LESSONS AND PRACTICAL NOTES

STEAM,

THE STEAM ENGINE, PROPELLERS,

ETC., ETC.,

FOR

YOUNG MARINE ENGINEERS,

STUDENTS, AND OTHERS.

BY THE LATE

W. H. KING, U. S. N.

REVISED BY

CHIEF ENGINEER J. W. KING, II. S. N.

[SECOND EDITION, ENLARGED.]
NEW YORK:

D. VAN NOSTRAND 192 BROADWAY,

LONDON:

TRUBNEK & COMPANY.
1862.

Entered, according to Act of Congress, in the year 1860,

BY J. W. KING,

In the Clerk's Office of the District Court of the United States for the Southern District of

New York.

JOH\ F. TROW,

PH'VrKH, FTIRKOTYPER, AND ELICTKOTf PIE,

50 Greene Street, New York.

PREFACE TO SECOND EDITION.

THE flattering reception of the first edition or my
lamented brother's work has encouraged me to cause
the issue of a second, with a few additions on the
elements of machinery, withheld from the first edi-
tion. As the elements of machinery, like physical
laws, must be thoroughly understood by the young
engineer, before eminence in his profession can be
securely attained, and as but few young men learning
engineering practically, cultivate this knowledge un-
derstandingly, if at all, it has been considered proper
to devote a short space to the subject, giving ex-
amples and explanations, both thorough and plain.

J. W. KING,

* Chief Engineer, U. S. Navy.

CONTENTS.

INTRODUCTION, PAGE 5.
CHAPTER I.

Steam, 7. Mechanical Effect, 9. Expansion of Steam, 12. Table of Hyperbolic
Logarithms, 14. Back Pressure, 16. Gain by Expanded Steam, 18.

EXPANSION VALVES.

Sickel's, 19. Stevens', 22. Allen & Wells', 23.

SLIDE CUT-OFFS.

Explanation, 24. Gridiron Valve, 26. Wabash Valve, 29.

OTHER KINDS OF VALVES.

Double Poppet, 30. Single Poppet, 81. Hornblower's, 32. Box Valve, 33-
Equilibrium Slide, 34. Double Slide Valve, 34. Piston Valve, 35. Long
D Slide, 36. Short D_ Slide, 37. Worthington Pump Valve, 38. Pitts-
burg Cam, 39.

CHAPTER II.

THE INDICATOR AND INDICATOR DIAGRAMS.

The Indicator, 41. Cylinder Diagrams, 44. Air-pump Diagrams, 56. Power
Required to Work the Air-pump, 60.

CHAPTER III.

THE HYDROMETER.

The Hydrometer, 62. Loss by Blowing-off, 64. Gain by the Use of Heaters,
68. Injection Water, 71. Evaporation, 72. Steam and Vacuum Gauges, 75.

4 CONTENTS.

CHAPTER IV.

CAUSALTIES, ETC.

Broken Eccentric, 79. Leaking Vessel, 79. Irregular Feed, 80. Foaming, 81.
Ilot Condenser, 83. Getting Under Way, 85. Coming into Port, 86.
Scaling Boilers, 88. On Coming to Anchor, etc., 89. Management of
Fires, 90. Patching Boilers, 93. Sweeping Flues, 95. Ash Pits, 95.
Smoke-pipe Stays, 96. Grate Bars, &c., 96. Broken Air-pump, 97. Bro-
ken Cylinder-head, 98. Selection of Coal, 98. Safety Valve, 99.

CHAPTER V.

MISCELLANEOUS.

Theory of the Paddle Wheel, 101. Centre of Pressure, 114. Screw Propeller,
116. Altering the Pitch, 132. Parallel Motion, 133. Strength of Mate-
rials, 136. Surface Condensers, 141. Cylindrical Boilers, 145. Boiler
Explosions, 148. Horse Power, 150. Vibration of Beams, 152. Marine
Economy, 154. Limit to Expansion, 155. Gravity, 156. Displacement of
Fluids, 158. Temperature of Condensers, 159.

APPENDIX.

MATERIALS.

How to Test Iron, 162. Cast Iron and 'Steel, 163. Tenacity of Materials, 164.
Resistance to Torsion, 165. Results of Repeated Heating Bar Iron, 166.
Strength of Joints of Boiler Plates, 167.

THE ELEMENTS OF MACHINERY.

Motion, 169. Application of Power, 1 70. The Lever, 172. Inclined Plane, 175.
Wheel and Axle, 177. The Pulley, 177. The Screw, 181. The Wedge, 182.
Table of Pressure, Temperature, and Volume of Steam, 183.

INTRODUCTION.

WETTING a book and then apologizing for having
written it, is hardly in accordance with our convic-
tions ; but considering, nevertheless, the eminent tal-
ent which has preceded us upon the subject we have
taken up, a few remarks of explanation may not be
out of place. Books heretofore appearing on the
steam engine, have been of two classes, or the work
itself has been divided into two parts the one for the
theorist, the other for the practical man. In the one
case long mathematical formulas have bsen produced,
and in the other nothing but simple rules. The prac-
tical man, therefore, who has not had the advantage
of a mathematical education, has nothing presented to
him but the bare rules, which he is compelled wholly
to reject, or take entirely upon trust. Besides, these
works extend over numerous volumes, the study of
which involve much time, labor, and expense, and
which usually disheartens the practical man before he
has made much progress. Having had many of these
difficulties to surmount in our earlier studies of the
steam engine, we were led to the course of keeping a
Steam Journal, in which we noted, from time to time,
as we progressed, whatever we thought important, and
was made clear to our mind ; and this course we would
also recommend the young student ; for, however well

6 INTKODUCTION.

it may be to study books containing other mens 1
thoughts, when we write we are led to the habit of
thinking for ourselves, which is of the highest impor-
tance ; and, by keeping a journal, we have also the
very great advantage of having always at our com-
mand, in a condensed form, those things which are the
more important, and which can be referred to at any
time.

Much of the present work has been taken from the
Author's Journal, and the remainder has been sup-
plied, from time to time, as he found leisure from his
hours of business.

Our object has not been so much to supply want-
ing information, as to direct the student into the habit
of thinking and reasoning for himself on those subjects
which may be presented for his consideration, and
which, in order that he may become eminent in his
profession, he must thoroughly understand. It is not
sufficient to assert that Newton said this, or somebody
else said that. The reasons why they said it, and the
fundamental principles upon which they based their
conclusions, are necessary to be understood, in order
to have a clear understanding of the subject; and if
we have succeeded in making any thing more clear,
or in rendering any service to that class of persons
who are eagerly seeking for information, but who re-
quire some assistance to direct them in the proper
channel, our only object in launching this, our little
bark, on the troubled sea of authorship, is fully accom-
plished, conscious all the while, however, of the many
imperfections it contains.

LESSONS A^D PRACTICAL NOTES.

CHAPTER I.

STEAM.

STEAM is a thin, elastic, invisible fluid, generated
by the application of heat to any liquid, usually water.
That, however, which is generated while the water
is in a state of ebullition, is alone generally termed
steain, while that which is formed while the surface of
the water is quiescent, is denominated vapor a dis-
tinction, to our mind, without much difference.

The mean pressure of the atmosphere at the sur-
face of the ocean is equal to 14.Y pounds per square
inch, or is equivalent in pressure to a column of mer-
cury 29.9212 inches in height. Under this pressure,
fresh water boils at a temperature of 212 Fahrenheit.

The 212 is, however, not the total number of de-
grees in the steam, but simply that which is indicated
by the thermometer, and which is termed sensible
heat ; for we all know that to raise water from the
freezing to the boiling point requires a certain time,
and a certain amount of fuel ; and we know further,
that when the water commences to boil, it does not all
evaporate at once, but that the evaporation goes on

8 STEAM.

gradually, and the time, and hence the fuel required
to evaporate it, is much greater than that required to
raise it from the freezing to the boiling point. This
extra heat must have gone off somewhere, and must
be in the steam, but as it is not indicated by the ther-
mometer, it is termed latent heat. When the steam is
reconverted into water, the latent heat becomes again
sensible, which is evidenced by the large amount of
water required to condense a small amount in the
shape of steam. The precise ratio the one bears to
the other shows the latent, compared with the sensible
heat.

The subject of latent heat has been one of unusual
interest, ever since the invention of the steam engine,
and numerous theories have been advanced, and nu-
merous experiments made some of them not very
carefully in order to determine the exact law it fol-
lowed ; but none, up to Regnault's time, seem to have
settled the subject satisfactorily. Some maintained
that the latent heat of steam was a constant quantity,
some that the sum of sensible and latent heat was a
constant quantity, and that quantity was 1202 Fahr-
enheit. This was the most popular theory, and was
the one generally adopted by engineers. Others,
again, maintained that neither the sensible, latent, nor
sum of the sensible and latent heats, were a constant
quantity, but that they all varied. The exact ratio,
however, in which they varied was not established
until Regnault undertook his able series of experi-
ments at the instigation of the French Government.
These are the latest and most reliable experiments,
and we subjoin, therefore, a table compiled from his
labors, which we earnestly recommend to the attention
of the reader.

MECHANICAL EFFECT.

REGNAULT'S EXPERIMENTS.

Degrees of heat contained in saturated steam, in Fahrenheit degrees
of heat and English inches.

Iff!

Corresponding elastic

if. 3

f|f|

Corresponding elastic

|l oS j

force

Ji||

ijlj

force

~JJ|
1-S^

0) 3^,0

|J if

In Atmo-

!|fej

In Atmo-

I^JI

1*6*

Inches.

spheres.

Ill's

Inches.

spheres.

ll b

Fah.

0.1811

0.006

1123.70

248

517116

1.962

1189.58

0.3606

0.012

1129.10

266

79.9321

2.671

1194.98

0.6846

0.023

1134.68

284

106.9930

3.576

1200.56

1.2421

0.042

1140.16

302

140.9930

4.712

1205.96

104

2.1618

0.072

1145.66

320

183.1342

6.120

1211.54

122

3.6212

0.121

1151.06

338

234.7105

7.844

1216.94

140

5.8578

0.196

1156.64

356

297.1013

9.929

1222.52

158

9.1767

0.306

1162.04

374

371.7590

12.425

1227.92

176

13.9621

0.466

1167.62

392

460.1943

15.380

1233.50

194

20.6869

0.691

1173.02

410

560.9673

18.848

1238.90

212

29.9212

1.000

1178.60

428

684.6584

22.882

1244.48

230

42.3374

1.415

1184.00

446

823.8723

27.535

1249.88

FIG. 1.

FIG. 2.

MECHANICAL EFFECT.

We will now take into consideration the mechani-
cal effect of steam, and a common-place demonstration
will serve our purpose.

Suppose a cylinder, A, Fig.
1, to be one square inch in
area of cross section, and fitted
with a steam tight piston, at-
tached by means of a flexible
cord to the weight , which is
of sufficient size to balance the
weight of the piston, and all
the parts to work without
friction. Now suppose a quan-
tity of water, equal to one

cubic inch, to be placed in the bottom of this cylinder,

10 MECHANICAL EFFECT.

and a fire to be lighted under it. The temperature
of the water will gradually rise until it attains 212,
when it will commence to boil, and the piston will
soon begin, and continue to rise if the cylinder be
long enough until it obtains a height of 1700 inches
from the base. This IT 00 is the volume of steam at
atmospheric pressure, the water being 1, from which it
is generated. If, now, we suppose to be added to the
weight, 3, another weight equal to the pressure of the
atmosphere or a fraction less, so that motion may en-
sue and the steam under the piston to be condensed,
the piston will return to the bottom of the cylinder
by the pressure of the atmosphere, through a space
of 1700 inches, and will have raised the extra weight of
14.7 Ibs. appended to 0, up that distance. Hence this
cubic inch of water, by its evaporation, produced a
mechanical effect of raising 14.7 pounds through a
space of 1700 inches = (14.7 X 1700).= 24,990 pounds
through one inch.

Let us now take another cylinder, B, Fig. 2, similar
in every respect to A, excepting that the piston has a
weight laid upon it equal to the pressure of the atmo-
sphere, viz., 14.7 pounds, and suppose a fire to be
lighted under this cylinder. The water, as in the
other case, will be heated up to the boiling point,
which, in this case, will be 250, corresponding to the
pressure of two atmospheres when it will commence
to evaporate, and the piston will rise until it obtains a
height of 900 inches from the base, this being the
volume of steam under the pressure of two atmo-
spheres, water being 1. If, now, we suppose this pis-
ton to be fixed where it is, the weight removed from
the top of it and applied to <?, then the steam condensed
and the piston unfixed, it will return to the bottom of

MECHANICAL EFFECT. 11

the cylinder, raising the weight applied to c, up a dis-
tance of 900 inches. Now, then, since the weight of
14.7 Ibs. was first raised 900 inches on the top of the
piston, and afterwards raised the same distance by be-
ing attached to c, the total distance moved = (900 X 2)
= 1800 inches, which is equal to (14.7 X 1800) = 26460
pounds raised one inch. The difference, therefore, be-
tween the work done in the first and second case
= (26460 24990) = 1470 Ibs. raised one inch high,
which is 5.88 per cent, of the first number. If this
extra work was obtained without any extra fuel, which
would be the case were the total heat in steam at all
temperatures a constant quantity, it would be all gain,
but as such is not the case, and as more heat is required
in the latter than in the former case, we will see what
this amounts to, and the difference between this loss
and the other gain will show the true gain. In the
first instance, it will be seen that the total heat in the
steam was 1178.6, and in the second, 1190 ; hence,
supposing the water in both cases to be at a tempera-
ture of 100 before the fires are lighted which is
about the temperature at which water is fed into ma-
rine boilers there would be required in the latter
case (1190- 100) = 1090 from the fuel, and in the
former case (1178.6- 100) = 1078.6 from the fuel ;
difference 11.4, which is 1.057 per cent, of 1078.6.

The extra fuel, therefore, required under the pres-
sure of two atmospheres is 1.057 per cent., and the
extra work done is 5.88 per cent., leaving a gain of
4.823 per cent.

In the same way we could ascertain what the gain
would be at any other pressure, either higher or lower ;
but these examples suffice to show that the' higher the
pressure of the steam, the greater is the mechanical

12 EXPANSION OF STEAM.

effect with the same amount of fuel, but the gain is
small, and in practice, therefore, where great accuracy
is not required, it is neglected altogether.

Starting, therefore, from the assumption that the
mechanical effect performed by the same amount of
fuel is the same, no matter what the pressure may be
under which the steam is generated, we shall proceed
to the study of the

EXPANSION OF STEAM.

Opening a communication with the cylinder and
shutting it off again before the piston arrives at the
end of the stroke is called expansion of steam, or work-
ing steam expansively. Thus, supposing steam to be
admitted into the cylinder until the piston arrives at
half stroke, and the communication then to be shut off,
the steam already in the cylinder, by its expansion,
will force the piston to the end of the stroke ; by
which arrangement we gain all the work performed
after the steam is cut-off.

FIG. s. Take, for instance, a cylinder, A, Fig. 3,

two units in length, one unit in area of
cross section, and an initial pressure of 1,
the work performed during the first half
stroke, i. e., while the piston travels from
b to , will be 1 X 1 X 1 (area x pressure
X distance travelled =) 1, and the work
.69 performed during the latter half stroke
1 X .69 X 1 = -69, the total work, there-

fore, performed throughout the stroke

= 1.69. Now, if the steam, instead of be-
ing expanded from c to d, had been exhausted at <?, the
total work performed would have been only 1 instead

EXPANSION OF STEAM.

of 1.69, and the quantity of steam would have been the
same, hence we see that by cutting off at one half the
same steam performs 69 per cent, more work. This 69
per cent, is what is termed the gain in cutting off, but it
does not, however, represent the saving in fuel, as we
will show presently ; but before proceeding to illus-
trate that subject we will explain to the student, from
what source we derive this 69.

Marriotte's law of gases is, that the spaces occupied
are inversely as the pressures. That is to say, if steam
of 20 pounds pressure per square inch, be allowed to
expand into double the space, the pressure will be
10 Ibs. ; if triple, 6| Ibs. ; if four times, 5 Ibs. ; if five
times, 4 Ibs., and so on. This theory would be liter-
ally correct did the temperatures remain constant ; but
as the temperature of all gases becomes reduced by ex-
pansion, the law does not hold good ; nevertheless, in
the steam engine, where there are so many extraneous
circumstances which practically affect all calculations
appertaining to the same, it is considered all that is
ever required, and from its extreme simplicity is uni-
versally adopted.

From this law the pressure can be
ascertained approximately by dividing
the cylinder into a number of equal
parts, say eight, ascertaining the pres-
sure at each of those points, and taking
the mean. If the initial pressure, as
before, be supposed to be unity, the
pressure at each of the first four divi-
sions cutting off at half stroke will be
1 ; at the fifth division (| =) .8 ; at the
6th (|) = .6666; at the 7th (4- =) .5714;
at the 8th ( =) .5 ; the mean pressure, therefore, by

Fio. 4.

.8000

.5714
.5000

TABLE OF HYPEKBOLIC LOGAKITHMS.

this process, after the steam is cut off .6345, and the
mean pressure before it is cut off = 1, the mean, there-
fore, throughout the stroke = (- f^-- -) = .8172.-

This, however, is only an approximation, and in order-
to arrive at any degree of accuracy, the divisions would
have to be very numerous, which would render the
operation tedious and lengthy. Fortunately, however,
we can dispense with this part of the calculation alto-
gether, for the Naperian or Hyperbolic logarithms, as
set forth in the following table, furnish to our hand
the ratios of pressures :

TABLE OF HYPERBOLIC LOGARITHMS.

,Q si

J> ^

ja so

"3
,0 t*

I s

1.05

.049

3.05

1.115

5.05

1.619

7.05

1.953

9.05

2.203

1.1

.095

3.1

1.131

6.1

1.629

7.1

1.960

9.1

2.208

1.15

.140

3.15

1.147

5.15

1.639

7.15

1.967

9.15

2.214

1.2

.182

3.2

1.163

6.2

1.649

7.2

1.974

9.2

2.219

1.25

.223

3.25

1.179

5.25

1.658

7.25

1.981

9.25

2.225

1.3

.262

3.3

1.194

5.3

1.668

7.3

1.988

9.3

2.230

1.35

.300

3.35

1.209

5.35

1.677

7.35

1.995

9.35

2.235

1.4

.336

3.4

1.224

5.4

1.686

7.4

2.001

9.4

2.241

1.45

.372

3.45

1.238

5.45

1.696

7.45

2.008

9.45

2.246

1.5

.405

3.5

1.253

6.5

1.705

7.5

2.015

9.5

2.251

1.55

.438

3.55

1.267

6.55

1.714

7.55

2.022

9.55

2.257

1.6

.470

3.6

1.281

5.6

1.723

7.6

2.028

9.6

2.262

1.65

.500

3.65

1.295

6.65

1.732

7.65

2.035

9.65

2.267

1.7

.531

3.7

1.308

5.7

1.740

7.7

2.041

9.7

2.272

1.75

.560

3.75

1.322

6.75

1.749

7.75

2.048

9.75

2.277

1.8

.588

3.8

1.335

5.8

1.758

7.8

2.054

9.8

2.282

1.85

.615

3.85

1.348

6.85

1.766

7.85

2.061

9.85

2.287

1.9

.642

3.9

1.361

6.9

1.775

7.9

2.067

9.9

2.293

1.95

.668

3.95

1.374

5.95

1.783

7.95

2.073

9.95

2298

.693

1.386

1-792

2.079

10.

2.303

2.05

.718

4.05

1.399

6.05

1.800

8.05

2.086

15.

2.708

2.1

.742

4.1

1.411

6.1

1.808

8.1

2.092

20.

2.996

2.15

.765

4.15

1.423

6.15

1.816

8.15

2.098

25.

3.219

2.2

.788

4.2

1.435

6.2

1.824

8.2

2.104

30.

3.401

2.25

.811

4.25

1.447

6.25

1.833

8.25

2.110

35.

3.555

2.3

.833

4.3

1.459

6.3

1.841

8.3

2.116

40.

3.689

2.35

.854

4.35

1.470

6.35

1.848

8.35

2.122

45.

3.807

2.4

.875

4.4

1.482

6.4

1.856

8.4

2.128

50.

3.912

2.45

.896

4.45

1.493

6.45

1.864

8.45

2.134

55.

4.007

2.6

.916

4.5

1.504

6.5

1.872

8.5

2.140

60.

4.094

2.55

.936

4.55

1.515

6.55

1.879

8.55

2.146

65.

4.174

2.6

.956

4.6

1.526

6.6

1.887

8.6

2.152

70.

4.248

2.65

.975

4.65

1.537

6.65

1.895

8.65

2.158

75.

4.317

2.7

.993

4.7

1.548

6.7

1.902

8.7

2.163

80.

4.382

2.75

1.012

4.75

1.558

6.75

1.910

8.75

2.169

85.

4.443

2.8

1.032

4.8

1.569

6.8

1.917

8.8

2.175 '

90.

4.500

2.85

1.047

4.85

1.579

6.85

1.924

8.85

2.180

95.

4.554

2.9

1.065

4.9

1.589

6.9

1.931 i

2.186

100.

4.605

2.95

1.082

4.95

1.599

6.95

1.939 !

8.!)">

2.192

1000.

6.908

1.099

1.609 ,

1.94'i

2.197

10000.

9.210

EXPANSION OF STEAM. 15

The hyperbolic logarithm of any number can be
found by multiplying the common logarithm by
2,30258509.

From the nature of hyperbolic logarithms they are
tli us very useful in working steam expansively.

Let the Line A, B, Fig. 5, represent Fl0 - 5 -
the pressure of steam which we will as-
sume to be unity at the time the cut-off
valve closes ; C, D, half the length of A,
B, and the line A, C, a hyperbolic curve,
.69+ from the table gives the mean length A
of all the ordinates, 1, 2, 3, 4, <fec., which
before we had to arrive at by approxima-
tion. If the cut-off valve, instead of closing
at half stroke, had closed at some other
point, say, when the piston had traveled
only one-fourth its distance, C, D, would be one-fourth
of 0, , and the curve A, C, would have extended from
a to c, giving 1.38+ as a mean of all the ordinates
below <z, 1).

All we require then in working examples in ex-
pansion of steam, according to Marriotte's law, is to
know the initial pressure and point of cutting off, from
which we can deduce the mean pressure, pressure at
the end of the stroke, percentage of gain, <fec., by
having before us a table of hyperbolic logarithms ;
but if it be required to make such calculations, when a
table of this kind is not come-at-able, it can be done in
the manner we have previously shown.

EXAMPLE 1st. Suppose you have a cylinder in
which you are using steam of 20 pounds pressure per
square inch, inclusive of the atmosphere, and cut off at
half stroke, what is the mean pressure, pressure at the
end of the stroke, and per centage of gain.

16 BACK PRESSURE.

Ans. \st. From the foregoing considerations we
know that had the pressure of steam been 1 pound in-
stead of 20, all we would have to do would be to take
.69314 out of the table, add 1 to it and divide by 2 ;
therefore to find the mean pressure we have this rule :
As the number of times the steam is expanded, is to tlie
hyperbolic logarithm of that number plus 1, so is the
initial to tlie mean pressure, hence 2 : 1.69314:: 20:
16.9314lbs. mean pressure.

Ans. 2d. 20-^2=10 Ibs. pressure at the end of the
stroke.

Ans. 3< Work performed before expansion, 1.
after expansion, .69314. Therefore 1 : .69314: : 100 :
69.314 per cent, gain by cutting off at half stroke.

BACK PRESSURE.

Inasmuch as it is impossible in practice to obtain
a perfect vacuum, there is always a certain amount of
steam in the cylinder opposed to the motion of the
piston, and this is termed back pressure. Suppose for
example, there was in the above instance 4 Ibs. per
square inch back pressure, the mean effective, or un-
balanced pressure, would be 16.93144=12.9314 Ibs.,
and the unbalanced pressure at the end of the stroke
would be 10 4 = 6 Ibs.

EXAMPLE 2d. Suppose the steam in example 1st
had been cut off at a \ from commencement of stroke,
what would have been the mean pressure, pressure at
the end, and percentage of gain in that case ? Also
the mean unbalanced pressure, and unbalanced pressure
at the end, the back pressure being 4 Ibs per square
inch?

BACK PRESSURE. 17

Ans. \st. 4 : 2.38629 : : 20 : 11.93145 Ibs. mean pres-
sure.

Ans. 2d. 20 -f- 4 = 5 Ibs. pressure at the end.

Ans. 3d. 1 : 1.38629 : : 100 : 138.629 per cent.

Ans. till. 11.931454=7.93145 mean unbalanced
pressure.

Ans. 5th. 5 4 = lib. unbalanced pressure at the
end.

It is useless hereto multiply examples ; those already
given we consider sufficient to give the student a clear
understanding of the manner in which these calcula-
tions are made, but we would recommend him to make
a number of others for himself, and work them out so
as to render himself the more familiar and ready with
the mod^s operandi.

We come now to the percentage of gain of fuel by
using steam expansively. It has been previously
shown that when the steam is cut off at one half, the
work done before expansion takes place being repre-
sented by 1, the work done afterwards is .69; the total
work therefore performed is 1.69 ; now had not the
cut-off valve closed at all, the total work performed
would have been 2. Hence by this operation we have
the power of the engine reduced from 2 to 1.69. It is
therefore necessary to increase the initial pressure of
steam to make up this decreased power ; and keeping
in view Marriotte's law, we will let this pressure be
represented by x hence 2 : 1.69 : : x : .845 a?, the mean
pressure. It is manifest that the mean pressure in this
case must be the same as if the steam followed full
stroke, in order that the powers may be the same ;
consequently

.845 x 1 Ib.

x = 1.18 Ib. initial pressure.

18 GAIN BY EXPANDED STEAM.

But only half a cylinder full of this steam is used to
every full cylinder of the other, consequently the dif-
ference between 1.18-^-2 and 1, equals the saving,
which is 41 per cent.

To ascertain the saving of steam at any other point
of cutting off, take the hyperbolic log. of 3, 4, 5, 6,
<fec. as the cutting-off point may be i, , i, , <fec., and
proceed in the same manner, or, in other words, divide
the whole length of the stroke by the portion traveled
before the steam is cut off; take the hyperbolic log. of
the quotient and proceed as above.

The 41 per cent, in the above example, is the
saving in steam that is to say, should a steamer,
using steam full stroke, perform a certain distance
in a certain time, cut the steam off at half-stroke,
and increase the initial pressure in the ratio of 1
to 1.18, she would perform the same distance in the
same time with 41 per cent, less steam. Not 41 per
cent, less coals pmt into the furnaces, but 41 per cent,
of that which reaches the cylinders minus the loss
from condensation due to expansion, i. e. that por-
tion of the fuel not combustible, and that portion pass-
ing out of the chimney in the shape of heat to produce
draft, together with the loss from radiation and con-
densation before the steam reachers the cylinders must
first be deducted. When this is done it will be found
that the actual saving will be reduced to less than 20
per cent., which is about the real saving of fuel in
practice cutting off at half stroke, and pro rata for any
other point varying somewhat according to better or
worse constructions. Any engineer can satisfy himself
on this point by using his steam with and without ex-
pansion for a sufficient given time, carefully weighing
all the coals and recording all the data.

EXPANSION VALVES.

This should not therefore be confounded with the
69 per cent., which is theoretically the increased work
performed by the same steam over what it would have
performed had it not been cut off at all.

EXPANSION VALVES.

There are a variety of expansion valves and arrange-
ments for cutting off steam ; the principles operating
the more important of which we will now proceed to
examine. The following diagrams or sketches will
serve our purpose. We shall simply explain the lead-
ing features of each, in order to give an understanding
of the principles that govern them, leaving the student
to suggest for himself the Fig. i.

alterations in the mechani-
cal arrangement to adapt
them to different types
and arrangements of en-
gines.

Figure 1 is a diagram
of Sickel's momentarily
adjustable cut-off, in which
A, A, is the steam valve
of the double poppet con-
struction ; B, B, valve
stem ; C, dash-pot, filled
with water up to the line d
1, 2; D, plunger, fitting
in the dash-pot ; E, stuf-
fing-box, which is packed
air and water-tight; 0,
hole in the bottom of the
plunger D, to allow the
water to enter when the plunger strikes it; ~b, a

20 EXPANSION VALVES.

rod communicating motion to the wiper F, which
trips the valve ; A, a rod receiving motion from the
air-pump beam or .any other part having motion coin-
cident with that of the piston. The motion of li is
communicated through the vertical rod, having c as a
fixed centre to &, and thence to the wiper F. The
manner in which this cut-off operates is this: The
valve stem, instead of being permanently attached to
the lifting rod, is secured to it by a clutch and spring.
The valve is lifted by the eccentric, (operating as in
other cases,) but before it reaches its seat again, the
wiper F, which vibrates back and forth, strikes the
clutch, and detaches the valve from the lifter; the
valve then, from the action of gravity, would fall, and
strike its seat with a heavy blow ; to prevent which,
and allow the valve at the same time to fall quickly,
it is attached to the plunger D, working in the dash-
pot C. By this arrangement, before the valve reaches
its seat, the plunger D strikes upon the water in the
lower part of the dash-pot C, which is called the secon-
dary reservoir, and thereby allows the valve, to close
without slamming, the water escaping into the cavity x,
and also around the plunger, into the upper or primary
reservoir. The plunger D, being hollow, small holes
are bored into it in the vicinity of the line 1, 2, to
allow the water to escape into it also.

