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THE

YOUNG MILL. WRIGHT

amiLa^^

IN FIVE PARTS.

CONTAINING :—

Part I. — Mechanics and Hydraulics ;
showing Errors in the old, and esta-
blisiiing-a new System of Theories
of Water- Mills, by which the power
of Mill-Seats, and the effects they
will produce, may be ascertained by
calculation.

Pabt II. — Rules for applying the The-
ories to practice ; Tables for pro-
portioning Mills to the power and
fall of the Water, and Rules for
finding Pitch Circles, with Tables
from 6 to 136 cogs.

Part III — Djrectionsfor constructing
and using all the Author's patented
Improvements in Mills.

Part IV. — The Art of manufacturing
Meal and Flour in all its parts, as
practised by the most skilfal Mil-
lers in America.

Part V.— The Practical Mill- Wright;
containing instmctions for building
Mills, with Tables of their Propor-
tions, suitable for all Falls from 3
to 36 feet.

Appendix. — Containing Rules for dis-
covering New Improvemenis — ex-
emplified in Improving the Art of
cleaning Grain, hulling Rice, warm-
ings Rooms, and venting tjmoke by
Chimnies, &c.

EMBELLISHED AVITH TWENTY-FIVE PLATES.

BY OLIVER EVANS.

FOURTH EDITION.

PHILADELPHIA :

M. CAREY & SON— CHESNUT STREET.

1831.

DISTRICT OF PENNSYLVANIA— TO wit:

Be It R'^m mbereil. That on the twenty fifth day of November, in the

r » thirty.'hird year of the Independence of the United Statt-s of America,

OLIVKR EVANS, of ihe said District, halh deposited in this office the

title of a book, the right whereof he claims as Author and Proprietor

in the following words — to wit:

" The Young Mill Wright's and Miller's Guide In five parts. Embel-
lished with twenty-five plates, 8cc. By Oliver Evans, of Philadelphia."
In conformity to the Act of Congress of the United Slates, intituled,
" An Act for the encouragement of learning, by securing the copies of
maps, charts, and books, to the authors and proprittors of such copies,
during the times therein mentioned."

SAMUEL CALDWELL,
Clerk of the District of Pennsylvania.

PREFACE.

The reason why a book of this kind, although
so much wanted, did not sooner appear, may be
— because they who have been versed in science
and literature, have not had practice and experi-
ence in the arts ; and they who have had prac-
tice and experimental knowledge, have not had
time to acquire science and theory, those neces-
sary quahtications for completing the system, and
which are not to be found in any one man. Sen-
sible of my deficiencies in both, I should not have
undertaken it, was I not interested in the explana-
tion of my own inventions. I have applied to
such books and men of science as I expected as-
sistance from, in forming a system of theory ; and
to practical mill-wrights and millers for the prac-
tice ; but finding no authors who had joined prac-
tice and experience with theory, (except Smeaton
whom I have quoted) finding many of their theo-
ries to be erroneous, and losing the assistance of
the late ingenious William Waring, the only sci-
entific character of my acquaintance, who ac-
knowledged that he had investigated the principles
and powers of water acting on mill-wheels, I did
not meet the aid 1 expected in that part.

Wherefore it is not safe to conclude that this
work is without error — but that it contains many.

IV PREFACE.

both theoretical, practical, and grammatical ; is
the most natural, safe, and rational supposition.
The reader, whose mind is free and unbiassed by
the opinion of others, >vill be most likely to attain
the truth. Under a momentary discouragement,
finding I had far exceeded the prescribed limits,
and doubtful what might be its fate, I left out se-
veral expensive draughts of mills, ^c. But since
it went to press the prospects have become so en-
couraging that I may hope it will be well received:
Therefore I request the reader, who may prove
any part to be erroneous, can point out its defects,
propose amendments, or additions ; to inform me
thereof by letter ; that T may be enabled to cor-
rect, enrich, and enlarge it. in case it bears another
edition, and I will gratefully receive their commu-
nications : For if what is known on these subjects
by the different ingenious practitioners in America
could be collected in one work, it would be pre-
cious indeed, and a sufficient guide to save thou-
sands of pounds from being uselessly expended.
For a work of this kind will never be perfected by
th»* abilities and labours of one man.

The practical part received from Thomas Elli-
cottwill doubtless be useful, considering his long
experience and known genius.

Comparing this with other oridnal, difficult
works, with equally expensive plates, the price
will be found to be low.

CONTENTS.

PART I.

MECHANICS.

Articles,

1. \xioMs, or self evident truths .-.-..- Page 9

2. Of the first principles of mechanical motion ... - 10
S. — elasticity, its power unknown ..--.- H

4. — motion, absolute and relative .--.-. 12

5. — do. accelerated and retarded -«--.- IS

6. — the momentum or quantity of motion - . - . . 13

7. — general laws of motion ..--..-- 15

8. — the momentum of clastic and non-elastic bodies in motion - 16

9. — laws of motion and force of falling bodies ; table and scale of their

motion .-..--. 20
10. — the laws of motion of bodies descending inclined planes, and curved

surfaces -------- 25

12 — the motion of projectiles ------ 26

13. — circular motion and central forces _ . - - 27

14. — centres of motion, magnitude and gravity - - - 30

15. — general laws of mechanical powers _ - . _ 31
16 — 21. OF levers, simple and compound ; their laws applicable to mill-
wheels ; general rule for calculating their power - - 33

21. Power decreases as the motion increases - - - . 39
22 — 23. No power gained by enlarging undershot-wheels, nor by double

gearing mills .----.- 39
24. The pulley, 25 the axk and wheel, 26 the inclined plain, 27 the wedge,

and 28 the screw _-_... 4I
30. The fly-wheel, its use ..---- 45
31 — 33. Of friction, its laws, and the inventions to reduce it - - 46
34. Of maximums, or the greatest eflFect of machines - - - 50
35 — 37. Old theory of the motion of undershot-wheels investigated ; new the-
ory proposed; scale of experiments - - - - 51
38 — 39. William Waring's new theory ----- 60

40. ■ theory doubted - - . - 64

41 — 42. Search for a true theory on a new plan, and one established agreeing

with practice -------65

43 — 44. The maximum motion of overshot-wheels, with a scale thereof - 74

HYDRAULICS.

45 — 47. Laws of the motion and effects of spouting fluids ; their application

to undershot-mills ... - - - 79

VI GONTENTS.

Articles, Pagp
48 — 50. Hydrostatic paradox ; on which is founded a theorem for finding the

pressure of wattf on any surface - - - - 85

51. Rule for finding the velocity of spouting water ... 87

52. Rule for finding the effect of any gate of water on undershot-wheels 8f
53 — 54. Water applied by gravity ; the power thereof on the principles of

overshot-mills. equal in theory to the best application possible - 90

55. Friction of the aperture on spouting fluids - - - - 94

56. Pressure of the air the cause of fluids rising in pumps and cyphons, &c. 95

57. Directions for pump-makers, with a table - - - - 97

58. Tubes for conveying w^ater over hills wnd under valleys - - 99

59. Paradoxical mill explained, that will not move empty; the difference of

force of indefinite and definite quantity of water - - 99

60. The motion of breast and pitch-back wheels. They do not run before the

gravity of the wHtei- on account of the impulse - - - 101

61. Simple rule for calculating the power of a mill-seat - - - 104

62. Theory compared, with a table of experiments of 18 mills in practice,

and found to agree .---.- 108

63. Rules for proportioning the size of mill- stones to the power ; with a table

of their areas, powers required, and quantity ground, &c. - 110

The surface passed by mill-stoues of different size and motion - 115

C4 — 65. Of digging canals; with their proper fall and size to suit the stones 117

65. Of air-pipes, to prevent trunks from bursting . - - 12#

67. Smeaton's experiments concerning undershot-mills - - 121

68. ——— experiments concerning OMTshot-mills - - - 137
89. __— experiments concerning wind-mills - - _ 144

PART II.

70. Of undershot-mills, with a table containing the motion of the water and

wheels, and proportion of the gears, suitable to any hi-ad from 1 to
25 feet, both double and single gear; the quantity of water required

to turn them, and the size of the gate and canal - - 155

71. Of tub mills, with a table showing the diameter of the wheels to suit any

size stone, or head of water - - - - - 1C§

72. Of breast and pitch -back wheels, with a table complete for them - 165

73. Of overshot-mills, with tables for them - - - . 171
Of mills moved by re-action ------ 17S

74. Rules for calculating the motion of wheels, and number of cogs to pro-

duce ih^ desired motion . . _ _ - 175

75. Rules for finding the pitch circles - - . , . I8I

76. A true, simple, and expeditious method for finding the diameter of the

pitch circle, with a table showing the diameter of pitch circles, &c. 182

77. Rules for measuring garners, hoppers, &c. - - - 18S

78. Of the different kind of gears and forms of cogs . - _ i8g
79 — 81. Of spur, face, and bevel gears ----- igg

82. Of matching wheels, to make them wear even and well - - 194

83. Theories of rolling-screens and fans for cleaning the grain, improved ap-

plication of them ------- 195

84. Of gudgeons, the cause of their heating and getting loose, with the reme-

dies therefor - - - - - - -197

55. On building mill-dams --.... 2OO

56. On laying foundations and building mill-walls - _ _ 202

CONTENTS. Vll

PART III.

Article!, Page

8". General account of the new improvements . . - . 207

88. Particular dt-scriptioii of the machines > _ - - 209

89. Application of the machines in the process of manufacturing flour - 213

90. Of elevating grain from ships - - - - - ■ i 216

91. .\ mill for grinding parcels -..--- 217

92. A grist-mill improved .-.-.-- 219

93. Of elevating from ships and storehouses by a horse . - - 221

94. Of an elevator wrought by a man - - - - - 222

95. Construction of the wheat elevator, particularly directed - - 226
96 — 100. Of the meal elevator, the meal conveyer, the grain conveyer, the

hopper-boy, and the drill - - - - - - 233

101 Of the utility of the machines . . - - ■ 242

102. Bills of materials, both of wood and iron, &c. to be prepared for building

the machines ...---- 246

103. A mill for hulling and cleaning rice ----- 249

PART IV.

104. The principles on which grinding is performed, explained - - 257

105. Of the draught necessary to be given to the furrows of mill-stones - 260

106. Directions for facing new mill-stones ----- 264

107. Of hanging mill-stones -..--.- 266

108. Of regulating the feed and water in grinding ... 268

109. Rules for judging of good grinding . - . - _ 269

110. Of dressing and sharpening the stones when dull - - . 270

111. Of the most proper degree of fineness lor flour - - - 271

112. Of garlic, with directions for grinding wheat mixed therewith; and for

dressing the stones suitable thereto - - . - 273

113. Of grinding over the middlings, stuff" and bran, or shorts, if necessary,

to make the most of them ------ 275

114. Of the quality of the mill-stones, to suit the quality of the wheat - 277

115. Of bolting-reels and cloths, with directions for bolting and inspecting

flour ---.--.. 280

116. Directions for keeping the mill, and the business of it, in good order - 283

117. Peculiar accidents by which mills are subject to catch fire - - 284

118. Observations on improving of mill-seats - - - - 285

PART V. [See the contents at the beginning of it.]

CONTENTS OF THE APPENDIX.

Rules for discovering new improvements, exemplified. — I. In Cleaning grain by
wind. II. Distillation of spiiits. III. Inventing smoke from rooms by chim-
neys. IV. Warming rooms by fire to save fuel. V. Hulling and cleaning rice.
VI. Saving ships from sinking at sea. VII. Preserving fruits and liquors from
.putrefaction and fermentation.

VHl CONTENTS.

EXPLANATION OF THE TECHNICAL TERMS, kc.
USED IN iHIS WUKK.

aperture, The opening by which water issues.

^rea. Plane suiface, superficial contents.

Atmosphere, The surrounding air.

Mgebruic djmis used are _^ for more, ar addition. — Less, subtracted, y^ Mul-
tiplication ^ Division. ^^ Equality. ^ The square root of 863 for 86
squired, 883 for' 88 cubed.

Biquudrate, A number twice squared : the biquadrate of 2 is 16.

Corollurij, Inference.

Cuboch, A name for the unit or integer of power, being one cubic foot of water
multiplied into one foot perpendicular descent.

Cubic fo':t (ijioater. What a vessel one foot wide and one foot deep will hold.

Cvbe of a number. The product of the number multiplied by itself twice.

Cube root of a number. Say of 8, is the number, which multiplied into itself twice
will produce 8, viz. 2. Or it is that number by which you divide a number twice
to quote itself.
Decimal point, set at the left hand of a figure shows the whole number to be di-
vided into tens, as ,5 for 5 tenths; ,57 for 57 hundredths; ,557 for 557 thousandth
parts.
Eq^nlibrio, Equilibrium. — Equipoise, or balance of weight.
Elastic. Springing.
Friction, The act of rubbing together.
Gravity, That tendency all matter has to fall downwards.
Hydrostatics, Science of weighing fluids.
Bydruidics, Water-works, the scierice of motion of fluids.
Impulse, Force communicated by a stroke.
Impetus, Violent effort of a body inclining to move.
Momentum, The force of a body in motion.
Maxivmm, Greatest possible.
J^'owelastic, Without spring.

Ocmble, Eight limes told.

Paradox, Contrary to appearance.

P'.icussiun, Striking a stroke, impulse.

Problem, A question.

Qnadmiple, Four times, fourfold.

Radius, Hiilf the diameter of a circle.

Sipht angle, A line square, or perpendicular to another.

Squared, Multiplied into itself; -2 squared is 4.

Theory, Speculative plan existing only in the mind.

Tangent, A line perpendicular or square with a radius touching the periphery qf a

circle.
Theorem, Position of an acknowledged truth.
Velocity, Swiftness of motion.
Virtual or effective descent of -water : See Art. 61.

SCALE FROM WHICH THE FIGURES ARE DRAWN.

PLATE 11 Fig. 1 1 , 12, 8 feet to an inch ; fig. 19, 10 feet to an inch.
HI. Fig. 19, 20, 23, 86, 10 feet to do.
IV. Fig. 28. 29, 30, 31 , 32, 33, 10 feet do.

VI. Fig. I, lOfeettoaninch; fig. 2, 3, 8,9, 10, 11, 2 feet do.

VII. Fg. 12. 13,14, 15, two feet to an inch; fig. 16, 10 do.

X. F;g. 1, 2, 18 feet do. fig. H, I in fig. 1 , four feet to ao iaiA,

XI. Fig. 1, 2, 3, two feet do. fig. 6, 8, one foot to de.

THE

YOUNG MILL-WRIGHT'S

AND

MILLER'S GUIDE.

PART THE FIRST.
CHAPTER L

ARTICLE 1.

OP THE FIRST PRINCIPLES OF MECHANICS.

MOTION may be said to be the beginning or
foundation of all mechanics ; because no mechanical
operation can be performed without motion.

AXIOMS ; or, Self-evident Truths,

1. A body at rest will continue so for ever, unless it is
put in motion by some force impressed.*

2. A body in motion will continue so for ever, with the
same velocity in the same direction, unless resisted by
some force. t

3. The impulse that gives motion, and the resistance
that destroys it, are equal.

* This sluggish, inactive principle, or resistance, by which a body in-
clines to a state of rest, is called Inertia.

t The same principle of inertia, which inclines a body to remain atrest«
also inclines it to continue in motion for ever, if once put in motion, and
that in a right-lined direction, unless changed by some force : therefore no
body, moving in a straight line, can be turned into a curve line, but by
some force ; the consideration of which may lead us to the knowledge of
the true principles of some mills. See the latter part of art, 7o.

1© MECHANICS. [Chap. 1.

4. Causes and effects are equals or directly propor-
tional.

POSTULATUMS ; or, Positions without Proof.

A quadruple impulse, or moving power, is requisite
to communicate double velocity to a body ;* therefc^re
a quadruple resistance is requisite to destroy double
velocity in a body, by axiom 3d.

The impulse we may call power, and the resistance
that it overcomes, the effect produced by that power.

COROLLARY.

Consequently, the powers of bodies in motion, to- pro-
duce effects, are as the squares of their velocities ; that is,
a double velocity, in a moving body, produces four times
the effect.

ART. 2.

OF THE PRINCIPLES OF MECHANICS.

There are two principles which are the foundation of
all mechanical motion and mechanical powers, viz. Gra-
vity and Elasticity ; or. Weight and Spring.

By one or the other of tliese principles or pow'ers, every
mechanical operation is performed.

Gravity, in the extent of the word, means every species
of attraction ; but more especially that species which is
common to, and nmtual between, all bodies ; and is evi-
dent l^etween the sun and its planetary attendants, as also
the earth and the moon.f But we will only consider it,

* In the course of this work, I shall shew, that a quadruple impulse
produces onlv double velocity. See art. 7 ami 46. We should folio >• phi-
losophers only in the p^ths of truth ; because, if all men are subject ta
err, even the most eminent philosophers may have erred.

If a thf-ory will not at^ree with practice, we may suspect it is not true;
and the theory of tlie momentum, or force of bodies in motion, beinj^- as their
velocities simply, does not agree with practice, with respect to the effects
they produce, either in circular motion, art. 13, falline^ bodies, art. 9,
spoutingr fluids, art. 45, wind on mill sails, art. 69, therefore we have rea-
son to suspect that this theory may not be true, in every respect.

f It is this attraction of gravity between the heavenly bod. es, that keeps
up the order of their motion, in their revolution round each other. See
Ferguson's Lectures, page 23-

Chap. 1.] MECHANICS. 1^

as it relates to that tendency which all bodies on the earth
have to fall towards its centre ; thus far it concerns ths-
mechanical arts, and its laws are as follows, viz. :

Laxvs of Gravity.

1. Gravity is common to all bodies, and mutual be
tween them.

2. It is in proportion to the quantity of matter in bo-
dies.

3. It is exerted every way from the centre of attracting
bodies, in ris^ht- lined directions ; therefore all bodies on
the earth tend to the centre of gravity of the earth.*

4. It decreases as the squares of the distance increase ;
that is, if a body., on the earth, was to be removed to
double the distance from the centi-e of gravity of the eardi,
about 4000 miles high, it would there have but one-
fourth of the gi'avity or weight it had when on the ground :
but a small height from the surface of the earth (50, or
100 feet) makes no sensible difference in gravity.f

By the 3d law, it follows, that all bodies descending
freely by their gravity, tend towards the earth, in right
lines, perpendicular to its surface, and with equal velo-
cities (abating for the resistance of the air) as is evident
by the 2d law.:j:

* The centre of gravity of a body, is that point on which, if the body
be suspended, it will remain at rest in any posiiion ; or, it is the centre
of the whole weight or matter of the body. Art 14

f The diameter of the earth is allowed to be ahout 8000 miles; there-
fore we may suppose the centre of gravity of the earth to be about 4000
miles from its surface; and any sm 11 distance from its surface, such as
one mile high, wdl make no sensible difference in gravity. But when the
distance is so great as to bear a considerable proportion to the distance of
the centre of gravity of the earth, then the power of gravity will decrease
sensibly. Thus, at the distance of the movXi, which at a mean, is about
60 semi-diameters of the earth, the power of gravity is to that on the sur-
face of the earth, as 1 to 3600- See Martin's Philosophy.

\ This resistance will be as the surface'- of the bodies; therefore the
smaller the body of equal matter, the greater will be the velocity of its
fall. But it has been proved, by experiment, that a feather w;ll fall with
the same velocity as a guinea, in vacuo- See Ferguson's Lectures, p. 183.

12 MECHANICS^ [Chap. 1.

ART. 3.

ELASTICITY.

Elasticity is that strength or repulsive power, which
any bcidy or quantity of matter, being confined or com-
pressed, has to expand itself; such as a spring that is
bent or wound up, heated air or steam confined in a ves-
sel, &c. and by it many mechanical operations are per-
formed.

Elasticity, in the full sense of the word, here means
every species of repulsion.

The limits of the prodigious power of repulsion which
takes place between the particles of heated air and steam,
are not yet known. Their effects are seen in the ex-
plosion of gunpowder, the bursting anjd cracking of wood
in the fire, &c. In short, in every instance, where steam
could not find room to expand itself, it has burst the ves-
sel that confined it, endangering the lives of those who
were near it.*

Having premised what was necessary to the right un-
derstanding of the science of mechanics, which mostly
depends upon the principles of gravitation.

We come to consider the objects thereof, viz. the
nature, kinds, and various effects of motion and moving
bodies, and the structure and mechanism of all kinds of
machines, called mechanical powers, whether simple or
compound.

• A worthy and ing'enious young man, having prepared a vessel of
wrout^ht iron, about 3 indies diameter, and 9 inches long, partly filled
Willi water, had put it into a smith's fire, and was trymg some experiments,
when tlie aperture, by which the steam was meant to issue, got stopped by
some means (as is supposed) and the vt^ssel burst with noise like a can-
non, carried off his right arm, and left it laying across one of the upper
beams of the shop, and otherwise desperately wounded him. This pro-
digious power is applied to raise water out of coal mint s, &c- from great
depths, in surprising quantities, and to turn mills : it may (m my opinion),
be applied to many other useful purposes, which it is not yet applied to.

On tiiis subject mucii might be said ; but as it does not immediately
concern this work, perhaps 1 have said enough to excite the reader to pe-
ruse the several late authors on philosophy, who have treated largely on
it, and to tliem I must refer. Also to my new work entitled The Abor-
tion of the Young Steam-engineer's Guide.

€hap. 2.] MECHANICS. 13

CHAPTER n.

ART. 4.

OF MOTION AND ITS GENERAL LAWS.

MOTION is the continual and successive change of
space or place, and is either absolute or relative.

Absolute motion is the change of space or place of
bodies, such as the flight of a bird, or the motion of a ball
projected in the air.

Relative motion is the motion one body has with re-
spect to another, such as the difference of motion of the
flight of two birds, or of two ships sailing.*

ART. 5.

Motion is either equable, accelerated, or retarded.

Equable motion is when a body passes over equal
distances in equal times.

Accelerated motion, is that which is continually in-
creased ; such is the motion of falling bodies. f

Retarded motion, is that which continually decreases;
such is the motion of a cannon ball thrown perpendicu-
larly upwards.^

* If two ships, A an;l B, move with the same velocity, in the same di-
rection, thtn their absolute motion is the same, and they liave no relative
motion, and neither of them will appear to a person on board of ihe other
to move at all. Hence it is, that although the earth is continually revolv-
ing about its axis, with a velocity, at the equator, of about 1042 miles ia
an hour, and round the sun, in continual absolute motion, with a velocity
of about 58,000 miles tn an hour — yet, as all -bjects on its surface have
the same absolute motion, they appear to be at rest, and not to move at
all : therefore all motion of bodies on the earth, appears to us to be ab-
solute motion, when compared with the objects fixed on the earth; yet, if
we take into consideration the absolute motion of the earth, all motion on
it will appear to be merely relative.

If two ships, A and B, moving' with equal velocities, pass each other,
then they will appear, to a spectator on board of either, to move with dou-
ble their respective real velocities.

Hence the reason, why a person, ridini^ against the wind, finds its force
greater, and with it, its force less, than it really is.

+ A falling body is constantly acted upon by all the powerof its own gra-
vity; therefore its motion is continually increased.

t A cannon ball, projected perpendicular tipwards, is constantly resisted
by the whole power of its own gravity ; therefore its motion will be conti-

14 MECHANICS. [Chap. 2

ART. 6.

The momentum or quantity of motion, is all the power
or force which a moving body has to strike an obstacle to
produce effects, and is equal to that impressed force by
which a body is compelled to change its place, by axiom
3, art. 1 ; \a hich, I think, ought to be distinguished by
two names, viz. instant and effective momentums.

1. The instant momentum, or force of moving bodies,
is in the compound ratio of their quantities of matter and
simple velocities conjointly ; that is, as the weight of the
body A, multiplied into its velocity, is to the weight of
the body B, multiplied into its velocity, so is the instant
force of A to the instant force of B. If A has 4lbs. of
matter, and 1 degree of velocity, and B has 21bs. of mat-
ter, and 4 degrees of velocity ; then the momentum of
their strokes will be as 4 is to 8 ; that is, supposing them
to be instantaneously stopped by an obstacle.

2. The effective momentum, or force of moving bo-
dies, is all the effect they will produce by impinging on
any yielding obstacle, and is in the compound duplicate
ratio of iheir quantities (or weights) multiplied into the
squares of their velocities ; that is, as the weight of the
body A, multiplied into the square of its velocity, is to the
weight of the body B, muliplied into the square of its

nually decreased, and totally stopped as soon as the sum of this resistance
amounts to the first impulse, by axiom 3d, art- 1, when it will begin to de-
scend, and its motion wdl be continually increased by the same power of
its own gravity : its motion downwards will be equal to its motion up-
wards, in every part of its path, and will return to the mo.ith ot the can-
non with the velocity and force that it left it ; and the time of its ascent
and descent will be equal, supposing there was no resistance from the air
— but this resistance will make a considerable difference

From this prmciple of a -celerated motion in falling bodies, may appear
the reason, why water po'ired from the spout of a tea-kettle, will not con-
tinue in a stream farther than about two feet, and this stream becomes
smaller as it approaches the place where it breaks into drops ; because the
attraction of cohesion keeps the water together, until the accelerated mo-
tion of its fall, which stretches the stream smaller and smaller, overcomes
the ohesion, and then it breaks into drops, and these drops become fur-
ther asunder whde they continue to fall; therefore, if the clouds were to
empty themselves in torrents, the water would fall on the ear'h in drops.
This may serve to shew the disadvantage of drawing the gate of a water-
mdl at a great distance from the float-board, but more of this hereafter.
See art. 59.

Chap. 2.] MECHANICS. 15

velocity, so is the effective momentum of A to that of B.
If A has 21bs. of matter and 2 degrees of velocity, and B
21bs. of matter and 4 degrees of velocity, then their ef-
fective momentums are as 8 to 32 ; that is, a double ve-
locity produces a quadruple effect.

ART. 7.

The general laws of motion are the three following,
viz.

Law 1. Every body will continue in its present state,
whether it be at rest or moving uniformly in a right line,
except it be compelled to change that state by some force
impressed.*

Law 2. The change of motion or velocity is always
proportional to the square root of the moving force im-
pressed, and in a right line with that force, and not as
the force directly. f

Law 3. Action and re-action are always equal, and in
contrary directions to each other. J

• By the first law, a body at rest inclines to continue so for ever, by its
vis inertia or inactive power, and a body in motion inclines to continue so
for ever, passing over equal distances in equal times, if it meets with no
resistance, and will more on in a riglit line. For want of resistance the
planets and comets continue their motions undimmished, while moving
bowls or wheels are reduced to a state of rest by the resistance of the
air, and the friction of the parts on which they move. See Ferguson's
Lectures on Mechanics.

It is this friction of the parts, and resistance of the air, which renders
it impossible for us to m;ike a perpetual motion ; because this friction and
resistance are to be overcome, and although it may be reduced to be very
small, yet man cannot, with ill his art, by mechanical combinations, gain
as much power as will overcome it. Philosophers have demonstrated the
impossibility of making it; but I think none ought to assert that it will
never be found ; for there are many perpetual motions in the heavens. If
any man wo' Id spend his time in this way, it should be to seek for a cre-
ated power that he might apply to this purpose, and not to rreate one.

t This is evident, when we consider that a body must fall a quadruple
distance to obtain double velocity, by art. 9 ; and a quadruple head or
pressure of fluid produces a double velocity to the spout, by art. 46 The
velocity, in both these cases, is as the square root of the impulse, and the
impulse as the squares of the velochy, therefore the change of elec-
tive motion or velocity will always be as the square root of the impulse
or force impressed, and the force impressed as the squares of the velocity
or effective motion.

+ Action and re-action are equal; that is, if a hammer strikes an anvil^
the anvil will re-act against the hammer with an equal force to the action
of the hammer.

16 MECHANICS. [Chap. 3.

CHAPTER III.

ART. 8.
OF THE MOMENTUM OR FORCE OF BODIES IN MOTION.

1. IF two non- elastic bodies, A and B, fig. 1 ,each hav-
ing the same quantity of matter, move with equal velo-
cities against each other, they will destroy each other's
motion, and remain at rest after the stroke : because
their momentums will be equal ; that is, if each has 21bs.
of matter and 10 degrees of celerity, their instantaneous
momentums will each be 20.

But if the bodies be perfectly elastic, they will recede
from each other with the same velocity with which tl^.ey
meet ; because action and re-action are equal, by the 3d
general law of motion, art. 7.*

2. If two non-elastic bodies, A and B, fig. 2, moving
in the same direction with different velocities, impinge
on each other, they will (after the stroke) move on to-
gether with such velocity, as being multiplied into the
sum of their weights, will produce the sum of their in-
stant momentums which they had before the stroke; that
is, if each weigh lib. and A has 8 and B 4 dei^rees of
celerity, the sum of their instant momentuins will be 12,
then, after the stroke, their velocity will be 6; which,
multiplied into their quantity of matter 2, produces 12,
the sum of their instant momentums. But if they had
been elastic, then A would have moved with 4 and B

The action of our feet against the ground, and the re-action of the
ground against our feet, are equal.

The action of the hand to project a stone, and the re-action of ihe stone
against the hand, are equal.

If a cannon weighing 6400 lbs. gives a 24 lb. ball a velocity of 640 feet
per second, the action of the powder on the ball, and its re action ag^nst
the cannon, are equal ; and if the cannon has liber'y to move, it will have
a velocity, which multiplied into its weight, will be equal lo the velocity
of the ball multiplied by its weight ; their instant momentums are always
equal See Martin's Philosophy.

* This shews that non elastic bodies communicate onlv half their origi-
nal force ; because the force required to cause the bodies to recede from
each other, is equal to the force that gave them velocity <o meet ; and the
force that caused the body to recede with velocity 10, is equal to the force
that checked velocity 10.

Chap. 3,] MECHANICS. 17

with 8 degrees of velocity after the stroke, and the sum
of their instant momentums would be 12, as before.*

3. If a non-elastic body A, with quantity of matter 1,
and 10 degrees of \ elocity, strike B at rest, of quantity
of matter 1, they will both move on together with velocity
5 ; but if they be elastic, B flies off" with velocity 10, and
A remains at rest, by 3d general law of motion, art. Y.f
It is universally true, that whatever instant momentum is
communicated to a body, is lost by the body that commu-
nicates it.

4. If die body A, fig. 4, receive two strokes or impulses
at the same time, in different directions, the one sufficient
to propel it from A to B, and the other to propel it from
A to D, in equal time, then this compound force will pro-
pel it in the diagonal line A C, and it will arrive at C in
the same time that it would have arrived at B or D, by
one impulse only; and the projectile force of these strokes
are as the squares of the sides of the parallelogram, by
law 2, art. 7.|

• Because elastic bodies impinginpf, recede, after the stroke, with tiie
same velocity with which ihey id' et : therefore, a heavy body in motion,
impingint^ on a lighter body at rest, will give it a greater velocity than that
with which it was struck; for if tlie heavy body be not stopped, but move
forward after the stroke, with a certain velo iiy, that velocity, added to
the velocity before the stroke, will be the velocity of the lighter body.

f This also shews evidently, that non-elastic bodies communicate only
half their force. A kno^\ ledge of this is of greai use in establishing a
true theory of water-mills.

tThis doctrine of the momentum of bodies in motion, and communica-
lion of motion, being as their velocities simply, was taught by Sir Isaac
Newton, and has been ref-eived by his followers to this d.iy ; which ap-
pears to be true, where the whole force is instantaneoHsly spent or commu-
nicated : therefore I have changed the term to instant momentum. I have
tried the experiment, by causing different weights to strike eacii other
with diflferent velocities, both on the principle of pendulums, and by caus-
ing them to move in horiznntul circles; and, in both cases, 4 lbs with
velocity 1, balanced 2 lbs. with velocity 2; their momenuims each wer. 4:
so that the theory appears to be proved to be true. Yet I think we have
reason to doubt its being true in any other sense ; because it does not
agree with practice. All the bodies we put in motion, to produce effects,
produce them in proportion to the squares of their velocities, or nearly, as
will appear in the course of this work. But I fear I shall draw on me the
ridicule of some, if I should doubt a theory long establis'ied ; but I th'hk
we should follow others only in the paths of truth. Doubtless Sir Isaac
meant the force to be instantly spent: and I have understood that the
Dutch and Italian philosophers have held and taught, these 100 years past,
thi.t the momentum of bodies in motion, is as the squares of their veloci-
ties : and I must confess it appears to be really the case, with respect to
the eflTecls they produce ; wbicii is generally as their quantity or weight

18 MECHANICS. [Chap. 3.

5. If a perfect elastic body be let fall 4 feet, to strike a
perfect elastic plain, by the laws of falling bodies, art. 9,
it will strike the plain with a velocity of 16,2 feet per se-
cond, and rise, by its re-action, to the same height from
whence it fell, in half a second: if it falls 16 feet, it will
strike with a velocity of 32,4 feet, and rise 16 feet in one
second. Now, if we call the rising of the body the effect,
we shall find that a double velocity, in this case, produces
a quadruple effect in double time. Hence it appears, that
a body moving through a resisting medium, with a double
velocity, will continue in motion a double time, and go 4
times the distance ; which will be a quadruple effect.*

Of Non- elasticity in impinging Bodies.

1. If A and B, fig. 3, be two columns of matter in mo-
tion, meeting each other, and equal in non-elasticity,

multiplied into the squares of their velocities. I found it impossible to
reconcile the theory of the force of bodies in motion, being as their sim-
ple velocities, to the laws of circular motion, art. 13, where a double ve-
locity produces a quadrtiple central force ; of falling bodies, art. 9, where
the velocity is as the square root of the impulse or distance fallen, and
the effects as the squares of the velocities; of projectiles, where a dou-
ble velocity produces a quadruple randum, art. 12 ; ot bodies descending
on inclined plains, art. 10, where the velocities are as the square roots of
the perpendicular descents, and the effects as the squares of their veloci-
ties ; of spouting fluids, art. 45, where their velocities are as the square
roots of iheir perpendicular heights or pressures, and their effects as the
squares of their velocities, with equal q amities; of w.nd on mill-sails,
art. 69, where the effects are as the cube of the velocity of the wind; be-
cause here the quantity is as the velocity, and tlie effect of equal quanti-
ties being as the squares of the velocity, amounts the effects to be as the
cubes.

But when I discovered that a quadruple impulse was requisite to give
double velocity, both in falling bodies and spoalmg fluids, and, by axiom 3,
the power that produced a motion in a body, and the power that destroyed
said motion, were equal, I concluded that the effects produced by bodies
in motion, were as the squares of their velocities ; and then I found the
whole theory to agree with practice Hereafter I shall say, that the ef-
fective momentum, or force of bodies in motion, is as the squares of their
velocities.

• We should pay no regard to time, in calculating the effective force of
bodies in motion. Because, if 1 lb. of matter move with 1 degree of velo-
city, it will produce a certain effect (before it ceases moving) in an un-
known time- Every other pound of matter, moving with equal velocity,
will produce an equal effect in equal time. But if each pownd of matter
move with double velocity, it will produce 4 times the effect, but requires
a double time; which difference in nme no way affects the sum total of
the effects oP the matter put in motinn to move any practical machine.
Therefore we should totally leave time out of this calculation, seeing it
tends to lead us into errors.

Chap. 3.] MECHANICS. 19

quantity, and velocity, they will meet at the dotted line
e e, destroy each other's motion, and remain at rest, pro-
vided none of their parts separate.

2. But if A is elastic, and B non-elastic, they will meet
at e e, but B will give way by battering up, and both will
move a little further ; that is, half the distance that B
shortens.

3. But if B is a column of fluid, and when it strikes
A, flies oflf in a lateral perpendicular direction, then what-
ever is the sum total of the momentums of these particles
laterally, has not been communicated to A ; therefore A
will continue to move, after the stroke, w ith that said mo-
mentum.

4. But with what proportion of the striking velocity the
fluid, after the stroke, will move in the lateral direction, I
do not find determined ; but from small experiments I
have made (not fully to be relied on) I suppose it to be
more than one half ; because water falling four feet, and
striking a horizontal plain, with 16,2 feet velocity, will
cast some few drops to the distance of 9 feet (say 10 feet,
allowing one foot to be lost by friction, &c.) which we
must suppose take their direction at an angle of 45 de-
grees, because it is shewn in Martin's Philosophy, page
135, Vol. I, that a body projected at an angle of 45 de-
grees will describe the greatest possible horizontal ran-
dum ; also, that a body falling 4 feet, and reflected with
its acquired velocity 16,2 feet, at 45 degrees, will reach 16
feet horizontal randum, or 4 times the distance of the fall.
Therefore, by this, 1-4 of 10 feet, equal to 2,5 feet, is the
fall that will produce the velocity that produced it, viz.
Velocity 12,64 feet per second, about 3-4 of the striking
velocity.

5. And if the force of striking fluids be as the squares
of their velocities, as proved in ai't. 67, by experiment,
and demonstrated by art. 46 ; then the ratio of the force
of this side velocity, 12,64 feet per second, is to the force
of forward velocity, as 160 to 256, more than half (about
,6) of the whole force is here lost by non-elasticity.

6. This side force cannot be applied to produce any
further forward force, after it has struck the first obstacle;

29 MECHANICS. [Chap. 4.

because its action and re-action balance each other after-
wards : which I demonstrate by fig. 27.

Let A be an obstacle, against which the column of wa-
ter G A, of quantity 16 and velocity per second 16,
strikes ; as it strikes A, suppose it to change its direction,
at right angles, with 3-4 velocity, and strike B B ; then
change again, and strike forward against C C, and back-
wards against D D : then again in the side direction E E;
and again in the forward and backward directions, all of
which counteract each other, and balance exactly.

Therefore, if we suppose the obstacle A to be the float
of an undershot water-wheel, the water can be of no fur-
ther service, in propelling it, after the first impulse, but
rather a disadvantage ; because the elasticity of the float
will cause it to rebound in a certain degree, and not keep
fully up with the float it struck, but re-act back against
the float following ; therefore it will be better to let it es-
cape freely as soon as it has fully made the stroke, but
not sooner, as it will require a certain space to act in,
which will be in direct proportion to the distance between
the floats.

7. From these considerativons, we may conclude, thatthe
greatest effect to be obtained from striking fluids, will not
amount to more than half the power that gives them mo-
tion ; but much less, if they be not applied to the best ad-
vantage : and that the force of non-elastic bodies, strik-
ing to produce effects, will be in proportion to their non-
elasticity.

CHAPTER IV.

ART. 9.
OF FALLING BODIES.

BODIES descending freely by their gravity, in vacuo,
or in an unresisting medium, are subject to the following
laws :

1st. They are equably accelerated.*

* It is evident, that in every equal part of time, the body receives an
impulst from gravity, that will propel it an equal distance, and give it an
equal additional vclociiy ; iherelbre it wdl produce equal effects in equal
times, and their velocity will be proportioned to the time.

Ghap. 4.] MECHANICS. 21

2d. Their velocity is always in proportion to the time
of their fall, and the time is as the square root of the dis-
tance fallen.*

3d. The spaces through which they pass, are as the
square of the times or velocities.! Therefore,

4Th. Their velocities are as the square root of the space
descended through ;% and their force, to produce effects,
as their distances fallen directly.

5th. The space passed through the first second, is veiy
nearly 16,2 feet, and the velocity acquired, at the lowest
point, is 32,4 feet per second.

6th. A body will pass through twice the space, in a
horizontal direction, with the last acquired velocity of the
descending body, in the same time of its fall.§

7th. The total sum of the effective impulse acting on
them to give them velocity, is in direct proportion to the
space descended through,]) and their velocity being as
the square root of the space descended through ; or, which
is the same, as the square root of the total impulse.
Therefore,

8th. Their momentums, or force to produre effects,
are as the squares of their velocities,T[ or directly as their

* If llie velocity, at the end of one second, be 32,4 feet, at the end of
two seconds it will be 64,8, at the end of three seconus 97,2 feet per se-
cond, and so on.

f That is, as the square of 1 second is to the space passed through 16,2,
so is the square of 2 seconds, which is 4, to 64,8 feei, passed through at
the end of 2 seconds, and so on, for any number of seconds. Thtrefore
the spaces passed through at the end of every second, wdl be as the
square numbers 1, 4, 9, 16, 25, 36, &c. and the spaces passed through,
in each second separately, will be as the odd numbers 1, 3, 5, 7, 9, 11, 13,
15, &c.

Jf That is, as the square root of 4, which is 2, is to 16,2, the velocity
acquired in fallinaj four feet : so is the square root of any other distance,
to the velocity acquired, in falling that distance.

§That is, supp se the body as it arrives at the lowest point of its fall,
and has acquired its greatest velocity, was to be turned in a horizontal
direction, and the velocity to continue uniform, it would pass over double
the distance, in that direction ihat it had descended through in the same
time.

II This is evident from the consideration, that in every equal part of dis-
tance it descends through, it receives an equal efllective impulse from gra-
vity. Therefore 4 times the distance, gives 4 times the effective (but not
instant) impulse.

1[This is evident, when we consider, that a quadruple distance or im-
pulse, produces only double velocity, and by axiom 3 a quadruple resist-
ance will be required, to stop double velocity ; consequently their force is

22 MECHANICS. [Chap. 4.

distances fell through ; and the times expended in produ-
cing the effects, are as the square root of the distance
fallen through.*

9th. The resistance they meet with in any given time,
in passing through a resisting medium, is as their surfaces,
and as the cubes of their velocities.f

as the squares of their velocities, which brin^^s them to be directly as
their distances descended through : and this agrees with the second law
of spouting fluids. Art. 45.

* That is, if a body fall 16 feet, and strike a nonelasiic body, such as
hot iron, soft lead, clay, &c. it will strike with velocity "2, and produce a
certain efff ct in a certain time. Again, if it fall 64 feet, it w II stnke with
velocity 64, and produce a quadruple effect, in a double time; because,
if a perfectly elastic body fall 16 feet in one second ot time, and strike a
perfectly elastic plain, with velocity 32 fee , it vviU rise 16 feel in one se-
cond of time. Again, if the body fall two seconds of time, it wilt fall 64
feet, and strike with velocity 64, and rise 64 feet in two seconds ot time.
Now, if we call the rising of the body the efiect of ihe striking velocity
(which it really is) then all will appear clearly. But any thing here ad-
vanced, if contrary to the opmion of many learned and ingenious authors,
ought to be doubted, unless known to agree with practice.

"t" This is evident when we consider,

1. That it is a proportion of the surfaces, that meets the resistance ; and,

2. That a double velocity strikes a double quantity of resisting parti-
cles in the same time.

3. That a double velocity strikes each particle with double the instant,
and four times the effective force, by art. 6.

Therefore, the instant resistance is as the squares of their velocities,
and will soon amount to the whole force of gravity, and reduce the mo-
tion to be uniform. This is the reason why hail and rain falls with such
moderate force ; whereas if it was not for the resistance of the air. they
would prove fatal to those they tall upon. Compare this with the effect
of wind on mill sails, proved by experiment, to be as 'he c bes of the ve-
locity, art 69, and with the effects of spoutin„ fl ids, proved to be as the
cubes of their velocities, witb equal apertures. Art. 67, and 7th law of
spouting fluids.

Again, consider that the solid content of bodies decreases, as the cubes
of their diameters, while their surfaces decrease only as the squaies of
their diameters ; consequently the smaller the body, the greater the re-
sistance, in proportion to its weight: and this is the reason why heavy bo-
dies, reduced to dust, will float in the air; as, likewise, feathers, and ma-
ny other bodies of great surface and little matter- This seems to shew,
that air is, perhaps, as heavy as any other matter whatever, of an equal
degree of fineness or smallness of particles.

These are the laws of falling bodies supposing them to fall m vacuo, or
jn an unresisting medium; and without considering »hai gravity increases,
as the square of the distance from the centre of gravity of the attracting
power decreases (4- law of gravity, art. 2;) because any small distance,
such as comes in our practice, will make no sensible difference. But as
they fall in the air, which is a medium, of great resistance, the instant re-
sistance is as the opposing surfaces of the falling bidy, and as the squares
of their velocities, their motion will greatly differ from these laws, m tail-
ing great distances, or with light bodies ; but in small distances, such as
SO feet or less, and heavy bodies, the difference will be imperceptible in
common practice.

Chap. 4.]

MECHANICS.

A TABLE

MOTION OF FALLING BODIES.

SUPPOSED IN VACUO.

us' O

5'^i.

»
a
o
o

~ to
n K
n n

S 2 85
r» "^ O

o o

•m

«3

— an

M 3 -a

r o-

P-c.o

o n

z "> "

n cr

n
p ?

? rt =

S.O

eg.

O V-

c ^

5"cr
crp o

•ocfi

5 ="

• a.

2 3

F 5'

i^a.

.125

•25

11.4

.25

101

14.

405

16.2

.75

911

24 3

18.

16-2

32.4

19.84

64 8

21.43

145 8

97.2

22.8

2592

1296

24.3

305.

162.

25.54

583 2

194.4

26.73

793 8

226.8

28.

1036.8

259.2

2916

1312.2

2916

30.2

1620.

324.

31 34

14580.

972.

32.4

58320.

1944-

33.32

34.34

35.18

56.2

37 11

48.6

56 7

64.8

100

144

97.2

24 MECHANICS. [Chap. 4.

A SCALE

OF THE

MOTION OF FALLING BODIES.*

O (-1

16. 2 tei t is thi- space fullen throui^h the 1st second, by law

5, which let be eqaal to

Which is also the whole space fallen through at the end of
iht- 1st second, which let be equal to - - -
ot32 4 fee- 1 per second is the velocity acquired by the fall,

io ditto -

. a

.' 48 6 feet is the space fallen through the 2d second, ditto
j 3^64 8 feet do. at the end of 2 seconds, ditto
•j oo64-8 feet is the velocity per second, acquired at the end of
the 2d second, ditto -

(81. feet IS ihe space fallen through the 3d second of time, do-
1458 feet ditto in 3 seconds of time, ditto

d ■ 97 feet is the velecity acquired by the fall at the end of 3
S;-conds, ditto .......

113 4 iert IS the sp.ce fallen through in the 4th second of

< mt, ditto - -

259-2 feet ditto in 4 seconds, ditto - . - .

129 6 feet per second, is the velocity acquired at the end of
4 seconds, ditto .......

• In this table, the first column contains the total space fallen through,
which is as the squares of the times or velocities, by law 3 The second
column contains the velocity acquired, which is as the square root of the
dis arice fallen, and as the time of the fall, by laws 2 and 4. The third
column contains the space fallen through each second, which is as the odd
numbers-

Chap, 5.] MECHANICS. 25

This scale shews at one view, all the laws to be per-
formed by the falling body o, which falls from o to 1,
16,2 feet, the first second, and acquires a velocity that
■would carry it 32,4 feet, from 1 to a, the next second,
by laws 5 and 6 ; this velocity would also carry it down
to b in the same time, but its gravity, producing equal
effects, in equal times, will accelerate it so much as to
take it to 3 in the same time, by law L It Avill now have
a velocity of 64,8 feet per second, that will take it to c
horizontally, or down to d, but gravity will help it on to
5 at the same time. Its velocity will now be 97,2 feet,
which w'\\\ take it horizontally to e, or down to f, but gra-
vity will help it on to 7 ; and its last acquired velocity
will be 129,6 feet per second from 7 to g.

If either of these horizontal velocities be continued, the
body will pass over double the distance it fell, in the same
time, by law 6.

Again, if o be perfectly elastic, and falling, strikes a
perfect elastic plane, either at 1, 3, 5 or 7, the effective
force of its stroke will cause it to rise again to o in the
same space of time it took to fall.

Which shews, that in every equal part of distance, it
received an equal effective impulse from gravity, and that
the total sum of their effective impulse is as the distance
fallen directly — and the effective force of their strokes will
he as the squares of their velocities, by laws 7 and 8.

CHAPTER V.

ART. 10.

OF BODIES DESCENDING INCLINED PLANES AND CURVED
SURFACES.

BODIES descending inclined planes and curved sur-
faces, are subject to the following laws :

1. They are equably accelerated, because their motion
is the effect of gravity.

2. The force of gravity propelling the body A, fig. 5, to
descend an inclined plane A D, is to the absolute gravity

26 MECHANICS. [Chap. 6.

of the body, as the height of the plane A C is to its length
AD.

3. The spaces descended through are as the squares of
the times.

4. The times, in which the different planes A D, A H,
and A I, or the altitude A C, are passed over, are as their
lengths respectively.

5. The velocities acquired in descending such planes,
in the lowest points D, H, I or C, are all equal.

6. The times and velocities of bodies descending
through planes alike inclined to the horizon, are as the
square roots of their lengths.

7. Their velocities, in all cases, are as the square roots
of their perpendicular descent.

From these laws or properties of bodies descending
inclined planes, are deduced the following corollaries,
viz.

1. That the time, in which a body descends through
the diameter A C, or any chord A a, A e, or A i, are equal.
Hence,

2. All the chords of a circle are described in equal
times.

3. The velocity acquired in descending; through any
arch, or chord of an arch, of a circle, as at C, in the low-
est point C, is equal to the velocity that would be acquir-
ed in falling through the perpendicular height F C.

The motion of pendulums have the same properties,
the rod or string acting as the smooth curved surface.

For demonstration of these properties, see Martin's
Philosophy, vol. i. page 111 — 117.

CHAPTER VI.

ART. 13.

OF THE MOTION OF PROJECTILES.

A PROJECTILE is a body thrown or projected in
any direction ; such as a stone from the hand, water
spouting from any vessel, a ball from a cannon, &:c.
fig. 6.

Chap, r.] MECHANICS. 27

Every projectile is acted on by two forces at the same
time, viz. the Impulse and the Gravity.

By the impulse, or projectile force, the body will pass
over equal distances, A B, B C, &.c. in equal times, by
1st general law of motion, art. 7, and by gravity, it de-
scends through the spaces AG, G H, &c. which are as
the squares of the times, by 3d law of falling bodies, art.
9. Therefore, by these forces compounded, the body
will describe the curve A Q, called a parabola ; and this
will be the case in all directions, except perpendicular ;
but the curve will vary with the elevation, yet it will still
be what is called a parabola.

If the body is projected at an angle of 45 degrees ele-
vation, it will be thrown to tlie greatest horizontal distance
possible ; and, if projected with double velocity, it will
describe a quadruple randum.

For a full account and demonstration, see Martin's Phil,
vol. i. p. 128—135.

CHAPTER VII.

ART. 13.

OF CIRCULAR MOTION AND CENTRAL FORCES.

IF a body A, fig. 7, be suspended by a string A C, and
caused to move round the centre C, that tendency which
it has to fly from the centre, is called the centrifugal force ;
and the action of the string upon the body, which con-
stantly solicits it towards the centre, and keeps it in the
circle A M, is called the centripetal force. Speaking of
these two forces indefinitely, they are called centi-al
forces.*

The particular laws of this species of motion, are,

• It may be well to observe here, that this central force is no real power,
but only an effect of the power that gives the body the motion. Its inertia
causes it to recede from the centre, and fly off in a direct tangent line,
With the circle it moves in. Therefore this central force can neither add
to, nor diminish from, the power of any mechanical or hydra-jlic engine,
unless it be by friction and inertia, where water is the moring power and
the machine changes its direction.

28 MECHANICS. [Chap. 7.

1. Equal bodies describing equal circles in equal times»
have equal central forces.

2. Unequal bodies describing equal circles in unequal
times, their central forces are as their quantities of matter
multiplied into their velocities.

3. Equal bodies describing unequal circles in equal
times, their velocities and central forces are as their dis-
tances from their centres of motion, or as the radius of
their circles.*"

4. Unequal bodies describing unequal circles in equal,
times, their central forces are as their quantities of mat-
ter multiplied into their distance from the centre or ra-
dius of their circles.

5. Equal bodies describing equal circles in unequal
times, their central forces are as the squares of their
velocities ; or, in other words, a double velocity gene-
rates a quadruple central force. f Therefore,

6. Unequal bodies describing equal circles in unequal
times, their central forces are as their quantities multi-
plied into their velocities.

* This shews, that when mill-stones are of unequal diameters, and re-
volve in equal times, the largest would have the draught of their furrows
less, in proportion as their central force is more, which is inverse propor-
tion ; also that the draught of a stone should vary, and be in inverse pro-
portion to ilie distance from the centre. That is, the greater the distance
the less the draught.

