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WORKS OF
PROFESSOR CECIL H. PEABODY

PUBLISHED BY

JOHN WILEY & SONS, Inc.

Thermodynamics of the Steam-engine and
other Heat-engines.

This work is intended for the use of students in
technical schools, and gives the theoretical training
required by engineers. Sixth Edition, Revised.
vii+543 pages, 119 figures. 8vo, cloth, $4. 50, net.
Tables of the Properties of Steam and other
Vapors, and Temperature-Entropy Table.

These tables were prepared for the use of students
in technical schools and colleges and of engineers in
general. Eighth Edition, Rewritten. 8vo, vi+133
pages, cloth, $1.00, net.

Valve-gears for Steam-engines.

This book is intended to give engineering students
instruction in the theory and practice of designing
valve-gears for steam-engines. Second Edition,
Revised and Enlarged. 8vo, v +142 pages, 33 fold-
ing-plates, cloth, $2.25, net.
Manual of the Steam-engine Indicator.

154 pages, 98 figures. 12mo, cloth, $1.50, net.
Naval Architecture.

Third Edition, Revised and Enlarged, vii+641
pages, 217 figures. 8vo, cloth, $7.50, net.
Thermodynamics of the Steam Turbine.

vi +282 pages, 103 figures. 8vo, cloth, $3.00, net.
Propellers.

iii+132 pages, 29 figures. 8vo, cloth, $1.25, net.
Computation for Marine Engines.

8vo, iv+209 pages, 52 figures. Cloth, $2.50, net.

BY PROFESSORS PEABODY AND MILLER
Steam-boilers.

By Prof. Cecil H. Peabody and Prof. Edward F.
Miller. Third Edition, Revised and Enlarged, vi +
543 pages, 236 figures, 5 folding-plates. 8vo, cloth,
$3.75, net.

MANUAL

OF THE

STEAM-ENGINE INDICATOR

CECIL H. PEABODY,

Professor of Naval Architecture and Marine Engineering,
Massachusetts Institute of Technology,

FIRST EDITION.

SECOND THOUSAND.

NEW YORK

JOHN WILEY & SONS, INC.

LONDON: CHAPMAN & HALL, LIMITED

1914

•*A^

CECIL H. PEABODY.

THE SCIENTIFIC PRESS
IERT DRUMMOND AND OOMPANV
BROOKLYN. N. Y.

THE STEAM-ENGINE INDICATOR.

THE steam-engine indicator is an instrument in-
vented by Watt to measure and record the pressure
of the steam in the cylinder of an engine. The dia-
grams drawn by an indicator enable us to calculate
the power of the engine, to examine and adjust the
actions of the engine va'ves, and to make certain in-
ferences concerning the transformation of heat into
work and the influence of the metal of the cylinder
on that operation. Too much emphasis cannot be
given to the fact that the sole office of the indicator
is to measure and record pressure; actions which are
commonly said to be revealed by the indicator are
really inferences based on the pressure or on changes
of pressure.

The Watt Indicator. — While the exact form of the
original indicator is not known, it is interesting to
consider the form ascribed to it by tradition, more
especially as that form presents the elements of the
instrument clearly. In Fig. i P is a piston that moves
freely in the cylinder C, which is open at the top, and

359953

INDICATOR

can be put in communication with the interior of the
engine cylinder by the cock T and a short system of

FIG. i.

piping. The piston-rod HP passes up through a hole
in the block H, and carries a pencil p at the upper end.
A helical spring between the piston P and the guide-

THE STEAM-ENGINE INDICATOR. 3

block H measures the pressure at the under side of
the piston P. At the top of the indicator there is a
light board B which slides freely in the frame EF.
This board has a motion like that of the piston of the
engine, on a reduced scale, which is obtained from a
proper reducing motion attached to the crosshead,
and is communicated by the cord S. The weight W
on the end of the string S' pulls the board B toward

FIG. 2.

the right and keeps the strings taut. A piece of paper
is attached to the board B, against which the pencil
p can be pressed when a diagram is desired. Fig. 2
represents the diagram on a larger scale. To take a
diagram, the string S is connected to the reducing
motion so that the board B moves back and forth,
keeping time with the piston of the engine. The cock
T is now turned to open communication with the en-
gine cylinder, and the pencil p rises when steam is
admitted and falls when steam is exhausted. If the
engine runs slowly the pencil can be pressed against
the paper at any position of the piston of the engine;
for example, at the beginning of the stroke. Admis-

4 THE STEAM-ENGINE INDICATOR.

sion of steam at the beginning of the stroke gives a
sudden rise of pressure represented by the line AB;
then the piston of the engine moves forward under
nearly constant pressure of steam coming from the
boiler, until the admission of steam is interrupted by
the closing of the admission-valve; during the re-
mainder of the stroke of the piston the steam in the
cylinder expands in volume and loses pressure as in-
dicated by the curve CD; at D the exhaust-valve
opens and the pressure rapidly falls to the exhaust;
during the greater part of the return-stroke of the
piston, steam is exhausted to the condenser at con-
stant pressure, as represented by the line EF; finally
the steam caught in the cylinder by the closure of the
exhaust-valve is compressed as shown by the curve
FA. After the diagram is completed the cock T is
turned so as to shut off communication with the en-
gine cylinder and open communication from the lower
end of the cylinder C, Fig. i, and the atmosphere.
The pencil then comes to its neutral position with
atmospheric pressure both above and below the
piston P, and with no tension (or compression) on
the spring. A reference-line //' is now drawn by press-
ing the pencil once again on the paper; this is called
the atmospheric line. Every point of the diagram
corresponds to a definite position of the engine
piston; thus, n corresponds to one-fourth stroke of the
piston, and further the distance of n from the line //'
measures the pressure of the steam in the cylinder at

THE STEAM-ENGINE INDICATOR. 5

quarter-stroke, reckoned above the pressure of the
atmosphere. During exhaust, when the steam is flow-
ing into the condenser, the vacuum in the cylinder is
measured by the distance of the pencil below the
atmospheric line; the spring is of course stretched in
tension while this occurs.

Recent indicators differ from the original proto-
type in two principal ways: in the first place, the
sliding-board B is replaced by a drum or cylinder
turning on a vertical axis, and in the second place
the pencil is carried by a parallel motion which multi-
plies the motion of the piston. The drum gives a
smoother and truer motion to the paper, and the mul-
tiplication of the motion of the piston by the parallel
motion permits of the use of a short and stiff spring.
A few well-known indicators are chosen for descrip-
tion; it will be seen that they differ in detail only.

The Crosby Indicator. — Figs. 3 and 4 represent the
Crosby indicator, made by the Crosby S'eam-gage
and Valve Company. Here 8 is the piston of the
indicator, above which is the spring which measures
the steam-pressure. The motion of the piston is mul-
tiplied by the pencil-motion 13, 14, 15, 16, and com-
municated to the pencil 23, which draws a diagram
on a slip of paper that may be wound around the
paper-drum 24.

The body or barrel of this indicator is made in three
pieces, i, 4, and 5. The part i carries the paper-drum
at the end of an arm or bracket; the part 5 has at its

THE STEAM-ENGINE INDICATOR.

lower end a device for securing" the indicator to the
cock leading to the engine cylinder; the part 4 is
bored out to receive the piston 8. The part 4 is
more conveniently made separate, and may readily

FIG. 3.

be replaced if its inner surface should become cut or
scored; it is also surrounded by a steam-jacket, which
insures a uniform temperature.

The spring, which is shown separately by Fig. 5,
is a double helix wound from one piece of round wire,

THE STEAM-ENGINE INDICATOR. 7

and screwed through the four flanges of a brass head.
The length and stiffness of the spring are adjusted by
screwing it into or out of the head, and then the wire

FIG. 4.

is secured by soldering it to the head. The head is
screwed to the cap 2, Fig. 4, which in turn is screwed
into the top of the piece i. A steel bead at the lower
end of the spring affords the means of connecting
the spring to the piston, as shown by Fig. 4 and

THE STEAM-ENGINE INDICATOR.

Fig. 6. The hub of the piston is bored through and
threaded. A hollow piston-rod is screwed down on
top of the bead, and a screw is screwed up from
below, and adjusted to take up all looseness or back-
lash without giving too much pressure and friction.
The hub is slotted transversely above the piston to
allow the cross-wire of the spring to enter and bring

FIG. 5.

FIG. 6.

the bead to the proper place. The lower end of the
piston-rod has a lip which comes over the ends of
the slotted hub and binds the piston-rod and hub
firmly together.

The piston-rod slides through the cap 2 and carries
the head n, which may be screwed up or down to
adjust the position of the pencil on the paper-drum.
The pencil-motion consists of the pencil-bar 1 6, which
is guided by the link 13, and receives motion from the
piston-rod head n, through the transmission-piece

THE STEAM-ENGINE INDICATOR. 9

14, which itself is guided by the link 15. This forms
a kind of transformed grasshopper parallel-motion,
so that the pencil 23 moves on a vertical line which
is very nearly straight within the range of motion
allowed, and gives a close copy of the motion of the
piston, but on an enlarged scale. The pencil-motion
is carried by a sleeve 3, which can turn on the body
of the indicator, and thus throw the pencil onto the
paper-drum, or withdraw it after a diagram is taken.
A handle with a wooden knob and a steel shank is
screwed through the wing x of the sleeve, and bears
against a stop in the arm i, when the pencil comes in
contact with the drum. The pressure of the pencil
against the paper-drum is adjusted by screwing this
handle in or out.

To assemble the piston and spring, etc., slack back
the screw 9 in the piston 8; place the spring in the
transverse slot through the top of the hub of the
piston; screw down the piston-rod 10 firmly onto
the top of the piston-hub, using a socket-wrench pro-
vided for this purpose; adjust the screw 9 so that the
piston may turn slightly on the 'bead without friction
and without backlash. Take the sleeve 3 with pencil-
motion attached in one hand and the piston and
spring in the other; catch the hollow piston-rod into
the head n, and then screw the head of the spring
firmly onto the cap 2. Slip the piston into the cylin-
der 4, and the sleeve onto the body of the indicator,
and screw down the cap into place. Should the pen-

IO THE STEAM-ENGINE INDICATOR.

cil be too low down on the paper-drum, dismount
the sleeve with the spring and piston, and turn the
cap 2 toward the left, thus running the head 1 1 further
out of the piston-rod; then replace the sleeve and
screw down the cap. Should the pencil be too high,
it may be lowered in a similar way, but the cap is then
turned to the right to run the head 1 1 into the piston-
rod.

The paper-drum consists of the thin shell 24 and
the hub or body 27. The shell can be removed to ex-
pose the drum-spring and other internal parts. The
hub turns on the spindle 28, which is screwed firmly
into the arm i ; it can turn through about five-sixths
of a rotation and is checked by stops. A spring 31 is
clamped to the hub by a plate 32, and is attached to
the spindle by a cap with a square hole, resting on
a square bearing on the spindle. The paper-drum
may be turned in one direction by drawing out the
cord which is wrapped around the hub, and it is re-
turned by the drum-spring. The cord may be led in
any direction through the fitting 34. In the first
place, this fitting can be revolved about a vertical
axis and clamped in place by the milled head 38; then
the fitting can be rotated around a horizontal axis
and clamped by a milled head 37; two rollers in the
fitting 34 afford means of changing the direction of
the cord at the fitting.

The Thompson Indicator. — Fig. 7 shows the exter-
nal appearance and Fig. 8 gives a vertical section

THE STEAM-ENGINE INDICATOR. II

FIG. 7.

FIG. 8.

THE STEAM-ENGINE INDICATOR.

of the Thompson indicator. It uses a single helical
spring as shown by Fig. 9, which is screwed onto the
piston at the lower end and onto a cap for the indica-
tor-piston at the upper end. The pencil-motion is a
modified grasshopper parallel motion with the piston-

FIG. 9.

FIG. 10.

rod attached directly to the pencil-bar. For com-
parison we have a diagram of an exact parallel motion
in Fig. 10, in which it is to be noted that the guiding-
link ab is half the length of the bar cp, and that the
point p moves on straight lines through a. The guid-
ing-link of the pencil-motion of the Thompson
indicator is shortened and moved in toward the
piston-rod, and the pencil describes a slightly curved
line; but the deviation from a straight line is scarcely
perceptible within the range of motion of the pencil.

THE STEAM-ENGINE INDICATOR. 13

The paper-drum spring is a flat spiral like a watch-
spring. The fitting through which the cord is led
has one wheel instead of two, as shown by Fig. 3 for
the Crosby indicator; this, by the way, is the original
form of the fitting, and other forms are derived from

FIG. ii.

it. The Thompson indicator is intended to be simple
and substantial so that it may not get out of adjust-
ment if used with ordinary care.

The Tabor Indictor. — This indicator is represented
by Figs, ii and 12. The most notable peculiarity is
its pencil-motion, which is guided by a'roller moving

14 THE STEAM-ENGINE INDICATOR.

in a curved slot, as shown by Fig. 12. The slot is
cut to such a form that the pencil is guided cor-
rectly on a stra:ght line, and there is the in-
cidental advantage that the weight of the guid-
ing-link of the pencil-motion of the Thompson in-
dicator is dispensed with. But since the roller must

FIG. 12.

be slightly smaller than the slot in order that it
may touch one side only, the actual motion of the
pencil may deviate from a straight line, and it is a
question whether this pencil-motion is appreciably
better than those which make use of approximate
parallel motions. A double helical spring made of two
wires is used in this indicator, as shown by Fig. 13.
The cord from the paper-drum is led through a disk

THE STEAM-ENGINE INDICATOR. IS

with a roller, giving- the same effect as the correspond-
ing fixtures of the Thompson and the Crosby indi-
cators. Fig. ii has a detent and Fig. 12 a drum-stop
attachment; these details will be considered later.

The Bachelder Indicator, shown by Figs. 14 and
15, has a flat spring instead of the helical springs
used in other indicators. This spring, which is shown

FIG. 13.

in full size by Fig. 16, is securely pinned at the farther
end and is connected to the piston-rod by a pin-joint
as shown in Fig. 15. The effective length of the
spring is the distance from the piston-rod to the clamp
a, Fig. 15, and this length may be changed by loosen-
ing the screw at a and sliding the clamp along. Con-
sequently the scale of the spring can be varied
through a wide range, and a very few springs will
suffice for all uses of the indicator.

Indicator for Gas-cngincs. — Recent gas-engines
commonly have a pressure of 250 or 300 pounds per

T6 THE STEAM-ENGINE INDICATOR.

FIG. 14.

FIG. 15.

THE STEAM-ENGINE INDICATOR. \f

square inch in the cylinder, generated by a very rapid
combustion or explosion of the gas and air which
form the working substance. Ordinary steam-en-
gine indicators, when used on such engines, are liable

FIG. 17.

to get out of order; consequently it has been found
desirable to use a special indicator for such work,
like that shown by Fig. 17. The piston has an area
of one-fourth of a square inch, that is, half the area

1 8 THE STEAM-ENGINE INDICATOR.^

of the piston of a steam-engine indicator. Springs
supplied for steam-engine indicators can be used
in this instrument if rated at twice the scale marked
on them; for example, a loo-pound spring is rated
at 200 pounds, and can be used for a pressure of 300
pounds to the square inch, or more. The pencil-bar
is made rigid to withstand the shock of the explosion
in the gas-engine cylinder; extra weight in the pencil-
motion is of less consequence as a stiff spring is al-
ways used. The upper part of the barrel is bored
out to the usual diameter to accommodate the spring,
which is of the usual size and form as already pointed
out. If desired, the small piston shown in Fig. 17
can be taken out and a piston of the pattern used for
steam-engine indicators, having an area of half a
square inch, can be put in, and thus this indicator can
be used for general purposes; but such a use of the
instrument cannot be recommended.

The gas-engine indicator shown by Fig. 17 is made
by the Crosby Company, who also make an instru-
ment shown by Fig. 18, which has a piston or plunger
with an area of 1/40 of a square inch. This plunger
bears on a ball-joint below a piston of the ordinary
size, above which is the usual helical spring. Springs
furnished for steam-engine indicators must be rated
at 20 times the scale marked on them when used with
this instrument. A side passage controlled by a plug-
valve may be opened to give direct communication
with the large cylinder when moderate pressures are

THE STEAM-ENGINE INDICATOR. 19

to be measured; but though this may occasionally be
a convenience it is not to be recommended, as the
side passage is small and the pencil-motion is extra
heavy to give rigidity. The post near the paper-drum

FIG. 18.

is intended to steady the pencil-bar when desired.
This instrument is intended to be used with hydraulic
pumps and hydraulic apparatus, and on pneumatic
gun-carriages for heavy ordnance. ~

Ammonia Indicators. — Special indicators made en-
tirely of steel are supplied for indicating the compres-

THE STEAM-ENGINE INDICATOR.

sors of ammonia refrigerating-machines; for am-
monia would attack and soon destroy those parts of
a steam-engine indicator that are made of brass.
Indicator Cock. — The indicator is put in communi-

FIG. 19.

FIG. 20.

cation with the engine cylinder through a cock
and a short system of piping as shown by Fig. 19.
When the handle is vertical, as shown by Fig. 19,
there is a straight passage from the cylinder of the en-
gine to the indicator; but when the handle is turned
down the passage from the engine is closed, as shown

THE STEAM-ENGINE INDICATOR.

by Fig. 20, and communication is opened to the at-
mosphere through a side passage. The cock is set in
this last position when the atmospheric line is drawn.
Fig. 21 shows the elevation and Fig. 22 the section
of a three-way cock that may be used for taking dia-
grams from both ends of a cylinder with one indica-

FlG. 21.

FIG. 22.

tor. A pipe from one end of the cock leads to the
head end of the engine cylinder, and a pipe from the
other end leads to the crank end of the cylinder; a
side passage leads to the atmosphere. Fig. 22 shows
communication open from one end of the engine
cylinder to the indicator; if the handle is thrown to
the other side the other end of the cylinder will be in
communication with the indicator; the indicator will
be open to the atmosphere when the handle is in mid-
position. When convenient it is better to use two in-

22 THE STEAM-ENGINE INDICATOR.

dicators and avoid the considerable lengths of piping
required for a three-way cock.

Inspection of the Instrument. — The truth of a dia-
gram taken by an indicator depends on the construc-
tion of the instrument, the condition in which it is
maintained, and the skill with which it is used.
Indicators from reliable makers are carefully and
thoroughly made and are in good condition when
sent out. An instrument which is out of condition
from use or accident should be at once returned to
the makers for repair.

The sleeve which carries the pencil-motion should
turn smoothly on the body of the indicator and
be free from looseness or backlash. Friction at
this place may be inconvenient, but will not af-
fect the truth of the diagram; looseness will affect
the truth of the diagram and should not be tol-
erated. The makers only can remedy defect in this
part. The universal joint in the piston-rod should
have just enough freedom to avoid cramping the
indicator piston in the cylinder. This joint for the
Crosby indicator is made on the bead at the bot-
tom of the spring and must be adjusted when the
spring is put in. The universal joint of the Thomp-
son indicator is at the middle of the piston-rod and
should be adjusted by the makers; a careful mecha-
nician may be able to .take up backlash due to wear
by grinding the end of the hollow guiding-rod which
runs through the cap, and screws onto the lower half

THE STEAM-ENGINE INDICATOR. 2$

of the piston-rod. The several joints of the pencil-
motion should be free and without appreciable back-
lash; there is no way of detecting looseness in these
joints individually, but when the instrument is set
up with a stiff spring in place, looseness in any part
of the sleeve, universal joint, or pencil-motion will
appear if the pencil is carefully moved up and down
with the fingers. If the sleeve and universal joint are
known to be right such looseness must be attributed
to the pencil-motion, and will show that the indica-
tor must be returned to the makers. Skill in detecting
and locating looseness can be acquired only by prac-
tice. The pencil-motion and sleeve should be oiled
when necessary with watch-oil.