We see that the cutting-off is effected by the wiper
F tripping the valve ; the sooner therefore the valve
is tripped, the sooner the steam will be cut off. Now
the manner in which this is made an adjustable cut-off,
is accomplished by moving the handle f backward or
forward on the arc <7, which will move the centre c to
one side or the 6ther of its present position, the center e
remaining constantly fixed, and therefore giving the

EXPANSION VALVES. 21

wiper F a greater or less distance to travel before
striking the clutch. By this means the cutting-off
point can be varied for any part of the stroke. The
handle /can be pat in such a position that the valve
will not be tripped at all, or it can be placed so that
the valve will not lift at all, being exactly in the ver-
tical position when the lifter commences to rise. The
engine can be thus stopped by this cut-off. For the
other end of the cylinder there is another dash-pot,
<fec., similar to the one described, the wiper being ope-
rated by a rod similar to >, attached to the center d.

Should there be too much water in the dash-pot,
the valve will not seat quickly, but " hang," as it is
technically termed. At a there is a cock for the pur-
pose of supplying it with water. Attached to the
dash-pot, there is usually another cock or valve for
the purpose of letting out any superfluous water. In-
sufficient water is evidenced by the slamming of the
valve.

This cut-off was formerly made without the wiper
F, there being used instead a sliding cam, shaped
something like this <] . As the valve rose up, the
clutch struck thebevel on this cam, which forced the
clutch out of its position, and allowed the valve to fall.
With this arrangement, however, it will be seen that
the valve must trip while it is rising, and as it is at its
highest position when the piston is about half stroke, it
cannot be possible to cut off by this mode longer than
half stroke ; but with the arrangement of the wiper, it
will be seen, inasmuch as it vibrates back and forth,
that the valve can be just as well tripped on its descent
as when rising, and this is the reason why it was sub-
stituted for the cam.

" Stevens"'' The next cut-off that we shall take

EXPANSION VALVES.

FIG. 2.

into consideration is Stevens's, a diagram of which is
shown in figure 2. A A are the steam toes ; B B,
the steam-lifting toes ; D, rock-shaft arms ; C C, the
valves ; #, pin in rock-shaft

arm for eccentric hook. The
manner in which this is
made an adjustable cut-off,
is by raising or lowering the
toes A A, thereby giving
them more or less lost mo-
tion. In the position in
which they are shown in the
diagram, it will be seen that
they will have to travel a
considerable distance before
touching the toes B, B, and
as the piston is in motion
during this time; and the
steam valve closed, the
steam will be acting expan-
sively. If the end of the toes A A be dropped lower
down, the steam will be cut off shorter ; if raised higher
up, longer. By dropping the toes down, however, we
diminish the lift of the valve, and also alter the lead.
To retain the one, we raise the pin a in the rock-shaft
arm, and the other we turn the eccentric a little ahead.
To alter the point of cut-off, therefore, while the engine
is in motion, so as to cut off shorter, we have first to
drop the toes A A, then raise the pin , and set the ec-
centric ahead. To cut off longer, reverse the operation.
The number of things required to be altered in
changing the point of cutting-off is a very great objec-
tion to this arrangement. In practice it has seldom
been accomplished without stopping the engine.

EXPANSION VALVES.

Allen and Wells. This cut-off is represented by
sketch, figure 3. A, A, are the exhaust toes ; B B.
steam toes ; C C lifting toes ; D D, the valves ; E E',

FIG. 3.

palls fitted to the end of the toes B, B' ; F, rock-shaft
arm, which is operated from the eccentric in the usual

24 SLIDE CUT-OFFS.

way ; G G, a cross arm secured to the end of the rock-
shaft arm ; a a, rollers on the end of the cross-arm G, '
G' ; II H, two arms fitted loosely on the rock-shaft.
These arms receive their motion from any part of the
engine having motion nearly coincident with that of
the piston ; b &', rollers on these arms. This cut-off
operates thus : The rock-shaft is put in motion by the
eccentric. The pall E resting upon the roller , is
raised, and with it the toe B, and lifter toe C ; but
after the pall E is raised up so as to clear the roller I,
the pall E slides in on top of Z>, which, having a down-
ward motion, lowers the valve, while the rock-shaft
arm continues to rise. The rollers b Z>', being attached
to the arms H H, which having motion nearly coinci-
dent with that of the piston, start to go down at nearly
the same time the rock-shaft arm starts to. rise. Now
then by turning around the right and left-hand screw
c c, the rollers b &', will be set further apart, or closer
together, and will therefore alter the time they will
clear the end of the pall E, and hence the point of cut-
ting off. To follow farther separate the rollers b //,
to cut off shorter, screw them closer together. In
altering the point of cutting off we have nothing to do
but to turn around the screw c c.

This cut-off is like " Sickel's," momentarily adjust-
able, but it cannot, however, be made to cut off quite
so short as " Sickel's."

SLIDE CUT-OFFS.

In the use of the ordinary three-ported slide-valve,
or other slide-valves combining, both the steam and
exhaust, the expansive principle can be carried only
to a very small extent, owing to the derangement of

SLIDE CUT-OFFS. 25

the exhaust passages. Suppose, for instance, that suffi-
cient lap be given to the steam side of the valve to
cause the steam to be shut off at half-stroke, and sup-
pose the same amount of lap be given also to the ex-
haust side, it is manifest, that when the steam is shut
off, the exhaust will be shut off also, and the pent up
steam, therefore, having no escape, and increasing in
pressure as the piston approaches the end of the stroke,
will act as a serious retarding force. This arrange-
ment, therefore, cannot operate.

Now, then, suppose that we put lap on the steam
side, as before, but none on the exhaust, in which
event another difficulty equally great presents itself.
It is this :

Supposing the valve, Fig. 4, to have neither lap
nor lead, when the end a arrives at a', steam will just
begin to be admitted into the cylinder, but the point

Fio. 4.

7;, at the same time, will have arrived at the point Z>',
and steam just begin also to exhaust ; now, then, let
half an inch be added to each end of the valve at a
and , when the valve begins to open to steam in this
case, a, instead of being at ', will be half an inch past
it ; and, as there has been no lap added to the exhaust
side, I will be half an inch past V, so that the exhaust

SLIDE CUT-OFFS.

must have opened considerably before the piston ar-
rived at the end of the stroke ; hence, in this case, we
exhaust too soon.

All we can do, therefore, in practice, is to strike a
mean between these evils ; that is to say, when we add
lap to the steam side, add lap also to the exhaust side,
but not so much so that we open the exhaust before
the piston arrives at the end, and close it again before
it reaches the other end. The shortest this kind of
valve can be made to cut-off to advantage in practice,
is considered about J- from commencement of stroke ;
but even this we consider most too short for beneficial
working of large engines.

Owing to these confined limits, the beneficial re-
sults obtainable from the expansive principle by this
arrangement is very small, which has led to the adop-
tion of an independent slide cut-off valve, situated on a
separate face, back of the steam valve, as shown in

FIG. 5.

Fig. 5, in which a' is the steam, and b b the cut-off
valve. The valve a having only sufficient lap to cover
the ports a! a' fairly, when it is in the middle of
the stroke, operates as in other cases, but the lap
on b b can be made to any required extent, so that

SLIDE CUT-OFFS. 27

during a large part of the stroke the ports V I'
are closed, preventing further access of steam to the
cylinder, notwithstanding the steam valve itself is
open. The valve b b is operated by an independent
eccentric, through the valve stem E. In the position
shown in the figure the steam is cut off about half
stroke: d' shows another opening covered with the
valve d, having a stem c sliding loosely through the
valve b b / the other end of the stem passing through
the chest, has a handle attached to it for the purpose
of moving the valve d, in order to open the port </,
when the engine is stopped. This is necessary, for the
reason that the engine may stop when the valve 1) b is
in such a position as to prevent the steam from enter-
ing to the steam valve #, and the engine could not,
therefore, be started. In the figure, the cut-off valve
has but two ports for the admission of steam, but any
number of ports can be made the more numerous,
the less stroke will be required to get the necessary
opening. This is what is termed the gridiron valve,
from the resemblance it bears to that very use/id in-
strument.

After this valve is once made, the point of cutting
off usually remains fixed, but it can, however, be varied

FIG. 6.

counters
Kcnrrnic

within narrow limits by altering the stroke of. the
valve. Thus, in Fig. 6, supposing the end of the valve
stem to be raised from a to 5, the valve, instead of

28 SLIDE CUT-OFFS.

being closed, as shown, will be open the distance b c,
and will therefore have that much additional to travel
before the steam is cut off; hence, by increasing the
travel of the valve we increase the point of cutting off,
and conversely, supposing the pin a had been lowered
in the rock-shaft arm the distance a e, equal to a Z,
the ports, instead of being closed, as shown, would
be closed the distance b c; the steam, therefore, would
be cut off sooner. But by altering the point of cutting
off we also alter the lead of the valve ; for, taking the
case in which we increased the travel of the valve, we
see that when it would have been closed with the
original lead, it lacked the distance b c. If its travel
had been reduced, it would have lacked that much of
being open. To obviate this, whenever the travel of
the valve is altered, the eccentric should also be altered,
so as to retain the original lead.

If the travel of the valve be made too great, the
valve d will pass entirely over the port d', and gradu-
ally close ^, unless they be set some distance apart.
If the travel be made too small, the steam will be shut
off, and the motion of the eccentric being reversed
long before the piston arrives at the end of the stroke,
steam will be admitted to it again before the steam
valve closes.

From the above facts, and the figure before us, we
draw the following general conclusions in reference to
this kind of slide cut-off valves :

That, with a given amount of lap, the cutting off
point can be varied from the longest point of cutting
off allowable by said lap, to a certain point within the
stroke, by reducing the stroke of the valve and alter-
ing the eccentric so as to retain the original lead. If
the stroke be reduced beyond this, steam will be shut

SLIDE CUT-OFFS.

off and given to the piston again before it arrives at
the end of the stroke. In practice, this variation will
not amount to more than from about J- to f of the
stroke.

In altering the stroke of the valve, the slot through
which the pin a moves should be an arc of a circle,
struck with a radius equal to the length of the link d a,
and with d as a centre.

With equal leads, the cutting off point cannot be
effected equally on both ends of the cylinder with a
slide valve, owing to the connecting rod acting out of
parallelism, or, in other words, owing to the crank not
being at 90 when the piston is half way. The shorter
the connecting rod, the greater the discrepancy.

FIG. 6j.

CONNECTSTO CONDENSER

Fig. (>, is an arrangement of cut-off valve as con-
structed by Messrs. Merrick & Son, of Philadelphia,
in 1855, for the U. S. Steam Frigate " Wabash."

In consequence of the satisfactory manner in which
it worked on board that vessel; its simplicity, and
easy adjustment for cutting off at any portion of the

30 OTHER KIND OF VALVES.

stroke likely to be required, it lias been applied to
nearly all the U. S. Screw ships recently constructed,
as also to a number of other engines. C is the steam
valve ; D D are the cut-off valves, attached to the valve
stem E by right and left hand screws working in nuts
let into the valves ; F F, rings in the steam chest cover,
fitting close down on the back of the main steam valve,
enclosing the space Gr, which is connected to the con-
denser by the pipe H, for the purpose of balancing
the valve.

This cut-off can be worked by a separate eccentric,
or from any part of the engine having a motion coin-
cident with that of the piston.

To alter the point of cutting-off, a wheel is on the
end of the valve stem E, which, if turned in one direc-
tion, will draw the valves closer together, and the
openings will not be closed so soon, consequently the
steam will follow the piston farther, i. e. cut off longer.
To cut off shorter, the operation is reversed.

OTHER KIND OF VALVES.

Having explained the principles of the leading cut-
offs, we will now take a glance at some of the most
prominent steam and exhaust valves now in use ; but,
inasmuch as the student is supposed to understand the
leading features of most of these, we will not devote
much time to this part of our study.

Figure Y is a diagram of a double poppet valve,
in which the rectangular space, abed is the open-
ing to the cylinder ; A B, the steam valves, and C D,
the exhaust valves. The object of this arrangement is
to make the valve a balance valve. Thus the steam
acting on the top of A and bottom of B, if they were

OTHER KIND OF VALVES.

of equal size, an equilibrium would be established, but
the valve B is made just small enough to slip througli

Fio. 7.

FIG. 8.

the upper seat, so that the difference in area serves to
keep the valves fairly in their seats.* On the exhaust
side the reverse is the case. The steam acts under C,
and on top of D, the lower valve D is usually made
the larger. In order to get D into its place, the upper
seat is either made removable by being secured in its
place by tap-bolts, or a hand-hole is cut in the side of
the steam-chest, or, in some cases, it is passed in through
the cylinder nozzle.

Figure 8 is a diagram of the single poppet valve,
in which A is the steam valve, and B, the exhaust.
With these kinds of
valves we see that we
require considerable
power to operate
them by hand, as we
have the full pressure
of steam on the back
of A, and also the
exhaust on B; but
when the engine is hooked on the pressure is in part
balanced. On the steam valve this is occasioned at
the time the valve is opened, by the exhaust valve

* In some cases, tha area* of the valves are equal, and they are seated by their own weight.

OTHER KIND OF VALVES.

being closed before the piston arrives at the end of the
stroke, producing the pressure called cushion. And
on the exhaust valve the pressure is reduced (at the
time the valve is opened) by expansion. In some
cases this pressure is but little above that in the con-
denser. It is therefore obvious that these valves can
be made to work with but little power from the engine.
They also have the advantage of being easily made
tight and occupying but little room.

The disadvantage of working by hand, however,
led to the adoption of the double poppet valve, the
single poppet being the earlier invention. The double
poppet valve is the one now almost universally used in
American low-pressure river, or marine paddle-wheel
engines.

Figure 9 is a representation of what is termed
" Hornblower's " valve, in which a a b b are the valve

FIG. 9.

seats ; A A, the valve ; B, one of a number of cross-
bars secured to the top of the valve, to which the

OTIIER KIND OF VALVES.

valve stem is attached. From the figure it will be
seen that the only surface the steam has to act upon
to keep the valve in its seat, is the upper edge, c <", of
the valve ; it is therefore an equilibrium valve.

Figure 10 is what is termed a box valve; a <(
are the parts communicating with the cylinder; &,

Fio. 10.

steam-pipe ; <?, the exhaust ; A A, the valve having an
opening through its center communicating with the
exhaust, c ; d d, packing. An inspection of the figure
will show the operation of the valve. The object of
this kind of valve is also to establish an equilibrium.
Figure 11 is a longitudinal section, and figure 12

FIG. 11

a top view of what is termed the equilibrium slide.

OTHER KIND OF VALVES.

Fie. 12-

This valve has a ring, A A, on the back of it, which
being made steam tight, the
pressure is taken off the space
enclosed by the ring. The pres-
sure is taken off the back of
nearly all the valves of large en-
gines now-a-days, fitted with the
short slide, either in this way or
by having the ring secured to
the top of the chest, and the valve sliding under it.

Figure 13 shows a slide valve A A A, having
openings b b through it for the admission of steam ;

FIG. 13.

a a a is another valve sliding on the back of the
valve A A A; a a a is the cut-off, which operates
thus : The valve A A A being put in motion, and
the cut-off valve lying loosely on its back, is carried
with it until the end of the valve , , , strikes the
steam chest, when its motion is arrested, while the
steam valve continues to move, the result is the clos-
ing the opening &, and the cutting off the steam. The
sooner, therefore, the slide a a a strikes the chest, the
sooner the steam is cut off. The point of cutting-off
can be varied by having a screw running through the

OTHER KIND OF VALVES.

ft!

chest, which can be moved further in or out and
against which the valve a a a strikes.
With this arrangement it will be seen
that the cut-off must close at further-
est a little before the piston arrives at
half stroke, or not close at all. This
cut-off is applicable to horizontal sta-
tionary engines.

Fig. 14 is a piston valve, in which
a a' are the openings into the cylin-
der ; C, exhaust opening ; A B D E
the valve packed at b c d e with
rings or other packing. In the position
shown in the figure, steam is being
exhausted through the openings a'
and C into the condenser, while steam
is being admitted into the opposite
end of the cylinder through the open-
ing a. When the valve has its full
throw in the opposite direction, steam
will be admitted through the opening
a' while it is being exhausted through
, and the opening F F througji the
valve and through C into the con-
denser.

36 OTHER KIND OF VALVES.

Figure 15 shows the long D slide, with the full

FIG. 15.

opening for steam under the piston; Fig. 16, same

FIG. 16.

valve showing full opening for steam on top of the
piston ; Fig. IT, longitudinal section of the valve alone,

FIG. 18.

FIG. 17.

and Fig. 18, cross section of the same. A is the steam
pipe, B, the exhaust, C, packing to keep the steam and
exhaust separate, steam "being admitted into the chest
or valve casing at A, fills the vacant space under and
around the valve, but cannot escape past the ends

OTHER KIND OF VALVES.

FIG. 19

Fio. 20.

owing to the packing C C ; and, when, the valve is
placed in the position shown in Fig. 15, steam is ad-
mitted under the piston in the direction shown by the
arrows, at the same time that it is exhausted through
the upper opening, and the valve being hollow
through it and pipe B into the condenser. When the
valve is moved in the opposite direction, steam is ad-
mitted above the piston in the direction shown by the
arrows in Fig. 16, and exhausted
through the lower opening directly
through the pipe B to the condenser.

This style of valve is in extensive
use on English marine, and other
engines. The objection to it is the
friction, requiring several men to
work the starting bar when the en-
gine is operated by hand.

Fig. 19 is a longitudinal section
of the short D slide, and Fig. 20, an
end view of the same. A A' are the
openings into the cylinder ; B B, the
communications to the condenser ; C,
steam pipe. In the position shown
in the figure, steam is being admitted
through A into the cylinder, and ex-
hausted through A' into the con-
denser, c c is packing on the back of
the valve.

(o,

OTHER KIND OF VALVES.

FIG. 21.

FIG. 22.

VALVE

FACE

Figure 21 is a view of the Worthington pump

steam valve; figure
22, the valve face,
and figure 23, the
valve seat. The fig-
ures explain them-
selves. In the or-
dinary slide valve,
when it is moved
in one direction,
steam is given to
the piston in the
same direction, but
the object of this
valve, as invented
by H. E. Worth-
ington, of N. York,
is to cause it, when
moved in one direc-
tion, to give steam
to the piston in the
opposite direction.
The valve being operated by an arm projecting from
the piston rod, which strikes collars on the valve stem,
renders it necessary that when the valve is moved in
one direction, steam should be given to the piston in
the opposite direction, in order to reverse its motion ;
by this arrangement the intervention of levers is un-
necessary, as the end is accomplished direct.

FIG. 23.

VALVE

SEAT

THE PITTSBUKO CAM.

FIG. 24.

FIG. 25.

The Pittsburg Cam. Figures 24, 25, and 26, show

different forms of this
cam. Like letters refer
to like parts. A B C D
is a yoke fitting over the
cam a b c ; E is a rod
attached to the valve
stem. F, main shaft of
the engine to which the
cam is secured. It will
be seen that by the revo-
lution of the cam a b c,
within the yoke ABC
D, the rod E will be
paused to move back and
forth, and thereby open
and shut the valve.

Fig. 24 is a cam made
to cut off at half stroke ;
figure 26, stroke, and
figure 25 follows full
stroke. The manner in
which these cams are
laid off is this. From
the centre F, with a ra-
dius dependent upon the
stroke of the valve, de-
scribe a circle, as shown

_ _/T\ _ k partly in dots and partly

in full lines in the fig-
ures ; divide this circle
into any convenient even
number of equal parts,
say sixteen ; then, supposing we wish to cut off at half

40 OTHER KIND OF VALVES.

stroke, taking figure 24, place one foot of the dividers
having a radius equal to the diameter of the circle at
C, and describe the arc terminating at <5, then move
the foot of the dividers from c to #, and describe
another arc terminating also at b then, with the same
radius, and I as a centre, describe the arc a c; the
figure thus enclosed will be the required cam. It will
be observed that, while the cam is traveling the dis-
tance a 1 that being an arc of a true circle no mo-
tion can be given to the valve, but while it travels
from 1 to 2 the valve is opened and shut. Now, then,
inasmuch as the piston moves from one end of the cyl-
inder to the other for each semi-revolution of the cam,
and inasmuch as the distance from a to 1 is the same
as from 1 to 2, the valve remains necessarily closed
during one-half of the stroke.

In figure 25, as no part of the outline of the cam is
concentric to the shaft F, the valve must be in motion,
all the time the cam is in motion. In figure 26, as
three-quarters of the semi-periphery of the cam is con-
centric to the shaft F, the valve will remain closed
during three-quarters of the stroke. Instead of making
the points Z> sharp, as shown in the figures, they can be
turned off, and, to retain the same dimensions on the
cam, an equal amount added to the arc a c. Thus,
taking figure 25, suppose we cut off the point of the
cam to cc y, and increase the lower extremity to H I,
this will not alter the point of cutting off, but it re-
duces the travel of the valve, and has the effect of
keeping the valve stationary when wide open, while
the cam travels through the arc cc y.

CHAPTER II.

THE INDICATOR AND INDICATOR DIAGRAMS.

THE steam engine indicator is an instrument used
tor the purpose of exhibiting the performance of the
steam engine. By its application to the steam cylinder
we can ascertain the following particulars: Whether
the valves are properly constructed and set ; steam and
exhaust passages of the right size ; whether the piston
or valves leak; the amount of vacuum or back pres-
sure, and pressure of steam -upon the piston ; the power
of the engine ; power required to overcome its friction,
and also to work any machinery attached to the same,
<fcc. In truth, it is the stethoscope of the physician,
revealing the internal working of the engine.

The following description of the instrument and cut,
Fig. 27, we take from Paul Stillman's Treatise on the
Indicator. The cut shows the style manufactured at
the Novelty Iron Works, New York city :

A is a brass case enclosing a cylinder, into which a
piston is nicely fitted. To the piston-rod a spiral
spring is attached to resist the steam and vacuum
when acting against it. B is a pencil attached to the
piston rod. C is an arm attached to the case, and sup-
porting a cylinder D, which may be caused to rotate
back and forth a part of a revolution in one direc-
tion, by means of a line or cord 0, attached to a suit-
able part of the engine and in the other by means of

THE INDICATOR AND INDICATOR DIAGRAMS

FIG. 2T.

a strong watch spring within the cylinder D.
this cylinder is to be wound a
paper, upon which a diagram
will be made, by the combined
action of the piston and paper
cylinder, representing, by its
area, the power exerted on one
side of the piston during the
whole revolution of the engine,
//are springs to secure the paper
to the cylinder ; g is a scale
divided into parts corresponding
to the pounds of pressure on the
square inch. These divisions,
for convenience of measuring the
diagrams with a common rule,
are generally made in some re-
gular parts of an inch, as 8ths,
lOths, 12ths, 20ths, 30ths; h is
a cock by means of and through
which it is connected with the
engine cylinder.

Outside

HOW TO ATTACH THE INDICATOR.

Into whatever part of the
engine it may be desired to ap-
ply the indicator, there must
first be inserted a small stop-cock, with a socket to
receive the one connected with the indicator. The
instrument is to be set into this in such a position that
the line attached to the paper cylinder shall lead
through or over the guide pulley toward the place
whence it is to receive its motion. An extension of
this line should be connected with some part of the

THE INDICATOR AND INDICATOR DIAGRAMS. 43

engine, the motion of which is coincident with that of
the piston, and which would give the paper cylinder a
motion of about three-fourths of a revolution. If the
engine is of the construction denominated beam or
lever engine, and is provided with a " parallel motion "
the parallel bar, or a pulley on the radius shaft, fur-
nishes the proper motion; if otherwise, the beam
centre may be resorted to. In the kind denominated
square engines, the centre of the air pump gives it. In
horizontal and vertical direct acting engines, it will
frequently be found necessary to erect a temporary
rock-shaft, or lever, connected with the cross-head.
Particular care should be taken, when the power of the
engine is to be estimated, that the motion communi-
cated be perfectly coincident with that of the piston.

In nearly all forms of the steam engine, the proper
motion may be obtained by attaching a line to the
cross-head, and passing it over a delicately constructed
pulley, to the axis of which should be attached a
smaller one, from which a line shall connect with the
indicator. The proportional sizes of the two pulleys,
of course, should be as the distance traveled by the
piston to the length of motion given to the paper
cylinder of the indicator. It will be necessary to at-
tach a strong spring to the axis of these pulleys, to
produce the reverse motion promptly. In an oscillat-
ing engine, it will be necessary that the indicator, with
its fixtures, should be attached to the cylinder.

As the paper cylinder cannot make more than
about three-fourths of a revolution without disturbing
the point of the pencil, it will be seen that the line
communicating the motion must be of a definite length.
It also requires to be readily connected and discon-
nected.

THE INDICATOR AND INDICATOR DIAGRAMS.

The indicator having been attached to the steam
cylinder, the paper secured smoothly on the cylinder
D, figure 27, and the length of the line e being ad-
justed so that by the vibration of D it does not strike
the stops, we will proceed to take a diagram, first
taking care to see that the paper cylinder D is so fixed
that the springs ff do not come in contact with the
pencil B. The pencil B being adjusted so that it
touches lightly on the paper, throw it back and attach
the hook on the line E to the line receiving motion
from the engine ; then open the cock h, and allow the
piston to work up and down several times, in order to
heat and expand all the parts of the instrument. This
being accomplished, turn the pencil on and take the
diagram. Shut off the cock /*, and apply the pencil
again to the paper, and it will describe the atmospheric
line.

Figure 28 is a diagram taken from the U. S. S.

FIG. 28

10) 204.5

20.45 Ibs. mean unbalanced pressure.

THE INDICATOR AND INDICATOR DIAGRAMS. 45

Frigate " Powhatan," fitted with the double-poppet
balanced valves, and Sickels' cut-off, on the 15th of
January, 1854, while on the passage from Hong Kong,
China, to the Loo-Choo Islands. At #, the piston of
the indicator being at the bottom of its stroke, steam
is admitted, forcing it up to b ; at b the cylinder upon
which the paper is wound having motion coincident
with that of the steam piston starts to turn, describ-
ing the line b <?/ at c the expansion valve closes, and
the pressure therefore gradually falls to d, where the
exhaust valve opens and the pressure falls suddenly to
e the steam piston now starts on the return stroke,
and the spring within the cylinder D, fig. 27, forces it
back to the beginning a of the diagram. The line
from a to b is called the receiving line ; from b to c the
steam line ; from c to d, the expansion line ; d to 0, the
exhaust ; e to , the vacuum line. The numbers in
the vertical column on the right-hand side of the figure,
are the pounds pressure ; 14.7 is the true vacuum line,
0, the atmospheric line, and 14, the initial pressure of
steam above the atmosphere. The figures along the
top line are the feet in length of the cylinder. It will
be seen that the cut-off valve closed when the piston
had traveled a very little beyond half stroke. The
rounding at d and a is the lead and cushion on the
exhaust. That is to say, the exhaust valve opened at
d, before the piston arrived at the end of the stroke,
and it also closed again at , before the piston reached
the other end of the stroke. Had there been no lead
both of these corners would have been well defined.

In order to calculate the power of the engine, the
mean pressure on the piston must be known, and from
no source but the indicator can it be accurately ascer-
tained. The manner of arriving at this is simply by

INDICATOR DIAGRAMS.

taking the total pressure at different points and adding
them up and taking the mean, as shown in fig. 28.

Figure 28 is what would be termed among en-
gineers a good diagram; so is also figure 29, which we
will take for a further elucidation of the subject.

Steam, 10

Vacuum, 27

Hot well, 106 Fahr.

Revolutions,.... 9.5
Throttle, 8.

FIG. 29.

" Powhatan " stb. cylinder, bottom

NOT. T, 1855, 10 A. M.
One engine and one wheel in
operation.
Smooth sea.

It appears from this diagram, however, that the
piston of the indicator worked rather tightly, which
occasioned it to stick a little in some places, as is evi-
denced by the steps in the expansion line, and also at
a f> in the vacuum line. If the piston of the indicator
become much scratched, similar effects will be produced.
Great care should, therefore, be taken in its use, to see
that neither the piston works too tightly nor too loose-
ly ; for on the one hand it will stick, and thereby pro-
duce an imperfect outline, and on the other hand will
produce the same effect by exhibiting false vacuum and
expansion lines.