Hence we conclude, that if stones revolve in equal times, their draught
must be equal next the centre : that iF> so much of the large stones, as is
equal to the size of the small ones, must be of equal draught. But that
part which is greater, must have less draught in inverse proportion, as the
distance from the centre is greater, the furrows must cross at so much less
angle; which will be neax'ly the case (if their furrows lead to an equal
distance from their centres) at any considerable distance from the centre of
the stone ; but near the centre the angles become greater than the propor-
tion: if the furrows be straight, as appears by the lines, g 1> h 1, g2, h 2,
g 3, h 3, in fig. 1, pi. XI. the angles near the centre are too great, whicli
seems to indicate, that the furrows of mill-stones should not be straight,
but a little curved ; but what this curve should be is very difficult to de-
termine exact!}' by theory. By theory it should be such as to cause the
angle of furrows crossing, to change in inverse proportion with the dis-
tance from the centre, which will require the furrows to curve more, as
they approach the centre.

-j- This shews that mill-stones of equal diameters, having their velocities
unequal, should have the draught of their furrows, as the square roots of
their number of revolutions per minute- Thus, suppose the revolutions of
one stone to be 81 per minute, and the mean draught of the furrows 5
inches, and found to be right ; the revolutions of the other to be 100 ; then
to find the draught, say. As the square root of 81, which is 9, is to the 5
inches draught ; so is the square root of 100, which is 10, to 4,5 inches,
the draught required (by inverse proportion) because the draught must
decrease as the central force increases-

Chap, r.] MECHANICS. 29

7. Equal bodies describing unequal circles widi equal
celerities, dieir central forces are inversely as their dis-
tances from the centre of motion or radius of the circles. *^

8. Equal bodies describing unequal circles, having
their -central forces equal; their periodical times areas
the square roots of their distances.

9. Therefore the squares of the periodical times are
proportional to the cubes of their distances, when neither
the periodical times nor the celerities are given. In that
case,

10. The central forces are as the squares of the dis-
tances inversely.!

* That is, the greater the distance the less the central force. This
shews that niill-stunes of different diameters, having their peripheries re-
volving with equal velocities, should have the angle of draught, with which
their furrows cross each other, in inverse proportion to their diameters,
because their central forces are as tiieir diameters, by inverse proportion,
directly: and the angle of draught should increase, as the central force
decreases ; and decrease, as it increases.

But here we must consider, that, to give stones of different diameters
equal draughts, the distance of their furrows from the centre, must be in
direct proportion to their diameters. Thus, as 4 feet diameter is to 4
inches draught, so is 5 feet diameter to 5 inciies draught- To make the
furrows of each pair of stones cross each other at equal angles, in all pro-
portional distances from the centre, see fig 1. plate XI. w here g b, g d, g f,
h a, h c, and h e, shew the direction of the furrows of the 4, 5, and 6 feet
stones, with their proportional draughts ; now it is obvious that they cross
eacli other at equal angles, because the respective lines are parallel, and
cross in each stone, near the middle of the radius, which shews that in all
proportional distances, they cross at equal angles, consequently their
draughts are equal.

But the draught must be further increased, with the diameter of the
stone, in order to increase the angle of draught in the inverse ratio, as the
central force decreases.

To do which, say : If the 4 feet stone has central force equal 1, what
central force will the 5 feet stone have ? Answer : ,8 by the 7th law.

Then say, If central force 1 requires 5 inches draught, for a 5 feet stone,
what will central force ,8 require ? Answer: 6,25 inches draught. This
is, supposing the verge of each stone to move with equal velocity. This
rule may bring out the draught nearly true, provided there be not much
difference between the diameter of the stones. But it appears to me, that
neither the angles with which the furrows cross, nor the distance of the
point from the centre, to which they direct, is a true measure of the
draught.

f These are the laws of circular motion and central forces. For experi-
mental demonstrations of them, see Ferguson's Lectures on Mechanics,
page 27 to 47-

I may here observe that the whole planetary system is governed by these
laws of circular motion and central forces. Gravity acting as the string,
and is the centripetal force ; and as the power of gravity decreases, as the
squ»re of the distance increases, by the 4th law of gravity, art. 2 ; and as
the centripetal and centrifugal forces must always be equal, in order to
keep the body in a circle- Hence appears the reason why the planets most

30 MECHANICS. [Chap. 8.

CHAPTER VIII.

ART. 14.

GF THE CENTRES OF MAGNITUDE, MOTION, AND GRAVITY.

THE centre of magnitude is that point which is equal-
ly distant from all the external parts of a body.

2. The centre of motion is that point which remains
at rest, while all other parts of the body move round it.

3 The centre of gravity of bodies, is of great conse-
quence to be well understood, it being the principle of
much mechanical motion, and possesses the following
particular properties :

1. If a body is suspended on this point, as its centre of
motion, it will remain at rest in any position.

2. If a body is suspended on any other point than its
centre of gravity, it can rest only in such position, that a
right line drawn from the centre of the earth through the
centre of gravity, will intersect the point of suspension.

3. When this point is supported, the whole body is
kept from falling.

4. When this point is at liberty to descend, the whole
body will fall.

5. The centre of gravity of all homogeneal bodies, as
squares, circles, spheres, &c. is the middle point in a line
connecting any two opposite points or angles.

remote from the sun have their motion so slow, while those near him have
their motions swit't ; because their celerities must be such as to create a
centrifugal force equal lo ihe attraciion of f^ravity.

I may here observe, that modern philosophers begin to doubt the exist-
ence of inertia, as dtfined by Newton, to be different and independent
from gravity, but seem to conclude that they are both one thing; but when
we consider that the whole force of s^ravity is exerted as centripetal force,
to keep the heavenly bodies in a circle, it cannot be that same power,
cause, or principle, that causes the bodies to continue their motion, unless
one cause can produce two effects each equal to itself, contrary to axiom 4.
Again we may consider, that gravity decreases, as the squares of the dis-
tance of the body from the attracting power increases, but inertia is the
same every where; and if we suppose the body to be removed out of the
sphere of attraction of gravity, there will be no gravity at all, yet inertia
will act in its full power, to continue the motion or rest of a body, by ax-
iom 1 and 2- Hence in this light gravity and inertia appear to be two very
difTereni principles, and ought to be distinguished by different names: but
here we may dispute about words, for in other lights they appear to be
the very same thing.

Chap. 9.] MECHANICS. 31

6. In a triangle, it is in a right line drawn from any
angle to bisect the opposite side, at the distance of one
third of its length from the side bisected.

7. In a hollow cone, it is in a right line passing from
the apex to the centre of the base, and at the distance
of one third of the side from the base.

8. In a solid cone, it is one fourth the side from the
base, in a line drawn from the apex to the centre of the
base.

Hence the solution of many curious phasnothena, as,
why many bodies stand more firmly on their bases than
others ; and all bodies will fall, when their centre of gra-
vity falls without their base.

Hence appears the reason, why wheel- carriages, load-
ed with stones, iron, or any heavy matter, will not over-
turn so easy, as when loaded with wood, hay, or any light
matter ; for when the load is not higher than a b, fig. 12,
the centre of gravity will fall within the centre of the base
at c ; but if the load is as high as d, it will then fall out-
side the base of the wheels at e, consequently it will over-
turn. From this appears the error of those, who hastily
rise in a coach or boat, when likely to overset, thereby
throwing the centre of gravity more out of the base, and
increasing the danger.

CHAPTER IX.

ART. 15.

OF THE MECHANICAL POWERS.

HAVING now premised and considered all that is
necessary for the better understanding those machines
called m.echanical powers, we come to treat of them, and
they are six in number, viz.

^ The Lever, the Pulley, the Wheel and Axle, the In-
clined Plane, the \\ edge, and the Screw.

32 MECHANICS. [Chap. 9.

They are called Mechanical Powers, because they in-
crease our po^^er of raising or moving heavy bodies ; and,
although they are six in number, they seem to be redu-
cible to one, viz. the Lever, and appear to be governed
by one simple principle, which I shall call the First
General Law of Mechanical Powers ; which is this, viz.
the momentums of the power and weight are always
equal, when the engine is in equilibrio.

Momentum, here means the product of the weight of
the body multiplied into the distance it moves ; that is,
the power multiplisd into its distance moved, or into its
distance from the centre of motion, or into its velocity, is
equal to the weight multiplied into its distance moved, or
into its distance from the centre of motion, or into its
velocity ; or, the power multiplied into its perpendicular
descent, is equal to the weight multiplied into its per-
pendicular ascent.

The Second General Lav/ of Mechanical Powers, is,

The power of the engine, and velocity of the weight
moved, are always in the inverse proportion to each
other; that is, the greater the velocity of the weight
moved, the less it must be ; and the less the velocity,
the greater the weight may be, and that universally in all
cases. Therefore,

The Third General Law is.

Part of the original power is always lost in overcoming
friction, inertia, &c. but no power can be gained by en-
gines, when time is considered in the calculation.

In the theory of this science, we suppose all planes to
be perfectly smooth and even, levers to have no weight,
cords to be perfectly pliable, and machines to have no
friction : in short, all imperfections are to be laid aside,
until the theory is established, and then proper allowan-
ces are to be made.

Chap. 9.] MECHANICS. 33

ART. 16.

Of the Lever.

A bar of iron, wood, &c. one part of which is sup-
ported by a prop, and all other parts turn or move on that
prop, as their centre of motion, is called a lever : and its
length, on each side of the prop,, is called its arms ; the
velocity or motion of every part of these arms is directly
as its distance from its centre of motion, by 3d law of
circular motion.

The lever — Observe the following laws :

1. The power and weight are to each other, as their
distances from the centre of motion, or from the prop,
respectively.*

2. The power is to the weight, as the distance the
weight moves is to the distance the power moves, re-
spectively, f

3. The power is to the weight, as the perpendicular
ascent of the weight is to the perpendicular descent of
the power.J

4. Their velocities are as their distances from their
Gentre of motion, by 3d law of circular motion.

These simple laws hold universally true in all mecha^
nical powers or engines ; therefore it is easy (from these
simple principles) to compute the power of any engine,
either simple or compound ; for it is only to find how
much swifter the power moves than the weight, or how
much farther it moves in the same time ; and so much is
the power, (and time of producing it) increased by the
help of the engine.

* That 18, the power P, fig-. 8. Plate I- which is 1 multiplied into its dis-
tance B C, from the centre 12, is equal to the weight 12 multiplied into its
distance AB l.each product being 12.

t That is, the power multiplied into its distance moved, is equal to the
weight multiplied into its distance moved.

\ That is, the power multiplied into its perpendicular descent| is equal
to the weight multiplied into its perpendicular ascent.

34. MECHANICS. [Chap. 9.

ART. 17.

GENERAL RULES FOR COMPUTING THE POWER OF ANY
ENGINE.

1. Divide either the distance of the power from its
centre of motion, by the distance of the weight from its
centre of motion. Or,

2. Divide the space passed through by the power, by
the space passed through by the weight. This space
may be counted either on the arch described, or per-
pendiculars. And the quotient will shew how much the
power is increased by the help of the engine.

Then multiply the power applied to the engine, by
that quotient, and the product will be the power of the
engine, whether simple or compound.

EXAMPLES.

Let ABC, Plate L fig. 8, represent a lever ; then to
compute its power, divide the distance of the power P
from its centre of motion B C V^, by the distance of the
weight W, A B 1, and the quotient is 12 : the power is
increased 12 times by the engine ; which, multiply by
the po\ver applied 1, produces 12, the power of the en-
gine at A, or the weight W, that will balance P, and
hold the engine in equilibrio. But suppose the arm A B
to be continued to E, then, to find the power of the en-
gine, divide the distance B C 12, by B E 6 ; and the
quotient is two ; \\hich multiplied by 1, the power ap-
plied, produces 2, the power of the engine, or weight w
to balance P. • -

Or divide the perpendicular descent of the power C D
equal 6, by the perpendicular ascent E F equal 3 ; and
the quotient 2, multiplied by the power P equal 1, pro-
duces 2, the power of the engine at E.

Or divide the velocity of the power P equal 6, by the
velocity of the weight w equal 3 ; and the quotient 2,
multiplied by the power 1, produces 2, the power of the
engine at E. If the power P had been applied at 8, then
it would have required to have been 1 1-2 to balance VV,
or w: because 11-2 timqs 8 is 12, which is the mo-
mentum of both weights W and w. If it had been ap-

Chap. 9.] MECHANICS. 35

plied at 6, it must have been 2 ; if at 4, it must have
been 3 ; and so on for any other distance from the prop
or centre of motion.

ART. 18.

THERE ARE FOUR KINDS OF LEVERS.

1. The common kind, where the prop is placed be-
tween the weight and power, but generally nearest the
weight.

2. When the prop is at one end, the power at the
other, and the weight between them.

3. When the prop is at one end, the weight at the
other, and the power applied between them.

4. The bended lever, which differs only in form, but
not in properties, from the others.

Those of the first and second kind have the same
properties and powers, and are real mechanical powers,
because they increase the power ; but the third kind is
a decrease of power, and only used to increase velocity,
as in clocks, watches, and mills, where the first mover is
too slow, and the velocity increased by the gearing of the
wheels.

The machinery of the human frame is composed of
the last kind of lever ; for when we lift a weight by the
hand, resting the elbow on any thing, the muscle that
exerts the force to raise the weight, is fastened at about
one tenth of the distance from the elbow to the hand,
and must exert a force ten times as great as the weight
raised ; therefore, he that can lift 561bs. with his arm at
a right angle at the elbow, exerts a force equal to 5601bs.
by the muscles of his arm. Wonderful is the power of
the muscles in these cases. Here appears the reason,
why men of low stature are stronger than those of high,
in proportion to their thickness, as is generally the case.

ART. 19.

COMPOUND LEVER,

If several levers are applied to act one upon another,
as 2 ] 3, in fig. 9, Plate I. where No. 1 is of the first

36 MECHANICS. [Chap. 9.

kind, No. 2 of the second, and No. 3 of the third. The
power of these levers, united to act on the weight w, is
thus found by the following rule, which will hold uni-
versally true in any number of levers united, or wheels
(which is similar thereto) acting upon one another.

RULE.

1st. Multiply the power P, into the length of all the
driving levers successively, and note the product.

2d. Then multiply all the leading levers into one
another successively, and note the product.

3d. Divide the first product by the last, and the quo-
tient will be the M'eight w, that will hold the machine in
equilibrio.

This rule is founded on the first law of the lever, art.
16, and on this principle, viz.

If the weight w, and power P, are such, that when
suspended on any compound machine, whether of levers
united, or of wheels and axles, they hold the machine in
eqi.ilibrio. Then, if the power P, is multiplied into the
radius of all the driving wheels, or lengths of the driving
levers, and the product noted ; and the weight w multi-
plied into the radius of all the leading wheels, or length
of the leading levers, and the product noted ; these pro-
ducts will be equal. If we had taken the velocities or
circumferences of the wheels, instead of their radius, they
would have been equal also.

On this principle is founded all rules for calculating
the power and motion of wheels in mills, &c. See art,
20 and 74.

EXAMPLES.

Given, the power P equal to 4, on lever 2, at 8 distance
from the centre of motion. Required, with what force
lever 1, fastened at 2 from the centre of motion of lever
2, must act, to hold the lever 2 in equilibrio.*

• In order to abbreviate the work, I shall hereafter use the following
Algebraic signs, \\z.

Chap. 9.] MECHANICS. 37

By the rule, 4x8 the length of the long arm, is 32, and
divided by 2, the length of the short arm, quotes 16, the
force required.

Then 16 on the long arm, lever 1, at 6 from the cen-
tre of motion. Required, the weight on the short arm,
at 2, to balance it.

By the rule, 16x6=96, which divided by 2, the short
arm, quotes 48, for the weight required.

Then 48 is on the lever 3, at 2 from the centre. Re-
quired, the weight at 8 to balance it.

Then 48x2=96, which divided by 8, the length of the
long arm, quotes 12, the weight required.

Given, the power P=4, on one end of the combination
of levers. Required, the weight w, on the other end, to
hold the whole in equilibrio.

Then by the rule, •4x8x6x2=384 the product of the
power multiplied into the length of all the driving levers,
and 2x2x8=32 the product of all the leading levers,
and 384 1 32=13 the weight w required.

ART. 20.

The same rule holds good in calculating the powers of
machines, consisting of wheels whether simple or com-
pound, by counting the radius of the wheels as the levers ;
and because the diameters and circumferences of circles
are proportional ; we may take the circumference instead
of the radius, and it will be the same. Then again, be-
cause the number of cogs in the wheels constitute the
circle, we may take the number of cogs and rounds in-
stead of the circle or radius, and the result will be the
same.

Let fig. 11, Plate II. represent a water-mill (for grinding
grain) double geared :

The sign -f- more, for addition.
— less, for subtraction.
X multiplied, for multiplication.
•]• divided, for division.
= equal, for equality.
Then, instead of 8 more 4 equal 12, I shall write 84-4=12. Instead of
32 less 4 equal 8, 12 — 4=8. Instead of 6 multiplied by 4 equal 24, 6x4=24.
And instead of 24 divided by 3 equal 8, 24.|.3=8.

38 MECHANICS. [Chap. 9.

Number 8 The water-wheel,

4 The great cog-wheel,

2 The wallower,

3 The counter cog-wheel,

1 The trundle,

2 The mill stones,

And let the above numbers also represent the radius
of the wheels in feet.

Now suppose there be a power of 5001b. on the wa-
ter-wheel, required what will be the force exerted on the
mill- stone, 2 feet from the centre.

Then by the rule, 500x8x2^1=8000, and 4x3x2
=24, by which divide 8000, and it quotes 333,331b. the
power or force required, exerted on the mill- stone two
feet from its centre, which is the mean circle of a 6 feet
stone. — And as the velocities are as the distance from
the centre of motion, by 3d law of circular motion, art.
13, therefore, to find the velocity of the mean circle of
the stone 2, deduce the following rule, viz.

1st. Multiply the velocity of the water-wheel into the
radius or circumference of all the driving wheels, suc-
cessively, and note the product.

2. Multiply the radius or circumference of all the
leading wheels, successively, and note the product ; di-
vide the first by the last product, and the quotient will
be the answer.

But observe here, that the driving wheels in this rule,
are the leading levers in the last rule.

EXAMPLES.

Suppose the velocity of the water-wheel to be 12 feet
per second ; then by the rule 12x4x3x2=288 and 8x2
Xl=16 by which divide the first product 288, and it
quotes 18 feet per second, the velocity of the stone, 2
feet from its centre.

Chap. 9.J MECHANICS. .'J9

ART. 21.

POWER DECREASES AS MOTION INCREASES.

It may be proper to observe here, that as the velocity
of the stone is increased, the power to move it is decreas-
ed, and as its velocity is decreased, the power on it to
move it is increased, by 2d general law of mechanical
powers. This holds universally true in all engines that
can possibly be contrived ; which is evident from the 1st
law of the lever, viz. the power multiplied into its velo-
city or distance moved, is equal to the weight multiplied
into its velocity or distance moved.

Hence the general rule to compute the power of any
engine, simple or compound, art. 17. If you have the
movine: power, and its velocity or distance moved, given,
and the velocity or distance of the weight, then, to find
the weight,(\\hich, in mills, is the force to move the stone,
&c.) divide that product by the velocity of the weight or
mill-stone, Sec. and it quotes the weight or force exerted
on the stone to move it: But a certain quantity or pro-
portion of this force is lost, in order to obtain a velocity
to the stone ; which is shewn in art. 29.*

ART. 22,

NO POWER C^AttsTED BY ENLARGING UNDERSHOT WATER-

■• , i WHEELS.

This seems a proper time to shew the absurdity of
the idea of increasing the power of the mill, by enlarging
the diarneter of the water-wheel, on the principle of
lengthening the lever, or by double gearing mills where
single gears will do ; because the power can neither be
increased nor diminished by the help of engines, while
-the velocity of the body moved is to remain the same.

EXAMPLE.

Suppose we enlarge the diameter of the water-wheel
from 8 to 16 feet radius, fig. 11, Plate II. and leave the

* Philosophers have hitherto attributed this loss of power to fricti0n>
which is owing to the vis inertia of matter.

40 MECHANICS. [Chap. 9.

other wheels the same ; then, to find the velocity of the
stone, allowing the velocity of the periphery of the water-
wheel to be the same ( 12 feet per second) ; by the rule
12x4x3x2=288, and 16x2x1=32, by which divide
288, it quotes 9 feet in a second, for the velocity of the
stone.

Then to find the power by the rule for that purpose,
i;irt, 20, 500x16x2x1=16000, and 4x3x2=24, by
which divide 16000, it quotes 666,661b. the power.
But as velocity as well as power, is necessary in mills,
we shall be obliged, in order to restore the velocity, to
enlarge the great cog-wheel from 4 to 8 radius.

Then, to find the velocity, 12x8x3x2=576, and
16x2x1=32, by which divide 576, it quotes 18, the
velocity as before.

Then to find the power by the rule, art. 20, it will be
333,33 as before.

Therefore no power can be gained, upon the principle
of lengthening the lever, by enlarging the water-wheel.

The true advantages that large wheels have over small
ones, arises from the width of the buckets bearing but a
small proportion to the radius of the wheel ; because if
the radius of the wheel be 8 feet, and the width of the
bucket or float-board but 1 foot, the float takes up 1-8 of
the arm, and the water may be said to act fairly upon the
end of the arm, and to advantage. But if the radius of
the wheel be but 2 feet, and the width of the float I foot,
part of the water will act on the middle of the arm, and
act to disadvantage, as the float takes up half the arm.
The large wheel also serves the purpose of a fly-wheel ;
(art. 30), it likewise keeps a more regular motion, and
casts off back water better. See art. 70.

But the expense of these large wheels is to be taken
into consideration, and then the builder will find that
there is a maximum size, (see art. 44), or a size that
will yield him the greatest profit.

Chap. 9.] MECHANICS. 41

ART. S3.

NO POWER GAINED BY DOUBLE GEARING MILLS, BUT SOME

LOST.

I might also go on to shew that no power or advan-
tage is to be gained by double gearing mills, upon any
other principles than the following, viz!

1. The motion necessary for the stone, can sometimes
be obtained without having the trundle too small, be-
cause we are obliged to have the pitch of the cogs and
rounds, and the size of the spindle, large enough to bear
the stress of the power. This pitch of gear, and size of
spindle, may bear too great a proportion to the radius of
the trundle (as does the size of the float to the radius of
the water-wheel, art. 22), and may work hard. There-
fore there may be a loss of power on that account ; as
there can be a loss but no gain, by 3d general law of me-
chanical powers, art. 15.

2. The mill may be made more convenient for two
pair of stones to one water-wheel.*

ART. S4.
OP THE PULLEY-

2. The pulley is a mechanical power well known.
One pulley, if it be moveable by the weight, doubles the
power, because each rope sustains half the weight.

But if two or more pulleys be joined together in the
common way, then the easiest way of compudng their
power is, to count the number of ropes that join to the
lovver or moveable block, and so many times is the pow-
er increased ; because all these ropes have to be shor-
tened, and all run into one rope (called the fall) to which
the moving power is applied. If there be 4 ropes the
power is increased fourfold.f See plate 1. fig. 10.

* Many and great have been the losses sustained by mill-builders, on ac-
count of their not properly understanding- these principles. I have often
met with great high wheels built, where those of half th- size and expense
would do better ; and double gears, where single would do better, &c- &c.

t In this engine there is ^reat loss of origmal power, by the great fric-

43 MECHANICS. [Chap. 9.

ART. 25.

OF THE WHEEL AND AXLE.

3. The wheel and axle, fig. 17, is a mechanical pow-
er, the same as the lever of the first kind ; therefore the
po\'> er is to the weight, as the diameter of the axle is to
the diameter of the wheel ; or the power multiplied into
the radius of the wheel is equal to the weight multiplied
into the radius of the axle,* in an equilibrium of this
engine.

ART. 26.
OF THE INCLllNED PLANE.

4. The inclined plane is the fourth mechanical power;
and in this the power is to the weight, as the height of
the plane is to its length. This is of use in rolling heavy
bodies, such as barrels, hogsheads, &c. into wheel car-
riages, Sec. and for letting them down again. See plate
I. fig. 5. If the height of the plane be half its leni^th,
then half the force will roll the body up the plane, that
would lift it perpendicularly.

ART. 27.
OF THE WEDGE.

5. The wedge is only an inclined plane. Whence, in
the common form of it, the power applied will be to the
resistance to be overcome, as the thickness of the wedge
is to the length thereof. This is a very great mechanical

tion of the pulleys and ropes in bending-, &c. But there is a very great im-
provement lately discovered, on the pully, which is as follows : Make a
system of puUies of such constmction, that when those of the upper block
all fixed logt ther on one pin will revolve in equal lime, and the same in
the lower block; which effectually evades all the friction of the sides uf the
pulleys and ropes passing through tlie blocks. But as it is almost impossi-
ble to proportion tiie diameters of the pullies to the motion of the ropes
so exactly, it will be best to let them have liberty to turn on the pin, so as
to stretch all the ropes equally-

* There is but little loss of original power in this engine, because it has
but little friction.

ehap. 91] MECHANICS. 43

power, and may be said to excel all the rest ; because
with it we can effect, what we cannot with any other in
the same time, and I think may be computed in the fol-
lowing manner.

If the wedge be 12 inches long and 2 inches thick,
then the power to hold it in equilibrio is as 1 to balance
12 resistance ; that is, 12 resistance pres^ng on each
side of the wedge,* and when struck with a mallet, the
whole force of the gravity of the mallet, added to the
whole force of the agent exerted in the stroke, is com-
municated to the wedge in the time it continues to move :
and this force to produce effect, is as the square of the
velocity, with which the mallet strikes, multiplied into
its weight : therefore the mallet should not be too large,
(see art. 44), because it may be too heavy for the work-
man's strength, and will meet too much resistance from
the air, so that it will lose more by lessening the velocity,
than it will gain by its weight. Suppose a mallet of
lOlb. strike with 5 velocitv, its effective momentum 250 ;
but if it strike with 10 velocity, then its effective mo-
mentum is 1000. The effects produced by the strokes
will be as 250 to 1000 ; and all the force of each stroke,
except what may be destroyed by the friction of the
wedge, is added in the wedge, until the sum of these
forces amount to more than the resistance of the body to
be split, therefore it must give way ; but when the wedge
does not move, the whole force is destroyed by the fric-
tion. Therefore the less the inclination of the sides of
the wedge, the greater resistance we can overcome by it,
because it will be easier moved by the stroke.

* Now, if we consider that (he one 12 acting on the one side of the
wedge represents the re-action of the ground on the underside of the in-
clined plane, we will then plainly see thai the wedge and inclined plane
are both one thing; for if this wedge be applied to raise a weight of 12, it
will require 2 instead of 1 to drive it under the weight. But if 'he ground
would give way under the wedge as easily, and move the same distance thaV
the weight raises, then the weight would be raised only half the height;
consequently, 1 would drive the wedge under the weighi,and this yielding
of the ground equal to the raising of the weight, will truly represent the
yielding of the cleft on each side of the wedge. And 'his is the true prin-
ciple o< fhe wedge, notwithstanding; so inwrh has been said to prove it to
be equal to 2 inclined plaries. See Ferguson's Lectures.

44 MECHANICS. [Chap. 9.

ART. es.

OF THE SCREW.

6. The screw is the last mentioned mechanical power,
and is a circular inclined plane (which will appear by
wrapping a paper, cut in form of an inclined plane, round
a cylinder) and the lever of the first kind combined (the
lever being applied to force the weight up in the inclined
plane), and is a great mechanical power ; its use is both
for pressure and raising great weights. The power ap-
plied is to the weight it will raise, as the distance through
which the weight moves is to the distance through
which the power moves ; that is, as the distance of the
threads of the screw is to the circle the power describes;
so is the power to the weight it will raise. If the dis-
tance of the thread be half an inch, and the lever be 15
inches radius and the power applied be 101b. then the
power will describe a circle of 94 inches, while the
weight raises half an inch ; then, as half an inch is to 94
inches, so is 101b. to 18881b. the weight the engine would
raise with 101b. power. But this is supposing the screw
to have no friction, of which it has a great deal.

Perhaps an improvement might be made on the screw,
for some particular uses, by introducing rollers to take off
the friction. See art. 33.

ART. 29.

We have hitherto considered the action and effect of
these engines, as they would answer to the strictness of
mathematical theory, were there no such thing as fric-
tion or rubbing of parts upon each other ; by which
means, philosophers have allowed, that one-third of the
effect of the machine is, at a medium, destroyed : which
brings us to treat of it next in course.*

* But I think it is evident, that this loss of 1-3 of the original power in
producing- effects by machines, arises fronn the vis inertia of the matter that
is to be mo»ed. For suppose the machine be an elevator, applied to ele-
vate wheat, Plate 11. fig- 17, art. 34, it is evident, that if we apply only as
much poiver as will hold the weight of the wheat in the buckets in equili-
brio, we will have no motion : then in order to oblaiH a lively motion, we

Chap. 9.] MECHANICS. 45

ART. 80.

OF THE FLY-WHEEL, AND ITS USE.

Before I dismiss the subject of mechanical powers, 1
shall take notice of the fly-wheel, the use of which is to
regulate the motion of engines, and should be made of
cast metal, of a circular form, that it may not meet with
much resistance from the air.

Many have taken this wheel for an increaser of power,
wheras it is, in reality, a considerable destroyer of it ;
which appears evident, when we consider that it has no
motion of its own, but receives all its motion from the
first mover, and, as the friction of the gudgeons and re-
sistance of the air are to be overcome, it cannot be done
without some power ; yet this wheel is of great use in
many cases, viz.

1st. For regulating the power, where it is irregularly
applied, such as the treadle or crank moved by foot or
hand, as spinning-wheels, turning lathes, flax-mills, or
where steam is applied, by a crank, to produce a circular
motion.

2d. Where the resistance is irregular, by jerks, &c.
such as saw-mills, forges, sHtting- mills, powder-mills,
&c.

The fly -wheel, by its inertia, regulates the motion ;
because, if it be very heavy, it will require a great many
litde shocks or impulses of power to give it a considera-
ble velocity, and it will require as many equal shocks of
resistance to destroy said velocity, by axiom 3. art. 1.

While a rolling or slitting mill is running empty, the
force of the water is employed in generating velocity to
the fly-wheel [a heavy water-wheel will have the same
effect], which force, summed up in the fly, will be suffi-
cient to continue the motion, without much abatement,
while the sheet is running between the rollers ; whereas,

will be obliged to apply a further power, which I expect we will find will
be nearly 1-3 of the whole, art. 41; and this 1-3 part of the power will be
continually emplojed in changing the state of the wheat from rest to a
lively motion- Besides, it is shewn in art. 31, that the friction of most
machines is not more than 1-20 part the weight upon a plane; and by the
difference between the diameters of the wheels and gudgeons, is reduced
to 1.1000 part of the weight, or the moving power.

46 MECHANICS. [Chap. 10.

had the force of the water been lost while the mill was
empty, she vv^ould have slackened in motion too much
before the sheet got through. This may be the case
where water is scarce.

CHAPTER X.

ART. 31.

OF FRICTION.

FROM what I can gather from different authors,* and
by my own experiments, I conclude that the doctrine of
friction is as follows, and we may say it is subject to the
following laws, viz.

Laws of Friction.

1. It is neither increased nor decreased by increasing
or decreasing the surfaces of contact of the moving

body.t

2. It is in proportion to the weight and velocity, con-
jointly, of the moving body. J

• Philosophers treating of friction, seem to agree in telling us, that If a
perfectly hard body of any weight could be made perfectly smooth and
even, and laid on a horizontal plane, perfectly hard, smooth, and even, that
thi n the least force would move the said weight in any horizontal direc-
tion ; and that it is the roughness of the best polished and smoothed bo-
dies, that is the whole cause of friction ; because the body in being moved^
has first to be raised over the prominent parts, which is of the nature of an
inclined plane. They also say, in treating of the attraction of cohesion,
that if two bodies of the same kind of matter could be made perfectly
sm 'oth and even, so that the parts would meet exactly, they would strong-
ly cohere or stick together by a' traction ; by which it appears that the
doctrine of friction is not yet well explained.

\ They also say, that it is prov(^d by experiment, that if a square piece
of wood or brass, as F, Plate II- fig- 13, four inches wide, and 1 inch thick,
be made smooth, and laid on a smooth plane, A B C D, and the weight P
hung over a pulley, that it will require the weight P to be nearly 1-3 part
of the weight of the body F, to draw it along; and that the same, whe-
ther it be on its flat side or edge. This proves law 1st, that friction is not
increased by iftcneasing the surface of contact.

\ It has also been proved by experiment, that if we fix the lever L, to
draw the weight F, making o its centre of motion, and by a cord make F
fiist to the lever at the point 1, and hang the weight Q at the end of the
lever over a pulley, and make Q just sufficient to move F, Q wdl then be
found to be 1-7 of P. because it will have to move F but 1 7 of the distance.
Thfn move the cord from 1 to 2, and we find the weight Q must now be
doubled equal to 2-7 of P to moye F ; (the reason is evident from the laws

Chap. 10.] MECHANICS. 47

3. This proportion decreases as the weight and velo-
city increases, but by what ratio is not determined.*

of the lever) because F is double the distance from the centre of motion
that it was at 1, and \\ will have to move double the distance if the lever,
or power Q, move the same distance. This shews that friction is as the dis-
tance from the centre ot motion; that isi it is as the diameter of the gud-
geons, double diameter, double friction ; therefore ^{udgeons ought to be
as small as possible, so as to be sufficiently strong to endure the stress of the
weight.

* They have also proved by experiment, that if F be a brass plate of 6
ounces, and A B C D a brass plute, both well polished and oiled, » hen it will
require the weight P lo be nearly 2 ounces to move F. But if F be loaded
with 6, 8, or 10 lb. then a sixth part of that weight will be sufficient to draw
it along. This proves that the ratio of the friction to the weight decreases,
as the weight increases • the reason of which decrease of proportion I take
to be as follows, viz. Great part of the friction arises from the cohesion of
the parts, even the grease put on to destroy the cohesion, has a cohesion of
its own ; and this cohesion of pans or of the grease, will not increase with
the weight or velocity. Again, if we allow the friction to be occasioned by
the weight of the body having to be raised over the prominent parts of the
rubbing surface, it is evident, that when it is raised by being started, that
it has not to be raised again ; therefore the greater the velocity, the less
proportion will this resistance (occasioned by the raising of the body) bear
to the velocity.

I have made an experiment similar to that of Plate 11- fig. 13, with a
flat -sided glass bottle, on a smooth poplar plank, oiled ; also on a well po-
lished steel plate oiled, and when loaded with 10 lb. it was drawn by 1 lb.
and when loaded with 22 lb. it was drawn by 21b. and when loaded with
601b. it was drawn by 4 1-2 lbs. which is about 1 13 part : and the motion
was greatly accelerated, which gives reason to conclude, that less weight
would have continued the motion when once begun.

We may reasonably suppose, that the gudgeons of mills, &c. well polish-
ed, running on good stones or brass boxes, &c. and well oiled, have as l.ttle
friction as the bottle and plank ; and as we find that the proportion of fric-
tion decreases as the weight increases, we may suppose that in great
weights it will not amount to more than 1 20 part of the weight, supposing
the gudgeons to be the full size or diameter of the wheels, for so they
must be in order to be on the same principles of planes rubbing together.
Upon these principles I compute the friction of the gudgeons of a well
hung water-wheel, as follows : viz. As the diameter of the wheel is to the
diameter of the gudgeons, so is 1 20 part of the weight of the wheel, to
the weight that will balance the friction.

EXAMPLE,

Suppose a wheel 15 feet diameter, with gudgeons 3 inches diameter, and
weighing 40001b. by supposition ; then, say as 15 feet is to 3 inches, so is
400 I 20 to 3,31b. the weight on the periphery of the wheel that will ba-
lance the friction of 4000 lb.: which is less than 1-1000 part of the weight;
but note 'hat for the same reasons, that friction does not increase with the
velocity m direct proportion, neither will it decrease in direct proportion
with the velocity of the rubbing surface of the gudgeon: hence we must
conclude again that the friction is more than l-lOOO part. By which it ap-
pears, that the friction of the gudgeons, well set on good stones or brass
boxes, is not in mills worthy the expense of evading. It bears but a small
proportion to the friction or resistance of 'he air, especially where the VS'
locity is great. See art. 9, and 9th kw of falling bodies.

48 MECHANICS. [Chap. 10,

4. It is greatly varied by the smoothness or roughness,
hardness or softness, of the surfaces of contact of the
moving bodies.

5. A body without motion has no friction ; therefore,
the less the motion, the less the friction.

ART. 3S.

OF REDUCING FRICTION.

To reduce friction, we must, by mechanical contriv-
ances, reduce the motion of the rubbing parts as much
as possible ; which is done, either by making the gud-
geons small and the diameter of wheels large, or by fix-
ing the gudgeons to run on friction-wheels. Tlius, let
A, Plate II. fig 14, represent the gudgeon of a wheel
set to run on the verge of two wheels of cast metal pas-
sing each other a little, and the gudgeon laving between
them. It is evident, that as A turns, it will turn both
friction-wheels ; and, if the diameter of gudgeon A is 2
inches, and that of the wheels 12, then the wheels will
turn once while A turns 6 times, so that the velocity of
the gudgeons C C of the wheels, is to the velocity of the
gudgeon A, as 1 is to 6, supposing them to be equal in
size ; but as there are 4 of them to bear A, they may be
but half the diameter, and then their velocity will be to
that of A, as 1 is to 12 ; or A might be set on one
wheel, as at B, with supporters to keep it on ; and, if
friction-wheels are added to friction-wheels, the friction
may be reduced to almost nothing by that means.

ART. 33.
LATE INVENTION TO REDUCE FRICTION.

Wheel-carriages, pullies, and such wheels as have
large axles in proportion to their diameters, have much
friction. There has been a late discovery in England, of
applying the principle of the roller to them ; which may
be so done as almost totallv to destrov the friction.

Ghap. 10.] MECHANICS. 49

The easiest method possible, of moving heavy bodies
horizontally, is the roller.

Let A B, Plate 11. fig. 15, represent a body of 100 tons
weight (with the under side perfectly smooth and even)
set on two rollers, perfectly hard, smooth and round, roll-
ing on the horizontal plane C D, perfectly hard, smooth,
and even ; it is evident that this body is supported by
two lines perfectly perpendicular, and, if globes were
used instead of rollers, the least force would move it in
any horizontal direction ; even a spider's web would be
sufficient, giving it time to overcome the vis inertia of
the body : But as perfect hardness, smoothness, &c. are
not attainable, a litde friction will still remain.

This principle is, or may be, applied to wheel- car-
riages, in the following manner :

Let the outside ring BCD, Plate IL fig 16, represent
the box of a carriage- wheel, the inside circle A the axle,
the circles a a a a a a the rollers round the axle between
it and the box, and the inner ring a thin plate for the
pivots of the rollers to run in, to keep them at a proper
distance from each other. When the wheel turns, the
rollers pass round on the axle, and on the inside of the
box, and we may say without friction, because there is
no rubbing of the parts past one another.*

* To explain this, let us suppose the rollers a a a a a a to have cogs, and
the shaft A, and box to have cogs also, the rollers gearing into the shaft
and into the inside of the box. Now it is evident, ihat if the box will turn
round the axle, it must be without any sliding of parts ; (and in fact, the
prominent parts of the rollers, axle and box, will act as cogs) then, if the
rollers and axle be all of one diameter, they will have an eq lal number of
cogs; and as the diameter of the box wdl be 3 times the diameter of the
rollers, it will have 3 times as many cogs. Now it is evident, that the axle
must turn 1 1-3 times round, before the same cogs of the rollers and shaft
will meet, that were together when it started; because, in that time the
rollers will have moved over 1-3 of the box: therefore the axle mus^ turn
3 3-3 times equal to 4 times round, by the time the box is once measured
by the rollers. Then suppose we hold the axle at rest, and turn the box
round like a carriage wheel; then, while the box turns 1 1-3 times round
the axle, it will cause the rollers to move once round ; and while the box
or wheel turns round the axle 4 times, the rollers vvill run round it three
times. For suppose we divide the box into 3 parts, B C and D, then begin-
ning to turn the box from B to D, it is evident, that while the roller a b
measures once round the axle and returns to the same place, it wdl .ilso
measare the box from B to C, and C will have taken ihe place of B, and
the next revolution of the roller D will take the place of C, and the third
revolution B returns to where it was at first, and the box has made 4 revo-

50 I^ECHANICS. [Chap, ll-

CHAPTER. XL

ART. 34.
OF MAXIMUMS, OR THE GREATEST EFFECTS OF ANY MACHINE.

THE effect of a machine, is the distance which it
moves, or the velocity with which it moves any body to
which it is applied to give motion, in a gi^en time; and
the weight of the body multiplied into its distance mov-
ed, or into its velocity, shews he effect.

The theory published by philosophers, and received
and taught as true, for several centuries past, is, that any
machine \vill work with its greatest perfection when it
is charged with just 4-9 of the power that would hold it
in equilibrio, and then its velocity will be just 1-3 of the
greatest velocity of the moving power.

To explain this, they suppose the water-wheel, Plate
n. fig. 17, to be of the undershot kind, 16 feet diameter,
turned by water issuing from under a 4 feet head, with a
gate 1 foot wide, 1 foot high drawn ; then the force will
be 250lbs. because that is the weight of the column of
water above the gate, and its velocity will be 16,2 feet
per second, as shall be shewn under the head of Hy-
draulics ; then the wheel will be moved by a power of
2501bs. and if let run empty, will move with a velocity
of 16 feet per second : but if we hang the weight W to
the axle (of 2 feet diameter) with a rope, and continue
to add to it until it stops the wheel, and holds it in equi-
librio, the weisrht will be found to be 2000lbs. by the
rule, art. 19 ; and then the effect of the machine is no- .
thing, because the velocity is nothing : But as we de-
crease the weight W, the wheel begins to move, and
its velocity increases accordingly ; and then the product
of the weight multiplied into its velocity, will increase
until the v/eight is decreased to 4-9 of 2000=888,7,

lotions, while the rollers have made 3 round the axle, and without any slid-
ing of pans, therefore without friction. I might goon to shew, th.t if Ihe
axle be much larger than the rollers, they will also work without sliding.

^hap. 11.] MECHANICS. 51

which multiplied into its distance moved or velocity,
will produce the greatest effect, and the velocity of the
wheel then be 1-3 of 16 feet, or 5,33 feet per second.
So say those who ha^'e treated of it.

This will appear plainer to a young learner, if he will
conceive this wheel to be applied to work an elevator, as
E, Plate II. fig. 17, to hoist wheat, and suppose that the
buckets, when all full, contain 9 pecks, and will hold the
wheel in equilibrio, it is evident it will then hoist none,
because it has no motion ; then, in order to obtain mo-
tion, we must lessen the quantity in the buckets, when
the wheel will begin to move, and hoist faster and faster
until the quantity is decreased to 4-9, or 4 pecks, and
then, by the theory, the velocity of the machine will be
1-3 of the greatest velocity, when it will hoist the great-
est quantity possible in a given time : for if we lessen
the quantity in the buckets below 4 pecks, the quantity
hoisted in any given time will be lessened.

This is the theory established, for demonstration of
which, see Martin's Philosophy, vol. i. p. 185 — 187.

ART. 35.

OLD THEORY INVESTIGATED.

In order to investigate this theory, and the better to
understand what has been said, let us consider as follows,
viz.

1. That the velocity of spouting water, under 4 feet
head, is 16 feet per second, nearly.

2. The section or area of the gate drawn, in feet,
multiplied by the height of the head in feet, gives the
cubic feet in the whole column, which multiplied by 62,5
(the weight of a cubic foot of water) gives the weight
or force of the whole column pressing on the wheel

3. That the radius of the wheel, multiplied by the
force, and that product divided by the radius of the axle,
gives the weight that will hold the wheel in equilibrio.

4. That the absolute velocity of the wheel, subtracted
from the absolute velocity of the water, leaves the rela-

52 MECHANICS. [Chap. 11.

tive velocity with which the water strikes the wheel in
motion.

5. That as the radius of the wheel is to the radius of
the axle, so is the velocity of the wheel to the velocity
of the weight hoisted on the axle.

6. That the effects of spouting fluids are as the squares
of their velocities (see art. 45, law 6), but the instant
force of striking fluids are as their velocities simply.
See art. 8.

7. That the weight hoisted, multiplied into its per-
pendicular ascent, gives the effect.

8. That the weight of water expended, multiplied into
its perpendicular descent, gives the power used per
second.

On these principles I have calculated the following
scale ; first supposing the force of striking fluids to be
as the square of their striking or relative velocity, which
brings out the maximum agreeably to the old theory,
viz.

When the load at equilibrio, is 2000, then the maxi-
mum load is §88,7=4-9 of 2000, when the effect is at
its greatest, viz. 591,98, as appears in the 6th column,
. and then the velocity of the wheel is 5,333 feet per se-
cond, equal to 1-3 of 16, the velocity of the water, as
appears in the 5th line of the scale : but as there is an
evident error in the first principle of this theory, by
counting the instant force of the water on the wheel to
be as the square of its striking velocity, therefore it can-
not be true. See art. 41.

I then calculate upon this principle, viz. That the
instant force of striking fluids is as their velocity simply,
then the load that the machine will carry, with its dif-
ferent velocities, will be as the velocity simply, as ap-
pears in the 7th column, and the load, at a maxim, is
1000lb.=| of 2000, the load at equilibrio, when the ve-
locity of the wheel is 8 feet=| of 16 the velocity of the
water per second ; and then the effect is at its greatest,
as shewn in the 8th column, viz. 1000, as appears in the
4th line of the scale.

This I call the new theory, (because I found that
William Waring had also, about the same time, esta-

Chap. 11.] MECHANICS. 33

blished it, see art. 38) viz. That when any machine is
charged with just 1-2 of the load that will hold it in
equilibrio, its velocity will be just 1-2 of the natural ve-
locity of the moving power, and then its effect will be at
a maximum, or greatest possible.

This appears to be the way by which this great error
has been so long overlooked by philosophers, and which
has rendered the theory of no use in practice, but led
many into expensive errors, thereby bringing great dis-
credit upon philosophy.

For demonstrations of the old theory, see Martin's
Phil. vol. i. p. 185—187.

MECHANICS.

[Chap. 11.

Ritioof the power and ef
feet at a niaximum, the

-a ^

6 & . b: 6 J

power being 4000 in each

e = o^ -^ e^

case.

^.S^ls -^"3

s ;: 2§

oN-ot^aoo^ oio

Effect, by new theory.

i«.0>OOl0000I^C0

Weight hoisted, according

to new theory.

T-4 '^ 1-< p4 l-l .-• C4

■

00
in o> ?> (O lo h.

Effect, by the old theory.

isT-^ o «^ -T o «' cT

OOO'OOCOO^OiOQO

.^ CO <D •- to lo »r) ■>

Weight hoisted, according

to the old theory.

CQOOOOOOO-^tNCOO
-H rt CN

Velocity of the weight as-

«3 ifl
«0 «0 'O (N "i^

cending.

VJ «N I^ VO <0^ •O (N O

Velocity with whicti the wa

ter strikes the wheel in

motion, or relative velo-

'.i

0'^<00000'-<C^'?<0

city.

Velocity of the wheel per

second, by supposition

<ONO00<o>rriOT}<irNO

00,-l r1 ^'O ■<=> O

^ 2 »o o

.i>

r»A^ ,->A.*«>r^A^

CO S

4* O" 1

ius of the wheel
ins of the axle

ion of the gate in square feet

j;hi of the head of water

jcity of the water per second -

ght of the column of water pr

g on the wheel

weight that holds the wheel in e

jrio

■TJ "o o — :: jj c 4) .-

f Chap. 11, MECHANICS. BS

ART. 36.

NEW THEORY DOUBTED.

But although that I know the velocity of the wheel,
by this neu theor}', is much nearer practice than the old,
(though rather slow) yet I am led to doubt the theory,
for the following reasons, viz.

When I consider that there are 16 cubic feet of water,
equal lOOOlbs. expended in a second, which multiplied
by its perpendicular descent, 4 feet, produces the power
4(;00. The ratio of the power and effect by the old
theory is as 10 to 1,47, and by the new as 4 to 1 ; as
appears in the 9th column of the scale ; which is a proof
that the old theory is a great error, and sufficient cause of
doubt that there is yet some error in the new. And as
the subject is of the greatest consequence in practical
mechanics, therefore I proceed to endeavour to dis-
cover a true theory, and will shew my work, in order
that if 1 establish a theory, it maybe the easier understood,
if right, or detected, if wrong.

Attempts made to discover a new Theory.

In the search, I constructed fig. 18, pi. II. which re-
presents a simple wheel with a rope passing over it and
the weight P, of lOOlbs. at one end to act by its gravity,
as a power to produce effects, by hoisting the weight w
at the other end.

This seems to be on the principles of the lever, and
overshot wheel ; but with this exception, that the quan-
tity of descending matter, acting as power, will still be
the same, although the velocity will be accelerated,
whereas in overshot wheels, the power on the wheel is
inversely, as die velocity of the wheel.

Here we must consider,

1. The perpendicular descent of power P, per se-
cond, multiplied into its weight, shews the power.

2. That the weight w when multiplied into its per-
pendicular ascent gives the effect.

3. That the natural velocity of the falling body P, is
16 feet the first second, and the distance it has to fall
16 feet.

56 MECHANICS. [Chap. 11.

4. That we do suppose that the weight w, or resis-
tance, will occupy its proportional part of the velocity.
That is, if w be =z i P, the velocity with which P will
then descend, will be § 16=8 feet per second.

5. If w be = P, there can be no velocity, consequent-
ly no effect ; and if w = o then P will descend 16 ^eet
in a second, but produces no effect ; because, the power,
although 1600 per second, is applied to hoist nothing.

Upon these principles 1 have calculated the following
scale.

Chap. 11.]

MECHANICS.

A SCALE

DETERMINING THE MAXIMUM CHARGE,

i'i. I.

io r

VELOCITY OP itfoftis'.' BESCENDmO' 6T its" GkAVl^hr.

;:'f ■

' :,■ (M

i ' ; , ; •

-3

'^ o

-co

f.i

^ B

-J 1

(T) ■* "^

a-»

is^

2. o

:«5

5'1

= 1

, '5- . ■

— 1 '*

•^

(n 3

n 3- 3

' :■

is.

o- 2. o

^.2l

!.i:

1) ^

3 O

2. «' 3-

£ ^

s <

jq ^ o

T C-

1) r»

•0 ■

? '»"'

." O

*^ o

i. 3- <

r* rt t

I ^

/ !■

-5 ""

2. o

3rq —

^ re

2. -a

►3

»3

ft ^
O

3-^
" O
<: o
*= o

3* C

1"^

?
^3

§3

?o-

§■3

p- £.

3- ?

lbs

feet.

lb.

feet.

100

1600

10 :

.16

15.84

15 84

1584

10 :.01

1.6

144

1440

10 : 1

3.2

12.8

256

1280

10 : 2

ii.y

336

1120

10 : 3

6.4

9.6

384

960

10 : 4

; . !

^00

800

10 .5

maximura,

6.4

384

640

10 : 6

by new theo-

11.2

336

480

10 : 7

ry.

12.8

256

320

10 : 8

14.4

1.6

144

160

10 : 9

15.84

.16

15.8

16 10 :9.9

100

16.

^ MECHANICS. [Chap. 11.

By this scale it appears, that when the weight w is
=50= I P the power ; the eiFect is at a maxiinum, viz.
400, as appears in the 6th column, when the velocity is
half the natural velocity, viz. 8 feet per second ; and
then the ratio of the power to the effect is as 10 to 5, as
appears in the 8th line.

By this scale it appears, that all engines that are
moved by one constant power, which is equably acce-
lerated in their velocity (if any such, there be) as appears
to be the case here, must be charged with weight or re-
sistance equal to half the moving power, in order to
produce the greatest effect in a given time ; but if time
be not regarded, then the greater the charge, so as to
leave any velocity, the greater the effect, as appears by
the 8th column. So that it appears, that an overshot
wheel, if it be made immensely capacious, and to move
very slow, may produce effects in the ratio of 9,9 to 10
of the power.

ART. 37.