The piston should be a good, but not a tight, fit in
the cylinder of the indicator; excessive piston-friction
will destroy the truth of the diagram; a moderate
leakage past the indicator does not appear to have
much influence. The condition of the piston and cyl-
inder may be tested by putting the indicator together
without a spring; in this condition the piston should
fall freely from any position when the pencil is raised
and let fall; failure to fall freely indicates friction
somewhere. Excessive friction may occasionally be
detected in the pencil-motion or in the universal joint
of the piston-rod, but usually such friction will be
found at the piston. When there is evidence of fric-
tion the piston and pencil-motion should be removed
and both the piston and the cylinder wiped clean; this

24 7W.E STEAM-ENGINE INDICATOR.

may be done with a piece of clean cloth or with the
fingers, which should of course be free from grit; and
the piston should be examined to detect roughness
or scoring if that has occurred. A slight roughness
of the piston or the cylinder can often be reduced by
grinding the piston up and down in the cylinder, turn-
ing it round and round at the same time. For this
purpose the piston should simply be screwed onto the
piston-rod, which can be held in the fingers by the
upper end. Both piston and cylinder must be wiped
dry and clean before beginning this process; emery
powder or other grinding material should not be
used, the idea being merely to rub down small rough-
nesses. After the piston and cylinder are smooth and
clean the test for freedom with the spring removed
should be made, together with an inspection for fric-
tion at the joints of the pencil-motion or the universal
joint. If the piston and cylinder are so much scored
that this process is ineffective it will in general be bet-
ter to return the indicator to the maker; if this cannot
be done the work may be intrusted to a skilful me-
chanic, who may grind the piston smooth in a lathe,
using fine emery or crocus paper, and afterwards
grind the piston in the cylinder, using emery or
crocus powder, bearing in mind that the object is to
remove the roughness due to scoring, and that the
sizes of the piston and cylinder must not be changed.
Friction at the piston is frequently betrayed by the
diagram, as will be explained later, and in such case

THE STEAM-ENGINE INDICATOR. 2$

it is usually sufficient to clean both piston and cylin-
der and immediately put the instrument together
without disturbing the spring. When diagrams are
taken at intervals of five minutes or more the indi-
cator can be cleaned and adjusted between times, but
when diagrams are taken frequently and for some
considerable time it may be advisable to have a re-
serve indicator set up and adjusted which may im-
mediately replace the one in use when it shows signs
of clogging and consequent friction.

The indicator-piston may be occasionally oiled with
a little clean cylinder-oil; some engineers prefer to
use no oil, merely keeping the piston and cylinder
wiped clean.

Preparation for taking Diagrams. — When the indi-
cator is ready for use the indicator cock should be
opened and blown through several times to blow out
dirt and grit that may be present. The cock is then
closed and the indicator secured to the cock and
adjusted so that the cord may lead fairly to the reduc-
ing mechanism. It is very important that the indi-
cator shall be properly secured before the steam is
let on to take a diagram; failure to do so may lead to
serious damage to the instrument, and to delays and
annoyances that may be as bad. The indicator com-
monly stands erect, but if necessary it may be set
with the paper-drum horizontal or at an angle.

The cord leading from the paper-drum is now to be
adjusted to the proper length to hook on to the re-

THE STEAM-ENGINE INDICATOR.

ducing mechanism or to a loop in a cord tied to that
mechanism. It is convenient to tie the hook at the
end of the drum cord by a bowline knot, as shown by
Fig. 23, since that knot is not likely to slip and may

FIG. 23.

be readily loosened. Fig. 24 shows the same knot
partly tied. Some indicator-makers furnish a slip of

FIG. 24.

metal like that represented by Fig. 25, to facilitate the
adjustment of the length of the cord. The hook is
strung on the loop at a. This device gives added

FIG. 25.

weight at the hook and will not be found so con-
venient as a bowline knot.

The cord should always be tested for length before
hooking onto the reducing motion, and must never
be too short, as in that case the cord will be broken
or the indicator will be injured. When the cord is
hooked on the paper-drum should run freely without
striking against its stops at either end of its swing.

THE STEAM-ENGINE INDICATOR. 2/

On high-speed engines striking will be revealed by a
clicking noise; with a slow-speed engine striking
may be detected by holding the cord lightly in the
fingers and following its motion without interfering
with the tension of the drum spring. Striking can
sometimes be detected from its influence on the dia-
gram, as will appear later.

There are two ways in vogue of putting the paper
on the paper-drum. Thus, the paper may be taken by
its two lower corners and looped over the drum, and
then the end can be drawn in succession under the
longer and then the shorter of the paper-clips.
The paper is now drawn taut and true and slipped
down to its place. Some prefer to fold and crease
one end of the paper before beginning this operation.
Again the paper may simply be wrapped around the
drum, slipping one end under both the clips, and the
other over it and under the shorter clip. The first
way is more likely to draw the paper snugly onto the
drum, and the second avoids the projecting edges of
the first method.

Paper and PendL — Two kinds of paper are used for
indicator diagrams, plain unprepared paper and a
paper which has a special lead glaze which will take a
mark from a brass point, called metallic paper. The
plain paper should have a smooth surface with little
if any glaze, without ruling or water-marks. For such
plain paper a graphite pencil is used; it should be of
the best quality and of medium hardness, so that it

28 THE STEAM-ENGINE INDICATOR.

will give a fine clear line with a light pressure on the
paper; its point must be kept fine and true, for a one-
sided point will spoil the geometric design of the
pencil motion. A short piece of graphite from a cedar
pencil, or a piece of the graphite made for a pencil-
case, may 'be used.

The metallic paper will usually be obtained from
the indicator-maker cut to the proper size for indicator
cards, but in some cases it may be convenient to get
sheets of such paper from dealers and cut it to size.
One side of the paper has a thick smooth glaze, which
takes a fine clear mark from a brass point. This
glaze is poisonous, and may even give trouble at any
abrasion of the skin if handled freely. When metallic
paper is used the pencil will be replaced by a brass
point furnished with the indicator. Its point should
be true and fine, but not sharp enough to cut the
paper.

Indicator Cord. — A special braided cord is supplied
for indicators, which is of uniform size, strong and
comparatively inelastic; but all fibrous cord is elastic
and gradually stretches under tension, consequently
the use of long pieces of cord is to be avoided.

Drum Detent. — As it is sometimes troublesome to
hook the indicator-drum cord onto the reducing
motion, various devices have been invented for stop-
ping the paper-drum without unhooking. At the left
hand of the paper-drum in Fig. 1 1 the rim of the base
above the cord is cut into ratchet-teeth, and there is

THE STEAM-ENGINE INDICATOR. 2Q

a click on the post that serves as a stop for the pencil-
motion, which may engage these teeth when the
drum cord is drawn out. The click may be thrown
forward to engage the ratchet, or may be thrown back
to release the drum, and is held in either position by a
spring. To stop the drum, throw the click forward
and draw the cord out by hand till it remains slack.
The paper for a diagram may then be put on. To
release the drum, draw the cord taut by hand, throw
out the click and release the drum carefully so that
the slack in the string shall not be taken up with a
jerk by the drum spring. The drum will now move
with the engine crosshead and a diagram can be
taken.

Another way of stopping the paper-drum is shown
by Fig. 12. Here there is a long slotted bar which is
secured just under the fitting which carries the guide-
roller for the cord. In the slot is a sliding piece which
can be clamped anywhere in the slot. The upper end
of the slide carries a second guide-roller over which
the cord passes on the way from the drum to the ad-
justable guide-fitting. The cord is given such a length
that it will rotate the paper-drum properly when the
slide is clamped at the outer end of the slot. To stop
the drum the slide is slid toward the inner end of the
slot, which slackens the cord so that the drum stops.
An india-rubber band is tied on the cord in such a way
that it takes care of the slack of the cord while the

30 THE STEAM-ENGINE INDICATOR.

drum is at rest; when the cord is drawn taut the band
is pulled out and lies along- the cord.

It will frequently be found convenient to provide
for slack in a cord, or to hang up the free end of a
cord by a rubber band. For this purpose a long
band is required, strong enough to take care of the
cord, but not so stiff as to give much additional ten-
sion when the drum is in motion. If a long rubber
band cannot be had, two or three may be united to
give the proper length.

Electrical Attachment. — When simultaneous dia-
grams are desired from the several cylinders of a
compound, triple-expansion, or other multiple-cylin-
der engine, the electrical attachment shown by Fig.
26 will be found convenient. It consists of an elec-
tromagnet M with its armature A attached to the
pencil-motion in such a way that the pencil is ap-
plied to the paper on the drum when an electric cur-
rent is passed through the magnet and the armature
is drawn up. The magnet is carried by a .fixture S
which is clamped to the body of the indicator by the
screw E. CC are binding-posts for the wire from a
galvanic battery, and D is a spring which holds the
armature in the field of the magnet when the circuit
is open, and throws back the armature and removes
the pencil from the paper when the current is broken.
All the indicators to be operated are provided with
such electromagnets which are in the same circuit, and
all can be operated by closing the circuit by a push-

THE STEAM-ENGINE INDICATOR. 3 1

button or otherwise. Sometimes one indicator is
worked by hand and is provided with a push-button,
which is pushed up when the pencil-motion is forced
against its stop. The same principle is used by
other makers with various arrangements of details.

FIG. 26.

If an engine runs regu1arly a single operator can
take diagrams from the several cylinders in succes-
sion by hand, just as well as by aid of the electrical
device. Again, if diagrams are taken frequently it
will require a number of observers to keep the indi-
cators working properly. It is seldom, if ever, that
the electrical device is more than a convenience.

32 THE STEAM-ENGINE INDICATOR.

Reducing Motions. — Some form of reducing motion
is required to give a reduced copy of the motion of
the crosshead of the engine, and impart it to the
paper-drum. A few common forms will be de-
scribed; the engineer will have to apply them to
special cases or will have to devise new ones as occa-
sion may require. The design for a reducing motion
should be geometrically correct, or else the error
should be determined and be kept within limit. In
general, the moving parts should be light and rigid
and the joints free from backlash.

Brumbo Pulley. — A simple form of reducing mo-
tion, known as a Brumbo pulley, is shown by Fig.
27. PN is a vibrating arm pivoted at P. The lower

3
C

FIG. 27.

end N is connected by a link NC with the crosshead
of the engine. The cord ,S from the indicator runs
on the arc AB. Usually the arc AB is a circular arc
centred at the pivot P, and the reducing motion

THE STEAM-ENGINE INDICATOR. 33

gives only an approximate copy of the motion of the
crosshead. This device can be made to give an exact
copy by giving a correct form to the arc AB\ which
form must be constructed much as a cam is laid out.
As arranged it will commonly be found sufficient to
retain a circular ^rc, but to centre it at a point a little
below P. If more convenient the arc AB may be in-
verted and placed above P. The cord may be led
from the arc AB in any convenient direction, but if
it is led at an angle with the horizon the arc AB
should be turned to the same angle from the vertical.

This device may be made of wood if for temporary
use, or of metal if permanent. If it is made of wood,
it will be proper to bush the bearing surfaces at the
pins with brass; but if made of hard wood, with the
pins a tight fit in the holes, it will run for some time
without backlash. The bearing surfaces at N and
C should be ample and the link NC should be light,
especially when used for a high-speed engine. The
arm PN should be rigid and the pivot free from
backlash. It is also important that the support for
the pivot shall be rigid.

A simple method of stopping the paper-drum
without unhooking can be used with this reducing
motion. The cord after passing over the arc AB may
be led through an eye at the pivot P. Adjus: the
cord S to the proper length and tie a knot in it just
before it passes through the eye at P. If the free end
of the cord beyond the eye at P is slackened the indi-

THE STEAM-ENGINE INDICATOR.

cator drum will stop, and it can be set in motion by
drawing the free end taut so that the knot shall come
up to the eye. The cord may be drawn up by hand
while the diagram is taken, or it may be drawn up
and hitched at some convenient point.

Pantagraph. — A correct reducing motion may be
designed in the form of a pantagraph, whLh is well

adapted to slow-moving engines; high-speed en-
gines will quickly shake a pantagraph to pieces. Fig.
28 shows a pantagraph fixed to the engine-room
floor, and Fig. 29 shows one fixed to the frame of
the engine. The first has adjustable parts and can
be used for various engines as may be found conven-
ient; the second is designed for, and used on, one
particular engine. The pantagraph has for its essen-
tial part a four-bar cell, such as BEFD, Fig. 28,

THE STEAM-ENGINE INDICATOR. 35

which maintains the moving parts in their proper re-
lation. A point of the pantagraph, in this case the
joint F, is pivoted to a fixed support; a point, as C,
on the prolongation of EB is pivoted to the cross-
head of the engine; and a point, as A, carries the in-
dicator cord. The point A must be on the line CF
through the moving point C and the fixed point F,
and must divide it so that AF is to CF as the length
of the diagram is to the stroke of the engine. The
cord AP must be led off parallel to the motion of
the crosshead; if necessary the cord may be led
round a guide-wheel, as at P, on the way to the indi-
cator. To make this pantagraph adjustable a series
of holes is provided for the pivot C, and the bar BD
can be set at various distances from FE; the point A
is sometimes carried by an adjustable sliding piece
that can be clamped to the bar BD, but more com-
monly the adjustment is made by providing a series
of holes for a pin that can be screwed into the bar
BD. In this latter case the point A will not always
be exactly on the line CF, but a slight deviation will
have little effect. This pantagraph can be made of
metal, or of wood bushed with brass, or of wood with
metallic pins only if the latter are a tight fit for the
holes.

In laying out a pantagraph for a particular engine
as represented by Fig. 29, we may proceed as fol-
lows. In the first place AI is to be drawn at the
proper height to lead correctly from the indicators;

$6 THE STEAM-ENGINE INDICATOR.

it may be a piece of indicator cord or it may be a
rod sliding in guides at the end /. The line FC is
to be made of a proper length to avoid awkward po-
sitions of the pantagraph when the crosshead is at
the ends of the stroke; it will be well to limit the
total angular motion of the line FC (from side to
side) to 60°. The line FC will now be divided at A
so as to give the proper length to the indicator dia-
gram. Ordinarily the points F and C will have to
be located, one on a post on the engine frame and
the other on an arm projecting downward from the
crosshead. The bars FE, EC, HK, and HG must be
drawn ir by trial to give a convenient arrangement
of joints and other details. This pantagraph will be
preferably made of metal throughout. If the joints
wear loose the holes may be rebored and fitted with
larger pins. When applied to a vertical engine the
mechanism will be turned through a right angle so
that I A will be vertical.

A modification of the pantagraph, known as the
lazy-tongs, is shown by Fig. 30. The joint B is
pivoted to a convenient fixture near the engine, and
the pin A is slipped into a ho1e in the crosshead or
in a piece which is fastened to it. The indicator cord
is led from the pin E parallel to the motion of the
crosshead. The bar DC is set so as to give the proper
length of diagram, and the pin E is set on a line from
A to B. The lazy-tongs is commonly made of wood
and has considerable flexibility, which, with the large

THE S7*EAM-ENGINE INDICATOR.

number of joints to get loose, makes it rather a crude

device.

FIG. 30.

Swinging-lever and Slider. — A simple and service-
able reducing motion is shown by Fig. 31. It con-

sists of a swinging-lever AB which is connected to
the crosshead by a link BC\ a parallel link ED

38 THE STEAM-ENGTNE INDICATOR.

moves a sliding-rod DF, which moves in guides par-
allel to the motion of the crosshead. The point D
is on the line AC, and divides it so that AD is to AC
as the length of the diagram is to the stroke of the
engine. The rod DF is made long enough to reach
to the indicator, which can be hooked directly onto
a pin set in the rod for that purpose. The links may
be made double or may have forked ends at D, E,
and B.

Reducing-whcel. — A portable reducing motion is
shown attached to an indicator in Fig. 32. The in-
dicator cord is wound round a drum A which can
turn on a vertical post or spindle, and which is kept
wound up by a clock-spring in its base. The wheel
B is geared to the drum by spur gears (not shown
in the figure) so that it makes three turns for one
turn of the drum A. A long cord is wound in a
helical groove on the wheel B and is led directly to
the crosshead of the engine. The wheel turns on a
screw-thread cut on its spindle, so that it descends as
the cord is drawn out and rises as the cord is wound
up, and the cord is consequently wound truly in the
helical groove. The drum A may be varied in size
to conform to the stroke of the engine; a small drum
is used for a long-stroke engine and vice versa. Since
the wheel B turns rapidly and must start and stop
with the crosshead, it is made of aluminium for sake
of lightness.

ig. 33 shows a form of reducing motion which

THE STEAM-ENGINE INDICATOR

has a cord from the engine crosshead wound on the
wheel 0, and which drives the paper-drum by a
worm gear R. Several sizes of wheels are supplied

to conform to the stroke of the engine. A spring
for winding up the cord is contained in the case d.
At u is a milled head which controls a clutch on
the wheel-shaft. When this clutch is released the

THE STEAM-ENGINE INDICATOR.

wheel turns freely on its shaft and the paper-drum
remains at rest against one of its stops. When the
clutch is thrown into gear the wheel is clamped to
its shaft, which now drives the paper-drum by aid
of the worm gear. To start the paper-drum, turn it

FIG. 33.

forward by the milled head above it, so that it stands
at least a quarter of an inch free from its stop, and
throw in the clutch at u. It may be released by
throwing out the clutch.

Wire instead of Cord. — On large engines the indi-
cators are at a considerable distance from the cross-

THE STEAM-ENGINE INDICATOR. 41

head and the reducing motion. It is sometimes
recommended to use wire to transfer the motion to
the indicator, and this may be of service with slow
engines, especially if the wire can be kept taut by a
weight or spring. On high-speed engines the wire
is likely to sway from side to side and give more
trouble than cord. Properly the motion should be
transferred by a sliding rod used in connection with
a correct and rigid reducing motion.

Taking Diagrams. — When the indicator is ready
and a diagram is desired, start the paper-drum by
hooking on the cord or by aid of the starting device
when one is provided, and turn on the steam; let
the indicator move idly until it is hot and clear of
water; press the pencil-motion against its stop until
a complete diagram is drawn; shut off the steam
from the indicator and again press the pencil-motion
against the stop to draw the atmospheric line; stop
the paper-drum and remove the diagram and num-
ber or otherwise identify it. If other diagrams are
to be taken it is well to place another paper on the
drum.

The atmospheric line must be taken after the in-
dicator is hot; it will be wrongly located if drawn
when the instrument is cold. The instruction to
draw the atmospheric line after the diagram is taken
is for this purpose. If the engine runs slowly the
pencil may be applied during exhaust, because this is
a long line which is little liable to change, and thus

42 THE STEAM-ENGINE INDICATOR.

a single complete diagram can be drawn. If the en-
gine runs rapidly such refinement is impossible, and
it will be sufficient to hold the pencil-motion against
the stop for a revolution of the engine as nearly as
may be. In indicating high-speed engines it will
be found that two or more diagrams are super-
imposed even though the pencil is applied to the
paper for an instant only; but as the diagrams
usually change little if at all no inconvenience will
result. Some engineers prefer to get several super-
imposed diagrams and thus get a rough average.
For important work it is essential that the engine
shall run regularly, and then the diagrams will re-
main constant or change slowly.

Care of the Instrument. — After all the diagrams de-
sired are taken, the indicator is to be removed from
the engine, cleaned and dried, oiled and put in its
case. In taking the indicator from the engine the
hands should be protected to avoid burning them,
and consequent danger of dropping the instrument
or some part of it. If the indicator is taken apart
while hot and the several pieces cleared from water
as well as may be, and allowed to lie exposed to the
air, they will dry off so that they may be readily
cleaned and wiped dry. The spring and other parts
that are made of steel should be oiled to guard
against rust.

Scale of Spring. — The spring used should be
chosen with reference to the highest expected pres-

THE STEAM-ENGINE INDICATOR. 43

sure; the height of the diagram should not exceed
if to 2 inches. If the diagram lies entirely above
(or below) the atmospheric line this height is to be
measured from that line; if partly above and partly
below the height is that of the diagram itself. In
general, the use of a spring weaker than 20 pounds
to the inch should be avoided, and for high-speed en-
gines it is well to use a 4O-pound spring or even a
siiffer one. A small clear diagram is to be preferred
to a large irregular one.

Indicator Diagram. — Fig. 34 may be taken to rep-
resent a typical diagram from a non-condensing en-

FIG. 34.

gine. Steam is admitted to the cylinder when the
piston has nearly reached the end of its stroke, due
to the lead of the steam-valve, as represented by the
line fa, which inclines toward the left in the figure.
From a to b is the steam-line which is drawn by the
indicator while steam is admitted to the cylinder, and
d represents the cut-off or closure of the steam-valve.
After cut-off the steam expands with increase of vol-

THE STEAM-ENGINE INDICATOR.

ume and fall of pressure, as represented by the ex-
pansion-line be, until the exhaust-valve opens at c.
From release at c to the end of the stroke there is a
rapid fall of pressure, represented by cd. During the
return-stroke steam is forced out of the cylinder
against the pressure of the atmosphere, as repre-
sented by de (which is called the back-pressure line)
until the exhaust-valve closes at e. From e to f steam
is compressed ahead of the piston with diminution of
volume and rise of pressure. The atmospheric line
is represented by mn.

A diagram like Fig. 34 with straight lines and
sharp corners is never obtained in practice, for valves
do not open and close instantly and the indicator has

(* ft *

FIG. 35.

a tendency to run one line into another. The actual
diagram is more like Fig. 35, which shows some loss
of pressure during the admission of steam from a to
X^ and a rounded corner at cut-off. The release cd
is shown with a convex curve outward, as is usually
found with quick-running engines. Finally efa ap-
pears as a continuous curve without corners and

THE STEAM-ENGINE INDICATOR. 45

without a well-defined separation of compression (ef)
from admission (fa).