INDICATOR DIAGRAMS. 47

Should figure 29, instead of being as shown in full
lines, have the lower right hand corner cut off as shown
in dots at c d, the defect would have been that the ex-
haust valve closed too soon at c instead of e occa-
sioning excessive cushioning. With some engines,
however, a large amount of cushioning is necessary to
prevent them from thumping on the centres.

Had the upper right-hand corner been rounding, as
shown by the dotted line f g, the defect would have
been that the steam valve opened too late. Had the
exhaust corner been cut off, as shown by the dotted
lines li i, the exhaust valve would have opened too
soon ; but had it been in the form shown by the dot-
ted line & , it would have opened too late, and after it
did commence to open, would move with too slow a
velocity, preventing the free escape of steam, or the
exhaust passages would have been too small, which
would produce a similar effect to the valve opening too
slowly. Had the steam line, instead of being parallel
to the atmospheric line, fallen down in the direction
in, n, it would have shown that the throttle was par-
tially closed, or the steam passages too small, prevent-
ing the full flow of steam into the cylinder.

Should there be excessive lead given to the steam
valve, the line d m, instead of being at right angles to
the atmospheric line, will have the top inclined to the
right as from L to M.

In taking a diagram for the purpose of estimating
the power of the engine only, the atmospheric line is
not necessary ; but in order to ascertain the vacuum
it cannot be dispensed with, unless the indicator piston
be forced down to the perfect vacuum and held there
until that line be described.

Tn a diagram taken from a non-condensing engine,
4

48 INDICATOR DIAGRAMS.

the atmospheric line will of course be entirely below
it, owing to the back pressure occasioned from the
passage of the exhaust steam through the openings
and pipes. Had figure 29 been taken from a non-con-
densing engine, A B would have been the atmospheric
line.

Figure 30 we have copied from Main and Brown's
Treatise on the Indicator and Dynamometer. It was

Fio. 30.

taken from an engine fitted with the long D slide.
There are two defects exhibited in this diagram ; the
steam communication is opened too late and the ex-
haust too soon. At C the exhaust closes, causing the
steam to be compressed to O, when the piston having
arrived at the end of the' stroke starts on its return,
and the pressure falls to O' ; at O' steam is admitted,
causing the line O' A to be traced ; at B the exhaust
opens long before the piston arrives at the end of the
stroke, allowing the steam to escape too soon. The
hook, as shown at O, would only be made in very
aggravated cases, where the steam is very much be-
hind time.

INDICATOR DIAGRAMS.

Fig. 31 is obtained from the same source as figure
30. In this case the engine was working as a non-

Fio. 81.
B

FIG. 32.

condensing engine with a very low pressure of steam.
The exhaust closes at A, causing the pent-up steam to
be compressed to B, where the steam valve opens,
and the pressure in the cylinder being greater than
that in the boiler, immediately falls to C. The hook
at C is occasioned by the momentum of the indicator
piston. At D the cut-off closes, causing the steam to be
expanded to E, below the atmosphere. At E the
exhaust valve opens and the pressure rises up equal to
the back pressure, causing the loop on that corner of
the diagram.

Figure 32 is a diagram drawn from memory, from
one of a non-condensing
engine that was once
shown the author, with
the request that he
point out the defect in
the engine from which
such a diagram was
taken. At first we did
not see any reason why
the pressure should rise from b to <?, for supposing the
exhaust to open at 3, there could be no reason why
the pressure should rise beyond ^/, the amount of back
pressure on the opposite side of the piston. After
looking at it a little closer, however, it occurred to us

INDICATOR DIAGRAMS.

that such a diagram could be formed from a slide valve
engine, and in this manner : Steam being admitted in
the usual way until the piston arrived at a, the inde-
pendent slide cut off the steam, whence it was expanded
to the point b ; at I the steam valve having neither
lap nor lead, and consequently still open the cut-off
again opened the communication with the cylinder,
admitting fresh steam, which caused the line I c to be
traced, partaking of the motion of the steam and piston.
At c the steam is shut off by the steam valve itself,
and the exhaust opened, the pressure therefore falls
from that point to ^/, and the exhaust line is traced.
In a non-condensing engine diagram, where of course
there can be no vacuum line, the line from c to e in-
clusive is termed the exhaust.

A perfect Diagram. According to the law laid
down by Marriotte, which we have previously studied
under the head of expansion of steam, the expansion
curve of an indicator diagram should be a true hyper-

Fio. 33.

bolic curve, were there no extraneous circumstances to
cause it to be otherwise ; but unfortunately in practice
this perfection is not attainable were Marriotte's law

INDICATOR DIAGRAMS. 51

literally true, owing to the time required for steam to
enter and leave the cylinder clearance of piston, space
in nozzles between the valves, leakage of valves, piston
condensation in the cylinder, <fec. Fig. 33 is intended
to show a perfect diagram, having all the corners well
defined and the expansion line a true hyperbolic curve.
From this figure we purpose explaining the manner of
laying out a true hyberbolic curve. Let A E be the
true vacuum line, and B C the steam line. Divide
A E into any number of equal parts, and erect the
perpendiculars A B, 1 1', 2 2', <fec. Now we see that
the steam follows the distance A, 2, or two divisions
before it is cut off the length of the ordinate 3 3',
being three divisions from the commencement should
be | of 2, 0', the length of 4 4', f- ; of 2, C ; of 5 5' f ;
of 6 6' |; of 7 r i ; of E D, |, With the lengths
of all these ordinates marked on the diagram drawn
through the points 3', 4', 5', 6', T', <fec., the line C I),
and you have the required curve.

An experienced engineer can tell at a glance
whether an engine is in good working order from its
diagram ; but nevertheless, in most cases it would be
well to draw the true curve, in order to ascertain how
much the actual one differs from it, for by this means
we can ascertain, while under way, whether the valves
or piston leak; but in drawing the true curve, the
clearance of the piston and space in the nozzles, &c.,
must be ascertained, and that much added to the length
of the diagram, in order to obtain the curve accurately.
Thus, supposing this space to be equal in capacity to
six inches in length of the cylinder, make the diagram
six inches longer than it actually is, and proceed in the
manner we have shown.

Should the steam valves leak while every thing

5:2

1 XDICATOR DIAG R A MS.

else remains tight, the termination of the expansion
line will be too high, and if the exhaust valves or pis-
ton leak, it will be too low, allowance beinor made

' * ~

for condensation in the cylinder.

Steam 10 Ibs.

Rev 9

Vac 26

Hot well 100

Throttle wide.

FIG. 34.

" Powhatan " stb. cylinder-top.
February 13th, 1854.

Figures 34 and 35 are two diagrams taken from
the U. S. Steamer Powhatan, on the 13th of February,
1854; 34 was taken about ten minutes after 35. In
both of these figures we have the true hyperbolic
curves drawn in, with and without taking the clear-
ance, <fec., into account. The upper curve in small
dots is the true curve, when the clearance, <fec., is
taken into consideration, and the lower one in large
dots is the true curve without reference to the clear-
ance, <fec. In figure 35, where the steam was cut off
at a very early part of the stroke, the importance of
taking the clearance, <fec., into consideration, is very
conspicuous. The dotted lines on the right of these

INDICATOR DIAGKAMS.

diagrams show the amount they are lengthened by
adding the clearance, space in nozzles, <fec., to them.

Steam Si

Rev 6

Vac 26

Hot well 82

Throttle wide.

FIG. 35.

Ibs. " Powhatan" stb. cylinder-top.

February 13th, 1854.

From a casual inspection of these diagrams, they
seem to present an anomaly that at first is difficult to
solve. Thus, in figure 34, the termination of the true
expansion curve, considering clearance, <fec., is about
one pound above the actual curve, whereas in figure
85 it is two pounds below it. The first would indicate
that the exhaust valves or piston leaked, and the
second that the steam valves leaked, while the exhaust
valves and piston were tight. Now, then, since one
was taken only about ten minutes after the other, it is
not at all probable that this sudden change was
brought about in that short space of time ; hence we
must look for some defect in the engine that would
occasion it. We account for it in this way : In the

54 INDICATOR DIAGRAMS.

first case the steam valve leaked, and also the steam
piston, but the piston leaked to a greater extent than
the valve, that is to say, more steam passed through
the piston and into the condenser from the leakage of
the piston than entered the cylinder from the leakage
of the valve ; therefore, the actual curve must fall be-
low the true curve. In the second case, the steam
valve also leaked, but the pressure on the piston fell
so rapidly, from expansion, that it became too low to
force a passage through the piston, the elasticity of the
packing being sufficient, in this case though not in
the other, where it had a greater pressure to sustain-
to keep it tight ; hence, the true curve in this case
must be below the actual curve, agreeing precisely
with the conditions of the figures.

There is, however, another thing which would pro-
duce diagrams similar to those before us, and which
most probably caused the formation of these, viz., leak-
age about the cylinder heads. Thus, supposing the
stuffing box, for instance, to leak. So long as the
pressure in the cylinder remained above the atmo-
sphere, steam would blow out, occasioning the curve
to fall ; on the other hand, when cutting off short, the
pressure in the cylinder would soon fall below the
atmosphere, and air would enter, causing the curve to
rise, exactly as shown in the figures.

INDICATOR DIAGRAMS. f>;>

Fig. 36 is a diagram taken from the U. S. Steamer
" San Jacinto," fitted with Allen & Wells' cut-off.

FIG. 30.

Steam in boilers ll^lbs. November 7th, 1855, 11J A. M.

Revolutions 18 After Engine, inboard end.

Vacuum 25 Coal 18 tons in 24 hours.

Hot well 104

Throttle 4 holes open. Scale = Vio.

From inspection of the expansion curve of this dia-
gram, it appears that this cut-off does not close so
quickly as Sickel's, occasioning the corner a to be
more rounding.

Steam in boilers ...... 9 Ibs.

Revolutions ............ 5

Hot well ................ 100

Throttle.... 4

FIG. 37.

"Powhatan," Feb. 13th, 1854.
stb. cylinder bottom, working by hand.

Figure 37 is a diagram showing the operation of

AIR-PUMP DIAGRAMS.

the valves while working by hand. This valve ex-
hibits large cushioning arid steam lead, the exhaust
valve closing at , and the steam valve opening at ,
so that the engine actually passed the centre against a
pressure of 6 Ibs. above the atmosphere.

Steam 16.5 Ibs.

Revolutions 0.25

Hot well 106

Vacuum gauge out of order.

" Powhatan " stb. air-pump, 10.50 A. M.
January 18th, 1854.

_ o

Calculated for Vs full of water.

Number 1 is a diagram taken from the " Powhat-
an's " starboard air-pump. The Powhatan's air-pumps
are of the lifting kind, and the .piston fitted with one
large brass conical valve. We will explain the dia-
gram. At $, the piston being at the bottom of the
stroke, starts to rise, compressing the air and vapor
above it, until it arrives at #, at which place a sudden
discharge of air and vapor seems to have taken place,
and the pressure fell to , from which point the pres-
sure again gradually rose until it arrived at <;/, where
the water began to be delivered and continued to the
end of the stroke.

AIR-PUMP DIAGRAMS.

Attached to the top of the air-pumps is a pipe, run-
ning down into the bilge, for the purpose of pumping
off the bilge water. Where this pipe is attached to
the pump is fitted a valve, operating like an ordinary
check valve, a handle being made to screw down on
the top of it to keep it firmly in its seat, when there is
no water in the bilge.

Steam lolbs. "Powhatan." stb. air-pump, 10.55 A. M.

Revolutions. 10 January 18th, 1854.

' Hot well, 106

Vacuum gauge out of order.

Resistance of vapor and water in Air-pump

= (6.6-j- 312 x .0969=) .6697 lb. per square inch of steam piston.
Calculated for ' 3 full of water.

There being no water in the bilge at the time ~No. 1
was taken, No. 2 was taken five minutes after, for the
purpose of ascertaining what effect the opening of this
valve and admitting air would produce. It shows
that no extra power, from the admission of this air,
was required to work the pump, the average pressure
being about the same as in No. 1, and that the vacuum
in the pumps at no time was more than 4^ Ibs. There
was no alteration in the vacuum, as shown by the
gauge, however attached to the condenser, and the
engines continued to work in the same manner as be-

AIll-PUMP DIAGRAMS.

fore the bilge valve attached to the air-pump was
opened.

Steam 15lbs. " Powhatan " port air-pump, 11.6A.M.

Revolutions 10 January 18th, 1854.

Hot well 108

Vacuum gauge out of order.

Resistance of vapor and water in Air-pump

= (0.46 -f. 223 x .0969 =) .6476 Ib. per square inch of steam piston
Calculated for '/T full of water.

Nos. 3 and 4 were taken in the same manner from
the port air-pump a few minutes after 1 and 2 were
taken from the starboard pump.

In these diagrams the pressure at the termination
of the up stroke, it will be seen, is about 2^ Ibs. per
square inch above the atmosphere, which is due to the
height of the level of the water surrounding the ship
above the top of the air-pump. The pressure increased
to between 7 and 8 Ibs. per square inch, as shown in
other parts of the diagram, is occasioned by the fric-
tion of the water and vapor through the delivery pipes
and valves. The slanting off in the diagram, 'No. 1,
from x to y, we think partly owing to two causes :
First, the decreased velocity of the piston as it ap-

AIK-PUMP DIAGEAMS. &V

preaches the end of its stroke does not expel the water
with such force, and hence there is not so much fric-

Steam 15lbs. " Powhatan " port air-pump, 11.15A.M.

Revolutions 10 January 8th, 1854.

Hot well 108

Vacuum gauge out of order.

Resistance of vapor and water in air-pump

= (8.16 -(-'223 x .0969=) .8123 Ibs. per square inch of steam piston.
Calculated for J / 7 full of water.

tion ; but this would not occasion the slanting off from
h to z on the return stroke ; and secondly, there-
fore, we are inclined to think that the string slipped or
stretched a little from a? to y, and recoiled again to its
original place from li to z.

We will npw proceed to ascertain the

Power required to work the Air-puny).

Ascertain the capacities of the steam cylinder and
air-pump, by multiplying the areas of their cross-sections
by the lengths of their strokes, and divide the latter
by the former, which will give the r atio of the cylinder
capacity to that of the air-pump. But the air-pump
makes but one delivery stroke to every two strokes of
the steam piston, consequently divide this ratio by
two, which Avill give the coefficient for our present

60 POWER REQUIRED TO WORK THE AIR-PUMP.

calculation, and this coefficient multiplied by the mean
pressure per square inch of air-pump piston which
can be ascertained from an indicator diagram will
give the mean pressure per square inch required to
expel the air and vapor.

This of course must be augmented by the weight
of the water raised.

The indicator diagram will show very nearly at
what part of the stroke the pump begins to deliver
the water, and therefore what fraction of the pump is
filled, from which can be easily ascertained the number
of cubic feet of water lifted ; and this number multi-
plied by 64.3 or 62.5, as the vessel may be running in
salt or fresh water, will give the number of pounds.
And the number of pounds of water lifted, divided by
the area of the air-pump piston, and multiplied by the
coefficient before obtained, will give the pressure per
square inch of steam piston required f o expel the water
from the pump.

The sum of these results will give the pressure per
square inch of steam piston required to work the air-
pump independent of friction, an amount that is usually
estimated.

Example: The capacity of the "Powhatan's" cyl-
inder, i. ., the space displaced by the steam piston per
stroke, is 267.25 cubic feet: ditto in air-pump, 51.8
cubic feet ; proportion of steam piston displacement to
that of half of air-pump piston displacement, 1.000 to
.0969; area of air-pump piston, 2134 square inches.
The pump was filled \ full of water, as shown by dia-
gram No. 1, and the mean pressure throughout the
stroke was 6.5 Ibs. per square inch ; hence, 6.5 X .0969
= .6298 Ib. per square inch of steam piston resistance
from vapor in air-pump, and .312 x .0969 .0302 Ib.

POWER REQUIRED TO WORK THE AIR-PUMP. 61

per square inch of steam piston resistance from the
weight of water lifted ; total = (.6298 -f .0302 =) .66
pounds per square inch of steam piston, required to
work the air-pump, independent of friction.

Now, supposing the mean unbalanced pressure on
the steam piston per square inch to have been 20 Ibs.,
we have 20 : .66 : : 100 : 3.3 per cent, of the total
power of the engine required to work the air-pump.

CHAPTER III.

FIG. 42

THE HYDROMETER.

THE Hydrometer is an instrument used for the
purpose of determining the specific gravi-
ties of liquids. When applied to the
water of marine boilers, it indicates the
amount of saline matter the water con-
tains. Figure 42 shows the. kind of hy-
drometer usually used on board Ameri-
can steamers. The lower globe is filled
with shot, or other weighty substance,
for the purpose of keeping the instru-
ment upright. When the hydrometer is
placed in fresh water, the point O stands
even with the surface of the water ; when
placed in water containing one pound of
saline matter in thirty-two pounds of
water, it stands at % 2 ; when the water
contains two pounds of saline matter in
thirty two pounds of water it stands at
% 2 , and so on. So that by placing this
instrument in a small quantity of water,
drawn from the boilers at intervals, it
will show the exact density, by which
we know how to regulate the bio wing-off.

In the boilers of sea-going vessels the
water is usually carried from 1% to "2 per
hydrometer, i. <?., from the point a to /;,
figure 42. In the Gulf of Mexico, how-
ever, in the vicinity of the Florida reefs, where the

*/
32

THE HYDROMETER. 63

water is impregnated with, an unusual amount of lime,
it is found not to be prudent to carry it beyond iy 2 .

The hydrometer, when made for a certain temper-
ature, is not adapted to any other, but the water
should be allowed to cool down to the temperature
marked on the hydrometer before observing the indi-
cation, and for this purpose it becomes necessary also
to use a thermometer. The hydrometers used in this
country are usually graduated for a temperature of
200 Fahr. We can allow, however, for a few degrees
either above or below this figure, without appreciable
error a difference of 10 in temperature making a
difference of about an eighth of % 2 in the scale. Thus,
supposing the water to be at a temperature of 210,
and the hydrometer graduated for 200 to stand at #,
or 1%, the actual density of the water will not be 1%,
but ! 7 / 8 , or halfway between a and 1). On the other
hand, if the temperature be 190, and the hydrometer
stand at 1%, the true density will be 1%. Neverthe-
less, in practice, it is always best to allow the water to
cool to the temperature for which the hydrometer is
graduated, whenever it can be done without the waste
of too much time.

It will be observed that the divisions on the scale
are not of equal lengths. Thus : the distance from O
to %2 i g greater than from % 2 to % 2 , and from % 2 to
%2j greater than from % 2 to % 2 , and so on. The reason
of this can be explained in this manner : When the
instrument stands at O, the two bulbs, and all the
tube below O, of course, are immersed, having the
weight due to the length of the tube only above O to
support. When it rises to y 32 it has more weight to
support, from the fact of there being more tube out

of water, and it also has less bulk immersed ; at % 2 it
5

64 LOSS BY BLOWING OFF.

has still more weight to support, while there is still
less of the instrument immersed, and so on down to
the bottom of the scale, occasioning the lengths of the
divisions to become less and less.

The proportional quantity of saline matter con-
tained in sea water, at different localities, varies very
considerably, as will be seen in the following

TABLE :

Baltic Sea, .
Black Sea,
Arctic Sea,
Irish Sea, .
British Channel,

Mediterranean, i

Atlantic at Equator. . . a s

South Atlantic, .

North Atlantic,

Dead Sea, ....

LOSS BY BLOWING OFF.

When water contains 3 per cent, by weight of sa-
line matter, no deposit takes place at the boiling
point ; under atmospheric pressure or 212 Fahr.
When it contains 10 per cent, it makes a deposit of
lime, principally sulphate, and at 29, 5 per cent, com-
mon salt.

The precise saturation, however, at which deposit
commences to take place is not well established, but
there is one thing which is well known, and that is,
the higher the temperature of the water, the greater
will be the deposit, and from this we conclude that
common sea water would deposit a portion of its saline
matter if heated to a sufficiently high temperature.
The reason of the increase in deposit, as the tempera-
ture is increased, is probably owing to the expansion
of the water, or the separation, as it were, of the par-
ticles.

Water carried at a density that would cause no

LOSS BY BLOWING OFF. 65

deposit at a temperature of 220, would make consid-
erable deposit at a temperature of 260 or 270; and
this is the reason why we are limited to comparatively
low steam in boilers using sea water. Independent of
the saving of the loss by blowing off, repairs to boilers,
labor of cleaning them, <fec., this is a powerful reason why
inventive genius should endeavor to bring forth a relia-
ble fresh water condenser, and why steamship owners
and others, having it within their power, should encour-
age all such attempts, from the fact of the great advan-
tage to be derived from carrying high pressure steam,
and using the expansive principle to its fullest extent.

To the minds of those who cannot clearly see that
an increase of temperature occasions an increase in de-
posit, a practical demonstration can be obtained by
examining the crown sheets, and other parts of marine
boilers, subject to the highest temperature, where it
will be found the largest deposit takes place.

The deposit of lime, or " scale," as it is technically
termed, on the heating surface of boilers, being nearly a
non-conductor of caloric, prevents a large portion of the
heat from entering the water, allowing it to escape up
the chimney, and is therefore lost ; and, if the deposit
of scale be large, the metal of the boiler, being no
longer protected by the water, becomes over-heated
and " burnt." To prevent these results, a portion of
the water is extracted periodically, or continuously,
by the brine pump, or is discharged by the blow-off,
in order to keep the density of the water below the
point at which any serious deposit may take place.
But as all the water discharged from the boiler has
first to be heated, and as it is replaced by water of a
lower temperature, a loss of heat (which is virtually a
loss of fuel) is occasioned thereby. This is technically

66 LOSS BY BLOWING OFF.

termed " loss by blowing off," and we shall proceed to
illustrate the manner of calculating it. Take an ex-
ample.

Supposing the density of the water entering the
boiler to be -gV, and that of the boiler to be maintained
at -g 2 , there will be one part converted into steam, and
one part blown out. Supposing also the temperature
of the water entering the boiler to be 100 Fahr., and
the temperature of the water in the boiler to be 248
Fahr., we have all the data required.

Referring to Regnault's experiments, (page 9), we
see that the total heat in steam having 248 for the
sensible heat, is 1189.58, now then

1189.58 = total heat;
100.00 = temperature of the water entering the

boiler ;
1089.58 = heat required from the fuel for the

water to be evaporated ;
248 = temperature of the water in the boiler ;
100 = " " " entering "

148 = heat lost by blowing off.

Therefore, since one part (requiring 1089.58) is
converted into steam, and the other part (requiring
148) is blown off, the total heat required of the fuel is
(1089.58 + 148 =) 1237.58; and as 148 of this is
blown off, we have 1237.58 : 148 : : 100 : 11.95 + per
cent, loss by blowing at the above density and tem-
perature.

If the water had been carried at a density of If
per hydrometer, one part would have been blown off
as before, but only three-quarters part would have

LOSS BY BLOWING OFF. 67

been converted into steam, hence we would have pro-
ceeded thus

1189.58
100.00

1089.58
.75

817.1850 = heat required from the fuel for the
water to be evaporated.

248
100

148 = heat lost by blowing off.

Therefore (817.185 + 148 =) 965.185 : 148 : : 100 :
15.33 + per cent,

And had the water been carried at a density of
3, i. e. -fa, two parts would have been used for steam
and one part blown off, hence the following :

1189.58
100.00

1089.58

2179.16 = heat required from the fuel for the
water to be evaporated.

248
100

148 = heat lost by blowing off.

Therefore (2179.16 + 148) = 2327.16 : 148 : : 100 :
6.35 per cent., and so on for any density. These per

08 GAIN BY THE USE OF HEATERS.

cents, are the losses in fuel, combustible, minus that
lost from radiation and heated gases passing up the
chimney.

The above calculations apply only to cases where
the water enters the boiler at a density of ^ ; should
it enter at a lower density, the loss will be less, or a
greater density more, because to retain the water in
the boiler at the density assumed in the above ex-
amples, there would either have to be a less or greater
quantity blown off than we have considered to be the
case.

In order not to lose entirely all the heat in the
water blown off, some boilers are fitted with heaters,
or as they are sometimes termed incorrectly, " refrige-
rators." These are a series of pipes surrounded by the
feed water, and through which the water leaving the
boilers has to pass ; by this means the temperature of
the feed water is considerably increased before it
enters the boiler. The following will illustrate

THE GAIN BY PUMPING WATER INTO THE BOILER AT AN
INCREASED TEMPERATURE.

For this purpose two examples will be sufficient,
and we will commence with the first one given above
in the calculation on the loss by blowing off; viz.
steam, 248 ; feed water, 100 ; and density, -^. Now
suppose by the application of the heater, the feed-
water, instead of entering the boiler at 100, is made
to enter at 150, what will be the saving in fuel by its
application ?

GAIN BY THE USE OF HEATEES. 69

Solution.

1189.58 total heat in the steam ;
100.00 = temperature of the feed water ;

1089.58 = heat required from the fuel to evapo-
rate one part of water ;
248 = temperature of the water blown off;
100= " " feed water;

148 = heat lost by blowing off;
and 1089.58 + 148 = 1237.58 = total heat required
from the fuel where the water is pumped into the
boiler at 100. Let us now see what the total heat
will be when the water is pumped in at 150, and the
difference between these results will be, of course, the
saving

1189.58 = total heat in the steam ;
150.00 = temperature of the feed water ;

1039.58 = heat required from the fuel to evapo-
rate one part of water ;
248 = temperature of the water blown off ;
150= " " feed water;

98 = heat lost by blowing off ;

and 1039.58 + 98 = 1137.58 = total heat required
from the fuel when the water is pumped into the boiler
at 150. Therefore

1237.58
1137.58

100=: saving in degrees;

whence 1237.58 : 100 : : 100 : 8.08 per cent. That is
to say, if without the heater the boilers consumed 100

TO GAIN BY THE USE OF HEATEKS.

tons of coal per day, with it they would produce the
same quantity of steam with 91.92 tons.

EXAMPLE 2D.

Suppose that the density of the water in Example 1
was If, and all the other conditions to remain unalter-
ed, what would be the saving in that case ?

Solution.

1189.58 = total heat in the steam ;
100.00 = temperature of the feed water ;

1089.58 = heat required from the fuel to evapo-
rate one part of water ;
.75 = part of water evaporated ;

817.185 = heat required from the fuel for the

water that is evaporated ;
248 temperature of the water blown off ;
100= " " feed water;

148 = heat lost by blowing off;
817.185+ 148 = 965.185 = total heat required from
the fuel when the water is pumped into the boiler at
100.

1189.58 = total heat in the steam ,
150.00 = temperature of tho feed vrr.ter;

1039.58 = heat required from the fuel to evapo-
rate one part of water ;
.75 = part of water evaporated;

779.685 = heat required from the fuel for the
water that is evaporated ;

INJECTION WATEE. 71

248 = temperature of the water blown off;
150= " " feed water;

98 = heat lost by blowing off;

779.685 + 98 = 877.685 = total heat required from
the fuel when the water is pumped into the boiler at
150. Therefore

965.185

877.685

87.5= saving in degrees.

Whence 965.185 : 87.5 : : 100 : 9.06 per cent. And
in this manner the calculation can be made for any
density and temperature.

In making calculations on the theoretical saving
from the use of the heater, we have seen some engineers
who calculate the loss by blowing off without it, and
again with it, and take the difference between these
two results for the saving; but it will require but
little reflection for any one at all conversant with such
subjects, to perceive the .error of this mode of calcu-
lation, as it takes no cognizance whatever of the extra
heat given to that portion of the water which is evap-
orated. The mode of calculation given above is the
only correct one, as it takes into consideration all the
elements.

INJECTION WATEE.

After the steam has performed its duty in the
cylinder, and been exhausted into the condenser, a cer-
tain amount of cold water is admitted into that vessel
for the purpose of condensing it, and this quantity
depends upon the temperatures of the water and the
steam. We will take an example.

72 EVAPORATION.

Suppose the temperature of the injection water to
be 60; steam as it enters the condenser, 212; and
water in the condenser, 110. Required the proportion
of injection water to the water evaporated in the
boiler :

Solution.

1 1*78.6 = total heat in the steam at the sensible

temperature of 212 ;

110.0 = temperature of the water after conden-
sation ;
1068.6 = heat to be destroyed ;

110 = temperature of the water after conden-
sation ;
60 = temperature of the injection water,

50 difference.

Now then we see that we have 1068.6 of heat to
be destroyed, and only 50 to do it with, therefore we
must make up this difference in quantity ; hence 1068.6
-f-50 = 21.372 times the evaporated water to be ad-
mitted into the condenser to condense the steam and
retain the condenser at the temperature of 110.

EVAPORATION.