SCALE OF EXPERIMENTS.

The following scale of actual experiments were made
to prove whether the resistance occupies its proportion
of the velocity, in order that I might judge whether the
foregoing scale was founded on true principles ; the ex-
periments were not very accurately performed, but often
repeated, and proved always nearly the same. See Plate
11. fig. 18.

Chap. 11.]

MECHANICS.

A SCALE

EXPERIMENTS.

o
n

T C 3

re
1

■a

•-♦ 3 O

CO o^ ft

«
?

S.S

^o-s-

5"o

3*
P

a.
o

« i'

2. rt

o c

3
p.

n
o

E =

r»orq

US.-

1§?

CO —

n c.

■o-E

Q-
3

< zr
n

IT 5'

3 *?

fid v^

^1'

3^"

re ^

3*
3-

r* re

o
c

<•

^ £.3
o a o

i"i.

•^ CO O,

OR.

« ^

is-

n ^

'^ 2.

3-(B

' o _

•a —

• -^

cr"^

•

3
O

sr0

- o

S 3

CD ^

. 5"

re rt.
,11 re

re o

n 3-

3 C
C P

^2.

. s

o 2.

tro

« 2

re -n

< r*

-J

re 3"

. 3^

C
p

• 3"

o «
2.«
^2.

• c 3

. 3

. f»

^orij

cr
n

2X6

10 : 8.5

15.5

2.6X5

18.2

10 : 7.1

33.8

3.33x4

13.32

23.31

10 : 5.7

44.35

3.5

4X3.5

10 : 5.

maximum
new theory.

4 44x3

13.32

31.08

10 : 42

59.14

6.5

5X2

10 : 28

72 maximum.

5.6X1

6.6

46.2

10 : 1.4

33.56

■—

60 MECHANICS. [Chap. II.

By this scale it appears, that when the power P falls
freely without any load, it descends 40 feet in five equal
parts of time, but, when charged with 3,51bs.=iP, which
was 7lbs. it then took up 10 of those parts of time to de-
scend the same distance ; which seems to shew, that the
charge occupies its proportional part of the whole velo-
city, which was wanted to be known, and the maximum
appears as in the last scale.* It also shews, thai the ef-
fect is not as the weight multiplied into the square of its
ascending velocity, this being the measure of the effect
that would be produced by the stroke on a non-elastic
body.

This experiment partly confirmed me in what I have
called the New Theory ; but still doubting, and after I
had formed the foregoing tables, I called on the late in-
genious and worthy friend, William Waring, teacher in
the Friends' Academy, Philadelphia, for his assistance.
He told me he had discovered the error in the old theory
and corrected it in a paper which he had laid before the
Philosophical Society of Philadelphia, wherein he had
shewn that the velocity of the undershot water-wheel, to
produce a maximum effect, must be just one half the ve-
locity of the M'ater.

ART. 38.
WILLIAM WARING'S THEORY.

The following are extracts from the above mentioned
paper, published in the third volume of the Transactions
of the American Philosophical Society, held at Philadel-
phia, p. 144.

After his learned and modest introduction, in which
he shews the necessity of correcting so great an error as
the old theory, he begins with these words, viz.

" But to come to the point, I would just premise these

* Since writinp the above, I have seen Atwood's Treatise on Motion,
wherein he gives a set of accurate experiments, to prove (beyond doubt)
that ihe conclusion I have drawn is riglit, viz. That the charge occupies its
proportional part of the whole velocity. See the American Encyclopedias
vol. X. p. 786.

Chap. 11.] MECHANICS. 61

DEFINITIONS.

If a stream of water impinge against a wheel in motion,
there are three different velocities to be considered ap-
pertaining thereto, viz.

First, The absolute velocity of the water.

Second, The absolute velocity of the wheel.

Third, the relative velocity of the water to that of
the wheel; i. e. the difference of the absolute velocities,
or the velocity with which the water overtakes or strikes
the wheel.

Now the mistake consists in supposing the momentum,
or force of the water against the wheel, to be in the du-
plicate ratio of the relative velocit}^; Whereas,

PROP. I.

The force of an invariable stream, impinging against a
mill-wheel in motion, is in the simple proportion of the
relative velocity.

For, if the relative velocity of a fluid against a single
plane, be varied, either by the motion of the plane or of
the fluid from a gi^'en aperture, or both, then the number
cr particles acting on the plane, in a given time, and like-
wise the momentum of each particle being respectively
as the relative velocity, the force, on both these accounts,
must be in the duplicate ratio of the relative velocity,
agreeable to the common theory, with respect to this sin-
gle plane ; but the number of these planes or parts of the
wheel, acted on in a given time, will be as the velocity
of the wheel, or inversely as the relative velocity ; there-
fore the moving force of the wheel must be as the simple
ratio of the relative velocity. Q. E. D.

Or the proposition is manifest from this consideration,
that while the stream is invariable, whatever be the ve-
locity of the wheel, the same number of particles, or
quantity of the fluid, must strike it somewhere or other
in a given time ; consequently, the variation of the force
is only on account of the varied impingent velocity of
the same body, occasioned by a change of motion in
the wheel; that is, the momentum is as the relative
velocitv.

62 MECHANICS. [Chap. 11.

Now this true principle, substituted for the erroneous
one in use, will bring the theory to agree remarkably
with the notable experiments of the ingenious Smeaton,
published in the Philosophical Transactions of the Royal
Society of London, for the year 1751, vol. 51; for which
the honorary annual medal was adjudged by the so-
ciety, and presented to the author by their president.

An instance or two of the importance of this correction
may be adduced, as follows :

PROP. II.

The velocity of a wheel, moved by the impact of a
stream, must be half the velocity of the fluid, to produce
the greatest effect possible.

C V=the velocity, M=the momentum, of the fluid.

^ v=:the velocity, P=the power, of the wheel.

Then V — v=their relative velocity, by definition 3d.
M

And, as V:V— v::M:— xV--v=P, (Prop. 1.) which

xt=P, v= — xVv — v^=a maximum; hence Vv — v'=

V
a maximum and its fluxion (v being a variable quantity)
=Vv — 2vv=o; therefore=|V; that is, the velocity of
the wheel=:half that of the fluid, at the place of impact,
when the effect is a maximum. Q. E. D.

The usual theory gives v=4V, where the error is not
less than one sixth of the true velocity.

Wm. waring.

Philadelphia^ 7th
9th mo. 1790.

Note, I omit quoting prop. III. as it is in algebra, and
refers to a figure, because I am not vnriting so particular-
ly to men of science, as to practical mechanics.

Chap. 11.] MECHANICS. 63

ART. 39.

Extract from a further paper ^ read in the Philosophical
Society, April 5th, 1793.

" Since the Philosophical Society were pleased to
favour my crude observations on the theory of mills,
with a publication in their transactions, I am apprehen-
sive some part thereof may be misapplied, it being there-
in demonstrated, that ' the force of an invariable stream,
impinging against a mill-wheel in motion, is in the sim-
ple direct ratio of the relative velocity.' Some may sup-
pose that the effect produced, should be in the same
proportion, and either fall into an error, or finding by
experiment, the effect to be as the square of the velocity,
conclude the new theory to be not well founded ; I there-
fore wish there had been a little added, to prevent such
misapplication, before the Society had been troubled with
the reading of my paper on that subject : perhaps some-
thing like the following.

The maximum effect of an undershot wheel, produ-
ced by a given quantity of water, in a given time, is in
the duplicate ratio, of the velocity of the water : for the
effect must be as the impetus acting on the wheel, mul-
tiplied into the velocity thereof: but this impetus is
demonstrated to be simply as the relative velocity. Prop.
I. and the velocity of the wheel, producing a maximum,
being half of the water by Prop. II. is likewise as the
velocity of the water; hence the power acting on the
wheel, multiplied into the velocity of the wheel, or the
effect produced, must be in the duplicate ratio of the
velocity of the water. Q. E. D.

CoROL. Hence the effect of a given quantity of wa-
ter, in a given time, will be as the height of the head,
because this height is as the square of the velocity. This
also agrees with experiment.

If the force, acting on the wheel, were in duplicate
ratio of the water's velocity, as usually asserted, then the
effect would be as the cube thereof, when the quantity
of water and time are given, \^•hich is contrary to the
result of experiment.''

64. MECHANICS. [Chap. 11

ART. 40.
WAKING'S THEORY DOUBTED.

From the time I first called on William Waring, un-
til I read his publication on the subject, (after his death)
I had rested partly satisfied, with the new theory, as I
have called it, with respect to the velocity of the wheel,
at least; but finding that he had not determined the
charge, as well as the velocity, by which we might
have compared the ratio of the power and the effect pro-
duced, and that he had assigned reasons somewhat dif-
ferent for the error ; and having found the motion to be
rather too slow to agree with practice, I began to suspect
the whole, and resumed the search for a true theory,
thinking that perhaps no person had ever yet considered
every thing that affects the calculation, I therefore pre-
mised the following

POSTULATES.

1. A given quantity of perfect, elastic or solid matter,
impinging on a fixed obstacle, its effective force is as the
squares of its different velocities, although its instant
force may be as its velocities simply, by annotation,
art. 8.* '

2. An equal quantity of elastic matter, impinging on
a fixed obstacle with a double velocity, produces a quad-
ruple effect, art. 8 ; i. e. their effects are as the squares
of their velocities. Consequendy,

3. A double quantity of said matter, impinging with
a double velocity, produces an octuble effect, or their
effects are as the cubes of their velocities, art. 47 and 67.

4. If the impinging matter be non-elastic, such as
fluids, then the instant force will be but half in each
case, but the ratio will be the same in each case.

5. A double velocity, through a given aperture, gives
a double quantity to strike the obstacle or wheel, there-
fore the effects, by postulate 3, will be as the cubes of
the velocity. See art. 47.

* Because the distance it will recede after the stroke through any re-
sisting medium, will be as the squares of its impinging velocities.

Ghap. 11.] MECHANICS. 65

6. But a double relative velocity cannot increase the
quantity that is to act on the wheel, therefore the effect
can only be as the square of the velocity, by postulate 2.

7. Although the instant force and effects of striking
fluids on fixt obstacles, are only as their simple velocities,
yet their effects, on moving wheels, are as the squares of
their velocities; because,' 1, a double striking velocity
gives a double instant force, which bears a double load
on the wheel ; and 2, a double velocity moves the load
a double distance in an equal time, and a double load
moved a double distance, is a quadruple effect.

ART. 41.
SEARCH FOR A TRUE THEORY, COMMENCED ON A NEW PLAN.

It appears that we have applied wrong principles in
our search after a true theory of the maximum velocity
and load of undershot water-wheels, or other engines
moved by a constant power, that does not increase or
decrease in quantity on the engine, as on an overshot
water-wheel, as the velocity varies.

Let us suppose water to issue from under a head of 16
feet, on an undershot water-wheel: then, if the wheel
moves freely with the water, its velocity will be 32,4 feet
per second, but will bear no load.

Again, suppose we load it, so as to reduce its motion
to be equal the velocity of water spouting from under
15 feet ; it appears evident that the load will then be just
equal to that 1 foot of the head, the velocity of which is
checked ; and this load multiplied into the velocity of
the wheel, viz. 31,34x1=31,34 for the effect.

This appears to be the true principle, from which we
must seek the maximum velocity and load, for such en-
gines as are moved by one constant power; and on this
principle I have calculated the following scale.

66 MECHANICS. [Chap. 11.

A SCALE

FOR SETEBIUIIVINO THE '

TRUE MAXIMUM VELOCITY AND LOAD

FOR

UNDERSHOT WHEELS.

ft
o

elocity
cond,
the W!
unbal

oad o
parti
whic

flfect
of t
load.

_ -*»

3- 3 -»J

3-3

S; »

-*3

(t ft

oft
beii
ter
ncei

r> n '^

^ S

0.
o

§ 5

^3^S-

%l%

cr ft
re n
ft o

wheel
equal
n und

•z

f8 3

- s

-1^

— O

ft <! "

rt ft

S' 5"

;? ft

'•L'O

&< ft

tr ■r-"

3 c

per se
acity
ead lef

o ^

•^l

crtj

•<

5' ^

O w

o
" 2.

- -^ •

-r, r^

ft ■<

f.e.

tef* 1

feet.

32-4

31.34

3134

30 2

60 4

112

25.54

153.24

22 8

182.4

2143

192.87

19.84

198.4

5.66

19.27

1033

198.95

5.33

18.71

10.66

199 44

Maximum motion

18.

198

and load.

16.2

194 4

14.

172

11,4

159.6

120.

Chap. 11.] MECHANICS. 67

In this scale let us suppose the aperture of the gate to
be a square foot; then the greatest load that will balance
the head, will be 16 cubic feet of water, and the different
loads will be shewn in cubic feet of water.

And then it appears, by this scale, that when the
wheel is loaded with 10,66 cubic feet of water, just 2-3
of the greatest load, its velocity will be 18,71 feet per
second,' just ,577 parts of the velocity of the water, and
the effect produced is at a maximum, or the greatest pos-
sible, viz. 199,44.

To make this more plain, let us suppose A B, plate
II, fig. 19, to be a fall of water 16 feet, which we wish
to apply to produce the greatest effect possible, by hoist-
ing water on its side opposite to the power applied ; first,
on the undershot principle, where the water acts by its
impulse only. Now let us suppose the water to strike
the wheel at I, then, if we let the wheel move freely
without any load, it will move with the velocity of the
water, viz. 32,4 feet per second, but will produce no
effect, if the water issue at C ; although there be 32,4
cubic feet of water expended, under 16 feet perpendicu-
lar descent. Let the weight of a cubic foot of water be
represented by unity or 1, for ease in counting; then
32,4>: 16 will show the power expended, per second, viz.
518,4; and the water it hoists multiplied into its per-
pendicular ascent, or height hoisted, will shew the effect.
Then, in order to obtain effect from the power, we load
the wheel; the simplest way of doing which, is, to cause
the tube of water C D to act on the back of the bucket
at I; then, if CD be equal to AB, the wheel will be held
in equihbrio; this is the greatest load, and the whole of
the fall AB is balanced, and no part left to give the
wheel velocity; therefore the effect=0. But if we make
CD=12 feet of AB, then from 4 to A=4 feet, is left un-
balanced, to give velocity to the wheel, which is now
loaded with 12 feet, and exactly balanced by 12 on the
other side, and perfectly free to move either way by the
least force applied: Therefore it is evident, that the
whole pressure or force of 4 feet of AB will act to give
velocity to the wheel, and, as there is no resistance to
oppose the pressure of these 4 feet, the velocity will be

68 MECHANICS. [Chap. 11.

the same that water will spout from under 4 feet head,
viz. 16,2 feet per second, which is shewn by the hori-
zcntal line 4=16,2, and the perpendicular line 12=12
rejnesents the load of the wheel; the rectangle or pro-
duct of these tu o lines, form a parallelogram, the area of
\\hich is a true representation of the effect, viz. the load
12 multiplied into 16,2 the distance it moves per second
= 194,4, the effect. In like manner w^e may try the ef-
fect of different loads ; the less the load, the greater will
be the velocity. The horizontal lines all shew the velo-
city of the wheel, produced by the respective heads left
unbalanced, and the perpendicular lines shew the load on
the M heel ; and we find, that when the load is 10,66=|16,
the load at equilibrio, the velocity of the wheel \\\\l be
18,71 feet per second, which is -^^-^^^-^ parts, or a little less
than 6 tenths, or | the velocity ot the water, and the effect
is 199,44 the maximum or greatest possible; and if the
aperture of the gate be 1 foot, the quantity will be 18,71
cubic feet per second. The power being 18,71 cubic
feet expended per second, multiplied by 16 feet the per-
pendicular descent, produces 299,36, and the ratio of the
power and effect being 10 to 6-j\, or as 3 : 2; but this is
sup]:)osing none of the force lost by non-elasticity.

This may appear plainer, if we suppose the water to
descend the tube A B, and, by its pressure, to raise the
water in the tube C D; now it is evident, that if we raise
the water to D, we have no velocity, therefore effect=0.
Then again, if we open the gate at C, we have 32,4 feet
per second velocity, but because we do not hoist the wa-
ter any distance, effect=0. Therefore, the maximum is
somewhere between C and D. Then suppose we open
gates of 1 foot area, at different heights, the velocity v/nl
shew the quantity of cubic fefit raised ; \^ hich multiplied
by the perpendicular height of the gate from C, or
height raised, gives the effect as before, and the maxi-
mum as before. But here we must consider, that in
both these cases the water acts as a perfect definite
quantity, which will produce effects equal to elastic bo-
dies, or equal to its gravity (see art. 59), which is im-
practicable in practice: Whereas, when it acts by per-
cussion only, it communicates only half of its original

Chap. 11.] MECHANICS. 69

force, on account of its non-elasticity, the other half be-
ing spent in splashing!; about (see art. 8); therefore the
true effect will be j-^-^ (a little more than 1-3) of the mov-
ing power; because near 1-3 is lost to obtain velocity,
and half of the remaining 2-3 is lost by non- elasticity.
These are the reasons, why the eifects produced by an
undershot wheel is only half of that produced by an
overshot wheel, the perpendicular descent and quantity
of water being equal. And this agrees with Smeaton's
experiments (see art. 68); but if we suppose the velocity
of the wheel to be one-third that of the water=10,8, and
the load to be 4-9 of 16, the greatest load at equilibrio;
which is=7,lll, as by old theory, then the effect will be
10,8x4,9 of 16=76,79 for the effect, which is quite too
little, the moving power being 32,4 cubic feet of Avater,
multiplied by 16 feet descent=518,4, the effect by this
theory being less than -^-^-^ of the poA^er, about half equal
to the effect by experiment, which effect is set on the
outside of the dotted circle in the fig. (19). The dotted
lines join the corner of the parallelograms, formed by the
lines that represent the loads and velocities, in each ex-
periment or supposition, the areas of which truly repre-
sent the effect, and the dotted line A a d x, meeting the
perpendicular line x E in the point x, forming the paral-
lelogram ABCx, truly represents the power=518,4.

Again, if we suppose the w heel to move with half the
velocity of the water, viz. 16,2 feet per second, and be
loaded with half the greatest load=8, according to War-
ing's theory, then the effect will be 16,2x8=129,6 for
tlie effect, about -^^\ of the power, which is still less than
by experiment. All this seems to confirm the maximum
brought out on the new principles.

But, if we suppose, according to the new principle,
that, when the wheel moves with the velocity of 16,2
feet per second, which is the velocity of a 4 feet head,
that it will then bear as a load the remaining 12 feet,
then the effect will be 16,2x12=194,4, which nearly
agrees with practice: but as most mills in practice
move faster, rather than slower, than what I call the
true maximum, shews it to be nearest the truth, the
true maximum velocity being ,577 of the velocity of the

to MECHANICS. [Chap. 11.

water, and the mills in practice moving with 2-.3, and
generally quicker.*

This scale also establishes a true maximum charge
for an overshot wheel, when the case is such, that the
power or quantity of water on the wheel at once, is al-
ways the same, even although the velocity vary, which
would be the case, if the buckets were kept always full :
for, suppose the water to be shot into the wheel at a, and
by its gravity to raise the whole water again on the oppo-
site side ; then, as soon as the water rises in the wheel
to d, it is evident that the wheel vvill stop, and effect=0 ;
therefore we must let the water out of the wheel, before
it rises to d, which will be in effect to lose part of the
power to obtain velocity. If the buckets both descen-
ding and ascending, carry a column of water 1 foot square,
then the velocity of the wheel will shew the quantity
hoisted as before, which, multiplied by the perpendicular
ascent, shews the effect, and the quantity expended, mul-
tiplied bv the perpendicular descent shows the power;
and we find, that when the wheel is loaded with 2-3 of
the power, the effect will be at a maximum, i. e. the whole
of the water is hoisted, 2-3 of its whole descent, or 2-3 of
the water the whole of the descent, therefore the ratio of
the pcjwerto the effect is as 3 to 2, double to the effect of
an undershot wheel ; but this is, supposing the quantity in

• The reason why the wheel bears so great a load at a maximum, ap-
pears 10 be as follows, viz.

A 16 feet head of water over a gate of 1 foot, issues 32,4 cubic feet of
wuier in a second, to strike the wheel in the same time, that a heavy body
W'il lake up in filling through the height of the head. Now if 16 cubic
feet ofeliistic nnaiter, was to fall 16 feet, and s rike an elastic plane, it wonld
rise by the force of the stroke, to the height from whence it fell; or, in
other words, it will have force sufficient, to bear a load of 16 cubic feet.

Again, if 32 cubic feet of non elastic matter, moving with the same veio-
city, (with vi> hich the 16 feet of elastic matter struck the plane) strike a
w':eel in the same time, alihough it communicate only half the force, that
gave \\ motion; yet, because there is a double quantity striking in the
same time, the effects will be equal, that is, it will bear a load of 16 cubic
feel, or the whole column to hold it in equilibrio.

Again, to check the whole velocity, req lires the whole column, that pro-
duces the velocity, consequently, to check any part of the velocity, will re-
quire such a part of the column that produces the part checked; and we
find by art. 41, that, to check the velocity of the wheel, to be ,577 of the
velocity of the water, it requires 2 3 of the whole column, and this is^the
maximum load When the velocity of the wheel, is multiplied by 2^3 of
the col mn, it produces the effect, which will be to the power, as 38 to
100 ; or as 3,8 to 10. somewhat more than 1-3, and the friction and resist-
ance of the air may reduce it to 1-3.

Chap. 11.} MECHANICS. Ti

tlie buckets to be always the same ; whereas, in overshot
wheels, the quantity in the buckets is inversely as the velo-
city of the u heel, i. e. the slower the motion of the wheel,
the greater the quantity in the buckets, and the greater the
velocity the less the quantity ; but, again, as we are oblig-
ed to let the overshot wheel move with a considerable ve-
locity, in order to obtain a steady, regular motion to the
mill, we will find this charge to be always nearly right x
hence I deduce the following theory.

ART. 4S.

THEORY.

A TRUE THEORY DEDUCED.

This scale seems to have shewn,

1. That when an undershot mill moves with ,577 cd
nearly ,6 of the velocity of the water, it will then bear
a charge, equal to 2-3 of the load, that will hold the
wheel in equilibrio, and then the effect will be at a maxi-
mum. The ratio of the power to the effect will be as S
to 1, nearly.

2. That when an overshot wheel is charged with 2-S
of the weight of the water acting upon the wheel, then
the effect will be at a maximum, i. e. the greatest effect,
that can be produced by said power in a given time, and
the ratio of the power to the effect will be as 3 to 2,
nearly.

3. That 1-3 of the power is necessarily lost to obtain
velocity, or to overcome the vis inertia of the matter, and
this will hold true with all machinery that requires velo-
city as well as power. This I believe to be the true
theory of water-mills, for the following reasons, viz.

1. The theory is deduced from original reasoning,
without depending much on calculation.

2. It agrees better than any other theory, with the in-
genious Smeaton's experiments.

3. It agrees best with real practice, from the best of
my information.

72 MECHANICS. [Chap. IK

Yet I do not wish any person to receive it implicitly,
without first informing himself, whether it be well found-
ed, and agrees with practice : for this reason I have
quoted said Smeaton's experiments at full length, in
this work, that the reader may compare them with the
theory.

true theorem for finding the maximum charge for
undp:rshot wheels

As the square of the velocity of the water or wheel
empty, is to the height of the head, or pressure, v»hich
produced that velocity, so is the square of the velocity
of the wheel, loaded to the head, pressure, or force,
which will produce that velocity ; and this pressure, de-
ducted from the whole pressure or force, will leave the
load moved by the wheel, on its periphery or verge,
which load, multiplied by the velocity of the wheel,
shews the effect.

PROBLEM.

Let V=32,4, the velocity of the water or wheel,

P=16, the pressure, force, or load, at equilibrio,
v=the velocity- of the wheel, supposed to be 16,2

feet per second,
p=the pressure, force or head, to produce said ve-
locity,
l=the load on the wheel.
Then to find 1, the load, we must first find p ;
Then, by

Theorem VV : P::vv:p,
And P— p=l
VVp=vvP
vvP
p=VV=4
l=P—p=12, the load.
Which, in words at lens^th, is, the square of the veloci-
ty of the M heel, multiplied by the whole force, pressure,
or head of the water, and divided by the square of the
velocity of the water, quotes the pressure, force, or head
of water, that is left unbalanced by the load, to produce
the velocity of the wheel, which pressure, force or head,

Chap. ll.J MECHANICS. TS

subtracted from the whole pressure, force or head, leaver
the load that is on the wheel.

ART. 43.

Theorem for finding the velocity of the wheels when xve
have the velocity of the water, Load at equilibrio, and
Load on the wheel given.

As the square root of the whole pressure, force or load
at equilibrio, is to the velocity of the water, so is the
square root of the difference, between the load on the
wheel, and the load at equilibrio, to the velocity of the
wheel.

PROBLEM.

Let V=: velocity of the water=32,4,

P= pressure, force, head, or load at equilibrio=.16',
l=the load on the wheel, suppose 12,
v=velocity of the wheel.

Then by the

Theorem yP: V:: y/P— l:v
And v'Pxv=Vv/P— 1
VyP— 1

v= =-«-=16,2. C The velocity of th€

v'P \ wheel.

That is, in words at length, the velocity of the water
32,4, multiplied by the square root of the difference, be-
tween the load on the wheel, 12, and the load at equili-
brio 16=2=64,8, divided by the square root of the load
at equilibrio, quotes 16,2, the velocity of the wheel.

Now, if we seek for the maximum, by either of these
theorems, it will be found as in the scale, fig. 19.

Perhaps here may now appear the true cause of the
error of the old theory, art. 35, by supposing the load on
the wheel, to be as the square of the relative velocity, of
the water and wheel.

74 MECHANICS. [Chap. 11.

And of the error of what I have called the new the-
ory, by supposing the load to be in the simple ratio of
the relative or striking velocity of the water, art. 38 ;
whereas it is to be found by neither of these propor-
tions.

Neither the old nor new theories agree with practice ;
therefore we may suspect they are founded on error.

But if what I call the true theory, should continue to
agree with practice, the practitioner need not care on
what it is founded.

ART. 44.

Of the Maximum velocity for Overshot Wheels^ or those
that are moved by the weight of the Water.

Before I dismiss the subject of maximums, I think it
best to consider, whether this doctrine will apply to the
motion of the overshot wheels. It seems to be the ge-
neral opinion of those, who consider the matter, that it
will not ; but, that the slower the wheel moves, provided
it be capacious enough to hold all the water, without
losing any imtil it be delivered at the bottom of the
wheel, the greater will be the effect, which appears to
be the case in theory (see art. 36) ; but how far this
theory will hold good in practice is to be considered.
Having met with the ingenious James Smeaton's expe-
riments, where he shews, that, when the circumference
of his little M'heel, of 24 inches diameter, (head 6 inches)
moved with about 3,1 feet per second (although the
greatest effect was diminished about J^ of the whole) he
obtained the best effect, with a steady, regular motion.
Hence he concludes about three feet to be the best ve-
locity for the circumference of overshot mills. See art.
68. I undertook to compare this theory of his, with the
best mills in practice, and, finding that those of about 17
feet diameter, generally moved about 9 feet per second,
being treble the velocity assigned by Smeaton, I be-
gan to doulDt the theory, which led me to inquire into
the principle that moves an overshot wheel, and this 'I

Chap, 11.] MECHANICS. 75

found to be a body descending by its gravity, and sub-
ject to all the laws of falling bodies, (art. 9) or bodies of
descending inclined planes, and curved surfaces (art.
10, 11,) the motion being equably accelerated in the
whole of its descent, its velocity being as the square root
of the distance descended through, and the diameter of
the wheel Avas the distance the water descended through.
From thence I concluded, that the velocity of the cir-
cumferance of the overshot wheels, was as the square
root of their diameters, and of the distance the water has
to descend, if it be a breast or pitch-back wheel : then,
taking Smeaton's experiments, with his wheel of 2 feet
diameter, for a foundation, I say. As the square root of
the diameter of Smeaton's wheel, is to its maximum ve-
locity, so is the square root of the diameter of any other
wheel, to its maximum velocity. Upon these principles
I have calculated the following table ; and, having com-
pared it with at least 50 mills in practice, found it to agree
so nearly with all the best constructed ones, that I have
reason to believe it is founded on true principles.

If an overshot wheel moves freely without resistance,
it will require a mean velocity, between that of the wa-
ter coming on the wheel, and the greatest velocity it
would acquire, by falling freely through its whole de-
scent : therefore this mean velocity will be greater, than
tlie velocity of the water coming on the wheel ; conse-
quently the backs of the buckets will overtake the wa-
ter, and drive a great part of it out of the wheel. But,
the velocity of the water being accelerated by its gravi-
ty, overtakes the wheel, perhaps half way down, and
presses on the buckets, until it leaves the wheel : there-
fore the water presses harder upon the buckets in the
lower, than in the upper quarter of the wheel. Hence
appears the reason why some wheels cast their water,
which is always the case, when the head is not suffi-
cient to give it velocity enough to enter the buckets.
But this depends also much on the position of the
buckets, and direction of the shute into them. It, how-
ever, appears evident that the head of water above the
wheel, should be nicely adjusted, to suit the velocity of

76 MECHANICS. [Chap. II

the wheel. Here we may consider, that the head above
the wheel acts by percussion, or on the same principles
with the undershot wheel, and, as we have shewn (art.
41.) that the undershot wheel should move with nearly
2-3 of the velocity of the water, it appears, that we
should allow a head over the wheel, that will give such
velocity to the water, as will be to that of the wheel as 3
to 2. Thus the whole descent of the water of a mill-
seat should be nicely divided, between head and fall, to
suit each other, in order to obtain the best effect, and a
steady-moving mill. First find the velocity that the
wheel will move with, by the weight of the water, for
any diameter you may suppose you will take for the
wheel, and divide said velocity into two parts ; then try
if your head is such, as will cause the water to come on
with a velocity of 3 such parts, making due allowances
for the friction of the water, according to the aperture.
See art. 55. Then if the buckets and direction of the
shute be right, the wheel will receive the water well, and
move to the best advantage, keeping a steady, regular
motion when at work, loaded or charged with a resistance
equal to 2-3 of its power, (art. 41, 42.)

Chap. 11.]

MECHANICS.

A TABLE

VELOCITIES OF THE CIRCUMFERENCE

OVERSHOT WHEELS,

Suitable to their Diameters, or rather to the Fall, after the Water strikes
the Wheel ; and of the head of Water above the Wheel, suitable to said
Velocities, also of the Number of Revolutions the Wheel will perform iji
a Mmute, when rightly charged

!25

3
n

-i
o

-*>

= 0^

=• _"

• r> ^

- ?

,- ^ D.

els-

1 c

1^^

^^g-

m _ <

3 5-
1-

^ '^ «

3 M

• ^ 3
7 01

-»
•

3,1

3.78

4,38

4,88

5,36

5, 8

6,19

6,57

1,41

1,51

14,3

6,92

1,64

1,74

13,

7,24

1,84

1,94

12,6

7,57

2,2

12,

7,86

2,17

2,47

1154

8,19

2,34

2,74

11.17

8,47

2,49

2,99

10,78

8,76

2,68

3,28

10,4

2, 8

3,5

10,1

9,28

r»
0,0

9,8

9, 5

3,13

4,03

9,54

9,78

3,34

4,34

9,3

10,

3,49

1.05

4,54

10,28

3,76

1,1

4,86

8,9

10, 5

3 84

1,15

4.99

8.7

10, 7

4,97

1,2

5,27

8,5

10,95

4, 2

1,25

'5,45

8,3

11,16

4,27

1,3

5,57

8,19

11,36

4,42

1,35

5,77

8,03

11.54

4,56

3,4

5,96

7,93

11,78

4, 7

1,45

615

7,75

11,99

4, 9

6,4

7,63

78 MECHANICS. [Chap. 11.

This doctrine of maximums is very interesting, and
is to be met with in many occurences through life.

1. It has been shewn, that there is a maximum load
and velocit}' for all engines, to suit the power and velo-
city of the moving power.

2. There is also a maximum size, velocity, and feed
for mill-stones, to suit the power ; and velocity for roll-
ing screens, and bolting-reels, by which the greatest
work can be done in the best manner, in a given time.

3. A maximum degree of perfection and closeness,
with which grain is to be manufactured into flour, so as
to yield the greatest profit by the mill in a day or week,
and this maximum is continually changing with the
prices in the market, so that what would be the greatest
profit at one time, will sink money at another. See
art. 113.

4. A maximum weight for mallets, axes, sledges, &c.
according to the strength of those that use them.

A true attention to the principles of maximums, will
prevent us from runnmg into many errors.

Ghap.l2.] HYDRAULICS, 79

CHAPTER XII.

HYDRAULICS.

UNDER the head of Hydraulics we shall only consi-
der such parts of this science, as immediately relate to
our purpose, viz. such as may lead to the better under-
standing of the principles and powers of water, acting on
mill-wheels, and conveying water to them.

ART. 45.

OP SPOUTING FLUIDS.

%)outing fluids observe the following laws :

1. Their velocities and powers, under equal pressures,
or equal perpendicular heights, and equal apertures, are
equal in all cases.*

2. Their velocities imder different pressures or per-
pendicular heights, are as the square roots of those pres-
sures or heights ; and their perpendicular heights or
pressures, are as the squares of their velocities. f

• It makes no difference whether the water stands perpendicular above
the aperture, or incliningly (see plate III, fig. 22) providing the perpendi-
cular height be the same ; or whether the quantity be great or small, pro-
viding it be sufficient to keep up the fluid to the same height.

t This law is similar to the 4th law of falling bodies, their velocities
being as the square root of their spaces passed through ; and by experi-
ment it is known, that water will spoilt from under a 4 feet head, 16,2 feet
per second, and from under a 16 feet head, 32,4 feet per second, and from
under a 16 feet head, 32,4 feet per second, which is only double to that of
a 4 feet head, although there be a quadruple pressure. Therefore by this
law we can find the velocity of water spou'ing from under any given head ;
for as the square root of 4 equal 2 is to 16,2 its velocity, so is the square
root of 16 equal 4, to 32,4 squared, to 16 its head : by which ratio we cna
find the head that will produce any velocity.

80 HYDRAULICS. [Chap. 12.

3. Their quantities expended through equal apertures,
in equal times, under unequal pressures, are as their ve-
locities simply.*

4. Their pressures or heights being the same, their
effects are as their quantities expended.f

5. Their quantities expended being the same, their
effects are as their pressure, or heighi of their head di-
rectly.|

6. Their instant forces with equal apertures, are as
the squares of their velocities, or as the height of their
heads directly.

7. Their effects are as their quantities, multiplied into
the squares of their velocities. §

* It is evident that a double velocity will vent a double quantity.

f If the pressure be equal, the velocity must be eq al ; and it is evident,
that double quantity, witheqial velocity will produce a double effect.

i That is, if we suppose 16 cubic feet of water to issue from under n 4
feet head in a second, and an equal quantity to issue in the same time
from under 16 feet head, then 'heir effects will be as 4 to 16. But we must
note, that the aperture in the last case must be only half of 'hat in the first,
as the velocity will be double.

§ This is evident from this consideration, viz. that a quadruple impulse
is required to produce a double velocity, by law 2nd, wlitre ihe velocities
are as the square roots of their heads : therefore their effects must be as
the squares of their velocities-

ART. 46.

DEMONSTRATION.

Let A F, (plate III, fig'. 26) represent a head of water 16 feet high, and
suppose it divided into 4 different heads of 4 feet each, as B C D E; ihea
suppose we draw a gate of 1 foot square at each head successively, always
sinking the water in the head, so that it will be but 4 feet above the centre
of the gate in each case.

Now it is known that the velocity under a four feet head, is 16,2 feet per
second; say 16 feet to avoid fractions, which will issue 16 cubic feet of
water per second, and for sake of round numbers, let unity or 1 represent
the quantity of a cubic foot of water ; then, by the 7th lav the effec will be
as the quantity multiplied by the square of the velocity ; that is, 16 mulii-
plied by 16 is equal to 256, which multiplied by 16, the quantity is equal
to 4096, the effect of each 4 feet head ; and 4096 multiplied by 4 is eq al
to 16384, for the sum of effects, of all the 4 feet heads.

Then as the velocity under a 16 feet head is 32,4 feet, say 32 to avoid
fractions ; the gate must be drawn to only half the sizp, to vend the 16 'u-
bic feet of water per second as before (because the velocity is double); ,iitn,
to find the effect, 32 multiplied by 32, is equal to 1024;"which mnltipl ed
by 16, the quantity, gives the effect, 16384, equal the sum of all the 4 teet

Chap. 12.] HYDRAULICS. 8t

head which ag^rees with the practice and experience of the best teachers.
But if their effects were as their velocities simply, then the effect of each 4
feet head would be, 16 multiplied by 16, equal to 256 ; which, multiplied
by 4, is equal to 1024, for tlie sum of the eJlects of all the 4 feet heads;
and 16 multiplied by 32 equal to 512, for the effect of the 16 feet head,
which is only half of the effect of the same head when divided into 4 partsj
which is contrary to both experiment and reason.

Again, let us suppose tlie body A of quantity 16, to be perfectly elastic,
to fall 16 feet and strike V, a perfect el.isiic plane, it will (by laws of fall-
ing bodies) strike with a velocity of 32 feet per second, and rise 16 feet
to A again.

B<it if it fall only to B, 4 feet, it will strike with 16 feet per second, and
rise 4 feet to A ag-ain. Here the effect of the 16 feet fall is 4 times the
effect of the 4 feet fall, because the body rises 4 times the height.

But if we count the effective momentum of their strokes to be as their
velocities simply, then 16 multiplied by 32 is equal to 512, the momentum
of the 16 feet fall; and 16 multiplied by 16 is equal to 256; which, multi-
plied by 4, IS equal to 1024, for the sum of the momentums of the strokes
of 16 feet divided into 4 equal falls, which is absurd. But if we count their
momentums to be as the squares of their velocities, the effects will be
equal.

Again, it is evident that whatever impulse or force is required to give a
body a velocity, the same force or resistance will be required to stop it;
therefore, if the impulse be as the square of the velocity produced, the
force or resistance will be as the squares of the velocity also. But the im-
pulse is as the sqnares of the velocity produced, which is evident from this
consideration, Sfippose we place a light body at the gate B, of 4 feet head,
and pressed with 4 feet of water ; when the gate is drawn it will fly off"
with a velocity of 16 feet per second ; and if we increase the head to 16
feet, it will fly off with 32 feet per second. Then, as the square of 16 equal
to 256 is to the square of 32 equal to 1024, so is 4 to 16. Q. E. D.

ART. 47.

To compare this 7th law with the theory of undershot mills, established
art. 42, where it is shewn that the power is to the effect as 3 to 1 ; then,
by the 7th law, the quantity shewn by the scale, plate II, to be 32,4 mul-
tiplied by 1049,76 the square of the velocity, which is equal to 3401,2124,
the effect of the 16 feet head ; then, for the effect of a 4 feet head, with
equal aperture quantity, by scale, 16,2 multiplied by 262,44. the velocity-
squared, is equal to 425,1528, the effect of a four feet head ; here the ratio
of the effects are as 8 to 1.

Then, by the theory, which shews that an undershot wheel will hoist
1-3 of the water that turns it, to the whole height from which it descended,
the 1-3 of 32,4 the quantity, being equal to 10,8 multiplied by 16, perpen-
dicular ascent, which is equal to 172,8, effect of a 16 feet head : and 1 3 of
16,2 quantity, whicii is equal to 5,4 multiplied by 4, perpendicular ascent,
IS equal to 21,6 effect of 4 feet head, by the theory: and here again the
ratio of the effects are as 8 to 1 ; and,

as 3401,2124, the eff. ct of 16 feet head, 7 . ,.,. ,

is to 425,1528, the effect of 4 feet head,5 ''^ ^'^'^ '*"''

so is 172,8 the effect of 6 feet head, 7 . ., ,.

to 21,6 the effect of 4 feet head, $ ^y ^''* *^^°'>'-
The quantities being equal, their effects are as the height of their heads
direcily,as by5ih law, and as the squ -res of their velocities as by 7th law.
He.jce It appears, that the theory agrees with the established laws, which
I take to be a confirmation that it is well founded.

HYDRAULICS.

[Chap. 12.

8. Therefore their effects or powers with equal aper-
tures, are as the cubes of their velocities.*^

9. Their velocity under any head is equal to the velo-
city that a heavy body would acquire in falling from the
same height. |

10. Their velocity is such under any head or height, as
will pass over a distance equal to twice the height of the
head, in a horizontal direction, in the time that a heavy
body falls the distance of the height of the head.

11. Their action and re-action are equal. ^

12. Their being non-elastic, communicate only half
their real force by impulse, in striking obstacles ; but by

* The effects of striking fluids with equal apertures are as the cubes of
their velocities, for the following reusons, viz. 1st. If an equal quantity strike
with double velocity, the effect is quadruple on that account by the 7th
law; and a double velocity expends a double quantity by 3d law; there-
fore, the effect is amounted to the cube of the velocity. — The theory for
undershot wheels agrees with this law also.

A SCALE

Founded on the 3d, 6th and 7th laws, shewing the effects of striking Fluids,
with different Velocities.

n
c

•c

■a
ft

3
C^
m

cr ~

zr c

•5'

S
p.

cr.

2. ?

£5'

cr
ft

2."^

<
ft

2
3

5IS

• s

i The falling body is acted on by the whole force of its own gravity, in
the whole of its descent through any space ; and the whole sum of this ac-
tion that is acquired as it arrives at the lowest point of its fall, is equal to
the pressure of the whole head or perpendicular height above the issue :
therefore their velocities are equal.

% That is, they re-act back against the penstock with the same force that
it issues against the obstacle it strikes; this is the principle by which Bar-
ker's mills, and all those that are improvements thereon, move-

thap. 12.] HYDRAULICS. 83

their gravity produce effects, equal to elastic or solid
bodies.*

.IppUcatwn of the Laws of Motion to Undershot JVheels.

To give a short and comprehensive detail of the ideas
I have collected from the different authors, and from the
result of my own reasoning on the laws of motion, and
of spouting fluids, as they apply to move undershot mills,
I constructed fig. 44, plate V.

Let us suppose two large wheels, one of 12 feet, and
the other of 24 feet radius, then the circumference of
the largest, will be double that of the smallest : and let
A 16, and C 16, be two penstocks of water, of 16 feet
head, each.

1. Then, if we open a gate of 1 square foot at 4, to
issue from the penstock A 16, and impinge on the small
wheel at I, the water being pressed by 4 feet head, ^vill
move 16 feet per second, (we omit fractions.) The in-
stant pressure or force on that gate, being four cubic
feet of water, it will require a resistance of 4 cubic feet
of water, from the head C 16 to stop it, and hold it in
equilibrio, (but we suppose the water cannot escape un-
less the wheel moves, so that no force be lost by non-
elasticity.) Here equal quantities of matter, with equal
velocities, have their momentums equal.

2. Again, suppose we open a gate of 1 square foot at
A 16 under 16 feet head, it will strike the large wheel
at k, with velocity 32, its instant force or pressure being
16 cubic feet of water, it will require 16 cubic feet re-
sistance, from the head C 16, to stop or balance it. 1\\
this case the pressure or instant force is quadruple, and
so is the resistance, but the velocity only double, to the
first case. In these two cases, the forces and resistances

• When non-elastic bodies strike an obstacle, one half of their force is
spent in a lateral direction, in changing' their figure, or in splashing about.
See art. 8.

For want of due consideration or knowledge of this principle, many have
been the errors committed by applying water to act by impulse, when it
would have produced a double effect by its gravity.

84 HYDRAULICS. [Chap 12.

being equal quantities, with equal velocities, their mo-
mentums are equal.

3. Again, suppose the head C 16 to be raised to E, 16
feet above 4, and a gate draw n -} of a square foot, then
the instant pressure on the float I of the small wheel,
will be 4 cubic feet, pressing on | of a square foot, and
"will exactly balance 4 cubic feet, pressing on 1 square
foot, from the head A 16 ; and the wheel will be in
equilibrio, (supposing the water cannot escape until the
■wheel moves as before), although the one has power of
velocity 32, and the other only 16 feet per second.
Their loads at equilibrio are equal, consequendy their
loads at a maximum velocity and charge, will be equal,
but their velocities different.

Then, to try their effects, suppose, first, the wheel to
move by the 4 feet head, its maximum velocity to be
half the velocity of the water, which is 16, and its maxi-
mum load to half its greatest load, which is 4, by Wa-
ring's theor}- ; then the velocity 16 | 2>cby the load
4 I 2=16, the effect of the 4 feet head, with 16 cubic
feet expended; because the velocity of the water is 16,
and the gate 1 foot.

Again, suppose it to move by the 16 feet head and
gate of I of a foot ; then the velocity 32 | 2xby the
load 4 ( 2=3S, the effect, with but 8 cubic feet expend-
ed, because the velocity of the water is 32, and the gate
but I of a foot.

In this case the instant forces are equal, each being
4; but the one moving a body only I as heavy as the
other, moves with velocity 32, and produces effect 32,
while the other, moving with velocity 16, produces effect
16. A double velocity, with equal instant pressure,
produces a double effect, which seems to be according
to the Newtonian theory. And in this sense the mo-
mentums of bodies in motion are as their quantities,
multiplied into their simple velocities, and this I call the
instant momentums.

But when we consider, that in the above case it was
the quantity of matter put in motion, or water expended,
that produced the effect, we find that the quantity 16,
with velocity 16, produced effect 16; while qu. 8, with

Chap. 12.] HYDRAULICS. 85

velocity 32, produced effect 32. Here the effects are as
their quantities, niultiphed into the squares of their
velocities ; and this I call the effective momentums.

Again, if the quantity expended under each head, had
been equal, their effects would have been 16 and 64,
which is as the squares of their velocities, 16 and 32.

4. Again, suppose both wheels to be on one shaft,
and let a gate of 1-8 of a square foot be drawn at 16 C,
to strike the wheel at k, the head being 16 feet, the in-
stant pressure on the gate will be 2 cubic feet of water,
which is half of the 4 feet head with 1 foot gate, from A
4 striking at I ; but the 16 feet head, with instant pres-
sure 2, acting on the great wheel, will balance 4 feet on
the small one, because the lever is of double length,
and the wheels will be in equilibrio. Then, by Waring's
theory, the greatest load of the 16 feet head being 2,
its load at a maximum will be 1, and the velocity of the
water being 32, the maximum velocity of the wheel will
be 16. Now the velocity 16x1=16, the effect of the 16
feet head, and gate of 1-8 of a foot. The greatest load
of the 4 feet head being 4, its maximum load 2, the ve-
locity of the water 16, and the velocity of the wheel 8,
now 8x2=16, the effect. Here the effects are equal:
and here again the effects are as the instant pressures,
multiplied into their simi)le velocities : and the resistances
that would instantly stop them, must be equal thereto, in
the same ratio.

But v\hen we consider, that in this case the 4 feet
head expended 16 cubic feet of water, with velocity 16,
and produced effect 16; while the 16 feet head expended
only -l cubic feet of water, with velocity 32, and produced
effect 16, we find, that the effects are as their quantities,
multiplied into the squares of their velocities.

And when we consider, that the gate of 1-8 of a square
foot, with velocity 32, produced effects equal to the gate
of 1 square foot, with velocity 16, it is evident, that if
we make the gates equal, the effects will be as 8 to 1 ;
that is, the effects of spouting fluids, with equal apertures,
are as the cubes of their velocities ; because, their instant
forces are as the squares of their velocities by 6th law,
although the instant force of solids are as their velocities,

86 HYDRAULICS. [Chap. 12.

simply, and their eiFects as the squares of their velocities,
a double velocity does not double the quantity of a solid
body to strike in the same time.

ART. 48.
THE HYDROSTATIC PARADOX.

The pressure of fluids is as their perpendicular
heights, without any regard to their (juantity : and their
pressure upwards is equal to their pressure downwards.
In short, their pressure is every way equal, at any equal
distance f^om their surface.*

• To explain whicl», let A B C D, plate III, fig. 22. be a vessel of water of
a Ci'bical form, with a small lube as H, fixed there n; let a hole of the same
size of the tube be made at o, and covered wiih a piece of pliant leather,
nailed ll>ereon, so as to hold the water. Then fill the vessel with water by
the tube H, and it will press upwards agamst the leather, and raise it in a
convex form, requiring just as much weight to press it dou n, as will be
equal to the weight of water in the tube H. Or if we set a glass tube over
the hole at o, and pour water therein, we will find tliat the water in the
tube o, nr.ust be of the same lieight of that in the tube H, beibre the leather
ffill subside, even if the tube O be much larger than H; w-hicli shews, that
the pressHre upwards is equal to the pressure downwards; because the
water pressed up against the leather with the whole weiglit of the water in
the tube H. Again, if we fill 'he vessel by the tube I, it will rise to the
same height in H that it is in I; the pressure being the same in every part
of the vessel as if it had been filled by H ; and the pressure on the bottom
of the vessel will be the same, whether the tube H be of the whole size of
the vessel, or only one quarter of an inch diameter. For suppose H to be
1-4 of an inch diameter, and the whole top of the vessel of leather as at o,
Hnd we powr water down H, it will press the leather up with such force,
that it will require a column of water of the whole size of the vessel, and
height of H, to cause the leather to subside. Q. E. D.

ART. 49.

And again, suppose we make two holes in the vessel, one close to the
bottom, and the other in the bottom, both of one size, the water will issue
with equal velociiy out of each; which may be proved by holding equal
vessels under each, which will be filled in equal time; which shews, that
the pressure on the sides and bottom are equal under equal distances fi'om
the surface. And this velocity will be the same whether the tube be filled
by pipe 1, or H, or by a tube the whole size of the vessel, provided the
perpendicular height be equal in all cases.

From what has been said, it appears, that it makes no difference in the
power of water on mill-wheels, whether it be brought on in an open fore-
bay and perpetidicular penstock, or down an inclining one, as I C ; or under
ground in a close trunk, in any form that may best suit the situation and

€hap. 12.] HYDRAULICS. 87

In a vessel of cubic form, whose sides and bottom are
equal, the pressure on each side is just half the pressure
on the bottom ; therefore the pressure on the bottom and
sides, is equal to three times the pressure on the bottom,*

And in this sense fluids may be said to act, with three
times the force of solids. Solids act by gravity only, but
fluids by gravity and pressure jointly. Solids act with a
force proportional to their quantity of matter ; but fluids
act with a pressure proportional to their altitude only.

ART. 50.

The weight of a cubic foot of water is found by ex-
perience, to be 1000 ounces avoirdupoise, or 62,5Ib.
On these priciples is founded the following

THEOREM.

The area of the base or bottom, or any part of a ves-
sel, of whatever form, multiplied by the greatest perpen-
dicular height of any part of the fluid, above the centre
of the base or bottom, whatever be its position with the
horizon, produces the pressure on the bottom of said
vessel.

PROBLEM L

Given, the length of the sides of the cubic vessel (fig.
22, pi. III.) 6 feet required the pressure on the bottom
when full of water.

Then 6x6=36 feet the area, multiplied by 6, the al-
titude,=216, the quantity or cubic feet of water, press-
ing on the bottom ; which multiplied by 62,5= 135001b.
the whole pressure on the bottom-
circumstances, provided that tlie trunk be large enough to supply the water
fast enough to keep the head from sinking.

This principle of the Hydrostatic Paradox has sometimes taken place m
undershot mills, by pressing up against the bottom of tiie buckets, tlitrebj
destroyingorcounteractinggreat part of the force of impulse- See art. 53-

* For demonstration, see Philosophia P.ritannia

8» HYDRAULICS. [Chap. 12.

PROBLEM IL

Given, the height of a penstock of water, 31,5 feet,
and its dimensions at bottom 3 by 3 feet, inside, requir-
ed the pressure on 3 feet high of one of its sides,

Then, 3x3=9 the area, multipUed by 30 feet, the
perpendicular height or head above its centre=270 cu-
bic feet of water pressing, which x62,5=. 16 8751b. the
pressure on one yard square, which shews what great
strength is required, to hold the water under such great
heads.

ART. 51.

RULE FOR FINDING THE VELOCITY OP SPOUTING WATER.

By experiments it has been found, that water will
spout from under a 4 feet head, with a velocity equal to
16,2 feet per second, and from under 16 feet head, with
a velocity equal to 32,4 feet per second.