Summing up we have

ab, steam-line. o, initial pressure.

be, expansion-line. b, cut-off.

cd, release. c, release.

de, back-pressure line. e, compression.
ef, compression. f, admission.

fa, admission.

Fig. 35 is drawn with a scale of 60 pounds to
the inch, and the point a is one inch from the
atmospheric line and represents a pressure of 60
pounds to the square inch initial pressure above the
atmosphere. Or more conveniently, if the distance
of a from mn is measured by a scale divided into
6oths of an inch, it will be found at the 6oth division
of the scale. In the same way the pressure of release
is found by a scale of 6oths (called a 60 scale) to be
1 8 pounds above the atmosphere, while the back-
pressure is found to be about one pound above the
atmosphere.

The location of the point of cut-off and the point
of release is always somewhat uncertain on account
of the rounding of the corners already spoken of. It is
customary to consider that the cut-off is at the point
b, Fig. 36, when the convex rounding of the corner
due to the closing of the steam-valve changes into the
concave expansion-curve be. Release is assumed to
take place at c where the expansion-curve runs into

THE STEAM-ENGINE INDICATOR.

the release line cd. Compression is located at e where
the pressure begins to rise above the back-pressure
line. To determine the per cent of the stroke at
which cut-off, release, and compression occur draw
lines ma and nd perpendicular to the atmospheric
line mn and just touching the diagram at its ends;

FIG. 36.

also draw vertical lines at b, c, and e, the points of
cut-off, release, and compression; select a scale such
that 100 divisions on it shall be a little longer than
the diagram, and lay it diagonally across the diagram
so that the zero shall be on the line ma and the di-
vision 100 on the line nd\ the per cents may now be
read directly from the scale — for example, cut-off is
at 29 per cent, release is at 83 per cent, and com-
pression is at 22 per cent of the stroke.

Errors of the Indicator. — The steam-engine indi-
cator is the engineer's main reliance in investigations

THE STEAM-ENGINE INDICATOR. 47

of the performance of steam-engines, and its indica-
tions are commonly accepted implicitly by the en-
gineer who seldom has the time or the means of
properly standardizing his indicators. Unfortunately
the indicator is subject to errors which are neither
small nor well known, even though indicator-makers
have given much thought and skill to the perfecting
of their instruments, and though much time has been
given by engineers to experimental investigations of
the errors of indicators.

There are two ways of considering the errors of
indicators: firstly, the errors may be analyzed to the
end that imperfections may be located and the proper
remedies may be sought; and secondly, the actual
error of the instrument in service may be investi-
gated in order that the proper estimate may be at-
tributed to its indications.

In the first place the errors of the pencil-motion
piston and attached parts may be considered sepa-
rately from those of the paper-drum. The latter will
be considered first as they are comparatively simple
and may be almost entirely eliminated by using
proper reducing motions.

Errors of Paper-drum. — It is apparent that if the
paper or card could have a positive motion given to
it by a correct indicator-motion, it would give an
exact reproduction of the motion of the engine cross-
head and there would be no paper-drum errors. If
necessary the card could be carried by a proper flat

48 THE STEAM-ENGINE INDICATOR.

board on the slide FD of Fig. 31, page 37; or a posi-
tive connection from such a slide to the paper-drum
could be devised. The entire error of the paper-
drum is to be attributed to the cord and spring by
which the drum is drawn out and returned.

There are three sources of error of the paper-drum
that can be identified, namely, the paper-drum
spring, the inertia of the drum, and the friction of the
drum.

Paper-drum Spring. — A long flat spiral spring like
a clock spring is used by some makers for returning
the paper-drum; others use a helical spring, as shown
by Fig. 4, page 7. The first form is intended to give
a uniform tension on the cord, and the second form
is intended to give an increasing tension as the cord
is drawn out. Both give increasing tension, though
the increase due to a flat spiral spring may be the
smaller. The increase of tension lengthens the cord,
and the diagram is shortened to just that extent. As
the cord is uniform in strength and elasticity the re-
duction in the length of the diagram is evenly dis-
tributed and the truth of the diagram is but little
affected. This effect is found in indicating an engine
at slow speed when a long cord is used. On high-
speed engines this effect is obscured by the influence
of the inertia of the paper-drum.

Inertia of the Paper-drum. — At the beginning of
the stroke of the engine, the paper-drum is started
from rest and it reaches its highest speed near the

THE STEAM-ENGINE INDICATOR. 49

middle of the stroke; it comes to rest at the end of
the stroke. On a high-speed engine an appreciable
force is required to start the drum; this force de-
creases regularly and becomes zero when the drum
attains its highest speed; a regularly increasing force
in the contrary direction is required to stop the drum.
If we consider the drum at the beginning of a stroke
with the cord wound on the base of the drum, it is
evident that the cord must exert a pull equal to the
sum of the tension of the spring and the force required
to start the drum; and the stretch of the cord will
be proportioned to the total pull it exerts, so that
the cord is longer at the beginning of the stroke.
As the drum moves toward the middle of the stroke
the extra force decreases and becomes zero, so that
the cord attains its normal length under the tension
of the spring when the drum attains its highest
speed. As the drum slows down during the latter
part of its stroke the force required to bring it to
rest is subtracted from the tension of the spring, and
the pull on the cord is decreased and its length di-
minishes. The effect of this action is to lengthen the
diagram at both ends. During the return-stroke the
sequence of events is repeated in reversed order. At
the beginning of the stroke the drum is started by
the spring, and the pull on the cord is reduced; at
the middle of the stroke the cord attains its normal
length; at the end of the stroke the drum is brought
to rest by an additional pull on the cord.

$0 THE STEAM-ENGINE INDICATOR.

The action just described is well illustrated by dia-
grams taken at regular intervals from an engine as
it starts from rest and comes up to a high speed, pro-
vided, of course, that a long cord is used. At first
the diagrams are notably short on account of the
varying tension of the drum spring, as stated in the
preceding section. As the speed of the engine in-
creases the inertia of the paper-drum lengthens the
diagram till it attains its normal length, and at high
speed it may show a notable excess of length.

If the engine had a slotted crosshead instead of a
connecting-rod, the force required to give velocity
to the drum would vary uniformly from the middle
to the end of the stroke, and the cord would stretch
and contract uniformly so that the only effect of the
inertia of the drum would be to change the length
of the diagram, but not to change its form. A dia-
gram from an engine with a connecting-rod will suf-
fer distortion from the effect of the inertia of the
paper-drum, which distortion will be larger as the
speed increases, and will increase with the length of
the cord. The conclusion is that a long cord is to
be avoided especially for a high-speed engine. The
effect of inertia may be reduced by using a smaller
and a lighter drum, as is sometimes done for high-
speed engines.

Some indicator-makers purposely use a short
drum spring with the idea that its increasing ten-
sion will compensate for the effect of inertia. But

THE STEAM-ENGINE INDICATOR. 51

the compensation cannot be exact, and to be of use
would require adjustment for varying speeds, which
would be troublesome, if not practically impossible.

Friction of the Paper-drum. — The most serious
error of the paper drum \\hen a long cord is used is

FIG. 37.

due to friction, which depends en the condition of
the bearing surfaces. Consequently if a long cord is
unavoidable the bearing surfaces should be carefully
cleaned and oiled to avoid friction.

If there is appreciable friction of the drum, then,
with a long cord, the drum will pause at the begin-
ning of a stroke till the tension of the cord is in-

52 THE STEAM-ENGINE INDICATOR.

creased enough to overcome the friction and start
the drum. On the return-stroke there will be a
similar pause till the pull of the cord is reduced
enough to allow the tension of the spring to s art the
drum. The effect is to shorten the diagram at both
ends and to distort the diagram. If Fig. 37 repre-
sents the true indicator diagram the effect of friction
and a long cord is equivalent to leaving gaps at aa
and bb' and closing up the two partial diagrams to
give an apparently complete diagram as shown by
Fig. 38. Like other errors of the paper-drum, this
may be eliminated by using a short cord.

In conclusion attention should again be called to
the fact that elasticity (i.e., lack of rigidity) of the
reducing motion or of its support will have the fame
effect as elasticity of cord, and that wire can be sub-
stituted for cord only when it can be kept taut so that
it will not sway back and forth.

Errors affecting the Pencil-motion. — The errors that
affect the record of pressures may be distinguished as

(1) errors of geometric design of the pencil-motion;

(2) errors due to friction and backlash; (3) errors due
to pencil-friction; (4) errors due to size of piston; (5)
errors due to the spring; (6) errors due to inertia.

A discussion of these several errors is of import-
ance in so far as it may show how they can be re-
duced, but it is not possible as yet to determine the
gross error of an indicator from the sum of the in-
dividual errors.

THE STEAM-ENGINE INDICATOR. 53

Design of Pencil-motion. — The geometric design of
a pencil-motion can be tested by drawing a diagram
on an enlarged scale, with extreme positions and a
proper number of intermediate positions. The de-
sign will usually be found to be imperfect; the pencil
does not draw an exactly straight line and the mo-
tion of the pencil is not an exact copy (on an en-
larged scale) of the motion of the piston; but the
imperfections are insignificant compared with other
unavoidable errors.

Backlash and Friction. — The backlash and friction
of an indicator may be tested as follows: first press
the pencil up with the tip of the finger, release it and
draw an atmospheric line, then draw another atmos-
pheric line after the pencil has been pressed down.
The distance between the atmospheric lines with a
good indicator is liable to be from o.oi to 0.02 of an
inch. It is, however, probable that the influence of
friction and backlash will be less than the amount
thus determined when the indicator is in service, as
jar and vibration are likely to diminish their effect.

Pencil- friction. — The pressure of the pencil on the
paper should be only enough to give a clear line that
can be seen in a good light. The influence of pencil-
friction is to make the pencil lag behind its true po-
sition. The steam-line is likely to be too low and the
back-pressure line too high; the expansion-line will
not be as steep as it should be, and the compression-
line will be too steep. If there are oscillations in the

54 THE STEAM-ENGINE INDICATOR.

diagram due to inertia they may change some of
these effects; thus the steam-line may be too high
if the pencil falls to it after an oscillation. In gen-
eral the tendency of pencil-friction is to reduce the
area of the diagram. With light pressure the re-
duction is not large; pressure enough to give a bold
diagram may reduce the area from three to five per
cent. A heavy pencil-pressure will entirely spoil the
diagram.

Error due to Expansion of Piston. — The piston of
an indicator is made with an area of one square inch
when it is cold and has a slightly larger area on ac-
count of expansion when hot. The error from this
source may amount to one-half of one per cent.

Error of the Spring. — The pressure of the steam in
the cylinder of the engine is weighed by the indi-
cator spring; all other parts of the indicator may be
considered as conveniences for recording the indica-
tions of the spring. A spring, when used for weigh-
ing or measuring force, has certain inherent defects,
and further, when used in an indicator, is subjected
to unfavorable conditions; all of which require par-
ticular attention.

In the first place a spring is slow. For example,
if a ten-pound weight is cautiously applied to a ^ood
spring balance, the balance is likely to show a trifle
less than ten pounds. On the other hand, if there
are two weights hung on the balance, a ten-pound
weight and a five-pound weight, and if the five-

THE STEAM-ENGINE INDICATOR. 55

pound weight is cautiously removed, the balance is
likely to show a trifle more than ten pounds. In
either case the spring is said to be slow, that is, the
true record is not shown immediately. The slowness
may be almost entirely overcome by jarring the bal-
ance. The spring of an indicator is not likely to show
much error from this source in service, as the piston
is in almost continuous motion and there are likely to
be vibrations transmitted to it from the engine; but
careful tests of an indicator spring out of the indica-
tor always show slowness, which must not be mis-
interpreted.

In the second place a spring gives only coarse in-
dications. This is well illustrated by comparing a
spring balance with a platform balance which has
knife-edges in good condition. But a spring bal-
ance weighing up to 20 pounds will weigh to
ounces, which corresponds to about one-third of one
per cent. Careful investigations of indicator springs
out of the indicator and at ordinary temperatures
show that they may be expected to have an ac-
curacy of one-fourth of one per cent. It may be con-
sidered that under favorable circumstances a spring
is good enough for engineering tests.

Now it is customary to consider that the steam
which leaks past the piston of an indicator falls at
once to the pressure of the atmosphere and to 212°
F., and further to assume that the indicator spring
which works in that steam has the same tempera-

$ THE STEAM-ENGINE INDICATOR.

ture. To test this assumption a thermometer was
placed inside the spring of an indicator and the tem-
perature was observed while the indicator was in
communication with the cylinder of a steam-engine.
For this purpose the piston-rod and pencil-motion
were removed and the thermometer was inserted
through the hole for the piston-rod. The thermome-
ter showed a higher temperature than 212° F., and
the temperature further increased with the steam-
pressure in the cylinder; a series of experiments
showed that the temperature indicated by the ther-
mometer corresponded nearly, though not exactly,
to the average steam-pressure in the cylinder. Tests
on another indicator with a loose piston which gave
excessive leakage showed lower temperatures than
were found for an indicator which had its piston in
normal condition. From these tests it appeared
clearly that the temperature of the spring is main-
tained at a high degree by heat transmitted through
the piston and along the barrel of the indicator, and
that the effect of steam leaking past the piston is to
cool the spring, rather than to heat it.

The investigations of the temperatures to which an
indicator spring is exposed are of the greatest im-
portance, because it is well known that springs be-
come weaker at high temperatures. Thus a certain
indicator spring which was marked 80 pounds to the
inch gave that scale at 100° F.; at 212° F. its real
scale was 78 pounds to the inch, and at 300° F. its

THE STEAM-ENGINE INDICATOR. 57

scale was hardly 75 pounds to the inch. A certain
6o-pound scale was found to be correct at 212° F.,
but at 300° F. ils scale was 58 pounds to the inch.
Both springs gave fairly uniform scales for a given
temperature, whether hot or cold.

Indicator-makers have long been aware of the in-
fluence of heat on the scale of a spring, and have fur-
nished springs for indicating steam-engines, and
other springs for air or water pressure. They also
test springs in the indicator with the intent that they
shall have the proper scale when in use.

The proper conclusion from the experiments on
the effect of temperature on the scale of a spring is
that the spring should be outside of the barrel of the
indicator and so exposed to the air that its tempera-
ture would not be much, if any, greater than that of
the atmosphere. If springs were so placed they
could be rated and tested cold, and the most trouble-
some source of error could be avoided.

Indicator-testers. — Some device for testing indi-
cators under steam is employed by every reliable in-
dicator-maker, and such devices have been used by
steam-engine experts and others. Such an indicator-
tester usually consists of a receptacle that can be
filled with steam at varying pressures, to which in-
dicators can be attached, as to a steam-engine; there
is also provision for measuring the pressure of the
steam by a mercury column or by a pressure-gauge.
For convenience in testing several indicators at the

58 THE STEAM-ENGINE INDICATOR.

same time it is customary to provide an electrical de-
vice (much like that shown by Fig. 26 in general
principle) for throwing all the pencils of indica-
tors undergoing test onto their cards at the same in-
stant; there is also a device for drawing out the pa-
per-drums at the same time. Evidently the same
end could be attained by a mechanical device such
that one motion of the hand should apply the pencils
to the cards and draw the drum cords; by having
enough observers the work can be as well done by
hand. There is no difficulty in making either elec-
trical or mechanical devices, and they are convenient
if not essential for commercial work; but they do
not add to the accuracy or reliability of the fu ida-
mental method of testing.

In using such a tester it is customary to raise the
steam-pressure in the receptacle by stated, amounts,
five or tea pounds at a time, and then set in motion
the device for drawing the drum cards and applying
the pencils. Thus there are drawn a series of
straight lines on the cards, which are drawn to rep-
resent the several pressures chosen. An atmos-
pheric line is drawn from which the pressures are
afterwards measured with the proper scale. At the
instant that the pencils are applied to the cards the
pressure of steam is read from a mercury column or
a pressure-gauge; or in some cases the mercury col-
umn is made to close the electrical circuit and work
the device for applying the pencils and moving the

THE STEAM-ENGINE INDICATOR. 59

drums, when it reaches heights that give the desired
pressures. Here again the added complication is to
be considered as a convenience, and care must be
taken that it does not introduce an additional error.

After a series of tests has been made with rising
pressures it is customary to repeat it in inverse or-
der with falling pressures, before removing the cards
for measurement. Lines drawn at the same pressures
but in inverse order of procedure seldom, if ever,
coincide; the lines drawn with decreasing pressures
are always the higher. Two atmospheric lines are
drawn, one before the series with rising pressure and
one after the series with falling pressure. Finally
the cards are all removed and measured.

It has been considered that the discrepancy be-
tween tests with rising and with falling pressures can
be attributed to friction and to the slowness of the
spring to respond to a change of pressure; they cer-
tainly tend to produce such discrepancy. But the
discrepancy is due in larger degree to the varying
temperature of the spring. Tests on an experimental
indicator which has its spring out of the steam con-
firm this view. The indicator and spring are heated
rapidly by rising steam-pressure, but lose heat slowly
by radiation when the pressure falls. Tests made with
rising pressures are the more regular, and there is
reason for relying on them alone.

All indicator-testers of the sort described have one
radical defect, namely, the indicator should be in con-

60 THE STEAM-ENGINE INDICATOR.

tinual motion in order to simulate the conditions of
service, while the pressure-gauge or the mercury col-
umn (more especially the latter) should be at rest
when the pressure is read. These conditions are
clearly incompatible; it is customary to change pres-
sures rather slowly, since by that means only can the
gauge or mercury column be made to work prop-
erly. It has been thought that this slow change of
pressure and the consequent slow motion of the in-
dicator piston gives rise to excessive friction at the
piston, and the discrepancy of tests with rising and
with falling pressures has been charged to this ac-
tion. It is not possible at present to confirm or con-
fute this idea.

An indicator-tester in the laboratory of the Massa-
chusetts Institute of Technology is designed to over-
come the difficulty attributed to testers already de-
scribed. In the first place the indicators are attached
to a cylinder to which steam is supplied and from
which steam is exhausted by a plain slide-valve.
There is no piston in the cylinder, and it is necessary
to drive the slide-valve by power. Reservoirs are
provided from which steam is supplied to the valve-
chest and to which the exhaust may pass; the pres-
sures in these reservoirs can be controlled so that the
steam-pressures and exhaust-pressures in the cylin-
der may be made to vary as desired. It is customary
to make the exhaust-pressure five or ten pounds less
than the steam-pressure, and to vary both together

THE STEAM-ENGINE INDICATOR. 6 1

so as to maintain this difference. Diagrams are
taken as in ordinary service at any desired speed of
revolution, and it is seen that the indicator is not
affected by excessive friction as charged against
other testers. Two mercury columns are employed,
one to measure the steam-pressure and the other to
measure the back-pressure. Communication be-
tween the first mercury column and the cylinder is
open only when the slide-valve is wide open, and
the second mercury column is in communication
with the same cylinder when the slide-valve is closed
to the steam and is open for exhaust. There is con-
sequently no difficulty about reading the mercury
columns, which remain steady or nearly so. The pa-
per-drum is given only a short motion, and the indi-
cator draws a small rectangular diagram with hori-
zontal lines drawn at known pressures. The error
of one line (for example, the steam-line) is charge-
able to friction and to error of scale; but the mean
error of both lines should be free from error due to
friction and should be chargeable to error of scale
only. The instrument described lacks conveniences
for rapid testing and could not be used commer-
cially; even for laboratory work it has been found
troublesome until observers have acquired facility
after much practice. It is believed that its princi-
ples are correct and that the difficulties in using it
can be overcome. The conclusion from tests that
have been made shows that springs are liable to an

62 THE STEAM-ENGINE INDICATOR.

error of 5 per cent from their rated scales; if a
true mean scale of a spring is determined the devia-
tion from that scale is liable to be 2 per cent.
Springs are liable to be weak, that is, they record
too high pressures and give too large powers for en-
gines indicated.

Effect of Piping. — It is advisable especially with
high-speed engines, that the connection from the in-
dicator to the cylinder shall be short and direct. In
some cases the indicator cock may be screwed directly
into the wall of the cylinder, or a short nipple and
coupling may suffice. Commonly an elbow is re-
quired to bring the indicator erect; an indicator may,
however, be used with the paper-drum horizontal
when convenient.

Sometimes the indicator is connected to both ends
of the cylinder of a steam-engine so that diagrams
may be taken from either end as desired. This in-
volves the use of a pipe leading to each end of the
cylinder, with a three-way cock (see Fig. 20) at the
middle; the steam on the way to the indicator must
make two turns, one at the elbow near the end of the
cylinder and one at the three-way cock, and it must
traverse a length of pipe depending on the size of
the engine. The resistance of the pipe and the turns
causes the changes of pressure at the indicator to
lag behind the changes in the cylinder. The steam-
line will be too low and the back-pressure line too

THE STEAM-ENGINE INDICATOR. 63

high; on the other hand the cut-off will be delayed
and the expansion-line will be too high.