Among the important elements to be ascertained
in the performance of the steam engine, is the quantity
of water evaporated in the boilers per unit of coal, or
other fuel. In sea boilers using salt water, one pound
of coal evaporates from 4 to 9 pounds of water, de-
pendent upon the quality of the coal, the construction
and cleanliness of the boilers. Those boilers are of
course the best which evaporate the largest quantity,
and hence the importance of knowing the exact per-
formance of each boiler, as well as of the different kinds

EVAPORATION. 73

of fuels used in the same. To secure this desirable end
we proceed thus :

Ascertain from indicator diagrams the fraction of
the cylinder filled at each stroke, from which, know-
ing the diameter of the cylinder, we ascertain the
number of cubic feet of steam required to fill that
space, and to this we add the space in nozzles, clear-
ances, &c., which gives the number of cubic feet of
steam used per stroke ; and the number of cubic feet of
steam used per stroke, multiplied into the number of
strokes per hour, and divided by the relative volumes
of steam and water, at the pressure the steam is admit-
ted into the cylinder, gives the number of cubic feet
of water evaporated per hour, and the number of cubic-
feet of water evaporated per hour, multiplied by 64.3,
(the weight in pounds avoirdupois of one cubic foot of
sea water,) and divided by the number of pounds of
coal used per hour, gives the number of pounds of water
evaporated per pound of coal, provided there is no
blowing off done ; but wherever there is blowing off,
this last result has to be increased to the extent of the
loss by blowing.

Suppose for instance, proceeding in the manner
given above, we find 6 Ibs. of water to be evaporated
per pound of coal ; and the loss by blowing off to keep
the water at the proper density to be 15 per cent.,
the remaining 85 per cent, is that which evaporates
the 6 Ibs. ; hence 85 : 6 : : 100 : 7.06 Ibs. of water evap-
orated per pound of coal.

EXAMPLE. Suppose you have a cylinder 70 inches
diameter by 10 feet stroke ; the initial pressure of
steam in the cylinder 24.5 Ibs. per square inch, in-
clusive of the atmosphere, cut off at \ from commence-
ment of stroke ; clearance, <fec., 10 cubic feet ; revolu-

74 EVAPOEATION.

tions, 15 per minute; coal consumed per hour, 1,500
Ibs.; water carried at If per hydrometer; temperature
of feed water, 107 Fahr. ; required the number of
pounds of water evaporated per pound of coal :

Solution.
W 854 X ~ + 10 = 76.8125 cubic feet of

144 4

steam used per stroke; and 76.8125 x 15 x 2 X 60
138262.5 cubic feet of steam used per hour.

The relative volumes of steam and water at the
pressure of 24.5 Ibs. are 1064 to 1 ; hence

1S8262 5

rj X 64.3 1500 = 5.57 Ibs. of water per pound
1064

of coal, neglecting the loss by blowing off; but, ac-
cording to the conditions of the example, the loss by
blowing off is found to be 14.1 per cent., the remain-
ing 85.9 per cent, is that therefore which evaporated
the 5.57 Ibs. of water; hence the true evaporation is
found to be 85.9 : 5.57 : : 100 : 6.48 Ibs. of water per
pound of coal.

The above calculation takes no cognizance of the
leakage of the valves, loss by radiation, or condensa-
tion in the cylinder, pipes, <fec. ; hence the results show
too small, but it is the only standard of comparison.

Some parties calculate the evaporative power of
boilers by measuring the quantity of water pumped
into them during any given time, and also the quantity
of coal consumed in the furnaces during the same time,
and dividing the weight of the former by the latter,
which they conceive gives the weight of water evapo-
rated per unit of coal. Upon first sight this mode of
operating appears very simple and correct ; but unfor-
tunately, notwithstanding its simplicity, the results are

STEAM AND VACUUM GAUGES. 75

never accurate, the evaporation being always shown
too large, for the very simple reason, that all the water
pumped into a steam boiler is never evaporated. All
boilers, and pipes, and cocks attached thereto, leak
more or less, and sometimes boilers foam, occasioning
water to be worked into the cylinders, and as, accord-
ing to this mode of calculation, all water escaping by
this means is supposed to be evaporated, the result
manifestly cannot be correct.

Steam and vacuum Gauges.

As applied to the marine steam engine, the mer-
curial steam and vacuum gauges are the most common,
though of late years there have come into use a variety
of metallic gauges, many of which, from the little
attention they require, appear to be very well adapted
to the purpose for which they were intended.

The most prominent of these are " Schaffer's,"
"Hearson's," "Schmidt's," " Ashcroft's," "Eastman's,"
" Stubblefield's," and "Allen's." In the first three,
the spring is a thin corrugated plate, upon which the
steam acts, communicating motion to a hand or pointer
which moves around a circular disc marked in pounds :
the spring in Ashcroft's gauge is a bent tube, which
the elasticity of the steam tends to straighten. East-
man's gauge is a combination of springs and levers.
As these gauges are all constructed on the same prin-
ciple, viz., the elasticity of metal, we shall not stop
here to describe them, as it is more directly our object
to deal with principles, rather than mechanical ar-
rangements, which are the chief peculiarities of these
gauges. We will pass on to the mercurial closed top
vacuum gauge.

STEAM AND VACUUM GAUGES.

Fig. 43.

a b c d, figure 43, is a basin filled
with mercury up to the point A ; the
tube B is also filled with mercury.
The pipe e communicates with the
condenser, and when that vessel is
filled with air of the atmospheric
pressure, the surface of the mercury
in the basin is pressed with a pres-
sure of about 15 Ibs. per square inch,
causing the tube B to remain filled ;
but when a partial vacuum is created
in the condenser, the mercury having
no longer the atmospheric pressure
to sustain, falls in the tube B, and
the figures marked on the scale will
exhibit the extent of the vacuum.
With this arrangement, therefore, there is no necessity
of making the tube 30 inches in length, as all engines
are supposed to maintain at least 17 or 18 inches of
vacuum, and a tube long enough to show this is all
that is required. Could the surface of the mercury
remain constantly at A, the divisions on the scale
would be of equal lengths, and one inch apart, but as
the mercury rises a little in the reservoir as it falls in the
tube, the lengths of these divisions vary a little, depend-
ent upon the relative volumes of the tube and reservoir.
The aperture in the lower end of the tube is made
very small, to prevent the oscillation of the mercury.
At A is a small hole fitted with a screw. This is left
open, while filling the gauge, as an overflow to the
surplus mercury, it being so situated that the contents
of the tube B is just sufficient to fill the reservoir to
the point 30, or the true vacuum line.

The pressure of the atmosphere, as it varies from
time to time, does not alter the indications of this

STEAM AJSD VACUUM GAUGES.

FIG. 44.

gauge, inasmuch as it always exhibits the difference
between the vacuum in the condenser and a perfect
vacuum.

Had the top of the tube B communicated with the
condenser, and the basin abed been open to the
atmosphere, the gauge would then have been what is
termed an open-top vacuum gauge, and would require
to have been 30 inches in length the scale being
reversed, the lowest figure commencing at the bottom.
With such a gauge, all variation in the pressure of the
atmosphere affects its indications.

Figure 44 is a siphon steam gauge,
filled with mercury to the level a a.
The short leg connects to the boiler,
and the long leg is open to the atmo-
sphere. The steam pressing upon the
mercury at , forces up the stick resting
on the mercury in the other leg at ',
showing the pressure in pounds per
square inch, marked on the scale at the
top of the gauge. These divisions are
one inch apart, and indicate pounds
pressure, for the reason that the descent
of one inch in the short leg causes a rise
of one inch in the long leg, making a
difference in the level of the mercury
of two inches, which corresponds to one
pound pressure ; that is to say, a column
of mercury two inches high, and having
a base equal in area to one square inch,
will weigh in round numbers one pound.
In making a gauge, it matters not
what may be the diameter of the tube,
but whatever it may be, it should be uniform through-
out, in" order that the indications may be correct.

T8 STEAM AND VACUUM GAUGES.

The stick that is put in the long leg, when there is
no steam on, has one end resting on the mercury, while
the other stands at 0. This stick should be made of
some very light wood soft white pine answers the
purpose very well, with the lower end a little the
largest, in order to have a good bearing on the mer-
cury.

To convert this gauge into a vacuum gauge, it
would be necessary only to connect the long leg to
the condenser, and attach a scale to the short leg with
the lowest number commencing at the top.

CHAPTER IV.

CASUALTIES, ETC.

How to act if the Eccentric be broken in an irreparable

manner.

IF there be two paddle engines connected at an angle
of 90, connect the starting bar of the deranged engine,
by means of a line and guide pulleys, to the cross-tail,
air-pump beam, air-pump cross-head, or other part
having motion coincident with the piston of the other
engine, to give the bar motion in one direction, and
attach a heavy weight to it, with a line running over
a pulley, to give it motion in the opposite direction.

If there be but one engine, connect by similar
means, to the connecting rod of the deranged engine,
which will give the proper motion.

How to act lulien a Steamer springs alealc and com-
mences to fill rapidly.

Put on immediately all bilge injections and bilge
pumps, and shut off all other injections. If they do
not keep the water down, break the joints on the bot-
tom, or side injections, and allow them to draw water
from the bilge, taking care to station a man at each
one to prevent any thing from passing in that would
choke the valves.

Vessels are sometimes saved from foundering by
6

80 CASUALTIES, ETC.

covering the leak with a sail-cloth passed over the
bows and under the bottom.

If the leak be a large one, such as one occasioned
by a collision, it may be possible to force a mattress, or
something of that nature, into it from the outside.

Hoio to proceed when all the feed is on and the water
does not rise in tlie boilers.

It sometimes happens that when all the feed is on,
and the feed pumps are apparently performing their
usual duty, the water does not rise in the boilers, but
either retains its level at the time the feed was put on,
or gradually falls. In this event, one of two things
must be manifest either that the water does not enter
the boiler, or if it does enter, is escaping through some
other orifice. The first thing, therefore, to do, is to
examine the check valve to see if it is in operation.
This can be done by applying the ear to the chamber,
to ascertain if the valve rises and falls, at each stroke
of the pump, and also by applying the hand to the
pipe, immediately below the check valve, in order to
ascertain if it be cool. If these are found to be all
right, examine the blow-off cocks, and all other water
connections with the boilers, to ascertain if they be
closed ; some of which, in all probability, will be par-
tially open, but if they should all be found closed, the
pump must be pumping air into the boilers instead of
water. The next step would therefore be, to examine
the pump and induction pipe, in order to ascertain and
stop the air leak.

Upon examining the check valve, should it not be
found in operation, the next step would be to examine
the pump, to see if it was hot ; also relief and pump

CASUALTIES, ETC. 81

valves, to see if they were gagged ; and lastly, the
eduction pipe, to see if it were burst either of which
causes would prevent the pump from delivering water.
A feed pump may get hot from four causes :

First. There may be so small a quantity of injec-
tion water used as to cause it, when delivered to the
hot well, to be of sufficiently high temperature to heat
the pump.

Second. Friction, occasioned from muddy water, or
tight packing.

Tkird. The check and delivery valves may be
caught up or very leaky, allowing the hot water from
the boiler to run back to the pump.

Fourth. External application of heat, the pump
being situated near the boiler or other hot body.

A feed-pump cannot deliver water when hot, for
the reason that the vapor constantly generated within
it, by its elasticity prevents the induction valve from
opening and admitting water.

Should the feed pipe burst, it can be repaired tem-
porarily by wrapping it with canvas coated with white
lead ; this being secured by strong twine or marline,
wound closely around the pipe the full length of the
canvas.

Should the pipe be split open for a considerable
distance, it might first be closed with wood or iron
clamps, as came most convenient, before applying the
canvas and twine.

Foaming.

Foaming, or pruning, as it is sometimes termed, is
violent ebullition or agitation of the water, occasioned
by an undue relation of temperature between the
steam and water. Thus, supposing a large quantity

8 "2 CASUALTIES, ETC.

of steam to be suddenly taken from the boiler, the
pressure of steam is immediately reduced below what
is due to the temperature of the water, and the result
is a sudden rising up of the water from all parts of the
boiler. Foam can, therefore, be defined to be a mix-
ture of steam and water. Boilers are known to be
foaming when the water does not come out of the
gauge cocks solid, or when there is a considerable agi-
tation of the water in the glass gauges.

To suppress foaming, put on a strong feed arid
blow off, cut off shorter or partially close the throttle.
Oil or melted tallow, injected into the boilers through
the feed pumps, will also prevent foaming, but these
are somewhat expensive expedients.

Boilers constructed with insufficient steam room,
are most likely to foam, because at each stroke of the
piston a large proportion of the steam is taken from
the boiler, and the pressure therefore becomes mate-
rially reduced. Boilers also constructed in such a
manner as to prevent the easy escape of steam from
the surfaces on which it is generated, are likely to
foam. Thus, supposing there be a large amount of
heating surface on the crowns and other parts towards
the bottom of the boiler,, and that the steam generated
on these surfaces in consequence of coming in contact
with the flues, tubes, braces, &c., can find but a com-
paratively small exit to the surface of the water,
the result will be, that where it does escape, it will
force a large body of water up, mixing it with the
steam.

To cany too much water in boilers will cause them
to foam by reducing the steam room. Running from
salt to fresh water, or vice versa, will also cause foam-
ing; in the former case, because fresh water boils at a

CASUALTIES, ETC. 83

lower temperature, but a satisfactory explanation of
the latter case appears to be difficult to arrive at. The
boilers of sea steamers, when running in muddy rivers,
usually foam considerably.

It sometimes occurs, while the boilers are foaming
badly, that the engines have to be stopped in order to
take soundings, or from other causes. Now, the first
thing after stopping the engines, in any case, is always
to try the water; for it will mostly always be found
to be lower when the engines are standing still than
when under way, but when the boilers are foaming, it
is of the highest importance to try immediately the
height of the water, for as the foaming ceases after the
engines are stopped, it may happen that the water has
fallen entirely out of the gauges and left the flues, in
which event, if the engines were going to be started
again in three or four minutes, the better plan would
be to open the safety valve to keep the water foaming,
so as to keep the flues covered, and when the engines
are started again to put all the feed on. But if the
engines were going to stand still for a considerable
time, blow off a portion of the steam, if it be too high,
dampen the fires a little, and put on the auxiliary feed.

The Condenser heats.

When engines are standing still, it sometimes
occurs that the condenser gets so hot, that when it
becomes necessary to start again, the pressure has be-
come so great in it, that the injection water will not
enter. Leaky steam and exhaust valves will alone
cause this, but in no case should it ever be allowed to
occur. When an engine begins to get hot, the crack-
ing noise in the condenser, and about the foot valves,

84 CASUALTIES, ETC.

will always indicate what is going on, time enough to
check it, which can be done by giving a little injec-
tion, and causing the engines to make two or three
revolutions back and forth. If, however, the engine
should become too hot to take the injection water, the
only plan will be to blow through, or pump water into
the condenser if there be such an arrangement, or to
cool the condenser by external application of cold
water.

If when under way it is indicated by the gauge
that the engine is gradually losing its vacuum, apply
the hand to the condenser, in order to ascertain if it
be getting hot, and if such be found to be the case
give a little more injection ; but if that does not help
the cause, give more still. If the vacuum continues to
grow less, the probability is that the injection pipe
has become choked ; in which event shut off that in-
jection and put on another. Should both the bottom
and side become choked, inject from the bilge. Should
the bilge injection also be out of order, the engine will
have to be stopped, and the snifting valve secured
down (if there be one) while the injections are blown
through to clear them. Sea weed, and things of that
nature, sometimes get over the strainers of injection
pipes, preventing the entrance of water.

Most if not all marine engines of modern construc-
tion are fitted with a thermometer to the hot well, to
ascertain the temperature of the water, which is usually
carried from 100 to 115 Fahr. This instrument is
very important, in order to maintain an even temper-
ature (the sense of touch of the engineer's hand not
being delicate enough for that purpose), for it may
often occur that there may start small leaks about the
condenser and exhaust pipe joints, which would cause

CASUALTIES, ETC. 85

a decrease in the vacuum, and, as without the ther-
mometer, the first impulse would be to give more
injection, with it we would turn our attention to find-
ing and stopping the leak. This can be done by hold-
ing a lighted candle around the joints, and wherever
there is a leak the flame will be drawn in. To stop it,
mix a little putty, of white arid red lead, and apply it
to the crevice ; the presence of the atmosphere will
force it in.

Getting under way.

When lying in port, where the steam will not be
required for at least four or five days, it is proper that
the water should be blown or pumped out of the
boilers, and a portion of the man and hand-hole plates
removed, to allow a circulation of air. When, there-
fore, the order is given to get up steam, the first thing
is to see that all these plates are put on, and the joints
properly made, and this duty should receive the direct
superintendence of the engineer having charge of the
same ; for should any one of them leak badly after the
steam is raised, the departure of the ship might be de-
layed some hours in consequence. After this duty has
been properly attended to, open the blow-off cocks and
run the water up in the boilers to the proper level, or,
if the boilers are so situated that the water will not run
up high enough, finish the supply with the hand
pumps, wood the furnaces while the water is entering
the boiler, and when the proper height of water is
attained start the fires. If it be important to raise
steam quickly, start the fires as soon as water is dis-
covered in the gauges, continuing the supply while the
fires are burning. As a small quantity of finely split
wood, with a little shavings or oily waste placed in

86 CASUALTIES, ETC.

the mouth of the furnaces, is all that is necessary to
start the fires, the back part of the furnaces, particu-
larly in boilers with inferior draft, should be covered
with a layer of coal to keep out the cold air.

In raising steam it has been the custom to recom-
mend that the valves of the engine be blocked open,
so as to allow the heated air from the boilers to pass
in and warm up the engine before steam begins to be
generated ; but as in many cases this is attended with
considerable trouble, and as the advantages to be de-
rived from it are very small, it hardly appears to the
author's mind to " pay." The safety or vacuum valve
should, however, be kept open until steam begins to
form, in order to let the heated air escape. The strain
upon boilers being from the inside, they are con-
structed and braced with the special view of with-
standing this strain, many of the braces being entirely
useless in sustaining a pressure from without ; marine
boilers are therefore fitted with a small valve opening
inwards, and weighted so as to open and admit air
whenever the pressure from within falls to about five
pounds per square inch below the atmosphere. These
valves are called differently by different parties, as
follows : vacuum valve, air valve, reverse valve, &c.

After steam has been raised to 3 or 4 Ibs., the
engine should then be blown through and warmed up,
and after sufficient steam is raised to move the piston,
the engine should be turned over two or three times,
to see that every thing is right, before reporting
ready.

On Coming into Port.

After the engines are no longer needed, before
hauling the fires, after a long run, it would be well

CASUALTIES, ETC. 87

to try the pistons and valves, in order to ascertain
if they be leaky. To try the piston, open the water
valve on one end of the cylinder and the steam
valve on the opposite end ; if the piston leaks, the
steam will escape through the water valve. To ascer-
tain if the steam valves leak, open the water valves on
both ends of the cylinder. To ascertain if the exhaust
valves leak, open the steam valves and any cock
in the exhaust side of the steam chest or exhaust
pipes.

While under way it may be discovered that there
is a slight thump in the engine when passing one or
or the other or both centres, and the indicator hav-
ing been applied shows the usual lead, the inference
is that some part of the working engine is loose ; it is
important, therefore, to find out what it is on coming
into port. To do this place the engine on the centre,
and give the piston steam suddenly by raising and
lowering the starting bar ; observe closely the cross-
head, crank-pin, main-shaft, and other main connections,
to see where the jar is. Should it not be discovered
after this, jam the cross-head fast, so as to prevent the
slightest motion, and then give steam as before, in
which event, if the thump be still felt, the piston will
doubtless be found to have worked a little loose.

If it be the intention to remain in port several
days, before hauling the fires, sufficient steam should
be raised, if the boilers be capable of bearing the
pressure, to blow all the water out of the boilers. After
the boilers become cool, the hand-hole plates, over the
furnaces particularly, should be taken off, to examine
the crowns, where the greater amount of scale will be
found deposited, and from which we can judge if the
boilers require scaling. Mere dampness in boilers is

88 CASUALTIES, ETC.

found to be injurious, by occasioning a rapid oxida-
tion, and in order to prevent this, one or two hand-
hold plates should be taken off the bottom of the
boilers, in order to let the water drain out dry. It
would be well also to remove a man-hole plate from
the top of the boilers to allow a circulation of air.
If these things cannot be done it will be better to keep
the boilers filled with water, rather than a small
quantity in the bottoms. In damp climates, such as
the Isthmus of Panama, light fires should be made in
the ash-pits occasionally.

Scaling Boilers.

Notwithstanding the water in the boilers is not
allowed to exceed in density If to 2 per saline hydrom-
eter, it will be found after a time that a quantity of
scale, composed principally of lime, has accumulated
on the crown sheets, tubes or flues, and other parts of
the boiler. If this be allowed to remain the metal
will become overheated and burned ; it becomes ne-
cessary, therefore, to remove it, which can be alone
done by mechanical means. Sharp-faced " scaling
hammers" can be used to knock the scale off those
places that are within the arm's reach, and long bars
flattened at both ends, and sharpened, called " scaling
bars," will knock it off the more remote parts. In the
Martin tubular boiler, which is accessible in every
part, it is only necessary to condense the steam in the
boilers for a day or so after the ship comes to anchor ;
this will soften the scale so that a gang of men may be
put into them as soon as the man-hole plates are re-
moved, and scrape off all of it in a few hours. The
scale, however, must never be allowed to exceed the
thickness of writing paper.

COMING TO ANCHOE. 89

It has been proposed in some quarters to heat the
tubes or flues by burning shavings, or some other such
substance in them, and then to cool them off suddenly
by pumping cold water upon them, the sudden con-
traction causing the scale to crack off. This plan, how-
ever, to our mind, does not deserve much favor, and
never should be resorted to, if the scale can be reached
in any other manner, for the production of leaks will
mostly always be the result.

It is, however, hoped that engineers will 'soon be
relieved from this duty, and steamer owners benefited
by the introduction of fresh water condensers into all
sea steamers.

Preparatory to coming to Anchor, or securing to the

Wharf.

Fifteen or twenty minutes before coming to anchor,
or making fast to the wharf, the chief engineer should
be informed of the fact by the officer of the deck, or
some other person informed on the matter, so that the
fires can be allowed to burn down, and the pressure of
steam, permitted to fall to such an extent that the
necessity for blowing off is avoided. By this means
the great nuisance of blowing off steam is not only
obviated, but there is a considerable saving in fuel,
the fires being permitted to burn down sufficiently low
to supply only the amount of steam required while
working the engines by hand, rendering it much easier
also on the firemen (whose duties on any occasion are
arduous enough) by having a very light, instead of a
very heavy fire to haul.

In coming to anchor it is usually well to pump a
little extra water into the boiler, so as to insure a
proper supply while operating the engines by hand.

90 THE FIRES WHILE UNDER WAY.

When it is desired to raise steam, the order from
the captain should always be what time it is intended
to get underway, leaving to the discretion of the chief
engineer to start the fires at such time as he may con-
sider proper, in order to secure steam and every thing
ready at the proper time.

Regarding the Fires while under Way.

Small as this may appear in the eyes of one not
practically conversant with the management of the
steam engine, it is one of the most important things
that the engineer is called upon to regulate : on the
one hand, that a proper and uniform supply of steam
is maintained, and on the other, that more fuel is not
consumed than is actually necessary to produce the re-
sult. Different fuels and differently constructed boil-
ers require the fires to be regulated in a different
manner, and notwithstanding the repeated efforts, the
adoption of specific rules, which shall apply alike to
all, is positively absurd. A few general hints, how-
ever, touching the leading features, may be useful to
those who have not had much experience in this mat-
ter, but they must bear in mind, nevertheless, that
actual service and observation for themselves, will
alone make them proficient, no matter how well they
may understand the chemistry of coal, or the natural
laws governing the combustion of matter.

The proper supply of atmospheric air, and the
proper time for the combustion, are the important ele-
ments in the consumption of coal. A slow rate of
combustion, and a moderate draft, always producing a
better evaporative result, than when the fires are urged,
occasioning them to be more rapid; and hence, on

THE FIEES WHILE TJKDEK WAY. 91

no occasion, should " blowers " be resorted to, if the
proper supply of steam can be maintained without
them.

The fire should be spread uniformly all over the
grate bars, and in the use of bituminous coal, should
be from 6 to 8 inches in thickness, but with anthracite
coal, 4 or 5 inches will be thick enough. So long as
the ash pit remains bright, there is no necessity for
slicing or stirring up the fire, but whenever the spaces
between the bars become choked with clinker, or
ashes, it will be indicated by the darkness in the ash
pit, and, if burning bituminous coal, a slice bar should
be run in through the stoke holes or furnace doors to
break up the fire and clear out the air spaces. A pick
applied from below is also very useful in this respect.
In the use of anthracite coal the pick alone should be
used ; the breaking up of the surface of such fire, as
it does not amalgamate or run together, forming a
crust like the bituminous, prevents the regular uni-
form combustion by allowing too much air to enter
among the disturbed parts of the coal, it requiring
considerable time for them again to unite in regular
ignition after being once disturbed. It is very impor-
tant that no part of the grate bars be left bare, as the
admission of cold air, through such space, deadens the
fire, and cools the flues. It has been ascertained of
late, that better results are obtained by admitting air
through a number of small holes in the furnace doors,
on the plan of W. Wye Williams, Esq., of England.

No two furnaces should be fired at the same time ;
the fresh coal of the one should be fairly ignited before
a new supply is added to another, in order to keep a
regular supply of steam. Anthracite coal requires less
frequent firing than bituminous, but with either, the

92 THE FIRES WHILE UNDER WAY.

coal should not be thrown upon any particular part
of the furnace, but uniformly all over it. Before
firing with bituminous coal, it is well to break up the
upper crust of the fire, which sometimes amalgamates
so closely as to exclude the proper supply of air. The
trouble with most firemen is, that they are disposed to
heap their fires too much, particularly in front, some-
times half way to the crowns ; this they do for three
reasons : first, because they suppose the larger the fire
the greater the supply of steam ; second, the more
coal there is piled in at one time, the less frequent
they will have to fire ; and third, it requires much less
labor to shovel the coal into the mouth of the furnace,
than to supply it uniformly, all over the grates. No
coal larger than one's fist should be allowed to enter
the furnace, nor in cleaning the fires, should more than
one be cleaned at the same time, which should be done
at stated intervals, unless it so happens, that they all
or many of them, have got so dirty that a further sup-
ply of coal is useless, when the engine can be throttled
off a little while the cleaning is going on. In cleaning
anthracite fires, care should be taken not to reduce
them too low, otherwise they will take a long time to
recover.

In cleaning fires, as well as when supplying them,
the furnace doors should not be kept open longer than
necessary, admitting an undue supply of cold air ; and
the party, therefore, who, performing his 'duty as well,
does it the quickest, is the best fireman.

The slower a steamer runs the greater distance she
will perform with the same amount of fuel, provided
she has not an adverse tide or head winds to contend
with ; with men-of-war, therefore, it often occurs that
the saving of fuel is a more important consideration

PATCHING BOILERS. 93

than high speed, and for this reason the consumption
of coal is reduced far below what would be required
to keep the vessel up to her maximum speed. This
can be done in two ways : either by shutting off a por-
tion of the furnaces entirely, by shutting the ash pit
doors and closing up the cracks around them with wet
ashes, or else reducing the quantity of coal consumed
in each, by covering the back part of the grates with
a thick layer of ashes. When the diminution in the
quantity of coal is not very large, this latter plan is
the better, by retaining the original heating surface at
the same time that the combustion of coal is allowed
to go on very slowly, an end very desirable to secure.
When, however, the reduction in coal is very consid-
erable, some of the furnaces can be shut off, while the
back ends of the grates of the remainder can be kept
covered with ashes. Men-of-war sometimes proceed at
half or less speed, and as a large extent of boiler sur-
face occasions considerable loss from radiation, in such
cases it will be more economical to shut off some of the
boilers and continue with a moderate supply of fuel in
the remainder. The furnaces and ash pits of the boil-
ers shut off should be closed tightly, to prevent cold
air from passing in to cool the surfaces of the other
boilers, or to injure the draft.

After a boiler is shut off, the steam should not be
allowed to escape, but to remain in it and condense, to

freshen the water.

Patching Boilers.

Inasmuch as all things constructed by human hands
are liable to decay, steam boilers are not exempt from
this infallible law ; they therefore frequently require
to be patched, new stay bolts and braces to be put in,

94 PATCHING BOILERS.

old rivets cut out and replaced with new ones, <fec. In
patching boilers, wherever the defective part can be
reached so as to work at it well, it is best to cut it out
and rivet a patch on, calking the seams ; but as this
cannot always be done, the most common practice is
to put a patch over the defective part, securing it with
bolts and nuts, or tap bolts, and making the joint with
stiff putty, composed of white and red lead, and a
small quantity of fine iron borings. A piece of sheet
lead fitted over the place to be patched, will answer
for the pattern to make the patch by, which, however,
before the joint is made, should be fitted snugly to its
place while hot.

Owing to imperfection in the iron, small cracks are
sometimes discovered in the flues or other parts of the
boiler, subject to a high temperature. Should these
not be more than two or three inches in length, they
can be stopped by drilling holes and putting in three
or four small rivets, hammering the heads well down
so as to cover the crack.