On these experiments, and the 2nd law of spouting
fluids, is founded the following theorem, or general rule
for finding the velocity of water under any given head.

THEOREM IL

As the square root of a four feet head (=2) is to 16,2
feet, the velocity of the water, spouting under it, so is the
square root of any other head, to the velocity of the wa-
ter spouting under it.

PROBLEM L

Given, the head of water 16 feet, required the velocity"
of water spouting under it.

Then, as the square root of 4 (=2) is to 16,2, so is the
square root of 16, (=4) to 32,4, the velocity of the wa-
ter under the 16 feet head.

PROBLEM XL

Given, a head of water of 11 feet, required the velocity
of water spouting under it.

Ciiap. 12.] HYDRAULICS. 89

Then, as 2: 16,2:: 3,316: 26,73 feet per second, the
velocity required.

ART. 52,

From, the laws of spouting fluids, theorems I. and II.
the theory for finding the maximum charge and velocity
of undershot wheels, (art. 42) and the principle of non-
elasticity, is deduced the following theorem for finding
the eftect of any gate, drawn under any given head, upon
an undershot water-wheel.

THEOREM III.

Find by theorem I. (art. 50^ the instantaneous pres-
sure of the water, which is the load at equilibrio, and 2-3
thereof is the maximum load, which, multiplied bv ,577
of the velocity of the water, under the given head, (found
by theorem 11.) produces the effect.

PROBLEM.

Given, the head 16 feet, gate 4 feet wide, ,25 of a foot
drawn, required the effect of an undershot wheel, per
second. The measure of the effect to be the quantity,
multiplied into its distance moved, (velocity) or into its
perpendicular ascent.

Then by theorem L (art. 50) 4x,25=l square foot
the area of the gate x 16= 16 the cubic feet pressing;
but, for the sake of round numbers, we call each cubic
foot 1, and although 32,4 cubic feet strike the wheel per
second, yet, on account of non-elasticity, only 16 cubic
feet is the load at equilibrio, and 2-3 of l6 is 10,666,
the maximum load.

Then, by theorem II. the velocity is 32,4, ,577 of
which is=i8,71, the maximum velocity of the wheel
X 10,66, the load= 199,4, the effect.

This agrees with Smeaton's observations, where he
says, (art. 67) " It is somewhat remarkable, that though
the velocity of the wheel, in relation to the velocity of
the water, turn out to be more than 1-3, yet the impulse

90 HYDRAULICS. [Chap. 12.

of the water, in case of the maximum, is more than
double of uhat is assigned by theory ; that is, instead of
4-9 of the column, it is nearly equal to the whole co-
lumn." Hence I conclude, that non-elasticity does not
operate so much against this application, as to reduce
the load to be less than 2-3. And when we consider,
that 32,4 cubic feet of water, or a column 32,4 feet long,
strike the wheel while it moves only 18,71 feet, the ve-
locity of the wheel being to the veloci- y of the water as
577 to 1000, may not this be the reason why the load
is just 2-3 of the head, which brings the effect to be just
,38 (a little more than 1-3 of the power.) This I admit
because it agrees with experiment, although it be difficult
to assigTi the true reason thereof. See annotation, art. -12.
Therefore ,577 the velocity of the water= 18,71, .nul-
tiplied by 2-3 of 16, the whole colum.n, or instantaneous
pressure, pressing on the wheel — art. 50 — which is 10,66,
produces 199,4 the effect. This appears to be the true
effect, and if so, the true theorem will be as follows,
viz.

THEOREM.

Find, by theorem I. art. 50, the instantaneous pres-
sure of the water, and take 2-3 for the maximum load;
multiply by ,577 of the velocity of the water — which is
the velocity of the wheel — and the product will be the
effect.

Then 16 cubic feet, the column, multiplied by 2-3=
10,66, the load which multiplied by 18,71 the velocity
of the wheel, produces 199,4, for the effect; and if we
try different heads and different apertures, we find the
effects to bear the ratio to each other, that is agreeable
to the laws of spouting fluids.

ART. 53.
WATER APPLIED OX WHEELS TO ACT BY GllAVITV.

But when fluids are applied to act on wheels to pro-
duce eflects by their gravity, they act on very different

Chap. 12.] HYDRAULICS. 91

principles, producing double effects, to what they do by
percussion, and then their powers are directly as their
quantity or weight, multiplied into their perpendicular
descent.

DEMONSTRATION.

Let fig. 19, plate III. be a lever, turning on its centre
or fulcrum A. Let the long arm A B represent the
perpendicular descent, 16 feet, the short arm" A D a de-
scent of 4 feet, and suppose water to issue from tiie
trunk F, at the rate of 50lb. in a second, falling into the
buckets fastened to the lever at B. Now, from the prin-
ciples of the lever — art. 16 — it is. evident, that 50!b. in a
second at B, will balance 2001b. in a second, at D, is-
suing from the trunk G, on the short arm ; because
50x16=4x200=800, each. Perhaps it may appear
plainer if we suppose the perpendicular line or diameter
F C, to represent the descent of 16 feet, and the diame-
ter G I a descent of 4 feet. By the laws of the lever —
art. 16 — it is shewn, that, to multiply 50 into its perpen-
dicular descent 16 feet or distance moved, is=200, mul-
tiplied into its perpendicular descent 4 feet, or distance
moved; that is, 50xl6=200x'i=800 ; that is, their
power is as their quantity, multiplied into their perpen-
dicular descent ; or in other words, a fall of 4 feet u ill
require 4 times as much water, as a fall of 1(5 feet, to
produce equal power and effects. Q. E. D.

Upon these principles is founded the following simple
theorem, for measuring the po^^■er of an undershot mill,
or of a quantity of water, acting upon any mill-wheel by
its gravit}'.

THEOREM IV.

Cause the water to pass along a regular canal, and
multiply its depth in feet and parts, by its width in feet
and parts, for the area (jf its section, which product
multiply by its velocity per second in feet and parts, and
the product is the cubic feet used per second, which
multiplied by 62,51b. tlie weight of 1 cubic foot, pro-

92 HYDRAULICS. [Chap. 12

duces the weight of water per second, that falls on the
wheel, which multiplied by its whole perpendicular de-
scent, gives a true measure of its power.

PROBLEM L

Given, a mill seat with 16 feet fall, width of the canal
5,333 feet, depth 3 feet, velocity of the water passing
along it 2,03 feet per second, required the power per
second.

Then, 5,333x3=15,999 feet, the area of the section
of the stream, multiplied by 20,3 feet, tlie velocity, is
equal 82,^ cubic feet, the quantity per second, multiplied
by 65,5 is equal :^025lb. the weight of the water per se-
cond, multiplied by 16, the perpendicular descent, is
equal 32400, for the power of the seat per second.

PROBLEM IL

Given, the perpendicular descent 18,3, width of the
gate 2,66 feet, height ,145 of a foot, velocity of the wa-
ter per second, issuing on the wheel 15,76 feet, required
the power.

Then, 266x,145=,3857 the area of the gate, x 15,76
the vel()city=6,178 cubic feet, expended per second
x62,5=375,81b. per second xl8,3 feet perpendicular
desceiit=6877 for the measure of the power per second,
which ground 3,75lb. per minute, equal 3,75 bushels in
an hour, \vith a five feet pair of burr stones.

ART. 54.

INVESTfGxVTION OF THE PRINCIPLES OF OVERSHOT MILLS,

Some have asserted, and many believed, that' water is
applied to great disadvantage on the principle of an over-
shot mill ; because, say they, there are never more than
two buckets, at once, that can be said to act fairly on
the end of the lever, as the arms of the wheel are called
in these arguments. But we must consider well the laws
of bodies descending inclined planes, and curved sur-
faces. See art. 10, 11. This matter will be cleared up,

Chap. 12.] HYDRAULICS. 93

if we consider the circumference of the wheel to be the
curved surface : for the fact is, tliat the water acts to
the best advantage, and produces effects equal to what
it would, in case the whole of it acted upon the very end
of the lever, in the whole of its perpendicular descent.*

DEMONSTRATION.

Let A B C, Plate III. fig. 20, represent a water-wheel,
and F H a trunk, bringing water to it from a 16 feet head.
Now suppose F G and 16 H to be two penstocks under
equal heads, down which the water descends, to act on
the wheel at C, on the principle of an undershot, on op-
posite sides of the float C, with equal apertures. Now
it is evident from the principles of hydrostatics, shewTi by
the paradox, (art. 48, and the first law of spouting fluids
art. 45,) that the impulse and pressure will be equal
from each penstock respectively. Although the one be
an inclined plane, and the other a perpendicular, their
forces are equal, because their perpendicular heights are ;
(art. 4?8) therefore the wheel will remain at rest, because
each side of the float is pressed on by a column of water
of equal size and height, as represented by the lines on
each side of the float. Then suppose we shut the pen-
stock F G, and let the water down the circular one r x,
which is close to the point of the buckets ; this makes it
obvious, from the same principles, that the wheel will be
held in equilibrio, if the columns of each side be equal.
For, although the column in the circular penstock, is
longer than the perpendicular one, yet, because part of
its weight presses on the lower side of the penstock, its
pressure on the float is only equal to the perpendicular.

Then, again, suppose the column of water in the cir-
cular penstock, to be instantly thrown into the buckets,
it is evident, that the wheel will still be held in equilibrio,
and each bucket will then bear a proportional part of
the column, that the bucket C bore before ; and that
part of the weight of the circular column, which rested
on the under side of the circular penstock, is now on the

* This error has been the cause of many expensive errors in the appli-
cation oF water.

94 HYDRAULICS. [Chap. 12.

gudgeons of the wheel. This shews that the effect of a
stream, applied on an overshot wheel, is equal to the
effect of the same stream, applied on the end of the lever,
in its whole perpendicular descent, as in fig. 21, where
the water is shot into the buckets fastened to a strap or
chain, revolving over two wheels; and here the whijle
force of the gravity of the column acts on the very end
of the lever, in the whole of the descent. Yet, because
the length of the column in action, in this case, is only
16 feet ; whereas on a 16 feet wheel the length of the
column in action is 25,15, therefore the powers are
equal.

Again, if we divide the half circle into 3 inches Ab,
be, eC, the centre of gravity of the upper and lower
arches, will fall near the point a, 3,9 feet from the centre
of motion, and the centre of gravity of the middle arch,
near the point o, 7,6 feet from the centre of motion. Now
each of these arches is 8,38 feet, and 8,38x2x3,9=6.^,36,
and 8,38x7,6 feet=63,07, which two products added=
128,13, for the momentum of the circular column, by
the laws of the lever, and for the perpendicular column
16x8 the radius of the wheel=128, for the momentum ;
by which it appears, that if we could determine the exact
points on which the arches act, the momentums would
be equal, all which shews, that the power of water on
overshot wheels, is equal to the whole power it can any
way produce, through the M^hole of its perpendicular
descent, except what may be lost to obtain velocity, (art.
41) overcome friction, or by part of the water spilling,
before it gets to the bottom of the wheel. Q. E. D.

I may add, that I have made the following experi-
ment, viz. I fixed a truly circular wheel on nice pivots,
to evade friction, and took a cylindric rod of thick wire,
cutting one piece exactly the length of half the circum-
ference of the wheel, and fastening it to one side, close
to the rim of the wheel its whole length, as at G x r a. I
then took another piece of the same wire, of a length
equal to the diameter of the wheel, and hung it on the
opposite side, on the end of the lever or arm, as at B.,
and the wheel was in equilibrio. Q. E. D.

Chap. 12.J HYDRAULICS. 95

ART. 55.

OF THE FRICTION OF THE APERTURES OF SPOUTING FLUIDS.

The doctrine of this species of friction appears to be
as follows;

1. The ratio of the friction of round apertures, are as
their diameters, nearly, while their quantities expended,
are as the squares of their diameters.

2. The friction of an aperture, of any regular or irre-
gular figure, is as the length of the sum of the circum-
scribing lines, nearly ; the quantities being as the areas
of the aperture.* Therefore,

3. The less the head )r pressure, and the larger the
apertnre, the less the ratio of the friction; therefore,

4. This friction need not be much regarded, in the
large openings or apertures of undershot mills, where
the gates are from 2 to 15 inches on their shortest sides ;
but it very sensibly affects the small apertures of high
overshot or under hot mills, with great heads, where
their shortest sides are from five-tenths of an inch to two
inches.f

ART. .56.
OF THE PRESSURE OF THE \IR ON FLUIDS.

The second cause of the motion or rise of fluids, is
the pressure of the air on the surface of them, in the

• This will .-^pp -ar, if we consWler ami suppose, that the friction does
sensibly retard the velocity of ih>- fluid to a certain distance. Say halt an
inch from the side or edge of the aperture, towards its centre ; and we
may reasonably coiicliiiie, that this distance will be nearly the same in a 2
and 12 inch apertme; so that in tlie 2 inch aperture, a ring on the out-
side, half an inch wide, is sensibly retarded, which is about 3-4 of ;he
whole ; while, in t|it- 12 inch pe lure, there is a ring on the outside half
an inch wide, retarded about 1 6 of its ^vhoie area.

t This seems to tf proved by S'lieaion, in h s experiments; (see table,
art. 67 ) where, when the heail w .s 33 nchts, the sluice small, dra^vnonly
to the 1st hole, the velocity was only such as is assigned by iheory, to a
head of 15,85 inches, which hf call.-, virtual head- But when the sluice was
larjjer, drawn to the 6 h hole, and head 6 inches, the virtual head was 5,33
inches. But seeing there is no theorem yet discovered by which we can
truly de'ermine the quantity or efiec of their friction, according to the
size of the aperture, and height of the head ; therefoie, we cannot, by the
established laws of hydrostatirs, df 'ermine exa tly 'he velocity or quan-
tity expended ihrotigh any bmall apevmre; which renders the theory but
little belter than conjecture in these cases.

96 HYDRAULICS. [Chap. 12.

fountain or reservoir; and this pressure is equal to a
head of water of 33 1-3 feet perpendicular height, under
which pressure or height of head, the velocity of spout-
ing water is 46,73 feet per second.

Therefore, if we could by any nleans take off the
pressure of tlie atmosphere, from any one part of the
surface of a fluid, that part would spout up with a velo-
city of 46,73 feet per second, and rise to the height of
33 1-3 feet nearly.^

On this principle act all syphons or cranes, and all
pumps for raising water by suction, as it is called. — Let
fig. 23, pi. in. represent a cask of water, with a syphon
therein, to extend 33 1-3 feet above the surface of the
water in the cask. Now if the bung be made perfectly
air-tight, round the syphon, so that no air can get into
the cask, and the cask be full, then, if all the air be
drawn out of the syphon, at the bended part A, the fluid
will not rise in the syphon, because the air cannot get
to it to press it up ; but take out the plug P, and let the
air into the cask, to press on the surface of the water,
and it will spout up the short leg of the syphon B A,
with the same force and velocity, as if it had been press-
ed with a head of water 33 1-3 feet high, and will run
into the long leg and will fill it. Then if we turn the
cock c, and let the water run out, its weight in the long
leg will overbalance the weight in the short one, drawing
the water out of the cask until the water sink so low,
that the leg B A will be 33 1-3 feet high, above the sur-
face of the water in the cask ; then it will stop, because
the weight of water in the leg, in which it rises, will be
equal to the weight of a column of the air of equal size,
and of the whole height of the atmosphere. The waiex
will not run out of the leg A c, but will stand full 33 1-3

• This seems to be the principle of whirlwind* at sea, called water
spouts; the wind meeting- from different points, forms a qiMck circiilai*
motion; and by the centrifugal force forms a partial vacuum in the cen-
tre, which gives liberty to the water to rise a little, which is by the rapid-
ity of the motion of the air, rent into very small particles : which so in-
creases the surface, that the air takes sufficient hold of it to carry it up.
And as the wind meeting has no way to vent itself but in a perpendicular
direction, therefore, a brisk current is formed upwards, carrying th( wa-
ter with it, at sea; but on the land, it raises leaves of trees and other
light bodies. See Franklin's Letters.

Chap. 12.] HYDRAULICS. 97

feet above its mouth, because the air will press up the
mouth c, with a force that will balance 30 1-3 feet of
water in the leg c A. This will be the case, let the up-
per part of the leg be any size whatever — and there will
be a small vacuum in the top of the long leg.

ART. 57.
OF PUMPS.

Let fig. 24, pi. in. represent a pump of the common
kind used for drawing water out of wells. The move-
able valve or bucket A, is cased with leather, which
springs outwards, and fits the tube so nicely, that neither
air nor water can pass freely by it. When the lever L
is worked, the valve A opens as it descends, letting the
air or water pass through it. As it ascends again the
valve shuts ; the water which is above the bucket A is
raised, and there would be a vacuum between the
valves, but the weight of the air presses on the surface
of the water in the well, at W, forcing it up through the
valve B, to fill the space between the buckets : and as
the valve A descends, B shuts, and prevents the water
from descending again : But if the upper valve A be
set more than 33 1-3 feet above the surface of the water
in the well, the pump cannot be made to draw, because
the pressure of the atmosphere will not cause the water
to rise more than 33 1-3 feet.

HYDRAULICS.

[Chap. 12

A TABLE FOR PUMP.MAKERS.

Height of the

Diameter of

Water discharged

pump in feet

the bore.

in a minute m

above the snr-

wine measure.

face of the

3 a (-5

well.

1 pans
1 inch.

i
ches.

81 6

6 93

5 66

54 4

4 90

40 7

4 38

32 6

4 GO

27 2

3 70

23 3

3 46

20 3

3 27

18 1

3 10

16 3

2 95

14 7

? 84

13 5

2 72

12 4

2 62

11 5

2 53

10 r

2 45

10 2

2 38

9 5

2 31

9 1

2 25

8 5

" 100

2 19

8 1

" All pnmps should be so constructed as to work with equal ease, in
raising the water to any {jiven heijihi above the surface of the well and
this may be done by observing a due proportion between the diameter of
that part of the piim'p'bore in which the piston or bucket works, and the
height to which the water must be raised.

" For this purpose I have calculated the above table, in which the handle
of the pump is ssipposed to be a lever, increasing the power five limes :
that is, the distance or length of that part of the handle that lies between
the pin on which it moves, and the top of the pumprod to which it is fix-
ed, to be only one fifth part of the length of the handle, from the said pin
to the part where the man (who works the pump) applies his force or
power.

" In the first column of the table, find the height at which the pump
must discharge the water above the surface of the well ; then in the second
column, you have the diameter of that part of the bore in which the pis-
ton or bucket works, in inches and hundredth parts of an inch; in the
third column is the quantity of water, (in mine weasure) that a man of
common strength can raise in a minute — And by constructing according
to this method, pumps of all heights may be vi'roni^ht by a man of ordinary
streiiKlh so as to be able to hold out for an hour."

JAMES FERGUSON.

Chap. I2.j HYDRAULICS. 99

ART. 58.

OF CONVEYING WATER ^NDER VALLEYS AND OVER HILLS,

Water, by its pressure, and the pressure of the atmos-
phere, may be conveyed under valleys and over hills, to
supply a family, a mill, or a town. See fig. 20, pi. III.
F H is a canal for conveying water to a mill-wheel.
Now let us suppose F G 16 H to be a tight tube or
trunk — the water being let in at F, it will descend from
F to G, and its pressure at F will cause it to rise to H,
passing along if permitted, and may be conveyed over a
hill by a tube, acting on the principle of the syphon,
(art. 56.) But w'here some have had occasion thus to
convey water under any obstacle for the convenience of
a mill, which often occurs in practice, they have gone
into the following expensive error : They make the tube
at G 16 smaller than if it had been on a level, because,
say they, a greater quantity will pass though a tube,
pressed by the head G F, than on a level. But they
should consider that the head G F is balanced by the
head H 16, and the velocity through the tube G 16 will
only be such that a head equal to the difference between
tlie perpendicular height of G F and H 16 would give it;
(see art. 41, fig. 19,) therefore it should be as large at G
16 as if on a level.

ART. 59.

OF THE DIFFERENCE OF THE FORCE OF INDEFINITE AND DE-
FINITE QUANTITIES OF WATER STRIKING A Vv^HEEL.

DEFINITIONS.

1. By an indefinite quantity of water we here mean a
river or large quantity, much larger than the float of the
Avheel, so that, when it strikes the float, it has liberty to
move or escape from it in every lateral direction.

100 HYDRAULICS. [Chap. 12.

2. By a definite quantity of water we mean a quantity
passing throus^h a given aperture along a shute to strike
a wheel ; but as it strikes the float, it has liberty to escape
in every lateral direction.

3. By a perfectly definite quantity, we mean a quan-
tity passing along a close tube so confined, that when it
strikes the float, it has not liberty to escape in any lateral
direction.

First, When a float of a wheel is struck by an indefi-
nite quantity, the float is struck by a column of water,
the section of which is equal to the area of the float ; and
as this column is confined on every side by the sur-
rounding water, which has'tqual motion, it cannot escape
freely sideways ; therefore more of its force is commu-
nicated to the float than would be, in case it had free li-
berty to escape sideways in every direction.

Secondly, The float being struck by a definite quan-
tity, with liberty to escape freely in every side direction,
it acts as the most perfect non- elastic body ; therefore
(by art. 8) it communicates only a part of its force, the
other part being spent in the lateral direction. Hence it
appears, that in the application of water to actiDy im-
pulse, we should draw the gate as near as possible to the
float- board, and confine it as much as possible from
escaping sideways as it strikes the float ; but, taking
care at the same time, that we do not bring the principle
of the Hydrostatic Paradox into action, (art. 48.)

What proportion of the force of the water is spent in
a lateral direction is not yet determined, but see Art. 8.

4. A perfectly definite quantity striking a plane, com-
municates its whole force ; because no part can escape
sideways, and is equal in power to an elastic body, or
the weight of the water on an overshot wheel, in its
whole perpendicular descent. But this application of
water to wheels has been hitherto impracticable ; for
whenever we attempt to confine the water totally from
escaping sideu ays, we bring the paradoxical principle into
action, which defeats the scheme.*

• But this difficulty is no^v overcome by the valve wheel. See annotation,
art. 7\i.

Chap. 12.] HYDRAULICS. 101

To make this plain, let fig. 25, pi. III. be a water-
wheel ; and first, let us suppose the water to be brought
to it by the penstock 4.16, to act by impulse on the float
board, having free liberty to escape every uay as it strikes;
then by art. 8, it will communicate but half its force.
But if it be confined both at sides and bottom and can
escape only upwards, to which tlie gravity will make
some opposition, it will communicate perhaps more than
half its force, and will not re-act back against the float
c. But if we put soaling to the wheel' to prevent the
water from escaping upwards, then the space between
the floats will be filled, as soon as the wheel begins to
be retarded, and the paradoxical principle, art. 48, is
brought fully into action viz. the pressure of water is
every way equal, and presses backwards against the bot-
tom of the float c, with a force equal to its pressure on
the top of the float b, and the wheel will immediately stop
and be held in equilibrio, and will not start again although
all resistance be removed. This we may call the para-
doxical mill. There are many mills, where this principle
is, in part, brought into action, which very much lessens
their power.

ART. 60.
OF THE MOTION OF BREAST AND PITCHBACK WHEELS.

Many have been of opinion, that when water is put to
act on the wheel as at a (called a low breast) with 12
feet head, that then the 4 feet fall below the point of
impact a, is totally lost, because, say they, the impulse
of the 12 feet head, will require the wheel to move with
such velocity to suit the motion of the water as to move
before the action of gravity, therefore the water cannot
act after the stioke. But if they will consider well the
principles of gravity acting on falling bodies (art. 9),
they will find, that, if the velocity of a falling body be

1£)2 HYDRAULICS. [Ghap. 12.

ever so great, the action of gravity is still the same to
cause it to move faster, so that, although an overshot
wheel may move before the power of the gravity, of the
water thereon, yet no impulse downwards can give a
wheel such velocity, as that the gravity of the water act-
ing thereon can be lessened thereby.*

Hence it appears, that when a greater head is used,
than what is necessary to shoot the water fairly into the
wheel, the impulse should be directed downward a little
as at D, (which is called pitch-back,) and have a cir-
cular sheeting to prevent the water from leaving the
wheel, because if it be shot horizontally on the top of a
wheel, the impulse in that case will not give the water
any greater velocity downwards ; then, in this case, the
fall would be lost, if the head was very great, and the
wheel moved to suit the velocity of the impulse, the
water would be thrown out of the buckets by the centri-
fugal force ; and if we attempt to retard the wheel, so as
to retain the water, the mill will be so ticklish and unstea-
dy, that it will be almost impossible to attend it.

Hence may appear the reason why breast-wheels ge-
nerally run quicker than overshots, although the fall after
the water strikes be not so great.

1. There is generally more head allou^ed to breast-
mills than overshots, and the wheel will incline to move
with nearly 2-3 the velocity of the water, spouting from
under the head, (art. 41.)

2. If the water was permitted to fall freely after it
issues from the gate, it would be accelerated by the fall,
so that its velocity at the lowest point would be equal
to its velocity, had it spouted from under a head equal
to its whole perpendicular descent. This accelerated
velocity of the water, tends to accelerate the wheel;
hence, to find the velocity of a breast- wheel, where the
water is struck on in a tangent direction as in fig. 31,
32, I deduce the following

* if gravity could be either decreased by velocity downwards, or increased
by velocity upwards, then a vertical wheel without friction, either of gud-
geons or air, would require a great force to continue its motion ; because,
its velocity would decrease the gravity of its descending side, and increase
it on its ascending side, which would immediately stop it : whereas it is
known, that it requires no power to continue its motion, but what is neces-
sary to overcome the friction of the gudgeons, &c.

Chap. 12.] HYDRAULICS. 103

THEOREM.

1. Find the difference of the velocity of the water
under the head allowed to the wheel, above the point of
impact, and the velocity of a falling body, having fell
the whole perpendicular descent of the water. Call
this difference the acceleration by the fall : Then say,
As the velocity of a falling body acquired in falling
tlirough the diameter of any overshot wheel, is to the
proper velocity of that wheel by the scale, (art. 43) so
is the acceleration by the fall, to the acceleration of the
wheel by the fall, after the water strikes the wheel.

2. Find the velocity of the water issuing on the
wheel ; take ,577 of said velocity , to which add the
accelerated velocity, and that sum will be the velocity
of the breast- wheel.

This rule will hold nearly true, when the head is con-
siderably greater than is assigned by the scale (art. 43) ;
but as the head approaches that assigned by the scale,
tliis rule will give the motion too quick.

EXAMPLE.

Given, a high breast-wheel, fig. 25, where the water
is shot on at d, the point of impact — 6 feet head, and
10 feet fall — required the motion of the circumference
of the wheel, working to the best advantage, or maxi-
mum effect.
Then, the velocity of the water, issuing ? i q q^ p

on the wheel, 6 feet head, 5 ^^'"^^ *^^^-

The velocitv of a falling body, having 16 2. qo a ri

feet fall, the whole descent, 5 ^^'^ ^°'

Difference, - - 13,06 do.

Then, as the velocity under a 16 feet fall (32,4 feet)
is to the velocity of an overshot wheel=8,76 feet, so is
13,06 feet, to the 16 feet diameter velocity accelerated,
which is equal 3,5 feet, to which add, 577 of 19,34 feet
(being 11,15 feet); this amounts to 14,65 feet per second,
^he velocity of the breast-wheel.

104 HYDRAULICS. [Chap. U,

ART. 61.

RULE FOR CALCULATING THE POWER OF ANY MILL-SEAT.

The only loss of power sustained by usinj; too much
head, in the application of- water to turn a mill-wheel,
is from the head producing only half its po\ver. There-
fore, in calculating the power of 16 cubic feet per se-
cond, on the different applications of fig. 25, pi. III. we
must add half the head to the whole fall, and count that
sum the virtual perpendicular descent. Then by theo-
rem IV. (art. 53) multiply the weight of the water per
second by its perpendicular descent, and you have the
true measures of its power.

But to reduce the rule to a greater simplicity, let us
call each cubic foot 1, and the rule will be simply this —
Multiply the cubic feet expended per second, by its vir-
tual perpendicular descent in feet, and the product will
be a true measure of the power per second. This mea-
sure must have a name, which I call Cuboch ; that is,
one cubic foot of water, multiplied by one foot descent,
is one cuboch, or the unit of power.

EXAMPLES.

1. Given, 16 cubic feet of water per second, to be
applied by percussion alone, under 16 feet head, re-
quired the power per second.

Then, half 16=8x16=128 cubochs, for the measure
of the power per second.

2. Given, 16 cubic feet per second, to be apj^lied to
a half breast of 4 feet fall and 12 feet head, required the
power.

Then, half 13=6+4=10x16=160 cubochs, for the
power.

3. Given, 16 cubic feet per second, to be applied to a
pitch-back or high breast — fall 10, head 6 feet, required
the power.

Chap. 12.] HYDRAULICS. 1(^5

Then, half 6=3+13=10xl6=S08 cubochs, for the
power per second.

4. Given, 16 cubic feet of water per second, to be
applied as an ov^ershot^ — head 4, fall IS feet, required the
power.

Then, half 4=3+ 1 2=1 4x 16=231 cubochs, for the
power.

The powers of equal quantities of water 16 cubic feet
per second, and equal total perpendicular descents by the
different applications, stand thus :

C 16 feet head,*
The undershot, < fall,

(128 cubochs of power.
C 12 feet head,
The half breast, < 4 feet fall,

( 160 cubochs of power.
C 6 feet head,
The high breast, < 10 feet fall,

( 208 cubochs of power.
C 4 feet head,
The overshot, < 12 feet fall,

( 224 cubochs of power-
C 2,5 feet head.
Ditto, < 31,5 feet fall,

{ 263 cubochs of power.
The last being the head necessary to shoot the watei;
feirly into the buckets, may be said to be the best appli-
cation. See art. 43.

• Water by percussion spends its force on the wheel in the following^
time, which is in proportion to the distance of the float-board, and diffcF-
cnce of the velocity of the water and wheel.

If the water runs wit!) double the velocity of the wheel, it will spend
all its force on the floats, while the water runs the distance of two float-
boards, and while the wheel runs the distance of one ; therefore the water
need not be kept to act on the wheel from the point of impact further than
the distance of about two float-boards.

But if the wheel runs with two-thirds of the velocity of the water, then,
while the wheel runs the distance of two floats, and while the water would
have ran the distance of three floats, it spends all its force ; therefore the
water need be kept to act on the wheel only the distance of three floatf
past the point of impact.

If it be continued in much longer it will fsdl back, and re-act against the
following' bucket and retard the wheel.

106

HYDRAULICS.

[Chap. 12.

On these simple rules, and the rule laid down in art.
43, for proportioning the head and fall, I have calculated
the following table or scale of the different quantities of
water expended per second, with different perpendicular
descents, to produce a certain power, in order to present
at one view to the reader the ratio of increase or decrease
of quantity, as the perpendicular descent increases or
decreases.

A TABLE

Shewin.^ the quantity of water required with different falls, to produce by-
its gravity, 112 ciitiochs of power, wliich will drive a five feet stone about
^7 revolutions in a minute, grinding wheat about 5 bushels in an hour

-• S5 s s"

-..»«-

cr
n

01 Cl^ rj- <

s n

q- ft ft -

"■

c ^

5: =35 0.

ft 5:

esce
half
the

e wl

3 5

9-^

3 ft
CL ->

— -*- r» 3

9? -■

"" -•- r- —

• -5

?.£^;

►5

■ p: rr -^

p- ^ "**

^ t ^

•^

"♦: ft ^-

•-;

Q »: ~

n s" ^

-: O-ns

Tit

112

6,58

2.7,3

6,y2

5,99

224

5,6

18,6

5,33

16,

5,1

4,87

12,4

4,66

11,2

4,48

10,2

4,3

9,33

4,15

8,6

3,86

7,46

•^,7i

ART. 62.
THEORY AND PRACTICE COxMPARED.

I will here give a table of 18 mills in actual practice
out of about 50 that I have taken an account of, in order

6hap. 12.] HYDRAULICS. lOr

to compare theory with practice, and in order to ascer-
tain the power required on each superficial foot of the
acting parts of the stone : But I must premise the fol-
lowing

THEOREMS.

1. To find the circumference by the diameter, or the
diameter by the circumference of a circle given ; say.

As 7 is to 22, so is the diameter of the stone to the cir-
cumference, i. e. Multiply the diameter by 22, and di-
vide the product by 7, for the circumference ; or, multi-
ply the circuniference by 7, and divide the product by
22, for the diameter.

2. To find the area of a circle by the diameter given :
As 1, squared, is to ,7854, so is the square of the diaaie-
ter to the area ; i. e. Multiply the square of the diameter
by ,7854, and deduct 1 foot for the eye, and you have
the area of the stone.

3. To find the quantity of surface passed by a mill-
stone : The area, squared, multiplied by the revolutions
of the stone, gives the number of superficial feet, passed
in a given time.

OBSERVATIONS ON THE FOLLOWING TABLE OF EXPERIMENTS.

I have asserted in art. 44, that the head above the gate
of a wheel, on which the water acts by its gravity, should
be such, as to cause the water to issue on the wheel,
with a velocity to that of the wheel as 3 to S, to compare
this with the following table of experiments.

1. Exp. Overshot. Velocity of the water 12,9 feet
per second, velocity of the wheel 8,S feet per second,
which is a little less than 3-3 of the velocity of the wa-
ter. This wheel received the water well. It is at Stan-
ton, in Delaware state.

2. Overshot. Velocity of the water 11,17 feet per
second, S-3 of which is 7,44 feet, velocity of the wheel
8,5 feet per second. This received the water pretty
well. It is at the above-mentioned place.

3. Overshot. Velocity of the water 13,16 feet per
second, velocity of the wheel 10,3 ; throws out great

108 HYDRAULICS. [Chap. 1^.

part of the water by the back of the buckets ; strikes it
and makes a thumping noise. It is allowed to run too
fast ; revolves faster than my theory directs. It is at
Brandywine, in Delaware state.

4. Overshot. Velocity of the water 14,4 feet per se-
cond, velocity of the wheel 9,3 feet, a little less than 2-3
of the velocity of the water. It receives the water very
well ; has a little more head than assigned by theory,
and runs a little faster ; it is a very good mill, situate at
Brandywine, in the state of Delaware.

6. Undershot. Velocit}' of the wheel, loaded, 16, and
when empty 24 revolutions per minute, which confirms
the theory of motion for undershot wheels. See art. 42.

7. Overshot. Velocity of the water 15,79 feet, velo-
cit}' of the wheel 7,8 feet ; less than 3-3 of the velocity
of the water ; motion slower and head more than as-
signed by theory. The miller said the wheel ran too
slow, and would have her altered ; and that she worked
best \\hen the head was considerably sunk. She is at
Bush, Hartford county, Maiyland.

8. Overshot. Velocity' of the water 14,96 feet per
second, velocity of the wheel 8,8 feet, less than 2-3, very
near the velocity assigned by the theory ; but the head
is greater, and she runs best when the head is sunk a
little ; is counted the best mill ; and is at the same place
with the last mentioned.

9. 10, 11, 12. Undershot, open wheels. Velocity of
the wheels when loaded 20 and 40, and when empty 28
and 56 revolutions per minute, which is faster than my
theory for the motion of undershot mills. Ellicott's
mills, near Baltimore, in Maryland, serve to confirm the
theor}'.

14. Overshot. Velocity of the water 16,2 feet, velo-
city of the wheel 9,1 feet, less than 2-3 of the water,
revolutions of the stone 114 per minute, the head near
the same as by theory, the ^•elocity of the wheel less,
stone more. This shev\s her to be too high geared.
She receives the water well, and is counted a very good
mill, situate at Alexandria, in Virginia.

15. Undershot. Velocity of the water 24,8 per se-

Chap. 12.J HYDRAULICS. 109

cond, velocity of the wheel 16,67 feet, more than S-8 the
velocity of the water. Three of these mills are in one
house, at Richmond, Virginia — they confirm the theory
of undershots, being very good mills.

16. Undershot. Velocity of the water 25,63 feet per
second, velocity of the wheel 19,05 feet, being more than
2-3. Three of these mills are in one house, at Peters-
burg, in Virginia — they are very good mills, and confirm
the theory. See art. 43.

18. Overshot wheel. Velocity of the water 11,4 feet
per second, velocity of the wheel 10,96 feet, nearly as
fast as the water. The backs of the buckets strike the
water, and drive a gi'eat part over : and as the motion
of the stone is about right, and the motion of the wheel
faster than assigned by the theory, it shews the mill to
be too low geared, all which confirms the theory. See
art. 43.

In the following table I have counted the diameter of
the mean circle to be two-thirds of the diameter of the
great circle of the stone, which is not strictly true. The
mean circle to contain half the area of any other circle
must be ,707 parts of the diameter of the said circle, or
nearly ,7 or 2-3.

Hence the following theorem for finding the mean cir-
cle of any stone.

THEOREM.

Multiply the diameter of the stone by ,707, and it pro-
duces the diameter of the mean circle.

EXAMPLE.

Given, the diameter of the stone 5 feet, required a
mean circle that shall contain half its area.

Then, 5 x, 707=3,535 feet the diameter of the mean
circle.

110 HYDRAULICS. [Chap 12.

ART. 63.

FURTHER OBSERVATIONS ON THE FOLLOWING TABLE.

1. The mean power used to turn the 5 feet stones in
the experiments (No. 1. 7. 14. 17.) is 87,5 cubochs of
the measure established art. 6, and the mean velocity is
104 revolutions of the stones in a minute, the velocity of
the mean circle being 18,37 feet per second, and their
mean quantity ground is 3,8lb. per minute, which is 3,8
bushels per hour, and the mean power used to each foot
of the area of the stone is 4,69 of the measure aforesaid,
done by 36582 superficial feet passing each other in a
minute. Hence we may conclude, until better informed,

1. That 87,5 cubochs of power per second will turn
a 5 feet stone 104 revolutions in a minute, and grind 3-8
bushels in an hour.

2. That 4,69 cubochs of power is required to every
superficial foot of a mill-stone, when their mean circles
move with a velocity of 18,37 feet per second. Or,

3. That for every 36582 feet of the face of stones that
pass each other we may expect 3,81b. will be ground,
V hen the stones, grain, Sec are in the state and condi-
tion, as were the above stones in the experiments.

Chap. 12.]

HYDRAULICS.

Ill

A TABLE OF EXPERIMENTS OP EIGHTEEN MILLS IN PRACTICE.

JQuai.tily ground pt-r mi-
nute in pounds, or per
liour in bushels. . .

to m
CO iji

m
N.

co"

in m

Superficial feet passed in
a minute.

to lO

t^<H

36435

35741

108091

to
CO

95264
49678
39558

74850
35741

Vi locity of the mean cir-
cle.

CO to

l> 00

feto

to oo"

O) t^-*
CO oi 00

oo «> t-I

oi o> CT in 1^
Oj 00 ot) f^_ o> Oj
to to oi O oi N^

— — T-l 0-1 •- -rH

Power required to each
foot of face.

05 Oi

-4 in

t^ m

to "_
■^ in

Area of the stones.

CO OO
to -4

oo CO

18.63
18.63
38.48

36.63
23.76
18 63

28.38
18.63

Diauieter of the stone in
feet and inches.

CO 0« 00 tc to CO

in •* •* «}i .5f .* <}i

in "rt t^

»- to •* .* 00

tommintomtjit}!

Revolutions of the stones
per minute.

J^ 00

ci * ©J e» tf 00 to
a> c» o< o) o o •>»

in 2 «
o o t^

in
O

-«oo~jico>nco.*to
Koo-<— OTOOii-H

R'luiids in the trundles.

in «t •+ -.+ -?

-* CO

•*.* CO

— T-l 01

aitotot^.-Hj'int©

Cogs iu the coiuiter cog-
wheel.

.* O? -■♦ .* -.-t -* 00

^:S

.* •* .^ .^ 00 00

•* tji m «* ■* TT

Rounds in the wallowers.

t^ c;» -*.*•* CO o»
•M 0» 0» CM OJ 01 51

0> 01
01 01

m K^ in co to to

01 01 oi 01 01 01

Number of cogs in the
master-wheel.

00 00 o» to

00 00 !>. to

0»

00 01 .#
t-- t> oo

•1!

to to o tf to 01
o o to tf to t^

Velocity of the circumfe-
rence per second.

8.2

8.5

10.2

9.3

'' 00?

unloaded

7 8

8.8
loatled
unloaded

-§ 5
11

loaded
unloaded
loaded
unloaded
7.8

9.1

16.67

19.05

9.2

10.96

Number of revolutions
per minute.

00 ci CO o»

O to -* o> O O oo
— -" 01 — 01 01

O ti

rs-"

yx- |>-\^ in

00 o to 00 o 01 in to .*
O) -* .n CO -*■ — --

Diameter of the wheel.

00 00 in V)

to to to in

T-l .-H .-< rt

IT)

oo Oi »H ,^ r1

Powei- per secon d , by si m-
pl'- theorem. Art. 61.

to N.
l^ to

01 o

to to

00 C>

Cubic feet expended per
si cnnd, abating for fric-
tion by conjecture.

00 in

co' CO

oo to
in to'

in o

Velocity of the water per
second, by theory.

12.9
11.17
12.16
14.4

C O CO
N. O) tv.
irj -* to

16.2

24.3

25.63

11.4

\rvn ot the gate, abating
f' r contraction occasion-
e' by friction.

m m

00 01

CO CO

in 'n

CO -^

to
m

HtK(l above the centre of
the gate.

to 31 0) —

oi — o» CO

oc m

0^ CO

-*•<)• CO o»

\ iruial or effective de-
scent of the water.

.'0.
19 2
16.2

16.6

m
01

00 00

b, i^ -H

W in lo m

o — o>' o oi

-M 01 ii — .

dumber of Experiments.

— -■ -O .*

'.O t-, X Ci

CO •«• m to ■ ~ 00

In the ."d, 4th, 13ih and 18th experiments, in the above table, there are two pair of stones to
one water-wheel, the gears, &c. of which are shewn by the braces. If the reader will by a rate
araw small lines between the experiments, the table will be easiar read.

112 HYDRAULICS. [Chap. 12,

OBSERVATIONS CONTINUED FROM PAGE 110.

But as we cannot attain to a mathematical exactness
in those cases, and as it is evident that all the stones in
the said experiments have been working with too little
power, because it is known that a pair of good burr
stones of 5 feet diameter, will grind sufficiently well
about 125 bushels in 24? hours ; that is 5,3 bushels in
an hour, which would require 6,4 power per second —
we may say 6 cubochs per second, when 5 feet stones
grind 5 bushels per hour, for the sake of simplicity.
Hence we deduce the following simple theorem for de-
termining the size of the stones to suit the power of any
given seat, or the power required to any size of a stone.

THEOREM.

Find the power by the theorem in art. 6 1 ; then divide
the power by 6, which is the power required, by 1 foot,
and it will give you the area of the stone that the power
will drive, to which add 1 foot for the eye, and divide
by ,7854, and the quotient will be the square of the dia-
meter : or, if the power be great, divide by the product
of the area of any size stones you choose, multiplied by
6, and the quotient will be the number of stones the
power will drive : or, if the size of the stone be given,
multiply the area by 6 cubochs, and the product is the
power required to drive it.

EXAMPLES.

1. Given, 9 cubic feet per second, 12 feet perpendi-
cular, virtual, or effective descent, required the diame-
ter of the stone suitable thereto.

Then, by art. 61, 9xl2=i08, the power, and
108 I 6=18, the area, and 18x1 | ,785-l-=2+,3 the root
of which is 4,9 feet, the diameter of the stone required.

Observation 5th. The velocities of the mean circles
of these stones in the table are some below and some
above 18 feet per second, the mean of them all being
nearly 18 feet; therefore I conclude that 18 feet per
second is a good velocity in general, for the mean circle
of any sized stone.

Chap. 12.] HYDRAULICS. 113

Of the different quantity of Surfaces that are passed by
AlHl-stones of different diameters with different velo-
cities.

Supposing the quantity ground by mill-stones and
power required to turn them to be as the passing sur-
faces of their faces, each superficial foot that passes over
another foot requires a certain power to grind a certain
quantity : Then to explain this let us premise,

1. The circumference and diameter of circles are
directly proportional. That is, a double diameter gives
a double circumference.

2. The areas of circles are as the squares of their dia-
meters. That is, a double diameter gives 4 times the
area.

3. The square of the diameter of a circle multiplied
by ,7854 gives its area.

4. The square of the area of a mill stone multiplied
by its number of revolutions, gives the surface passed.
Consequently,

5. Stones of unequal diameters revolving in equal
times. Their passing surfaces, quantity ground, and
power required to drive them, aa ill be as the squares of
their areas, or as the biquadrate of their diameters. That
is, a double diameter will pass 16 times the surface.*

6. If the velocity of their mean circles or circumfe-
rences be equal their passing surfaces, quantity ground,
and power required to move them, will be as the cubes
of their diameters.f

7. If the diameters and velocities, be unequal, their
passing surfaces and quantity ground, &c. will be as the
squares of their areas, multiplied by their revolutions.

8. If their diameters be equal the quantity of sur-
faces passed, &c. are as their velocities or revolutions
simply.

• The diameter of a 4 feet stone squared, multiplied by ,7854 equal
12,56 its area; which squared is \57,75 feet, the surface passed at one re-
volution : and 8 multiplied by 8 equal 64, which m\iltiplied by .7854 equal
50,24 being the area of an 8 feet stone ; which squared is 2524,04 the sur-
face passed, which surfaces are as 1 to 16.

t Because the 8 feet stone will revolve only half as of»en as the 4 feet,
therefore their quantity of surface pussed, &.c. can only be half as much
more as it was in the last case ; that is, as 8 to 1-

114 HYDRAULICS. [Chap. 12,

But we have been supposing theory and practice to
a^ee strictly, which they will by no means do in this
case. The quantit)* ground and power used by large
stones more than by small ones will not be in the ratio
assigned by the theory; because the meal having to
pass a greater distance through the stone, is operated
upon oftener, which operations must be lighter, else it
will be overdone ; by which means large stones may
grind equal quantities with small ones, and with equal
power, and do it with less pressure ; therefore the flour
will be better.* See art. HI.

From these considerations, added to experiments, I
conclude, that the po\Aer required and quantity ground,
will nearer approach to be as the area of the stones,
multiplied into the velocity of the mean circles ; or,
which is nearly the same, as the squares of their dia-
meters. But if the velocities of their mean circles or
circumferences be equal, then it will be as their area,
simply.

On these principles I have calculated the following
table, shewing the power req ured and quantity ground
both by theory and what I suppose to be the nearest
practice.

* A French author (M. Pabre) says, that by experiments he has found,
that to produce the bMt flour, a stone 5 feet diameter should revolve be-
tween 48 and 61 times in a minute. This is much slower than prartice in
America, but we may conclude that it is best to err on the side of slower
than faster than common practice; especially when the power is too small
for the size of the stone-

Chap. 12.]

HYDRAULICS.

115

A TABLE

AREA OF MILL STONES,

DIFFERENT DIAMETERS,

Deducting 1 foot for the eye; and of 'he power required to move them
with a mean velocity of 18 feet per second, 8ic.

■V

o
-«»

cr
n

V-

"*>

s-
n

>-' o

n <i

-;?
^3

3 °"3

3 n> 3

"'^ = 't

^ W -T

ri
— ft

fo j:i

". c

° 5

->i (t

" pi

» at;

3
^ c

C. 3

p w S
■a c S

ft 8= -•
•^ ft ^^

5 2,1
zi =
s =

3
'0

o —

'^ 3
"» fl

2 S

='3 3'
fl 1) n

» 2

•5

3 -0
ft

ft 5 "O

l-f "^

_. ro ft

S.3

-^tt

1-5-^"

" r^XI

i. 3'

^ 05

ft ft X

ft C-

3^
:3

8= !f

ft -♦ ft

■ 0-3

ft ^

ft ■"

2 2>=^

■o

• "1

5' ^'

7q 3-

-■ 3
o_ 3

It, .-^

ft C
c M r.

^£

3 a-

3 -■

-a
ft tft

- CO

Ch3

= i

."11

3 I

3
c
3

— - w

3 -* m

3,5

s. t

cuhs.

fet-..

sup f

lbs.
1,49

cuhs.

lbs.

Ihs.

8,62

51.72

7,777

138,8

10312

33,1

2.3

2.45

3.75

9,99

59,94

2,8

11,56

69,36

8,888

121,5

16236

2,3

3,1

3.2

4.25

13,18

79,

3,6

4.5

14,9

89,4

9,99

108,1

23999

3,46

4,05

4,75

16,71

100,26

4,5

18,63 111,78

11,09

97,4

34804

111,78

5,25

20,64; 123,84

5,53

5,5

22,76 136,5 |

6,05

5,75

24,96

153,7

6.6

27,27

163,6

13,37

80,7

60012

8,6

192

7,3

7,2

6,25

29,67

178.

7.8

6,5

32,18

196,

8,4

6.75

34,77

208,6

9,1

37 48

225,

15,55

69,4

97499

14,06

313

9,8

Note. The reason why the quantity ground in the 7th column, is not
exactly as the cubes of the diameter of the stone, and m the 9ih column
not exactly as the squares of its diameter, is the deduction for the eye, be-
ing equal in each stone, destroys the proportion.

The engine of a paper-mill, roll 2 feet diameter, 2 feet long, revolving
160 tiroes in a minute, requires equal power with a 4 feet stone, grinding
5 bushels an hour.

116 HYDRAULICS. [Chap. 12.

Having now laid down in art. 61, 62, and 63, a theory
for measuring the power of any mill-scat, and for ascer-
taining the quantity of that power that mill-stones of
different diameters will require, by which we can find
the diameter of the stones to suit the power of the seat :
and having fixed on six cubochs of that power per se-
cond to every superficial foot of the mill- stone, as re-
quisite to move the mean circle of the stone 18 feet per
second, when in the act of grinding with moderate and
sufficient feed, and having allowed the passing of 34804
feet per minute to grind 51b. in the same time, which is
the effect of the five feet stone in the table, by which, if
right, we can calculate the quantity that a stone of any
size will grind with any velocity.

I have chosen a velocity of 18 feet per second, for the
mean circle of all stones, which is slower than common
practice, but not too slow for making good flour. See
art. 111. Here will appear the advantage of large stones
over small ones; for if we will make small stones grind
as fast as large ones, we must give them such velocity as
to heat the meal.

But I wish to inform the reader, that the experiments,
from which I have deduced the quantity of power to
each superficial foot to be six cubochs, have not been
sufficiently accurate to be relied on ; but it will be easy
for every ingenious mill-'wright to make accurate experi-
ments to satisfy himself as to this.*-

* After having' pablished the fist edition of lliis work, I have been in-
formed, that by accurate experiments made at the expense of the British
j^overnment, it was ascertained that the power produced by 40,000 cubic
feet of water descending^ 1 foot, will j^rind and bolt 1 bushel of wheat. If
this be true, then, to find the quantity that any sii-eatn will grind per hour,
xnuliiply the cubic feet of waf^r that it affords per hoiu-, by the virtual de-
scent, (that is, half of the head above the wiieel added to the fall after it
enters an overshot wheel,) and divide tiiat product by 40,000, and the quo-
tient is the answer in bushels per hour that the stream w dl grind.

EXAMPLE.

Suppose a streant affords 32,000 cubic feet water per hour, and the total
fall 19, .;8 feet ; then by the tisbie for overshot mills, art • 73, the wheel
shotilfl be 16 ftet diameter, head above the wheel, 3,28 feet. Then half
3,28 = 1,64. which added to 16=1764 feet virtual descent, and 17,64x
32000 =.5 63480, which drvlded by 40,000, quotes 14,08 bushels per hour
"the stream will grind.

Chap. 12.] HYDRAULICS. lit

ART. 64.

OF CANALS FOR CONVEYING WATER TO MILLS.

