
moment due to the spring weight. Between the extreme posi-
tions K and /li and the central position the action of such a

'ntre
bout
hich
[the

con-

iigth
\D,

cen-

the
half
iw a
n A

/
;

weight is not exactly equivalent to that of the spring, but with
a n. /derate arc the error is extremely small.

Tlie object of determining the location and amount of the
equivalent weight A' is to find the influence of the spring on the
location of a correct centre of gravity line B C.

G. Influence of the ivcight of the link.

Theorem : If a governor link be constrained to move at one
end in a circular path about the centre of the driving shaft, and

NOTES ON THE THEOBY OP SHAFT GOVERNORS.

at the other end in a circular path about the centre of the
weight pivot, then is the centrifugal e£fect of the link the same
as If that portion of the weight of the link were concentrated
at Its weiglit-arm pivot, which would rest on its support if the
link were placed in a horizontal position on two end supports

rnf'^'}^ ^^^ '^ ^^ ^^^ ^^'^^^ ^e"<^re, 6' the weight-arm pivot
I^ O the link, and G the centre of gravity of the link. G A =

1 1 "^7 ^^ *''^^'' *° represent the centrifugal force of the
link. Clearly, this force may be resolved into two forces, Om
and Z », the sum of which is equal to G A, while their ratio is
as 6^ ^ to G 0, and their direction of action parallel to G A.

Eesolye Om into the components Oj> and Oq, Op having a
radial direction from A, and q lying in the line of the link.
Lay off |> y from L to q„ in the direction of the link, and combine
^^, with Ln by the parallelogram of forces, which gives the
force Z. as the total resultant force of the link tending to rotate
tne weight-arm about its pivot.

DrawZ^, also Gt parallel to A, and tv parallel to ^ Z
By geometry G A is divided at ^•, and Z A at U in the same
ratio as Z O at G; therefore, since Om was made equal io Gv
m amount and direction, the triangles m Oq and Gvt are equal
Ln was made parallel to and equal iovA, and ns is parallel

NOTES ON THE THEORY OF SHAFT GOVERNORS.

to and equal to v t by construction ; therefore the triangle nsL
is equal to the triangle vf A, and Z« is equal to J. iJ in amount
and direction.

But

At
AL

OG
OL

or, At = AL -x

OG
T)L

Ir other words, when the centrifugal force acting at G is rep-
resented by the radius A G, that acting at L may be represented
by the radius .1 Z, multiplied by a fraction which is the ratio of
the weight G, which would be supported at L, provided the
link were to rest in a horizontal position on two supports at Z
and 0; which was to be proved.

If the centre of gravity of the link were at its centre, as is
common, then it would be exactly right to consider one-half the
link concentrated at Z.

7. FricHonal effect of valve.

In Fig. 12 let A C represent the maximum tension of spring
and B C the tension to inner position of weight arm. Let A D

and ^Z' represent the spring force corresponding to positions
A and B of weight-arm. Assuming perfect isochronism between
weight and spring, then .1 D and BE also represent the bal-
anced centrifugal force, and this force for any intermediate posi-
tion of weight-arm is the corresponding height from the line
A B to the line 1) K Up to this time we have neglected the
effect of valve-gear friction.

Supposing this effect to be a constant force acting in the same
direction as the centrifugal force of the weight, then it may bo

NOTES ON THE THEORY OF SHAFT QOVERNORS.

represented bj a line parallel to and above I) C, as FO^. If the

constant friction of the valve-gear acts against centrifngal force,
or with the spring, then F, (I, parallel to I) (\ may represent its

Fig. 13.

effect. In the former of these cases the maximum spring force
becomes .1 /; and the maximum spring tension A C^, while^in the
latter case these quantities become A F^ and A d.

In some constructions the connection between the governor
and the valve-gear is such as to produce a variable effect of fric-

Fi2. 14,

tion. This is the case with the " Buckeye " governor, shown in
Fig. 13, in which, moreover, this friction has a centripetal effect.

. If the
;al force,
esent its

iig force
e in the

overnor
1 of fric-

N0TE3 ON THE THEORY OF HIIAFT G0VERN0H8.

In Fig. 14 this variable resistance is illustrated by the curved
line F, A',.

By reference to Fig. 13 an auxiliary spring P will be seen,
which is designed to act through a little more than half the
range of the weight-arm, and to produce an effect illustrated by
the shaded portion of Fig, 14. The result is that a line F, 6\
approximately straight, illustrates the centripetal action of the
main spring, B C\ being its initial tension, and B Ei its total
force at first stop, or initial position.

8. Ttmrtia in a shaft gcvernor.

In Fig. 15 let A and C be the centres of shaft and weight
pivot, respectively, and consider the total effective weight of the
governor weight and arm centred at B. Inertia acts on the
weight B at right angles to the line A B.

From analytical mechanics (see Weisbach) the force of inertia
may be represented by the expression P = M B .^, while cen-
trifugal force is F — of MR; in both expressions oo is the angu-
lar velocity, J/ the mass, A' the radius A B, and d t the small
interval of time in which a change of velocity occurs.