A leaky stay-bolt, or rivet, has, like the toothache,
but one sure remedy, and that one is to cut it out and
put in a new one.

In cutting out a stay-bolt fitted with a socket, the
latter can usually be saved and retained in its place,
ready to receive another bolt ; but sometimes a screw
bolt is cut out which has to be replaced with a socket
bolt, and as this may be in such part of the boiler
which cannot be reached by the arm, or tongs, a very
good plan to get the socket in its place, is to pass a
string through both holes and secure the ends, drop-
ping the centre down and hauling it out through a
hand hole ; cut the string in two, pass the ends through
the socket, join them together again, and haul the

FLUES AND ASH PITS. 95

socket to its place. In the fitting of sockets, it is very
important that they should be the exact distance be-
tween the sheets, with the ends filed square, otherwise
the sheets will be drawn out of shape.

Sweeping Flues.

One of the most disagreeable parts of the duties is
that of cleaning flues, from the fact of its dirtying
every thing round about or in the vicinity of the boil-
ers, the slightest draft being sufficient to waft the light
dry ashes in every direction. A little water sprinkled
on them before they are hauled out of the connections
or smoke-boxes will prevent this in a measure, the
damper and ash-pit and furnace doors being closed, to
prevent the men from being suffocated who go inside.
The lower flues, particularly, are apt to leak a little,
and the salt water, mixing with the ashes, forms a solid
mass, which can only be removed by being cut out,
the flue brush being of no avail. The hammer and
chisel, and long, sharp-pointed bars, and sledge, are
best adapted to the purpose. In the use of these
instruments, care should be taken that they be not
driven through the metal or under the seams.

Ash Pits.

The ash pits should be cleaned out every watch,
and the ashes thrown overboard, picking out first any
lumps of coal that may have fallen among the ashes.
When not running at full speed, a portion of the cin-
ders may be thrown upon the fires again, after damp-
ing them with a little water. So also should fine
bituminous coal be dampened before being supplied
to the furnaces, the arguments to the contrary not-
7

96 STAYS AND GEATE BARS.

withstanding ; for though it does take a little heat from
the fire to evaporate the water mixed with the coal, a
saving is effected 1 , by preventing the coal from being
drawn particularly in boilers with strong draft-
through the flues and lodged in the connections, or out
of the smoke-pipe. No more water, however, should
be put on the coal than just sufficient to dampen it.

Smok&pipe Stays

Require to be looked to occasionally, when made
of rope, as they grow a little slack from time to time.
These should always be adjusted while the pipe is hot ;
otherwise, if they be set up while the pipe is cool, the
expansion after it becomes heated will, in all proba-
bility, " carry " either the stays themselves away, or
the band securing them to the pipe. In a gale of
wind, when the ship is rolling heavily, these stays
should be looked to, in order to tighten any of them
that may have become slack, so as to throw the strain
alike on all. Hemp rope is a very inferior article for
such purpose as stays for smoke pipes, and we can see
no good reason, unless it be prejudice, (which is always
a good reason to those under such influence,) why it
has been so long retained. Good wire rope looks bet-
ter, is cheaper, and will last a great deal longer, and
requires much less attention.

Grate Bars, &c.

When fitted new, are usually allowed plenty of
play, both fore and aft and sideways, to allow for ex-
pansion after they become heated. The. spaces at the
end of the bars, however, become choked up with
ashes, which become, by and by, so hard as to form

BROKEN AIR-PUMP. 9*7

almost a solid mass, defeating the objects for which
they were left. These spaces, therefore, in port,
should be cleaned out occasionally.

Ash pits, in port, should also be well cleaned and
painted, to prevent oxidation. At sea, no water should
be thrown into them upon the ashes, but they should
be kept as dry as possible. With these precautions,
they will last as long as other parts of the boiler.
Boilers unused for any considerable time should be
kept dry of water, and have fires made occasionally in
the ash pits, to evaporate all interior deposit of damp-
ness the neglect of this precaution is the sole cause
of the oxidation and deterioration of all boilers when
not in use.

Broken Air-Pump.

Should the air-pump become broken in an irrepar-
able manner, and the engine be a single one, there is
but one thing that can be done, and that is to work
non-condensing. If there be two engines, we have
three resorts: to work the broken engine non-conden-
sing, to disconnect from the crank pin and proceed
with one engine, or, if there be facilities on board, to
join the exhaust of both engines with a pipe, and use
one air-pump and one condenser for both engines.
This latter plan was tried very successfully for a short
run on board the U. S. Steam Frigate " Powhatan,"
on the China station, in the summer of 1855. Peculiar
facilities were, however, offered in this case, as the ex-
haust side pipe of each engine had a man-hole in it, to
which the connecting pipe was joined.

In running under such circumstances, care should
be taken not to overload the air-pump.

98 CYLINDER HEAD AND SELECTION OF COAL.

Broken Cylinder Head.

Water may be worked over into the cylinder sud-
denly, from boilers foaming badly, or otherwise, faster
than it can escape through the water valves, and being
nearly non-compressible, something must give way, the
cylinder head, or bottom, being the most likely thing to
go. In such an event, if there be a spare one on board,
put it on ; if not, while the old one is being repaired, if it
be reparable, the following plan can be resorted to ;
Disconnect the steam and exhaust valves from the
damaged end of the cylinder, if the engine be fitted
with poppet valves, and let the atmospheric pressure
force the piston in one direction, the steam being used
for the opposite direction. Should the engine be fitted
with a slide valve, close up the opening into the dam-
aged end of the cylinder, by fitting in, steam-tight and
in a substantial manner, a block of soft wood. This
should not, however, be resorted to, except in cases of
great emergency. Cylinder heads should have man-
hole plates of less strength than the heads ; this would
prevent the destruction of heads in all cases.

The selection of Coal.

The kinds and qualities of coals are so varied that
no general rules can be given for their selection, but
there is one point, however, which we think will not
be disputed, and that one is, whenever there is a
choice, the only sure plan is to select the best ; for,
though its first cost may be a little more, it will prove
to be the cheapest in the end. What economy is there
in purchasing one coal because it can be obtained 10

SAFETY VALVE. 99

or 15 per cent, cheaper than another, when there will
be burned, to produce the same effect, from 20 to 25
per cent, more than would be burned by the better
kind ? Yet this is a thing of daily occurrence. But,
regardless of the money view, there are other disad-
vantages attending the use of the inferior coal. From
the fact of there being more burne"d, the firemen have
more to supply to the furnaces, and it requires, on
their part, greater care and attention to keep the fires
in good order ; thus imposing extra duty on a portion
of the ship's crew whose energies are usually overtaxed.
Besides, to convey the vessel a given distance, an extra
quantity has to be taken on board, which, in the case
of merchant ships, diminishes their freight capacity, or,
in war ships, lumbers the deck with a useless number
of bags.

Some boilers are best adapted to bituminous coals,
others to anthracite, and the one or the other of these
coals which should be selected, depends upon the cir-
cumstances, therefore, for which they are intended.

In the selection of coals, it is an object to obtain
those free as possible from earthy impurities. Slate,
and such like matter, is to be avoided. Sulphur in
bituminous coals makes them the more liable to spon-
taneous combustion. So also receiving them on board
wet will endanger spontaneous ignition. Coals which
have been exposed a long while to the rays of the sun,
particularly in tropical climates, undergo a gradual
decay, reducing their evaporative qualities.

Safety Valve.

Steam, when once commencing to blow off, will
not cease when the pressure has fallen to the pressure

100 SAFETY VALVE.

due to that for which the safety valve is loaded, but
will continue to blow-off until the pressure has fallen
some pounds below this. This is owing to the increased
area which the steam has to act upon when the valve
is open over what it has when the valve is closed, oc-
casioned by the bevel of the valve face. In a heavy
sea, the safety valve may be forced open for a short
time, even when the pressure is below that for which
the valve is loaded, by the oscillation of the ship.

CHAPTER V.

MISCELLANEOUS.

TJie Theory of the Paddle Wheel / the Radial compared
with the Feathering Wheel.

To all those whose minds have a tendency to probe
beyond the superficial crust of any thing that may be
presented to their consideration, the theory of the ac-
tion of the paddle wheel on the water must be one of
interest, and any thing, therefore, tending to make
this subject the more clear, cannot fail to receive the
proper attention and a careful perusal.

In regard to the paddle wheel, many theories have
been advanced, some of them so positively absurd that
it is difficult for us to conceive how they ever found
their way into print. Even in reference to the subject
of centre of pressure of the paddles, such rules as the
following have been put forth from quarters to which
we should have looked for more correct information :

" The circle described by the point whose velocity
equals the velocity of the ship, is called the rolling cir-
cle, and the resistance due to the difference of velocity
of the rolling circle and the centre of pressure is that
which operates in the propulsion of the vessel." * * *

Rule : " From the radius of the wheel subtract the
radius of the rolling circle, to the remainder add the
depth of the paddle board, and divide the fourth

102 THEORY OF THE PADDLE WHEEL.

power of the sum by four times the depth ; from the
cube root of the quotient subtract the difference be-
tween the radii of the wheel and the rolling circle, and
the remainder will be the distance of the centre of
pressure from the upper edge of the paddle. The
diameter of the rolling circle is very easily found, for
we have only to divide 5280 times the number of miles
per hour by 60 times the number of strokes per min-
ute, to get an expression for the circumference of the
rolling circle, or the following rule may be adopted :
Divide 88 times the speed of the vessel in statute miles
per hour, by 3.1416 times the number of strokes per
minute ; the quotient will be the diameter in feet of
the rolling circle."

Now, then, I suppose no one who has given the sub-
ject the slightest attention would imagine, for one mo-
ment, that so long as the immersion remained constant, a
difference in the slip of a common radial wheel would
make a difference in the centre of pressure of the pad-
dles ; yet if any one will take the trouble to work out
the centre of pressure of any wheel by the above rule
with different slips, he will find the centre of pressure
continually changing. To suppose such a thing to be true
would be as absurd as to suppose the centre of pres-
sure of a plank immersed vertically in a stream moving
at the rate of 10 miles per hour, to be in a different
place from what it would be should the stream move
at the rate of 5 miles per hour.

We have thought it advisable, therefore, to go into
this subject the more fully, and give the following as
an illustration of our views :

It is generally admitted that the total loss of effect,
or power, in the common radial wheel, is the sum of
the losses of the oblique action on the water and the

THEORY OF THE PADDLE WHEEL.

103

slip. The former is calculated by taking the mean of
the squares of the sines of the angle of incidence at
which the paddles strike the water, or which is the
same thing, the means of the squares of the cosines of
the angles of the arm and water ; for one angle is the
complement of the other. This will appear plain from
an inspection of figure 1. A C is the arm, making

FIG, I

an angle at C, with the vertical line C A' ; A B, the
breadth of the paddles, and E F, the surface of the
water. Now, it is manifest, that, inasmuch as the ves-
sel is moving in a horizontal direction, the line B D at
right angles to that direction, represents the only por-
tion of the paddle A B that is efficient in propelling
the vessel, and the line A D represents that portion
of the paddle that tends to lift the vessel out of the
water, which, consequently, as it produces no propul-
sive effect, must be entirely lost. But the line A B,
being the breadth of the paddle, we will suppose rep-
resents the pressure it exerts on the water, which,

104 TIIEOEY OF THE PADDLE WHEEL.

according to the resolution of forces, is divided into
two other pressures. A D, tending to lift the vessel,
is the useless pressure, and B D, at right angles to the
vessel's path, is the efficient pressure, or the portion
that is utilized in propelling the vessel. Power, how-
ever, is not composed of pressure alone, but is com-
pounded of pressure and velocity, and as the velocities
of the columns of water, having A D B D for the base
depend upon the lengths of those lines respectively ;
that is to say, if we double the length of either one
of them, say B D, for instance, diminishing the angle
at C, we not only double the quantity of water dis-
placed in any given time, but it is also displaced with
double the velocity ; the power, therefore, developed
is the product of these two, or as the square. Hence,
it follows that, since A D represents the useless pres-
sure, the square of that line must represent the useless
or lost power ; or, more correctly, the loss of useful
effect, and the square of B D, the power that is applied
to propelling the vessel. Now, then, considering A B
to be unity, the square of B D will be the square of the
natural sine of the angle BAD, and the square of
A D the square of the natural sine of the angle A B D ;
but the triangles A B D, A C D', being similar, the
angles at B and C are equal, and the loss of effect is,
therefore, simply represented by the square of the sine
of the angle that the oblique arm makes with the per-
pendicular; but as the angle is continually changing,
as the arm moves through the water, we have to take
the mean, and the more numerous, therefore, the divi-
sions are made, the nearer correct will be the result.

Thus, supposing, as per figure 2, a wheel 26 feet
diameter, from outside to outside of paddles, 6 feet
immersion of lower edge of paddles, and 20 inches

THEORY OF THE PADDLE WHEEL.

105

breadth of paddles, the loss from oblique action is
calculated as follows, the arc being divided into divi-

Fio. 2.

sions of 5 each, which are considered sufficiently nu-
merous for practical purposes :

106

THEOEY OF THE PADDLE WHEEL.

Angles
of
Incidence.

Sines of the
Angles of
Incidence.

.81915

.33550

= half of the square of sine

.76604

.58681

= square of sine.

.10111

.50000

.64279

.41317

.57358

.32899

.50000

.25000

.42262

.17860

.84202

.11697

.25882

.06698

.17365

.03015

.08716

.00759

((

.00000

.08716

.00759

.17365

.03015

.25882

.06698

.34202

.11697

.42262

.17860

.50000

.25000

.57358

.32899

.62279

.41317

.70711

.50000

.76604

.58681

.81915

.33550

= half of the square of sine.

5.62952

As 22 : 5.62952 : : 100 : 25.588 per cent, of the
power applied to the wheels.

Half of the square of the sine at the angle of 55 is
taken, because the paddle in that position is only half
immersed, consequently only half the power can be
expended on it as if entirely immersed ; and the angles
are put down twice, because the loss is the same after
the paddle leaves the vertical position as before it
reaches it. The power in the latter case being ex-
pended in forcing the water downwards, and in the
former case in lifting the water, neither of which as-
sists in propelling the vessel, the only tendency being
to lift the bow, and depress the stern.

Slip.

The loss of effect from slip is usually considered
the difference between the velocity of the centre of
pressure of the paddles and the velocity of the vessel.

THEORY OF THE PADDLE WHEEL. 10 7

Thus, if the velocity of the centre of pressure of
the paddles exceeds the velocity of the vessel by 18
per cent, of the speed of the paddles, 18 per cent, is
considered the loss of effect from slip. This we con-
ceive to be an error. The 18 per cent, is the difference
between the velocity of the paddles and the velocity
of the vessel, nothing more ; and, therefore, simply
represents the slip in per cent, of the paddles, but not
the loss of effect from slip. For it has been shown
that the loss resulting from the oblique action of the
paddles on the water, is as the squares of the sines of
the angles of incidence, and if we suppose the wheel
to be immersed to its axis, the loss from this cause on
the paddle, when in the horizontal position the angle
being 90 is 100 per cent., and if the loss from slip
of 18 per cent, be added to that, we have a total loss
of 118 per cent., or more than the power applied. A
positive absurdity. Or, again, supposing the vessel to
be made fast to the wharf, the difference between the
velocity of the paddles and the velocity of the vessel
will be 100 per cent., and as the loss from oblique ac-
tion cannot, from this circumstance, be any less than
if the vessel was moving ahead, there will be a total
loss of the power applied to the wheels of 125.588 per
cent. A result equally absurd.

At the angle of 45 it has been seen that only
.70711 part of the area of the paddle is effective in
propelling the vessel, and that at this angle the ve-
locity of the column of water driven aft is only .70711
of what it is when the whole area of the paddle is
effective, hence the power expended in slip = .70711
X .70711 = 5, the slip in the vertical position being
considered 1.

Now, then, if 18 per cent, is the loss from slip

108 THEOKY OF THE PADDLE WHEEL.

when the paddle is in the vertical position which
must be the case if its velocity exceeds that of the
vessel by 18 per cent, of its own speed from what
has just been shown, at the angle of 45, the loss can-
not be more than half of 18, or 9 per cent. The same
reasoning will demonstrate, that at the angle of 30
the loss from slip cannot exceed f of 18, or 13.5 per
cent. Thus we see the loss from slip goes on decreas-
ing from the vertical to the horizontal position, at
which place it becomes nothing. We can, therefore,
approximate very nearly to the true loss in the present
radial wheel, by taking the mean of these losses at the
angles as laid down in figure 2. They are as follows:

At = 18 .0000 = 18 _ per cent.

" 5 = 18 - .1366 = 17.8634 " "

" 10 = 18 .5427 = 17.4573 " "

" 15 = 18 1.2056 = 16.7944 " "

" 20 = 18 - 2.1055 = 15.8945 "

" 25 = 18 - 3.2148 = 14.7852 " "

" 30 r= 18 - 4.5000 = 13.5000 " "

' " 35 = 18 - 5.9218 = 12.0782 " "

" 40 = 18 - 7.4371 = 10.5629 " "

" 45 = 18 9.0000 = 9.0000 " "

" 50 = 18 - 10.5626 = 7.4374 " "

" 55 = 18 12.078 = 5.9220 " "
~~2~~ 138.3343

Doubled for both sides of the vertical ) t) 7 / n / o /

position \ " Ai O.DDOO

18.0000

294.6686

= 13.394 per cent, of the power applied to

the wheels.

THEOEY OF THE PADDLE WHEEL. 109

The same result is obtained as follows :

100.000 (power applied) 25.588 (oblique action)

X 18 per cent, (slip of the vertical paddle) = 13.394

per cent.

We have, therefore, for a total loss in this radial

wheel, 25.588 + 13.394 = 38.982 per cent, of the power

applied to it.

Feathering Wheel.

Let us take a feathering wheel, of the same di-
ameter of centre of pressure, i. e., 26 feet 4 inches in
diameter from outside to outside of paddles same
immersion, breadth, and number of paddles, and see
how it compares with this.

It is conceived by some that the only losses in this
kind of wheel are the friction of the eccentrics, <fec.,
and the slip, but there is another loss with deep im-
mersions, or light slips, occasioned by the drag of the
paddles as they enter and leave the water.

In figure 3, the paddles are supposed to be verti-
cal from the time they enter until they leave the
water, and the positions of the arms will be seen at
the degrees there laid down. The perpendicular lines
drawn across the arcs are intended to represent the
breadth of the paddles. It is plain that while the axis
of tjie paddle moves from A to B, it moves horizon-
tally the distance A C, and vertically the distance
C B, and, supposing the vessel to be moving with the
same velocity as the paddles, it will travel the distance
A B, while the paddle travels horizontally the distance
A C. Now, the distance A C being less than A B,
the paddle in this position cannot be giving out any
power, but must be keeping the vessel back, by carry-

110

THEORY OF THE PADDLE WHEEL.

ing a column of water before it, the base of which is
equal to the area of the paddles, and the length equal
to the difference in the lengths of the two lines.

FIG. a

If A B be represented by unity, A C will be rep-
resented by the natural sine of the angle ABC, and
if the arc be supposed to be divided into an infinite

THEOEY OF THE PADDLE WHEEL. Ill

number of parts, or composed of an infinite number of
straight lines, A B will be at right angles to A D, and, by
consequence, the angle ABC will be equal to the angle
DAE; and as the sine of B represents the distance
traveled horizontally by the paddle, the sine of D A E
must manifestly represent the same thing, but the sine
of D A E is the cosine of D, which therefore repre-
sents the horizontal velocity of the paddle at the angle
of 50, its circular velocity being 1. The difference
between these two lines is, therefore, the loss from
'li'acj, supposing there to be no slip, but as all paddle
wheels must have some slip, when they are propelling
a vessel, the line A B, diminished by the amount of
slip, will represent the distance traveled by the vessel,
and the loss from drag will therefore, instead of being
the difference between A B and A C, be the difference
between a fraction of A B and the whole of A C, de-
pendent upon the amount of slip. If this fraction of
A B be just equal to A C, the loss from drag in this
position becomes ; for, though the paddle be giving
out no power to the vessel, it occasions no resistance
to the vessel's progress through the water, because it
is moving horizontally precisely as fast as the vessel
itself; and if the fraction be less than A C, the resist-
ance will, of course, be on the after instead of the for-
ward side of the paddle, and it must, in consequence,
necessarily be assisting in propelling the vessel.

Now, then, from the above, it must be evident to
any one, that so long as the paddle, after it enters the
water, is moving horizontally at a less rate than the
vessel, it cannot be giving out any power, but must be
an actual resistance to the vessel's progress through
the water. Taking figure 3, and giving the wheel the

same mean loss from slip as the radial wheel, viz.,
8

112 THEOEY OF THE PADDLE WHEEL.

13.394 per cent., we will ascertain the loss from slip
at the different angles there laid down, and attend to
the drag afterwards, which is merely slip in the oppo-
site direction, or what might be termed negative slip.

To give this wheel the same mean loss from slip as
the radial wheel, it has to have on the arm when in
the vertical position, or

At CoBlne , 26.225 per cent.

" 5 = .99619 - .73775 = 25.844 " "

" 10 = .98481 - .73775 = 24.706 " "

" 15 = .96593 - .73775 = 22.818 " "

" 20 = .93969 - .73775 = 20.194 " "

" 25 = .90631 - .73775 - 16.856 " "

" 30 = .86603 - .73775 = 12.828 " u

" 35 = .81915 - .73775 = 8.140 " "

" 40 - .76604 - .73775 = 2.829 " "

" 45 = 0.000 " "

" 50= 0.000 "

" 55= 0.000 " "

134.215

Doubled for both sides of the vertical P
position, 5

26.225

294.655

994 655

- = 13.394 per cent, of the power applied to
2i2

the wheel lost by slip.

At the angle of 55 the paddle is .445 part im-
mersed, but, being so near, we have taken it at a half
for simplicity, and for like reason have considered the
paddle at 50 entirely immersed.

It will be seen from the above, that the paddle,
from the time it enters the water until after it passes

THEORY OF THE PADDLE WHEEL. 113

45, is traveling horizontally at a less rate than the
vessel, and the same effect ensues as it rises out of the
water ; there must, therefore, be a loss from drag or
negative slip. Let us see what this amounts to.

Cosines.

.73775 - .57358
At 55 = - -g- - 8.208 per cent.

50 = .73775 - .64279 = 9.496 " "
" 45 = .73775 - .70711 = 3.064 " . "

20.768
2

Doubled for entering and leaving, 41.536

41.536

OS = 1.933 per cent.

We have, then, for a total loss in this wheel, slip
(13.394 per cent.) -f drag (1.933 per cent.) = 15.327
per cent, of the power applied to it.

The total loss in the radial wheel having been
shown to be 38.982 per cent, (and in the feathering
wheel 15.327 per cent.), we have 23.655 per cent,
in favor of the feathering wheel. But of the whole
power applied to the engines, about 20 per cent, is ex-
pended in overcoming friction of ditto, friction of load
on working journals, working air and feed pumps with
their loads, &c. Consequently, only 80 per cent,
reaches the wheels, and 23.655 per cent, of 80 per
cent, equals 18.924 per cent, of the total power applied
to the engines in favor of the feathering wheel.

To stand off against this, we have the friction of
the eccentrics, &e. (an amount that, perhaps, can only
be estimated) extra weight and wear and tear of the
wheels.

It will be seen also from the above, that the differ-
ence between the velocity of the feathering wheel and

114 CENTRE OF PKESSUEE.

the vessel being 26.235 per cent, of the speed of the
wheel, and the difference between the velocity of the
radial wheel and the vessel being 18 per cent, of its
speed, it follows that, making the same number of
revolutions, the speeds of the vessels will be as 73.775
to 82, or as 1.00 to 1.11 ; consequently, the speed of
the feathering wheel will have to exceed the speed
of the radial wheel 11 per cent, to give the vessel the
same velocity, but this speed of the wheel is as shown
consequent upon there being less resistance to the pad-
dles attained by an expenditure of 18.924 per cent.
less power.

Centre of Pressure.

The centre of pressure of a rectangular plane im-
mersed in a fluid, the upper extremity of which is even
with the surface of the fluid, is ^ from the bottom ;
but, inasmuch as the pressure is as the depth, when its
upper extremity is below the surface of the fluid, this
law no longer holds good. To ascertain the centre of
pressure in such case, " Jamieson on Fluids " gives the
following practical rule deduced from elaborate math-
ematical calculations :

" Divide the difference ot the cubes of the extremi-
ties of the given plane below the surface of the fluid,
by the difference of their squares, and two-thirds of
the quotient will give the distance of the centre of
pressure below the surface, from which subtract the
depth of the upper extremity, and the remainder will
show the point in the centre line of the plane in which
the centre of pressure is situated."

This rule can be applied directly to the feathering
wheel, by taking the mean immersion of the paddles

CENTRE OF PRESSURE. 115

as they move through the water, and assuming figure 3
to be of the same diameter from outside to outside of
paddles, as figure 2, viz : 26 feet, we find the mean
immersion of the lower edges of the paddles, after their
upper extremity gets below the surface, to be

(29.23 + 37.84+45.59 -f- 52.44 -f 58.32 -f- 63.09 + 67.02 -f- 69.78 + 71.44)
19

2 -j- 72 = 55.87 inches, and upper edge 35.87 inches.
The mean centre of pressure of the paddles in these

/ 55.87" 35. 87 s \
positions is ( 558r _ 3587 ij| = 46.59 35.8 7 = 10.72

inches from top, or 9.28 inches from bottom, and the
mean centre of pressure from the time the paddle
enters until it leaves the water,

In the radial wheel, however, as the outer ex-
tremity of the paddle moves more rapidly than the
inner extremity, and as the resistance is as the square
of the velocity, the centre of pressure must be consid-
erably nearer the outer extremity on this account.
One-third from the bottom, in this case, is, therefore,
probably, not much out of the truth ; but as a portion
of the paddle only part of the time is immersed, we
take the mean of the third of that portion and a third
of the whole breadth of the paddle during the time it
is entirely immersed.

TV. -- --

Thus : v ~^f- = b.tf inches from

, the bottom, showing the centre of pressure under these
circumstances to be (8.52 6.37 = ) 2.15 inches nearer
the lower edge of the paddle in the radial than it is in
the feathering wheel.

116 THE SCREW PROPELLER.

Practical Remarks on tlie Foregoing.

From what has been shown, it would appear that
the use of the feathering wheel over the radial wheel,
from the great saving it effects, would lead to its uni-
versal adoption ; but, unfortunately, the practical diffi-
culties are such that its use is confined within very
narrow limits. The increased weight of the wheel,
occasioned by the eccentrics, levers, arms, <fec., required
to work the paddles, amounting, in some cases, to
several tons, causing the pillow-block brasses to wear
away very rapidly, is a sad objection, to say nothing
of the excessive friction they produce. Besides, the
pins operating as the axis about which the paddles
vibrate are found to wear away very rapidly, requiring
not only to be replaced frequently, but the noise and
jar occasioned from the wear becomes very objec-
tionable. The latter objection, however, can be re-
moved by the use of lignumvitse pin bearings.

The Screw Propeller.

The great advantages derivable from the successful
adaptation of the screw propeller, particularly to ves-
sels of war, became well understood in its early his-
tory, and inventive genius set to work thenceforth to
perfect this important invention ; all kinds of propel-
lers sprang into use, many of them possessing neither
the merit of novelty nor usefulness. One, two, three,
four, five, six-bladed, true screws, expanding pitch and
no screw at all, are among the number that have been
tried experimentally and practically since the intro-
duction of the screw propeller, and, strange as it may
appear, notwithstanding the large share of attention it
has received, the theory of the screw propeller is yet not

THE SCREW PROPELLER. 117

generally understood; but, to our mind, this. is owing
to one great cause ; and that is, to the very important
fact, that those who have undertaken to explain and
illustrate it, have apparently thought it more impor-
tant to give the history and accounts of the experi-
ments though both very useful in themselves than
to explain the leading features and the laws governing
its action. Besides, a practical engineer does not wish,
or if he did, has not the time to spare, to examine
large volumes to find what might be condensed into a
few pages. We have, therefore, determined to make
our remarks on this subject brief, and to confine them
to those points which we think are the more impor-
tant, allowing the student to build upon them for him-
self.