In addition to the distortions of the diagram just
noted, it is liable to be affected by rather unaccount-
able oscillations. The mean effective pressure of the
distorted diagram may be either more or less than
the true mean effective pressure. In the first place,
lowering the steam-line and raising the back-pres-
sure line tends to reduce the mean effective pressure,
while delaying the cut-off and raising the expansion-
line tends to increase it. The only direct conclu-
sions from the somewhat discordant tests on the ef-
fect of piping on the mean effective pressure are that
piping should be avoided, especially on high-speed
engines, and that when such piping must be used it
should not be less than three-quarter-inch pipe, and
inch pipe is somewhat better. Very large engines
may have pipe as large as one and a half inches in
diameter. All such piping should be wrapped to
avoid radiation, especially when exposed to wind, as
on a locomotive. Marine engines are habitually in-
dicated in this manner, so that the results, unless for
very high-speed engines, are likely to be concordant.

Piping for indicators should be carefully done,
using only a little red-lead in making joints, and ap-
plying it so that it may not get into the pipe and
thence be blown into the indicator.

Mean Effective Pressure. — The diagram from an
engine without cut-off or compression and with

THE STEAM-ENGINE INDICATOR.

ample ports and passages is a rectangle. The width
of the diagram measured with the proper scale gives
at once the effective pressure on the piston; mean-
ing by the effective pressure, the difference between
the steam-pressure during the working-stroke and
the back-pressure during the exhaust-stroke. Now
the pressure of the steam for a diagram like Fig. 36
varies from point to point, and the mean effective
pressure may be determined from the mean width of
the diagram.

To determine the mean effective pressure it is con-
venient to divide the length of the diagram into ten
equal parts, as shown by light lines in Fig. 39. The
width of these several parts can be measured with
the proper scale on lines drawn at the middle of
them, as shown by heavy lines in Fig. 39. In pre-

FIG. 39.

paring a diagram for measuring the mean effective
pressure a scale of convenient length may be laid
across it diagonally so that zero shall come on a ver-
tical line at one end of the diagram, and 100 on the
line at the other end, as shown by Fig. 39. Then

THE STEAM-ENGINE INDICATOR.

draw lines as shown at 5, 15, 25, etc., and on them
measure the width of the diagram at ten points, using

FIG. 40.

the proper scale. The mean effective pressure may
be calculated by taking one-tenth of the sum of the
ten several widths, as follows:

ist width 42

2d
3d
4th
5th
6th
7th
8th
9th
loth

54
58
51
40
31
25

Sum 340.5

y1^ of sum, m. e. p 34 pounds

If desired more or less than ten widths can be
taken; for example, twelve widths can be measured
and then the mean effective pressure will be V12 of
the sum of the twelve several widths.

When a diagram is taken from an engine with a

THE STEAM-ENGINE INDICATOR.

short cut-off, the expansion-line may run below the
back-pressure line, forming a loop, as shown by Fig.
41. On this diagram the steam-pressure is greater

FIG. 41.

than the back-pressure on the first five lines drawn
across it. On the lines numbered from 6 to 10 the
back-pressure is the greater. Roughly, the steam
does work on the piston for the first half of the dia-
gram, while for the second half the piston does work
to force the steam out against the pressure of the
atmosphere. The mean effective pressure will be
calculated by adding the first five widths and by sub-
tracting the last five widths, and then dividing by ten
as before; thus:

ist width 43.0

3d
4th
5th

6th
7th
8th
gth
loth

Di
J* diffe

• II-5

4.8

* 13

« i.o

. 18 2

' 2.8

' J. O

- Sum. . . .

. 72 4.

THE STEAM-ENGINE INDICATOR.

The preceding explanation, while it leads properly
to the correct method of calculating mean effective
pressure for a diagram with a loop, is not strictly
logical, for in reality work is done by the steam on
the piston throughout the working-stroke, and the
piston does work on the steam to force it out of the
cylinder against the pressure of the atmosphere,
throughout the exhaust-stroke, Fig, 41 may be

To N

FIG. 42.

separated into two parts, as shown by Figs. 42
and 43.

In Fig. 42 the line CD represents the admission
and expansion of steam during the working-stroke of
the piston. The line MN, drawn at 14.7 pounds be-
low the atmospheric line, is called the line of zero
pressure, or the absolute vacuum line. Pressures
measured from this line give the real pressure of
steam; thus at the first line the pressure is 64
pounds, that is, 49.3 pounds above the atmosphere
(measured from the atmospheric line), plus 14.7
pounds, equal to 64 pounds. Since the steam in the
cylinder of the engine is shut off from the atmos-

68 THE STEAM-ENGINE INDICATOR.

phere, its total pressure does not depend on the at-
mosphere; it must, however, be calculated from the
pressure of the atmosphere as shown by a barometer,
for both indicators and steam-gauges show the pres-
sure above the pressure of the atmosphere.

In much the same way Fig. 43 shows the exhaust
and compression, referred both to the atmospheric
line AB and the line MN of zero pressure.

The work done by the steam on the piston can be
calculated from the mean effective pressure of Fig.
42, and the work done by the piston during exhaust
may be calculated from Fig. 43, as represented be-
low:

Fig. 42. Fig. 43. Difference.

ist line 64.0 21. o 43.0

17-0 30.0

16.8 11.5

16.5 4.8

16.4 1.3

90.6

16.2 — i.o

16.1 — 2.8

16.0 — 4.0

15-9 - 5-o

15-7 - 5-4

-18.2

10)167.6 Difference... 10)72.4

. .. 47.0

id "

28 i

ju
4.th "

. . . ^,U. 3

. 21.1

5th " ....

. ... 17.7

6th " ....

... 15-2

7th "

. Ill

8th "

9th "

. . . 10 9

Sum

10)240.0 Sum. . .

m. e. p. . .

24.0 m. e. p,

16.76 m. e. p 7.24

Resultant m. e. p. 24.0 — 16.76 = 7.24 pounds.

The column headed Fig. 42 gives the several
widths for the corresponding diagram, and the col-
umn headed Fig. 43 does the same for its diagram.
The resultant m. e. p. obtained by subtracting the

THE STEAM-ENGINE INDICATOR. 09

m. e. p. for the second column from the m. e. p. for
the first column is the same as that already found
from Fig. 41. Under the heading of Differences are
given the results obtained by subtracting the num-
bers of the second column from those in the first col-
umn. These differences are clearly the widths of
Fig. 41 at the corresponding lines; the differences

b-,

[

FIG. 43-

are negative for the 6th, 7th, 8th, 9th, and loth lines
corresponding to the widths of the loop for Fig. 41.
The calculation at the right hand is evidently a
transcript of the calculation for Fig. 41, and would
give a correct result whether or not there is a loop,
for without a loop there would be no negative differ-
ences. Finally it is evident that the subtraction of
widths of the loop in the calculation for Fig. 41 is
a purely arithmetical operation, due to the fact that
the back-pressure happens to be higher than the end
of the expansion-line.

It is evident that the mean width of an indicator
diagram can be obtained, when the area in square

70 THE STEAM-ENGINE INDICATOR.

inches is known, by dividing its area by the length in
inches. The area can be conveniently measured by
aid of a planimeter, which will now be described.

Amsler Planimeter. — It is customary to determine
the mean effective pressure of indicator diagrams
from the area of the diagram measured by aid of
a planimeter like that represented by Fig. 44. This
instrument has two arms, the tracing-arm HF and
the guiding-arm HP, hinged together at H. The

FIG. 44.

guiding-arm has a needle-point at P which serves
as a pivot to locate the instrument, and at -F is a
tracing-point. At D on the tracing-arm is a meas-
uring and recording wheel.

The planimeter is used on a drawing-board or
table covered with paper or cardboard so as to give
a flat, smooth, unglazed surface for the wheel to roll
on. The indicator diagram is pinned down on the
table and the planimeter is set as in Fig. 45, so that
the tracing-point may be carried around the outline
of the diagram without cramping the instrument and
without drawing the measuring-wheel over the edge
of the card or paper on which the diagram is drawn.

THE STEAM-ENGINE INDICATOR. ? 'I

The measuring-wheel is divided into ten parts and
subdivided into hundredths. A fixed vernier carries
an index and a special scale for finer readings; the
use of the vernier will be described later, it being

FIG. 45.

sufficient for the present to take account of the fixed
index only.

To measure the area of a diagram, locate a con-
venient point, as F, by a light prick with the point of
a needle. Place the tracing-point F of the planim-
eter at this point, and set the wheel by hand to read
zero at the fixed index. Move the tracing-point
over the outline of the diagram toward the right,
and stop at the point which was located by the

72 THE STEAM-ENGINE INDICATOR.

needle-prick. Read the scale of the wheel at the
fixed index; the main divisions represent square
inches, and the subdivisions represent tenths.

It is very important that the planimeter shall start
and stop at the same point; a slight deviation makes
a large difference in the reading of the scale on the
wheel. It is for this reason that the starting-point is
located with a needle; sometimes it may be prefer-
able to mark the starting-point by a pencil-line, in
which case greater care is required in starting and
stopping. It is also important that the diagram
shall be traced exactly; some practice is required to
gain skill and rapidity in the use of the planimeter,
which is an exact and delicate instrument.

Fig. 46 represents a scale with divisions and sub-
divisions into tenths, that can be moved past a fixed

it 1 I 1 I 1 1° 1

o1 ' ' '

1 1 1 1 1 1 t 1 1

1 1 1 1 Mill
1 2

FIG. 46.

index, which in the figure is something beyond the
division 1.2 of the scale. The scale of the vernier has
ten divisions, but they are shorter than the subdi-
visions of the main scale; the ten divisions of the
vernier occupy the same space as nine divisions of
the main scale, and consequently each division of the
vernier is one-tenth of a subdivision of the scale
shorter than one of the subdivisions of the scale. It

THE STEAM-ENGINE INDICATOR. ?$

will be noted that the 6th division of the vernier co-
incides with a subdivision of the scale; the 5th di-
vision is consequently 1/10 of a subdivision of the
scale from the adjacent division of the scale, that is
to say, it is 1/i0o of a whole division of the scale from
that mark; the 4th vernier division is 2/10o ahead of
the adjacent mark; the 3d division is 3/100; the 2d
division is ViooJ the Ist division is ViooJ and the in-
dex is Vioo ahead of the mark on the main scale.
The index consequently reads 1.26 of the scale.
Therefore we read forward on the scale to the mark
before the index, and then forward on the vernier to
that division of the vernier which coincides with a
mark on the scale.

The planimeter represented by Fig. 44 measures
areas in inches and decimals; the large divisions
give the number of square inches, the subdivisions
give tenths, and hundredths are read on the ver-
nier. This planimeter has a tracing-arm which is
four inches long measured from the hinje to the
tracing-point, and the circumference of the wheel is
two and a half inches; the diameter of the wheel is
0.7957 of an inch. Some planimeters have the same
size wheel and have an arm eight inches long; if
read as directed for Fig. 44, the readings are to be
multiplied by 2 to give the area of a figure in square
inches.

Fig. 47 shows a planimeter with an adjustable
tracing-arm; when set at the proper length (4 inches)

74 THE STEAM-ENGINE INDICATOR.

this instrument gives areas in square inches; it can
also be set to read in square feet and in square deci-
meters. When set to read in square feet one entire
revolution of the wheel corresponds to one-tenth of a
square foot, and the divisions, subdivisions, and the

FIG. 47-

vernier give hundredths, thousandths, and ten-thou-
sandths of a square foot; when set for square decime-
ters one revolution of the wheel corresponds, to a
square decimeter. If the tracing-arm is made eight
inches long, one revolution of the wheel corresponds
to 20 square inches.

The back of the tracing-arm carries two points,
one on the arm near the tracing-point and one on
the slide near the hinge. If the instrument is set as
represented by Fig. 48 so that the distance between
these points is equal to the length of the indicator
diagram, the instrument will give the mean height
of the diagram in fortieths of an inch; if the diagram
is drawn with a 40 scale the instrument gives the
mean effective pressure immediately. In this case
one revolution of the wheel corresponds to one
hundred, the main divisions of the scale give the tens,

THE STEAM-ENGINE INDICATOR.

and the subdivisions give the units, while tenths are
read on the vernier. If the diagram is drawn with
some other scale, then the reading of the instrument

is to be multiplied by the scale of the spring and di-
vided by 40; or an equivalent operation is to be per-

THE STEAM-ENGINE INDICATOR.

formed. Thus for an 80 scale the readings are to be
doubled; for a 50 scale the readings are to be in-
creased by one-fourth; while for a 30 scale they are to
be diminished by one-fourth.

To get a conception of the way in which a planim-
eter measures an area we may proceed as follows.
In Fig. 49 let hp represent the tracing-arm of a

FIG. 49.

planimeter measuring 4 inches from the hinge at h to
the tracing-point />. On this arm there is a wheel at w

which has the circumference of 2^ inches; its diam-
eter is .7957 of an inch. If the arm hp is moved di-
rectly down, parallel to itself, the wheel will measure
the distance hi that the arm is moved, and if hi is

THE STEAM-ENGINE INDICATOR.

made equal to 2| inches the wheel will make one
complete revolution. The area of the figure hpqi is
4 X 2^ = 10 square inches, and consequently if the
wheel w has its scale divided into ten main divi-
sions each one will correspond to one square inch of
area. If the arm hp is kept parallel to itself, as shown

in Fig. 50, but moved so that h passes along the in-
clined line ///, the wheel will roll and slide as it passes
from iv to ,r; it will roll the distance yx and will slide
the distance wy. The sliding does not affect the read-
ing of the wheel, but the distance rolled is as before
the height of the figure hpqi, and its area is again
4 X 2^ = 10 inches after the wheel has rolled one
complete revolution. But the same result will be .ob-
tained if the point h moves on a curved line hi in
Fig. 51, for the area is again 4 X 2^ = 10 inches for
one revolution of the wheel. It is evident that the
wheel can be placed anywhere on the arm hp, or it
may be on an extension of the arm, as in Fig. 52.

In the planimeters shown by Figs. 44 to 48 the
hinge is guided by the guiding-arm along the arc of

78 THE STEAM-ENGINE INDICATOR.

a circle, but that is only a matter of convenience, and
the hinge may be guided along a straight line, as

FIG. 52.

shown by Fig. 55, which represents a special form of
planimeter.

In Fig. 53 let ab be an arc of a circle on which the
hinge of a planimeter is guided by the guiding-arm

FIG. 53.

hg. If the wheel is set with its index at zero and the
tracing-point is carried around the figure pqrs, the
final reading of the wheel will give the area of the
figure. To see that this is true, consider that qi is
drawn parallel to hp and that the wheel will record
the area of hpqi while the tracing-point moves from
p to q; while the tracing-point moves from q to r

THE STEAM-ENGINE INDICATOR.

the wheel rolls over the path xy, but this action will
be compensated by a reverse operation later; again
hs is parallel to ri so that the wheel will record the
area of the figure rshi while the tracing-point moves
from r to s', the figure pqrs is completed by moving
the tracing-point from s to />, during which the wheel
rolls the distance zw, which is equal to xy, and is
rolled in the contrary direction so that it just com-
pensates the first action. Now we can get the area
of pqrs by adding the areas of hpqi and iqr and sub-
tracting the areas of rshi and hps\, but iqr and hps
are equal, consequently the area of pqrs is equal to
hpqi minus hsri', now the arm hp moves down in pass-
ing from p to q and up in passing from rs, so that the
wheel adds the area of hpqi and subtracts the area of
hsrif and consequently the final reading of the wheel
gives the area of the figure pqrs.

Coming now to an irregular figure, like an indi-
cator diagram, a first approximation to the* area can

FIG. 54-

be had by replacing the actual diagram by one hav-
ing the contour abfklh. The individual figures

8O THE STEAM-ENGINE INDICATOR.

abed, efgh, and iklm can be measured and their
areas summed up, or the tracing-point of the pla-
nimeter can be carried entirely round the figure,
omitting the lines dc and ig, which are common to
two individual figures, and which are traced in oppo-
site directions when the figures are traced separately.
The narrower and more numerous the individual
figures the closer will be the approximation; conse-
quently to get the true area of the indicator diagram
it is sufficient to trace its outline as already explained
in the description of the instrument.

The planimeter represented by Fig. 44 has an arm
which is 4 inches "long, and the circumference of its
wheel is 2\ inches; consequently one revolution of the
wheel corresponds to an area of 10 square inches. The
scale of the wheel is divided into ten main divisions,
each of which corresponds to one square inch of
area. The subdivisions of the wheel and the vernier
allow us to read to hundredths of a square inch.

The planimeter shown by Fig. 47 can be set so
that its arm is 4 inches long, and as its wheel has
a circumference of 2^ inches, the main divisions of its
wheel correspond to square inches of area. Another
way of considering this matter is to read the whole
number of turns of the wheel from a counter which
will be seen on the axis of the wheel, and three deci-
mal figures on the scale and vernier, and then multi-
ply by 10 to get the area in square inches. The
mark to which the tracing-arm is to be set is lettered

THE STEAM-ENGINE INDICATOR. 8 1

10 sq. in. A planimeter with an arm 8 inches long
and a wheel 2-| inches in circumference must have
the number of turns of the wheel (and decimals of a
turn) multiplied by 20 to give square inches.

Area and Mean Effective Pressure. — To get the
mean effective pressure for an indicator diagram, we
may (i) measure the area in square inches with a
planimeter, (2) divide the area by the length of the
diagram in inches to get the mean height, and (3)
multiply the mean height by the scale of the spring.
It is customary and convenient to change the order
of operations, so that the area is multiplied by the
scale of the spring, and the product is divided by the
length. Thus the diagram Fig. 39 has an area of 1.13
square inches; its length is 2 inches, and, with a scale
of 60 pounds to the inch, its mean effective pressure
is

Area X scale 1.13 X 60

length — ' = 33-9 »• e. p.

If a diagram has a loop, as shown by Fig. 41, page
66, the main portion of the diagram is traced by the
planimeter moving toward the right, but the loop
is traced moving toward the left. The planimeter
adds the main portion and subtracts the loop, which
is equivalent to subtracting widths of the loop as in
the calculation on page 68.

The planimeter shown by Figs. 47 and 48 has two
points on the back of the tracing-arm, and the dis-

82 THE STEAM-ENGINE INDICATOR.

tance between them is equal to the length of the arm
from hinge to tracing-point. As shown by Fig. 48,
these points may be adjusted to the length of the in-
dicator diagram, and then the reading of the wheel
gives the width of the diagram in fortieths of an inch,
each subdivision of the scale of the wheel (hun-
dredths of the circumference) being read as one-for-
tieth. If the scale of the diagrams is 40 pounds to
the inch, the reading of the wheel gives the mean
effective pressure directly. To understand the prin-
ciple of this way of using the planimeter, let us bear
in mind that the area corresponding to one turn of
the wheel of a planimeter is equal to the length of the
arm multiplied by the circumference of the wheel.
To get the mean height of a diagram we divide the
area by the length of the diagram. If then the length
of the arm is made equal to the length of the diagram,
the height of a diagram which gives one turn of the
wheel will be just equal to the circumference of the
wheel (2.5 inches). Since the wheel is divided to
hundredths of a turn, each hundredth will correspond
to 2'5/ioo — 1/4o °f an mcn- Thus we see why this
instrument gives' mean effective pressure directly for
a 40 scale. For any other scale, multiply by the scale
and divide by 40.

Coffin Averaging Instrument. — This is a planimeter
which has one end of the tracing-arm guided in a
straight groove, as shown by Fig. 55. It can be used
to measure areas just as the instrument represented

THE STEAM-ENGINE INDICATOR. 83

by Fig. 44 is used. Its tracing-wheel is 2.5 inches in
circumference, and its arm is six inches long, so that

FIG. 55.

one turn of the wheel corresponds to 15 square
inches. The scale of the wheel has 15 main divisions,
each of which corresponds to one square inch of

84 THE STEAM-ENGINE INDICATOR.

area; each main division is subdivided into fifths, so
that the subdivisions correspond to two-tenths of an
inch; finally the vernier has ten divisions, and enables
us to read to two one-hundredths of an inch. This
division is not so convenient as that for planimeters
described earlier, but the instrument is intended to
be used in another way to be explained.