In digging canals we must consider that water will
come to a level on its surface, be the form of the bottom
as it may. If we have once determined on the area
of the section of the canal necessary to convey a
sufficient quantity of water to the mill, we need only
mind to keep to that area in the whole distance, and
need not pay much regard to the depth or width, if there
be rocks in the way. Much expense may be oftentimes
saved, by making the canal deep where it cannot easily
be got wide enough, and wide where it cannot easily be
got deep enough. Thus, suppose we have determined
it to be 4 feet deep, and 6 feet wide, then the area of its
section will be 24. — Let fig. 36, plate IV. represent a
canal, the line A B the level or surface of the water,
C D the side, E F the bottom, A C the width 6 feet,
A E the depth 4 feet. Then, if there be rocks at G, so
that we cannot without great expense obtain more than
3 feet width, but 8 feet clepth at a small expense : then
8x3=24, the section required. Again, suppose a fiat
rock to be at H, so that we cannot, without great ex-
pense, obtain more than 2 feet depth, but can, with small
expense, obtain 12 feet width: then 2x12=24, the sec-
tion required ; and the water will come on equally well,
even if it were not more than ,5 of a foot deep, provided
it be proportionably wide. One disadvantage however
arises in having canals too shallow in places, because
the water in dry seasons, may be too low to rise over
them; but if the water was always to be of one height,
the disadvantage would be but little. The current will
keep the deep places open ; light sand or mud will not
settle in them. This will seem paradoxical to some,
but, seeing the experiment may be a saving of expense,
it may be worth trying.

118 HYDRAULICS. [Chap. 12.

ART. 65,

OF THE SIZE AND FALL OF CANALS,

As to the size and fall necessary to convey any quan-
tity of water required to a mill, I do not find any rule
laid down for either. But in order to establish one, let
us consider, that the size depends entirely upon the
quantity of water and the velocity with which it is to
pass: therefore, if we can determine on the velocity,
which I will suppose to be from 1 to 2 feet per second
— but the slower the better, as there will be the less fall
lost — we can find the size of the canal by the following

THEOREM.

Divide the quantity required in cubic feet per second,
by the velocity in feet per second, and the quotient will
be the area of the section of the canal. Divide that area
by the proposed depth, and the quotient is the width :
or, divide by the width, and the quotient is the depth.

PROBLEM L

Given, a 5 feet mill-stone to be moved 18 feet per
second, velocity of its mean circle on a seat of 10 feet
virtual or effective descent, required the size of the canal,
with a velocity of 1 foot per second.

Then, by theorem in art. 63 : The area of the stone
18,63 feet, multiplied by six cubochs of power, is equal
111,78 cubochs for the power (in common practice say
113 cubochs) which, divided by 10 the fall, quotes
11,178 cubic feet required per second, which, divided
by 1, the velocity proposed per second, quotes 11,178
feet, the area of the section, which divided by the depth
proposed, two feet, quotes 5,58 feet for the width.

PROBLEM IL

Given, a mill-stone 6 feet diameter, to be moved with
a velocity*of 18 feet per second of its mean circle, to be
turned by an undershot wheel on a seat of 8 feet per-

Ghap.l2.] HYDRAULICS. 119

pendicular descent, required the power necessary per
second to drive them, and the quantity of water per se-
cond to produce said power, likewise the size of the
canal to convey the water with a velocity of 1,5 feet per
second.

Then, by art. 61, 8 feet perpendicular descent, on the
undershot principle, is only=4 feet virtual or effective
descent : and the area of the stone by the table (art. 63)
=27,27 feetx6 cubochs=l63,62 cubochs, for the power
per second, which divided by 4, the effective descent=
40,9 cubic feet, the quantity required per second, which
divided by the velocity proposed 1,5 feet per second=
20,45, for the area of the section of the canal, which di-
vided by 2,25 feet, the depth of the canal proposed=9,l
feet, the width.*

As to the fall necessar}^ in the canal, I may observe,
that the fall should be in the bottom of the canal and
none on the top, which should be all the way on a level
■with the water in the dam, in order that when the gate
is shut down at the mill, the water will not overflow the
banks, but stand at a level with the water in the dam ;
that is, as much fall as there is to be in the whole length
of the canal, so much deeper must the canal be at the
mill than at the dam. From observations I conclude
that about 3 inches to 100 yards will be sufficient, if
the canal be long, but more will be better if it be short,
and the head apt to run down when water is scarce, for
the shallower the water the greater must be the velocity,
and more fall is required. — A French author, M. Fabre,
allovAS 1 inch to ^00 feet.

» An acre of a mill-pond contains 43560 cubic feet of water, for every
foot of its depth.

Suppose your pond contains 3 acres and is 3 feet deep, then 43560, mul-
tiplied by 3, is equi*l 130680, which multiplied by 3, is equal 392040 cubic
feet, its contents, which vided bv the cubic feet your mill uses per se-
conn (say 10) is equal 39204 seconds, or 10 hours, the time the pond will
keep the mill going.

120 HYDRAULICS. [Chap.12.

ART. 66.

OF AIR PIPES TO PREVENT TIGHT TRUNKS FROM BURSTING
WHEN FILLED WITH WATER

When water is to be conveyed under ground, or in a
tight trunk below the surface of the water in the reser-
voir, to any considerable length, there must be air-pipes
(as they have been called) to prevent the trunk from
bursting. To understand their use let us suppose a
trunk 100 feet long, 16 feet below the surface of the
water, to fill which draw a gate at one end of equal size
with the trunk. Then the water, in passing to the other
end acquires great velocity if it meets no resistance, which
velocity is suddenly to be stopped when the ti'unk is full.
This great column of water in motion, in this case, would
strike with a force equal to a solid body of equal weight
and velocity, the shock of which would be sufficient to
burst any trunk that ever was made of ^vood. Many
having thought the use of these pipes to be to let out the
air, have made them too small, so that they would vent
the air fast enough to let the water in u ith considerable
velocity, but would not vent the water fast enough when
full, to check its motion easily, in which case they are
worse than none at all, for if the air cannot escape freely,
the water cannot enter freely.

Whenever the air has been compressed in the trunk
by the water coming in, it has made a great blowing
noise in escaping through the crevices, and therefore has
been blamed as the cause of the bursting of the trunk ;
whereas it acted by its elastic principle^ as a great pre-
ventive against it. For I do suppose, that if we were
to pump the air all out of a trunk, 100 feet long, and 3
by 3 feet wide, and let the water in with full force, that
it would burst, if as thick as a cannon of cast metal : be-
cause in that case there would be 900 cubic feet of water,
equal to 562501bs. pressed on by the weight of the at-
mosphere, with a velocity of 47 feet per second, to be
suddenly stopped, the shock would be inconceivable.

* To prevent ice from gatlieringf on overshot wheels when standing', the
water is shut out of the trunk by a pate at the ranal, and what Iciks
throuf^h it is let through a hole in the bottom of the trunk ; the water is let
in again with full force-

Chap. 12.} HYDRAULICS. 121

Therefore I do conclude it best, to make an air- pipe
for every 30 or 30 feet, of the full size of the trunk ;
but this will depend much on the depth of the trunk
below the surface of the reservoir, and many other cir-
cumstances.

Having now said what was necessary, in order the
better to understand the theory of the power and prin-
ciples of mechanical engines, and water acting on the
different principles on water-wheels, and for the esta-
blishing new and true theories of the motion of the dif-
ferent kinds of water-wheels, I here quote many of the
ingenious Smeaton's experiments, that the reader may
compare them with the theories established, and judge
for himself.

ART. 67.

SMEATON'S EXPERIMENTS.

.4?i experimental Enquky^ read in the^^hilosophical So-
ciety in London^ May 3c/, and lOtkj 1759, concerning
the Natural Powers of Water to turn Mills and other
Machines, depending on a circular motion, by James
Smeaton, F. R. S.

What I have to communicate on this subject was
originally deduced from experiments made on working
models, which I look upon as the best means of obtain-
ing the outlines in mechanical enquiries. But in this
case it is necessary to distinguish the circumstances in
which a model differs from a machine in large : other-
wise a model is more apt to lead us from the truth than
towards it. Hence the common observation, that a
thing may do very well in a model that will not do in
large. And indeed though die utmost circumspection
be used in this way, the best structure of machines can-
not be fully ascertained, but by making trials w ith them
of their proper size. It is for this purpose that though
the models referred to, and the greatest part of the fol-
lowing experiments, were made in the years 1752, and
1753, yet I deferred offering them to the society till I had
an opjx)rtunity of putting the deduction made Xherefrom in

122 HYDRAULICS. [Chap. 12.

real practice, in a variety of cases and for various pur-
poses, so as to be able to assure the society, that I have
found them to answer.

PART I.

CONCERNING UNDERSHOT WATER-WHEELS.

Plate XII. is a view of the machine for experiments,
on water-wheels, wherein

ABCD is the lower cistern or magazine for receiving
the water after it has left the wheel, and for supplying

DE the upper cistern or head, wherein the water be-
ing raised to any height by a pump, that height is shewn

FG a small rod divided into inches and parts, with a
float at the bottom to move the rod up and down, as the
surface of the water rises and falls.

HI is a rod by which the sluice is drawn, and stopped
at any height required, by means of

K a pin or peg, which fits several holes placed in the
manner of a diagonal scale upon the face of the rod HI.

GL ^ the upper part of the rod of the pump for draw-
ing the water out of the lower cistern, in order to raise
and keep up the surface thereof to its desired height in
the head DE, thereby to supply the w'ater expended bj
the aperture of the sluice.

MM is the arch and handle of the pump, which is
limited in its stroke by

N a piece for stopping the handle from raising the
piston too high, that also being prevented from going too
low, by meeting the bottom of the barrel.

O is the cylinder upon which the cord winds, and
which being conducted over the pullies P and Q, raises.

R the scale, into which the weights are put for trying
the power of the water.

W the beam, which supports the scale that is placed
15 or 16 feet higher than the wheel.

XX is the pump-barrel 5 inches diameter and 11
inches long.

Y is the piston, and

Z is the fixed valve.

Chap. 12.] HYDRAULICS. 123

GV is a cylinder of wood fixed upon the pump-rod,
and reaches above the surface of the water; this piece of
wood being of such a thickness that its section is half the
area of the pump-barrel, will cause the water to rise in
the head as much while the piston is descendin^as while
it is rising, and will thereby keep the gauge-rod FG more
equally to its height.

a a shews one of the two wires that serves as a direc-
tor to the float.

b is the aperture of the sluice.

c a is a cant-board for canting the water down the open-
ing c d into the lower cistern.

c e is a sloping board for bringing back the water that
is thrown up by the wheel.

There is a contrivance for engaging and disengaging
the scale and weight instantaneously from the wheel, by
means of a hollow cylinder on which the cord winds by
slipping it on the shaft, and when it is disengaged it is
held to its place by a ratchet-wheel, for without this,
experiments could not be made with any degree of ex-
actness.

The apparatus being now explained, I think it neces-
sary to assign the sense in which I use the term power.

The word power is used in practical mechanics, I ap-
prehend, to signify the exertion of strength, gravity, im-
pulse, or pressure, so as to produce motion.

The raising of a weight relative to the height, to
which it can be raised in a given time, is the most pro-
per measure of power. Or in other words, if the weight
raised, is multiplied by the height to which it can be
raised in a given time, the product is the measure of the
power raising it, and consequently all those powers are
equal. But note all this is to be understood in case of
slow or equable motion of the body raised, for in quick,
accelerated, or retarded motions, the vis inertia of the mat-
ter moved will make a variation.

In comparing the eflTects procuced by water-wheels
with the powers producing them ; or in other words, to
know what part of the original power is necessarily lost
in the application, we must previously know how much
of the power is spent in overcoming the friction of the

134 HYDRAULICS. [Chap. 12,

machinery and the resistance of the air, also what is the
real velocity of the water at the instant it strikes the
wheel, and the real quantity of water expended in a
given time.

From the velocity of the water at the instant that it
strikes the w^heel, given ; the height of the head produc-
tive of such velocity can be deduced, from acknow^-
ledged and experienced principles of hydrostatics : so
that by multiplying the quantity or weight of water
really expended in a given time, by the height of head
so obtained ; which must be considered as the height
from which that weight of water had descended, in that
given time ; we shall have a product equal to the origi-
nal power of the water, and clear of all uncertainty that
would arise from the friction of the water in passing
small apertures, and from all doubts, arising from the
different measure of spouting waters, assigned by differ-
ent authors.

On the other hand the sum of the weights raised by
the action of this water, and of the weight required to
overcome the friction and resistance of the machine ;
multiplied by the height to which the weight can be raised
in the time given, the product will be the effect of that
power ; and the proportion of the two products will be the
proj:)ortion of the pow er to the effect : so that by loading
the wheel with different weights successively, we shall be
able to determine at what particular load and velocity of
the wheel the effect is a maximum.
To determine the Velocity of the Water striking the

Wheel.

Firt let the wheel be put in motion by the water, but
without any weight in the scale ; and let the number of
turns in a minute be 60 : now it is evident, that was the
wheel free from friction and resistance, that 60 times the
circumference of the wheel would be the space through
which the water would have passed in a minute ; with
that velocily wherewith it struck the wheel : But the
wheel being incumbered with friction and resistance,
and )'et moving 60 turns in a minute, it is plain that the
velocity of the water must have been greater than 60
circumferences, before it met with the wheel. Let the

Chap. 1:2.] HYDRAULICS. 125

cord now be wound round the cylinder, but contrary to
the usual way, and put as much weight in the scale as
will \vithout any water turn the wheel somewhat faster
than 60 turns in a minute, suppose 63, and call this the
counter-weight, then let it be tried again with the water
assisted by this counter-weight, the wheel therefore will
now make more than 60 turns in a minute, suppose 6'1<,
hence we conclude the water still exerts some power to
turn the wheel. Let the weight be increased so as to
make 64^ turns in a minute without the w^ater, then try
it with the water and the weight as before, and suppose
it now makes the same number of turns with the water,
as without, viz. 64|, hence it is evident, that in this case
the wheel makes the same number of turns as it would
with the water, if the wheel had no friction or resistance
at all, because the weight is equivalent thereto, for if the
counter-weight was too little to overcome the friction,
the water would accelerate the wheel, and if too great it
would retard it, for the water in this case becomes a
regulator of the wheel's motion, and the velocity of its
circumference becomes a measure of the velocity of the
water.

Li like manner in seeking the greatest product or
maximum of effect; having found by trials what weight
gives the greatest product, by simply multiplying the
weight in the scale, by the number of turns of the wheel,
find what weight in the scale, when the cord is on the
contrary side of the cylinder, will cause the wheel to
make the same number of turns, the same way without
water; it is evident that this weight will be nearly equal
to all friction and resistance taken together; and con-
sequently that the weight in the scale, with twice* the
weight of the scale, added to the back or counter- weight,
will be equal to the weight that could have been raised
supposing the machine had been without friction or re-
sistance, and which multiplied by the height to which it
was raised, the product will be the greatest effect of that
power.

• The weight of the scale makes part of the weight both ways, viz. both
ef the weight and counter-weight-

126 HYDRAULICS. [Chap. 12.

The Quantity of IVater expended is found thus :

The pump was so carefuOy made, that no water
escaped back through the leathers, it dehvered the same
quantity each stroke, whether quick or slow, and by
ascertaininf^ the quantity of 12 strokes and counting the
number of strokes in a minute, that was sufficient to
keep the surface of the water to the same height, the
quantity expended was found.

These things will be further illustrated by going over
the calculations of one set of experiments.

Specimen of a set of experiments.

The sluice drawn to the 1st hole.
The water above the floor of the sluice 30 inch.
Strokes of the pump in a minute, 39|

The head raised by 12 strokes, 21 inch.

The wheel raised the empty scale and

made turns in a minute.
With a c'ouiTter-weisrht of 1 lb. 8 oz. it 7 „-

made 5

Ditto, tried with water, 86

No. lbs. oz. tumsinamin. product,

1 4:0 45 180

2 5:0 42 210

3 6:0 36| 2ir|

4 7:0 33| 236|

5 8:0 30 240 max.

6 9:0 26i 238|
r 10 : 22 220

8 11:0 16i 181|

9 12 : O * ceased working.

Counter- weight for 30 turns without water 2 oz. in
the scale.

N. B. The area of the head was 105,8 square inches,
weight of the empty scale and pulley 10 ounces, circum-

* When the wheel moves so slow as not to rid the water so fast as sap-
plied by the sluice, the accumulated water falls back upon the aperture,
and the wheel immediately ceases moving-
Note. This note of the author argues in favour of drawing the gate near
the 60.115.

Chap. 12.] HYDRAULICS. " 127

ference of the cylinder 9 inches, and circumference of
the water-wheel 75 inches.

Reduction of the above Set of Experiments.

The circumference of the wheel 75 inches, multiplied
by 86 tons, gives 6450 inches for the velocity of the
water in a minute, 1-60 of which will be the velocity in
a second, equal to 107,5 inches, or 8,96 feet, which is
due to a head of 15 inches,* and this we call the virtual
or effective head.

The area of the head being 105,8 inches, this multi-
plied by the weight of water of one cubic inch, is equal
to the decimal of ,579 of the ounce avoirdupois, gives
61,26 ounces for the weight of as much water as is con-
tained in the head upon one inch in depth, 1-10 of which
is 3,831b. this multiplied by the depth 21 inches gives
80,431b. for the value of IS strokes, and by proportion
39| (the number made in a minute) will give 264,71b-
the weight of water expended in a minute.

Now as 364,71b. of water may be considered as hav-
ing descended through a space of 15 inches in a minute,,
the product of these two numbers 3970 will express the
power of the water to produce mechanical effects ; which
are as follows.

The velocity of the wheel at a maximum as appears
above, was 30 turns in a minute ; which multiplied by
9 inches, the circumference of the cylinder, makes 270
inches : but as the scale was hung by a pulley and dou-
ble line, the weight was only raised half of this, viz.
135 inches.

The weia;ht in the scale at the 7 on r.

• *=* S- 81b. oz.

maximum. ^

Weight of the scale and pul- ^ ^i, ,^
ley, ^ . oz.

Counter- weidit, scale, and7/->iu in
pulley, ^ ^^^^- 12 oz.

Sum of the resistance, 91b. 6 oz. or 9,375Ib.

* This is determined by the common maxim of hydrostatics; that the
velocity of spoutincj water is equal to the velocity that a heavy body would
require in fallinu from the height of the reservoir; and is proved by tbf
rising of .iets, to the height of tJieir reservoirs nearly.

128 HYDRAULICS. [Chap. 12.

Now, as 9,3751b is raised 135 inches, these two num-
bers being multiphed together produces 1266, which
expresses the effect produced at a maximum : so that
the proportion of the power to the effect is as 3970 : 1266,
or as 10:3,18.

But though this is the greatest single effect producible
from the power mentioned, by the impulse of the water
upon an undershot wheel ; yet as the whole power of the
water is not exhausted thereby, this will not be the true
ratio between the power and the sum of all the effects
producible therefrom : for as the water must necessarily
leave the wheel with a velocity equal to the circum-
ference, it is plain that some part of the power of the
water must remain after leaving the wheel.

The velocity of the wheel at a maximum is 30 turns
a minute, and consequently its circumference moves at
the rate of 3,123 feet per second, which answers to a
head of 1,82 inches: this being multiplied by the ex-
pense of water in a minute, viz. 264i,71b. produces 481
for the power remaining, this being deducted from the
original power 3970, leaves 34)89 which is that part of
the power that is spent in producing the effect 1266, so
that the power spent 34h9 is to its greatest effect 1266,
as 10:3,62, or as ll :4'.

The velocity of the water striking the wheel 86 turns
in a minute, is to the velocity at a maximum 30 turns a
minute, as 10 : 3,5 or as 20 to 7, so that the velocity of
the wheel is a little more than 1-3 of the velocity of the
water.

The load at a maximum has been shewn to be equal
to 91b. 6oz. and that the wheel ceased moving with 121b.
in the scale : to which if the weight of the scale be added,
viz. 10 oz.* the proportion will be nearly as 3 to ■*, be-
tween the load at a maximum and that by which the
wheel is stopped.f

* The resistance of the air in this case ceases, and the friction is not
added, as 12 lb. in the scale was sufficient to stop the wheel after it had
been in full motion, and therefore somewhat more than a counter-balance
for the impulse of the water.

f I may here observe, that it is probable, that if the g'ate of the sluice
had been drawn as near the float-boards as possible, (as is the practice in
America, where water is applied to act by impulse alone,) that the wheel

Chap. 12.] HYDRAULICS. 129

It is somewhat remarkable, that though the velocity
of the wheel in relation to the water turns out greater
than 1-3 of the velocity of the water, yet the impulse of
the water in case of the maximum is more than double
of what is assigned by theory ; that is, instead of -i-Q of
the column, it is nearly equal to the whole column.*

It must be remembered, therefore, that in the present
case, the wheel was not placed in an open river where
the natural current, after it has communicated its impulse
to the float, has room on all sides to escape, as the
theory supposes ; but in a conduit or race, to which the
float being adapted, the water cannot otherwise escape
tlian by moving along with the wheel. It is observable,
that a wheel working in this njanner, as soon as the water
meets the float, it receiving a sudden check, rises up
against the float, like a wave against a fixed object, in-
somuch, that when the sheet of water is not a quarter of
an inch thick before it meets the float, yet this sheet
will act upon the whole surface of a float, whose height
is three inches ; consequendy, was the float no higher
than the thickness of the sheet of water, as the theory
also supposes, a great part of the force ^vouId be lost by
the water dashing over the float.

In confirmation of what is already delivered, I have
adjoined the following table, containing the result of 27
experiments made and reduced in the manner above
specified. What remains of the theory of undershot
wheels, will naturally follow from a comparison of the
different experiments together.

would have continued to move until loaded with I 1-2 times the weight of
the maximum load, viz. 9lb. 6 oz. multiplied by 1 1.2, is equal to 141b. 1 oz.
Then it would have agreed with the theory established art. 41. This pier-
haps escaped the notice of our author.

• This observation of the author t think a strong confirmation of the
truths of the theory established art. 41 ; where the maximum velocity is
made to be ,577 parts of the velocity of the water, and the load to be 2-3
the greatest load : For if the gate had been drawn near the floats, the
greatest load would probably have been I41b. 1 oz. ocas ? to 2, of thft
maximum load.

130

HYDRAULICS.

[Chap. 1^

A TABLE OF EXPERIMENTS,

No. I.

', ■

-^H

•<

-■"-' ■

»:

o
cr

« 5-

o "

-a
5'

rc
o

n
ft

C
3_

c
o
re

CI-
S-
re

a
3

r*
3-

n
n

c
5"

a-
n

3
»

c
3

CI.
re
O-

3
P

•T3

c
re

<-»

Ei-
re

.p p-

r- P

= 3-

3 n

3 £.

o
3

3S"

n
P

c
3

inch.

lb. oz.

b. oz.

lbs.

15,85

13 10

10 9

275

4358

1411

10:3,24

10:3,4

10:7,75

15,

12 10

9 6

264,7

3970

1266

10:3,2

10:3,5

10:7,4

13,7

11 2

8 6

243

3329

1044

10:3,15

10:3,4

10:7.5

12,3

27.7

9 10

7 5

235

2890

901.4

10:3,12

10:3,55

10:7,53

11,4

25,9

8 10

6 5

214

2439

735,7

10:302

10:3,45

10:7,32

9,95

23,5

6 10

5 5

199

1970

561,8

10:2,85

10:3,36

10:8,02

8,54

23,4

5 2

4 4

178,5

1524

442,5

10:2,9

10:3 6

10:8,3

7,29

3 10

3 5

161

1173

328

10:2,8

10:3,77

10:9,1

5,47

2 12

2 8

134

733

213,7

10:2,9

10:3,65

10:9,1

3,55

1 12 1 10

114

404,7

117

10:2.82

10:3,8

10:9 3

14,2

30,75

13 10 10 14

342

4890

1505

10:3,07

10:3,66

10:7,9

13,5

11 10 9 6

297

4009

1223

10:3,01

10:3,62

10:8,05

18i72

10,5

9 10 8 7

285

2993

975

10:3,25

10:3,6

10:8,75

15|69

9,6

7 10

6 14

277

2659

774

10:2,92

10:3,62

10:9,

12|63

8,0

5 10

4 14

234

1872

549

10:2,94

10:3,97

10:8,7

9,56

6,37

4 01 3 13

201

1280

390

10:3,05

10:4,1

10:9,5

P-

l''

646

4,25

2 Sj 2 4

167,5

712

212

I0:2,98il0-4,55

10:9,

Irs

15i72

10,5

11 iOj 9 6

357

3748

I2ul

10:3,23

10:4,02

10:8,05

il9

1266

8,75

26,75

8 10

7 6

330

2887

878

10:3,05

10:4,05

10:8,1

'20

6.8

24,5

5 8

255

1734

541

10:3,01

10:4.22

10:9,1

I—

(21

6
12

48
68

4,7
9,3

23,5
27

3 2
9 2

3
8 6

228

1064

317

10:2,99

10:4,9

10-9,6

[22

523

359

OOOO

1006

10:3,02 iO:3,er

.0:9.17

6,8

26,25

6 2

5 13

332

2257

686

10:3,04 10:4,5;

.0:9,5

f24

48
60

4,7
7.29

24,5

27,3

3 12
6 12

3 8
6 6

262

1231

385

783

10:3,13 10:5,1

i0:9,35

tfi

|25

355

2588

10:3,03 10:4,55

10:9,45

6
6

5,03
5,03
4

24,6
26
5

4 6

4 15
6

4 1

4 9

307
360

1544
1811

456

534

10:2,9210:4,9

10:9,3

10:2,95,10:5,2

10:9,25

8 9

11 1 12

Chap. 12.] HYDRAULICS. 13i

Maxims and Observations deduced from the foregoing
Table of Experiments.

Max. 1. That the virtual or effective head being the
same, the effect will be nearly as the quantity of water
expended.

This will appear by comparing the contents of the
columns 4, 8 and 10, in the foregoing sets of experi-
ments, as for

Example I. taken from No 8 and S5, viz.

No. Virtual head. Water expended. Effect,

8 7,29 161 328

25 7,29 355 785

Now the heads being equal, if the effects are propor-
tioned to the water expended, we shall have by maxim
I. as 161 : 356 :: 328 : 723 ; but 723 falls short of 785, as it
turns out in experiment, according to No. 25 by 62.
The effect therefore of No. 25, compared with No 8, is
greater than, according to the present maxim, in the ratio
of 14 to 13.*

The foregoing example with four similar ones are seen
at one view in the foregoing table.

• If the true maximum velocity of the wheel be ^Sn of the Telocity of
the water, and (he true maximum load be 2-3 of the whole column, as
shewn in art. 42 ; then the effect will bethe power in the ratio of 100 to
38, or as 10 to 3,8, a little more than appears by the table of experiments,
in columns 9 and 10 : the difference is owing to the disadyantageous appli-
cation of the water on the wheel in the model.

132

HYDRAULICS.

[Ghap. 12.

A TABLE OF EXPERIMENTS,

No. II.

Proportional
variation.

T-t

<»
CO

Variation.

i-H

+
CO

^ COMPARISON.

v>
CO

»-t

00 >o
C^ 00

CO ts.

CM
V5

00
0»CN

-^
>o

c>>

CO
CO

r-l ^O
■<* CO

»>-

'O
CN

00
<N

r-l 00

COCO

rl
CO

o
in

Is.

o ^
«n CO

Expense of water.

r-l in

^ CO

00 VJ

(N CO

in CN
in CO

(N CO

00 CM
CM <0
CVCM

o to
CO CO

Virtual head.

in «n

cTo

I-t tH

00 CO

CO CO

o o
»n »n

No. Table I.
Examples.

00 >J0
(N

CO 00

<>i CO

c^J (N

r» CM

■5

to 1^

CM CM

Chap. 12.] HYDRAULICS. 133

By this table of experiments it appears that some fall
short and others exceed the maximum, and all agree as
near as can be expected in an affair w here so many dif-
ferent circumstances are concerned ; therefore we may
conclude the maxim to be true.

Max. II. That the expense of the water being the
same, the effect will be nearly as the height of the vir-
tual or effective head.

This also will appear by comparing the contents of
columns 4, 8 and 10, in any of the sets of e;5cperimentS;

Example I. of No. 2 and No. 24.

No. Virtual head. Expense- Effect.

S 15 264,7 1266

24 4,7 262 385

Now as the expenses are not quite equal, we must
proportion one of the effects accordingly, thus :
By maxim I. 292:26-1,7:: 385:389
And by max. II. 15 : 4,7 : : 1266 : 397

Difference, 8

The effect therefore of No. 24, compared with No. 2,
is less than, according to the present maxim, in the ratio
of 49 : 50.

Max. III. That the quantity of water expended being
the same, the effect is nearly as the square root of its
velocity.

This will appear by comparing the contents of co-
lumns 3, 8 and 10, in any set of experiments ; as for

Example I. of No. 2 xvith No. 24, viz.

No. Turns in a minute- Expense. Effect.

2 86 264,7 1266

24 48 262, 385

The velocity being as the number of turns, we shall
have

134. HYDRAULICS. [Chap. i2.

By maxim I. 2Q2 : 264,7 :: 385 : 389

And by max. III. > 4^« *^ f:: 1266: 394

•' / /39b: 230* S

Difference, 5

The effect of No. 24, compared with No. 2, is less
than by the present maxim in the ratio of 78 : 79.

Max. IV. The aperture being the same, the effect
will be nearly as the cube of the velocity of the water.

This also will appear by comparing the contents of
colmnns 3, 8 and 10, as for

Example of J\'o. 1, mid JVb. 10, viz.

No. Turns. Expense. EfFect.

1 88 275 1411

10 42 114 117

Lemma. It must here be observed, that, if water
passes out of an aperture in the same section, but with
different velocities, the expense will be proportional to
the velocity ; and therefore conversely, if the expense
is not proportional to the velocity, the section of water is
not the same.

Now comparing the water discharged with the turns
of No. 1 and 10, \Ve shall have 88 : 42 :: 275 : 131,2 ; but
the water discharged by No. 10 is only 1141b. therefore,
though the sluce was drawn to the same height in No.

10 as in No. 1 : yet the section of the water passing out,
was less in No. 10 than No 1, in the proportion of 114
to 131,2, consequently had the effective aperture or sec-
tion of the water been the same in No. 10 as in No 1, so
that 131,21b. of water h*d been discharged, instead of

11 lib. the effect would have been increased in the same
proportion : that is.

By lemma 88: 42 :: 275:131,2

Bv maxim I. 114 : 1312 :: 117:134,5

And by max. IV. j 681472 • ''^""" ^ '^'^^^ ' *^^'^

Difference 19

Chap. 12.] HYDRAULICS. 135

The effect therefore of No. 10, compared with No. 1,
is less than ought to be, by the present maxim, in the
ratio of y:8.

OBSERVATIONS.

Observ. 1st. On comparing columns 2 and 4, table I.
it is evident, that the virtual head bears no certain pro-
portion to the head of water, but that when the aperture
is greater, or the velocity of the water issuing therefrom
less, they approach nearer to a coincidence : and conse-
quently in the large opening of mills and sluices, where
great quantities of water are discharged from moderate
heads, the head of water and virtual head determined
from the velocity will nearer agree, as experience con-
firms.

Observ. 2nd. Upon comparing the several proportions
between the powers and effects in column 11th, the most
general is that of 10 to 3; the extremes are 10 to 3,2 and
10 to 2,8; but as it is observable, that where the quantity
of water or the velocity thereof is great, that is, where the
power is greatest, the 2nd term of the ratio is greatest
also, we may therefore well allow the proportion subsist-
ing in large works as 3 to 1 .

Observ. Srd. The proportion of velocities between
the water and wheel in column 12 are contained in the
limits of 3 to 1 and 2 to 1; but as the greater velocities
approach the limits of 3 to 1, and the greater quantity of
water approach to that of 2 to 1, the best general propor-
tion will be that of 5 to 2.*

Observ. 4th. On comparing the numbers in column
13, it appears, that there is no certain ratio between the

• I may here observe, that our friend Smeaton may be wrong' in his con-
clusion, that the best general ratio of the velocity of the water to that of
the wheel will be as 5 to 2 ; because, we may observe, that in the first ex-
periment, where the virtual head was 15,85 inches, and the gate drawn to
the 1st hole, the ratio is as 10 : 3,4. But in the last experiment, where
the head was 5,03 inches, and gate drawn to the 6th hole, the ratio is as
10 : 5,2; and that the 2nd term of the ratio increases gradually, as the head
decreases, and quantity of water increases ; therefore we may conclude,
that in the large openings of mills, that the ratio may approach to 3 to 2 ;
which will agree with the practice and experiments < f many able mill-
wrights, of America, and many experiments 1 have made on mills. And as
it is better to give the wheel a velocity too great than too slow, I conclude,
the wheel of an imdershot mill must have nearly 2-3d of the velocity of the
water to produce a jnaximum effect.

136 HYDRAULICS. [Chap. 12.

load that the wheel will carry at its maximum, and what
will totally stop it ; but that they are contained within
the limits of 20 to 19 and of 20 to 15 ; but as the effect
approaches nearest to the ratio of 20 to 15 or of 4 to 3,
when the power is greatest, whether by increase of velo-
city or quantity of water, this seems to be the most
applicable to large works : but as the load that a wheel
ought to have in order to work to the best advantage, can
be assigned by knowing the effect it ought to produce,-
and the velocity it ought to have in producing it, the
exact knowledge of the greatest load that it will bear is
of less consequence in practice.*

It is to be noted, that in almost all of the examples
under the three last maxims (of the four preceding) the
effect of the lesser power falls short of its due propor-
tion to the greater, when compared by its maxim. And
hence, if the experiments are taken strictly, we must
infer that the effects increase and diminish in an higher
ratio than those maxims suppose ; but as the deviations
are not very considerable, the greatest being about 1-8
of the quantity in question, and as it is not easy to make
experiments of so compound a nature with absolute
precision, we may rather suppose that the lesser power
is attended with some friction, or works under some
disadvantage, not accounted for : and therefore we may
conclude, that these maxims will hold very nearly,
vv'hen applied to works in large.

After the experiments above-mentioned were tried,
the wheel which had 24 floats was reduced to 12, which
caused a diminution in the effect on account of a greater
quantity of water ei^caping between the floats and the
floor, but a circular sweep being adapted thereto, of such
a length that one float entered the curve before the pre-
ceding one quitted it, the effect came so near to the
former, as not to give hopes of increasing the effect by
increasing the number of floats past 24, in this particular
wheel.

* Perhaps the author is here again deceived by the imperfection of the
model ; for had the water been drawn close to the float, the load that
would totally stop the wheel would always be equal to the column of water
acting on the wheel. See the note page 70. The friction of the shute and
air destroyed great part of the force of his small quantity of water.

Chap. 12.] HYDRAULICS. 13^

ART. 68.

PART II.

CONCERNING OVERSHOT WHEELS.

In the former part of this essay, we have considered
the impulse of a confined stream, acting on undershot
wheels; we now proceed to examine the power and
application of water, when acting by its gravity on over-
shot wheels.

It will appear in the course of the following deduc-
tions, that the effect of the gravity of descending bodies,
is very different from the effect of the stroke of such as
are non-elastic, though generated by an equal mechanical
power.

The alterations of the machinery already described,
to accommodate the same for experiments on overshot
wheels, were principally as follow.

Plate XII. The sluice I b being shut down, the rod
H I was taken off. The undershot water-wheel was
taken off the axis, and instead thereof, an overshot
wheel of the same size and diameter was put in its place.
Note, this wheel was 2 inches deep in the shroud or
depth of the bucket, the number of buckets was 36.

A trunk for bringing the water upon the wheel was
fixed according to the dotted lines f g, the aperture was
adjusted by a shuttle which also closed up the outer end
of the trunk, when the water was to be stopped.

i3 8 HYDRAULICS. [Chap. 12.

Specimen of a Set of Experime?ifs.

Head 6 inches — 14| strokes of the pump in a minute,
12 ditto=801b.* weight of the scale (being wet) 10|
ounces.

Counter-weight for 20 turns besides the scale, 3 ounces.

No.

wt. in the scale.

turns.

product.

observations.

) threw most part of

> the \\'ater out of

iiS

\ the wheel.

/ received the water

147 ;

188 '

\ more quietly.

335

43i

355

387

381

808

36i

3381

35|

355

33|

360|

31i

375

14.

38 i

370|

S7|

385

390

34i

393

331

386|

31|

391 1

S0|

394|;.

19|

395 <

> maximum.

18i

383| "

396 worked irre.8:ular.

overset

by its loa

* The small difierence in the value of 12 strokes of the pump from the
former experiments, was owing to a small diflf'erence in the length of the
stroke, occasioned by the warping of the wood.

Chap. 12.] HYDRAULICS. 139

Reduction of the preceding Specimen.

In these experiments the head being 6 inches, and the
heip;ht of the wheel 24 inches, the whole descent will
be 30 inches : the expense of watei' was 14^ strokes of
the pump in a minute, whereof 12 contained 80lb. there-
fore the water expended in a minute, was 96 S-31b.
which multiplied by 30 inches, gives the power=2900.

If we take the SOth experiment for the maximum, we
shall have 20| turns in a minute, each of which raised
the weight 4| inches, that is, 93.37 inches in a minute.
The weight in the scale was 19!bs. the weight of the
scale lOi oz. the counter-weight 3 oz. in the scale, which,
with the weight of the scale 10 1 oz. makes in the whole
20|lb. which is the whole resistance or load, this multi-
plied by 93,37, makes 1W14 for the effect.

The ratio therefore of the power and effect will be as
S900:191*, or as 10:6,6, or as 3 to 2 nearly.

But if we compute the power from the height of the
wheel only, we have 96 2-31b. xS4< inches=:S820 for the
power, and this will be to the effect as 2320:1914 or as
10:8,2, or as 5 to 4 nearly.

The reduction of this specimen is set down in No. 9
of the following table, and the rest were deducted from
a similar set of experiments, deduced in the same manner.

140

HYDRAULICS.

[Ghap. 12;

TABLE III.

CONTAINING THE RESULT OF 16 SETS OF EXPERIMENTS ON
OVERSHOT WHEELS.

—

P3 1

»=

crq

■*>

-0

' '

-t

B
3"

in'

-5
C

•a

re ^

a re

C-

-o

-1

-3

-•

f—

"»

-i

■■3

C-

3
C

iv
o

M
3

—

lbs.

UK hs

I b

6 1-2

810

720

0556

10 : 6,9

10 : 7,7

56 2-3

16 1-4

14 1-2

1530

1360

1060

10 : 6,9

10 : 7,8

^'^

56 2 3

20 3 4

12 12

1530

1360

1167

10 : 7,6

10 : 8,4

.. c.

63 1-3

20 12

13 1-2

1710

1524

1245

10 : 7,3

10 : 8.2

CO c

5
6

762-3

21 12
18 3-4

15 1-2

2070

1840
1764

1500
1476

10 : 7,3

10 : 8,2

2812

73 1-3

17 1-2

2090

10 : 7

10 : 8,4

~> c

7
8

281 2
30

96 2-3

20 14
20

20 1 2
19 1 2

2755
2700

2320
2160

1868
1755

10 : 6,8

10 : 8,1

to ■•

10 : 65

10 : 8,1

96 2 3

20 3-4

20 1-2

2900

2320

1914

10 : 6,6

10 : 8,2

10
11

113 13

20 1-4

23 1-2

3400

2720
1360

2221
1230

10 : 6,5

10 : 8,2

"k;

56 2-3

13 1-2

1870

10 : 6,6

10 : 8

>-*
o

106 23

22 1-4

21 1-2

352u

2560

2153

10 : 6,1

10 : '4

13
14

146 2-3

19 3 4

27 12

4840

3520

2846

10 : 5,9

10 : 8.ih-

16 12

2275

15601466

10 : 6.5

10 : 9,4

120

21 1-2

25 1-2

4200

2880 2467

10 : 5,9

10 : 8,6

163 1 2

25
4

26 1-2
5

:5728
i 6

39242981

10 : 5,_

10 : 7.6

i 3

1 10

Chap. 12.] HYDRAULICS. 141

OBSERVATIONS AND DEDUCTIONS FROM THE FOREGOING
EXPLRIMENTS

I. Concerning the Ratio between the Power and Effect
of Overshot JVheels.

The effective power of the water must be reckoned
upon the whole descent, because it must be raised to that
height in order to be in a condition of producing the same
effect a second time.

The ratios between the powers so estimated, and the
effects at a maximum deduced from the several sets of
experiments, are exhibited at one view in column 9 of
table III ; and hence it appears, that those ratios differ
from that of 10 to 7,6 to that of 10 to 5,S; that is, nearly
from 4 to 3 to 4:2. In those experiments, where the
heads of water and quantities expended are least, the
proportion is nearly as 4 to 3; but where the heads and
quantities are greatest, it approaches nearer to that of
4 to 2, and by a medium of the whole the ratio is that of
3:2 nearly. We have seen before in our observations
upon the effects of undershot wheels, that the general
ratio of the power to the effect, when greatest, was as
3:1. The effect, therefore, of overshot wheels, under the
same circumstances of quantity and fall, is at a medium
double to that of the undershot : and a consequence
thereof, that non-elastic bodies when acting by their im-
pulse or collision, communicate only a part of their ori-
ginal power : the other part being spent in changing
their figure in consequence of the stroke.*

The powers of v\ ater computed from the height of th^
wheel only, compared with the effects as in column 10,
appear to observe a more constant ratio : for if we take
the medium of each class, which is set down in column
11, we shall find the extreme to differ no more than
from the ratio of 10:8,1 to that of 10:8,5, and as the
second term of the ratio gradually increases from 8,1 to
8,5 by an increase of head from 3 inches to 11, the ex-

• These observations of the author agree with the theory, art. 41 — 42.
I may add, thai non-elas.lc bodies, when acting by impulse or collision,
communicate only half of their original power, by the laws of motion.

143 HYDRAULICS. [Chap. 12.

cess of 8,5 above 8,1 is to be imputed to the superior
impulse of the water, at the head of 11 inches above that
of 3 inches, so that if we reduce 8,1 to 8, on account of
the impulse of the 3 inch head, we shall have the- ratio of
the power computed upon the height of the wheel only,
to the effect at a maximum, as 10:8 or as 5:4 nearly.
And from the equality of the ratio, between power
and effect, subsisting where the constructions are similar,
we must infer that the effects as well as the powers, are
as the quantities of water and perpendicular heights, mul-
tiplied together respectively.

II. Concerning the most proper- Height of the Wheel in
Proportion to the whole descent.

We have already seen in the preceding observation,
that the effect of the same quantity of water, descending
through the same perpendicular space, is double, when
acting by its gravity upon an overshot wheel, to what
the same produces when acting by its impulse, upon an
undershot. It also appears, that by increasing the head
from 3 to 11 inches, that is, the whole descent, from S7
to 35, or in the ratio of 7 to 9 nearly, the effect is ad-
vanced no more than in the ratio of 8,1 to 8,4 ; that is,
as 7:7,^6, and consequently the increase of the effect is
not 1-7 of the increase of the perpendicular height.
Hence, it follows, that the higher the wheel is in propor-
tion to the whole descent, the greater will be the effect ;
because it depends less upon the impulse of the head,
and more upon the gravity of the water in the buckets :
and if we consider how obliquely the water issuing from
the head must strike the buckets, we shall not be at a
loss to account for the httle advantage that arises from
the impulse thereof; and shall immediately see of how
htde consequence this impulse is to the effect of an
overshot wheel. However, as every thing has its limits,
so has this : for thus much is desirable, that the water
should have somewhat greater velocity, than the circum-
ference of the wheel, in coming thereon : otherwise the
wheel will not only be retarded by the buckets striking
the water, but thereby dashing a part of it over: so much
of the power is lost.

Ghap.12.] HYDRAULICS. 143

The velocity that the circumference of the wheel
ought to have being known, the head requisite to give
the water its proper velocity is easily found, by the com-
mon rules of hydrostatics, and will be found much less
than what is commonly practised.

III. Concei'ning the Velocity of the circumference of the
Wheel in order to produce the greatest effect.

If a body is let fall freely from the surface of the head
to the bottom of the descent, it will take a certain time
in falling ; and in this case the whole action of gravity is
spent in giving the body a certain velocity : But, if this
body in falling is made to act upon some other body, so
as to prcjduce a mechanical effect, the falling body will
be retarded ; because, a part of the action of gi'avity is
then spent in producing the effect, and the remainder
only giving motion to the falling body : and, therefore,
the slower a body descends, the greater will be the por-
tion of the action of gravity applicable to the producing
a mechanical effect. Hence we are led to this general
rule, that the less the velocity of the wheel, the greater
will be the effect thereof. A confirmation of this doc-
ti'ine, together with the limits it is subject to in practice,
may be deduced from the foregoing specimen of a set
of experiments.

From these experiments it appears, that when the
wheel made about 20 turns in a minute, the effect was
nearly upon the greatest ; when it njade 30 turns, the
effect was diminished about 1-20 part ; but, that when
it made 40, it was diminished about \ : when it made
less than 18|, its motion was irregular ; and when it was
loaded so as not to admit its making 18 turns, the wheel
was overpowered by its load.

It is an advantage in jiractice, that the velocity of the
wheel should not be diminished farther than what will
procure some solid advantage in point of power; be-
cause, as the motion is slower, the buckets must be
made larger: and the wheel being more loaded with
water, the stress upon every part of the work will be
increased in propordon : the best velocity for practice,
therefore, will be such as when the wheel here used

144 HYDRAULICS. [Chap. 12.

made about SO turns in a minute ; that is, when the ve-
locity of tlie circumference is a little more than 3 feet in
a second.

Experience confirms, that this velocity of 3 feet in a
second, is applicable to the highest overshot wheels as
well as the lowest ; and all other parts of the work being
properly adapted thereto, will produce very nearly the
greatest effect possible. However, this also is certain,
from experience, that high wheels may deviate further
from this rule, before they will lose their power, by a
given aliquot part of the whole, than low ones can be
admitted to do ; for a wheel of 24 feet high may move
at the rate of 6 feet per second without losing any con-
siderable part of its power : and, on the other hand, I
have seen a wheel of 33 feet high that has moved very
steadily and well, with a velocity but little exceeding 2
feet.*

[Said Smeaton has also made a model of a wind-mill,
and a complete set of experiments on the power and
effect of the wind, acting on wind-mill sails of different
constructions. But as the accounts thereof are quite too
long for the compass of my work, I therefore only ex-
tract little more than a few of the principal maxims de-
duced from his experiments, which, I think, may not
only be of good sei-vice to those who are concerned in
building wind-mills, but may serve to confirm some
principles deduced from his experiments on water-
mills.]

ART. 69.

PART III.

ON THE CONSTRUCTION AND EFFECTS OF WIND-MILL SAILS.t

In trying experiments on wind-mill sails, the wind
itself is too uncertain to answer the purpose ; we must
therefore have recourse to artificial wind.

• Probably this wheel was working a forge or furnace bellows, which
have deceived many by their slow regular motion.

t Read May 31st and June 14th, 1759, in the Philosophical Society of
Tendon.

Ghap. 12.]

HYDRAULICS.

145

This may be done two ways ; either by causing the
air to move against the machine, or the machine to move
against the air. To cause the air to move against the
machine in a sufficient column, with steadiness and the
requisite velocity, is not easily put in practice : To car-
ry the machine forward in a right line against the air,
would require a larger room than I could conveniently
meet with. What I found most practicable, therefore,
was to carry the axis whereon the sails were to be fixed
progressively round in the circumference of a large
circle. Upon this idea the machine was constructed.*

Specimen of a Set of Experiments.

Radius of the sails, ... -

Length of do. in cloth, ...

Breadth of do.
( Angle at the extremity,

f < Do. at the greatest inclination,
( 20 turns of the sails raised the weight.

Velocity of the centre of the sails in the cir-
cumference of the great circle in a second,
in which the machine was carried round,

Continuance of the experiment,

No' Weight in the scale. Turns.

1 Olb. 108

2 6 85

3 6| 81

4 7 78

5 71 73

6 8 65

7 9

The product is found by simply multiplying the
weight in the scale by the number of turns.

• I decline p^iving any description or draught of this machine, as I have
not room ; but I may say, that it was constructed so as to wind up a
weight, (as did the other model) in order to find the effect of the power.'
I may also insert a specimen of a set of experiments, which I fear will not
be well understood for want of a full explanation of the machine.

t In the following experiments, the angle of the sail is accounted from
the plain of their motion ; that is, when they stand at right angles to the
axis, their angle is denoted ° deg. ; this notation being agreeable to the
language of practitioners, who call the angle so denoted the weather of the
sail ; which they denominate greater or less, according to the quantity of
the angle.

21 inches
18
5,6

10 degs.
25
11,3 inch.

6 feet.

52 seconds

Product.

510

526|
546

5*7 1 maxim.
520

146 HYDRAULICS. [Chap. 12.

By this set of experiments it appears, that the maxi-
mum velocity is 2-3 of the greatest velocity, and that
the ratio of the greatest load to that of a maximum is, as
9 to 7,5, but by adding the weight of the scale and fric-
tion to the load, the ratio turns out to be as 10 : 8,4, or as
5 to 4, nearly. The following table is the result of 19
similar sets of experiments.

By the following table it appears, that the most gene-
ral ratio between the velocity of the sails unloaded and
when loaded to a maximum, is 3 to 2, nearly.

And the ratio between the ijreatest load and the load
at a maximum (taking such experiments where the sails
answered best), is at a medium about as 6 to 5, nearly.

And that the kind of sails used in the 15th and 16th
experiments are best of all, because they produce the
greatest effect or product, in proportion to their quantity
of surface, as appears in column 12.

Xhap. 12j

HYDRAULICS.

TABLE IV.

Containing Nineteen Sets of Experiments on Wind-mill Sails of varioug
Structures, Positions, and Quantities of Surface.

z >

-3

-»

-J

« 5"

3-
t
■5

is,

S 5-

-n

e/q.

v: at;

^"S

p- =

»9

3 fD

->
n

S p

3
a.

c
3

3 S

3 Z

C o

3 o

.=^S.

•

c 9.

fi>

.-»

•^

7»»

35
12

42
70

lb.
7,56

•

lb.
12,59

318
441

sq.in
404
404

10:7

10:6

10: 7, 9

6,3

7,56

10:8,3

10:10, 1

II.

105

6.72

8,12

464

404

10:6,6

10:8,3

10:10.15

4
5

18
9

18
26,5

7,0

9,81

462
462

404
404

10:7

10:7.1

10:10,15

7,0

10:11, 4

III.

29,5

70,5

7,35

518

404

10:12, 8

7
8

32,5
15

,63,5
120 93

8,3
4,75

5,31

527

442

404

10:13,

404

10:7,7

10:8,9

10 11,

120 79

7,0

8.12

553

404

10:6,6

10:8.6

10:13, 7

IV.

7,5

8,12

585

404

10:9,2

10:14. 5

7,5

22.5

113 77

8,3

9,81

639

404

10:6,8

10:8 5

10:15, 8

108 73

8.69

10,37

634

404|10:^,8

10:8.4 10:15, 7

13
14

12
7,5

27
22.5

10066
123 75

8 41
10,65

10,94

580

404'10.6,6

10:7,7 il0:14, 4

12,59

799

505,10:6,1

10:8,5

10:15. 8

'25

117 74

11.08

13,69

820

505 10:6 3

10:8,1

10:16, 2

114 66

12.09

14,23

799

.i05

10:5.8

10.8,4

10:15, 8

17
18

15
12

30
22

96 63
10564,5

12,09
16,42

14,78
27,87

762

505

10:6,6

10:8,2 10:15, 1

1059

854

10:6,1

10:5,9 10:12, 4

12
2

99.64,5

18.06
6

1165
8

1146

10:5,9

f]0:IO, 1

11 12

I. Plain sails at an angle of 55 degrees.

II. Plain sails weathered according to common practice-
IIL Weathered according to Muclaurin's theorem.

IV- Weathered in the Dutch manner, tried in various positions.

V- Weathered in the Dutch manner, but enlarged towards the extre-
mities.

VI. 8 sails, being' sectors of ellipses in their best positions.

HYDRAULICS.

[Chap. 12.

TABLE V.

Containing- the Result of 6 Sets of Experiments, made for determining the
difference of Effect according to the difference of >he Wind.

Ratio of the greatest load to the load
at a maximum-

CO .-<_

CO oi

o o

10:8.5
10:8,7

Ratio of the greatest velocity to the
velocity at a maximum.

o o

,-r-> 1

Ratio of the two products . . . .

CO
O

Product of the lesser luad and great-
er velocity.

o
00

1-(

CJi

Turns of the sails therewith . . .

Maximum load for the half velocity.