The surface of a screw blade may be supposed to
be generated by a line revolving around a cylinder, at
right angles to the axis, at the same time that it moves
along it, and should the revolving motion be a constant
ratio to the motion lengthwise, it will be a true screw.
Should such a screw as this, Fig. 4, be developed upon
a plane it will form a FIG. 4.

right-angled triangle, in
which A B is the pitch,
A C the circumference
described by the extrem-
ity of the blade, and B C
the line described by any
point in the periphery
of the blade by one con-
volution of the thread. To make this the more clear,
suppose the triangle A B C to be wound round a cyl-
inder, having a circumference equal to A C, and sup-
pose at C we start to trace a line around the cylinder,

118 THE SCREW PEOPELLEE.

moving along it at the same time in a constant ratio.
and that when we have gone all the way around, ar-
riving over the starting point C, (C and A will be one
and the same point in the case supposed) we have
reached the point B, C B will be the line described,
which is technically termed the directrix, and A B,
being the distance moved in the direction of the axis,
will be the pitch. Should the line A B be a curve,
instead of a straight line, the screw would have an in-
creasing or expanding pitch, instead of an uniform
pitch. Figure 5 will illustrate this: Let the curve
FIG. 5. B C be the curve of the blade,

and the dotted lines B , C c
be tangents drawn to this
curve, it will be seen that, at
different points in the curve
B C, the velocity of rotation
remaining constant, the ve-
locity lengthwise of the axis
A B varies, growing greater
as we approach B. This is what is termed an expand-
ing pitch ; that is to say, the pitch at the anterior por-
tion of the blade, is less than the pitch at the posterior
portion. The object of such a pitch is this : the ante-
rior portion of the blade striking upon water at rest,
encounters the resistance due to a solid body moving
through water at rest, but this portion of the blade
puts the water in motion, it being a yielding medium,
so that when the posterior portion of the blade follows
it has to act on water in motion, instead of water at
rest, and in order, therefore, to make the resistance
due to all parts of the blade alike, the pitch of the pos-
terior portion of the blade is increased to the extent
of the motion given to the water by the anterior por-
tion.

TILE SCKEW PROPELLEK. 119

To measure the pitch of a screw blade, did it ex-
tend all the way round the shaft to a full convolution
of the thread, all we would have to do, would be to
measure along the line of the shaft from any point in
the blade to any point directly over it, and the dis-
tance would be the pitch, or the distance traveled in
the direction of the axis by one convolution of the
thread ; but since in practice, in order to secure the
proper resisting area, a full convolution of the thread
is not required a very small fraction of it being
used it becomes necessary, therefore, to find the pitch
from this fraction. Taking figure 4, for instance, let
B b be the length of the blade, measured on the peri-
phery, and A C the circumference described by the
extremity of the blade, B b will be the fraction of the
blade used, and B a the fraction of the pitch. We
know, therefore, that, starting from B, and traveling
along the line B , when we arrive at the point $, we
have traveled along the axis the distance B #, and from
this we can ascertain what distance will be moved
along the axis by continuing all the way round until
we arrive at C, which will be the pitch. Practically,
we can measure this in two ways : measure the length
B b of the blade, and also B , the length in line with
the axis, we have then two legs of a right-angled tri-
angle, from which we ascertain the third, a b. Now,
then, knowing the circumference described by the ex-
tremity of the blade, we derive the following simple
proportion :

As a b : the whole circumference : : B a : the whole
pitch.

Or we proceed thus : Lay a straight-edge across
the face of the propeller, at right angles to the axis,
and a bevel on the periphery of the blade, and look

120 THE SCREW PEOPELLEE.

them out of wind, the angle enclosed by the two legs
of the bevel will be the angle B b a, which is termed
the " angle of the propeller ; " and hence, if B b be
supposed unity, the fraction of the pitch of the one
blade will be (B a) the natural sine of the angle B b a,
therefore, knowing the angle B b a, and the length of
the blade B 3, we ascertain the pitch thus :

As cosine b : whole circumference of propeller : :
sine b : to whole pitch.

The pitch can also be determined by construction,
without any calculation whatever. Thus, supposing
the line a b represents the whole circumference of the
propeller, we draw the line B b at the angle to a b as-
certained from measurement, and erect the perpendic-
ular a B, which will give the pitch required.

. In a true screw, it matters not whether we take
the angle at the periphery or any other part of the
blade ; for, though the angle will be different, increas-
ing as we approach the centre, the pitch will be the
same, it only being necessary to know the circumfer-
ence at the point where we measure the angle.

Should the blade not be a true screw, but an ex-
panding pitch, we have to take the angle at two or
more points, by drawing tangents to the curve, and
take the mean, for the mean angle of the blade. Thus,
in figure 5, the mean of the angles B b A and c C A
will give the mean angle of the blade.

Some propellers are made to expand from hub to
periphery, instead of from anterior to posterior portion
of the blade.

To ascertain the pitch of such a propeller, take the
mean of the angles at several points in the blade, and
proceed as above. In order to ascertain the pitch of
any propeller, it is always proper to take the angles at

THE SCREW PEOPELLER. 121

two or more points in the blade, from which we learn
whether it expands from hub to periphery, whether it
be true screw, or no screw at all.

The fraction of the pitch, as we have explained it
above, is the fraction of the pitch of one blade, but as
screw propellers usually have two, three, four, six, <fec.,
blades, constituting fractions of a double-threaded,
treble-threaded, four-threaded, six-threaded, <fec., screw,
the sum of these constitute the fraction of what is
usually termed the fraction of the pitch of the screw ;
that is to say, if the screw have three blades, and the
fraction of the pitch of one of those blades be T '^-, the
real fraction of the pitch will be 3 times T V, or ;
for it evidently matters not, as far as this is concerned,
whether the screw be in one, or divided into a dozen
parts.

How to lay down a Propeller.

Knowing the diameter, number of blades, and frac-
tion of pitch, we intend to use, we proceed thus :

Taking figure 6, for in-
stance, draw the line A C,
equal the circumference of
the extremities of the blades,
and from A erect the per-
pendicular A B, equal the
pitch ; join B C. Now, then,
supposing we desire the pro- A
peller to have four blades, and v the fraction of the pitch
to be , lay off B a, equal to T V B A, and draw a c,
parallel to AC. a c will be the circumference of the
extremity of one blade viewed as a disc. Then, taking
figure T, we describe the circle a l> c, equal A C, figure

122 THE SCREW PEOPELLER.

6, and also the smaller circle, equal the circumference
of the hub of the propeller ; divide the
larger circle 1 into four equal parts, and,
from the centres thus obtained lay off
a d, h i, bf, e c, each equal to a e, fig-
ure 6, and draw lines from each of these
points to the centre, terminating in the
hub ; such will be the projection of a four-bladed, true
screw propeller, viewed from the stern, from which
the longitudinal elevation can be drawn. The dimen-
sions of the sections of the blade depend upon the
diameter of the propeller, the material of which it is
constructed, and the pressure it has to sustain.

Centre of Pressure.

All solid bodies moving through a fluid have a cer-
tain point called the centre of pressure, which is the
point where the outer and inner pressures just exactly
balance. In a screw propeller, the radius of the cir-
cle, which is equal to half the area of the whole circle,
described by the periphery of the blades, is the centre
of pressure from centre of motion. Thus, if a propeller
be 16 feet diameter, the area of the circle described by
the extremity of the blades = 201.06 square feet, and
the radius of the circle, having an area equal to half
this, is 5 feet T| inches, consequently the centre of
pressure in this propeller is 5 feet Y^ inches from the
centre of shaft.

The centre of pressure can also be ascertained in
the following manner :

1 +4 + 9+16+25+36+49+64 204

1 1 1 1 I 1 1 1 = = 5 feet 8

1 +2 + 3+ 4+5 + 6 + 7 + 8

inches, nearly as before.

THE SCEEW PROPELLEE. 123

The line per sketch represents the radius of the
propeller, and is divided into divisions of 1 foot each ;
the more numerous, of course, the divisions are made,
the nearer correct will be the result.

In these calculations, the area of the hub is
neglected.

The above rule holds good so long as there is no
variation in the pitch from hub to periphery ; but
should the pitch vary in this direction, the velocity of
the column of water driven aft from different parts of
the blade will also vary, effecting the centre of pres-
sure correspondingly.

Slip. The slip of a screw propeller is the differ-
ence between the velocity of the propeller and the
velocity of the ship.

EXAMPLE. A propeller having 20 feet pitch makes
70 revolutions per minute, which propels the vessel at
the rate of 12 knots an hour, required the slip, the sea
knot containing 6082| feet?

ANSWEE.

20 X 70 X 60=84000= speed of propeller in ft. per hour.
6082|xl2=72992= " vessel " "
11008= slip in feet.

84000 : 11008 : : 100 : 13.1 =slip in per cent, of
the speed of the propeller.

Thrust. A propeller being put in revolution throws
a column of water off from the blades in line with the
axis of the propeller, which, as explained above, is the
slip; the resistance of this water acting upon the pro-
peller blades, tends to force the shaft inboard, which

124 THE SCEEW PEOPELLEE.

resistance has to be sustained by heavy bearings called
thrust bearings, and the amount of this resisting pres-
sure is called the thrust. In order, in practice, to as-
certain the extent of the thrust, an instrument called
the dynamometer is attached to some part of the shaft.
This instrument consists of a combination of levers or
weighing beams, to the final end of which is attached
a spring balance, or scale, which indicates the pressure
in pounds ; and this pressure being augmented by the
number of times the levers are multiplied, gives the
total pressure, or thrust on the shaft. And the total
thrust being multiplied into the distance moved over
in a unit of time by the vessel, shows the actual power
absorbed in propelling the vessel.

In the application of the dynamometer, care must
be taken that it receives the entire thrust of the shaft
before the indication of the scale is noted.

Did the propeller and steam piston travel through
the same distance in any given time, and were all the
power applied to the piston transmitted to the water
through the propeller, the total pressure upon the
steam piston and the thrust of the propeller would be
identical, but since such is never the case, we ascertain
the theoretical thrust, thus :

Total effective pressure on piston in Ibs. x 2 length of stroke in ft. x Xo. of revols. per inin.
Pitch of propeller in feet x number of revolutions per minute.

= Theoretical thrust in Ibs. The difference between
this and the actual thrust, shows the amount lost in
friction of engines, propeller, and load, overcoming
resistance to edge of propeller blades, working pumps,
etc. The loss from slip is independent of this.

THE SCREW PROPELLER.

125

Strain upon a Screw Propeller-blade.

We can best illustrate this by an example.

Given, circumference of centre of pressure of a 3
bladed propeller, 30.9 feet ; distance from hub to cen-
tre pressure 41 inches ; pitch 22.5 feet ; thrust 12700
pounds : required, the strain upon each blade at the hub.

FIG

SOLUTION.

Let F G H be the

development of the he-

lix on a plane, draw B D

at right angles to F H,

and A E at right angles

to Gr H. Trigonometri

cally, we ascertain the c

angles at A and D to be

each = 3*7 9', and at C and B to be each = 52 5', and

the lengths of the lines A E, B D, to be relatively as

1.000 to 1.237.

Now, inasmuch as the whole thrust can be supposed
to be concentrated in the centre of pressure of the blade,
and as the 12700 Ibs. is in a line with the axis, it follows
that, if the line A E represents the direction and amount
of this thrust, the line B D, at right angles to the pro-
peller blade at the centre of pressure, according to the
resolution of forces, will represent the resultant of the
pressures on the blade, or the total pressure tending
to break it. But inasmuch as there are three blades,
the pressure will be divided equally among them all ;
therefore, each has to sustain but a third of this pres-
sure; hence

12700 X 1.237 (proportion B D bears to A E) __

Ibs. pressure on each blade at the centre of pressure.

1:20 THE SCREW PROPELLER.

The pressure at the hub on each blade equals
5236 Ibs. X 41 ins. = 21467G Ibs. acting with the
leverage of one inch.

EXAMPLE 2o. Suppose, in example 1, the breadth
of the blades at the hub to be 32 inches, and the pro-
peller to be made of composition, capable of sustaining
a pressure per square inch of cross-section of 520 Ibs.,
acting through the leverage of 1 inch ; required, the
mean thickness of the blade at the hub ?

SOLUTION. The strength of beams is directly as
their breadths and the squares of their depths, and in-
versely as their lengths. In the example before us,
the propeller resolves itself into a simple beam ; we

2146Y6X1 100 . , -,,

nave, then, - - = 12.9 inches = square 01 the

32 X 520

thickness, and \/12.9 = 3.59 inches in thickness.

Helicoidal Area. As has already been shown, the
development of the helix on a plane is the hypothe-
nuse of a right-angled triangle, having the pitch of the
screw for the height; and the circumference, corre-
sponding to the radii of the helix, for the base. Now,
as the propeller can be supposed to have an infinite
number of helices, each one becoming longer and longer
as we approach the periphery, which alter the lengths
at the same time, of the hypothenuse and base of the
triangle, we will suppose the propeller to be divided
into a number of concentric rings, taking the centre
line of each, for the helix or hypothenuse of the trian-
gle ; the circumference corresponding to radii of said
helix for the base, and the pitch for the height, from
which we have all the elements required for the cal-
culation.

THE SCEEW PROPELLER.

127

To make this the more clear, take the triangle
B A C ; the lines B 1, B 2, B 3, B C, represent the

helices having the corresponding circumferences of
A 1, A 2, A 3, and A C. Now, then, if these helices
he the lengths of the rings, or elements for one entire
convolution of the thread, all we have to do is to mul-
tiply it by the breadth of the element, which will give
the area for one convolution ; but as only a fraction
of a convolution is used in practice, we multiply by
this fraction, whatever it may be, and the product
gives the area for the part used. This mode of calcu-
lation is, of course, only an approximation ; but when-
ever the blade is divided into a considerable number
of elements, say 6 inches in breadth each, the result
obtains sufficiently near the truth for all practical pur-
poses.

The following is a calculation on the screw of the
U. S. Steam Frigate "Wabash," and which agrees,
within a very small fraction, of the area as projected
upon a plane:

128

THE SCEEW PKOPELLER.

Diameter of screw, 17 feet 4 inches ; diameter of
hub, 2 feet 4 inches.

> ,

. o"o .

^ K =13

rrj 03

03 *S .2 ^

O on

rt .

O 03

d 2

Pitch.

*3 0*0!

5*^5

55"*

.si

Sa
i

Radii o:

^* o

|J<9

^ i
M S

I s

ft.

2.B x 3.1416
ft.

VA 2 -j-C 2
ft.

DxE

ft.

FxG
sqr. feet.

1.5

9.42

24.89

! /T

7.11

3.555

12.56

26.20

7.48

3.74

2.5

15.70

27.85

7.96

3.98

18.84

29.73

8.49

4.245

3.5

21.99

31.82

9.09

4.545

25.13

34.07

9.73

4.865

4.5

28.27

36.44

10.41

5.205

31.41

38.93

11.12

5.56

5.5

34.55

41.50

11.86

5.93

37.69

44.15

14;
/61

12.12

6.06

6.5

40.84

46.87

12.86

6.43

43.98

49.63

3/
/ll

13.54

6.77

7.5

. 47.12

52.43

4 / 15

13.78

6.89

50.27

55.27

13.82

6.91

8.5

53.40

58.14

11.63

5.815

* HeliCoidal area of one side of both blades = 80.5 square feet.

Practical Remarks on the Screw Propeller.

In the application of power to the propulsion of
the hulls of vessels through water, a portion of the
effect is lost by the instrument through which it is
transmitted. In the common radial wheel this loss of
effect is compounded of two losses, slip, plus oblique
action ; in the feathering wheel, slip, plus drag, and in
the screw propeller, slip, plus friction of the propeller
blades on the water. That instrument, therefore, which,
possessing no more practical disadvantages than other

* For the calculations of the friction of a screw surface on the water, see
Isherwood's calculation on the " San Jacinto," (Journal of the Franklin Insti-
tute, Third Series, Vol. XXL, p. 349,) or on the " Arrogant," (Appleton's Me-
chanics' Magazine, Vol. I., p. 156,) from which the form for the above table is
taken.

THE SCREW PROPELLER. 129

instruments, and which has the sum of its losses the
least, must be the most economical propelling instru-
ment. The feathering wheel, from what we have
seen, would present itself very conspicuously to our
eye as being the best instrument within our knowledge ;
but, unfortunately, the practical difficulties are such as
to preclude its universal adoption. The loss from ob-
lique action in the common radial wheel, particularly
where the diameter is comparatively small and the dip
of the paddles considerable, amounts to an important
percentage of the total power of the engines; and
since this loss in the screw propeller does not exist, but
is replaced by one of much smaller magnitude, viz.,
friction of the blades, it follows, that were the slip of
the two instruments alike, the screw propeller would
be the more economical. In practice, however, with
the screw propeller, when contending against head
winds, or other increased resistance, the slip is increased
to a very serious extent. In fact, in some cases it has
occurred, when the engines were going ahead at nearly
full speed, the vessel stood nearly still. On the other
hand, however, when the sails are set to a fair wind,
the slip of the propeller is materially reduced, while
the thrust remains unaltered. The increased slip
when contending with head winds is also experienced
with paddle wheels, but they are not affected to the
same extent as the propeller, the increasing or decreas-
ing the resistance with the latter instrument, not
making a vast difference in the revolutions of the en-
gines (as is the case with the paddle wheel) so long as
the pressure on the piston remains unaltered.

In the application of the sere w propeller, it is well
to sink it as low as possible in the water, in order that
the hydrostatic pressure above may be sufficient to

130 THE SCREW PIIOPELLEE.

cause the water to flow in solid, even to the centre of
the propeller, which, therefore, having the proper
resisting medium, is less liable to excessive slip. This
will also prevent the centrifugal action the throwing
of the water off radially from the centre which exists
to a small extent in some very aggravated cases.

Increasing the helicoidal surface of the screw be-
yond what is barely sufficient to transmit the power
given to it, has no other effect than to occasion an
increased loss by friction, by the increased surface, in-
terposed. The friction of solids on fluids, unlike solids
on solids, depending upon the extent of rubbing sur-
face as one of the elements. The object, therefore, to
be sought after in practice, is to make the sum of the
loss by slip, plus friction, as little as possible, and this
sum, manifestly, must depend, to a considerable extent,
on the amount of helicoidal surface ; but, nevertheless,
there appears to be no general rules yet devised, from
theory or practice, which can be used as a reliable
guide ; different engineers making considerable differ-
ence in the areas of propellers applied to the propulsion
of the same sized and modeled steamers.

Negative Slip. It would certainly appear a very
strange anomaly, were one on board a vessel, which he
should discover from the indications of the log was mov-
ing actually faster through the water than the screw,
there being no other propelling instrument ; yet such
has been apparently the case, and there are, perhaps, to
this day, persons though we hope they are very
few who think that a screw propeller may drive a
vessel faster than it is moving itself. There have been
cases, it is true, where the log has shown that the ves-
sel was apparently moving faster than the screw, which

THE SCEEW PROPELLER. 131

alone was the propelling instrument, but that such a
thing could be true is absolutely absurd, and hence
attention was turned to discovering the anomaly. It
is accounted for in two ways.

When a body having a blunt stern is drawn through
water at a high velocity, the water, not being able to
flow in from the sides of the body sufficiently rapid to
fill the vacuity occasioned by its passage, flows in from
all other directions, and a column of water, therefore,
necessarily, follows in the wake of such a body. This
is the case with screw propeller vessels having blunt
runs, and, by consequence, the propeller, instead of
acting upon water at rest, acts upon water in motion,
having the same direction as the vessel. Now, then,
supposing a propeller, acting upon water at rest, to
have a slip of 10 per cent., if a column of water follow
the ship with the velocity of 11 per cent, of the speed
of the propeller, which still retains its ten per cent,
slip, the log, as it takes no cognizance of the velocity
of this water, would show a negative slip of 1 per cent.,
i. ., it would show the vessel to be actually moving 1
per cent, faster than the propeller, when in reality the
latter would be moving 10 per cent, the faster.

To produce such a result as this, of course, possesses
no mechanical or other advantage; for power must
have been originally taken from the engines to pro-
duce the current, which cannot be returned to its full
extent. It is, therefore, a very important element in
the design of a screw vessel to make the run very
sharp the lines fine in order that the water may
flow in solid at once, to fill the vacuity occasioned by
the vessel's progress, or the propeller's revolutions.

The other theory in regard to negative slip is this :
All known bodies yield to pressure, it being only

132 ALTJKIMNOJ- THE PITCH.

necessary in order to cause the amount of yield to be
measurable to make the pressure sufficiently great.
It is hence conceived, that when a screw propeller is
in motion, the pressure of the water on the blades causes
them to spring, thereby increasing the pitch ; conse-
quently, in calculating its speed through the water, if
we use the true pitch, instead of the pitch assumed,
while it is in motion, the velocity given to it will be
too small, and may be less than the velocity of the
vessel.

We would, however, remark, that negative slip in
a screw propeller, unassisted by sails, is more imaginary
than real, and could only exist under very aggravated
circumstances, for a screw propeller usually has about
20 per cent, slip, at least, and to reduce this to nothing,
even under the conditions set forth above, would be
rather a perversion of circumstances.

Altering the Pitch.

Propellers are sometimes constructed in such a
manner that the pitch can be altered, from time to
time, by altering the angle of the blades, which are
made adjustable in a large spherical hub. Thus, if it
be desired to increase the pitch, increase the angles by
turning round the blades ; or if it be desired to de-
crease the pitch, reverse the operation. Such an ar-
rangement, however, in practice, must be confined
within very narrow limits, for, inasmuch as the surface
of a screw propeller blade, being that of a helicoid,
every point in the blade must have a different angle,
which increases as the hub is approached, and if the
propeller be constructed so that all the angles be
adapted to one particular pitch, it is not very likely

PARALLEL MOTION. 133

that they will, after being distorted, be adapted to any
other pitch ; that is to say, if the propeller be a true
screw, for instance, and have a certain angle at the
periphery, if we move the blade so as to increase the
angle at that point 10, the angle at every other point
in the blade will also be increased 10, which should
not be the case, but should be correspondingly less as
the hub is approached; thus, by this arrangement, we
give a greater pitch at the hub than there is at the
periphery ; and if the operation be reversed, and we
decrease the angle at the periphery, the angle at the
hub, and every other point in the blade, is decreased
to precisely the same extent, thus giving less pitch at
the hub than there is at the periphery, or any other
point in the blade. "We therefore arrive at this con-
clusion :

That having three conditions presented to us, viz.,
true screw, expanding screw, from periphery to hub,
and expanding from hub to periphery the latter two
not in regular ratio it is more than probable that
one or the other of these must be found practically to
be the superior, and whichever it may be, and that
one adopted, the advantage to be derived from alter-
ing it, after it is once adopted, does not appear very
plain, the arguments to the contrary notwithstanding.

Parallel Motion.

Parallel motion is a combination of bars and rods,
having for its object the guiding of the piston-rod of a
steam-engine in a constant straight line, or as near a
straight line as can be practically attained. It is ap-
plicable, in different forms, to any type of engine, but

134

PARALLEL MOTION.

its adaptation to the side-lever engine is the more
general.

We have constructed figure 10 with the view of

FIG. 10.

illustrating its application to this type of engine, and
to clear it, if possible, of the mystery that usually
hangs over it in the shape of formulas. A B is half
the length of the side lever, vibrating on the centre B ;
A C, the side rod attached to the cross-head at C ;
Gr F, the parallel motion side rod ; D F, the parallel
bar, and E F, the radius bar vibrating on the centre E.
The object to be attained is to make the point C
travel vertically in a straight line, or as near so as pos-
sible ; and from the construction of the figure, it will
be seen that, when the point Gr moves to the right the
point F moves to the left, and vice versa ; hence it is
manifest, that there must be some point II, in the rod
F Cr, which will describe very nearly a straight line,
and if the lengths Gr B and E F were equal, that point
would be in the centre of F G ; but, since they are of
unequal lengths, H must be in such a position that

PAEALLEL MOTION. 135

Now, then, having secured the point H, draw the
line B C through H, which will determine C, the cen-
tre of the cross-head ; and the triangles B H G, B C A,
being similar, and joined together in such manner that,
no matter how much the angles of the one may alter,
the angles of the other must alter 'to precisely the
same extent ; and hence, these triangles always remain-
ing similar, it follows that if the apex (H) of the one
moves in a straight line, the apex (C) of the other
must move in a straight line also.

It matters not where the points D F G may be
situated, so long as D does not coincide with C, and
the figure A D F G is a parallelogram ; nor does it
matter about the respective lengths of the sides of the
parallelogram, so long asEFxFH = BGxGH.

In practice, it happens sometimes that the parallel
motion gets out of adjustment, the piston rod perhaps
rubbing hard on one side of the stuffing-box at the top
of the stroke, and hard on the opposite side on the
bottom of the stroke ; or it may rub hard on the stuff-
ing-box at one end of the stroke, and be quite free at
the other. Such a result can be brought about in
three ways only : either the sides of the parallelogram
A D F G have got out of parallelism, the radius bar
E F, of incorrect length from the wear of the brasses,
<fec., or the centre E has by some means been moved
from its true position.

These can be all remedied by interposing liners
at the proper places ; of course, taking care about
the centre A, in order not to endanger striking
the cylinder-head, by interposing too much at that
point.

136 STRENGTH OF MATERIALS.

Strength of Materials.

This is a subject which does not properly come
within the province of the present Notes; but we
have, however, thought it well to devote a short space
to it at this place, confining ourselves to a few practi-
cal examples.

Beams. The strength of beams are to each other
directly as their breadths and square of their depths,
and inversely as their lengths.

EXAMPLE. The depth of the beam of an engine
75 ins. diameter of cylinder, and 7 ft. stroke, at centre
is 42 ins., and using this as a standard, required the
depth of one for an engine of 80 ins. diameter of cyl-
inder, and 8 ft. stroke, the breadth, and also the maxi-
mum pressure on the steam piston to remain the same ?

ANSWER. 7 5 2 x 7 : 80 2 x 8 : : 42 2 : 2293.76 ins.
square of the depth ; the square root of which, 47.9
ins., is the depth required.

These figures, of course, do not apply to the truss,
but to the solid parabolic beam.

Shafts. The strength of shafts to resist a trans-
verse, or torsional strain, are to each other as the
squares of their diameters ; for the reason that, if the
diameter of a shaft be doubled, the quantity of metal is
increased fourfold, which would occasion the strength
to increase as the square, but at the same time there
being double the leverage interposed in consequence
of the double diameter, which, being multiplied by
the square (or 4), will give the cube (or 8).

STRENGTH OF MATERIALS. 137

EXAMPLE. The shaft of a steamer is 17 inches
diameter ; cylinder, 75 inches diameter ; by 7 feet
stroke ; required the diameter of a shaft for a steamer,
having an engine of 80 inches diameter of cylinder, by
8 ft. stroke, taking the shaft here given as the standard,
the maximum pressure on both steam pistons to be
alike.

ANSWER. 75 2 x 7 : 80 2 X 8 : : 17 3 : 6388.459, the
cube of the diameter, the cube root of which, 18.55
inches, is the required diameter of the shaft.

This is about the diameter of the shafts used in
practice for two engines of 80 inches diameter of cyl-
inder, and 8 feet stroke each. The proportion in prac-
tice for a shaft for a single engine of this size, is about
15.5 ins. diameter, which is a little more than half the
strength of the above shaft, owing to the weight of the
wheels, <fec., (which have also to be sustained by the
shaft) being more than half.

Screw Propeller Sliaft. The strain on the shaft of
a screw propeller is of two kinds one in line with the
axis tending to compress, the other at right angles to
the axis tending to twist it. And, inasmuch as the
strength of a shaft to resist compression, is much
greater than that to resist torsion, we need only take
the latter strain into consideration.

Hence, to ascertain the diameter of a screw shaft,
the dimensions of the propeller and thrust being given,
let A B, figure 11, be the pitch, B C, the circumference
at centre of pressure, and A C, the helix for one con-
volution at centre of pressure. Draw B D at right
angles to A C, and D E at right angles to B C ; the
lines D E and B E will be proportionally the com-
pressional and torsional strains on the shaft ; hence, if

138 STEEJSTGTH OF MATERIALS.

B E be multiplied by the thrust in pounds, and divid-
ed by D E, the quotient will be the pressure in Ibs.,
FIG. 11. acting at the centre of pressure

of the blade to twist the shaft.
This pressure being multiplied in-
to the leverage of the centre
of pressure, and divided by the
standard of the metal used, will
give the cube of the shaft's diame-
ter, the cube root of which will
be the diameter. But since the triangles A C B,
B D E, are similar, from the construction of the figure,
the angles being respectively equal, the sides must be
proportional, viz. : A C to B D, A B to B E, and B C
to D E. Therefore, having the lengths of the two
sides A B, B C, of the triangle ABC, we have

VATB'xT+WCyTb r

= diameter ot shaft in inches,

in which A B = pitch in feet,

B C = circumference at centre of pressure in

feet,

t = thrust in pounds,
1) distance from centre of shaft to centre

of pressure in feet,

c = practical coefficient of the metal used
for the shaft, per sq. inch of section
for a leverage of one foot.

Paddle Shafts. EXAMPLE 1 . Area of the piston
3848.4 sq. ins. ; maximum pressure per sq. inch 40 Ibs. ;
stroke 10 feet; one engine; required the diameter of
the paddle shaft, the practical value of the metal being
200 Ibs. per sq. inch of cross-section, with a leverage
of 1 foot.

STRENGTH OF MATERIALS. 139

V 3848.4 X 40 X 5 ,_,_. ,.
ANSWER. - = 15| ins. diameter.

EXAMPLE 2. Same as Example 1, excepting there
are two engines instead of one, connected at right
angles ?