The usual way of determining mean effective pres-
sure is as follows: The diagram to be measured is
placed under the fixed clips at the left so that one end
comes to the vertical edge, and the atmospheric line
(or a convenient line parallel to it) comes to the hori-
zontal edge as shown. The movable clip is brought
to the other end of the diagram. The tracing-point
D is placed at the end of the diagram near the mova-
ble clip, and the groove in which the " hinge," or
guided point, moves, if prolonged, would coincide
with the other end of the diagram. The wheel is set
at zero, and the diagram is traced as usual, stopping
at D] the point D is now slid along the movable clip
till the wheel turns back to zero; the distance that the
tracing-point is moved in this last operation is equal
to the mean height of the diagram, and can be meas-
ured with the proper scale. When the contour is traced
the wheel records the area of the diagram, and this
area, divided by the length of the diagram, gives the
mean height Dd, Fig. 56. When the tracing-point is
raised from D to d the area of the figure cdDe is
subtracted, and this area is equal to that of the figure

THE STEAM-ENGINE INDICATOR.

abDb; consequently the tracing-point will come to
d when the reading of the wheel is reduced to zero.

FIG. 56.

The height of the diagram measured with the proper
scale gives the mean effective pressure.

FIG. 57-

Lippincott and Willis Planimeters. — The Lippincott
planimeter as shown by Fig. 57 has a tracing-arm

86 THE STEAM-ENGINE INDICATOR.

HP, and a guiding-arm RH, hinged at H, and so far
resembles the Amsler planimeter; but it has a wheel
W on an arm CD which is at right angles with the
tracing-arm; the wheel W is free to slide on the arm

FIG. 58.

CD, but has a sharp edge so that it cannot slide on
the paper; the arm CD is a glass tube closed at the
ends, as shown more clearly by Fig. 58, and has a
paper scale inside on which the area of the diagram
or the mean effective pressure can be read.

Fig. 59 shows a modification of this type of planim-
eter, known as the Willis planimeter, in which the
glass tube is replaced by a steel spindle that slides
under the rollers R and S and carries the wheel W,
which traverses over an enameled scale. The prin-
ciple is of course just the same; the simpler arrange-
ment will be chosen for discussion.

To understand the action of this instrument, we
may, as for the Ams'er planimeter, consider the effect
of moving the tracing-arm parallel to itself from a
position hp, Fig. 60, to a position iq\ clearly the only
effect on the wheel is to make it slide on the arm cd
a distance equal to hi, the height of the rectangle
hpqi't perhaps in this case it may seem better to say

THE STEAM-ENGINE INDICATOR. 8/

that the arm cd is drawn through the wheel, which
remains a rest, neither rolling nor sliding on the
paper. If the arm hp is 4 inches long, and the area

of the rectangle hpqi is 10 square inches, then the
wheel slides 2.\ inches on the arm; in this
case the scale on the arm cd is made 2| inches
long, and is divided into ten parts each of which

THE STEAM-ENGINE INDICATOR.

corresponds to one square inch of area; the scale is
subdivided for tenths of a square inch, and hun-

FIG. 60.

dredths, if read, must be estimated, as the instrument
has no vernier. In Fig. 61 the wheel rolls from w to

w w d

FIG. 61.

w" , while the arm hp moves to iq, but this rolling
does not affect the reading, which is equal to w'w",

THE STEAM-ENGINE INDICATOR.

that is, the wheel slides on the arm cd a distance equal
to the height of the figure hpqi, and with a proper
scale can be made to measuie that area in square
inches.

If the arm hp is pivoted about a point as in Fig. 62,
the arm cd at any instant will have two motions: (i)
it will be drawn endwise through the wheel, and (2)

FIG. 62.

it will swing around just as fast as the arm hp does;
the first action affects the reading on the scale, and
the second, which makes the wheel roll, does not. A
little consideration will make it appear that the arm
cd is drawn endwise a distance equal to the circular
arc ce, as the arm hp swings to hr\ and also that the
distance the wheel w slides on the arm cd does not
depend on its position on the arm; it is true that the
wheel will roll further if it is more remote from c, but
that does not affect the reading.

We are now ready to consider a diagram like

THE STEAM-ENGINE INDICATOR.

pqrs, Fig. 63, similar to Fig. 53 , page 78. As
before, there are four operations to consider: (i) the
arm hp moves parallel to itself, and the wheel meas-
ures the area hpqi', (2) the arm lip swings through the
angle qir, and the wheel records the distance fg\ (3)
the arm moves parallel to itself, and the wheel meas-
ures the area rihs] and (4) the arm swings through

FIG. 63.

the angle shp, and the wheel records the distance ec.
But ec is equal to fg and is recorded in the contrary
sense, and therefore the pivoting about i and the piv-
oting about h have finally no influence on the read-
ing. The instrument records the difference between
the areas hpqi and hsri, because the latter is measured
in contrary direction, or is subtracted, which gives
the area of the figure pqsr. The extension of the
action of the instrument from a figure like pqrs to an
irregular figure is of course just like that set forth on
page 79.

It will be noted now that the arm cd may be placed

THE STEAM-ENGINE INDICATOR. 9 1

anywhere along the arm hp, and that the wheel may
have any diameter without affecting the action of the
instrument. The wheel should be truly circular or
the swinging of the tracing-arm back and forth will
not have equal and contrary effects, as is necessary
for the proper action of the instrument.

This instrument is commonly used in the manner
given on page 74 for the Amsler planimeter, Fig. 47
and Fig. 48; that is, the length of the tracing-arm
from the hinge to the tracing-point is made equal to
the length of an indicator diagram, and consequently
the reading of the planimeter is equal to the mean
width of the diagram in inches, or in pounds per inch,
depending on the graduation of the paper scale inside
the glass tube (Fig. 59) which forms the arm CD of
the instrument. Several tubes, with two scales each,
are furnished with a planimeter. A scale of inches
and tenths can be used for measuring the width of a
diagram in inches, or it may be considered to be a
scale of ten to the inch for reading mean effective
pressures directly; other scales are conveniently ar-
ranged for various indicator springs.

Through the hinge of this planimeter there is a
style that is retracted by a spring, but it can be thrust
down even with the tracing-point by pressing on its
head. With this point pressed down the length of
the tracing-arm can be conveniently made equal to
the length of the diagram when it is desired to deter-
mine the mean effective pressure of an indicator dia-

92 THE STEAM-ENGINE INDICATOR.

gram. If the area of a diagram is desired, the length
of the tracing-arm can be set by direct comparison
with a scale of inches; for example, the arm may be
made four inches long and a scale of fortieths may be
used for measuring areas in square inches, ten forti-
eths corresponding to one square inch; or the arm
may be made five inches long with a scale of fiftieths
in the glass tube.

Horse-power of an Engine. — Work is measured
mechanically in foot-pounds, and can be calculated
by multiplying the force which does the work by the
distance through which that force is exerted. Thus,
a force of five pounds moved through a distance of
ten feet will generate 5 X 10 = 50 foot-pounds.

Power is the amount of work done in a unit of
time. The unit of power for engineering purposes is
33,000 foot-pounds per minute. Thus, a force of
2500 pounds moving at the rate of 660 feet per min-
ute will generate.

660 X 2500 ~ 1,650,000 foot-pounds
per minute, and will develop

1,650,000 -r- 33,000 = 50 horse-power.

To find the horse-power of a steam-engine:

(1) Take indicator diagrams from both ends of the
cylinder and determine the mean effective pressure
of each separately.

(2) Ascertain the diameter of the cylinder and of

THE STEAM-ENGINE INDICATOR. 93

the piston-rod, and determine the area of the piston
and of the section of the piston-rod in square inches.
Subtract the area of the piston-rod from the area of
the piston to find the net area of the crank side of the
piston.

(3) Multiply the area of the piston by the mean
effective pressure from the head-end diagram; and
multiply the net area of the crank side of the piston
by the mean effective pressure from the crank-end
diagram; add the two products.

(4) Ascertain the stroke of the piston in feet and
multiply by the sum obtained under (3), and by the
revolutions of the engine per minute; divide by 33,-
ooo, and the final result will be the horse-power of
the engine.

To express this as an equation let

pi and /„ be the head-end and crank-end mean effec-
tive pressures ;
D be the diameter of the cylinder; its area is

3.I4I6/?1

d be the diameter of the piston-rod ; its area is

3.1416^'
4

5 be the stroke in feet;

R be the revolutions per minute ;

94 THE STEAM-ENGINE INDICATOR.

.I4I6Z?8

4 4

Here 7//P stands for indicated horse-power.

Instead of calculating the areas of the piston and
piston-rod, it is convenient to take them from Table I
of the Appendix.

If the engine has a tail-rod, the area of its section
must be subtracted from the area of the piston to
get the net area of the head side of the piston.

As an example, we will make the calculation for
the horse-power of an engine having the following
dimensions:

Diameter of cylinder ................ 1 6 inches

Diameter of piston-rod ............. 2-J- "

Stroke ............................ 2 feet

Revolutions per minute .............. 130

Head-end mean effective pressure ..... 59.8 pounds

Cranke-and mean effective pressure.. . . 59.2 "

The areas of the piston are:

. 3.1416X16'

Head end, - =201.06 square inches.
4

3.1416x6 .
Crank end, -- -- == 196.15 sq. in.
4 4

The horse-power is
{59-8 X 201.06 +"59. 2.X 196.15! X 2 X 130-^33,000= 186.2.

THE STEAM-ENGINE INDICATOR. 95

Engine Constant. — For a rough-and-ready calcula-
tion the average area of the piston may be multiplied
by the average mean effective pressure; this product
may now be multiplied by twice the stroke in feet and
by the revolutions per minute, and the result divided
by 33,000. This method applied to the preceding ex-
ample will give:

Average area of piston,

3.1416X16' I 3.1416X2.5'

X =198.6 square inches;

424

Average mean effective pressure,

4(59-8+ 59-2)= 59-5;
59.5 X 198.6 X 2 X 2 X 130 -f- 33,000 = 186.2.

Had the mean effective pressures been more unlike
the error would be important.

When this method is used -it is customary to unite
all the factors except the average mean effective pres-
sure into a constant called the engine constant.

The engine constant for the case. in hand is

198.6 X 2 X 2 X 130 -7- 33>ooo = 3.13,

and the horse-power for the average mean effective
pressure given above is

59-5 X 3.131 = 186.2.

Piston-displacement. — The piston-displacement of
an engine is obtained by multiplying the area of the

96 THE STEAM-ENGINE INDICATOR.

piston in square feet (allowing for the piston-rod at
the crank end) by the stroke in feet.

For example, the piston-disp'acement of the engine
mentioned above may be found as follows:

Area piston :

head end = 201. 06 -^ 144= 1.3965 square feet ;

crank end = 196. 1 5 -f- 144 = 1 .362 1 square feet.
Piston-displacement :

head end = 1.3965 X 2 = 2.7930 cubic feet;

crank end = 1.3621 X 2 = 2.7242 cubic feet.

The term piston-displacement means the space dis-
placed by the piston; the meaning is most evident for
a pump, which should displace or force out a volume
of water equal to the piston-displacement for each
stroke of the pump-piston, provided that there is no
leakage and the valve action is perfect. The configu-
ration of -the piston, whether it is flat, conical, or with
protruding 'boss or nuts, does not affect the piston-
displacement. A compressed-air engine will take its
piston-displacement of air per stroke, provided that
its valve gives free passage of air and allows the air
to enter till the stroke is completed; if the cut-off for
such an engine is at half-stroke, then it will take half
of its piston-displacement per stroke. This state-
ment for an air-engine ignores the effect of waste
space at the end of the cylinder and the effect of com-
pression. A steam-engine cannot have its steam con-

THE STEAM-ENGINE INDICATOR. 97

sumption calculated in so simple a manner because
much of the steam admitted is condensed on the walls
of the cylinder; during the expansion, and especially
during the exhaust, this condensed steam is re-
evaporated. A complete understanding of cylinder
condensation and its effect on the economy of a
steam-engine can be obtained only by an extended
study of the thermal theory of the steam-engine, and
of tests on steam-engines; an introduction to this
interesting subject can be obtained here by making
calculations of the indicated steam consumption of
a steam-engine.

Clearance. — The waste space in the steam-passage
leading to the cylinder, and between the cylinder-
head and the piston when the latter is at the end of
its stroke, is called the clearance of the engine. This
clearance is sometimes given in cubic inches or cubic
feet, but is more commonly given as a percentage of
the piston-displacement. The clearance here dis-
cussed must not be confused with the machinist's
clearance, or distance in fraction of an inch, between
the piston and the cylinder-head.

If the clearance of the engine discussed above is
0.279 of a cubic foot, it is said to have 10% clearance.

Absolute Pressure. — The indicator shows the pres-
sure in the cylinder of an engine measured from the
atmospheric line, or the pressure above the pressure
of the atmosphere. A pressure less than that of the
atmosphere is commonly called a vacuum; such a

98 THE STEAM-ENGINE INDICATOR.

vacuum is measured downwards from the atmos-
phere in pounds, on an indicator diagram. In much
the same way boiler-pressures are measured by steam-
gauges above the atmosphere. On the other hand,
a vacuum in a condenser is measured by a vacuum
gauge, or by a U tube filled with mercury, in inches
of mercury.

To convert a pressure (or vacuum) in inches of
mercury to pounds, multiply by 0.49. Thus a vacuum
of 25 inches corresponds to a pressure of

25 X 49 = I2j

pounds below the atmosphere.

The pressure of the atmosphere is to be obtained
by aid of a barometer. For the greater part of engi-
neering work the pressure of the atmosphere may be
taken at 30 inches of mercury, or 14.7 pounds.

The real pressure measured from an absolute
vacuum is obtained by adding the pressure by a
gauge, or by the indicator, to the pressure of the
atmosphere. A pressure measured on an indicator
diagram below the atmospheric line is to be sub-
tracted from the pressure of the atmosphere to get
the corresponding absolute pressure. And in like
manner a vacuum measured by a vacuum gauge is
to be reduced to pounds and subtracted from the
pressure of the atmosphere to get the absolute pres-
sure.

Absolute pressures are used in all the theoretical

THE STEAM-ENGINE INDICATOR. 99

discussions and calculations of steam, vapors, and
gases, and in tables of the properties of steam.

Temperature. — For engineering purposes it is cus-
tomary to measure temperatures by the Fahrenheit
scale, which has the freezing-point of water at 32° F.
and the boiling-point at 212° F.

Absolute Temperatures. — In computations for air
and other gases it is convenient to use absolute tem-
peratures, which are obtained by adding 460°. 7 to
temperatures on the Fahrenheit scale. For example,
the absolute temperature of freezing-point is 32° +
4607 = 492°7-

Pressures. — It is customary to measure pressures in
pounds on the square inch, but for certain calcula-
tions it is convenient to take pressures in pounds on
the square foot; this gives what is called the specific
pressure. The specific pressure is consequently 144
times the pressure in pounds on the square inch.

Density. — The weight of a cubic foot of any sub-
stance is called its density. For example, one cubic
foot of water at 32° F. weighs 62.4 pounds.

The densities of several gases at 32° F. and at at-
mospheric pressure are:

Air 0.08070 pounds

Nitrogen 0.07839 "

Oxygen 0.08923 "

Hydrogen 0.005590 "

Carbonic acid 0.1234 "

100 THE STEAM-ENGINE INDICATOR.

Specific Volumes. — The volume occupied by one
pound of a substance is called the specific volume. It
is the reciprocal of the density; that is, it can be calcu-
lated by dividing i by the density. The specific vol-
umes of ordinary gases are:

Air ......................... I2-39 cubic feet

Nitrogen .................... 12.76

Oxygen ..................... 11.21

Hydrogen ................... I7&-9

Carbonic acid ................. 8. 103

Properties of Gases. — The following simple equation
allows us to calculate the properties of gases:

T' T0 '

where p, v, and T represent the pressure, volume, and
temperature, while />0, VQ, and T0 are the standard
conditions; that is,

p0 = pressure of the atmosphere;

T0 = absolute temperature of freezing-point =

492.7;

Nonspecific volume at p0 and T0.
The use of this equation can be best illustrated by
an example. Suppose that air in a certain reservoir
or cylinder has a pressure of 92 pounds above the at-
mosphere and a temperature of 70° F., so that
/ = 92 + 14.7 = 106.7,
T= 70 + 460.7 = 530.7,

THE S TEA M-ENGINE lNJ?I<*A if tf J?/ ; \>\ J \O 1
and

106.7 X v _ H-7 X 12.39
530.7~ 492-7

I4.7XI2.39X5307 = 1<g cubic feet>
492.7 X 106.7

The corresponding density or weight per cubic
foot is 0.5439 pounds.

Calculated Air-consumption. — If we know the pis-
ton-displacement of a compressed-air engine, the air-
pressure, and the speed, the amount of air can be cal-
culated with a fair degree of approximation.

It can be shown that a compressed-air engine hav-
ing a diameter of 13^ inches and a stroke of 2 feet will
develop about 100 horse-power, provided that it
makes 150 revolutions per minute and is supplied
with air at 92 pounds pressure by the gauge and at
70° F., the cut-off being at quarter-stroke.

If the diameter of the piston-rod is two inches, the
average piston-displacement will be 1.974 cubic feet.
If the clearance and compression are neglected the
engine will use an average volume of

V4 X 1.974 = 4935 cubic feet

of air per stroke. The weight of air per stroke (using
the result of the preceding problem) will be

4935 X .5439 = 0.268

TfTE STEAM-ENGINE INDICATOR.

pounds. The engine makes 150 revolutions per min-
ute, or 2 X 150 strokes, and consequently will use

2 X 150 X 0.263 = 80.4
pounds per minute, or

60 X 80.4 = 4820

pounds per hour; so that the air-consumption per
horse-power per hour will be 48.2 pounds, the engine
being assumed to develop 100 horse-power. Taking
account of compression and clearance will give about
one-tenth larger consumption. But since this calcula-
tion is put in for sake of illustration, the method of
allowing for clearance and compression need not be
given at length.

Properties of Steam. — The properties of saturated
steam determined by experiments and calculations
vary in so complex a manner that it is customary to
take them from a table. The Appendix gives a brief
table (Table II); more complete and extensive tables,
together with tables of properties of other vapors,
will be found in various works on thermodynamics
or in the author's Tables of Properties of Saturated
Steam, etc. The properties are:
/>, the absolute pressure in pounds per square inch;
t, the temperature in degrees Fahrenheit;
q, the heat of the liquid, that is, the heat required to

raise the temperature of a pound of water from

32° to the temperature t° F.;

THE STEAM-ENGINE INDICATOR, IO3

h, the total heat, or the heat required to raise a pound
of water from 32° to the temperature t° F., and
to vaporize it against the corresponding pres-
sure />;

r, the heat of vaporization, or the heat required to
vaporize a pound of water against the pressure
p after it has been raised to the temperature
f°F.;

v, the volume of one pound of steam;
d, the weight of one cubic foot of steam.

Indicated Steam-consumption. — A calculation is
sometimes made of the steam-consumption of an en-
gine by a method like that briefly illustrated above
for finding the air-consumption for a compressed-air
engine. The actual steam-consumption is often half
again as much as the calculated consumption because
there is likely to be a considerable weight of water in
the cylinder in addition to the steam. This inter-
feres with the direct usefulness of making calcula-
tions of steam-consumption from indicator diagrams.
Nevertheless such calculations are customary and
have certain interesting features. The following ex-
ample wi1! illustrate the process.

A small Corliss engine in the laboratory of the
Massachusetts Institute of Technology has the fol-
lowing dimensions:

Diameter of cylinder 8.12 inches

D;ameter of piston-rod 1.5 "

Stroke 2 feet

104 THE STEAM-ENGINE INDICATOR.

Piston-displacement: crank end... 0.6791 cubic feet

head end. . . 0.7016

Clearance in per cent of displacement: crank end. 3. 72

head end. .5.42

A test on this engine gave the following data and
results:

Boiler-pressure above the atmosphere . . 71.9 poun Is

Pressure of atmosphere 14.8 "

Pressure at cut-off: crank end 57.8 "

head end 57.3 "

Pressure at release: crank end 5.9 "

head end 14.2 "

Pressure at compression: crank end .... 4.1

head end 4.0 "

Cut-off: crank end 0.19 of stroke

head end 0.29

Release: crank end 0.950

head end 0.960

Compression: crank end 02

head end 0.03 "

Mean effective pressure: crank end.. 26.92 pounds

head end . . 37.27 "
Revolutions per minute 60.36

When cut-off occurred at the crank end the piston
was 0.19 of the stroke from the beginning, and the
volume developed by the piston was

0.19 X 0.6791 — 0.12903

THE STEAM-ENGINE INDICATOR. IO$

of a cubic foot; but the clearance is 3.72 per cent of
the piston-displacement, and added the volume

0.0372 X 0.6791 — 0.02526

of a cubic foot, giving a total of 0.1526 of a cubic foot
to be filled with steam at cut-off. Another way of
finding this same quantity is to add the clearance
directly to the cut-off, giving for the volume

(0.194-0.0372)0.6791 = 0.1543 cubic foot.
The absolute pressure at cut-off is

57.8 + 14.8 = 72.6 pounds.