>C CI

O 00
O I^
CO •>!

o ■*

CO o

Greatest load

CO C5^
>r;' Qo"

00 CO
CM

Load at the maximum .....

£_

CO '-H
vi 00

Turns of the sails at a maximum

(C CO

Iv.rns of the sals, unloaded . . .

1 C l^

a-, o

Velocity of the wind in a second

T^l 00

-^ 00

'^ Ol
■<J" 00

1 Angle at the extremity ....

in V)

»0 'TS

o o

1 Number ,

f c^

CO 'i-

«n VO

i-t

N B- The sails were the same kind as those of Nos. 10, 11 and 12, table
IV. Continuance of the experiment one minute-

Chap. 12.] HYDRAULICS. 149

Concerning the Effects of Sails according to the different
Velocity of the fVind,

From the foregoing table the following maxims are de-
duced.

Maxim I. The velocity of wind-mill sails, whether
unloaded or loaded, so as to produce a maximum, is
nearly as the velocity of the wind, their shape and posi-
tion being the same.

This appears by comparing the respective numbers
of columns 4 and 5, table V, wherein those numbers 2,
4 and 6, ought to be double of No. 1, 3 and 5, and are
as nearly so as can be expected by the experiments.

Maxim II. The load ai the maximum is nearly but
somewhat less than as the square of the velocity of the
wind, the shape and position of the sails being the same.
This appears by comparing No. 2, 4 and 6, in column
6, with 1, 3 and 5, wherein the former ought to be quad-
ruple of the latter (as the velocity is double) and are as
nearly so as can be expected.

Maxim III. The effects of the same sails at a maxi-
mum are nearly, but somewhat less than, as the cubes
of the velocity of the wind.*

It has been shewn, maxim I, that the velocity of sails
at a maximum, is nearly as the velocity of the wind ;
and by maxim II, that the load at the maximum is
nearly as the square of the same velocity. If those two
maxims would hold precisely, it would be a consequence
that the effect would be in a triplicate ratio thereof.
How this agrees with experiment will appear by com-
paring the products in column 8, wherein those of No.
2, 4 and 6 (the velocity of the wind being double)
ought to be octuble of those of No. 1, 3 and 5, and are
nearly so.

Maxim. IV. The load of the same sails at the maxi-
mum is nearly as the squares of, and their effects as the
cubes of, their number of turns in a given time.

This maxim may be esteemed a consequence of the
hree preceding ones.

• This confirms the 7th law of spouting fluids.

150 HYDRAULICS. [Chap. 12.

[These 4 maxims agree with and confirm the 4 max-
ims concerning the effects of spouting fluids acting on
undershot mills : and, I think, sufficiently confirms as a
law of motion, that the effect produced, if not the instant
momentum of a body in motion, is as the square of its
velocity, as asserted by the Dutch and Italian philoso-
phers.

Smeaton says, that by several trials in large, he has
found the following angles to answer as well as any :]
The radius is supposed to be divided into 6 parts, and
1-6 reckoning from the centre is called 1, the extremity
being denoted 6.

No,

Angle with the a'Kis.

Angle

with the plain of motion.

72°

18°

18 middle.

771

121

6 83 7 extremity.

[He seems to prefer the sails being largest at the ex-
^emities.]

END OP PART FIRST

PART II.

THE YOUNG
MILL-WRIGHT'S GUIDE.

-f;ff .rrr/

INTRODUCTION.

WHAT has been said in the first part, was
meant to establish theories and easy rules. In
this part I mean to bring them into practice, in
as concise a manner as possible, referring only
to the articles in the first part, where the rea-
sons and demonstrations are given.

This part is particularly intended for the help
of young and practical mill-wrights, whose time
will not permit them fully to investigate the prin-
ciples of theories, which require a longer series
of studies than most of them can possibly spare
from their business ; therefore I shall endeavour
here to reduce the substance of all that has been
said, to a few tables, rules, and short directions,
which, if found to agree with practice, will be
sufficient for the practitioner.

There are but two principles by which water
acts on mill-wheels, to give tJiem motion, viz.
Percussion and Gravity.

154 INTRODUCTION.

That equal quantities of water, under equal
perpendicular descents, will produce double the
power by gravity that they will by percussion, has
been shown in articles 8 and 68.

Therefore, when the water is scarce, we ought
to endeavour to cause it to act by gravity as much
as possible, paying due regard to other circum-
stances noted in article 44, so as to obtain a steady
motion, §c. .i u ,:>

■ ■ ; > i ■ .

. . il!V,'

.v.tiv'ij'iO ba& itoigajjo , ' \

THE

YOUNG MILL-WRIGHT'S
GUIDE.

PART THE SECOND.

CHAPTER L

OF THE DIFFEHENT KINDS OF MILLS

ARTICLE 70.

OF UNDERSHOT MILLS.

UNDERSHOT wheels move by the percussion oi:
stroke of the water, and are only half as powerful as
Other wheels that are moved by the gravity of the wa-
ter. See art. 8. Therefore this construction ought not
to be used, except where there is but little fall or great
plenty of water. The undershot wheel, and all others
that move by percussion, should move with a velocity
nearly equal to two-thirds of the velocity of the water.
See art. 42. Fig. 28, plate IV. represents this construc-
tion.

For a rule for finding the velocity of the water, under
any given head, see art. 51.

Upon which principles, and by said rule, is formed
the following table of the velocity of spouting water,
under different heads, from one to twenty-five feet high
above the centre of the issue ; to which is added the
velocity of the wheel suitable thereto, and the number
of revolutions a wheel of fifteen feet diameter (which I
take to be a good size) will revolve in a minute : also,

156 HYDRAULICS. [Chap. 12.

the number of cogs and rounds in the wheels, both for
double and single gears, so as to produce about ninety-
seven or one hundred revolutions for a five feet stone per
minute, which I take to be a good motion and size for a
mill-stone, grinding for merchantable ftour.

That the reader may fully understand how the follow-
ing table is calculated, let him observe,

1. That by art. 42, the velocity of the wheel must be
just 577 thousandth parts of the velocity of the water ;
therefore if the velocity of the water, per second, be
multiplied by ,577 the product will be the maximum
velocity of the wheel, or velocity that will produce the
greatest effect, which is the third column in the table.

2. The velocity of the wheel per second, multiplied
by 60, produces the distance the circumference moves
per minute, which divided by 47,1 feet, the circumfe-
rence of a 15 feet wheel, quotes the number of revolu-
tions of the wheel per minute, which is the fourth column^

3. That by art. 20 and 74, the number of revolutions
of the wheel per minute, multiplied by the number of
cogs in all the driving wheels, successively, and that
product divided by the product of the number of cogs
in all the leading wheels, multiplied successively, the
quotient is the revolutions of the stones per minute,
which is the ninth and twelfth columns.

4. The cubochs of power required to drive the stone,
being, by art. 61, equal to 111,78 cubochs per second,
which, divided by half the head of water, added to all
tlie fall (if any), being the virtual or effective head by
art. 61, quotes the quantity of water, in cubic feet, re-
quired per second, which is the thirteenth column.

5. The quantity required, divided by the velocity with
which it is to issue, quotes the area of the aperture of the
gate — fourteenth column.

6. The quantity required, divided by the velocity of
the water proper for it to move along the canal, quotes
the area of the section of the canal — fifteenth column.

7. Having obtained their areas, it is easy, by art. 65,
to determine the width and depth, as may suit other
circumstances.

Chap. 1.]

OF UNDERSHOT MILLS.

157

THE MILLWRIGHT'S TABLE

UNDERSHOT MILLS,

CALCULATED FOR A WATER-WHEEL OF FIFTEEN FEET, AND
STONES OF FIVE FEET DIAMETER.

[3;;

o
o

"^'

«<

O S"

-• n

" n

— . T

3t3

-3 n

■3

P -s

2. "

^^.

».

feet.

p n>
p ^

3" en

p'5
3 S-

feel.

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

8,1
11,4
14,
16,2
18,
19,84
21,43
22,8
24,3
25,54
26,7
28,
29,16
30,2
31,34
32,4
33,32
34,34
35,18
36,2
37.11
37,98
38,79
39,6S
40,5

4,67
6,57
8,07

5,94

8,36

10,28

9,3411,19
10,3813,22
11,441 14,6
12,36!l5,74i

Il2i22 54

96'23
88'2o
78 23
66 24

6612448
66I2544

13,15
14,02
14,73
15.42
16,16
16.82
17,42
18,08
18,69
19,22
19,81

16,75
17,86
18,78
19,7
20,5
21,42
22,19
23,03
23,8
24,48
25,23
0,29j2j,82
20,88126,6
21,4127,26
21,86 27,84
22,38 28,5
22,9 29,17
23,3629,75

66:25
66I26
60;25
6026

101,6
99,

100,5
97,
97,
96,2
96,2
97,2

100,2
99,

100,

100,
99,8
99,
99,

112
112

104
96
96
96
96
96
96

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2U2

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sup. fl

98,66

96,2

100,

100,8

100,
99,5
98.4

102,6
97,63
96,5
99,7
97,9
96,1
98 3
98,3
97,
98.6
97,7
96,2
99,

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223,5

111,78

74,52

55,89

44,7

37,26

31,9

27,94

24,84

22,89

20,32

18,63

16,27

15,94

14,9

13,97

13.14

12,42

11,76

11,17

10,64

10,16

9.72

9,32

8,94

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sup. ft.

27,5
98
4,6
3,45
2.48
1,9 I
1,48
122
1,02
,9
,76
,66
,56
,53
,47
,43
,39
,36
,3:
,3
,29
,26
.25

TJ
,^0

,22

149,
74.5

43;
37,26
29,8
24,84
21,26
18,6
16,56
15,26
13,54
12,42
10,8
10,6
9,93
9.31
8,76
8,28
784
7.4
7,1
6.7/
6,48
6.21
5,96

158 OF UNDERSHOT MILLS. [Chap. 1.

Note, that five feet fall is the least that a single gear
can be built on, to keep the cog-wheel clear of the water,
and give the stone sufficient motion.

Although double gear is calculated to fifteen feet fall,
yet I do not recommend them above ten feet, unless for
some particular convenience, such as two pair of stones
to one wheel, &c. &c. The number of cogs in the wheels
are even, and chosen to suit eight, six, or four arms, so
as not to pass through any of them, this being the com-
mon practice. But when the motion cannot be obtained
without a trundle that will cause the same cogs and
rounds to meet too often, such as 16 into 96, which will
meet every revolution of the cog-wheel, or 18 into 96,
which will meet every third revolution — I advise rather
to put in one more or less, as may best suit the motion,
which will cause them to change oftener. See art. 82.

Note, that the friction at the aperture of the gate will
greatly diminish both the velocity and power of the wa-
ter in this application, where the head is great, if the
gate be made of the usual form, wide and shallow.
Where the head is great, the friction will be great. See
art. 55. Therefore the wheel must be narrow, and the
aperture of the gate of a square form, to evade the fric-
tion and loss that may be under a wide wheel, if it does
not run close to the sheeting.

Use of the Table.

Having levelled your mill-seat carefully, and finding
such fall and quantity of water as determines you to
make choice of an undershot wheel ; for instance, sup-
pose 6 feet fall, and about 45 cubic _ feet of water per
second, which you find as directed in art. So', cast oft"
about 1 foot for fall in the tail-race, below the bottom of
the wheel, if subject to back-water, leaves you 5 feet
head ; look for five feet head in the first column of the
table, and against it are all the calculations for a 15 feet
water-wheel and 5 feet stones ; in the thirteenth column
you have 44,7 cubic feet of water; which shews you
have enough for a five feet pair of stones j and the velocity

Chap. 1.] OF UNDERSHOT MILLS. 159

of the water will be 18 feet per second, the velocity of the
wheel 10,38 feet per second, and it will revolve 13,22
times per minute. And if you choose double gear, then
66 cogs in the master cog-wheel, 24 rounds in the wal-
lower, 48 cogs in the counter cog-wheel, and 18 rounds
in the trundle, will give the stone 97 revolutions in a
minute; if single gear, 112 cogs and 15 rounds give
98,66 revolutions in a minute ; it will require 44,7 cubic
feet of water per second ; the size of the gate must be
2,48 feet, which will be about 4 feet wide and ,62 feet
deep, about 71 inches deep ; the size of the canal must
be 29,8 feet; that is, about 3 feet deep, and 9,93 or nearly
10 feet wide. If you choose single gear, you must make
your water-wheel much less, say 7| feet, the half of 15
feet, then the cog-wheel must have half the number of
cogs, the trundle-head the same, the spindle will be
longer, husk lower, and the mill full as good ; but in this
case, it will not do, because a cog-wheel of 66 cogs would
reach the water ; but where the head is 10 or 12 feet, it
will do very well.

If you choose stones, or water-wheels, of other sizes,
it will be easy, by the rules by which the table is calcu-
lated, to proportion the whole to suit, seeing you have
the velocity of the periphery of a wheel of any size.*

* One advantag'e large wheels have over small ones is, they cast off the
back-water much better. The buckets of the low wheel will lift the water
much more than those of the high wheel ; because the nearer the water
rises to the centre of the wheel, the nearer the buckets approach the ho-
rizontal or lifting position.

To make a wheel cast off back-water, fix tlie sheeting below the wheel,
with joints and hinges, so that the end down stream can be raised to shoot
the water as it leaves the wheel on the surface of the backwater, to roll
it from the wheel, and it will drive off the back-water much better. So
says Adrian Dawes, mill-wright, Jersey.

Plate IV. Fig. 28, is an undershot wheel- Some prefer to slant the fore-
bay under the wheel, as in the figure, that the gate may be drawn near the
floats ; because (say they) the water acts with more power near the gate,
than at a distance; which appears to be the case, when we consider, that
the nearer we approach the gate, the nearer the column of water approaches,
to be what is called a perfect definite quantity. See art. 59.

Others again say, that it acquires equal power io descending the shute
(it will certainly acquire equal velocity abating only for the friction of the
shate and air.) When the shute has a considerable descent, the greater
the distance from the gate, the greater the velocity and power of the water;
but where the descent of the shute is not sufficient to overcome the friction
of the air, &c. then the nearer the gate, the greater t-he velocity and power

160 OF TUB MILLS. [Chap. 1.

Obsei-vations on the Table.

1. It is calculated for an undershot wheel constructed,
and the water shot on, as in plate IV, fig. 28. The head
is counted from the point of impact I, and the motion of
the wheel at a maximum, about ,58 of the velocity of
the water ; but when there is plenty of water, and great
head, the wheel will run best at about ,66 or two-thirds
of the velocity of the water ; therefore the stones will
incline to run faster than in the table, in the ratio of 58
to 66, nearly ; for which reason, I have set the motion of
5 feet stones under 100 revolutions in a minute, which is
slower than common practice ; they will incline to run
between 96 and 110 revolutions.

2. I have taken half of the whole head above the point
of impact, for the virtual or effective head, by art. 53 ;
which appears to me will be too little in very low heads,
and perhaps too much in high ones. As the principle
of non-elasticity does not appear to me to operate against
the power so much in low as in high heads, therefore
if the head be only 1 foot, it may not require 223,5
cubic feet of water per second, and if 20 feet, may re-
quire more than 11,17, cubic feet of water per second,
as in the table. See art. 8.

ART. 71.
OF TUB MILLS.

A tub mill has a horizontal water-wheel, that is acted
on by the percussion of the water altogether ; the shaft

of the water ; which argues in favour of drawing the gate near the floats.
Yet, wl>ere the tall is great, or water plenty, and the expense of a deep
penstock considerable, tlie small difference of power is not wortii the ex-
pense of obtaining. In these cases, it is best to have a shallow penstock,
and a long shute to convey the water down to the wheel, drawing the gate
at the top of the shnte: which is frequently done to save expense, in build-
ing saw-mills, with flutter-wheels, which are small undershot wheels, fixed
on the crank, so small as to obtain a suflScient number of strokes of the saw
in a minute, say about 120. This wheel is to be calculated of such a size
as to suit the velocity of the water at the point of impact, so as to make
that number of revolutions in a minutes.

For the method of shooting the water on an undershot wheel, where the
fall is great, see Thomas EUicott's plan, part 5, plate I, fig. 6.

€hap. 1.] OF TUB MILLS. 161

is vertical, carrying the stone on the top of it, and serves
in place of a spindle ; die lower end of this shaft is set
in a step fixed in a bridge-tree, by which the stone is
raised and lowered, as by the bridge-tree of other mills ;
the water is shot on the upper side of the wheel, in a
tangent direction with its circumference. See fig. 29,
plate IV, which is a top view of the tub- wheel, and fig.
30 is a side view of it, with the stone on the top of the
shaft, bridge- tree, &c. The wheel runs in a hoop, like
a mill-stone hoop, projecting so far above the wheel as
to prevent the water from shooting over the ^^heel, and
■whirls it about until it strikes the buckets, because the
water is shot on in a deep narrow column, 9 inches wide
and 18 inches deep, to drive a 5 feet stone, with 8 feet
head — so that all this column cannot enter the buckets
until part has passed half way round the wheel, so that
there are always nearly half the buckets struck at once ;
the buckets are set obliquely, so that the water may
strike them at right angles. See Plate IV. fig. 30. As
soon as it strikes it escapes under the wheel in every di-
rection, as in fig. S9.*

* Note, That in plate IV. fip;. 30, I have allowed the gate to be drawn
inside of the penstock, and not in the shute near the wheel, as is the com-
mon practice; L)eca ise the water will leak out much along side of the gate,
if drawn in the shute But here we must consider, that the gate must'
always be full drawn and the quantity of water regulated by a regulator
in the shute near the wheel; so that the shute will be perfectly full, and
pressed with the whole weight of the head, else a great part of the power
may be lost.

To shew this more plain, suppose the long shute A, from the high head
(shewn by dotted lines) of the undershot mill, fig. 28, be made tight by
being covered at top, then, if we draw the gate A, but not fully, if the shute
at bottom be large enough to vent all the water that issues through the
gate when the shute is full to A, then it cannot fill higher than A; there-
fore all that part of the head above A is lost, it being of no other service
than to supply the shute, and keep it full to A, and the head from A to the
wheel is all that acts on the wheel.

Ajj-ain, wht-n we shut the gate, the shute cannot run empty, because it
would leave a vacuum in the head of the shuie at A; therefore the pressure
of the atmosphere resists the water from running out of the shute, and
whatever head of water is in the shute, when the gate is shut, will balance
its weight of the pressure of the atmosphere, and prevent it from acting on
the lower side of the gale, which will cause it to be very hard to draw.
For, suppose 11 feet head of water to be in the shute when the gate was
shut, its pressure is equal to about 5 lb. per square inch ; then, if the gate
be 48 by 6 inches, which is equal to 288 inches, this multiplied by 5, is
equal to 1440 lb. the additional pressure on the gate.

Again, if the gale be full drawn, and the shuie be not much larger at
the upper than lower end, all these evils will take place to cause the loss

162 OF TUB MILLS. [Cliap. 1.

The disadvantages of these wheels are,

1. The water does not act to advantage on them, we
being obliged to make them so small to obtain velocity
to the stone (in most cases) that the buckets take up a
third part of their diameter.

2. The water acts with less power than on undershot
wheels, as it is less confined at the time of striking the
•wheel, and its non- elastic principle takes place more
fully. See art. 8.

3. It is with difficulty we can put a sufficient quantity
of water to act on them to drive them with sufficient
power, if the head be low ; therefore I advise to strike
the w^ater on in two places, as in Plate IV. fig. 29 ; then
the apertures need only be about 6 by 13 inches each,
instead of 9 by 18, and will act to more advantage ; and
then, in this case, nearly all the buckets will be acted on
at once.

Their advantages are.

Their exceeding simplicity and cheapness, having no
cogs nor rounds to be kept in repair ; their wearing parts
are few, and have but little friction ; the step-gudgeon
runs under water, therefore, if well fixed, will not get
out of order in a long time ; and they will move with
sufficient velocity and power with 9 or 10 feet total fall,
and plenty of water ; and, if they be well fixed, they will
not require much more \Aater than undershot \Aheels ;
therefore they are vastly preferable in all seats with
plenty of water, and above 8 feet fall.

In order that the reader may fully understand how
the following table is calculated, let him consider,

1. That as the tub-wheel moves altogether by percus-
sion, the water flying clear of the wheel the instant it

of power. To remedy all this, put the gate H at the bottom of the sliute
to regulate the quantity of water by, and make a valve at A to shut on the
inside of the shute, like the valve of a pair of bellows, which will shut when
the gate A is drawn, and open when the gate shu's, to let air into the
shute ; this plan will do better than long open shutes, for saw-mills with
flutter-wheels or tub-mills, as by it we evade the friction of the shute and
resistance of the air.

The reader will with difficulty understand what is here said, unless he
be acquainted with the theory of the pressure of the atmosphere, vacuums,
&.C. See these subjects, touched on in art. 56.

Chap.l.J OF TUB MILLS. 163

strikes, and it being better, by art. 70, for such wheels
to move faster instead of slower than the maximum ve-
locity ; therefore, instead of ,577, we will allow them to
move ,66 velocity of the water; then multiplying the
velocity of the water by ,66, gives the velocity of the
wheel, at the centre of the buckets; which is the 3d
column in the table.

2. And the velocity of the wheel per second, multi-
plied by 60, and divided by the number of revolutions
the stone is to make in a minute, gives the circumference
of the wheel at the centre of the buckets ; which circum-
ference, multiplied by 7, and divided by 22, gives the
diameter from the centre of the buckets, to produce the
number of revolutions required ; which are the 4th, 5th,
6th, and 7th columns.

3. The cubochs of power required, by art. 63, to drive
the stone, divided by half the head, gives the cubic feet
of water required to produce said power ; which are the
8th and 10th columns.

4. The cubic feet of water, divided by the velocity,
will give the sum of the apertures of the gates ; which
are the 9th and 11th columns.

5. The cubic feet of water, divided by 1,5 feet, the
velocity of the water in the canal, gives the area of a
section of the canal; which are the 12th and 13tti
eolumns.

6. For the quantit}' of water, aperture of gate, and
size of canal, for 5 feet stones, see table for undejrshot
mills, in art. 70.

164

OF TUB MILLS.

[Ghap. 1,

THE MILL- WRIGHT'S TABLE

TUB MILLS.

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fee:.

f e ei

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cub- fi

SU It.

cub. ft.

Sll.f' .

sup. fi.

sup. ft.

22.8

15,04

2,17

2,73

3,3

3,9

17,34

,76

40,9

1.79

11,56

27,3

24.3

16,03

2,5

3,12

3,68

4,37

15,41

,64

36,35

1,5

10,3

24,23

25,54

16,85

2.63

3,28

3.97

4,59

13,87

,54

32,72

1,28

9 25

21,7

26,73

17,64

2,75

3,44

4,15

4,8

12,61

,47

29,74

1,11

8,4

19,83

28,

18,48

2,9

3,6

4,34

4,9

11,56

,41

27,26

.97

7,7

18.17

29,16

19,24

3,01

5,74

4,53

.1.24

10,67

,36

25,17

.86

7,1

16 8

30,2

19,93

3,12

3,9

4,7

5,43

9,9

,33

23,36

6,6

15.56

31,34

20,68

3,24

4,03

4,87

5.67

9,24

,29

21,93

6,16

14,62

32,4

21,38

3,34

4,12

5,01

5,83

8,67

,27

20 45

5,71

13,('

33,32

21,99

3,43

4,25

5,18

5,95

8,16

,24

19,24

,57

5.44

12,15

34,34

22,66

3,54

4 41

5,32

6,18

7,7

,22

18,18

,52

5,13

12,12

35,18

23,21

3,63

4.52

5,47

6,33

7,3

17,

,48

4,9

11,33

20
1

36,2

23,89

3,71
4

4,62
5

5.49
6

6,47
7

6,93

,19

16,36

,45

4,62

10.9

9 1

Chap.l.] OF BREAST MILLS. 165

Use of the Table for Tub Mills.

Having levelled your seat, and finding that you have
above 8 feet fall, and plenty of water, and wish to build
a mill on the simplest, cheapest, and best construction to
suit your seat, you will, of course, make choice of a tub
mill.

Cast off 1 foot for fall in the tail-race below the bot-
tom of the wheel, if it be subject to back-water, and 9
inches for the wheel ; then suppose you have 9 feet left
for head above the wheel; look in the table, against 9
feet head, and you have all the calculations necessary
for 4, 5, 6, and 7 feet stones, the quantity of water re-
quired to drive them, the sum of the areas of the aper-
tures, and the areas of the canals.

If you choose stones of any other size, you can easily
proportion the parts to suit, by the rules by which the
table is calculated.

ART. 7S.
OF BREAST MILLS-

Breast wheels, which have the water shot on them in
a tangent direction, are acted on by the principles of both
percussion and gravity; all that part above the point of
impact, called head, acts by percussion, and all that part
below said point, called fall, acts by gravity.

We are obliged, in this structure of breast mills, to
use more head than will act to advantage ; because we
cannot strike the water on the wheel, in a true tangent
direction, higher than I, the point of impact in Plate IV,
fig. 31, which is a breast-wheel, with 12 feet perpendicu-
lar descent, 6,5 feet of which is above the point I, as head,
and 5,5 feet below, as fall. The upper end of the shute,
that carries the water down to the wheel, must project
some inches above the point of the gate when full drawn,
else the water will strike towards the centre of the
wheel ; and it must not project too high, else the watei

166 OF BREAST MILLS. [Chap. 1.

in the penstock will not come fast enough into the shute
when the head sinks a little. The bottom of the pen-
stock is a little below the top end of the shute, to leave
room for stones and gravel to settle, and prevent them
from getting into the gate.

We might lay the water on higher, by setting the top
of the penstock close to the wheel, and using a sliding
gate at bottom, as shewn by the dotted lines ; but this
is not approved of in practice. See Ellicott's mode,
part 5, plate III, fig. 1.

But if the water in the penstock be nearly as high as
the wheel, it may be carried over, as by the upper dotted
lines, and shot on backwards, making that part next the
wheel the shute to guide the water into the wheel, and
the gate very narrow or shallow, allowing the water to
run over the top of it when drawn; by this method
(called Pitchback) the head may be reduced to the same
as it is for an overshot wheel ; and then the motion of
the circumference of the wheel will be equal to the mo-
tion of an overshot wheel, whose diameter is equal to
the fall below the point of impact, and their power will
be equal.

This structure of a wheel, Plate IV. fig. 31, 1 take to
be a good one, for the following reasons, viz.

1. The buckets, or floats, receive the percussion of the
water at right angles, which is the best direction possible.

2. It prevents the water from flying towards the cen-
tre of the wheel, without re-acting against the bottom of
the buckets, and retains it in the wheel, to act by its gra-
vity in its descent, after the stroke.

3. It admits air, and discharges the water freely, with-
out lifting it at bottom ; and this is an important advan-
tage, because, if the buckets of a wheel be tight, and the
wheel wades a little in back-water, they will lift the
water a considerable distance as they empty ; the pres-
sure of the atmosphere prevents the water from leaving
the buckets freely, and it requires a great force to lift
them out of the water with the velocity of the wheel;
which may be proved by dipping a common water-
bucket into water, and lifting it out, bottom up, with a
quick motion, you have to lift not only the water in the

Chap. 1.] OF BREAST MILtS. 167

bucket, but it appears to suck a deal more up after it ;
which is the effect of the pressure of the atmosphere,
See art. 56. This shews the necessity of air-holes to let
air into the buckets, that the water may have liberty to
get out freely.

Its disadvantages are,

1. It loses the water much, if it is not kept close to
the sheeting. And,

2. It requires too great a part of the total fall to be
used as head, which is a loss of power, one foot fall
bejjig equal in power to two feet head, by art. 8.

Plate IV. Fig. 32 is a draught, shewing the position
of the shute for striking the water on a w^heel in a tangent
direction, for all the total perpendicular descents from 6
to 15 feet ; the points of impact are numbered inside the
fig. with the number of the total fall, that each is for
respectively. The top of the shute is only about 15 in-
ches from the wheel, in order to set the point of impact
as high as possible, allowing .3 feet above the upper end
of the shute to the top of the water in the penstock, which
is little enough, w-hen the head is often to be run down
any considerable distance ; but where the stream is stea-
dy, being always nearly the same height in the penstock,
2 feet would be sufficient, especially in the greatest total
falls ; where the quantity is less, raising the shute 1 foot
would raise the point of impact nearly the same, and
increase the power, because 1 foot fall is equal in power
to 2 feet head, by art. 61.

On these principles, to suit the applications of water,
as represented by fig. 32, I have calculated the following
table for breast mills. And, in order that the reader
may fully understand the principles on which it is cal-
culated, let him consider as follows :

1. That all the water above the point of impact, called
head, acts wholly by percussion, and all below said point,
called fall, acts wholy by gravity, (see art. 60,) and form
the 2d and 3d columns.

2. That half the head, added to the whole fall, con-
stitutes the virtual or effective descent, by art. 61 5 which
is the 4th column.

168 OF BREAST MILLS. [Chap. 1.

3. That if the water was permitted to descend freely
down the circular sheeting, after it passes the point of
impact, its velocity would be accelerated, by art. 60, to
be, at the lowest point, equal to the velocity of water
spouting from under a head equal to the whole descent ;
therefore the maximum velocity of this wheel will be a
compound of the velocit)^ to suit the head and the acce-
leration after it passes the point of impact. Therefore,
to find the velocity of this wheel, I first multiply the
velocity of the head, in column 5, by ,577, (as for under-
shot mills,) which gives the velocity suitable to the head ;
I then, (by the rule for determining the velocity of over-
shots,) say, as the velocity of water descending 21 feet,
equal to 37,11 feet per second, is to the velocity of the
wheel 10 feet per second, so is the acceleration of velo-
city, after it passes the point of impact, to the accelerated
velocity of the wheel ; and these two velocities added,
gives the velocity of the wheel ; which is the 6th column.

4. The velocity of the wheel per second, multiplied
by 60, and divided by the circumference of the wheel,
gives the revolutions per minute ; 7th column.

5. The number of cogs in the cog-wheel, multiplied
by the number of revolutions of the wheel per minute,
and divided by the rounds in the trundle-head, will give
the number of revolutions of the stone per minute ; and
if we di^'ide by the number of revolutions the stone is
to have, it gives the rounds in the trundle, and, when
fractions arise, take the nearest whole number ; columns
8, 9, and 10.

6. The cubochs of power required to turn the stone,
by art. 63, divided by the virtual descent, gives the
cubic feet of water required per second ; column 11.

7. The cubic feet, divided by the velocity of water
allowed in the canal, suppose 1,5 feet per second, gives
the area of a section of the canal ; column 12.

8. If the mill is to be double geared, take the revolu-
tions of the wheel from column 7 of this table, and look
in column 4 of the undershot table, art. 70, for the num-
ber of revolutions nearest to it, and against that number
you have the gears that will give a 5 feet stone the right
motion.

Chap. 1.]

OF BREAST MILLS.

169

THE MILL- WRIGHT'S TABLE

BREAST MILLS,

Calculated for a Water-wluel fifteen Feet, and Stones five Feet, diameter;
the Water being shot on in a tangent direction to the circutpferencc of
ihc Wheel.

-a 2

o :;.
c ft

>2 3

feet, feet fee'

4,5

5,5

5.9

6,2

6 5

6,8

6.8

6,9

1,5

3,1

3,8

4,5

5,3

6,2

7,1

feet.

feet

5,75 17,13
4,5 18,
5,25|18.99
6,05ll9,48
6,9 '20,16

feet.

No.

7,75
8,7
9.6
10,55
11,5

20,64

21,11

21.11

21,3

21,13

No.

10,61 13.5
11,3 14,4
12,07 15,3
12,5316,
13,0716,6
13,5317,
14,03 17.81
14,35 18,28
14,4118.35
14 7618,56

112
112
104

H-

*•

J- ^.

•^

Ct!

IT*

N.' No. cub. ft.| su. ft.

15100,8
16 100,8
16 99,41
104;i6'l02,7
9616; 99,6
96|l6l02,

9617
9618
96|l8
96118

6 I 7 \ 8 19

100,5
97,5
97,8
98,4

29,8 I
24,83
21,29
18,45
16,2
14,42
12,73
11,63
10,59
9,72

10 11

19.25

16,55

14,19

12,3

10,8

9,61

8,49

7,75

7,06

6,48

170 OF BREAST MILLS. [Chap. 1

Use of the Table for Breast Mills.

Having a seat with above 6 feet fall, but not enough
for an overshot mill, and the water being scarce, so that
you wish to make the best use of it, leads you to the
choice of a breast mill.

Cast off about 1 foot for fall in the tail race below the
bottom of the wheel, if much subject to back-water ; and
suppose you have then 9 feet total descent; look for it
in the first column of the table, and against it you have
it divided into 5,9 feet head above, and 3,1 feet fall be-
low the point of impact, which is the highest point that
the water can be fairly struck on the A^'heel, leading the
head 3 feet deep above the shute ; which is equal to
6,5 feet virtual or effective descent ; the velocity of the
water striking the wheel 18,99 feet, velocity of the wheel
12,07 feet per second, will revolve 16 times in a minute ;
and, if single geared, 104 cogs, and 16 rounds, gives the
stone 99,4 revolutions in a minute, requires 21,29 cubic
feet of water per second; the area of a section of the
canal must be 14,19 feet, about 3 feet deep, and 5 feet
wide. If the stones be of any other size, it is easy to
proportion the gears to give them any number of revo-
lutions required.

If you wish to proportion the size of the stones to the
power of your seat, multiply the cubic feet of water your
stream affords per second, by the virtual descent in
column 4, and that product is the power in cubochs ;
then look in the table, in art. 63, for the size of the stone
that nearest suits that power.

For instance, suppose your stream affords ji cubic
feet of water per second, then 14 multiplied by 6,05
feet virtual descent, produces 84,7 cubochs of power ;
which, in the table in art. 63, comes nearest to 4,5 feet
for the diameter of the stones ; but, by the rules laid
down in art. 63, the size may be found more exactly.

Note, 6 cubochs of power are required to every super
ficial foot of the stones.

Chap. 1.] OF OVERSHOT MILLS. 171

ART. 73.

OF OVERSHOT MILLS.

Fig. 33, plate IV, is an overshot wheel ; the water is
laid on at the top, so that the upper part of the column
will be in a true tangent direction with the circumference
of the wheel, but so that all the water may strike within
the circle of the wheel.

The gate is drawn about 30 inches behind the perpen-
dicular line from the centre of the wheel, and the point
of the shute ends at said perpendicular, with a direction
a little downwards, which gives the water a little velocity
downwards to follow the wheel ; for if it be directed
horizontally, the head will give it no velocity down-
wards and if the head be great, the parabolic curve,
which the spouting water forms, will extend beyond the
outside of the circle of the wheel, and it will incline to
fly over. See art. 44 and 60.

The head above the wheel acts by percussion, as on
an undershot wheel, and we have shewn, art. 43, that
the head should be such as to give the water velocity 3
for 2 of the wheel. After the water strikes the wheel
it acts by gravity ; therefore, to calculate the power, we
must take half the head and add it to the fall, for the
virtual descent, as in breast mills.

The velocity of overshot wheels is as the square roots
of their diameters. See art. 43.

On these principles, I have calculated the following-
table for overshot wheels ; and, in order that the reader
may understand it fully, let him consider well the follow-
ing premises :

'1 . That the velocity of the water spouting on the wheel
must be one and a half the velocity of the wheel, by art.
43 : then, to find the head that will give said velocity,
say, as the square of 16,2 feet per second, is to 4ieet,
the head that gives that velocity, so is the square of the
velocity required, to the head that will give that velocity :
but to this head, so found, we must add a little by con-
jecture, to overcome the friction of the aperture. See
art. 55.

172 OF OVERSHOT MILLS. [Chap. 1

In this table, I have added to the heads of wheels
from 9 to 12 feet diameter ,1 of a foot, and from IS to
20 I have added 1 tenth more, for every foot increase
of diameter, and from 20 to 30 feet I have added ,05
more to every foot diameter's increase ; which gives a
30 feet wheel 1,5 feet additional head, while a nine feet
wheel has only, 1 tenth of a foot, to overcome the fric-
tion. The reason of this great difference will appear
when we consider that the friction increases as the aper-
ture decreases, and as the velocity increases : but this
much depends on the form of the gate, for if that be
nearly square, there will be but little friction, but if very
oblong, say 24 inches by half an inch, then it will be
very great.

The heads, thus found, compose the 3d column.

2. The head, added to the diameter of the wheel,
makes the total descent, as is column 1.

3. The velocity of the wheel per second, taken from
the table in art. 43, and multiplied by 60, and divided by
the circumference of the wheel, quotes the number of
revolutions of the wheel per minute, and is column 4.

4. The number of revolutions of the wheel per minute,
multiplied by the number of cogs in all the driving
wheels successively, and that product divided by the
product of all the leading wheels, qiiotes the number of
revolutions of the stone per minute, and is column 9,
double gear, for 5 feet stones ; and column 12, single
gear, for 6 feet stones.

5. The cubochs of ])ower required to drive the stone,
by table in art. 63, divided by the virtual or effective
descent, which is half the head added to the (foil or)
diameter of the wheel, quotes the cubic feet of Avater
required per second to drive the stone, and is column 13.

6. The cubic feet required, divided by the velocity
you intend the water to have in the canal, quotes the
area c^ a section of the canal. The width multiplied by
the depth, must always produce this area. See art. 64.

7. The number of cogs in the wheel, multiplied by
the quarter inches in the pitch, produces the circumfe-
rence of the pitch circle : which, multiplied by 7, and

Chap. 1.] OF OVERSHOT MILLS. 173

divided by 23, quotes the diameter in quarter inches ;
which, reduced to feet and parts, is column 15. The
reader may here at once observe how near the cog-
wheel, in the single gear, will be to the water ; that is,
how near it is, in size, equal to the water-wheel.

Use of the Table.

Having with care levelled the seat on which you mean
to build, and found, that after deducting 1 foot for fall
below the wheel, and a sufficiency for the sinking of the
head race, according to its length and size, and having a
total descent remaining sufficient for an overshot wheel,
suppose 17 feet ; then look in column 1 of the table, for
the descent nearest to it, we find 16,74 feet, and against
it a wheel 14 feet diameter; head above the wheel 2.7
feet; revolutions of the wheel per minute 11,17 ; (and
double gears, to give a 5 feet stone 98,7 revolutions per
minute ; also, single gears, to give a 6 feet stone 76,6
revolutions per minute ;) the cubic feet of water required
for a 5 feet stone 7,2 feet per second, and the area of a
section of the canal 5 feet, about 2 feet deep, and 2,5
feet wide.

If you choose to proportion the size of the stones ex-
actly to suit the power of the seat, do it as directed in art.
63. All the rest can be proportioned by the rules by
which the table is calculated.

174

OF OVERSHOT MILLS.

[Chap.

THE MILLWRIGHT'S TABLE

OVERSHOT MILLS,

CALCULATED FOU FIVE FEET STONES, DOUBLE GEAR, AND SIX
FEET STONES, SINGLE GEAR.

Double gear, 5

Single gear,

~>S. p

r» CO —

; r. P

tr
re

feet stones,
r— -- ^ ,

6 ft. stones.

5^
0'

re »■

=• n P

0^ 3

sr^ re

*** fii m

., =■

■z,

fT'

■0 re ■

re fi c*
(o ^ re

:scent of the water, w hi
ible made to suit the d
wheel and head above i

—.

zr
re
re

3ve the wheel, allowing
n of the aperture, so as
t(-r velocity 3 for 2 of the

re
<

3 e
3 5-

S. 3

re »

■

0!)
CO

re
1

J!?

c
3

=r
re

re
o_
c"

3
%%

3
3-

re
<

7 re

^
re ;^

5 ;?

re B,
re

ii seciion of the canal, a
locity ot tlie water in it
er second.

• 3-1

re -

CO "Z.
ce _.

5"o

gt; 3-
fT 2.

3Z
"5.7

ch is i
iamete

it.

? o"
re < ET

n
re

•a

sr
re
2.

re
re

•a

re
3

re"

c"
re 3

"^ =

."" re re

-1

102,9

78,

-""

h-!rq

*. %■

feet.

ft.

feet.

cn.ft.

Slip, ft

feet, inches.

10,51

1,51

14,3

11,46

6:9 0-4 12 22

11,74

1,74

13,

98,

78,

10,3

12,94

1,94

12,6

96,

75,6

9,34

7:5 1-4

14,2

2,2

12,

97,

79,2

8,53

15,47

2,47

11,54

99,3

80,7

7,92

9:5 1-2

16.74

2.74

11,17

98,7

76,6

7.2

7,2

10:9 3-4 6-22

17,99

2,99

10,78

98,3

13'

81.9

6,77

19,28

3,28

10,4

99,5

120

76,

6,4

13:6 1.4 2-22

20,5

3,5

10,1

96,6

120

80,8

21,8

3.8

9,8

97.

128

78,4

5,56

14:5 0-4 8-22

23,03

4,03

9,54

98,3

128

81,4

5,32

5.32

24,34

4,34

9,3

2^.

100,

128

79.3

5,04

25,54

4.54

9,1

98,3

128

77,6

4,81

26,86

4.86

8,9

100.5

128

81,4

4,57

27,99 2]

4,99

8,7

100,2

4,34

29,27 24

5,27

8,5

103,

4,19

30,45j25

5,4.1

8,3

25 54

101,

31,57|26

5,57

8,19

25'54

99,6

3,82

32.77I27

5,77

8,03

104

25;54

100,2

3,7

^,7 i

33,96;28

5.96

7,93

104

?.5 54

99,

3,6

3.6 1

3.5,15:29

6,15

7,75

112

2654

100.1

3,4

3.4 i

36,4 30

6,4

7,6.S
4

2654

18
8

98,6

3,36

1 I2

' 3

14 i

Chap.!.] OF OVERSHOT MILLS. ITS

Observations oji the Table.

1. It appears, that single gear does not much suit this
construction ; because, where the water-wheels are low,
their motion is so slow that the cog-wheels, (if made large
enough to give sufficient motion to the stone, without
having the trundle too small, see art. 23,) will touch the
water : And again, when the w^ater-wheels are high,
above 20 feet, the cog-wheels require to be so high, in
order to give motion to the stone without having the
trundle too small, that they become unwieldy, and the
husk too high, spindle short, he. so as to be inconvenient.
Therefore, "single gear seems to suit overshots only where
the diameter of the water-wheel is between 12 and 18
feet; and even with them the water-wheel will have to
run rather too fast, or the trundle be rather too small,
and the stones should be 6 feet diameter at least.

2. I have, in the preceding tables, allowed the water
to pass along the canal with 1,5 feet per second velocity;
but have since concluded that 1 foot per second is nearer
the proper motion ; that is, about 20 yards per minute ;
then the cubic feet required per second, will be the area
of a section of the canal, as in column 14 of this table.

3. Although I have calculated this table for the velo-
cities of the wheels to vary as the square roots of their
diameters, which makes a 30 feet wheel move 11,99 feet
per second, and a twelve feet wheel to move 7,57 feet per
second; yet they will do to have equal velocity, and
head, which is the common practice among mill-wrights.
But, for the reasons I have mentioned in art. 43, I prefer
giving them the velocity and head assigned in the table,
in order to obtain steady motion.

4. Many have been deceived, by observing the ex-
ceeding slow and steady motion of some very high over-
shot wheels working forge or furnace bellows, conclud-
ing therefrom, that they will work equally steady with a
very slow as with any quicker motion, not considering,
perhaps, that it is the principle of the belloU's that regu-
lates the motion of the wheel, which is different from any

176 OF OVERSHOT MILLS. [Chap.l.

other resistance, for it soon becomes perfectly equable ;
therefore the motion will be uniform, which is not the
case with any kind of mills.

5. Many are of opinion, that water is not well applied
by an overshot wheel; because, say they, those buckets
near above or below the centre, act on too short a lever.
In endeavouring to correct this error, I have divided the
fall of the overshot wheel, fig- 33, plate IV, into feet, by
dotted lines. Now, by art. 53 and 54, every cubic foot
of water on the wheel produces an equal quantity of
power in descending each foot perpendicular, called a
cuboch of pouer; because, where the lever is shortest,
there is the greatest quantity of water within the foot per-
pendicular; or, in other words, each cubic foot of water
is a much longer time, and passes a gi'eater distance, in
descending a foot perpendicular, than where it is long-
est; which exactly compensates for the deficiency in the
length of lever. And, considering that the upper and
lower parts of the wheel do not run away from the
gravity of the water, so much as the breast of the wheel,
we must conclude, that the upper and lower feet of per-
pendicular descent (in theory) actually produce more
power than the middle two feet; but (in practice) the
lower foot is entirely lost, by the spilling of the water
out of the buckets. See this demonstrated, art. 54.*

Of Mills moved by Re-action.

We have now treated of the four different kinds of
mills that are in general use. There are others, the in-
vention, or improvements of the late ingenious James
Rumsey, which move by the re-action of the water. One

• The Messrs. EUicoHs have coiistructeil overshot wheels at their mills
wear Baltimore, so that they retain the water the whole of its descent, de-
livering- it under the centre ol the wheel. This is done by iialtsoaling the
wheel outside of the rim, and to prevent the water from splashing over
the sides as it conges on the wheel, they extend the rim outside of the buck-
ets by nailing ro ind it two pieces one and a iialf inch thick, on each ritn,
increasing the diameter three inches ; these also help to hold in the buckets
and soaling firmly. Two advantages are expected from this construction;
first, retaining tlie water the whole of the descent ; secondly, the wheel
wdl run more steadily, as it cannot fly off as rapidly when the resistance is
taken ofl", as it would have left the water on the rising side.

Chap. 1.] OF MILLS MOVED BY RE-ACTION. 177

of these is said to do well where there is much back-
water ; it being small, and of a true circular form, the
back-water does not resist it much. I shall say but little
of these, supposing the proprietors mean to treat of them ;
but may say, that there appears to me but two principles
by which water can be applied to move mill-wheels, viz.
Percussion and Gravity.

For the different effects of equal quantities of water,
with equal perpendicular descents, applied by these dif-
ferent principles, see art. 8 and 68.

Water may be applied, by percussion, two ways, viz.
by action (which is when it strikes the floats of a wheel)
and by re-action, which is when it issues from within the
wheel, and, by its re-action, moves it round ; and these
two are equal, by 3d general law of motion, art. 7.

For the effects of centrifugal force, and the inertia of
the water, on this application of re-action, see axioms I,
and II, art. 1 ; and art. 13. The principle of inertia will
operate in proportion to the quantity of water used ;
therefore this application will suit high heads better than
low ones.

Water may be applied, by gravity, two ways, viz.
either by spouting it high on the wheel, into tight buck-
ets, as on common overshots, or by causing the whole
head of water to press on the floats, at the lower side of
the wheel, which is so constructed that the water cannot
escape, but as the wheel moves, and at the same time
keeping clear of the paradoxical principle mentioned in
arts. 48 and 59 ; w^hich cannot be done unless the floats
are made to move on pivots, so as to fold in on one side
of the wheel, and open out, to receive the weight of the
water, on the other. And these two applications are
equal in theory, as will appear plain by art. 54, plate III.
fig. 20 ; yet they may differ greatly in practice.*

• In the year 1786, I invented and made a model of a wheel of this struc •
ture, intending thereby to apply steam to propel land-carriages, and exhi-
bited a drawing thereof to the legislature of Maryland, and obtained a
patent (for my improvements in mills, and also) for applying steam to
land-carriages, in that state; but coald not attend to put it iii practice.
Since which time, the late ingenions James Rumsey has applied this wheel
to water-mills, which I did not intend to do. This may properlv be crdlcd
the Valve Wheel. . i i .

178 RULES AND CALCULATIONS. [Chap. 2.

CHAPTER IL

ART. 74.
RULES AND CALCULATIONS.

THE fundamental principle, on which is founded all
rules for calculating the motion of wheels, produced by
a combination of wheels, and for calculating the number
of cogs to be put in wheels, to produce any motion that
is re(]uired, see in art. 20 ; \^'hich is as follows :

If the revolutions that the first moving wheel makes
in a minute be multiplied by the number of cogs in all
the driving wheels successively, and the product noted ;
and the revolutions of the last leading wheel be multi-
plied by the number of cogs in all the leading wheels
successively, and the product noted ; these products
will be equal in all possible cases. Hence \^e deduce
the following simple rules :

1st. For finding the motion of the mill-stone : the
revolutions of the water-wheel, and cogs in the wheels,
being given,

RULE.

Multiply the revolutions of the v\^ater-wheel per mi-
nute, by the number of cogs in all the driving v\heels
successively, and note the product; and multiply the
number of cogs or rounds in all the leading wheels suc-
cessively, and note the product; then divide the first
product by the last, and the quotient is the number of
revolutions of the stone per minute.

EXAMPLE.

Given, the revolutions of the water-uheel

per minute, ------ 10,4

No. of cogs in the master cog-wheel 78 7 D^Typj.,,

No. of do. in the counter cog-wheel 48 3

Chap. 2.] RULES AND CALCULATIONS. ir9

No. of rounds in the vvallower - ^^ ? t a
No. of do. in the trundle - ^ ^ ^ 1-eaders.

Then 10,4, the revolutions of the water-wheel, multi-
plied by 78, the cogs in the master wheel, and 48, the
cojTs in the counter wheel, is equal to 38937,6; and 23
rounds in the wallower, multiplied by 17 rounds in the
trundle, is equal to 391, by which we divide 38937,6,
and it quotes 99,5, the revolutions of the stone per mi-
nute; which are the calculations for a 16 feet wheel, in
the overshot table.

2d. For finding the number of cogs to be put in the
wheels, to produce any number of revolutions required
to the mill-stone, or any wheel,

RULE.

Take any suitable number of cogs for all the wheels,
except one; then multiply the revolutions of the first
mover per minute, by all the drivers, except the one
wanting (if it be a driver) and the revolutions of the
wheel required, by all the leaders, and divide the great-
est product by the least, and it will quote the number of
co,^s required in the w heel to produce the desired revo-
lutions.

Note, if any of the wheels be for straps, take their
diameter in inches and parts, and multiply and divide
with them, as with the cogs.

EXAxMPLE.

Given, the revolutions of the water-wheel
And we choose cogs in master wheel 78
Ditto in the counter wheel - 48

And rounds in the wallower - 23

The number of the trundle is required, to give the
stone 99 revolutions.

Then 10,4 multiplied by 78, and 48, is equal to 38937,6;
and 99, muhiplied by 23, is equal to 2277, bv which
divide 38937,6, and it quotes 16,66; instead of which,
I take the nearest whole number, 17, for the rounds in
the trundle, and find, by rule 1st, that it produces 99,5
revolutions, as required.

180 RULES AND CALCULATIONS. [Chap. 2.

For the exercise of the learner, I have constructed
fig. 7, plate XI; which I call a circle of motion, and
which serves to prove the fundamental principle on
which the rules are founded ; the first shaft being also
the last of the circle.

A is a cog-wheel of SO cogs, and is a driver.

do.

leader.

do.

24.

driver.

do.

leader.

do.

driver.

do.

leader.

do.

driver.

do.

leader.

But if we trace the circle the backward way, the lead-
ers become drivers.

I is a strap-wheel 14| inches diameter, driver.
K do. 30 do. - leader.

L cog-wheel 12 cogs, - driver.

M do. 29 do. - leader.

MOTION OF THE SHAFTS.

The upright shaft, and first driver, AH 36 revs, in a min.

BC 30 do.
DE24do.
FG20do.
HA 36 do.
M 4 do. which is
the shaft of a hopperbo}'.

If this circle be not so formed, as to give the first and
last shafts (which are here the same) exactly the same
motion, one of the shafts must break as soon as they are
put in motion.

The learner may exercise the rules on this circle, un-
til he can form a similar circle of his own; and then he
need never be afraid to undertake to calculate any motion,
&c. afterwards.

- I omit shewing the vrork for finding the motion of the
several shafts in this circle, and the wheels to produce

Chap. 2.] RULES AND CALCULATIONS. 181

said motion ; but leave it for the learner to practise the
rules on.

EXAMPLES.

1st. Given, the first mover AH 36 revolutions per
minute, and first driver A 20 cogs, leader B 24; required,
the revolutions of shaft BC. Answer, 30 revolutions per
minute.