ANSWER. With two engines connected at 90, the
position in which the greatest pressure on the shaft
will be interposed will be when both engines are in
such a position that a perpendicular, let fall from the
centre of the crank upon the centre line passing
through the centre of the shaft, will enclose an angle
of 45, which, with a 5 feet crank, will give a leverage
of 5 x .TOm (nat. sin. of 45) = 3.535 feet; hence,
supposing the pressure at this position of the engines
to be 40 Ibs. per square inch, we have

V 3848.4 X 40 X 3.535 ..-'. ,.

X 2 = 17.6 ins. diameter.

200

Piston Rods. The piston rod of a reciprocating
steam-engine is subject alternately to a tensile and
compressing strain ; and there is nothing more absurd
than the rules given in books on the steam-engine, de-
fining its diameter to be a certain fraction of the diam-
eter of the cylinder, independent of all other elements.
For instance, suppose a rod of a certain diameter and
length to be just able to sustain a certain weight
placed upon the top of it, without deflexion ; it is ab-
surd to suppose that it Would sustain the same weight
if the rod was made double the length, retaining the
same diameter ; yet the rules given for the diameters
of piston rods are regardless, not only of their lengths,
but also of the pressure of steam. We have, therefore,

140 STRENGTH OF MATERIALS.

thought it well to copy the following remarks and ta-
ble from Johnson's translations of the book of Indus-
trial design, by M. Armengaud, the elder, and M. M.
Armengaud, the younger:

" Compression is a force which strives to crush, or
render more dense, the fibres or molecules, of any sub-
stance which is submitted to its action.

" According to Rondelet's experiments, a prism of
oak, of such dimensions that its length or height is not
greater than seven times the least dimensions of its
transverse section, will be crushed by a weight of from
385 to 462 kilogrammes to the square centimetre of
transverse section, or a weight of from 54*70 to 6547
per square inch of transverse section.

" In general, with oak or cast iron, flexure begins
to take place in a piece submitted to a crushing force,
as soon as the length or height reaches ten times the
least dimension of the transverse section. Up to this
point the resistance to compression is pretty regular.

" Wrought iron begins to be compressed under a
weight of 4900 kilog. per square centimetre, or of
nearly 70000 Ibs. per square inch, and bends pre-
viously to crushing, as soon as the length or height of
the piece exceeds three times the least dimension of
the transverse section. 1 '

We show, in the following table, to what extent
per square inch we may safely load bodies of various
substances :

SURFACE CONDENSERS.

141

Table of the Weights which Solids such as Columns, Pilas-
ters, Supports will Maintain without l)eing Crushed.

WOODS AND METALS.

Description of Material.

Proportion of Length to Least Dimensions.

Up to 12.

Above 12.

Above 24.

Above 48.

Above 60.

Sound Oak

Ibs.
426.750
270.275
533.437
137.982
14225.000
28450.000
11707.175

Ibs.
355.625
119.490
440.975
116.645
11877.875
23755.750

Ibs.
213.375
71.125
266.007
69.709
7112.500
14225.000

Ibs.
71.125

106.687

2375.575
4741.666

Ibs.
35.562

1994.900

2375.575

Pitch Pine

Common Pine

Wrought Iron

Rolled Conner... .

EXAMPLE. What is the least diameter of a piston
rod for a cylinder having a cross-section of 3848.4
square inches, to sustain with safety a pressure per
square inch of piston of 40 Ibs., the proportion of
length to be about 24 to 1 ?

ANSWER. Taking one half the number in the
above table for the practical value, we have

' = 43.28604 sq. ins. cross section of the rod,

7.4 ins. diameter of the rod.

-7.-,-,

i 1 -L^.O 7-

43.28604

Surface Condensers.

A surface condenser is an instrument for condens-
ing steam by contact with cold metallic surfaces, in-
stead of bringing it directly into contact with a shower
of cold water. The object of using such a condenser in
lieu of the common jet, is to furnish boilers of marine
steamers with distilled instead of sea water, conse-

142 SURFACE CONDENSERS.

quently to provide against the loss of fuel otherwise
occasioned by blowing off a portion of the water, to
keep the concentration at a desired point, as shown at
pages 66 and 67. Also to prevent the loss due to the
little conducting power of the envelope of scale which
attaches to all heating surfaces of boilers using sea
water.

By the use of such an instrument there is also
gained the saving in labor of scaling and cleaning the
boilers, which belongs to all sea steamers using the
common jet, and this is of no small importance to
those having the care of steam machinery.

Again, by its use the expense of repairs to the
boilers is considerably reduced, their durability great! y
increased, the pressure of steam which can be ju-
diciously carried is unlimited, and the expansion of the
steam can be carried to a greater extent.

With these many marked advantages, it seems ex-
traordinary that the introduction of surface condensers
should have met with so little encouragement ; the
slow progress made has not been owing to any want
of engineering ability, but solely for the want of pat-
ronage ; for engineers of talent both here and in
Europe have devoted their time to the subject for
many years, and have produced many forms, some of
which have been so 'successful as to render, in our
opinion, the use of jet condensers absurd. Of the
number invented and introduced into practice, the one
known as Pirsson's has thus far met with the most
favor. It is termed a double vacuum condenser, i. e.,
it has a vacuum within and without the condensing
tubes. The injection water is received upon a scatter-
ing plate, and showered down on the tubes, which
condenses the steam within them; this injection water

SURFACE CONDENSERS. 143

with the air and uncondensed vapor is extracted by
au air-pump, in the same manner as when the jet con-
denser is used, and the water of condensation is drawn
away by a separate pump, called the fresh water pump,
and discharged into a reservoir, whence it is delivered
by the feed-pumps into the boilers.

Another variety of condenser, known as Sewell's,
has recently attracted considerable notice. It has been
highly reported upon by a Board of naval engineers
appointed by the Hon. Secretary of the Navy, and has
been introduced into some of the most successful
steamers. It is of the close surface type, that is, it has
a vacuum upon only one side of the condensing tubes,
the condensation being effected by currents of cold
water driven through the tubes by a pump. The joints
of the tubes are made with india-rubber sleeves, so that
they give perfect tightness, and allow each tube to ex-
pand or contract by itself, independent of the others,
and each or all of them can be taken out for cleaning
or repairs. The vacuum produced by this condenser
is unequalled, and as there is but one air-pump, it is
obtained with less power than by the other method.

Close tube surface condensers had been made with
the tubes secured at both ends without any provision
for expansion or contraction, except the buckling of
the tubes when hot, and stretching when cold. They
have also been made with one end of the tubes only
secured, the other ends being fitted to an expansion
plate. The advantages of Mr. Sewell's over the latter
named plans are manifest.

The following figure* will give the student a clearer
idea of the construction and operation of Pirsson's
condenser. A A, is the condenser, in which there is a

* Taken from "Steam for the Million'" by Commander WARD, U. S. N.

144

SURFACE CONDENSERS.

series of small tubes : p, the air-pump ; /, fresh water-
pump ; ft, the exhaust pipe ; Z, the injection pipe. The

operation is as follows: The engine being put in mo-
tion, the exhaust steam flows through the exhaust pipe
ft, into the chambers c c, thence in direction of the ar-
rows through the tubes to the lower chamber d, injec-
tion water being admitted at the same time from the
sea through the injection pipe /, is showered by the
scattering plate m over the tubes, and by its gravity
takes the direction of the arrows to the channel way ^,
from which it is removed by the air-pump p, and de-
livered into the hot well q to the delivery pipe r and
overboard.

The water resulting from condensation is drawn
by the fresh water pumpy from the chamber J, through
the pipe e e, and delivered into the fresh water reser-
voir g j from this reservoir it passes to the feed pump
/, through the pipe ^, and is delivered into the boilers
through the pipe &. The pipe s is for the purpose of
supplying salt water when deficiencies occur.

In this condenser, as drawn, all the tubes are firmly
secured to both tube heads, but one end of the tube
box is free, so that all the tubes can expand and con-

CYLINDKICAL BOILEES. 145

tract together ; those recently constructed have each
tube secured to the tube head at one head only, the
other ends being fitted so that they just pass through
the holes, thus allowing each tube to expand or con-
tract regardless of the others. There is also a com-
munication from the exterior to the interior side of the
tubes, so that the vacuum within created by the fresh
water pump is equal to that without, created by the
large air-pump. In close tube surface condensers, the
position of the steam and water, as shown in the figure,
is reversed. The exhaust steam is received on the ex-
terior of the tubes as at , and is condensed by water
entering at c f c, and driven through thetubes by a cir-
culating pump, attached at b / it is then discharged
through a pipe from d. The pump p is converted into
a fresh water air-pump, receiving the fresh water
through the channel-way n and foot-valve o, and dis-
charging it into the reservoir q, whence it is received
by the feed-pump and pumped into the boilers.

Cylindrical Boilers.

The force tending to rupture a cylinder along the
curved sides depends upon the diameter of the cylinder

and pressure of steam, and we
may regard, hence, the total
pressure sustained by the sides
to be equal to the diameter x
pressure per unit of surface x
length of boiler, neglecting any
support derivable from the heads,
which, in practice, depends on
the length. The shorter the
tube, the greater its powers of resistance. This is in

146 CYLINDRICAL BOILERS.

consequence of the ends being rigid and unyielding.
See latest experiments on this subject by William Fair-
bairn, Esq., C. E., F. E. S.

The force tending to rupture a boiler is termed, by
Professor Johnson, the divellant force, and the tenacity
or strength of the metal which resists the divellant
force is termed the quiescent force. When rupture is
about to take place, these two forces must be exactly
equal.

EXAMPLE. What pressure will a cylinder boiler,
12 ins. diameter, and i in thickness of metal, sustain
per square inch, the iron to be of the best English
iron?

The experiments of the Franklin Institute give for
the strength of single riveted seams, 56 per cent, of
the sheet, and assuming the tensile strength of the best
English iron to be 60,000 Ibs. per square inch of sec-
tion, we have

60,000 x .66 . 7001b

12 (diameter) x 4 (length of band to make 1 sq. in. area of crosa section)"'

But as the opposite side of the boiler will support an
equal amount, the true pressure will be double this, or
1400 Ibs. per square inch, one-fourth of which only
(350 Ibs.) would be safe to subject it to in practice.

From this we see that the bursting pressure of a
boiler of the dimensions above given, in a transverse
direction, is 1400 Ibs. per square inch. We will now
see what force this 1400 Ibs. exerts to tear the boiler
asunder in a longitudinal direction. To do this, we
have only to multiply the area of the head by the
pressure per square inch, and divide by the circum-
ference, (since the iron is inch thick,) which will
give the strain upon each square inch of sectional area.

CYLINDRICAL BOILERS. 147

rp, 113.09 X 1400 . ,

Inus , - = 16800 IDS. per square inch

o .oy ~^~ -I

of sectional area, in a longitudinal direction, and

1400 X 12 X 4 . ,

- = 33600 IDS. per square inch ot sec-
tional area in a transverse direction.

The 4 in the latter case is the length of the band
to give one inch square of sectional area, and we divide
by 2 because there are two sides of the boiler to sup-
port the pressure.

From these figures, it is observed that the strain
upon a cylindrical boiler, or other cylindrical vessels,
subject to internal pressure, transversely, is exactly
double what it is longitudinally. In cast iron, or other
cast metal cylindrical vessels, this is made amends for,
in a certain degree, by casting ribs, or bands, around
the external surface ; but with boilers there appears to
have been no attempt to increase the strength by riv-
eting bands at intervals on the outer surface, though
we see no good reason why such a thing could not be
done very advantageously.

We remark, from what has appeared, that the
strain upon cylindrical boilers increases transversely
directly as the diameters, and longitudinally as the
squares of the diameters because the areas of the
heads increase in that ratio but the circumferences
increase also as the diameters ; and hence, though we
obtain four times the pressure longitudinally by doub-
ling the diameter, we have double the metal in the
circumference of the boiler to sustain it, and, therefore,
the strain upon a unit of metal, in this direction, in-
creases also as the diameter. Hence, no matter what
may be the diameter of a boiler, the transverse pres-
sure tending to tear it asunder, will always be double
the longitudinal pressure.

148 BOILEK EXPLOSIONS.

Boiler Explosions.

There is only one grand direct cause of boiler ex-
plosions, and that is the incapacity of the metal, at the
time, to sustain the pressure to which it is subjected.
This can be brought about in several ways ; defective
material of which the boiler is constructed, defective
construction, all parts of the boiler being incapable of
sustaining the same pressure, gradual accumulated pres-
sure without the means of escape, sudden accumulated
pressure occasioned by pumping water on red-hot sheets,
collapse occasioned by a vacuum in the boiler, the re-
verse valve being inoperative ; collapse of flue occa-
sioned by internal pressure in the boiler and a partial
vacuum in the flue; overheating the plates, brought
about by the accumulation of large quantities of scale
upon them, thereby reducing their tenacity.

Boilers having been previously tested by hydros-
tatic pressure considerably beyond the limit to which
it is intended ever to allow the steam to reach, and
each and every boiler being fitted with steam and wa-
ter-gauges, proper sized safety-valves and such like in-
struments, there is never any good excuse, under any
circumstances, for the cause of boiler explosions. In-
competency or recklessness must be somewhere mani-
fest, for the engineer, knowing the pressure which his
boiler will with safety bear, should under no circum-
stances allow it to exceed that pressure. "We would,
however, observe here, that we have noticed in many
cases, both ashore and afloat where there are a number
of boilers connected together, instead of having a
steam gauge attached to each one separately, there was
but one gauge to the whole number ; and hence, if one
or more boilers be shut off from the others, there would

BOILER EXPLOSIONS. 149

be no means of ascertaining the pressure within them ;
and it is a very common thing with land boilers and
boilers of small river boats to have no steam-gauge
whatever. In such cases as these the owners take
upon themselves the responsibility, which would other-
wise be attached to the engineer, of any disastrous
result.

The legislation in regard to the inspection of steam-
boilers is hardly adequate to the cause ; for though the
testing the strengths of boilers, from time to time, is
very good as far as it goes, it falls short of what the
seriousness of the case demands. The same amount of
strict, unbiased inspection on the parties who have
charge of the very powerful, yet governable element
of steam, would be followed by far more beneficial
results. Place only those in charge of the steam-
engine, boilers, and dependencies, who are competent
to the task ; prevent owners from employing any one
simply because his services can be secured for a small
compensation, and then you touch the subject in a vital
point. It is too prevalent an opinion, that any one
who can stop and start an engine, have the fires started
and hauled, is an engineer, regardless of his knowledge
of the element of which he has charge.

It is true, however, that the system of rivalry and
competition, carried on by steamboat owners and others
using steam power, is such as to prevent any one inde-
pendently from paying a very high rate of compensa-
tion; but if all were compelled to employ equally
competent services, no difficulty could be experienced
on this head.

150 HOUSE POWER.

Horse Power.

The standard for a horse power in England and the
United States is pretty generally established at 33000
Ibs. raised one foot high in a minute ; but in France a
horse power is estimated at 75 kilogramrnetres, which is
75 kilogramme tres raised one metre high per second,
equal to 32554.7 Ibs. avoirdupois, raised one foot high
per minute. To ascertain the horse power of a steam
engine, multiply the mean unbalanced pressure per
square inch on the piston, by the area of the piston in
square inches, by the length of the stroke in feet, and
by the number of strokes in a minute; and divide by
33,000, the quotient will be the horse power.

From this figure, in order to ascertain the actual
power utilized in propelling the vessel, a deduction has
to be made for working the air and feed pumps with
their load, friction of working journals, friction of load
on working journals, amounting in all to about 20 per
cent, of the total power, leaving 80 per cent, to be ap-
plied to the propelling instrument, which 80 per cent,
has to be reduced by the amount of loss which obtains
in the propelling instrument.

EXAMPLE.^ Required the horse power of a con-
densing steam-engine, having a cylinder 70 inches
diameter, by 10 feet stroke, making 15 revolutions per
minute ; mean pressure of steam throughout the stroke
23 Ibs. ; back pressure 3 Ibs. ; and also the actual
power utilized in propelling the hull of the vessel, the
sum of losses in the propelling instrument being 40
per cent, of the power applied to it ?

ANSWER IST.

70 2 X.7854x23-3xlOxl5x2

-33000- --699.7 horse power.

HORSE POWER. 151

ANSWER 2o. Considering 20 per cent, of the total
power to be expended in working pumps, in friction,
<fec., we have 80 per cent, applied to the propelling
instrument, and 40 per cent, of 80 per cent. = 32 per
cent, of the total power expended in transmission
through the propelling instrument ; wherefore, 80
32 = 48 per cent, of the total power applied to pro-
pelling the hull of the vessel = 335.856 horses.

Nominal Horse Power, is a term which expresses
neither the actual power, the size of the engine, nor
any thing else which is useful ; and though it has be-
come almost obsolete among well-informed engineers
in this country, our trans-atlantic friends seem yet -to
cling to it with some tenacity.

The usual rule for determining it is this : Multiply
the square of the diameter of the cylinder in indies, by
the cule root of the length of the stroke in feet, and
divide by 47 ; the quotient is the horse power.

Now, the chief object for establishing a rule for
nominal horse power was to create a commercial unit,
by which the power of one engine could be compared
with that of another engine ; and this rule might meet
the wants of the case, did the lengths and breadths of
all cylinders bear the same ratio, and did the pressure
of steam remain an invariable quantity : but as these
elements are constantly varying, it is of no use what-
ever ; and further, if they did not vary, the simple
square of the diameter would express an unit equally
incorrect. In order to show further the utter useless-
ness of the term horse power, as expressed above, we
will take two engines, each having YO inches diameter
of cylinder, one 10 feet stroke, the other 5 feet stroke,
and ascertain the nominal horse power of each.

152

VIBRATION OF BEAMS.

70 2 X V'lO

70 2 X V5

= 224.7 horses.
= 178.2 horses.

Now, then, if the pressure of steam was the same
in these two cylinders, and the pistons moved with
the same velocity, it is manifest that the powers must
be the same ; yet, according to the rule for nominal
horse power, they are made widely different ; and if
so much difference is made while the pressure of steam
is supposed to remain constant, what must we expect
when that element also varies ?

Vibration of Seams.

Given, the length, O c, from centre of beam, to a &,
line passing through centre of cylinder = 10 feet ; and

FIG. ia

length of stroke =10 feet ; required, the length O A,
or O C, of half the beam ?

MARINE ECONOMY. 153

The line a b bisects the versed sine of the arc, and,
supposing one half (c C) of the versed sine to be = a?,
we have (10 + xf = (10 - xf + 5 2

100 -J-200 + a 2 =100 20# + a? 2 + 25

# = .625,

Hence, half the length of the beam = (10 + .625)
= 10.625 feet.

Marine Economy.

A body moving through water with a certain
velocity displaces a certain quantity of water in a given
time, with a certain velocity ; if the velocity be doubled,
the quantity of water displaced will also be doubled,
because the body moves double the distance, and each
particle of water will, therefore, be displaced with
double the velocity ; hence, the resistance to the body
will be as 2 X 2, or as the square of the velocity. Thus
it appears that, if a ship consumes 500 tons of coal to
perform a certain distance, at the rate of 5 miles the
hour, to perform the same distance at the rate of 10
miles the hour, would require 5 2 : 10 2 : : 500 : 2000
tons, or 4 times 500 ; but the quantity of coal required
for any one day, at the rate of 10 miles, will not be 4
times the quantity required at that rate for 5 miles,
but will be 8 times ; for, supposing the speed be in-
creased to 10 miles the hour, the same distance will be
performed in 5 days ; hence, we have, in the first case,
500 tons consumed in 10 days = 50 tons per day, and
in the latter case, 2000 tons in 5 days = 400 tons per
day, or 8 times 50 tons. Now, then, taking the coal
as the exponent of the power, we see that the power

154 MAEINE ECONOMY.

has to increase as 2x2x2, or as the cube of the
velocity. Hence the importance, wherever speed is
not an object, of running the engines as slow as possi-
ble, in order to economize the fuel.

But whenever there is an adverse current to con-
tend with, the most economical speed is half as fast
again as the current. That is to say, if the velocity
of the current be 4 miles the hour, the velocity of the
vessel should be 6 miles. We will endeavor to demon-
strate this without the use of mathematical formula.

Let 1 represent the power required for a speed of
one mile per hour, then, inasmuch as the power in-
creases as the cube of the velocity, the power required
for the speed of 6 miles = 6 3 = 216, and the ground
moved over = 4 2 2.

Suppose, now, the velocity of the ship be reduced
to 5 miles per hour, the power will be = 5 3 = 125, and
the ground moved over =5 4 = 1.

Suppose, again, the speed to be increased to 7 miles
per hour, the power will be =7 3 = 343, and the ground
moved over = 7 4 = 3.

Summing up these figures, we have for a speed of
7 miles per hour a power expended of 343, to make
good a distance of 3 miles = 114^ per mile; for a
speed of 5 miles, a power of 125 to make good 1 mile
= 125 per mile; and for a speed of 6 miles, 216, to
make good 2 miles = 108 per mile. Consequently,
the least power is required at the speed of 6 miles,
which is half as fast again as the current.

Had the calculation been made for any fraction of
a mile, either above or below 6, the same result would
have been obtained.

These calculations apply alike to head winds, <fec.,
at sea, as well as to a tide-way in a river ; whence it

LIMIT TO EXPANSION. 155

follows that a vessel can be run even too slow for
economy, but nevertheless, when having a heavy head
sea to contend with, there are other elements besides
economy of fuel to be taken into consideration ; the
strain upon the vessel and machinery, the plunging
and staving in of the light work about the bows and
other places, shipping of seas, <fec., are matters which
also require the judgment of the commanding officer.

Limit to Expansion.

Theoretically, supposing a perfect vacuum to ob-
tain in the cylinder, there is no limit to expansion ;
but, practically, there is. The unbalanced pressure at
the end of the stroke should never be less than suffi-
cient to overcome the friction of the engine, and ought
always to be a little more.

EXAMPLE. Length of stroke = 8 ft. ; initial pres-
sure of steam 30 Ibs. per square inch, inclusive of the
atmosphere ; back pressure 4 Ibs. per sq. inch ; friction
of engines, <fec., = 2 Ibs. per square inch ; required the
point where the steam should be cut off to yield all its
useful effect ?

x = the point,
4 + 2 = 6 = the pressure at the end,

x X 30 = 6 X 8
30a?=48

x = 1.6 ft. from commencement.

Tlie Proper Lift for a Valve

Is equal to the area of the valve divided by the
circumference.

156

GEAVITY.

Centre of Gravity.

The centre of gravity of a cone from the vertex
equals f- the axis.

In a paraboloid, the distance from vertex equals -f
the axis.

In a parabolic space, equals - the axis from the
vertex.

In a triangle, equals J- the axis from the vertex.

Centre of Pressure.

The centre of pressure of a parallelogram, when
the upper surface is level with the water, = \ from the
bottom ; of a right-angled triangle with
the base down \ from the bottom,
measured on the perpendicular line
B C ; with the base up ^ B C. See
Hanris Mechanics.

Semi-parabolic plane.

FOKMULA :

m = centre of pressure,
b m = \ of a (?,
m n -/ of a d.

Gravity.

The spaces described by a body acted upon freely
by gravity are as the squares of the times ; i. e., a body
falling 2 seconds, will describe 4 times the distance of

GRAVITY. 157

a body falling one second. Hence, in order to ascer-
tain the distance fallen by a body, it is only necessary
to multiply the square of the number of seconds by
the distance fallen in the first second ; the product will
be the total distance fallen.

All bodies fall with the same velocity in vacuo,
namely, 16.08 feet in the first second, having a velocity
of 32.166 feet at the end of the second. Where the
atmosphere is interposed, the velocity will be some-
what less, say for heavy bodies, such as the metals, 16
feet for the first second.

EXAMPLE. Which will strike with the greater
'effect, a weight of 200 Ibs., falling through 144 ft., or
100 Ibs. falling through 256 feet ?

The velocity of a body at the end of a fall is equal
to the number of seconds it is falling, multiplied into
(32 feet) the velocity at the end of the first second,
and the momentum of a body is equal to the weight
multiplied into the velocity. We have, then, first to
find the velocity, and afterwards the momentum.

v/16 : 1 : : v/144 : 3 seconds time of falling of 200 Ib.
v/16 : 1 : : v/256 : 4 " " " 100 Ib.

32 X 3 = 96 ft. per second velocity at end of fall

of200lb. weight.
32 X 4 = 128 ft. per second velocity at end of fall

of 100 Ib. weight.

96 X 200=19200= momentum of the 200 Ib. weight.
128x100=12800= momentum of the 100 Ib. weight.
6400= difference, which is 33^- per cent,
of the larger number.

158 DISPLACEMEISTT OF FLUIDS.

Centre of Gravity of Several Bodies taken together.

Suppose there be several weights placed as follows
in the same plane, required the centre of gravity of
them all taken together ?

Cylinder. Air-pump. Shaft. Boilers.

Tons. Tons. Tons. Tons.

5 2 10 30

< 8ft. x 10ft x 20ft. > a

Assume a point (a), at any distance (say 2 feet)
from either of the extreme weights, and multiply each
weight separately by its distance from this point ; the
sum of these products, divided by the sum of the
weights, will be the distance of the centre of gravity
from the assumed point. Thus :

30 X 2 = 60
10 X 22 = 220

i> x 32 = 64

5 x 40 = 200

47 ) 544 (11.57 ft. = centre of

gravity from the point #, or 9.57 feet from the boilers
towards the shaft.

Displacement of Fluids.

Solid bodies immersed in fluids will displace an
amount of the fluid equal to their own weight. If the
specific gravity of the body be greater than that of
the fluid, it will sink ; otherwise it will float.

EXAMPLE. Required the distance a cube of cherry,
one foot high, will sink in fresh water ?

TEMPERATURE OF CONDENSER. 159

The specific gravities of fresh water and cherry are
relatively as 1.00 to .606 ; the cherry will therefore
sink .606 feet.

Temperature of Condenser.

EXAMPLE. Water in the boilers, carried at a den-
sity of If per saline hydrometer; temperature of the
condenser, and water entering the boilers, 105 Fahr. ;
vacuum in condenser, 27.82 inches. Compare the eco-
nomic performance of the engine, under these circum-
stances, with the same engine, carrying the water in
the boilers at the same density, but the water in the
condenser at 120 Fahr. ; the mean pressure of steam
in both cases on the piston being 20 pounds per square
inch?

SOLUTION. Neglecting the difference of power in
the two cases required to work the air-pump, taking
the boiler pressure at 20 Ibs., and 2 inches of mercury
to be equal to 1 Ib. pressure, we proceed thus :

1184-105 X .75+228.5-105 : 228.5-105 : : 100 :
13.23 per cent, loss by blowing off, in the first case.

1184-120X.75+228.5-120 : 228.5-120 : : 100 :
11.96 per cent, loss by blowing off, in the second case.

20x2 : 2.18 (back pressure) : : 100 : 5.45 per cent,
of the effect of the engine lost by back pressure, in the
first case.

20 X 2 : 3.33 (back pressure) : : 100 : 8.325 per cent,
of the effect of the engine lost by back pressure, in the
second case.
11

160 TEMPERATURE OF CONDENSER.

Now, then, letting the fuel represent the power,
we observe, in the first case, that only (10013.23=)
86.77 per cent, reaches the engine, of which 5.45 per
cent, is lost in back pressure, and 5.45 per cent, of
86.77 per cent.=4.73 per cent, of the total effect lost
by back pressure, leaving (86.774.73=) 82.04 per
cent, to be applied to operating the engine.

In the second case, (10011.96=) 88.04 per cent,
of the power reaches the engine, of which 8.325 per
cent, is lost in back pressure, and 8.325 per cent, of
88.04 per cent. =7.33 per cent, of the total effect lost
by back pressure; leaving (88.047.33=) 80.71 per
cent, to be applied to operating the engine.

Therefore, under the conditions of the example,
the engine, in the first case, performs the same amount
of work with (82.0480.71=) 1.33 per cent, less fuel.

This calculation can be made accurate by taking dia-
grams from the cylinder and air-pump, under the con-
ditions of the example, and estimating the power in
each case ; then, the power to work the air-pump is
considered.

APPENDIX.

MATEEIALS.

IF Engineers possessed the proper knowledge of
the materials used in the construction of machinery,
and gave the attention and care to the subject which
it deserves, we should have fewer break-downs in our
sea-going steamers ; and might, with safety and great
advantage, reduce the weights of those parts made of
wrought and cast iron.

It can scarcely be expected, however, that, with
the onerous duties of constructing many kinds of ma-
chinery, they can be well versed in the manufac-
ture of every variety of iron ; but every engineer hav-
ing the superintendence of construction or repairs,
should make himself familiar with the materials used,
so as to be able to distinguish good from bad ; to know
the difference between superior and inferior brands of
pig iron, and the reasons thereof. The difference be-
tween superior charcoal boiler plate and that made
directly from the bloomery or puddling furnace. Also,
the peculiarities of open sand moulding, green sand
castings, dry sand castings, and loam moulding. The
manner of providing for expansion and contraction in
castings and forgings, as well as the necessity of avoid-

162 HOW TO TEST IKOX.

ing the process of cold-hammered forgings. We throw
out these few hints simply with a view of calling the
attention of engineers to this important branch of the
profession, in which practice alone can make them
proficient.