From the table of properties of steam in the Appen-
dix it appears that one cubic foot of steam at 72.6
pounds pressure weighs 0.1684 of a pound. Conse-
quently the weight of steam in the cylinder at cut-off
for the crank end was

0.1543 X 0.1684 — 0.02598 of a pound.

A similar calculation for the weight of steam at re-
lease of the crank end gives for the volume of steam
in the cylinder

(0.95 + 0.0372) 0.6791 = 0.6705
of a cubic foot; at release the absolute pressure is

5.9 + 14-8 = 20.7
pounds, at which pressure a cubic foot of steam

106 THE STEAM-ENGINE INDICATOR.

weighs 0.05188 of a pound, so that the weight of
steam at release appears to be

0.05188 X 0.6705 = 0.0348
of a pound.

Again, we have for the volume in the cylinder at
compression for the crank end

(0.02 + 0.0372) 0.6791 = 0.0388

of a cubic foot; the absolute pressure at compres-
sion is

4.1 + 14.8 = 18.9

pounds, at which one cubic foot of steam weighs
0.04762 of a pound, so that the steam caught and
saved in the cylinder at compression weighs

0.0388 X 0.04762 = 0.0018
of a pound.

The same sort of a calculation for the head end
gives the following results:
Weight of steam

at cut-off, head end . 0.0405 of a pound

at release 0.0507 "

at compression .... 0.0028

The average for the two ends gives for the steam
in the cylinder

at ct t-off 0.0332 of a pound

at release 0.0422

at compression .... 0.0023 "

THE STEAM-ENGINE INDICATOR. IO/

The steam used by this engine during the test was
condensed, collected, and weighed; it amounted to
0.0621 of a pound per stroke. Now there is good
reason to consider that there is no water in the cylin-
der at the end of the exhaust, as there is abundant
opportunity for evaporation during the exhaust; con-
sequently we may consider that there is nothing but
steam in the cylinder at compression. Adding this
amount to the steam exhausted from the engine gives

0.0621 + 0.0023 = 0.0644 pounds

for the average weight of steam in the cylinder of the
engine before release occurred.

If the steam calculated from the pressure at cut-off
is compared with the sum just obtained, it appears
that of the substance in the cylinder at cut-off

0.0332

X I0° == 52 per cent

is steam and 46 per cent is water. In like manner it
appears that there is

0.0422

— ^— x ioo = 66

0.0644

per cent of steam and 34 per cent of water at release.
The proportion of water and steam in the cylinder
of an engine either at cut-off or release depends on
the size, style, and manner of running the engine.
This same engine when developing 4 horse-power
with the cut-off at 5 per cent of the stroke showed

IO8 THE STEAM-ENGINE INDICATOR

only 33 per cent of steam at cut-off; again, when
using steam at 58 pounds above the atmosphere and
with cut-off at 69 per cent of the stroke, there was 72
per cent of steam at cut-off and 76 at release. Larger
engines are likely to show a larger proportion of
steam than do small engines; superheating also re-
duces the amount of water in the cylinder at both cut-
off and release; steam-jackets have a similar effect,
and, especially when applied to compound engines,
may give dry steam at release from the low-pressure
cylinder. The study of cylinder condensation and re-
evaporation of steam-engines is one of the most in-
teresting subjects for the steam-engineer, but it is
much too extensive to be printed here.

Returning to our calculation, it appears that the
indicator shows 0.0348 of a pound of steam in the
crank end of the cylinder at release, and 0.0018 of a
pound at compression. The calculated weight of
steam exhausted may be considered to be

0.0348 — 0.0018 = 0.0330

of a pound. In like manner the head end has 0.0507
of a pound at release and 0.0028 of a pound at com-
pression, so that the calculated exhaust from the
head end of the cylinder will be

0.0507 — 0.0028 = 0.0479

of a pound. The sum of these quantities may be taken
for the exhaust per revolution, giving

0.0330 + 0.0479 = 0.0810

THE STEAM-ENGINE INDICATOR. 109

of a pound. The engine made 60.36 revolutions per
minute, consequently the steam exhausted per hour
was

60 X 60.36 X 0.0810 = 293

pounds. The horse-power calculated from the dimen-
sions of the cylinder and the mean effective pressures
is 11.7; so that the calculated steam-consumption per
horse-power per hour is

293-- 11.7 = 25

pounds. On the other hand, the actual steam-con-
sumption from the weight of steam condensed and
weighed in an hour was 37 pounds. It is well to re-
call what was laid down in the first paragraph of this
book, namely, that the indicator shows only the pres-
sure of the steam in the cylinder. The so-called indi-
cated steam-consumption of an engine is likely to be
seriously in error because it does not and cannot take
account of the water in the cylinder, which at release
is liable to be as much as one-third of the working
substance in the cylinder. When a test of an engine
has been made and the actual steam-consumption has
been determined, a calculation of the proportions of
steam and water in the cylinder at cut-off and release
is instructive, as it gives some idea of the influence of
the cylinder walls on the action of the steam. When
sufficient observations are taken during a test, it is
possible to determine more exactly the influence of
the cylinder walls by aid of an analysis proposed by
Hirn; thus a test on the engine under consider-

HO THE STEAM-ENGINE INDICATOR.

ation when running under nearly the same con-
ditions and developing n.i horse-power showed
that of the heat supplied to the cylinder by the'
entering steam 37 per cent was absorbed by the
cylinder walls during the admission up to cut-
off, that 17 per cent was returned by the walls
during expansion, and that 15 per cent was thrown
out from the walls during exhaust; the last quantity,
called exhaust waste, plays an important part in the
discussion of the losses of the steam-engine.

Steam per Horse-power per Hour. — A common way
of stating the performance of a steam-engine is to
give the steam-consumption in pounds per horse-
power per hour. The horse-power is habitually de-
termined by aid of the indicator, which affords the
means of calculating the power developed in the cylin-
der. The steam may be determined by condensing it
in a surface condenser and collecting and weighing it;
or if the engine is supplied from a boiler, or a battery
of boilers, which is used for that purpose only, the
feed-water supplied to the boilers can be weighed or
measured. In either case the test gives the means of
calculating the steam used by the engine per hour,
which may be divided by the horse-power to find the
steam per horse-power per hour.

This method of stating steam-engine performance
is open to criticism because the amount of heat re-
quired to evaporate water depends on the tempera-
ture of the feed-water supplied to the boiler and on

THE STEAM-ENGINE INDICATOR. Ill

the pressure under which the steam is evaporated.
To exhibit this, consider first the effect of supplying
the feed-water to a boiler at 102° F. and evaporating
it at 61.3 pounds by the gauge (76 pounds absolute),
as compared with supplying feed-water at 212° to the
same boiler. Now the heat of the liquid at 102° F. is
70 thermal units, and at 76 pounds pressure the heat
of the liquid is 277.8 thermal units, while the heat of
vaporization at 76 pounds is 898.2; consequently the
heat required to raise water from 100° F. and bring it
up to boiling at 76 pounds pressure is

277.8 — 70 = 207.8

thermal units, and the heat required to heat it and
vaporize it is

207.8 + 892.2 = 1106

thermal units; again, the heat required to raise the
water from 212° F. to boiling temperature at 76
pounds is

277.8 — 180.8 + 898.2 = 995.2

thermal units, the heat of the liquid at 212° F. being
180.8. The difference in this case is about eleven
per cent. Again, consider the effect of carrying 135.3
pounds by the gauge (150 absolute) instead of 61.3
pounds by the gauge. The heat of the liquid at 150
pounds absolute is 330, and the heat of vaporization is
861.2, so that the heat required to vaporize one pound
of water from 100° F. is

33° — 7° + 861.2 = 1 121.2,

112 THE STEAM-ENGINE INDICATOR.

consequently the effect of raising the pressure is
about one and a half per cent.

When part of the steam is supplied to the cylinder
of an engine and part is used in a steam-jacket from
which the condensation is returned directly to the
boiler, the inadequacy of reporting steam-consump-
tion in pounds per horse-power per hour is even more
marked.

Thermal Unit. — Heat may be measured in British
thermal units (B. T. u.); the thermal unit being de-
fined as the heat required to raise one pound of water
from 62° F. to 63° F. The properties of saturated
steam, such as heat of the liquid, heat of vaporization,
and total heat, are given in thermal units.

Thermal Units per Horse-power per Minute. — To
avoid the ambiguity of stating engine performance in
pounds of steam per horse-power per hour engi-
neers resort to the expedient of using thermal units
per horse-power per minute. This method is best
presented by an example.

Referring to the calculation of indicated steam-con-
sumption we find that the engine when developing
11.7 horse-power used 37 pounds of steam per horse-
power per hour, with a boiler-pressure of 71.9 pounds
by the gauge, or, allowing 14.8 pounds for the atmos-
phere, of 86.7 pounds absolute. With an exhaust
feed-water heater the feed-water for a boiler supplying
steam to a non-condensing engine may be raised to
212° F. The heat of the liquid at 212° F. is 180.8

THE STEAM-ENGINE INDICATOR. 1 13

B. T. u., the heat of the liquid at 86.7 pounds absolute
is 287.3 B. T. u., and the heat of vaporization is 891.2
B. T. u. The heat required to heat the water from
212° F. to a pressure of 86.7 pounds was

287.3 -- 180.8 = 106.5 B. T. u.

Now it appeared from a calorimeter test of the
steam supplied to the engine that it contained two per
cent of water; consequently the heat required to va-
porize 0.98 of a pound of steam was

0.98 X 891.2 = 873.4 B. T. u.

The heat required to form a pound of steam from
a pound of water was consequently

106.5 + 873-4 = 979-9 B- T- u-

The engine used 37 pounds of steam per hour or
37 -r- 60 pounds per minute, and consequently it re-
quired

979.9 X 37 -r- 60 = 604 B. T. u.

per horse-power per minute.

When an engine has a steam-jacket the steam sup-
plied to the jacket must be determined separately, and
the thermal units for the jacket are to be calculated
separately and added to the thermal units for the cyl-
inder.

114 THE STEAM-ENGINE INDICATOR.

Hyperbola. — It is sometimes interesting to com-
pare the expansion line of an indicator diagram with
some regular curve of the same general character.
The curve commonly chosen for this purpose is called
the rectangular hyperbola; this curve is easily drawn
and it agrees fairly well with the expansion line of
many large engines of good type. In the design of a
new engine it is customary to use the hyperbola for
the expansion line in laying out the probable indi-
cator diagram.

The method of drawing the hyperbola is shown by
Fig. 64, which represents a diagram taken from the

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V
FlG. 64.

high-pressure cylinder of a triple-expansion engine at
the Massachusetts Institute of Technology. In the first
place the diagram is referred to the axes OP and 0V
of no volume and no pressure. For this purpose lines

THE STEAM-ENGINE INDICATOR. 11$

are drawn at ab and cd which are perpendicular to the
atmospheric line and which touch the diagram at its
ends. Then st is laid off equal to the pressure of the
atmosphere (14.7 pounds), and OFis drawn parallel to
the atmospheric line. Pressures measured from 0V
are consequently absolute pressures. From b the dis-
tance Ob is laid off equal to the length of the diagram
multiplied by the clearance in per cent of the piston-
displacement, and OP is drawn perpendicular to OF;
distances measured from OP along the axis OF are
proportional to the volumes in the cylinder, including
clearance. This construction may be conveniently
made by laying a scale across the diagram so that
the zero shall come on the line dc produced, and the
one hundredth division shall come on the line ba, and
then the clearance (.09) can be read directly from the
scale beyond the one-hundredth division. Draw a line
rs through the point of release; if the release is not well-
marked a point near release may be chosen at ran-
dom. Divide the distance Ot into a convenient num-
ber of equal parts, ten for example; draw lines at the
points thus located and number them as shown.
Measure the absolute pressure tr at release; on the
diagram the pressure is 30 pounds. To find a point of
the curve on a given line divide the pressure at r by
the number of the line expressed as a decimal as indi-
cated on the diagram. For example, the pressure on
the ninth line is 30 -=- 0.9 = 33.3 pounds. The pres-
sures on the several lines are'.

THE STEAM-ENGINE INDICATOR.

30 -7- 0-9 =

30 -f- 0.8 =
30 ~ 0.7 =
30 -f- 0.6 =
30 -H 0.5 =
30 + 0.4 =

33.3 pounds
37-5 "
42.7

50.0 "
60.0 "
75-0

30 -j- 0.3 = 100.0

30 -4- 0.2 = 150.0

Sometimes the hyperbola is drawn from a point at
or near cut-off as shown by Fig. 65.

FIG. 65.

In such case after the axes 0V and OP are drawn a
line, as ef, can be drawn at or near cut-off, and
spaces equal to Of can be laid off as shown with half
or quarter spaces if necessary. The pressure on any
line can be found by dividing the pressure at cut-off
by the number of the line expressed as a whole num-
ber. For example, the pressure on the ordinate 2.\ is

125

-.- 50 pounds.

THE STEAM-ENGINE INDICATOR.

117

The hyperbola drawn on the diagram Fig. 64 from
the point of release rises above the expansion-line;
small steam-engines are likely to give diagrams on
which the hyperbola will rise even higher above the
expansion-line; large steam-engines with steam-jack-
ets may give diagrams on which the hyperbola will
cut into the expansion line as shown by Fig. 66,

FIG. 66.

which is a diagram taken from a pumping-engine
at the Chestnut Hill Station, Boston Water Works.

After the relation of the hyperbola to the expansion-
line of the diagram from an engine has been well es-
tablished some defects of the 'engine may be inferred
from drawing the hyperbola on a diagram which
has such a defect. For example, a leak through
an admission-valve will tend to keep up the pressure
and prevent the expansion-line from falling as rapidly
as it should; in such case the hyperbola will rise
rapidly away from the expansion-line when 'drawn
from a point at release. If the exhaust-valve leaks
a contrary effect will be produced and the expansion-
line will fall too rapidly.

Il8 THE STEAM-ENGINE INDICATOR.

Oscillations in Diagrams. — Diagrams taken from an
engine with high speed of rotation are likely to be de-
ranged by oscillations of the piston and pencil-motion,
as shown by Fig. 67, which was taken from a Porter-
Allen engine making 350 revolutions per minute.

FIG. 67.

On this diagram it is difficult to determine the
point of cut-off, and individual measurements of pres-
sure are liable to large errors; the mean effective
pressure and the horse-power calculated from it are
not likely to be affected by much error on account of
the oscillations; all diagrams from very high-speed
engines, whether or not they are deranged by oscilla-
tions, are liable to have larger errors than diagrams
from slow-speed engines.

Piston-friction. — Even if an indicator is in perfect
condition when put onto an engine it is likely to be-
come fouled by burnt oil or other material from the
c}4inder of the engine, which will cause excessive
friction of the indicator piston. Fig. 68 shows a dia-

THE STEAM-ENGINE INDICATOR.

gram which is slightly affected by piston-friction.
The steam-line is suspiciously straight, but that alone
might not show excessive friction; the successive

FIG. 68.

steps in the expansion-line are, however, conclusive
evidence of friction of the piston. This diagram was
taken from a slow-speed engine, so that oscillations
are not to be expected.

Fig. 69, which was taken from a locomotive, shows

FIG. 69.

an excessive amount of piston-friction. The right-
hand diagram is the normal diagram from one end of
the cylinder, and the smooth diagram at the left is

120 THE STEAM-ENGINE INDICATOR.

the normal diagram from the other end. When the
indicator was started the piston came up under the
sudden application of pressure, but stuck fast before
it had come to the top of the diagram; the pencil then
drew a straight line with the piston stuck fast till the
fall of pressure during expansion freed the piston
suddenly so that it made a number of quick oscilla-
tions, during which action the pencil moved so rap-
idly that it drew a succession of dots instead of a con-
tinuous curve; for the next revolution the pencil rose
during compression and admission until the piston

FIG. 70.

stuck again and was freed suddenly, making a char-
acteristic square step in the diagram, after which the
pencil followed the normal diagram; the succeeding
revolution shows only a little sticking after admission,
and the fourth revolution gives the normal diagram.
Whenever an indicator gives a straight line and a
square step it is well to look for friction; for example,

THE STEAM-ENGINE INDICATOR. 121

Fig. 70, from a yacht-engine shows piston-friction
very plainly.

When diagrams are taken at intervals during a
long test, the indicators must be cleaned occasionally
to avoid friction. When diagrams are taken in rapid
succession, as during speed tests of steamships, it is
advisable to keep indicators in reserve ready for im-
mediate use when there is evidence of friction in the
indicators attached to the engine.

Valve Setting. — The valves of an engine should
always be set mechanically by measurement; after the
valves are set it is well to take diagrams to detect
errors or defects, if there are any. The indicator dia-
gram may also call attention to improper restrictions
of steam pipes or passages, or to obstructions in them.

Figs. 71 and 72 were taken from a slide-valve en-

FIG. 71.

gine which was set to give equal cut-off; in such case
the lead at the head end is likely to be too small and
that at the crank end too large. Fig. 71 from the
head end of the cylinder has an admission-line that
leans slightly to the right, wrhile the admission-line of
Fig. 72 leans toward the left. Fig. 71 shows also a
peculiarity of a slide-valve which gives a large com-

122 THE STEAM-ENGINE INDICATOR.

pression; the compression-line at first rises rapidly,
then its rise is checked, and finally it falls so as to

FIG. 72.

form a hook; this action is to be attributed to leakage
under the valve to the exhaust-space or past the
piston.

Fig. 73, taken from the same engine, shows the
effect of slipping the eccentric; the cut-off is de-

FIG. 73.

layed, the release is late, and the exhaust is defective,
especially at the beginning of the return-stroke; the
compression has almost disappeared, and admission
does not occur till after the piston has started on the
forward stroke. Fig. 74 was taken after the eccentric
had been given an excessive angular advance, which
gave the engine an excessive lead, a short cut-off, and
an early release. A notable feature is the oscillation

THE STEAM-ENGINE INDICATOR. 12$

at admission, which is here spread out instead of being
confined as in Fig*. 71.

Compound Engines. — With the use of high-pres-
sure steam it has become the practice to use the
steam in two or more cylinders successively, as by
that means the ill effects of cylinder condensation can
be ameliorated. A compound engine has two cylin-
ders, a small cylinder which receives steam from the

FIG. 74-

boiler, and a large cylinder which takes the steam
from the small cylinder and delivers it to the con-
denser. A triple engine has three successive cylin-
ders, and a quadruple engine has four successive
cylinders. Sometimes the large or low-pressure cylin-
der is divided, or two cylinders are used together in
place of the low-pressure cylinder. Many marine en-
gines at the present time have four cylinders, a high-
pressure cylinder, an intermediate cylinder, and two
low-pressure cylinders.

If a compound or multiple-expansion engine has a
large receiver between the successive cylinders, into

124

THE STEAM-ENGINE INDICATOR.

which the steam is exhausted by the smaller cylinder
and from which steam is supplied to the larger cylin-
der, then the diagrams look much like those taken
from simple engines; if there is but a small space
the diagrams may appear to be much distorted.

Diagrams of the first type are given by Figs. 75

FIG. 75.

FIG. 76.

and 76, taken from a compound pumping-engine with
cranks at right angles and with an intermediate re-
ceiver. The back-pressure line of the high-pressure
diagram rises a little at the middle of the stroke, cor-
responding with the admission to the low-pressure
cylinders. The low-pressure diagram shows a distinct
falling-off in the admission-line at about one fifth
stroke, due to the closing of the exhaust-port of the

THE STEAM-ENGINE INDICATOR.

125

high-pressure cylinder; from that point to the cut-off
at about 3/10 stroke the low-pressure cylinder draws
steam from the receiver with falling pressure. With
these exceptions the diagrams resemble those taken
from simple engines.

Figs. 77 and 78 give diagrams from a compound
pumping-engine at Louisville, Ky., which has the

FIG. 77-

FIG. 78.

high-pressure and low-pressure pistons connected to
opposite ends of a short beam, so that one rises while
the other falls. Steam is transferred from the upper
end of the high-pressure cylinder to the upper end of
the low-pressure cylinder through a receiver, and in
the same way from the lower end of the small cylin-
der to the same end of the large cylinder. Admis-
sion to the low-pressure cylinder from the begin-
ning of the stroke up to cut-off consists of a direct
transfer of steam to it from the high-pressure cylin-

126

THE STEAM-ENGINE INDICATOR.

der; the low-pressure piston has four times the area
of the high-pressure piston, so that the volume of
the steam increases during this transfer and the pres-
sure falls. The back-pressure line of the high-pres-
sure diagram is affected by this fall of pressure until
cut-off occurs on the low-pressure cylinder; after that
the back-pressure line of the high-pressure diagram

FIG. 79.

rises. The relation of the diagrams during the action
just described is made clearer by redrawing the dia-

THE STEAM-ENGINE INDICATOR.