Substituting for co its equivalent value 2 tt T, in which T is
the number of revolutions per second, and differentiating the
equation for centrifugal force, since it is only the difference of
force due to change of speed which is effective, we have

own in

r= 2

I effec!;.

and

dF =

MBTdT.

NOTES ON THE THKORY OF SHAFT GOVERNORS.

li B L or Ji li, accordiiip; to the direction of motion, repre-
sents the force P, and // ^1, the force il F, tlien li A, or /> Ifi is
the resultant of these forces, and the tangent of the angle .li li Z„
or Ai B Ai, which angle we designate by n\ is

tangent rr = ^-p ,

or, substituting above values,

tangent a =-. ^^-^^

We see from this that the effect of inertia to increase or
decrease (according to the direction of motion) the moment of

Fig. 16.

force about the weight pivot is less the greater the number of
revolutions per unit of time, and is greater the less the interval
of time in which the change of speed takes place.

Let us assume that the weight B is no longer concentrated in
a point, but is spread out into a disk of considerable size, as in
Fig. 16, whose radius we call r ; then the force of inertia relative
to the axis A is greater than before.

By a well-known law of inertia, the radius of gyration of the

— , therefore the force of inertia acting at B is
V'2

B -,-!)'

V'2 / , r d GO

B '^^ dt '

weight is i? +

NOTES ON THE THEORY OF SHAFT 00VERN0R8.

Substituting Irr Tior ro, and dividing by d F as before, we have

ri + ---V

tangent a

^n TdT

Suppose r to be \ of R, T to be three revolutions per sec-
ond, and d t to be one second ; then tangent (^ becomes 0.0406,
and a is less than 2i°. If o?< is ' of one second, then (x
becomes about 22', and if dt is rJn of one second, a is about
70''. The extremes of these three cases are shown grapnically
in Fig. 16 for both right and left hand motion. This illustrates
to how great an extent, when changes of speed are sudden, iner-
tia force may be useful to assist centrifugal force ; also to what
a slight extent inert i;i acts when changes are not sudden.

It also shows that if the direction of motion be badly chosen,

Fig. 17.

the combined forces may produce an instantaneous moment
about the weight pivot in the wrong direction, thus interfering
with sensitive governing.
As to the actual value of d t in practice, it may often be a very

NOTES ON THE THEORY OF SHAFT QOVERNORS.

small quantity, for in an engine having dead points the velocity
changes a number of times, to a greater or less extent, during
each revolution. These changes are loss the heavier tl.o fly-wheel,
therefore with a light fly-wheel an inertia governor should be
specially efficient.

In one of tlie papers referred to at the beginning of this ar-
ticle, Mr. Armstrong advocates the use of inertia in the way
wliich wouLl reduce the efl'ectivc moment about (\ for the sake
of " stability."

The fiict seems to be, however, that stability and sensitive-
ness are best arrived at by using the force of inertia to aid cen-
trifugal force, as in the left-hand motion of Fig. 16.

Fig. 17 illustrates a governor for a single-valve engine — de-
signed by Mr. J. W. Thompson — which is said to have performed
so perfectly that no perceptible variation of spoed in the range
of the governor could be detected by careful test, and there was
no trouble from racing.

Fig. 18.

It will be noted that the arc through which the weight-arm
moves is so small that isochronism could be practically perfect,
while inertia was utilized to a great degree.

In Fig. 18 is represented a very ingenious method of combin-
ing a separate inertia weight with a shaft governor. This was

NOTES ON Till". THKOnV OF flnAPT GOVERNOIIP. 21

applie.l l.y Mo88r8 Buiicn^ft ct Lewin. of Plnla<leli.lnft. tc. a Buck-
oye oiigine in the workn of Wrn. SellerH A Co

Tho inertia weight consints of a wheel, which, being centre.!
on the shaft, han its centrifugal force completely balan "ed w 1,1 1
Its inertnt force acts to ./,/ the centrifugal force of the governor
Instead of causing racing this is said to have overcome aU ten^
dency to race thus enabling the governor to be adjusted for
practically perfect isochronism.

It is well known that an increase in the amount of the bal-
anced forces-centrifugal and centripetal -of a governor tends
o increase the effectiveness of the governor to overcome dis-
turbing influences ; yet an increase in these forces may pr.)duce
an increase of friction in the pivots, which may defeat the desired
object. The friction of pivots is not increased, however, by so
dt^s^gning the governor as to utilize inertia to aid centrifugal

In this respect the shaft governor may have a decided advan-
tage over the old ball governor, which is purely centrifugal.

Referring back to Fig. 18. it is not essential tha^ the inertia
weigh be centred on the shaft. It may be centred at the
weight-arm pivot, thus forming a part of the weight-arm If its
centre of gravity is coincident with the centre of pivot it will
not afl-ect the centrifugal adjustment of the governor weight, but
will aid the governing moment by its inertia.