2d. Given, first mover 36 revolutions per minute,
drivers 20 — 24 — 25, and leaders 24 — 30 — 30 ; required,
the revolutions of the last leader. Answer, 20 revolu-
tions per minute.

3d. Given, first mover 20 revolutions per minute, and
first driver, strap-wheel, 14^ inches, cog-wheel IS, and
leader, strap-wheel, 30 inches, cog-wheel 29; required,
the revolutions of the last leader, or last shaft. Answer,
4) revolutions.

4th. Given, first mover 36 revolutions, driver A 20,
C 2% leader B 24, D 30 ; required, the number of
leader F, to produce 20 revolutions per minute. Answer,
30 cogs.

5th. Given, first mover 36 revolutions per minute,
driver A 20, C 24, E 25, driver pulley 14| inches dia-
meter, L 12, and leader B 24, D 30, F 30, M 29 ; re-
quired, the diameter of strap-wheel K, to give shaft 4
four revolutions per minute. Answer, 30 inches dia-
meter.

The learner may, for exercise, work the above ques-
tions, and e^•ery other that he can propose on the circle.

ART. 75.

Mathematicians have laid down the following propor-
tions for finding the circumference of a circle by its dia-
meter, or the diameter by the circumference given, viz.

As 1 is to 3,1416, so is the diameter to the circumfe-
rence ; and as 3,1416 is to 1, so is the circumference to
the diameter : Or, as 7 is to 22, so is the diameter to the
circumference ; and as 22 is to 7, so is the circumference

182 RULES AND CALCULATIONS. [Chap. 2.

to the diameter. The last proportion makes the diameter
a little the largest ; therefore it suits mill-vvrights best
for finding the pitch circle ; because the sum of the dis-
tances, from centre to centre, of all the cogs in a wheel,
makes the circle too short, especially where the number
of cogs are few, because the distance is taken in straight
lines, instead of the circle. In a wheel of 6 cogs only,
the circle will be so much too short, as to give the dia-
meter -jI^ parts of the pitch or distance of the cogs too
short. Hence we deduce the following

RULES FOR FINDING THE PH CH CIRCLE.

Multiply the number of cogs in the wheel, by the
quarter inches in the pitch, and that product by 7, and
divide by 23, and the quotient is the diameter in quarter
inches, which is to be reduced to feet.

EXAMPLE.

Given, 84 cogs 4)| inches pitch ; required, the diameter
of the pitch circle.

Then, by the rule, 84< multiplied by 18 and 7i is equal
to 10584; which, divided by 22, is equal to "^81^% quar-
ter inches, equal to 10 feet ^^~JL inches, for the diameter
of the pitch circle required.

ART. 7Q.

A true, simple, and expeditious method of finding the
diameter of the pitch circle, is to find it in measures of
the pitch itself that you use.

RULE.

Multiply the number of cogs by 7, and divide by 22,
and you have the diameter of the pitch circle, in mea-
sures of the pitch, and S2 parts of said pitch.

EXAMPLE.

Given, 7^ cogs ; required, the diameter of the pitch
circle. Then, by the rule,

Chap. 2.] RULES AND CALCULATIONS. 183

22)546(24|| C Measures of tlie pitch for the diame-
44 I ter of the 'circle required.

106
88

Half of which diameter. IS/^of the pitch, is the radi-
us, or half diameter, by which the circle is to be swept.

To use this rule, set a pair of compasses to the pitch,
and screM' them fast, not to be altered until the wheel is
pitched ; divide the pitch into 22 equal parts ; then step
12 steps on a straight line with the pitch compasses, and
9 of these equal parts of the pitch makes the radius that
is to describe the circle.

To save the trouble of dividing the pitch for every
wheel, the workman may mark the different pitch, which
he commonly uses, on the edge of his two foot rule (or
make a little rule for the purpose) and carefully divide
them there, where they will be always ready for use.
See plate IV, fig. 35.

By these rules, I have calculated the following table
of the radiuses of pitch circles of the different wheels
commonly used, from 6 to 136 cogs.

184 RULES AND CALCULATIONS. [Chap. 2.

A TABLE

OF THE

PITCH CIRCLES OF THE COGWHEELS

COMMONLY USED,

From 6 to 136 cogfs, both in measures of the Pitch, and in feet, inches,
and parts.

_. ?

T% =-0 ?• I— O C

K 2 S

S. :: o
01 re -'.
o " =.

— -d c re T c ^

■*> 3 -' C

C -a C-g =

= 3 -o S ^

o " c Q - -^ci.
^ lo £ w - - =

55° = -^ 3 2 ,- c

p 2.1 "^^ !. i- ""

~ -• -^ to o ■^. z.

^ 2^ ».- i = _ 5
^ 3- »■ ":: q — ,,

7, - ^ E 3 '^ =

re to c -: _ s:
t: " re >s .; ^

-. re

— CO

" S to _ 2. c

- -H- ^ „ .2 re re

1 =

re =■

— 2.

3 - O

^•o 2.

pitch circl
s in colum
nches, quai

parts of
n the pitc

for boltin

^ o n

, 3" O

u re

3 _.

piu-.h cirri
s in the 4i

infcet,incl
and 22 pari
', when th

inches, lb
Sec.

2 re
■ -o^

4>-

to S" a

crq 3" S5 ,• 3 rt

C 3

-; re (c 7 3- re

tc;-

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^ to

o O^

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w ^— «
f» n S

-J to

re' a s -^

r+ O O 1^

1 1

re r:

to
•a

w i-j 3-

W 1 ^

a> —

ca (0

cn 'X

2:2:0

5 5 1-2

1 : 10 : 1 : 5 1-2

1 :

11 : 2

: 11

7 1

3,5

2 : 3: 12

5 9

1:10:3:21

: 1

8 1

6,7

3:1:3

5 121-2

1:1] : 2: 14 1-2

1 :

9 1

10,2

3 : 2: 14

5 16

2: 0:1: 8

1 : 3

10 1

n 1

13,6

4:0: 3

5 191-2

2: 1:0: 11-2

2 : 1

17,1

4 : 1 : 17

6 1

2: 1:2:17

3 :

12 1

20,5

4:3:5

6 41-2

2: 2:1:10 1.2

3 : 3

13 2

1,9

5 : : 17

6 8

2: 3:0: 4

4 : 2

14 2

5,3

5:2: 8

6 15

2: 4:1:13

6 :

15 2

8,8

5 : 3 : 20

2: 5:3:

7 : 2

16 2

12,2

6 : 1: 11

7 14

2: 8:1:18

10 : 1

17 2

15,7

6:3: 2

8 4

2:11:0:14

1 :

18 2

19,1

7 : 0: 15

8 11

3: 0:2: 1

2:2:

19 3

0,6

7:2:6

8 20

3: 1:3:10

4 :

20 3

4,1

7 : 3: 18

9 13

3: 4:2: 6

6:3:

21 3

^,5

8:1:9

10 11

3: 8:2:11

o :

11 : 1 :

22 3

11,

8:3:0

11 10

4: 0:2:16

3:2:

23 3

14,5

9 : : 13

12 9

4: 4:2:21

7:3:

24 3

18,

9:2:4

13 8

4: 8:3: 4

5 :

?5 3

21,5

9 : 3: 17

4:11:2:

3:0:

j26 4

10 : 1 : 8

14 7

5: 0:3: 9

4:1:

27 4

6,5

10 : 2: 21

15 6

5: 4:3:14

8:2:

28 4

10,

11 : 0: 12

104

16 13

5:10:1: 6

2:1:

29 4

13,5

11 : 2: 3

112

17 18

6: 3:2:20

8:0:

30 4

17,

11 : 3: 16

120

19 2

6: 9:0:12

1:3:

14'

31 4

20,5

12 : 1: 7

128

20 8

7: 2:2: 4

7:2 =

32 6

12 : 2: 20

136

21 14

7: 7:3:18

1:1 =

3 I 4"l

~ 7 1

Ghap. 2.] RULES AND CALCULATIONS. ±8i

Use of the Jbregoing Table.

Suppose you are making a cog-wheel with &6 cogs;
look for the number in the 1st or 4th column, and against
it, ill the 2d or 5th column, you find 10, 11 ; that is, 10
steps of the pitch (you use) on a straight line, and 11 of
22 equal parts of said pitch added, makes the radius that
is to describe the pitch circle.

The 3d, 6th and 7th columns, contain the radius in
feet, inches, quarters, and 22 parts of a quarter ; which
may be made use of in roughing out timber, and fixing
the centres that the wheels are to run in, so that they may
gear to the right depth; but, on account of the difierence
in the parts of the same scales or rules, and the difficulty
of setting the compasses exactly, they can never be true
enough for the pitch circles.

RULE COxMMONLY PRACTISED.

Divide the pitch into 1 1 equal parts, and take in youF
compasses 7 of those parts, and step on a straight line,
counting 4 cogs for every step, until you come up to
the number in your wheel ; if there be an odd one at
last, take 1-4 of a step, if 2 be left, take 1-2 of a step,
if 3 be left, take 8-4 of a step, for them; and these steps,
added, makes the radius or sweep-staff of the pitch circle :
but on account of the difficulty of making these divisions
sufficiently exact, there is little truth in this rule — and
where the number of cogs are few, it will make the dia-
meter too short, for the reason mentioned before.

The following geometrical rule is more true and con-
venient, in some instances.

RULE.

Draw Uie line AB, plate IV. fig. 34, and draw the
line 0,2S at random; then take the pitch in your com-
passes, and beginning at the point 22, step 11 steps to-
wards A, and 3 1-2 steps to point X, towards O; draw
the line AC through the point X ; draw the line DC
parallel to AB; and, without having altered your com-

A a

186 RULES AND CALCULATIONS. [Chap. 2.

passes, begin at point O, and step both ways, as you did
on AB; then, from the respective points, draw the cross
lines parallel to 0,22 ; and the distance from the point,
where they cross the line AC, to the line AB, will be
the radius of the pitch circles for the number of cogs
respectively, as in the figure. If the number of cogs be
odd, say 21, the radius will be between 20 and 22.

This will also give the diameter of all wheels, that
have few cogs, too short ; but where the number of cogs,
is above twenty, the error is imperceptible.

All these rules are founded on the proportion, as %%
is to 7, so is the circumference to the diameter.

ART. 77'
A TABLE OF ENGLISH DRY MEASURE.

Solid"

mci-.es. X The bushel contains SI 50,4

.3 j.6 1 Pint. X solid inches. Therefore, to

268,8 I 8 I Gallon, x^ mcasurc the contents of any

| 215.,4|64|8 TrTT^^^N §^^"^^' ^^^^ ^^^^ following

RULE.

Multiply its length by inches, by its breadth in inches,
and that product by its height in inches, and divide the
last product by 3150,4, and it will quote the bushels it
contains.

But to shorten the work decimally; because 2150,4?
solid inches are 1,244 solid feet, multiply the length,
breadth, and height in feet, and decimal j^arts of a foot
by each other, and divide by l,2i44; and it will quote the
contents in bushels.

EXAMPLE.

Given, a garner 6,25 feet long, 3,5 feet wide, 10,5 feet
high; required, its contents in bushels. Then, 6,25
multiplied by 3,5 and 10,5, is equal to 229,687; which,
divided by 1,244, quotes 184 bushels and 6 tenths.

Chap. 2.] RULES AND CALCULATIONS. 187

To find the contents of a hopper, take the following

RULE.

Multiply the length by the width at the top, and that
product by one- third of the depth, measuring to the very
point, and divide by the contents of a bushel, either in
inches or decimals, as you have wrought, and the quo-
tient will be the contents in bushels.

EXAMPLE.

Given, a hopper 43 inches square at top, and S4) inches
deep; required, the contents in bushels.

Then IS multiplied by 43 and 8, is equal to 14112
solid inches; which, divided, by 2150,4, quotes 6,56
bushels, or a little more than 6| bushels.

To make a gamer to hold any given quantity, having
two of its sides given, take the following

RULE.

Multiply the contents of 1 bushel by the number of
bushels the garner is to hold ; then multiply the given
sides into each other, and divide the first by the last
product; and the quotient will be the side wanted, in the
sanie measure you have wrought in.

EXAMPLE.

Given, tu'-o sides of a garner 6,25 by 10,5 feet; re-
quired, the other side, to hold 184,6 bushels.

Then, 1,244 multiplied by i84,6 is equal to 339,642;
which, divided by the product of the two sides 65,635,
the quotient is 3,5 feet for the side wanted.

To make a hopper to hold any given quantity, having
the depth given.

RULE.

Divide the inches contained in the bushels it is to
hold, by 1-3 the depth in inches; and the quotient will
be the square of one of the sides at the top in inches.
Given, the depth 34 inches; required, the sides to hold
6,56 bushels.

18g OF SPUR GEARS. [Chap. S.

Then, 6,56 multiplied by 2150,4 is equal to 1*107,624;
which, divided by 8, quotes 1764, the square root of
which is 4-2 inches; which is the length of the sides of the
hopper wanted.

CHAPTER III.

ART. 78.
OF THE DIFFERENT KINDS OF GEARS, AND FORMS OF COGS.

IN order to conceive a just idea of the most suitable
form or shape for cogs in cog-wheels, we must consider,
that they describe with respect to the pitch circles, a
figure called Epicycloid.

And when one wheel works in cogs set in a straight
line, such as the carriage of a saw- mill, the cogs or
rounds, moving out and in, form a curve figure called a
Cycloid.

To describe which, let us suppose the large circle in
plate V, fig. 37, to move on the straight line from O to A;
then the point O in its periphery will describe the arph
OD A, called a Cycloid; and we may conceive, by the
way that the curve joins the line, what should' be the
form of the point of the cog.

Again, suppose the small circle to run round the large
one; then the point o in the small circle, will describe
the arch o b c, called an Epicycloid ; by which we may*
conceive the form the point of the cogs should be. But
in common practice, we generally let the cogs extend
but a short distance past the pitch circle ; so that the
form of the cogs is not so particular.

ART. 79.

OF SPUR GEARS.

The principle of spur gears, is that of two cylinders
rolling on each other^ with their shafts or axes truly

Ch^3.} OF SPUR GEARS. 189

parallel to each other. Here the touching parts move
with equal velocity, therefore have but little friction.
And to prevent these cylinders from slipping, we are
obliged to indent them, or to set in cogs. And here it
appears to me, that the pitch of the driving wheel should
be a little larger than the leading wheel, for the follow-
ing reasons :

1. If there is to be any slipping, it will be much easier
for the driver to slip a little past the leader, than for the
cogs to have to force the leader a little before the driver ;
which would be very hard on them.

3. If the cogs should bend any by the stress of the
work (as they surely do ; because lib. falling on a beam
a foot square, will jar it, which cannot be done without
bending it a little) this will cause those that are coming
into gear to touch too soon, and rub hard at entering.

3. It is much better for cogs to rub hard as they are
going out of gear, than as they are coming in ; because
then they work with the grain of the wood ; whereas, at
entering they work against it, and would wear much
faster.

The advantage of this kind of gear is, we can make
the cogs as wide as we please, so that their bearing may
be so large that they will not cut each other, but only
polish and wear smooth ; therefore they will last a long
time.

Their disadvantages are,

1st. That if the wheels be of different sizes, and the
pitch circles are not made to meet exactly, they will not
run smooth. And,

2d.^ We cannot change the direction of the shafts so
conveniently.

Fig. 38, plate V, is two spur wheels working into
each other ; the dotted lines shew the pitch circles,
which must always meet exactly. The ends of the cogs
are made circular, as is common ; but if they were made
ef the true epicycloids that would suit the size of the
wheels, they would work smoother, with less friction.

Fig. 39, is a spur and face wheel or wallower ; whose
pitch circles should always meet exactly also.

190 • OF FACE GEARS. [Gha^a.

The rule for describing the sides of the cogs of a form
near the figure of an epicycloid, is as follows, viz. De-
scribe a circle a little inside of the pitch circle, for the
point of your compasses to be set in, so as to describe
the sides of the cog as the four cogs at A, Plate V. fig.
38 — 39, as near as you can to the curve of the epicycloid
that is formed by the little wheel's moving round the
great one ; the greater the difference between the great
and small wheels, the greater distance must this circle,
be inside of the pitch circle ; of this the practitioner is
to be the judge, as no certain rules is yet formed, that
I know of.*

ART. 80.
OF FACE GEARS.

The principle of face gears, is that of two cylinders
rolling with the side of one on the end of the other, their
axes being at right angles. Here the greater the bearing,
and the less the diameter of the wheels, the greater will be
the friction ; because the touching parts move with dif-
ferent velocities, therefore the fricti(3n will be great.

The advantages of this kind of gear are,

ist. Their cogs stand parallel to each other ; therefore
moving them out or in gear a little, does not alter the

* Mr. Charles Taylor's rule for ascertaining the true cycloidical or epi-
cycloidical form for the point of cogs.

-Vl ike a sepfment of the pitch circle of each wheel, which gear into each
other; fasten one to a plane surface, and roll tlie other roinid it as shewn,
plaie V, fig. 37, art. 79, and with a point in the moveable segment, describe
the epicycloid o b c, set off at tlie end o one-fourth part of the pitch for the
length of the cog outside of the pitch circle Then fix the compasses at
such an opening, that with one leg tliereof in a certain point (to be found
by repeated trials,) the other leg will trace the epicycloid from the pitch
circle to the end of the cog: preserve the set of the con. passes, and through
the pomt where the fixed leg stood, sweep a circle from the centre of the
wherl, in which set one pomt of the compasses to describe the point of all
the cogs of that wheel whose segment 'vas made fast to the plane

If the wheels be bevel gear, this rule may be used to find the true form
fif both the outer and inner ends of the cogs, especially if the cogs be long,
as the epicycloid is different in different circles. In making cast-iron
wheels, it is absolutely necessary to attend to forming the cogs to the true
epicycloidical figure, without which they cannot work smooth and easy.

The same rule serves for ascertaining the cycloidical form of a right line
of cogs, such as those of a saw-mill carriage, &c. or of cogs set inside of a
circle or hollow cone; «here a wiieel works within a wheel, the cogs re'
qtiire a very different shape-

Chap. 3.] OF FACE GEARS. 191

pitch of the bearing parts of the cogs, and they will run
smoother when their centres are out of place, than spur
gears.

2. They serve for changing the direction of the
shafts.

The disadvantages are,

1st. The smallness of the bearing, so that they wear
0ut very fast.*

2d. Their great friction and rubbing of parts.

The cogs for small wheels are generally round, and
put in with round shanks. Great care should be taken
in boring the holes for the cogs, with a machine to direct
the auger straight, that the distance of the cogs may be
equal, without dressing. And all the holes of all the
small wheels in a mill should be bored with one auger,
and made of one pitch ; then the miller may keep by
him a quantity of cogs ready turned, to a gauge to suit
the auger, and when any fail, he can drive out the old
ones, and put in a new set, without much loss of time.

Fig. 40, plate V, represents a face cog-wheel working
into a trundle ; shewing the necessity of having the cor-
ners of the sides of the cogs sniped off in a cycloidical
form, to give liberty for the rounds to enter between the
cogs, and pass out again freely. To describe the sides
of the cogs of the right shape to meet the rounds when
they get fairly into gear, as at c, there must be a circle
described on the ends of the cogs, a little outside of the
pitch circle, for the point of the compasses to be set in,
to scribe the ends of the cogs ; for if the point be set in
the pitch circle, it will leave the inner corners too full,
and make the outer ones too scant. The middle of the
cog is to be left straight from bottom to top, or nearly so,
and the side nearly flat at the distance of half the diame-
ter of the round from the end, the corners only being
sniped off to make the ends of the shape in the figure ;
because when the cog comes into gear fully, as at c,
there is the chief stress, and there the bearing should be

• Fnr if ihe bearing of the cogs be smull, and the stress so great that
they cut one another, iliey will wear exce-ilingly fast; but if it be so large,
and tiie stress so light, that they only polish one another, they will lasc
very long.

192 OF BEVEL GEARS. {Chap. 3.

as large as possible. The smaller the cog-wheel, the
larger the trundle, and the wider the cogs, the more will
the corners require to be sniped off. Suppose the cog-
wheel to turn from 40 to b, the cog 40, as it enters, will
bear on the lower corner, unless it be sufficiently sniped
off; when it comes to c, it will be fully in gear, and if the
pitch of the cog-wheel be a litde larger than that of the
trundle, the cog a will bear as it goes out, and let c fairly
enter before it begins to bear.

Suppose the plumb line A B to hang directly to the
centre of the cog-wheel, the spindle is (by many mill-
wrights) set a little before the line or centre, that the
working round or stave of the trundle may be fair with
said line, and meet the cog fairly as it comes to bear : it
also causes the cogs to enter with less, and go out with
more friction. Whether there be any real advantage in
thus setting the spindle foot before the centre plumb
line, does not seem determined.

ART. 81.

OF BEVEL GEARS.

The principle of bevel gears, is that of two cones
rolling on the surface of each other, their vertexes meet-
ing in a point, as at A, fig. 41, plate V. Here the touch-
ing surfaces move with equal velocities in every part of
the cones ; therefore there is but little friction. These
cones being indented, or fluted with teeth diverging from
the vertex to the base, to prevent them from slipping,
become bevel gear ; and as these teeth are very small at
the point or vertex of the cone, they may be cut off 2 or
3 inches from the base, as 19 and 25, at B ; they then
have the appearance of wheels.

To make these wheels of a suitable size for any num-
ber of COSTS vou choose to have to work into one another,
take the following

RULE.

Draw lines to represent your shafts, in the direction
they are to be, with respect to each other, to intersect at

Chap. 3.] OF BEVEL GEARS. 19:>

A ; then take from any scale of equal parts, either feet,
inches or quarters, &c. as many as your wheels are to
have cogs, and at that distance from the respective shafts,
draw the dotted lines a b, c d, for 2i and 20 cogs ; and
from where they cross at e, draw e A. On this line,
which makes the right bevel, the pitch circles of the
wheels will meet, to contain that proportion of cogs of
any pitch.

Then to determine the size of the wheels to suit any
particular pitch, take from the table of pitch circles, the
radius in measures of the pitch, and apply it to the centre
of the shaft, and the bevel line A e, taking the distance
at right angles with the shaft ; and it will show the point
in which the pitch circles will meet, to suit that particu-
lar pitch.

By the same rule, the sizes of the wheels at B and C
are found.

These kind of wheels are frequently made of cast
metal, and do exceedingly well.

The advantages of this kind of gear are,

1. They have very little friction, or sliding of parts.

2. We can make the cogs of any width of bearing we
choose ; therefore they will wear a great while,

3. By them we can set the shafts in any direction de-
sired, to produce the necessary movements.

Their disadvantages are,

1. They require to be kept exactly of the right depth
in gear, so that the pitch circles just meet, else they will
not run smooth, as is the case with spur gears.

2. They are expensive to make of wood ; therefore
few in this country use them.

; The universal joint, as represented fig. 43, may be
applied to communicate motion, instead of bevel gear,
where the motion is to be the same, and the angle not
more than 30 or 40 degrees. This joint may be con-
structed by a cross, as in the figure, or by 4 pins fasten-
ed at right angles on the circumference of a hoop or
solid ball. It may sometimes serve to communicate the
motion, instead of 9 or 3 face wheels. The pivots at the
end of the cross play in the ends of the semicircles. It

194 OF MATCHING WHEELS, &c. [Chap.S.

is best to screw the semicircles to the blades, that they
may be taken apart. •

ART. 83.
OF MATCHING WHEELS, TO MAKE THE COGS WEAR EVEN-

Great care should be taken in matching or coupling
the wheels of a mill, that their number of cogs be not
such that the same cogs will often meet ; because if two
soft ones meet often, the)?- will both wear away faster
than the rest, and destroy the regularity of the pitch ;
whereas if they are continually changing, they will wear
regular, even if they are at first a little irregular.

For finding how often they will revolve before the
same cogs meet again, take the following

RULE.

L Divide the cogs in the greater wheel by the cogs
in the lesser; and if there be no remainder, the same
cogs will meet once every revolution of the great wheel.

2. If there be a remainder, divide the cogs in the
lesser wheel by the said- remainder ; and if it divide them
equally, the quotient shows how often the great wheel
Avill revolve before the same cogs meet.

3. But if it will not divide equally, then the great
wheel will revolve as often as there are cogs in the small
wheel, and the small wheel as often as there are cogs in
the large wheel, before the same cogs meet : oftener they
can never be made to change.

EXAMPLES.

1. Given, wheels 13 and 17 cogs ; required, how
often each will revolve before the same cogs meet again.
Then 13)17(1
13

4)13(3

12 Answer,

— Great wheel 13, and

1 Small do. 17 revs.

Chap. 3.] OF ROLLING SCREENS AND FANS. 195

ART. 83.

THEORY OP ROLLING SCREENS AND FANS, OR WIND MILLS FOR
SCREENING AND FANNING THE WHEAT IN MILLS.

Let fig. 42, plate V, represent a rolling screen and
fan, fixed for cleaning wheat in a merchant- mill. DA
the screen, AF the fan, AB the wind tube, 3 feet deep
from A to b, and 4< inches wide, in order that the grain
may have a good distance to fall through the wind, to
give time and opportunity for the light parts to be carried
forward before the heavy parts. Suppose the tube to be
of equal depth and width the whole of its length, except
where it communicates with the tight boxes or garners
under it, viz. c for the clean wheat, S for the screenings
and light \\ heat, and C for the cheat, chaff, &c. Now it
is evident, if wind be by the fan drove into the tube at
A, that if it can escape no where, it will pass on to B,
with the same force as at A, let the tube be of any length
or direction; and any thing which it will move at A, it
W'ill carry out at B, if the tube be of an equal size all the
way.

It is also evident, that if we shut the holes of the fan
at A and F, and let no wind into it, none can be forced
into the tube ; hence, the best way to regulate the blast
is, to fix shutters sliding at the air holes, to give more
or less feed or air to the fan, so as to produce a blast
sufficient to clean the grain.

The grain is let into the screen at D, into the inmost
cylinder, in a small stream. The screen consists of tuo
cylinders of sieve wire, the inmost one has the meshes
so open, as to pass all the wheat through it to the outer
one, retaining only the white caps, large garlic, and every
thing larger than the grain of the wheat, which falls out
at the tail A.

The outer cylinder is so close in the mesh, as to re-
tain all good wheat, but sift out the cheat, cockle, small
wheat, garlic, and every thing less than good grains of
wheat ; the wheat is delivered out at the tail of the outer
cylindef, which is not quite as long as the inner one.

196 OF ROLLING SCREENS AND FANS. [Chap. 3.

where it drops into the wind tube at a, and as it falls
from a to b, the wind carries off every thing lighter than
good wheat, viz, cheat, chaff, light garlic, dust, and light
rotten grains of wheat ; but, in order to effect this more
completely, it should fall at least 3 feet through the cur-
rent of wind.

The clean wheat falls into the funnel b, and thence
into the garner c, over the stones. The light wheat,
screenings, &c. fall into garner S, and the chaff settles
into the chaff room C. The current slackens passing
over this room, and drops the chaff, but resumes its full
force as soon as it is over, and carries out the dust
through the wall at B. To prevent the current from
slackening too much as it passes over S and c, and un-
der the screen, make the passages, where the grain
come in and goes out, as small as possible, not more
than half an inch wide, and as long as necessary. If the
wind escapes any where but at B, it defeats the scheme,
and carries out the dust into the mill. Or fix valves to
shut the passages by a weight or spring, so that the
weight of the wheat, &c. falling on, will open them just
enough to let it pass, without suffering any wind to
escape.*

Note, the fan is set to blow both the wheat and screen-
ings, and carry the dust out.

Note also. That the wind cannot escape into the gar-
ners or screen room, if they are tight ; for as soon as
they are full, no more can enter.

By attending duly to the foregoing principle, we may
fix fans to answer our purposes.

The principal things to be observed in fixing serenes
and fans, are,

1. Give the screen 1 inch to the foot fall, and between
15 and 18 revolutions in a minute.

2. To make the fan blow strong enough, let the wings
be 3 feet wide, 20 inches long, and revolve UrO times
in a minute.

3. Then regulate the blast, by giving more or less
feed of wind.

• This 1 have from Timothy Kirk, being one principle of his improved
fan.

Chap. 4.] OF GUDGEONS. %^7

4. Leave no place for the wind to escape, but at the
end through the wall.

5. Wherever you want it to blow hardest, there make
the tube narrowest.

6. Where you want the chaff and cheat to fall, there
make the tube sufficiently wider.

7. Make them blow both the wheat and screenings,
and carry the dust clear out of the mill.

8. The wind tube may be of any length, and either
crooked or straight, as may best suit ; but no where less
than where the wheat falls.

CHAPTER IV.
ART. 84.

OF GUDGEONS, THE CAUSE OF THEIR HEATING AND GETTING
I-OOSE, AND REMEDIES THEREFOR.

THE cause of gudgeons heating, is the excessive
friction of their rubbing parts, which generates the heat
in proportion to the weight that passes the rubbing sur-
faces together, and the velocity with which they move.
See art. 31.

The cause of their getting loose is, their heating, and
burning the wood, or drying it, so that it shrinks in the
bands, and gives the gudgeon room to work.

To avoid the effects, we must remove the causes.

1. Increase the surface of contact or rubbing parts,
and, if possible, decrease their velocity ; the heat will not
then be generated so much.

S. Conduct the heat away from the gudgeon as fast
as generated, if possible.

To increase the surface of contact, without increasing
its velocity, make the neck or bearing part of the gud-
geon longer. If the length be doubled, the weight will
be sustained by a double surface, and velocity the same ;
there will not then be so much heat generated : and even

198 OF GUDGEONS. fChap. 4.

supposing the same quantity of heat generated, there
will be a double space of surface exposed to air, to con-
vey it away.*

To convey the heat away as fast as generated, cause
a small quantity of water to drop slowly on the gudgeon,
to carry off the heat by evaporation.! A small quantity
is better than a large ; because it should be just suffi-
cient to keep up the evaporation, and not destroy the
polish made by the grease ; which it will do if the quantity
be too great, and will let the bear box and gudgeon come
in contact; which will cause both to wear away very
fast.J

The best form that I have seen for large gudgeons
for heavy wheels, is made of cast iron. Fig. 6, plate
XI. is a perspective view of one ; a a a a, are four wing«
at right angles with each other, extending from side to
side of the shaft. These wings are larger, every way,
at the end that is farthest in the shaft, than at the outer
end, for convenience in casting them, and also that the
bands may drive on tight, one over each end of the
wings. Fig. 4, is an end view of the shaft, with the
gudgeon in it, and a band on the end ; these bands, be-

• To understand this subject better, let us consider, that when we strike
a flint with steel, we choose the sharpest part of the flint ; then the surface
of contact is so small, that the force of the stroke creates friction enough
to strike or generate fire ; but if we strike a thick snjooth part of the flint,
the force will not be sufficient to strike fire, the surface being too large.
Hence we ma}- conclude, that the smaller the rubbing surface, the greater
the heat ; and if tiie surface was so small as to strike fire continually, it
would be very difiicult to keep the gudgeon cool- If a gudgeon heats at 3
inches bearing on the box, lengthen it to 6 or 8 inches. I have seen them
in use from 2 1 2 to 10 inches bearing on the box ; and those who had the
longest (being men of the greatest experience in the milling business)
accounted their length to be a good remedy against the heating.

f Water is a great conductor of heat, and wonderful is the effect of the
principle of evaporation, in carrying off the heat from bodies; every par-
tide of water that evaporates, carries ofi" a quantity of heat with it. Dr.
Franklin asserts, that by evaporation a man could be froze to death the
warmest day in summer.

t The grease operates in lessening friction, perhaps in three ways. 1st.
The particles of the grease, by filling up the pores of the box and gudgeon,
makes the sliding surface more perfectly smooth. 2. The particles of
grease act as rollers between the sliding surfaces. 3- It destroys the
cohesion that might otherwise take place between the surfaces- See art.
31, and 33-

Oil is said to answer best for spindle feet and step gudgeons, tallow for
common gudgeons, and black lead mixt with tallow for cogs, which forms
a glossy polish on them that will wear a long time-

Chap. 4.] OF GUDGEONS. 199

ing put on hot, become very tight as they cool, and if
the shaft is dry will not get loose ; but will if it is ^:eei\ :
but by driving a few wedges along side of each wing, it
can be easily fastened, by any ordinary hand, without
danger of moving it much from the centre.

One great use of these wings is, to convey away thse
heat from the gudgeon to the bands, which are in con-
tact with the air ; and by thus distributing the heat
through so much metal, with so large a surface exposed
to the air, the heat is carried off as fast as generated ;
therefore can never accumulate to a degree sufficient to
burn loose, as it will often do in common gudgeons of
wrought iron. Wood will not conduct the heat as well
as the wings of metal ; therefore it accumulates in the
small space of the gudgeon, to such a degree as to burn
loose.

These gudgeons should be made of the best hard
metal, well refined, in order that they may wear well,
and not be subject to break ; but of this there is but little
danger, if the metal is good : should it prove to be the
case, I propose to have wings cast separate from the
neck, as represented by fig. 4 : where the inside light
square shows a mortise for the steeled gudgeon, Plate
XI. fig. 8, to be fitted into, with an iron key behind the
wings, to draw the gudgeon in tight, if ever it should
work loose ; by which means it may be taken out, at any
time, to repair.

This plan would do well for step gudgeons for heavy
upright shafts, such as tub-mills, &c.

When the neek is cast with the wings, the square part
in the shaft need not be larger than the light square re-
presenting the mortise.*

* Grease of any kind used to the drill, in boring cast iron, prevents it
from cutting, but on the contrary will make it cut wrought iron or steel
much faster This quality in cast iron renders it most suitable for gud-
geons, and may be the principal cause why cast iron gudgeons have proved
much better than any one expected. Several of the most experienced
and skilful mill-wrights and millers do assert that they have experienced
cast gudi^eons to run on cast boxes better than on stone or brass, in one
instance carrying heavy overshot wheels which turned seven feet mill-
stones. They have run ten years, doing much work, and have hardly
worn off the sand marks ; may we not expect them to last ten times a».

2Q0 ON BUILDING MILL-DAMS. [Chap. 5.

CHAPTER V.
ART. 85,

ON BUILDING MJLL-DAIMS, LAYJNG FOUNDA.TIONS, AND
BUILDING MILL WALLS.

THERE are several things to be considered, and
dangers to be guarded against, in building mill-dams.

i. Construct them so, that the water, tumbling over
them, cannot undermine their foundations at the lower
side.*

2. So that heavy logs, large pieces of ice, &c. float-
ing down, cannot catch against any part of them, but slide
easily over.f

long, and make up 100 years ? In other instances they have worn out in a
few days, and let the wheel drop, owing no doubt, to theif being made of
unsuitable metal op wrongly tempered.

• If you have not a foundation of solid rocks, or so heavy, that the wa-
ter tumbling over, will never move them, there should be such a founda-
tion made with great stones, not lighter than mill-stones (if the stream
is heavy, and the tumble great) well laid, as low and close as possible,
with their upstream end lowest, to prevent any thing from catching under
them. But if the bottom is sand or clay, make a foundation of the trunks
of long trees, laid close together on the bottom of the creek, with their
butt ends down stream, as low and close as possible, across the whole tum-
bling space. On these may be built the dam, either of stone or wood,
leaving 12 or 15 feet below the breast or fall, for the water to fall upon.
See fig. 3, plate X, which is a front view of a log dam, showing the posi-
tion of the logs, also of the stones in the abutments.

f if the dam is built of timber and small stones, &c. make the breast
perpendicular of straight logs, laid close one upon another, putting the
largest, longest, and best logs on the top ; make another wall of logs 12
or 15 feet upstream, laying them close together, to prevent lamprey eels
from working through them, not so high as the other, by 3 feet; tie these
walls together, at every 6 feet, with cross logs, with the butts down
stream, dovetailed and bolted strongly to the logs of the lower wall, espe-
cially the upper log, which should be strongly bolted down lo them. The
spaces between these log walls, are to be filled up with stones, gravel. Sec.
Choose a dry season for this work ; then the water will run through the
lower part while you build the upper part tight.

To prevent any thing from catching against the top log, flag the top of the
dam with broad or long stones, laying the downstream end on the upstream
side of the log, to extend a little above it, the other end lowest, so that the
next tier of stones will lap a little over the first; still gettmg lower as you
advance upstream. This will ;■ lance logs, &c. over the dam, without catch-
ing against any thing. If suitable stones cannot be had, I would recommend
strong plank, or small logs, laid close together, with both ends pinned to the
top logs of the wall, the upstream end being 3 feet lower than the other:
But if plank is to be used, there need only be a strong frame raised on the

Chap. 5.] ON BUILDING MILL-DAMS. 201

3. So that the pressure or force of the current of the
water will press their parts more firmly together.*

^. Give them a sufficient tumbling space to vent all
the water in time of freshets.f

5. Make the abutments so high, that the water will
not overflow them in time of freshets.

6. Let the dam and mill be a sufficient distance apart ;
so that the dam will not raise the water on the mill, in
time of high floods. J

foundation logs, to support the plank or the timber it is pinned to. See a
side view of this frame, %. 45, plate IV. Some plank the breast to the
front posts, and fill the hollow space with stone and gravel ; but this may
be omitted, if the foundation logs are sufficiently long upstream, under the
dam, to prevent the whole from floating away. Stone first, and then gravel>
sand, and clay, are to be filled in above this frame, so as to stop the water.
Jf the abutments are well secured, the dam will stand well.

General Ira Allen, of the state of Vermont, ascertained by experiment,
that a plank laid in a current of water, with the upstream end lowest set
at an angle of 22 1-2 degrees with the horizon or current of the water, will
he held firmly to its place by the force of the current, and in this position
at requires the greatest force to remove it, and the stronger the current
"the firmer it is held to its place, that is, supposing there remains a partial
■vacuum under the plank, this points out the best position for the breast of
idams.

* If the dam is built of stone, make it in the form of an arch or semicircle,
Standing upstream, and endeavour to fix strong abutments on each side, to
support the arch ; then, in laying the stones, put the widest end upstream,
and the more they are drove downstream, the tighter they will press to-

fftther. All the stones of a dam should be laid with their upstream ends
owest, and the other end lapped over the preceding, in manner of the
ehingles or tiles of a house, to glance every thing smoothly over, as at the
tside 3, of fig. 3, plate X. The breast may be built up with stone, either on
(a good rock or log foundation, putting the best m front, leaning a little
upstream, and on the top lay one good log, and another 15 feet upstream
en the bottom, to tie the top log to, by several logs, with good butts, down*
stream, dovetailed and bolted strongly, both at bottom and top of the top
»nd upstream logs ; fill in between them with stone and gravel, laying large
©tones slanting next the top log, to glance any thing over it. This will be
much better than to build all of stone ; because if one at top give way, the
fcreach will increase rapidly, and the whole go down to the bottom.

t It the tumbling space is not long enough, the water will be apt to
overflow the abutments, and if they are earth or loose stones, they will be
broken down, and perhaps a very great breach made. If the dam is of
logs, the abutments had best be made of stone, laid as at the side 3, in
fig. 3; but if stone is not to be had, they must be made of wood, although
subject lo rot soon, being above water.

+ I have, in many instances, seen the mill set so close to the dam, that
the pier head or forebay was in the bre:st; so that in case of a leak or
breach about the forebay or mill, there is no chance of shutting off the
water, or conveying it another way ; but all must be left to its fate. The
mill is frequently broken down, and carried away; even the mill stones
are carried a considerable distance down the stream, and sometimes buried
under the sand, and never found.

C C

202 ON BUILDING MILL-WALLS. [Chap; 5.

ART. 86.

ON BUILDING MILL-WALLS.

The principal things to be considered in building
mill- walls, are,

1. To lay the foundations with good large stones, so
deep as to be out of danger of being undermined, in
case of any accident of the water breaking through at
the mill.*

2. Set the centre of gravity, or weight of the wall, on
the centi'e of its foundation. }-

The great danger of this error will appear more plain, if we suppose six
mills on one stream, one above the other, each at the breast of the dam ;
and a great flood to break the first or uppermost dam, say through the
pierhead, carrymg with it the mill, stones and all; this so increases the
flood, that it overflows the next dam, which throws the water against the
mill, and it is taken away; the water of these two dams has now so aug-
mented the flood, that it carries every mill before it, until it comes to the
dam of the sixth, which it sweeps away also; but suppose this dam to be
a quarter of a mile above the mill, which is set well into the bank, the extra
water that is thrown into the canal, runs over at the waste left in its banks
for the purpose ; and the water having a free p;issage by the mill, does not
injure it; whereas, had it been at the breast of the dam, it must have went
away with the rest- A case similar to this, actually happened in Virginia
in 1794; all the mills and dams on Falling Creek, in Chesierfield county,
were carried away at once, except the lowest, (Mr. Wardrope's :) whose
dam, having broke the year before, was rebuilt a quarter of a mile higher
up ; by which means his mill was saved.

* If the foundation is not good, but abounding with quicksands, the wall
cannot be expected to stand, unless it be made good by driving down piles
until they meet the solid ground : on the top of which may be laid large
flat pieces of timber, for the walls to be built on ; they will not rot under
water, totally excluded from the air.

f It is a common practice to build walls plumb outside, and batter them
all from the inside ; which throws the centre of their gravity to one side of
their base. See art. 14. Therefore if it settles any, it will incline to fall
outwards. Mill-walls should be battered as much outside, as to be equal to
the offsets inside^ to cause the whole weight to stand on the centre of the
foundation, unless it stand against a bank, as the wall next the wagon,
in plate VIII. The bank is very apt to press the wall inwards, unless it
stands battering. In this case, build the side against the bank plumb,
even with the ground, and then begin to batter it inwards. The plumb
rules should be made a little widest at the upper end, so as to give the
wall the right inclination, according to its height ; to do which,
tiike a line, the length equal to the height of the wall, set one end,
by a compass point, in the lower end of the plumb rule, and strike
the plumb line; then move the other end just as much as the wall
is to be battered in the whole height: and it will show the inclination
of the side of the rule that will batter the wall exactly right. This error
of building walls plumb outside, is frequently committed in building he
abutments of bridges ; the consequence is, they fall down in a short lime ;

Chap. 5.] ON BUILDING MILL-WALLS. 203

3. Use good mortar, and it will, in time, petrify and
become as hard as stone.*

4. Arch over all the windows, doors, &c.

5. Tie them well together by the timbers of the
floors.

because the earth balween the walls is expanded a little by every hard
fropt, and tumbles the walls over.

• I have but little experience in this ; but will quote an experienced
author (George Sample, on Free Trade.) He says,

" CoNCERNiiirG Lime, Moktar, and Grout.

" I have, from my childhood, been well acquainted with the nature of
lime and sand made into mortar, of all sorts that have been used in build-
ings in these countries, and tried numerous experiments with them. On
which, together with what I have observed and learned from old expe-
rienced workmen, during the course of upwards of sixty years, I think I
can safely affirm, that good mortar, that is made of pure and well-burnt
limestone, properly made up with sharp clean sand, free from any sort of
earth, loam or mud, will, within some considerable time, actually petrify,
and, as it were, turn to the consistence of a stone. I remember I had one
of my remarks from an old Scotch mason; which 1 shall give you in his
own identical words; that is,

" when a hundred years are past and gane,

*' Then gude mortar is grown to a stain (or stone.)

"I need not explain what I mean by sharp clean sand ; but I shall giva
you this one caution, that it is better to put too much sand in your mortar,
than too little. I know workmen choose their mortar rich, because it works
pleasanter; but rich mortar will not stand the weather so well, nor grow
so hard, as poor mortar will do. If it was all lime, it would have no more
strength, in comparison, than clay."

PART III.

CONTAINING

EVANS'S PATENTED IMPROVEMENTS

ON THE

ART OF MANUFACTURING GRAIN INTO MEAL
AND FLOUR.

INTRODUCTION.

THESE improvements consist of the inven-
tion, and various applications, of the following
machines, viz.

1. The Elevator.
S. The Conveyer.

3. The Hopper-boy.

4. The Drill.

5. The Descender.

Which five machines are variously applied,
in different mills, according to their construction,
so as to perform every necessary movement of
the grain and meal, from one part of the mill to
another, or from one machine to another, through
all the various operations, from the time the grain
IS emptied from the wagoner's bag, or from the
measure on board the ship, until it is completely
manufactured into supei^fine flour, and other dif-
fereni qualities, and completely separated, ready

208 INTRODUCTION.

for packing into barrels, for sale or exportation.
All which is performed by the force of the water,
without the aid of manual labour, except to set
the different machines in motion, ^c. Which les-
sens the labour and expense of attendance of
flour mills, fully one-half See the whole applied,
plate VIII.

THE

YOUNG MILL-WRIGHT'S
GUIDE.

PART THE THIRD.

CHAPTER L

DESCRIPTION OF MACHINES.

ART. 88.

1. Of the Elevator.

THE elevator is an endless strap, revolving over
two pullies, one of which is set where the grain or meal,
&c. is to be hoisted from, and the other where it is to be
hoisted to ; to this strap is fastened a number of small
buckets, which fill themselves as they pass under the
lower pulley, and empty as they pass over the upper
one. To prevent waste of what may spill out of these
buckets, the strap, buckets and pullies, are all enclosed,
and work in tight cases ; so that what spills will descend
to the place from whence it was hoisted. A B, in fig. 1,
plate VI, is an elevator for raising grain, which is let in
at A, and discharged at B into the spouts leading to the
different gamers. Fig. S is a perspective of the strap and
different kinds of buckets, and the various modes of
fastening them to the strap.

S. Of the Conveyer.

The conveyer K I, plate VI, fig. 1, is an endless screw
of two continued spires, put in motion in a trough ; the

D d

21© DESCRIPTION OF MACHINES. [Chap. 1.

grain is let in at one end, and the screw drives it to the
other, or collects it to the centre, as at y, to run into the
elevator, (see plate VIII, 37 — 36 — 1, and 44 — h5) or it is
let in at the middle, and conveyed each way, as 15 — 16,
plate VIII.

Plate VI, fig. 3, is a top view of the lower pulley of a
meal elevator in its case, and a meal conveyer in its trough,
for conveying meal from the stones, as fast as ground, into
the elevator. This is an 8 sided shaft, set on all sides
w'nh small inclining boards, called flights, for conveying
the meal from one end of the trough to the other ; these
flights are set in a spiral line, as shown by the dotted
line ; but being set across said line, changes the princi-
ple of the machine from a screw to that of ploughs, which
is found to answer better for conveying warm meal.

Besides these conveying flights, half their number of
others are sometimes necessary ; which are called lifters,
and set with their broadsides foremost, to raise the meal
from one side, and let it fall on the other side of the
shaft to cool ; these are only used where the meal is hot,
and the conveyer short. See SI — 22, in plate VIII ; which
is a conveyer, carrying the meal from 3 pair of stones to
the elevator, 23 — 24.

3. Of the Hopper -hoy.

Fig. 13, plate VII, is a hopper-boy ; which consists
of a perpendicular shaft, A B, put in a slow m.otion (not
above 4 revolutions in a minute) carrying round with it
the horizontal piece C D, which is called the arms, and
set on the under side, full of small inclining boards, called
flights, so set as to gather the meal to\vards the centre,
or spread it from the centre to that part of the arm which
passes over the bolting hopper; at which part, one board
is set broadside foremost, as E, (called the sweeper) which
drives the meal before it, and drops it into the hoppers
H H, as the arms pass over them. The meal is generally
let fall from the elevator, at the extremity of the arm, at
D, where there is a sa\ eeper, which drives the meal before
it, ti'ailing it in a circle the whole way round, so as to dis-
charge nearly the whole of its load, by the time it returns

6hap. 1.] DESCRIPTION OF MACHINES. 211

to be loaded again : the flights then gather it towards
the centre, from every part of the circle ; which would
not be the case, if the sweepers did not lay it round ;
but the meal would be gathered from only one side of
the circle. These sweepers are screwed on the back of
the arm, so that they may be raised or lowered, in order
to make them discharge sooner or later, as necessary.

The extreme flight of each end of the arms are put on
with a screw passing through its centre, so that they may
be turned to drive the meal outwards ; the use of which
is, to spread the warm meal as it falls, from the elevator,
in a ring round the hopper- boy, while it at the same time
gathers the cool meal into the bolting hopper ; so that
the cold meal may be bolted, and the warm meal spread
to cool, by the same machine, at the same time, if the
miller chooses so to do. The foremost edge of the arms
is sloped up, in order to make them rise over the meal,
and its weight is nearly balanced by the weight w, hung
to one end of a cord, passing over the pulley P, and to
the stay iron F. About 4-| feet of the lower end of the
upright shaft is made round, passing loosely through a
round hole in the flight arm, giving it liberty to rise and
fall freely, to suit any quantity of meal under it. The
flight arm is led round by the leading arm L M, by a
cord passing through the holes L M, at each end, and
made fast to the flight arm D C. This cord is lengthen-
ed or shortened by a hitch-stick N, with two holes for
the cord to pass through, the end of the cord being pass-
ed through a hole at D, and fastened to the end of a
stick ; this cord must reeve freely through the holes at
the end of the arms, in order that the ends may both be
led equally. The flight arm falls behind the leader about
1 6th part of the circle. The stay-iron C F E, is a ring
at F, which fits the shaft loosely, and is for keeping the
arm steady, and hanging the ends of an equal height by
the screws C E.

Plate VII, fig. 13, is a perspective view of the under
side of the flight arms. The arm a c, with flights and
sweepers complete; s s s shews the screw^s which fasten
the sweepers to the arms. The arn- c-b, is to shew the
rule for laying out for the flights. Wnen the sweeper at

212 DESCRIPTION OF MACHINES. [Chap. 1

b, is turned in the position of the dotted line, it drives
the meal outwards. Plate VII, fig. 14, is a plate on the
bottom of the shaft, to keep the arm from the floor, and
15 is the step gudgeon.

4. Of the Brill.

The drill is an endless strap revolving over two pullies,
like an elevator, but set nearly horizontal, and instead of
buckets, there are small rakes fixed to the strap, which
draw the grain or meal along the bottom of the case.
See G H, in plate VI, fig. 1. The grain is let in at H,
and discharged at G. This can sometimes be applied
with less expense than a conveyer ; if it is set a little
descending, it will move grain or meal with ease, and will
do well a little ascending.

5. Of the Descender.

The descender is a broad endless strap of very thin
pliant leather, canvas, or flannel, &c. revolving over two
pullies, which turn on small pivots, in a case or trough,
to prevent waste, one end of which is to be lower than
the other. See EF, plate VI, fig. 1. The grain or meal
falls from the elevator on the upper strap, at E, and by its
own gravity and fall, sets the machine in motion, and it
discharges the load over the lower pulley F. There are
two small buckets to bring up what may spill or fall off"
the strap, and lodge in the bottom of the case.

This machine moves on the principles of an overshot
water-wheel, and will convey meal a considerable dis-
tance, with a small descent. Where a motion is easily
obtained from the water, it is to be preferred to that of
working itself, it being easily stopped, is apt to be trou-
blesome.

The crane spout is hung on a shaft to turn on pivots
or a pin, so that it may turn every way like a crane ; into
this spout the grain falls from the elevator, and, by turn-
ing, it can be directed into any garner. The spout is made
to fit close, and play under a broad board, and the grain is
let into it through the middle of this board, near the pin,
so that it will always enter the spout. See it under B, plate
VI, fig. 1. L is a view of the under side of it, and M is a top
view of it. The pin or shaft may reach down so low, that
a man may stand on the floor and turn it by the handle x.

Chap.2.] APPLICATION OF MACHINES.

CHAPTER II.

ART. 89.

APPLICATION OF THE MACHINES, IN THE PROCESS OF MANU-
FACTURING WHEAT INTO SUPERFINE FLOUR.

PLATE VIII, is not meant to shew the plan of a
mill ; but merely the application and use of the patented
machines.

The grain is emptied from the wagon into the spout

1, which is set in the wall, and conveys it into the scale

2, that is made to hold 10, 20, 30, or 60 bushels, at plea-
sure.

There should, for the convenience of counting, be
weights of 601bs. each; divided into 30, 15, and 7|lbs.
then each weight would show a bushel of wheat, and
the smaller ones halves, pecks, &c. which any one could
count with ease.