127

grams one above the other and with the same scale
of pressure as in Fig. 79.

Diagrams from the triple-expansion engine at the
Massachusetts Institute of Technology are shown by
Figs 80, 81, and 82; this engine has three horizontal

FIG. 80.

FIG. 81,

FIG. 82.

cylinders with diameters 9, 16, and 24 inches, and a
stroke of 30 inches; all the cylinders are jacketed with
steam on the heads and barrels. The back-pressure
lines of the high-pressure and intermediate diagrams
show some fluctuation of pressure due to the exhaust
of steam to receivers, and to the supply of steam from

128

THE STEAM-ENGINE INDICATOR.

the receivers to the intermediate and low-pressure cyl-
inders. The steam-lines of the intermediate and low-
pressure cylinders are also affected to some extent.

Compound and triple-expansion marine engines
commonly have no other receiver-spaces between suc-
cessive cylinders than is provided by steam-chests and
steam-pipes. There are consequently large fluctua-
tions of pressure due to the irregular way in which

FIG. 83.

FIG. 84.

FIG. 85.

steam is exhausted into and drawn from these spaces!
Figs. 83, 84 and 85 give diagrams from the U. S. S.
Manning; the back-pressure lines of the high-pressure

THE STEAM-ENGINE INDICATOR. 129

and intermediate diagrams, and the steam-lines of the
intermediate and low-pressure diagrams, show con-
siderable irregularity due to the causes named.

Combined Diagrams. — Attempts are sometimes
made to get a diagram which will show the combined
action of the several cylinders of a compound or mul-
tiple-expansion engine. The simplest method of mak-

FIG. 86.

ing a combined diagram is shown by Fig. 86, where
the diagrams from a triple engine (Figs. 83, 84, and
85) are redrawn, using the same vertical scale and
making the horizontal scale proportional to the pis-

1 30 THE STEAM-ENGINE INDICATOR.

ton-displacements of the several cylinders. The dia-
grams are then referred to axes of zero volume and
zero pressure as explained on page 114, Fig. 64; each
diagram being drawn separately and with its own
clearance. The diagram is completed by drawing a
hyperbola through the cut-off of the high-pressure
cylinder.

It does not appear that any combined diagram is
satisfactory, or that any important lesson can be
learned from such a diagram. This may be attributed
to the clearances of the cylinders, and to the restric-
tion of the capacity of the receiver-spaces between
the cylinders. If one could have an engine without
clearances, with very large receiver-spaces, and with
cylinders made of non-conducting material, then a
logical and useful combined diagram could be drawn;
the discussion of such an engine and the drawing of
the diagram is properly considered in a treatise on
thermodynamics. It may be noted that the discussion
includes that of an engine with concordant pistons,
like the Louisville engine, and without receiver-
spaces. In order that a logical combined diagram
may be drawn with clearances it is essential that the
clearances and the compressions shall be chosen so
that the weight of steam caught at compression shall
be the same for all cylinders; this is not done in prac-
tice, and there seems to be no good reason for doing
so. Again, the transfers of steam from a cylinder to
a receiver and from that receiver to the succeeding

THE STEAM-ENGINE INDICATOR. 13 l

cylinder, as, for example, that shown by Figs. 77 and
78 for the Louisville engine, have certain relations
which are not shown at all in the combined diagram,
or else they are misrepresented. Finally the hyper-
bola has a doubtful place on any steam-engine dia-
gram, and can have no relation to more than one indi-
vidual diagram of any combined diagram. Attempts
have been made to meet the several objections that
have been mentioned to the method here given for
combining diagrams from compound engines which
have on the whole added to the complexity of the
diagram without making it more logical or more
useful. Other curves than the hyperbolae have some-
times been drawn on combined diagrams, such as the
adiabatic line which would be drawn by an indicator
for expansion in a non-conducting cylinder; such
curves, again, increase the labor of drawing the dia-
gram without adding to its usefulness.

Pump Diagrams. — Indicator diagrams are taken
from the pump cylinders or pump chambers of pump-
ing-engines to reveal the losses of pressure on the
way to and from the pump, to determine the power ex-
pended in the pump, and to investigate the action of
the pump valves. A discussion of the actions of
pumps and their valves is too large a subject to take
up here. It will suffice to give a few examp^s. Fig.
87 gives a diagram taken from the engine at Louis-
ville, and Fig. 88 a diagram from the engine at Ches*>
nut Hill; the former makes 18.5 revolutions per min-

132

THE STEAM-ENGINE INDICATOR.

ute, and the second makes 50.5 revolutions per min-
ute. It is but proper to call attention to the fact that

FIG. 87.

FIG. 88.

while the oscillations in a pump diagram are due to
shocks and sudden changes of pressure, they belong

FIG. 89.

FIG. 90.

rather to the indicator than to the pump, as is also
the case with oscillations in a steam-engine diagram.
Direct-acting Pumping-engine. — Figs. 89 and 90 give

THE STEAM-ENGINE INDICATOR. 133

diagrams from the steam-cylinders and the pump-cyl-
inder of a compound duplex direct-acting pumping-
engine. The diagrams from the high-pressure cylinder
and the low-pressure cylinder are superimposed in
their proper relation. Steam is supplied to the high-
pressure cylinders through the whole forward stroke,
and is transferred through a receiver to the low-
pressure cylinder through the whole return-
stroke. This engine has no fly-wheel and cannot
have a cut-off for either cylinder; moreover, there
must be a large receiver-space so that the fall
of pressure during the transfer of steam from the
high-pressure to the low-pressure cylinder shall be
moderate. The high-pressure diagram shows a rise
of pressure at about quarter-stroke due to the pause
which the other engine makes at the end of a stroke
before beginning another. Each low-pressure cylin-
der of the engine has separate steam and exhaust pas-
sages, the latter being inside. When the piston nears
the end of its stroke it overruns and closes the ex-
haust-passage, and thus produces a compression to
stop the engine at the end of the stroke. The exact
compression required is attained by providing a by-
pass valve through which the steam caught at com-
pression can leak out; if this valve is closed the en-
gine makes a short stroke; the valve can then be
opened to such an extent that the piston shall nearly
but not quite strike the cylinder head.

The pump diagram shows a ragged line at the left

134 THE STEAM-ENGINE INDICATOR.

end caused by the superposition of oscillations of the
indicator-pencil, due to the sudden rise of pressure in
the pump chamber when the pump is reversed; there
are also oscillations near the right end which are
transmitted from the other pump when that engine
reverses.

Air-compressor. — A diagram from an air-com-
pressor is represented by Fig. 91; at the beginning of
the stroke the air in the clearance-space is expanded
down to or a little below the pressure of the atmos-

FIG. 91.

phere as represented by ab] the pressure rises to that
of the atmosphere as soon as the admission-valve
opens and the cylinder is filled as represented by be;
the compression is represented by cd; and from d to a
the air is forced into a reservoir, the variations of
pressure being due to the action of the delivery-
valves. This diagram was taken from the larger cyl-
inder of a compound or two-stage compressor, which
compresses air to about 37 pounds above the atmos-
phere and delivers it to a tubular intercooler. Cold
water circulated through the pipes of the intercooler
cools the air to the temperature of the atmosphere,
with a notable reduction in volume. The cooled air is

THE STEAM-ENGINE INDICATOR.

135

drawn in by a smaller cylinder, where it is further
compressed to about 95 pounds above the atmosphere.
Fig. 92 shows a combined diagram of the diagrams
from both the cylinders of this compound compres-
sor, drawn with the same scales of pressure and vol-
ume as explained for steam-engines on page 129; the

objections urged against combined diagrams at that
place apply equally here.

On Fig. 92 are drawn two theoretical curves for
air, the adiabatic curve, which represents compression
in a perfectly non-conducting cylinder, and the iso-
thermal line, which represents compression at a con-
stant temperature; the isothermal line is a rectangular
hyperbola for which the construction is given on page
114. The construction of adiabatic and isothermal

136

THE STEAM-ENGINE INDICATOR.

curves for air has a real significance because there is no
question of the composition of the fluid in the cylin-
der; the case is quite different from the drawing of a
hyperbola on a steam-engine diagram. It is custom-
ary to cool the cylinder of a compressor by injecting
water into the cylinder or by circulating water
through a water-jacket; the effect of the water is
mainly to keep the cylinder cool, for the air is cooled
but little at ordinary pressures. Three- or four-stage
compressors, which deliver air at 1000 to 2000 pounds
to the square inch, show an appreciate cooling of the
air at high pressures in the small cylinders. Fig. 92
shows that, there is but little cooling of the air in the
large cylinder, for the compression-line falls only a
little below the adiabatic line along which it would lie
were there absolutely no cooling. The isothermal line

passes through the beginning of each diagram, which
shows that the intercooler reduces the temperature cf
the air to that of the atmosphere. To avoid confusion,
the adiabatic line for the small cylinder is omitted.

THE STEAM-ENGINE INDICATOR. 137

The overlapping of the diagrams exhibits the fact that
some pressure is required to force the air through the
intercooler into the small cylinder.

The isothermal line can be drawn as explained on
page 114, Fig. 64, and shown by Fig. 93, by di-
viding the space from c to the axis (including
the clearance) into a convenient number of equal
parts, ten for example. The dividing points may
be numbered o.i, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8,
and 0.9; on lines drawn through these points we
may lay off pressures obtained by dividing the
pressure at c by the decimals at the points of division;
or the required pressures can be obtained by multi-
plying the pressure at c by the factors given in the sec-
ond line of the following table:

TABLE FOR DRAWING ISOTHERMALS AND ADIABATICS OF AIR.

Points 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Isothermal.. 5 3.33 2.5 2.0 1.67 1.43 1.25 i.n

Adiabatic 9.6 5.43 3.62 2.65 2.05 1.65 1.37 1.16

The points on the adiabatic line may be found by
laying off from the points of division pressures found
by multiplying the pressure at c by the factors given
on the third line of the table; the method of calcu-
lating these factors can be deduced from the theoreti-
cal investigation of air in any treatise on thermody-
namics.

Air-pump. — An air-pump has for its main duty the
removal of air from the condenser; this air is brought
in by the condensing water of a jet condenser, or else

138

THE STEAM ENGINE INDICATOR.

it leaks in around the piston-rod of the engine or else-
where; a surface condenser is subject to accumulation
of air mainly, if not entirely, by such leakage. A com-
parison of Fig. 94, taken from an air-pump, with Fig.
91, from an air-compressor, will show the essential
similarity between the two machines.

Air and vapor in the clearance of the air-pump are
expanded from a to b till the pressure is somewhat less

FIG. 94.

than the absolute pressure in the condenser; during
this operation there may be some vaporization of
water in the air-pump. The pump draws air and wa-

FIG. 95.

ter from the condenser from b to c; from c to d the air
and any vapor in the pump are compressed up to the
pressure of the atmosphere; from d to a air and water

THE STEAM-ENGINE INDICATOR. 139

are forced out through the delivery-valves of the air-
pump.

Fig. 95 gives the diagram from the steam-cylinder
which drives the air-pump from which Fig. 94 was
taken. This air-pump is arranged like a direct-acting
steam-pump with the steam-piston and pump piston
on one rod and without a fly-wheel. Such an arrange-
ment for a water-pump is good mechanically, because
the constant resistance of the pressure of the water
requires a constant pressure in the steam-cylinder for
smooth running; but the air-pump diagram shows no
resistance at the beginning of the stroke; indeed the
air in the clearance urges the pump piston forward till
the admission-valves open to supply air to the filling
end of the pump cylinder. After the pump has made
half to three-quarters of its stroke the pressure of the
air on the delivering end of the air-pump is raised by
compression so that it offers a large resistance; the
effect of this action is that the pump and steam pis-
tons jump quickly half or more of their stroke, then
they are checked, and complete the stroke slowly.
To avoid too great irregularity of action the steam-
passages are restricted so that the steam is throttled
from e to f while the pistons jump forward; the steam-
pressure rises from f to g, and the stroke is completed
under nearly full steam-pressure from g to h. During
the return-stroke the back-pressure line is raised dur-
ing the sudden motion of the piston for half or more
of the stroke, but when the pistons slow up and com-

140 THE STEAM-ENGINE INDICATOR.

plete the stroke quietly the back-pressure line drops
as shown by klm. In conclusion we see that the
steam-cylinder is finally filled at full steam-pressure,
and that it exhausts its steam completely, but the
effective area is much reduced; from which we recog-
nize that the direct-acting air-pump must use a large
amount of steam per horse-power per hour.

Gas-engines. — The explosive or internal-combus-
tion gas-engine is a single-acting engine which makes
two revolutions, and four strokes of its piston, for
each working impulse. Fig. 96 is a diagram from a

FIG. 96.

35-horse-power gas-engine at the Massachusetts In-
stitute of Technology. The first or filling stroke
draws in an explosive mixture of gas and air as repre-
sented by ab; the second stroke compresses the charge
from b to c, giving a pressure of 60 pounds at c; at c
the charge is ignited by an electric spark, and the
pressure rises to 310 pounds at d; work is done during
the expanding or working stroke, represented by de\
at e release occurs, and the contents of the cylinder are
exhausted during the fourth stroke, bringing the dia-
gram to its close at a.

THE STEAM-ENGINE INDICATOR. 141

Gasoline-engines are explosion engines which are
charged with a mixture of air and vapor of gasoline
which is made as it is used. Oil-engines use a safe oil
like kerosene; as kerosene will not vaporize com-
pletely like gasoline, special arrangements are re-
quired for spraying it or otherwise mixing it with air.
Deisel Motor. — This engine is an internal-combustion
engine which makes four strokes for each impulse, as
does the gas-engine. During the filling stroke only
atmospheric air is drawn in, and this air is compressed
during the second stroke to 500 pounds pressure and is
heated to 1000° F. Oil of any character, including
heavy petroleum refuse, may be injected into the cyl-

FIG. 97.

inder after the compression is completed, and will burn
immediately in the strongly heated air; after the oil
has been injected the engine makes its expansion or
working stroke. Fig. 97 shows the similarity to the
ordinary gas-engine.

Ammonia Refrigerating-machine. — An intense de-

142

THE STEAM-ENGINE INDICATOR.

gree of cold can be attained by vaporizing a volatile
liquid like ammonia, which boils at — 27° F., under
the pressure of the atmosphere. In order to use the
vapor again it must be compressed, and liquefied at
or about the temperature of the atmosphere, by the aid
of a stream of cooling water. Fig. 98 shows a dia-
gram from the compression-cylinder of an ammonia
refrigerating-machine. From a to b the pressure falls

FIG. 98.

until the inlet-valves open, and then the compression-
cylinder fills with vapor of ammonia, which comes
from the vaporizing coils of pipes, where a low tem-
perature is produced. At the end of the filling stroke
be the compression begins, and is carried at d to the
pressure in the condenser; da represents the forcing
of the vapor through the delivery-valves into the con-
denser; the irregularity of the line da is due to the
fluttering of the valves. The condenser is made of
coils of pipe cooled by water, which may flow
over the pipes or may circulate among them, ac-

THE STEAM-ENGINE INDICATOR. 143

cording to the arrangement of the condenser.
The vapor drawn into the compressor cylinder is
usually dry, that is, it contains no liquid am-
monia. If that is so, the compression-curve agrees
nearly with the adiabatic line for superheated or gas-
eous ammonia. This adiabatic line may be constructed
in the same way as the adiabatic line for a perfect gas,
as shown by Fig. 93, page 136, except that the multi-
pliers must be taken from the following table:

TABLE FOR ADIABATIC LINE FOR AMMONIA.

Points 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Multipliers. 8.55 4.98 3.39 2.52 1.98 1.61 1.35 1.15

If the engineer in charge of an ammonia compres-
sor has found, by drawing adiabatic lines on diagrams
taken when the compressor is in good condition, the
proper relation between the compression-line and the
corresponding adiabatic line, then he may infer from
the application of that line to a given diagram what
the condition of the compressor is; he may be able
thus to locate leaks in valves or past the piston.

APPENDIX.

TABLES:— AREAS OF CIRCLES— PROPERTIES OF
SATURATED STEAM— HEAT OF THE LfQUID
—LOGARITHMS.

APPENDIX.
TABLE I.

AREAS OF CIRCLES.

147

Diam.

Area.

Diam.

Area.

Diam.

Area.

Diam.

Area.

Diam.

Area.

.1963

132-7

615.8

1662

4537

.2485

13*

137-9

28}

^26.8

46*

1698

4596

.3068

^3*

28*

637-9

1735

4657

• 3712

13*

148.5

28}

649.2

47*

1772

77*

47>7

.4418

J53-9

660.5

1810

4778

.5185
.6013

14*
M*

159-5
165.1

29*
29*

672.0
683.5

48*
49

1847
1886

78*
79

4840
4902

.6903

14*

170.9

29*

605.1

49*

1924

79*

4963

.7854

176.7

706.9

1964

5027

.9940

15*

182.6

30*

718.7

50*

2003

8oj

5090

1.227

'5*

188.7

30*

730.6

2043

5153

»t

1.485

i5*

194.8

3o*

742.6

5i*

2083

81}

5217

1.767

20 1 . i

754.8

2124

5281

2.074

16*

207.4

3i*

767.0

2165

82*

5346

2.405
2.761

16*
16*

213.8
220.4

3'*

779-3
791-7

2206

2248

83
83*

54"
5476

3-142

227.0

804.2

2290

5542

4-909

I7i
17*

233-7
240.5

32*

816 9
829.6

54*

2333
2375

84*
85

5608
5675

5-940

17*

247-5

32*

842.4

55*

2419

85*

5742

7.069

254-5

855.3

2*63

5809

8.296

18*

261.6

33*

868.3

56*

2507

86*

5877

9.621
11.04

18*

18}

268.8
276. i

33t
33*

881.4
894.6

2552
2597

87*

5945
6013

"•57

283-5

907.9

2642

6082

14.19

19*

291.0

34*

921.3

58*

2688

88*

6151

15.90

19*

298.6

34*

934.8

2734

6221

17.72

19*

306.4

34*

948.4

59*

2781

89*

6291

19.64

314.2

962.1

2827

6362

21.65

20*

322.1

35*

975.9

60*

2875

90*

6432

23.75

20*

330.1

35*

989.8

2922

6504

25.97

20}

338.2

35*

1004

61*

2971

6576

28.27

346.4

1018

3019

6648

30.68

21}

354-7

36*

1032

62*

3068

92*

6720

33-i8

21*

363.1

36*

1046

31*7

6793

35.78

21}

371-5

36*

1061

63*

3l67

93*

6866

38.48

380.1

1075

3217

6940

7*
7*

41.28
44-18

388.8
397-6

37*
37*

1090
1105

64*
65

3268
33'8

94*
95 1

7014
7088

7*
8

47.17
50.27

22}
23

406.5
4I5.5

37*
38

1 120

"34

65*
66

3370
3421

7163
7238

53-46

23*

424.6

38*

1149

66*

3474

96*

73M

56.75

23*

433-7

1164

7390

60. i

23*

443-0

38*

"79

67*

3578

97*

7466

63.62

452.4

"95

3632

7543

67.20

24*

461.9

39*

1210

68 i

3685

98*

7620

70.88

24*

471.4

39*

1225

3739

7697

74-66

24}

481.1

39*

1241

69*

3794

99*

7776

78.54

490-9

1257

3848

100

7854

10}

82.52

25*

500.7

40*

1288

70*

39°4

101

Son

10*

86.59

25*

510.7

1320

3959

102

8171 -

10}

90.76

25*

520.8

4'*

1352

4015

lO^

8332

95-03

530-9

1385

4072

104

8495

99-50

26}

541.2

42*

1418

72*

4128

105

8659

11*

103.9

26*

551-5

H52

4185

106

8825

108.4

26}

562.0

43*

1487

73*

4243

107

8992

"3-1

572.6

1521

4301

108

9161

12}

117.9

27*

583.2

44*

T555

74*

4359

109

9331

12*
12}

122.7
127.7

27*
27*

'590
1626

4418
4477

110

9503
9677

148

APPENDIX.
TABLE II.

PROPERTIES OF SATURATED STEAM.

Volume

Weight

Pressure
Pounds
per
Square
Inch.

Tempera-
ture
Degrees
Fahren-
heit.

Heat
of the
Liquid.

Total
Heat.

Heat
of
Vaporiza-
tion.

in
Cubic
Feet
of
One

in
Pounds
of
One
Cubic

Pressure
Pounds
per
Square
Inch.

Pound.

Foot.