* To Test tlie Quality of Bar Iron. Cut a notch
on one side with a cold chisel, then bend the bar over
the edge of an anvil at sharp angles. If the fracture
exhibits long silky fibres, of a leaden gray color, co-
hering together, and twisting or pulling apart before
breaking, it denotes tough, soft iron, easy to work and
hard to break. In general, a short, blackish fibre, in-
dicates iron badly refined. A very fine close grain
denotes a hard steely iron, which is apt to be cold
short, but working easily when heated, and making a
good weld. Numerous cracks on the edges of the bar
generally indicate a hot short iron, which cracks or
breaks when punched or worked at a red heat, and
will not weld. Blisters, flaws, and cinder holes are
caused by imperfect welding at a low heat, or by iron
not being properly worked, and do not always indicate
inferior quality.

To Test Iron when Hot. Draw a piece out, bend
and twist it, split it and turn back the two parts, to
see if the split extends up ; finally, weld it, and observe
if cracks or flaws weld easily. Good iron is frequently
injured by being unskilfully worked : defects caused
by this may be in part remedied. If, for example, it
has been injured by cold hammering, moderate anneal-
ing heat will restore it.

* Ordnance Manual, 1858.

CAST IRON AND STEEL. 163

Cast Iron. There are many varieties of cast iron,
differing from each other according to the kind of fuel,
of ore, and the temperature of the blast from which
the pigs are made the pig iron being known as char-
coal cold blast, charcoal hot blast, anthracite cold
blast, and anthracite hot blast. The former is much
the superior, and the latter the inferior varieties. Be-
sides these general divisions, the manufacturers distin-
guish more particularly the different varieties of pig
metal by numbers, according to their relative hard-
ness : for instance, No. 1 is the softest iron, has a dark
gray appearance ; No. 2 is harder, close grained, and
stronger than No. 1 ; it has a gray color also, and con-
siderable lustre. No. 3 is still harder than Ijb. 2 ; its
color is gray, but inclining to white ; it is principally
used for mixing with other irons. No. 4 is a bright
iron, also used to mix with other irons.

When a piece of iron is broken, and the fracture
presents grains very large, or very small, and a dull
earthy aspect, loose texture, dissimilar crystals mixed
together, it indicates an inferior quality.

All cast iron expands forcibly at the moment of be-
coming solid, and again contracts in cooling. The
color and texture of the castings depend greatly on
the size of the casting, and the rapidity of cooling.
Care should always be taken to cool them slowly.

Steel. To test steel, break a few bars, taken at
random, make tools of them, and try them in the
severest manner.

164

TENACITY OF MATERIALS.

Tenacity of Materials.

Cast Steel ...134,000 Ibs.

'Swedish 72,000 "1 Experiments by Frank-
Salisbury, Conn 66,000 I lin Institute, on bars

Bar-iron - Bellefonte, Pa 58,500 [ whose cross section

English 56,000 J was about one-fifth

Pittsfield, Mass 57,0001 of a square inch.

Tig metal 15,000

r . Good common castings 20,000 Experiments of Maj. W.

" S p^ S fro^n bead, j-jjjj Sftpa^nt

Cast Steel 128,000 on pieces whose cross

. , ( 30,000 section was nearly 1

Bronze-gun metal j 42 | 000 & ^^ ^

Copper, cast, (Lake Superior) 24,138 ,

Brass 18,000

S Wrought 34,000

C PP er \ Cast..?. 19,000

Tin, cast 4,800

Zinc 3,500

Platinum 56,000

Silver. 40,000

Gold , 80,000

Lead 1,800

WOODS.

Ash 15,800

Mahogany 11,500

Oak 11,600

White Pine 11,800

Walnut 7,700

In general, the tenacity of metals is increased by
hammering and wiredrawing. The strength of Pitts-
field bar iron, given in the above table, is the mean of
four trials, with cylinders 1 inch long and 0.9 inch di-
ameter. They were extended in length, before frac-
ture, to 1.4 in., and they were reduced in diameter to
0.6 in. in the middle.

A bar of wrought iron is extended about one-hun-
dredth part of its length for every ton of strain on a
square inch.

Transverse Strength.

S = the weight in pounds required to break a beam
1 in. square and 1 in. long, fixed at one end and loaded
at the other ; I the breadth, d the depth, and I the

RESISTANCE TO TORSION. 165

length, in inches, of any other beam of the same mate-
rial, and W the weight which will cause it to break,
neglecting the weight of the beam itself.

1. If the beam is supported at one end, and loaded at the other :

M*
W = S -y-

2. If the beam is supported at one end, and the load distributed over its

whole length :

b<P
W = 2S -y

3. If the beam is supported at both ends, and loaded in the middle :

bd*
W = 4S y-

4. If the beam is supported at both ends, and loaded uniformly over its
whole length :

bd?
W = 8S y~

5. If the beam is supported at both ends, and loaded at the distance m from
one end :

Ibd*

W = S /, r
m (lm)

Resistance to Torsion.

S = the weight in pounds required to break, by
twisting, a solid cylinder, 1 inch diameter ; the weight
acting at the distance of 1 inch from the axis of the
cylinder ; d, the diameter in inches of any other cylin-
der of the same material ; r, the distance from its axis
to the point where the breaking weight W is applied ;
then:

d 3

Results of Repeated Heating Bar Iron.

In a series of experiments, with regard to the im-
provements and deterioration which result from oft-
repeated heating and laminating of bar iron, made by
William Clay, Esq., of the Mersey steel and iron works,
Liverpool, he says that, taking a quantity of ordinary

166 RESULTS OF EEPEATED HEATING BAK IEON.

fibrous puddled iron, and reserving samples marked
No. 1, we piled a portion five high, heated and rolled
the remainder into bars marked No. 2, again reserving
two samples from the centres of these bars, the remain-
der were piled as before, and so continued until a por-
tion of the iron had undergone twelve workings.

" The following table shows the tensile strain which
each number bore :

No. Pounds.

1. Puddled bar 43,904

2. Re-heated 52,864

9.
10.
11.
12.

59,585
59,585
57,344
61,824
59,585
57,344
57,344
54,104
51,968
43,904

" It will thus be seen that the quality of the iron
increased up to No. 6, (the slight difference of No. 5
may, perhaps, be attributed to the sample being slightly
defective) ; and that from No. 6 the descent was in a
similar ratio to the previous increase."

TENSILE STRENGTH OF IRON AND STEEL BARS PER SQUARE INCH.

Description of Iron and Steel.

Tensile Strength.

Authority.

62 644

56,532

American Board of

56,103

Ordnance.

American Hammered

53,913

Krupp's Cast Steel, average of 3 samples...
Cast Steel, highest

111,707
142,222

Min. of War, Berlin.
Mallett.

88,657

do.

U <(

134,256

150,000

Shear Steel

124,400

Blister "

133,152

Mersey Steel and Iron Co. Puddled steel,
highest

173 817

Dito another sample

160 8:32

Average of three samples tested at the Liv-
erpool Corporation testing machine

1 1 -V^O

STRENGTH OF JOINTS OF BOILER PLATES. 167

On the strength of the joints of single and double riveted
boiler plates, by William Fairlairn, Esq., F.R. S.

On comparing the strength of plates with their
riveted joints, it will be necessary to examine the sec-
tional areas taken in a line through the rivet-holes with
the section of the plates themselves. It is perfectly
obvious, that in perforating a line of holes along the
edge of a plate, we must reduce its strength : it is also
clear that the plate so perforated will be to the plate
itself, nearly as the areas of their respective sections,
with a small deduction for the irregularities of the
pressure of the rivets upon the plate ; or, in other
words, the joint will be reduced in strength somewhat
more than in the ratio of its section through that line
to the solid section of the plate. It is evident that the
rivets cannot add to the strength of the plates, their ob-
ject being to keep the two surfaces of the lap in contact.

When this great deterioration of strength at the
joint is taken into account, it cannot but be of the
greatest importance that in structures subjected to such
violent strains as boilers and ships, the strongest
method of riveting should be adopted. To ascertain
this, a long series of experiments
were undertaken by Mr. Fairbairn,
some of the results of which will
be of interest here. The joint or-
dinarily employed in ship building
is the lap joint, shown in Figs. 1
and 2. The plates to be united
are made to overlap, and the rivets
are passed through them, no cov-
ering-plates being required, except

a , a a 9

at the ends of the plate, where they butt against each

168 STRENGTH OF JOINTS OF BOILER PLATES.

other. It is also a common practice to countersink the
rivet-heads on the exterior of the vessel, that the hull
may present a smooth surface for her passage through
the water. This system of riveting is only used when
smooth surfaces are required ; under other circum-
stances, their introduction would not be desirable, as
they do not add to the strength of the joint, but, to a
certain extent, reduce it. There are two kinds of lap-
joints, those said to be single-riveted (Fig. 1), and those
which are double-riveted (Fig. 2). At first, the former
were almost universally employed, but the greater
strength of the latter has since led to their general
adoption in the larger descriptions of vessels. The rea-
son of the superiority is evident. A riveted joint gives
way either by shearing off the rivets in the middle of
their length, or by tearing through one of the plates
in the line of the rivets. In a perfect joint, the rivets
should be on the point of shearing just as the plates
were about to tear ; but in practice, the rivets are
usually made slightly too strong. Hence, it is an estab-
lished rule, to employ a certain number of rivets per
lineal foot. If these are placed in a single row, the
rivet-holes so nearly approach each other, that the
strength of the plates is much reduced ; but if they
are arranged in two lines, a greater number may be
used, and yet more space left between the holes, and
greater strength and stiffness imparted to the plates at
the joint.

The experiments of Mr. Fairbairn and others have
established the following relative strengths as the
value of plates with their riveted joints :

Taking the strength of the plate at 100

The strength of the double-riveted joint would then be 70

And the strength of the single-riveted joint 50

MOTION. 169

THE ELEMENTS OF MACHTKEEY.

IN consequence of having found many young en-
gineers unacquainted with the principles of mechani-
cal powers, we have thought best to devote a short
space to the subject, prefacing it with the description
of motion, and application of power, by David A.
Wells, A. M.

Motion.

Motion is the act of changing place. It is absolute
or relative. Absolute motion is a change of position
in space, considered without reference to any other
body. Relative motion is motion considered in rela-
tion to some other body, which is either in motion or
at rest.

When a body commences to move from a state
of rest, there must be some force to cause its motion,
and this force is generally termed " Power." On the
contrary, a force acting to retard a moving body, de-
stroy its motion, or drive it in a contrary direction,
is termed " Resistance." The chief causes which tend
to retard or destroy the motion of a body are gravi-
tation, friction, and resistance of the air.

The speed, or rate, at which a body moves, is
termed velocity. The momentum of a body is its
quantity of motion, and this expresses the force with
which one body in motion would strike against
another. This momentum, or force, which a moving
body exerts, is estimated by multiplying its weight
by its velocity. Thus a body weighing 20 Ibs., and
moving with a velocity of 200 feet per second, will
have a momentum of 20 x 200 = 4000.

170 APPLICATION OF POWER.

Action and Reaction.

"When a body communicates motion to another
body, it loses as much of its own momentum, or force,
as it gives to the other body. The term Action is
applied to designate the power which a body in mo-
tion has to impart motion, or force, to another body ;
and the term Reaction to express the power which
the body acted upon has of depriving the acting body
of its force or motion. There is no motion, or action
without a corresponding and opposite action of equal
amount ; or, in other words, action and reaction are
always equal and opposed to each other.

Application of Power.

The principal agents from whence we obtain
power for practical purposes, are men and animals,
water, wind, steam, and gunpowder.

When work is performed by any agent, there is
always a certain weight moved over a certain space,
or resistance overcome ; the amount of work per-
formed, therefore, will depend on the weight, or re-
sistance that is moved, and the space over which it is
moved. For comparing different quantities of work
done by any force, it is necessary to have some stand-
ard ; and this standard is the power, or labor, ex-
pended in raising a pound weight one foot high, in
opposition to gravity.

A machine is an instrument, or apparatus, adapted
to receive, distribute, and apply motion derived from
some external force in such a way as to produce a
desired result ; but it cannot, under any conditions,
create power, or increase the quantity of power or
force applied to it. Perpetual motion, or the con-
struction of machines which shall produce power
sufficient to keep themselves in motion continually, is,

APPLICATION OF POWER. 171

therefore, an impossibility, since no combination of ma-
chinery can create, or increase, the quantity of power
applied, or even preserve it without diminution.

The great general advantage that we obtain from
machinery is, that it enables us to exchange time and
space for power. Thus, if a man could raise to a cer-
tain height 200 pounds in one minute, with the
utmost exertion of his strength, no arrangement of
machinery could enable him unaided to raise 2000
pounds in the same time. If he desired to elevate
this weight, he would be obliged to divide it into ten
equal parts, and raise each part separately, consuming
ten times the time required for lifting 200 pounds.
The application of machinery would enable him to
raise the whole mass at once, but would not decrease
the time occupied in doing it, which would still be
ten minutes.

The power will overcome the resistance of the
weight, and. motion will take place in a machine,
when the product arising from the power multiplied
by the space through which it moves in a vertical
direction, is greater than the product arising from
the weight multiplied by the space through which it
moves in a vertical direction. Thus if a small power
acts against a great resistance, the motion of the lat-
ter will be just as much slower than that of the
power, as the resistance or weight is greater than the
power, or if one pound be required to overcome the
resistance of two pounds, the one pound must move
over two feet in the same time that the resistance,
two pounds, requires to move over one.

All machines, no matter how complex and intri-
cate their construction, may be reduced to one or
more of six simple machines, or elements, which we
call the

172 THE LEVEE.

Mechanical Powers.

The simple machines, six in number, are usually
denominated the lever, inclined plane, wheel and
axle, pulley, screw, and wedge.

The wheel and axle is, however, a revolving lever,
the screw a revolving inclined plane, and the wedge
a double inclined plane, thus reducing them to three
in number, viz. : lever, inclined plane, and pulley.

All these machines act on the same fundamental
principle of virtual velocities ; accordingly, tlie weight
multiplied into the space it moves through is equal to
the power multiplied into the space it moves through.
This is the general law which determines the equi-
librium of all machines ; and keeping this principle
in mind, there will be no difficulty in solving any of
the propositions appertaining to the simple machines.

In all machines, a portion of the effect is lost in
overcoming the friction of the working parts; but,
in making calculations upon them, it is made first as
though no friction existed, a deduction being after-
wards made. And so also we have to assume a per-
fection in the machine itself which does not exist ;
that is to say, the inclined plane, screw, wedge, <fec.,
to be a perfectly smooth hard inflexible substance,
and the rope of the pulley, and wheel and axle, to be
perfectly flexible and non-elastic, conditions, for which
allowance has to be made after the calculation is
completed.

Lever. Of the lever there are three orders, as
shown respectively by the figures 1, 2, 3.

THE LEVEK.

Tig. 2

Tig. 3

W = weight, P = power, F = fulcrum.

EXAMPLE 1. Given the Weight W = 1000 Ibs.,
required the power P, the lengths of the arms re-
spectively as marked in the figures ?

ANS. 1. P x 3 = 1000 X 1
3P = 1000
P = 333 Ibs.

Aire. 2. P x 4 = 1000 X 1
4P = 1000
P = 250 Ibs.

ANS. 3. P X 1 = 1000 X 4
P = 4000 Ibs.

EXAMPLE 2. Given a compound lever with lengths

and weight as marked in fig. 4, required the power P.

174 THE LEVEE.

p X 16 = 1000 X 4
16p = 4000

p = 250 Ibs. = weight required at
p, supposing there to be but one lever therefore

P X 10 = 250 X 2
10P = 500

P = 50 Ibs.
Or,

1000 x4x2i=Px!Ox!6
8000 = 160P
P= 50

EXAMPLE 3. Given, as per figure 5, a safety valve

Tig. 5.
< s x ao

100 sqr. ins. area

20 Ibs. per sq. in. pressure
2000 Ibs. total pressure.

100 sq. ins. area, subject to a pressure per square inch
above the atmosphere of 20 Ibs., lengths of the long
and short arms of the lever as shown in the figure,
required the weight W to balance the pressure on the
valve ?

W x 25 = 100 X 20 X 5
25W = 10000
W = 400 Ibs.

EXAMPLE 4. Suppose, in example 3, the valve and
stem should weigh 20 Ibs., and the lever, which is
uniform throughout its length, weigh 2 5 Ibs., what
would be the weight W, in that case, to balance the
same pressure of steam ?

The valve and stem being 5 inches from the ful-
crum, act with a leverage of 5 inches, but the lever
being uniform, its action is the same as though the

INCLINED PLANE.

whole weight was concentrated at x (the centre of
gravity) half way of its length, Wherefore

W X 25 + 20 X 5 + 25 X 12.5 = 100 X 20 x 5
25W + 100 + 312.5 = 10000

25 W = 10000 -412.5

W = 383.5 Ibs. the re-
quired weight.

Practically, the pressure a safety valve lever ex-
erts on the valve can be ascertained by fixing it in its
place, and attaching a spring balance to the pin hole
immediately over the valve. If the valve and weight
be also attached, the balance will indicate the total
pressure which tends to keep the valve in its seat,
which pressure being divided by the number of square
inches in the valve, will give the pressure per square
inch at which steam will commence to blow off.

Inclined Plane.
Ex. 1. Weight W 500 Ibs.,
length, and height of the plane,
as per figure 6, 20 and 9 ins.
respectively, required the pow-
er P?

Considering the weight W to be started at the
base of the plane and rolled up to the top, it will
travel vertically the height of the plane, (9 inches),
while the power, P, will descend a distance equal to
the length of the plane (20 ins.), therefore, according
to the principle of virtual velocities,

P x 20 = 500 X 9
20P - 4500
P = 225 Ibs.

QJP Ex. 2. Length and
height of the plane as
per fig. 7, weight 500
pounds, rpnuired the

176

INCLINED PLANE.

power P applied in a line with the base of the
plane ?

In this case, when the weight will have risen from
the base to the top of the plane, 9 ins., the distance
descended by P will manifestly not be equal to the
length but to the base. Wherefore

P X v/20 a -9'= 500 X 9
17.86P = 4500

P = 251.96 - Ibs.

In order to establish Equilibrium between the
weight and power, this calculation is also applicable

A. when the power is
applied in the di-
rection of the base
as shown in dots,
figure 7.

O If the power be
applied at an angle
with the plane, as
C A, figure 8, in
order to ascertain the proportion of weight to the
power, to establish equilibrium, we proceed thus :
Draw CD, the vertical of the centre of gravity of the
weight, of any convenient length ; CE, at right angles
to BF, and DE parallel to AC. CD can represent
the length of the plane, and DE the height. Where-
fore

Weight x DE = Power x CD
Power = Weight X DE

~CD~

Geometrically, the angles BC and CDE, from
the construction of the figure, can be demonstrated
to be equal, and also ECD, and BFG ; from which,
knowing the lengths of two legs of the triangle BFG,

WHEEL AND AXLE.

177

and the angle G, to be a right angle, the lengths of
the lines CD ED can be determined.

Wheel and Axle. In the wheel and axle, when
the power is applied tangentially to the wheel,

W x radius of axle = P x radius of wheel
W X diameter of axle = P x diameter of wheel
W X circumference of axle = P x circum. of wheel.

When the power is not applied
tangentially to the wheel, but in the
direction shown in fig. 9, the length
of the line ah at right angles to the
power will give the leverage of the
power, hence

W x radius of axle = P x oh.

Tig. 9.

Pulley. If a cord be pulled at one end the ten-
sion throughout its whole length must be alike.
Taking figure 10, and supposing the power to be 1,
the tension throughout the entire
length of the cord will be 1, but
as there are two parts of the cord
supporting the lower block, the
weight must be 2. The pressure
on the fulcrum or support must
be always equal to the weight,
plus the power. If there be
more than one support, the sum
of the pressures on them will be
equal to the sum of the weight
and power. Or, in figure 10,
according to the principle of virtual velocities, the
weight is double the power, because the power must
descend 2 feet for every foot ascent of the weight.

. 10

178

THE PULLEY.

The numbers above the top blocks in all the ex-
amples of pulleys here shown represent the pressure
on the supports.

In fig. 11, the power and weight are as 1 to 8, because
the power supports 4 weights, each one double its size.

In fig. 12 the tension
on the 1st cord is 1 ; on
the 2d 2 ; 3d 4 ; 4th 8 ;
5th 16 ; and as there are
2 parts of the cord hav.
ing a tension of 16, the
weight to establish equi-
librium, must be 32.

In fig. 13 the weight
to the power is as 3 to
1, there being 3 parts
of the cord having a
tension of 1 supporting
the weight.

THE PULLEY.

179

In fig. 14 the power
to the weight is as 1
to 12, the power being
multiplied four times
by the application of
the second set of pul-
leys, or luff-tackles,
as they are technically
termed.

In fig. 15 the power
is to the weight as
1 to 12, the tension
throughout the first
cord being 1 ; the sec-
ond cord 2 ; third 5,
and as there are two
parts of the cord hav-
ing a tension of 5, and
one part of the cord
having a tension of 2,
supporting the weight,
if all the cords be
supposed parallel, the
weight must be the
sum of these, or 12.

In fig. 16 the power
to the weight is as 1
to 4.

In figure 17, where
the power is applied
at an angle, we ascer-
tain the proportion of
the weight and power
thus: Draw AD, of
any convenient length^
and from the point A
draw AB parallel to

180

THE PULLEY.

Cc and AC parallel to BZ>. The
power and weight will be re-
spectively as the lengths of the
lines DC or DB and AD.

rig. 16

Eig-,17.

From which it will be seen that the greater the
angle CDB the longer will be the line DC or DB, and
hence the greater the power. So that the weight of the
line itself will be sufficient to prevent any power
whatever from drawing it mathematically straight.

QUESTION. In figure 18, two blocks of granite,
joined together as shown, are laid upon a horizontal
plane ; required their relative sizes in order that they
may commence at the same time to move, and con-
tinue to move with equal velocity ?

ANS. 2 to 1, because the larger block is supported
by two -parts of the cord, and has in consequence,
double the force exerted upon it of the smaller block.

THE SCREW.

181

rj nff. 19

Screw. In the screw,
like all other simple ma-
chines the power x space
moved through = weight
X space moved through.
Ex. Length of lever
20 ins., pitch of screw
inch, weight 500 Ibs., re.
quired the power P at
the end of the lever ?
ANS. Px 20x2x3.1416

= 500 X T
125.664P = 250

P = 1.989 Ibs.

Tig. 20

The screw is simply a
revolving inclined plane,
the power being applied
parallel to the base of
the plane, which is repre-
sented by the circumfer-
ence described by P, and
the height of the plane
by the pitch of the screw.

Fig. 20 is a compound
screw. The upper screw
AA is fitted to the thread
in the nut B which re-
mains fixed. The cylin-
der AA being hollow has
another screw C, of a finer
thread, fitting into it.
The nut D is fixed, al-
lowing C to slide up and
down within it, without

182

THE WEDGE.

turning. By this arrangement it will be seen, that
when the screw A A is turned once round, the distance
ascended by the weight will not be equal to the pitch
of AA, but the difference between the pitch of AA
and C.

EXAMPLE. Pitch of AA inch, of C T V inch,
weight 16000 Ibs.,' required the power P, applied 20
inches from the centre ?

ANS. P x 20 X 2 X 3.1416 = 16000 X T V - TT
125.664P - 1000

P = 7.957 Ibs.

In order to multiply the power the same number
of times with a single screw, the pitch would have to
be T ] g- inch, which would render the thread too weak
to withstand a heavy pressure.

Wedge. LetWW,

* 2 * fig. 21, be two weights

of 1000 Ibs. each, rest-
ing upon a horizontal
plane, required the
power to be applied
at P, to the wedge,
having the dimensions
shown in the figure to
"^ to separate them ?

P X 20 = 1000 X 2
20P = 2000
P = 100 Ibs.

Because, when the power P has descended to the
point A, the weights have been separated 2 inches
while the power has travelled 20 inches, the length
of the wedge.

Tig". 21.

FOECE, TEMPERATURE, AND VOLUME OF STEAM. 183

Table of the Elastic Force, Temperature, and Volume of Steam, from a
Temperature of 80 to 387.3, and from a Pressure of one to 410 Inches
of Mercury.

Elastic force In

Tempera-
ture.

Volume.

Elastic force in

Tempera-
ture.

Volume.

inches of
mercury.

>ounds per
sq. inch.

inches of
mercury.

pounds per
sq. inch.

.49

41031

53.04

243.3

1007

1.17

.573

35393

55.08

245.5

973

1.36

.666

30425

57.12

247.6

941

1.58

.774

26686

59.16

249.6

911

1.86

.911

100

22873

61.2

251.6

883

2.04

103

20958

63.24

253.6

857

2.18

1.068

105

19693

65.28

255.5

833

2.53

1.24

110

16667

67.32

257.3

810

2.92

1.431

115

14942

69.36

259.1

788

3.33

1.632

120

13215

71.4

260.9

767

3.79

1.857

125

11723

73.44

262.6

748

4.34

2.129

130

10328

75.48

264.3

729

2.45

135

9036

77.52

265.9

712

5.74

2.813

140

7938

79.56

267.5

695

6.53

3.1

145

7040

81.6

269.1

679

7.42

3.636

150

6243

83.64

270.6

664

8.4

4.116

155

5559

85.68

272.1

649

9.46

4.635

160

4976

87.72

273.6

635

10.68

5.23

165

4443

89.76

275

622

12.13

5.94

170

3943

91.8

276.4

610

13.62

6.67

175

3838

93.84

277.8

598

15.15

7.42

180

3208

95.88

279.2

586

8.33

185

2879

97.92

280.5

573

9.31

190

2595

99.96

281.9

564

21.22

10.4

195

2342

102

283.2

554

23.64

11.58

200

2118

104.04

284.4

544

26.13

12.7

205

1932

106.08

285.7

534

28.84

14.13

210

1763

108.12

286.9

525

29.41

14.41

211

1730

110.16

288.1

516

14.7

212

1700

112.02

289.3

508

30.6

212.8

1669

114.24

290.5

500

31.62

15.5

214.5

1618

116.28

291.7

492

32.64

216.3

1573

118.32

292.9

484

33.66

16.5

218

1530

120.36

294.2

477

34.68

219.6

1488

122.4

295.6

470

35.7

17.5

221.2

1440

124.44

296.9

463

36.72

222.7

1411

126.48

298.1

456

37.74

18.5

224.2

1377

128.52

299.2

449

38.76

225.6

1343

130.56

300.3

443

33.78

19.5

227.1

1312

132.62

301.3

437

40.80

228.5

1281

134.64

302.4

431

41.82

20.5

229.9

1253

136.68

303.4

425

42.84

231.2

1225

138.72

304.4

419

43.86

21.5

232.5

1199

140.76

305.4

414

44.88

233.8

1174

142.8

306.4

408

45.90

22.5

235.1

1150

144.84

307.4

403

46.92

236.3

1127 i 146.88

308.4

398

46.94

23.5

237.5

11 05

148.92

309.3

393

48.96

23S.7

1084

150.96

310.3

388

49.98

-24.5

239.0

I'HH

15?,. 02

311.2

383

51.

25 241

1044 . 15.-..06

312.2

379

184 FORCE, TEMPERATURE, AND VOLUME OF STEAM.

Elastic force in

Tempera-
ture.

Volume.

Elastic force in

Tempera-
ture.

Volume.

inches of
mercury.

pounds per
sq. inch.

inches of
mercury.

pounds per
sq. in.

157.1

813.1

374

254.99

125

349.1

240

159.H

314

370

265.19

130

352.1

233

161.18

314.9

366

275.39

135

355

224

163.22

315.8

362

285.59

140

357.9

218

165.26

316.7

358

295.79

145

360.6

210

167.3

317.6

354

306

150

363.4

205

169.34

318.4

350

316.19

155

366

198

171.38

319.3

346

826.39

160

368.7

193

173.42

320.1

342

336.59

165

371.1

187

183.62

324.3

325

346.79

170

373.6

183

193.82

328.2

310

357

175

376

178

203.99

100

332

295

367.2

180

378.4

174

214.19

105

335.8

282

377.1

185

380.6

169

224.39

110

339.2

271

387.6

190

382.9

166

234.59

115

342.7

259

397.8

195

384.1

161

244.79

120

345.8

251

408

200

387.3

158

V
731

THE LIBRARY
UNIVERSITY OF CALIFORNIA

Santa Barbara

THIS BOOK IS DUE ON THE LAST DATE
STAMPED BELOW.

Series 9482

SOUTHERN REGIONAL LIBRARY FACILITY

A 000 628 338 6