T02

70.0

1113.1

1043.0

334-6

0.00299

126.3

94.4

1120.5

1026.1

173-6

0.00576

141.6

109.8

1125.1

1015.3

118.4

0.00844

igg.I

121.4

1128.6

1007.3

90.31

0.01107

162.3

*30-7

1131 .5

1000.8

73.22

0.01366

170.1

138.6

"33-8

995-2

61.67

0.01622

176.9

M5-4

"35-9

990-5

53-37

0.01874

182.9

H37-7

986.2

47.07

0.02125

t88.3

156.9

"39-4

982.5

4a-I3

0.02374

193 .3

161 .9

1140.9

979.0

38.16

0.02621

197.78

166.5

"42 3

975-8

34-88

0.02866

202 o

1 70.7

1143.6

972.9

32- >4

0.03111

205.9

174.6

1144.7

970.1

29.82

0.03355

209.6

178.3

H45.8

967-5

27 -79

o . 03600

212.0

180.3

1146.6

965-8

26.60

0.03760

216.3

185.1

1147.9

962.8

24-59

0.04067

222.4

i9'-3

1149.8

958.5

22. CO

0.04547

228.0

196 9

"5'« 5

954-6

19.01

0.05023

233-1

202. o

1153.0

951.0

18.20

0-05495

»4

237-8

206.8

"54-4

947-6

16.76

0.05966

24O.2

211. 2

1155.8

944-6

15.55

0.06432

246.4

215-4

II57-I

94T-7

14.49

0.06899

250.3

219.4

"58.3

938.9

13.59

0.07360

254.0

223.1

"59-4

936.3

12.78

0.07820

257.5

226.7

1160.4

933-7

12.07

0.08280

260.9

230.0

1161.5

931 5

H-45

0.08736

264. t

233-3

1162.5

929.2

10.88

0.09191

267.1

236.4

1163 4

927.0

10.37

0.09644

27O. I

239-3

1164.3

925.0

9.906

0.1009

272.9

242.2

1165.2

923.0

9.484

0.1054

275-7

245.0

1166.0

921.0

9.097

0.1099

278.3

247.6

n66.8

919.2

8.740

0.1144

5°

280.9

250.2

1167.6

9I7-4

8.414

0.1188

5°

283.3

252 7

1168.4

9'5-7

8. 1 10

0.1233

285.7
288.1

255-1
257 5

1169. i
1169.8

914.0
912.3

7.829
7-568

0.1277
0.1321

290.3

259-7

1170.5

910.8

7-323

0.1366

292.5

261.9

1171.2

909-3

7.096

0.1409

294.7

264.1

1171.8

6.882

0.1453

296.7

266.2

1172.4

906.2

6.680

0.1497

298.8

268.3

1173.0

904.7

6.490

0.1541

300.8

270-3

1173.6

903.3

6.314

0.1584

302.7

272.2

"74-3

902.1

6.144

0.1628

304.6

274.1

1174.9

900 8

5-984

0.1671

306.5

276.0

"75-4

899.4

5-834

0.1714

308.3

277-8

1176.0

898.2

5.691

0.1757

310.1

279.6

1176.5

896.9

5 554

0.1801

3«.8

281.4

1177.0

895.6

5.425

0.1843

3I3.5I

283.2

1177.6

894.4

5.301

0.1886

APPENDIX.
TABLE II. — Continued.

PROPERTIES OF SATURATED STEAM.

149

Volume

Weight

Pressure
Pounds
per
Square
Inch.

Tempera-
ture
Degrees
Fahren-
heit.

Heat
of the
Liquid.

Total
Heat.

Heat
of

Vaporiza-
tion.

in
Cubic
Feet
of
One

in
Pounds
of
One
Cubic

Pressure
Pounds
per
Square
Inch.

Pound.

Foot.

316.0

285.8

1178.3

892.5

5-125

0.1951

320.0

290.0

1179.6

889.6

4 858

0.2058

323-9

294.0

1180.7

886.7

4.619

0.2165

100

327.6

297.9

1181.9

884.0

4-403

0.2271

IOO

JOS

33'-1

301.6

1182.9

801-3

4.206

0.2378

105

334-6

305.2

1184.0

878.8

4.026

0.2484

337-9

308.7

1185.0

876.3

3-86«

0.2589

1 20

34* -1

312.0

i i 86.0

874.0

3«7"

o 2695

T20

344-1

315-2

1186.9

871.7

3-572

0.2800

I2S

13°

347-1

318.4

1187.8

869.4

3-444

0.2904

130

»3S

350-0

321.4

1188.7

867 3

3-323

0.3009

*35

140

352.9

324.4

1189.5

865.1

3.212

o-3"3

140

145

355-6

327.2

1190.4

863.2

3-J07

0.3218

150

155

3f.3
360.9

330 0

332.7

1191.2
i 192.0

861.2
859-3

3.011

• Qi9

0.3321
0.3426

150
*55

160

36V4

335-4

1192.8

857-4

-833

0-3530

160

165

365-9

338.0

1193.6

855-6

•751

0-3635

165

170

368.3

340.5

JI94-3

853.8

.676

0-3737

170

175

370.7

343-0

1195.0

852.0

603

0.3841

175

1 80

373-0

345-4

iig5.7

849-3

•535

0-3945

i So

185

375-2

347-8

1196.4

848.6

•470

0.4049

185

190

377-4

350-1

1197.1

847.0

.408

0-4153

190

*95

379-6

352.4

1197.7

845.3

•349

0.4257

195

200

381-7

354-6

1,98 4

843 8

•294

0-4359

200

205

383.8

356.8

1199.0

842.2

.241

0.4461

205

2IO

385-9

358.9

1199.6

840.7

.190

o.4565

2TO

215

387-9

361.0

I2OO.2

839.2

.142

0.4669

215

2 2O

389.8

363.0

12OO.8

837.8

.096

0.4772

220

225

391.8

365.t

I20I.4

836.3

.051

o 4876

225

230

393-7

367-1

I2O2.O

834-9

.009

0-4979

230

235

395-6

369-0

1202.6

833-6

.968

0.5082

235

240

397-4

37i.o

I2O3.2

832.2

.928

0.5186

240

245

399-2

372.8

1203.7

830.9

.891

0.5289

245

250

401.0

374-7

1204.2

829.5

•854

0-5393

350

255

402.7

376.5

1204 8

828.3

.819

0.5496

2SS

260

4°4-5

378.4

1205-3

826.9

-785

0.5601

260

265

406.2

380.2

1205.8

825.6

•753

0-5705

265

270

407-9

381.9

1206.3

824.4

.722

o 5809

270

275

409-5

383-6

1206 8

823.2

.691

0-1913

280

411.1

385-3

1207.3

822.0

.662

0.602

280

285

412.7

387.0

1207.8

820.8

-634

0.612

285

290

4U-3

388.6

1208.3

819.7

.607

0.622

290

295

4IS.9

390.3

1208.8

818.5

.580

0.633

295

300

417.4

39T-9

1209.3

8,7.4

•554

0.644

300

305

418.9

393-5

1209.7

810.2

•529

0.654

305

310

420.4

395-0

I2IO.2

815.2

•505

0.664

310

3'5

421.9

396.6

I2IO.6

814.0

.48t

0-675

3*5

320

423-4

398.1

I2II.I

813.0

•459

0.685

320

325

424.8

399-6

I21I.5

811.9

•437

0.696

32S

APPENDIX.
TABLE III.

HEAT OF THE LIQUID.

Temp.
Deg. F.

Heat of
Liquid.

Temp.
Deg. F.
t

Heat of
Liquid.

Temp.
Deg. F.

Heat of
Liquid.

Temp.
Deg. F.

Heat of
Liquid.

46.10

124

92.

170

nS-s

1 .01

47.09

125

93-

171

139-5

2.01

48.09

126

94.

140.5

3-02

49.08

127

95-

141-5

4.03

50.08

128

96.

142-5

5-04

5!-07

129

97-

143-5

6.04

52.07

130

98.

T44-5

7.05

53-o6

131

99.

J45-5

8.06

54.06

132

100.

146-5

9.06

55-05

133

1OI .

H7-5

10.07

56.05

134

102. !

180

148.5

11 .07

57-04

135

103.

181

149-5

12. 08

58.04

136

104.

182

150.6

IJ.OS

59-03

137

IO5.

183

151 .6

14.09

60.03

138

106.

184

152-6

15.09

61 .03

139

107.

185

*53-6

16. 10

62.02

140

108.

186

154.6

17. 10

63.02

141

109.

187

I55-6

18.10

64.01

142

1 IO.

188

156.6

19.11

65.01

143

iti.

189

157-6

20.11

66.01

144

112. 2

190

158.6

21. II

67.01

145

I13-3

191

159.6

22.11

100

68 01

146

"4-3

192

160.6

23.11

101

69.01

147

JI5-3

193

161.6

24.11

102

70.00

148

116.3

194

162.6

25.12

103

71.00

149

"7-3

195

l63-7

26.12

104

72.0

150

118.3

196

164.7

27.12

105

73-o

151

119.3

197

T6s-7

28.12

106

74.0

152

120.3

198

166.7

29.12

107

75-o

153

121.3

199

167.7

30.12

108

76.0

154

122.3

200

168.7

31.12

109

77.0

155

123-3

201

169.7

32.12

110

78.0

156

124.3

202

170.7

33.12

111

79-o

157

125.4

203

171.7

34.12

112

80.0

158

126.4 i

204

172.7

35-12

113

Bx.o

159

127.4

205

T73-7

36.12

114

82.0

160

128.4

206

J74-7

37.12

115

83.0

161

129.4

207

175-8

38-11

116

84.0

162

130.4

208

176.8

39-"

117

85.0

163

I3I-4

209

177.8

40.11

118

86.0

164

132.4

210

178.8

41.11

119

87.0

165

I33-4

211

179.8

42.11

120

88.1

166

J34-4

212

180.8

43-11

121

89.1

167

I35-4

44.11

122

90.1

168

136.4

45-iQ

123

91.1

169

137-4

APPENDIX.
TABLE IV.

LOGARITHMS.

Proportional Parts,

123

456

7 8 9

oooo

0043

0086

0128

0170

0212

0253

0294

0334

0374

4 8 12

17 21 25

29 33 37

0414

°453

0492

053*

0569

0607

0645

0682

0719

0755

4 8 ii

15 19 23

26 30 34

0792

0828

0864

0899

°934

0969

1004

1038

1072

1106

3 7 >o

14 17 21

24 28 31

"39

"73

1206

1239

1271

1303

1335

1367

1399

1430

3 6 10

13 16 19

23 26 29

1461

1492

1523

1553

1584

1614

1644

1673

17°3

1732

369

12 15 18

21 24 27

,761

1790

1818

1847

1875

1903

1931

T959

1987

2014

3 6 8

IT 14 17

20 22 25

2041

2068

2095

2122

2148

2175

2201

2227

2253

2279

3 5 8

ii 13 16

18 21 24

2304

2330

2355

2380

2405

2430

2455

2480

2504

2529

5 7

IO 12 15

17 20 22

2553

2577

2601

2625

2648

2672

2695

27I8

2742

2765

5 7

9 12 14

16 19 21

2788

2810 2833

2856

2878 2900

2923

2945

2967

2989

4 7

9 " *3

16 18 20

3010

3032 3054

3075

3096 3118

3139

3160

318.

3201

4 6

8 ii 13

*5 »7 19

3222

3243

3263

J3°4

3324

3345

3365

3385

3404

4 6

8 10 12

14 16 18

2-2

3424

H44 3464

3483

3502

3522

3541

356o

3579

3598

4 6

8 10 12

M 15 17

3617

3636

3655

3674

36^2

37"

3729

3747

3766

3784

4 6

7 9 ii

13 15 17

3802

5820

3838

3856

3874

3892

3909

3927

3945

3962

4 5

79"

12 14 16

3979

3997

4014

403 *

4048 4065

4082

4099

4116

4133

3 5

7 9 10

12 14 15

4150

4166

4183

42OO

4216

4232

4249

4265

4281

4298

3 5

7 8 10

II 13 15

43H

4330 4346

4362

4378

4393

4409

4425

4440

4456

3 5

689

II 13 14

4472

4487

4502

4518

4533

4548

4564

4579

4594

4609

3 5

689

II 12 14

4624

4639 4654

4669

4683 4698

47*3

4728

4742

4757

3 4

679

10 12 13

4771

4786 4800

4814

4829 4843

4857

4871

4886

4900

3 4

679

IO II 13

4914

4928 4942

4955

4969 4983

4997

5011

5024

5038

3 4

678

10 II 12

5051

5065

5079

S092

5IO5

5"9

5i32

SHS

5159

5172

3 4

5 7 8

9 II 12

=^85

5198

52"

5224

5237

5250

5263

5276

5289

5302

3 4

568

9 10 12

5315

532^5340

5353

5366 5378

539'

5403

5416

5428

3 4

5 6 8

9 10 ii

5441

5453 5465

5478

5490 5502

55'4

5527

5539

555'

5 6 7

9 10 ii

5563

5575

5587

5599

5611

5623

5635

5647

5670

5 6 7

8 10 ii

5682

5694

5705

57[7

5729

5740

5752

5763

5775

5786

5 6 7

8 9 10

5798

5809 5821

5832

5343

5855

5866

5877

5888

5899

5 6 7

8 9 10

59"

5922 5933

5944

5955

5966

5977

5988

5999

6010

457

8 9 10

6021

6031

6042

6053

6064 6075

6085

6096

6107

6117

4 5 6

8 9 "

6128

6138

6149

6160

6170

6180

6191

6201

6212

6222

4 5 6

789

6232

6243 6253

6263

6274 6284

6294

6304

63M

6325

4 5 6

7 8 9

6335

6345

6355

6365

6375

6385

6395

6405

6415

6425

4 5 6

789

6435

6444

6454

6464

6474 6484

6493

6503

65*3

6522

4 5 6

7 8 9

6532

6542

6551

6561

6571

6580

6590

6599 6609

6618

4 5 6

789

6628

6637

6646

6656

6665

6675

6684

6693 6702 6712

4 5 6

778

6721

6730

6739

6749

6758

6767

6776

6785 6794

6803

455

6 7 8

6812

6821

6830

6839

6848 6857

6866

6875

6884

6893

445

678

6902

6911

6920

6928

6937

6946

6955

6964

6972

6981

445

6 7 8

6990

6998 7007

7016

7024

7033

7042

7050

7°59

7067

345

678

7076

7084

7093

7101

7110

7118

7126

7*35

7*43

7'52

345

678

7160

7168 7177

7185

7193 7202

7210

7218

7226

7235

345

6 7 7

7243

7251

7259

7267

7275

7284

7292

7300

345

667

7324

7332 734°

7348

7356 7364

7372

7380

7388

7396

345

667

152

APPENDIX.
TABLE IV '.—Continued.

LOGARITHMS.

Proportional Parts.

123

456

789

7404

7412

7419

7427

7435

7443

745'

7459 7466

7474

345

5 6 7

56 (7482

749°

7497

7505

75'3

7520 7528

7536 7543

755i

345

5 6 7

67 |7559

75^6

7574

7582

76^7

7589

7597 7604

7612 7619

7627

3 4 5

5 6 7

69 77°9

7716

7^49

7723

7°57
773'

7738

7745

/ v/ V

7752

7760 7767

7774

344

5 6 7

7782

7789

7796

7803

7810

781817821;

7832 7839

7846

344

566

61 7853

7860

7868

7875

7882

78897896

7903 7910

7917

344

5 6 6

62 (7924

7931

7938 7945

7952

7959:7966

7973 798o

7987

334

566

63 [7993

8000

8007

8014

8021

8028, 803 s

8041 8048

8055

334

5 5 6

64 8062

8069

8075

8082

8089

8096^102

8109 8116

8.22

334

5 5 6

65 8120

8176

8142

8l4Q

3i 6

8162 816

8176 8182

8189

66 Si.js

J I JU
?2O2

8209

O14v
8215

8222

3228 823;

8241 8248

8254

334

5 5 6

67 826!
68 832^

8267)8274
3331 8338

8280
8344

8287
8151

8293 8209
8357 8363

8306 8312
8370 8376

8319
8382

334
334

5 5 6
5 6

69 8388

3395

8401

8407

3420 ,8426

8432 8439

8445

234

5 6

70 8451

3457

8463

8470

8476

8482

8488

8494^8500

85of

234

5 6

71 '8513

8519

8525

8531

8537

8543

8549

8555856.

8567

234

5 5

72 8573

3579

8585

8591

8597

8603

8600

8615 8621

8627

2 3 4

5 5

73 ,8633
74 8692

lell

8645 8651
8704 8710

8657
8716

8663
8722

8660
8727

8675!868i
8733^739

8686
8745

75 8751

8756

8762

8768

8774

8779

8785

8701 8797

8802

233

5 5

76 [8808

88i4

8820 8825

8837

8842

8848 8854

8859

2 3 3

5 5

77 8865

887i

88768882

S837

8893

8899

8904 8910

8915

2 3 3

4 5

78 8921

8927

89328938

8943

8949

8954

8960 8965

8971

233

4 5

79 I8976

8982

89878993

8998

9004

9009

9015

9020 9025

233

4 5

80 19031

9036

9042 9047

9053

9058

9063

9069

9074

9° 79

233

445

81 9085

9090

9096 9101

9106

9112

9117

9122 9128

9!33

233

445

9138

9143

9149 9154

9*59

9*65

9170

9175 9i8o

9.86

233

445

9191

9196

9201 9206

9212

9217

9222

9227 9232

9238

233

445

9243

9248

9253 9258

)263

9269

9274

9279

9284

9280

233

445

9294

9299

9304 9309

9315

9320

9325

9330

9335

934"

233

445

9345

9350

9355 936o

9365

737°

9375

9380

9385

9390

233

445

9395

9400

9405 9410

9415

9420

9425

9430

9435

9440

2 3

344

9445

945°

9455 946o

9465

9469

9474

9479

9484

9489

2 3

344

9494

499

9504 9509

9513

95i8

9523

9528

9533

9538

» 3

344

90
91

9542
959°

9547
9595

9552 9557
9600 9605

9562
9609

9566
9614

9571
9619

9576
9624

9586
9633

2 3
2 3

344

9638

9643

9647 9652

9657

9661

9666

9671

9675

9680

2 3

344

9685

9689

9694 9699

9703

9708

9713

9717

9722

9727

2 3

344

973 i

9736

974^9745

9750

9754

9759

9763

9768

9773

2 3

344

9777

9782

9786^791

9795

9800

9805

9809

9814

9818

2 3

344

96
97

9823
9868

9827
9872

9832 9836
98779881

9841
9886

9845
9890

9850
9894

9854
9899

9859
9903

9863
9908

2 3

344
344

9912

9917

9921 9926

9930

9934

9939

9943 9948

9952

2 3

344

9956

9961

9965 9969

9974

9978

9983

9987999'

9996

2 3

334

INDEX.

Air, properties of, 100
Air-compressor, 135
Air-pump, 137
Brumbo pulley, 32
Clearance, 97
Combined diagrams, 128
Compound engines, 123
Cord and knots, 26, 28, 40
Density, 99

Diagrams, oscillations in, 118
Diesel motor, 140
Drum- detent, 28
Electrical attachment, 30
Engine constant, 95
Errors of indicator, 46
Gas-engines, 140
Gases, properties of, 100
Horse-power, 92
Hyperbola, 114
Indicator, Bachelder, 15

Crosby, 5

Tabor, 13

Thompson, IO

Watt, i

Indicator, care of, 42
Indicator cock, 20
Indicator diagram, 43
Indicator for gas-engines, 15
Indicator for ordnance, 18

Indicator- tester, 57
Inspection of indicator, 22
Mean effective pressure, 63, 81
Pantagraph, 54
Paper for indicator, 25
Piping, effect of, 62
Piston-friction, 120
Piston-displacement, 95
Plammeter, Amsler, 70

Coffin, 83

Lippincott, Willis, 85
Pressure, specific, 99
Pump diagrams, 131
Reducing motions, 32
Reducing wheel, 38
Refrigerating machine, 141
Scale of spring, 42, 54
Steam-consumption, 103
Steam per horse-power, no
Steam, properties of, 102
Swinging lever, 37
Taking diagrams, 41
Temperature, 99
Thermal unit, 112
Thermal units per horse-power, 112
Three-way cock, 21
Valve-setting, 121
Volume, specific, 100

153

•e

THIS BOOK IS DUE ON THE LAST DATE
STAMPED BELOW

AN INITIAL FINE OF 25 CENTS

WILL BE ASSESSED FOR FAILURE TO RETURN
THIS BOOK ON THE DATE DUE. THE PENALTY
WILL INCREASE TO SO CENTS ON THE FOURTH
DAY AND TO $1.OO ON THE SEVENTH DAY
OVERDUE.

OCT 26 1933

QCT

359953

UNIVERSITY OF CALIFORNIA LIBRARY

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