When the wheat is weighed, draw the gate at the bot-
tom of the scale, and let it run into the garner 3 ; at the
bottom of ^\hich there is a gate to let it into the elevator
4 — 5, which raises it to 5, and the crane spout being
turned over the great store gamer 6, which communi-
cates from floor to floor, to garner 7, over the stones 8,
which suppose to be for shelling or rubbing the wheat,
before it is ground, to take off" all dust that sticks to the
grain, to break smut or fly-et^en grain, lumps of dust,
&c. As it is rubbed it runs, b}- the dotted lines, into 3
again ; in its passage it goes throwh a current of \vind
blowing into the tight room 9, having only the spout a,
through the lower floor, for the wind to tsicape ; all the
chafi" will settle in the room, but most of the dust passes
out with the wind at a. The ^heat again runs into the
elevator at 4, and the crane spout, at 5, is turned over
die screen hoppers 10 or 11, and the grain lodged there,
out of which it runs into the rolling screen 12, and de-
scends through the current of wind made by the fan 13 ;
the clean heavy grain descends, by 14, into the conveyer
15 — 16, which conveys it into all the garners over the

214 APPLICATION OF MACHINES. [Chap.e.

stones 7 — 17 — 18, and these regularly supply the stones
8 — 19 — 30, keeping always an equal quantity in the hop-
pers, which will cause them to feed regularly; as it is
ground the meal falls to the conveyer 21 — 22, which
collects it to the meal elevator, at 23, and it is raised to
24, whence it gently runs down the spout to the hopper-
boy at 25, which spreads and cools it sufficiently, and
gathers it into the bolting hoppers, both of which it at-
tends regularly ; as it passes through the superfine cloths
26, the superfine flour falls into the packing chest 28,
which is on the second floor. If the flour is to be loaded
on wagons, it should be packed on this floor, that it
may conveniently be rolled into them ; but if the flour is
to be put on board a vessel, it will be more convenient
to pack on the lower floor, out of chest 29, and roll it
into the vessel at 30. The shorts and bran should be
kept on the second floor, that they may be conveyed by
spouts into the vessel's hold, to save labour.

The rublings which fall from the tail of the 1st reel
28, are guided into tlie head of the 2d reel 27; which is
in the same chest, near the floor, to save both room and
machinery. On the head of this reel is 6 or 7 feet of fine
cloth, for tail flour, and next to it the middling stuff", &c.

The tail flour which falls from the tail of the 1st reel
26, and head of the 2d reel 37; and requires to be bolt-
ed over again, is guided by a spout, as shown by dotted
lines 21—^23, into the conveyer 33 — 33, to be hoisted
again with the ground mea^? a litde bran may be let in
with it, to keep the cloth open in warm weather — But if
there be not a fall si'^cient for the tail flour to run into
the lower conveyer, there may be one set to convey it
into the elevatoi, as 31 — 33. There is a little regulating
board, turning on the joint x under the tail of the first reels,
to guide more or less with the tail flour.

TJie middlings, as they fall, are conveyed into the eye
of either pair of mill-stones by the conveyer 31 — 33,
and ground over with the wheat; which is the best way
of grinding them, because the grain keeps them from
being killed, and there is no time lost in doing it, and
they are regularly mixed with the flour. There is a
slanting sliding board, to guide the middlings over the

Chap.2.] APPLICATION OF MACHINES. 215

conveyer, that the miller may take only such part, for
grinding over, as he shall judge fit: and a little regulat-
ing board between the tail flour and middlings, to guide
more or less into the stones or elevator.

The light grains of wheat, screenings, &c. after being
blown by the fan 13, fall into the screenings garner 32;
the chaff" is driven further on, and settles in the chaff'-room
33 ; the greater part of the dust will be carried out with
the wind through the wall. For the theory of fanning
wheat, see art. 83.*

To clean the Screenings.

Draw the little gate 34, and let them into the eleva-
tor at 4, and be elevated into garner 10; then draw gate
10, and shut 11 and 34, and let them pass through the
rolling screen 12 and fan 13, and as they fall at 14, guide
them down a spout (shown by dotted lines) into the
elevator at 4, and elevate them into the screen-hopper
11; then draw gate 11, shut 10, and let them take tKe
same course over again, and return into garner 10, &c.
as often as necessary, and, when cleaned, guide them
into the stones to be ground.

The screenings of the screenings are now in gamer
32, \\ hich may be cleaned as before, and an inferior qua-
lity of meal made out of them.

By these means the wheat may be effectually sepa-
rated from the seed of weeds, &c. saved for food for
cattle.

This completes the w^hole process from the wagon
to the wagon again, without manual labour, except in
packing the flour, and rolling it in.

• The boUinjj-reels m'cy all be set in a line connected by joint gudgeons,
supported by bearers. The meal, as it leaves the tail of one reel, may be
intioduced into the head of tlie other, by an elevator bucket fixed on th*
head of the reel open at ihe side next the centrt, so that it will dip up the
njeal, arid as it passes over the centre drop in- This improvement was made
by Mr. Jonathan Ellicott, and by it in many cases manj wheels and shafts^
and much room may be saved, and suit the convenience of the house, &c»

2m APPLICATION OF MACHINES. [Chap.2.

ARTICLE 90.
OF ELEVATING GRAIN FROM SHIPS.

If the wheat comes to the mill by ships. No. 35, aiid
requires to be measured at the mill, then a conveyer,
35 — 4, may be set in motion by the great cog-wheel,
and may be under or above the lower floor, as may best
suit the height of the floor above high water. This con-
veyer must have a joint, as 36, in the middle, to give
the end that lays on the side of the ship, liberty to raise
and lower with the tide. The wheat, as measured, is
poured into the hopper at 35, and is conveyed into the
elevator at 4; which conveyer will so rub the grain as
to answer the end of rubbing stones. And, in order to
blow away the dust, when rubbed off", before it enters
the elevator, part of the wind made by the fan 13, may
be brought down by a spout, 13 — 36, and, when it
enters the case of the conveyer, will pass each way, and
blow out the dust at 37 and 4.

In some instances, a short elevator, with the centre of
the upper pulley, 38, fixed immoveable, the other end
standing on the deck, so much aslant as to give the ves-
sel liberty to raise and lower, the elevator sliding a little
on the deck. The case of the lower strap of this eleva-
tor must be considerably crooked, to prevent the points
of the buckets from wearing by rubbing the descent.
The wheat, as measured, is poured into a hopper, which
lets it in at the bottom of the pulley.

But if the grain is not to be measured at the mill, then
fix the elevator 35 — 39, to take it out of the hole, and
elevate it into any door convenient. The upper pulley
is fixed in a gate that plays up and down in circular rab-
bits, to raise and lower to suit the tide and depth of the
hole to the wheat. 40 is a draft of the gate and manner
of hanging the elevator in it. See a particular descrip-
tion in the latter part of art. 95.

This gate is hung by a strong rope passing over a
strong pulley or roller 41, and thence round the axis of
the wheel 42: round the rim of which wheel there is a
rope, which passes round the axis of wheel 'IS, round

Chap. 2.] APPLICATION OF MACHINES. £17

the rim of which is a small rope, leading down over the
pulley P, to the deck, and fastened to the cleet q ; a man
by pulling this rope can hoist the whole elevator ; be-
cause if the diameter of the axis be 1 foot, and the wheel
4 feet, the power is increased 16 fold, by art. 20. The
elevator is hoisted up, and rested against the wall, until
the ship comes to, and is fastened steady in the right
place, then it is set in the hold on the top of the wheat,
and the bottom being open, the buckets fill as tliey pass
under the pulley; a man holds by the cord, and lets the
elevator settle as the wheat sinks in the hold, until the
lower part of the case rests on the bottom of the hold,
it being so long as to keep the buckets from touching
the vessel ; by this time it will have hoisted 1, 2, or 300
bushels, according to the size of the ship and depth of
the hold, at the rate of 300 bushels per hour. When
the grain ceases running in of itself, the man may shovel
it up, till the load is discharged.

The elevator discharges the wheat into the conveyer
at 44, which conveys it into the screen-hoppers 10 — 11,
or into any other, from which it may descend into the
elevator 4—5, or into the rubbing-stones 8.

This conveyer may serve instead of rubbing-stones,
and the dust rubbed off thereby may be, by a wind-
spout from the fan 13, into the conveyer at 45, blown
out through the wall at p. The holes at 44 and 10 — 11
are to be small, to let but little wind escape any where
but out through the wall, where it will carry the dust.

A small quantity of wind might be let into the con-
veyer 15 — 16, to blow away the dust rubbed off by it.

The fan must be made to blow very strong, to be suffi-
cient for all these purposes, and the strength of the bbst
regulated as directed by art. 83.

ART. 91.
A MILL FOR GRINDING PARCELS. ^

Here each person's parcel is to be stored in a separate
garner, and kept separate through the whole process of

t^?l\

>/.-»

218 APPLICATION OF MACHINES. [Chap. a.

imaniifacture, w hich occasions much labour ; almost all
of which is performed by the machines. See plate VI.
fig. I ; which is a view of one side of a mill containing a
number of garners holding parcels, and a side view of
the wheat elevator.

The grain is emptied into the garner g, from the wa-
gon, as shewn in Plate VIII ; and by drawing the gate

A, it is let into the elevator AB, and elevated into the
crane-spout B, which being turned into the mouth of
the garner-spout BC, which leads over the top of a num-
ber of garners, and has, in its bottom, a litde gate over
each garner ; w hich gates and garners are all numbered
with the same numbers respectively.

Suppose we wish to deposit the grain in the garner
No. 2, draw the gate 3 out of the bottom, and shut it in
the spout, to stop the wheat from passing along the spout
past the hole, so that it must all fall into the garner ;
and thus for the other garners 3-4-5-6, &c. These gar-
ners are all made like hoppers, about 4 inches wide at
the floor, and nearly the length of the garner ; but as it
passes through the next story, it is brought to the form
of a spout 4 inches square, leading down to the general
spout KA, which leads to the elevator ; in each of these
spouts is a gate numbered with the number of its garner;
so that when we want to grind the parcel in gamer 2, we
draw the gate 2 in the lower spout, to let the wheat run
into the elevator at A, to be elevated into the crane-spout

B, v^hich is to be turned over the rolling-screen, as shewn
in Plate VIII.

Under the upper tier of garners, there is another tier
in the next story, set so that the spouts from the bottom
of the upper tier pass down the partitions of the lower
tier, and the upper spouts of the lower tier pass between
the partitions of the upper tier, to the garner-spout.

These garners, and the gates leading both into and
out of them, are numbered as the others.

If it is not convenient to fix the descending spouts
BC, to convey the wheat from the elevator to the gar-
ners, and KA to convey it from the garners to the eleva-
tor again, then the conveyers r-s and I-K may be used
for said purposes.

Chap.2.] APPLICATION OF MACHINES. 219

To keep the parcels separate, there should be a
crane- spout to the meal elevator, or any other method,
by which the meal of tlie second parcel may be guided
to fall on another part of the floor, until the first parcel is
all bolted, and the chests cleared out, when the meal of
the second parcel may be guided into the hopper-boy.

I must here observe, that in mills for grinding par-
cels, the tail flour must be hoisted by a separate elevator
to the hopper-boy, to be bolted over, and not run into
the conveyer, as shewn in plate VIII; because then the
parcels could not be kept separate.

The advantages of the machinery, applied to a mill
for grinding pai'cels, are very great.

1. Because without them there is much labour in
moving the different parcels from place to place, all
which is done by the machinery.

2. The meal, as it is ground, is cooled by the machi-
nery, in so short a time, and bolted, that when the grind-
ing is done, the bolting is also nearly finished : Therefore,

Ci. It saves room, because the meal need not be
spread over the floor to cool, there to lay 12 hours as
usual, and none but one parcel need be on the floor at
once.

4. It gives greater despatch, as the mill need never
stop either stones or bolts, in order to keep parcels sepa-
rate. The screenings of each parcel may be cleaned, as
directed in art. 89, with very little trouble; and the flour
may be nearly packed before the grinding is finished.
So that if a parcel of 60 bushels arrive at the mill in the
evening, the owner may wait till morning, when he may
have it all finished; he may use the offal for feed for his
team, and proceed with his load to market.

ART. 9S.
A GRIST MILL FOR GRINDING VERY SMALL PARCELS.

Fig. 16, plate VII, is a representation of a grist-mill,
so constructed that the grist being put into the hopper, it
will be ground and bolted, and return into the bags
again.

220 APPLICATION OF MACHINES. [Chap. 2.

The grain is emptied into the hopper at A, and as it
is ground it runs into the elevator at B, and is elevated
and let run into the bolting hopper down a broad spout
at C, and, as bolted, it falls into the bags at d. The
chest is made to come to a point like a funnel, and a
division made to separate the fine and coarse, if wanted,
and a bag put under each part ; on the top of this division
is set a regulating board on a joint, as x, by which the
fine and coarse can be regulated at pleasure.

If the bran requires to be ground over, (as it often does,)
it is made to fall into a box over the hopper, and by
drav.'ing the little gate b, it may be let into the hopper as
soon as the grain is all ground, and as it is bolted the
second time, it is let run into the bag by shutting the gate
b, and drawing the gate c.

If the grain is put into the hopper F, then as it is
ground it falls into the drill, which draws it into the
elevator at B, and it ascends as before.

To keep the different grists separate — When the miller
sees the first grist fall into the elevator, he shuts the gate
B or d, and gives time for it to get all into the bolting
reel ; he then stops the knocking of the shoe by pulling
the shoe line, which hangs over the pullies pp, from the
shoe to near his hand, making it fast to a peg; he then
draws the gate B or d, and lets the second grist into the
ielevator, to fall into the shoe or bolting hopper, giving
time for the first grist to be all into the bags, and the
bags of the second grist put in their places ; he then un-
hitches the line from the peg, and lets the shoe knock
again, and begins to bolt the second grist.

If he does not choose to let the meal run immediately
into the bags, he may have a box made with feet to stand
in the place of the bags, for the meal to fall in, out of
which it may be taken, and put into the bags, by the
miller or the owner, as fast as it is bolted, and mixed as
desired; and as soon as the first parcel is bolted, the
little gates at the mouth of the bags may be shut, while
the meal is filled out of the box, and the second grist
may be bolting.

The advantages of this improvement on a grist-mill
are,

Chap. 2.] APPLICATION OF MACHINES. 221

1. It saves the labour of hoisting, spreading, and cool-
ing the meal, and caiTying up the bran to be ground
over, sweeping the chest, and filling up the bags.

2. It does all with greater despatch, and less waste,
without having to stop the stones or bolting-reel, to keep
the grists separate, and the bolting is finished almost as
soon as the grinding ; therefore the owner will be the
less time detained.

The chests and spouts should be made steep to pre-
vent the meal from lodging in them, so that the miller,
by striking the bottom of the chest, will shake out all
the meal.

The elevator and drill should be so made as to clean
out at one revolution. The drill might have a brush or
two, instead of rakes, which would sweep the case clean
at a revolution ; and the shoe of the bolting hopper should
be short and steep, so that it will clean out soon.

The same machinery may be used for merchant-
work, by having a crane-spout at C, or a small gate, to
turn the meal into the hopper-boy that tends the mer-
chant bolt.

A mill thus constructed, might grind grists in the day-
time, and merchant- work at night.

A drill is preferable to a conveyer for grist-mills, be-
cause they will clean out much sooner and better. The
low er pulley of the elevator is twice as large in diameter
as the pullies of the drill ; the lower pulley of the elevator,
and one pulley of the drill, are on the same shaft, close
together, the elevator moves the drill, and the pulley of the
drill being smallest, gives room for the meal to fall into
the buckets of the elevator.

ART. 93.

OF ELEVATING GRAIN, SALT, OR ANYGRANULOUS SUBSTANCE,
!• ROM SHIPS INTO STOREHOUSES, BY THE STRENGTH OF A
HORSE.

Plate VII, fig. 17, represents the elevator, and the
manner of giving it motion ; the horse is hitched to the
end of the sweep-beam A, by which he turns the upright

222 APPLICATION OF HACHINES. [Chap. 2.

shaft, on the top of which is the driving cog-wheel, of 96
cogs, 2i inches pitch, to gear into the leading wheel of
20 cogs, on the same shaft with which is another driving
wheel of 40 cogs, to gear into another leading wheel of
19 cogs, which is on the same shaft with the elevator
pulley ; then if the horse makes about 3 revolutions in
a minute (which he will do if he walk in a circle of 20
feet diameter) the elevator pulley will make about 30
revolutions in a minute ; and if the pulley is 2 feet in
diameter, and a bucket be put on every foot of the strap,
to hold a quart each, the elevator will hoist about 187
quarts per minute, or 320 bushels in an hour, 3840
bushels in 12 hours; and for every foot the elevator is
high, the horse will have to sustain the weight of a quart
of wheat ; say 48 feet, which is the height of the high-
est store houses, then the horse would have to move 1|
bushels of wheat upwards, with a velocity equal to his
own walk; which I presume he can do with ease, and
overcome the friction of the machinery: By which will
appear the great advantages of this application.

The lower end of the elevator should stand near the
side of the ship, and the grain, salt, &c. &c. be emptied
into a hopper ; the upper end may pass through a door
or window, as may be most convenient ; the lower case
should be a little crooked to prevent the buckets from
rubbing in their descent.

ART. 94.

OF AN ELEVATOR APPLIED TO ELEVATE GRAIN, &c. WROUGHT
BY A MAN,

Plate VII, fig. 18, AB, are two ratchet wheels, with two
deep grooves in each of them, for ropes to run in ; they
are fixed close together, on the same shaft with the upper
pulley of the elevator, so that they will turn easily on the
shaft the backward way, but a click falls into the ratchet,
and prevents them from turning forwards. Fig. 19, is a
side view of the wheel, ratchet, and click. C D are two

Chap.2.] APPLICATION OF MACHINES. 223

levers, like weavers' treadles, and from lever C there is a
li^ht staff passes to the foreside of the groove wheel B,
and made fast by a rope half way round the wheel ; and
from said lever C there is a rope passing to the backside
of the wheel A ; and from lev er D there is a light staff
passing to the foreside of the groove wheel A, and a rope
to the backside of the groove wheel B.

The man, who is to work this machine, stands on the
treadles, and holds by the staffs with his hands : and as
he treads on D it descends, and the staff pulls forward
the wheel A, and the rope pulls backwards the wheel
B, and as he treads on C the staff pulls forward the wheel
B, and the rope pulls backward the wheel A : but as
the click falls into the ratchet, so that the wheels cannot
move forward without turning the elevator pulley, thus
it is moved one way by the treadles ; and in order to
keep up a regular motion, F is a heavy fly-wheel, which
should be of cast metal, to prevent much obstruction
from the air.

To calculate what quantity a man can raise to any
height, let us suppose his weight to be 15()lbs. which is
the power to be applied, and suppose he is able to walk
about 70 feet up stairs in a minute, by the strength of
both his legs and arms, or which is the same thing, to
move his weight on the treadles 70 steps in a minute ;
then suppose we allow, as by art. 29 — 42, to lose 1-3 of
the power to gain velocity and overcome friction, (which
will be a great plenty in this case, because in the experi-
ment in the table in art. 37, when 71bs. were charged
with 6lbs. they moved with a velocity of 2 feet in half
a second,) then there will remain lOOlbs. raised 70 feet
in a minute, equal to SOOlbs. raised 35 feet to the top of
the third story per minute, equal to 200 bushels per hour,
2400 bushels in 12 hours.

The great advantages of this application of the eleva-
tor, and of this mode of applying man's strength, will
apjiear from these considerations, viz. he uses the
strength of both his legs and arms, to move his weight
only, from one treadle to the other, which weight does
the work ; whereas, in carrying bags on his back, he
uses the strength of his legs only, to raise both the

224 APPLICATION OF MACHINES. [Chap. 2.

weight of his body and the burden, add to this that he
generally takes a very circuitous route to the place where
he is to empty the bag, and returns empty ; whereas the
elevator takes the shortest direction to the place of
emptying, and is always steadily at work.

The man must sit on a high bench, as a weaver does,
on which he can rest part of his weight, and rest himself
occasionally, when the machine moves lightly, and have
a beam above his head, that he may push his head
against, to evercome extraordinary resistances. This is
probably the best means of applying man's strength to
produce rotary motions.

DESCRIPTION OF PLATE IX,

The grain is emptied into the spout A, by which it
descends into the garner B ; whence by drawing the
gate at C, it passes into the elevator C D, which raises
it to D, and empties it into the crane spout E, which is
so fixed on gudgeons that it may be turned to any sur-
rounding granaries, into the screen-hopper F, for in-
stance, (which has two parts F and G,) out of which it
is let into the rolling screen, at H, by drawing the small
gate a. It passes through the fan I, and falls into the
little sliding-hopper K, which may be moved, so as to
guide it into either of the hanging- garners, over the
stones, L or M, and it is let into the stone-hoppers by
the little bags bb, as fast as it can be ground. When
ground it falls into the conveyer N N, wliich carries it
into the elevator at O O, this raises and empties it into
the hopper- boy at P, which is so constructed as to carry
it round in a ring, gathering it gradually towards the
centre, till it sweeps into the bolting hoppers Q Q.

The tail flour, as it falls, is guided into the elevator,
to ascend with the meal, and, that a proper quantity
may be elevated, there is a regulating board R, set un-
der the superfine cloths, on a joint x, so that it will turn
towards the head or tail of the reel, and send more or less
into the elevator, as may be required.

There may be a piece of coarse cloth or wire put on
the tails of the superfine reels, that will let all pass
through except the bran, which falls out at the tail, and

Chap. 2.] APPLICATION OF MACHINES. 225

a part of which is guided into the elevator with the tail
flour, to assist the bolting in warm weather ; the quantity-
is regulated by a small board r, set on a joint under the
"ends of the reels. Beans may be used to keep the cloths
open, and still be returned into the elevator to ascend
again. What passes through the coarse cloth or wire,
and the remainder of the bran, are guided into the reel
S, to be bolted.

To clean Wheat several Times.

Suppose the grain to be in the screen hopper E.
Draw the gate a ; shut the gate e ; move the sliding
hopper K over the spout K c d ; and let it run into the
elevator to be raised again. Turn the crane spout over
the empty hopper G, and the wheat will be all deposited
there nearly as soon as it is out of the hopper F. Then
draw the gate e, shut the gate a, and turn the crane
spout over F ; and so on alternately, as often as neces-
sary. When the grain is sufficiently cleaned, slide the
hopper K over the hole that leads into the stones.

The screenings fall into a garner, hopperwise, to clean
them draw the gate f, and let them run into the elevator,
to be elevated into the screen hopper F. Then proceed
with them as with the wheat, till sufficiently clean. To
clean the fannings, di*aw the litde gate h, and let them
into the elevator, &:c. as before.

Fig. II. is a perspective view of the conveyer, as it
lies in its troughs, at work ; and shows the manner in
which it is joined to the pullies, at each side of the
elevator.

Fig. III. exhibits a view of the pulley of the meal
elevator, as it is supported on each side, with the strap
and buckets descending to be filled.

Fig. IV. is a perspective view of the underside of the
arms of the hopper-boy, with flights complete. The
dotted lines show the track of the flights of one arm;
those of the other following, and tracking between them.
A A are the sweepers. These carry the meal round in a
ring, trailing it regularly all the way, the flights drawing
it to the centre, as already mentioned. B B are the
sweepers that drive it into the bolting hoppers,

F f

226 CONSTRUCTION OF MACHINES. [Chap. S.

FiV. V. is a perspective view of the bucket of the
Avheat- elevator ; and shows the manner in which it is
fastened, by a broad piece of leather, which passes
through and under the elevator-strap, and is nailed to
the sides with litde tacks.

CHAPTER III.

©F THE CONSTRUCTION OF THE SEVERAL MACHINES.

ART. 95.

OF THE WHEAT ELEVATOR.

FIRST determine how many bushels it should hoist
in an hour, and where it shall be set, so as to answer all
the following purposes, if possible.

1. To elevate the grain from a wagon or ship.

2. From the different garners into which it may be
stored.

3. If it be a two story mill, to hoist the wheat from
the tail of the fan, as it is cleaned, to a garner over the
stones.

4. To hoist the screenings to clean them several times.

5. To hoist the wheat from a shelling-mill, if there
be one.

One elevator may do all this in a mill rightly planned,
and most of it can be done in mills ready built.

Then if you wish it to hoist about 300 bushels in an
hour, make the strap 4| inches wide, of good, strong,
white harness-leather, only one thickness. It must be
cut and joined together in a straight line, with the thick-
est and consfiquently the thinnest ends together, so that
if they be too thin they may be lapped over and doubled,
until they are tliick enough singly. Then, to make
wooden buckets, take the butt of a willow or water-
birch, that will split freely, cut it in bolts 15 inches long,
and rive and shave it into staves 5| inches wide, and
three-eighths of an inch thick ; these will make one
bucket each. Set a pair of compasses to the width of
the strap, and make the sides and middle of the bucket
equal thereto at the mouth, but let the sides be only two-

Chap.3.] CONSTRUCTION OF MACHINES. 227

Ihiifls of that width at the bottom, Avhich will make it of
the form of fig. 9, plate 6 ; the ends being cut a little
circular, to make the buckets lay closer to the strap and
M'heel. As it passes over, make a pattern of the form
of fig. 9, to describe all the rest by. This makes a bucket
of a neat form, to hold about 75 solid inches, or some-
what more than a quart. Then to make them bend to
a square at the corners e c, cut a mitre square across
where they are to bend, about 2-8 through; boil them
and bend them hot, taking a strip of leather across them,
to hold them in that form until they get cold, and then
put bottoms to them of the thin skirts of the harness
leather. These bottoms are to extend from the lower
end to the strap that binds it on. Then, to fasten them
on M ell and with despatch, prepare a number of straps
1| inches wide, of the best cuttings of the harness leather,
wet them and stretch them as hard as possible, which
reduces, their width to about Ih inches. Nail one of
these straps to the side of a bucket, with 5 or 6 strong
tacks that will reach through the bucket and clinch inside.
Then take a 1| inch chisel, and strike it through the
main strap about a quarter of an inch from each edge,
and put one end of the binding-strap through the slits,
draw the bucket very closely to the strap, and nail it on
the other side of the bucket, which \^ ill finish it. See B
in fig. 2, plate 6. C is a meal-bucket fastened in the
same manner, but is bottomed only with leather at the
low-er end, the main strap making the bottom side of it.
This is the best way I have yet discovered to make wood-
en buckets. The scraps of the harness leather, out of
which the elevator-straps are cut, are generally about
enough to complete the buckets, which works it all up.

To make Sheet- Iron Buckets.

Cut the sheet in the form of fig. 8, plate VI. making
the middle part c, and the sides a and b nearly equal to
the width of the strap, and nearly 5\ inches long, as be-
fore. Bend them to a right angle at every dotted line,
and the bucket wiil be formed, c will be the bottom side
next to the strap ; and the litde holes a a and b b will
meet, and must be rivetted to hold it together. The two

228 CONSTRUCTION OF MACHINES. [Chap.3.

holes c are for fastening it to the straps by rivets. The
part a b is the part that dips up the wheat, and the point
being doubled back strengthens it, and tends to make it
wear well. The bucket being completely formed, and
the rivet-holes made, spread one out again, as fig. 8, to
describe all the rest by, and to mark for the holes, which
will meet again when folded up. They are fastened to
the strap by two rivets with thin heads put inside the
bucket, and a double burr of sheet iron put on the under
side of the strap, which fastens them on very tightly.
See A, plate VI, fig. 2. These buckets will hold about
1,3 quarts, or 88 cubic inches. This is the best way I
have found to make sheet-iron buckets. D is a meal-
bucket of sheet-iron, rivetted on by two rivets, with their
heads inside the strap; the sides of the buckets are turned
a little out, and holes made in them for the rivets to pass
through. Fig. 11 is the form of one spread out, and the
dotted lines show where they are bent to right angles to
form them. The strap forms the bottom side of these
buckets.

Make the pulleys 24 inches diameter, as thick as the
strap is wide, and half an inch higher in the middle than
at the sides, to make the strap keep on ; give them a
motion of 25 revolutions in a minute, and put on a sheet-
iron bucket for every 15 inches; then 125 buckets will
pass per minute, which will carry 162 quarts, and hoist
300 bushels in an hour, and 3600 bushels in 12 hours.
If you wish to hoist faster, make the strap wider, the
buckets larger in proportion, and increase the velocity
of the pulley, but not above 35 revolutions in a minute,
nor more buckets than one for every 12 inches, other-
wise they will not empty well. A strap of 5 inches, with
buckets 6 inches long, and of a width and proportion
suiting the strap (4^ inches wide) will hold 1,8 quarts
each; and 35 revolutions of the pulley will pass 175
buckets, which will carry 315 quarts in a minute, and
590 bushels in an hour. If the strap be 4 inches wide,
and the wooden buckets 5 inches deep, and in propor-
tion t© the strap, they will hold ,8 of a quart : then, if
there be one for every 15 inches, and the pulley revolves
27 revolutions in a minute, it will hoist 200 bushels in
arf hour, where tliere is a good garner to empty the

Chap. 3.] CONSTRUCTION OF MACHINES. 229

wheat into. This is sufficient for unloading wagons, and
the size they are commonly made.

Plate VI, fig. 6, represents the gudgeon of the lower
pulley ; fig. 7, the gudgeon for the shaft on which the
upper pulley is fixed. Fix both the pulleys in their places,
but not firmly, so that a line stretched from one pulley
to the other, will cross the shafts or gudgeons at right
angles. This must always be the case to make the
sti'aps w ork fairly. Put on the strap with the buckets ;
draw it tightly and buckle it ; put it in motion, and if it
does not keep fairly on the pulleys, their position may
be altered a little. Observe how much the descending
strap swags by the weight of the buckets, and make the
case round it so crooked, that the points of the buckets
will not rub in their descent, which will cause them to
wear much longer and work easier. The side boards
need not be made crooked in dressing out, but may be
bent sufficiently by sawing them half way or two-thirds
through, beginning at the upper edge, holding the saw
very much aslant, the point downwards and inwards, so
that in bending the parts will slip past each other. The
upper case must be nearly straight ; for if it be made
much crooked, the buckets will incline to turn under
the strap. Make the cases 3-4 of an inch wider than the
strap and buckets inside, and 1| inch deeper, that they
may play freely ; but do not give them room to turn
upside down. If the strap and buckets be 4 inches,
then make the si'de boards 5|, and the top and bottom
boards 6| inches wide, of inch boards. Be careful that
no shoulders nor nail-points be left inside of the cases,
for the buckets to catch in. Make the ends of each case,
where the buckets enter as they pass over the pulleys,
a little wider than the rest of the case. Both the pulleys
are to be nicely cased round to prevent waste, not leav-
ing room for a grain to escape, continuing the case of
the same width round the top of the upper, and bottom
of the lower pulley ; then if any of the buckets should
ever get loose, and stand askew, they will be kept right
by the case ; whereas, if there were any ends of boards
or shoulders, they would catch against them. See A B,
plate VI, fig. 1. The bottom of the case of the upper

230 CONSTRUCTION OF MACHINES. [Chap. 3,

pulley must be descending, so that what grain may be
falling out of the buckets in passing over the pulleys,
may be guided into the descending case. The shaft
passing through this pulley is made round where the
case fits to it : half circles are cut out of two boards, so
that they meet and embrace it closely. The undermost
board, where it meets the shaft, is ciphered off inside
next the pulley, to guide the grain inward. But it is
full as good a way to have a strong gudgeon to pass
through the upper pulley, Math a tenon at one end, to
enter a socket, which may be in the shaft, that is to give
it motion. This will best suit where the shaft is short,
and has to be moved to put the elevator out, and in
gear.

The way that I have generally cased the pulleys is as
follows, viz. The top board of the upper strap-case,
and the bottom board of the lower strap-case are ex-
tended past the lower pulley to rest on the floor ; and
the lower ends of these boards are made two inches
narrower, as far as the pulley- case extends ; the side
board of the pulley is nailed, or rather screwed, to them
with wood screws. The rest of the case boards join to
the top of the pulley-case, both being of one width.
The block which the gudgeons of this pulley run in, are
screwed fast to the outside of the case boards ; the gud-
geons do not pass quite through, but reach to the bottom
of the hole, which keeps the pulley in its place.

The said top and bottom boards, and also the side
boards of the strap-cases, are extended past the upper
pulley, and the side boards of the pulley- case are screwed
to them ; but this leaves a vacancy between the top of
the side boards of the strap-cases, and shoulders for the
buckets to catch against. This vacancy is to be filled up
by a short board, guiding the buckets safely over the
upper pulley. The case must be as close to the points
of the buckets, where they empty, as is safe, that as
little as possible may fall down again. There is to be a
long hole cut into the case at B, for the wheat to fall
out at, and a short spout guiding it into the crane spout.
The top of the short spout next B, should be loosely
fastened in with a button, that it may be taken off, to

Chap. 3.] CONSTRUCTION OF MACHINES. 231

examine if the buckets empty well, &c. Some neat
workmen have a much better way of casing the pulleys,
that I cannot here describe; what I have described is
the cheapest, and does very well.

The wheat should be let in at the bottom, to meet the.
buckets, and a gate to shut as near the point of them as
possible, as at A, plate VI, fig. 1. Then if the gate be
drawMi sufficiently to fill the backets, and the elevator be
stopped, the wheat will stop running in, and the eleva-
tor will be free to start again ; but if it had been let in
any distance up, then, when the elevator stopped, it
would fill from the gate to the bottom of the pulley, and
the elevator could not start again. If it be in any case
let in any distance up, the gate should be so fixed, that
it cannot be drawn so far, as to let in the wheat faster
than the buckets can take it, else the case will fill and
stop the buckets. If it be let in faster at the hindmost
side of the pulley, than the buckets will carry it, the
same evil will occur ; because the buckets will push the
wheat before them, being more than they can hold, and
give room for too much to come in ; therefore there
should be a relief gate at the bottom to let the wheat out,
if ever there happens to get too much in.

The motion is to be given to the upper pulley of all
elevators, if it can be done, because the weight in the
buckets, causes the strap to hang tighter on the upper,
and slacker on the lower pulley ; therefore the upper
pulley will carry the greatest quantity without slipping.
All elevators should stand a little slanting, because they
will discharge the better. The boards for the cases
should be of any unequal lengths, so that two joints will
never come close together, which makes the case strong.
Some have joined the cases at every floor, which is a
great error. There must be a door in the ascending
case, at the most convenient place, to buckle the strap,
&:c. &c.

Of the Crane Spout.

To make a crane spout, fix a board 18 or 20 inches
broad truly horizontal, or level, as a under B, in plate
\'l, fig. 1. Through the middle of this board the wheat

232 CONSTRUCTION OF MACHINES. [Chap. 3.

is conveyed, by a short spout from the elevator. Then
make the spout of 4 boards, 12 inches wide at the up-
per, and about 4 or 5 inches at the lower end. Cut the
upper end off aslant, so as to fit nicely to the bottom of
the board ; hang it to a strong pin, passing through the
broad board near the hole through which the wheat
passes, so that the spout may be turned in any direction
and still cover the ^vhole, at the same time it is receiving
the wheat, and guiding it into any garner, at pleasure.
In order that the pin may have a strong hold of the
board and spout, there must be a piece of scantling, 4
inches thick, nailed on the top of the board, for the pin
to pass through ; and another to the bottom, for the
head of the pin to rest on. But if the spout be long and
heavy, it is best to hang it on a shaft, that may extend
down to the floor, or below the collar-beams, with a pin
through it, as x, to turn the spout by. In crane spouts
for meal it is sometimes best to let the lower board
reach to, and rest on the floor. If the elevator-cases and
crane-spout be well fixed, there can neither grain nor
meal escape or be wasted that enters the elevator, until
it comes out at the end of the crane- spout again.

Of an Elevator to elevate fFheatfrom a Ship's Hbld.^

Make the elevator complete (as it appears '55 — 39,
plate 8) on the ground (and raise it afterwards.) The
pulleys are to be both fixed in their places and cased ;
and the blocks that the gudgeon of the upper pulley is
to run in, are to be rivetted fast to the case-boards of the
pulley, and these case-boards screwed to the strap-cases
by long screws, reaching through the case-boards edge-
ways. Both sides of the pulley-case are fastened by one
set of screws. On the outside of these blocks, round
the centre of the gudgeons, are circular knobs, 6 inches
diameter, and 3 inches long, strongly rivetted to keep
them from splitting off, because by these knobs the
whole weight of the elevator is to hang. In the move-
able frame 40. oo, oo, are these blocks with their knobs,
let into the pieces of the frame B C rs. The gudgeons

♦ See the description of this elevator in art- 90,

Chap. 3.] CONSTRUCTION OF MACHINES. !i33

of the upper pulley p pass through these knobs, and play
in them. Their use is to bear the weight of the elevator
that hangs by them ; the gudgeons, by this means, bear
only the weight of the strap and its load, as is the case
with other elevators. Their being circular gives the
elevator liberty to swing out from the wall to the hold of
the ship.

The frame 40 is made as follows : the top piece A B
is 9 by 8, strongly tenoned into the side pieces A D
and B C with double tenons, which side pieces are 8 by
6. The piece r s is put in with a tenon, 3 inches thick,
which is dovetailed, keyed, and drawpinned, with an
iron pin, so that it can easily be taken out. In each side
piece A D and B C there is a row of cogs, set in a circle,
that are to play in circular rabbets in the posts p. 41.
These circles are to be described with a radius, whose
length is from the centre of the joint gudgeons G, to the
centre of the pulley 39 ; and the posts must be set up,
so that the centre of the circle, will be the centre of the
gudgeon G ; then the gears will be always right, al-
though the elevator rise and fall to suit the ship or tide.
The top of those circular rabbets ought to be so fixed,
that the lower end of the elevator may hang near the
wall. This may be regulated by fixing the centre of
gudgeon G. The length of these rabbets is regulated
by the distance the vessel is to rise and fall, to allow the
elevator to swing clear of the vessel light at high water.
The best way to make the circular rabbets is, to dress
two pieces of 2 inch plank for each rabbet, of the right
circle, and pin them to the posts, at such a distance,
leaving the rabbet between them.

When the gate and elevator are completed, and tried
together; the gate hung in its rabbets, and played up and
down, then the elevator may be raised by the same pow-
er ; that is, to raise and lower it as described, art. 4.

ART. 96.

OF THE MEAL-ELEVATOR.

Litde may be said of the manner of constructing the
meal-elevator, after what has been said in art. 90, except

234 CONSTRUCTION OF MACHINES. [Chap. 3,

giving the dimensions. Make the pulleys 3| inches
thick, and 18 inches diameter. Give them no more
than SO revolutions in a minute. Make the strap 3|
inches wide, of good, pliant, white harness-leather ;
make buckets either of wood or sheet- iron, to hold about
half a pint eacli ; put one for every foot of the strap ;
make the cases tight, especially round the upper pulley,
slanting much at bottom, so that the meal which falls
out of the buckets, may be guided into the descending
case. Let it lean a little, that it may discharge the bet-
ter. The spout that conveys the meal from the elevator
to the hopper- boy, should not have much more than 45
degrees descent, that the meal may run easily down,
and not cause a dust ; fix it so that the meal will spread
thinly over its bottom ; in its descent it will cool the
better. Cover the top of the spout half-way down, and
hang a thin, light cloth at the end of this cover, to check
all the dust that may raise, by the fall of the meal from
the buckets. Remember to take a large cipher off the
inside of the board, where it fits to the undermost side
of the shaft of the upper pulley ; else the meal will work
out along the shaft. Make all tight, as directed, and it
will effectually prevent waste.

In letting meal into an elevator, it must be let in some
distance above the centre of the pulley, that it may fall
clear from the spout that conveys it in ; otherwise it will
clog and choak. Plate VI. fig. 4, is the double socket gud-
geon of the lower pulley, to which the conveyer joins. Fig.
3, a b c d, is a top view of the case that the pulley runs
in, which is constructed thus ; a b is a strong plank, 14?
by 3 inches, steped in the sill, dovetailed and keyed in
the meal-beam, and is called the main bearer. In this,
at the determined height, is framed the gudgeoiT^Dearers
a c b d, which are planks 15 by l| inches, set Ik inches
apart, the pulley running between, and resting on them.
The end piece c d 7 inches wide and 2 thick, is set in
the direction of the strap- case, and extends 5 inches
above the top of the pulley ; to this the bearers are nailed.
On the top of the bearers, above the gudgeons, are set
two other planks 13 by i\ inches, rabbetted into the
main bearer, and screwed fast to the end piece c d : these

€hap.3.] CONSTRUCTION OF MACHINES. 235

are 4 inches above the pulley. The bottom piece of
this case slides in between the bearers, resting on two
elects, so that it can be drawn out to empty the case,
if it should ever by any means be overcharged with
meal; this completes the case. In the gudgeon bearer
under the gudgeons are mortises, made about 12 by 2
inches, for the meal to pass from the conveyer into the
elevator; the bottom board of the conveyer trough rests
on the bearer in these mortises. The strap-case joins
to the top of the pulley case, but is not made fast, but
the back board of the descending case is steped into the
inside of the top of the end piece c d. The bottom of
the ascending case is to be supported steady to its
place, and the board at the bottom must be ciphered off
at the inside, with long and large ciphers, making them
at the point only 1-4 inch thick; this is to make tlie bot-
tom of the case wide for the buckets to enter, if any of
them should be a little askew, because the pulley- case is
wider than the strap-cases, to give rooirt for the meal
from the conveyer to fall into the buckets ; and in order
to keep the passage open, ihere is a piece 3 inches wide,
and 1| inch thick, put on each side of the pulley to
stand at right angles with each other, extending 3|
inches at each end past the pulley, and are ciphered off,
so as to clear the strap, and draw the meal under the
buckets; these are called bangers.

ART. 97.

OF THE MEAL.':ONVEYER.

Sea^t described, art. 88. Plate VI, fig. 3, is a conveyer
joined to the pulley of the elevator. Fig. 4 is the gudgeon
that is put through the lower pulley, to which the convey-
er is joined by a socket, as represented. Fig. 5 is a view
of the said socket and the band, as it appears on the end
of the shaft. The tenon of the gudgeon is square, that
the socket may fit it every way alike. Make the shaft
5| inches diameter, of eight equal sides, and put on the
socket and the gudgeon ; then, to lay it out for the flights,

336 CONSTRUCTION OF MACHINES. [Chap. a.

begin at the pulley, mark as near the end as possible,
on the one side, and turning the shaft the way it is to
work, at the distance of 1| inch towards the other end,
set a flight on the next side, and thus go on to mark
for a flight on every side, still advancing 1| inch to the
other end, which will form the dotted spiral line, which
would drive the meal the wrong way; but the flights
are to be set across this spiral line, at an angle of about
30 degrees, with a line square across the shaft ; and then
they will drive the meal the right way, the flights operat-
ing like ploughs.

To make the flights, take good maple, or other
smooth hard wood; saw it in 6 inch lengths; split it
always from the sap to the heart; make pieces 2| inches
wide, and 3-4 of an inch thick ; plane them smooth on
one side, and make a pattern to describe them by, and
make a tenon 2| inches long, to suit a 3-4 inch auger.
When they are perfectly dry, having the shaft bored,
and the inclination of the flights marked by a scribe, drive
them in and cut them oflf 2^ inches from the shaft, dress
them with their foremost edge sharp, taking all off" from
the back side, leaving the face smooth and straight, to
push forward the meal ; make their ends nearly circular.
If the conveyer be short, put in lifting flights, with their
broad side foremost, half the number of the others, be-
tween the spires of them ; they cool the meal by lifting
and letting it fall over the shaft.

To make the trough for it to run in, take 3 boards,
the bottom one 11, back 15, and front 13 inches. Fix
the block for the gudgeon to run in at one end, and fill
the comers with cleets, to make the bottom nearly cir-
cular, that but little meal may lay in it ; join it neatly to
the pulley-case, resting the bottom on the bottom t)f the
hole cut for the meal to enter, and the other end on a
supporter, that it can be removed and put to its place
again with ease, without stopping the elevator.

A meal-elevator and conveyer thus made, of good
materials, will last 50 years, with very litde repair, and
save more meal from waste, than will pay for building
and repairing them for ever. The top of the trough
trjust be left open, to let the sti'eam of the meal out :

. 3.] CONSTRUCTION OF MACHINES. 237

and a door may be made in the ascending case of the
elevator, about 4 feet long, to buckle the strap tighter,
&c. The strap of the elevator turns the conveyer, so
that it will be easily stopped if any thing should be
caught in it, being dangerous to turn it by cogs. This
machine is often applied to cool the meal, without the
hopper-boy, and attend the bolting-hopper, by extend-
ing it to a great length, and conveying the meal imme-
diately into the hopper, which does very well, and some
prefer it ; but a hopper- boy is preferable where there is
room for one.

ART. 98.
OF A GRAIN-CONVEYER.

This machine has been constructed in a variety of
ways, the best I take to be as follows, viz. Make a
round shaft, 9 inches diameter. Then, to make the
spire, take strong sheet- iron, make a pattern 3 inches
broad and of the true arch of a circle ; the diameter of
which (being the inside of the pattern) is to be 12 inches ;
this will give it room to stretch along a 9 inch shaft, so
as to make a hasty spire,- that will advance about 21
inches along the shaft every revolution. By this pattern
cut the sheet-iron into circular pieces, and join the ends
together by rivetting and lapping them, so as to let the
grain run freely over the joints ; when they are joined
together they will form several circles, one above the
other, slip it on the shaft, and stretch it along as far as
you can, till it comes tight to the shaft, and fasten it to
its place by pins, set in the shaft at the back side of the
spire, and nail it to the pins : it will now form a beauti-
ful spire 21 inches apart, which is too great a distance;
therefore there should be two or three of these spires
made, and wound into each other, and all be put on
together, because if one be put on first, the others can-
not be got on so well afterwards ; they will then be 7
inches apart, and will convey wheat very fast. If these
spires be punched full of holes like a grater, and the

238 CONSTRUCTION OF MACHINES. [Chap. 6.

trough lined with sheet- iron punched full of small holes,
it will be an excellent rubber ; will clean the wheat of
the dust and down, that adheres to it, and supersede the
necessity of any other rubbing-machine.

The spires may also be formed with either wooden
or iron flights, set so near to each other in the spiral
Hues, as to convey the wheat from one to another.

ART. 99.
OP THE HOPPER-BOY.

This machine has appeared in various constructions,
the best of which is represented by Plate VII. fig. 12 :
see the description, art. 88.

To make the flight-arms C D, take a piece of dry
poplar, or other soft scantling 14 feet long, 8 by 2| in-
ches in the middle, 5 by 1| inches at the end, and
straight at the bottom ; on this strike the middle line
a b, fig. 13. Consider which way it is to revolve, and
cipher off" the under side of the foremost edge from the
middle line, leaving the edge 3-4 of an inch thick, as
appears by the shaded part. Then to lay out the flights,
take the following

RULE.

Set your compasses at 4| distance, and, beginning
with one foot in the centre c, step towards the end b,
observing to lessen the distance one sixteenth part of an
inch every step ; this will set the flights closer together
at the end than at the centre. Then to set the flights
of one arm to track truly between those of the other, and
to find their inclination, with one point in the centre c,
sweep the dotted circles across every point in one arm,
then, without altering the centre or distance, make the
little dotted marks on the other arm, and between them
the circles are to be swept for the flights in it. Then,
to vary their inclination, regularly from the end to the
centi-e, strike the dotted line c d half an inch from the
centre c, and 2f inches from the middle line at d. Then
with the compasses set to half an inch, set off" the incli^

Chap. 3.] CONSTRUCTION OF MACHINES. 239

nation from the dotted circles on the line c d. Then,
because the line c d approaches the middle line, the in-
clination is greater near the centre than at the end, and
vary regularly. Dovetail the flights into the arm, observ-
ing to put the side that is to drive the meal to the line of
inclination. The bottoms of them should not extend past
the middle line, the ends being all rounded and dressed
off" at the back side to make the point sharp, leaving the
driving side quite straight like the flight r. See them
complete in the end c a. The sweepers should be 5 or
6 inches long, screwed on behind the flights, at the
back side of the arms, one at each end of the arm, and
one at the part that passes over the hopper : their use is
described art. 88.

The upright shaft should be 4 by 4 inches, and made
round for about 4^ feet at the lower end, to pass lightly
through the centre of the arm. To keep the arm steady,
there is a stay-iron iSi inches high, its legs i-2 inch by
3'4, to stride 2 feet. The ring at the top should fit the
shaft neatly, and be smooth and rounded inside, that it
may slide easily up and down ; by this the arm hangs to
the rope that passes over a pulley at the top of the shaft
8 inches diameter, with a deep groove for the rope or
cord to run in. Make the leading arm 6 by 1| inches
in the middle, 2 by I inch at the end, and 8 feet long.
This arm must be braced to the cog-wheel above, to keep
it from splitting the shaft by any extra stress.

The weight of the balance w must be so near equal to
the weight of the arm, that when it is raised to the top it
will descend quietly.

In the bottom of the upright shaft is the step-gudgeon
(fig. 15,) which passes through the square plate 4 by 4
inches, (fig-. 14,) on this plate the arm rests, before the
flights touch the floor. The ring on the lower end of the
shaft is less than the shaft, that It may pass through the
arm : this gudgeon comes out every time the shaft is
taken out of the arm.

If the machine is to attend but one bolting-hopper, it
need not be above 12 or 13 feet long. Set the upright
shaft close to the hopper, and the flights all gather as the
end c b, fig. 13. But if it is to attend for the grinding

240 CONSTRUCTION OF MACHINES. [Chap. S.

of two pair of stones, and two hoppers, make it 15 feet
long, and set it between them a Httle to one side of both,
so that the two ends may not both be over the hoppers
at the same time, which would make it run unsteady ;
then the flights between the hoppers and the centre must
drive the meal outwards to the sweepers, as the end c a,
%. 13.

If it is to attend two hoppers, and cannot be set be-
tween them for want of room, then set the shaft near to
one of them ; make the flights that they all gather to
the centre, and put sweepers over the outer hopper,
which will be first supplied, and the surplus carried to
the other. The machine will regulate itself to attend
both, although one should feed three times as fast as the
other.

If it be to attend three hoppers, set the shaft near the
middle one, and put sweepers to fill the other two, the
surplus will come to the centre one, and it will regulate
to feed all three ; but should the centre hopper ever
stand while the others are going (of either of these last
applications), the flights next the centre must be move-
able that they may be turned, and set to drive the meal
out from the centre ; hopper-boys should be moved by
a strap in some part of their movement, that they may
easily stop if any thing catch in them ; but several in-
genious mill-wrights do prefer cogs ; they should not
revolve more than 4 times in a minute.

This machine may be made of a great many diflferent
forms and constructions on the same principles, to an-
swer the same end, in a lesser degree of perfection.

• ART. 100.
OF THE DRILL.

See the description, art. 1. The pulleys should not
be less than 10 inches diameter for meal, and more for
wheat. The case they run in is a deep narrow trough,
say 16 inches deep, 4 wide, pulleys and strap 3 inches.
The rakes are little square blocks of willow or poplar.

Chap. 3.] CONSTRUCTION OF MACHINES. 241

or any soft wood, that will not split with the nails, all of
one size that each may take an equal quantity, nailed to
the strap with long, small nails, with broad heads, which
are inside the strap ; the meal should be let into them
always above the centre of the pulley, or at the top of it,
to prevent its choaking, which it is apt to do, if let in
low. The motion should be slow for meal; but may
be more lively for wheat.

Directions for itsing a Hopper-boy.

1. When the meal-elevator is set in motion to elevate
the meal; the hopper-boy must be set in motion also, to
spread and cool it ; and as soon as the circle is full, the
bolts may be started ; the grinding and bolting may
likewise be carried on together regularly, which is the
best way of working.

3. But if you do not choose to bolt as you grind, turn
up the feeding sweepers and let the hopper-boy spread
and cool the meal, and rise over it ; and when you be-
gin to bolt turn them down again.

3. If you choose to keep the warm meal separate from
the cool, shovel about 18 inches of the outside of the
circle in towards the centre, and turn the end flights, to
drive the meal outwards ; it will spread the warm meal
outwards, and gather the cool meal in the bolting-hop-
per. As soon as the ring is full with warm meal, rake
it out of the reach of the hopper-boy, and let it fill
again.

4. To mix tail-floiver or bran, &c. with a quantity of
meal that is under the hopper-boy, make a hole for it
in the meal quite to the floor, and put it in ; and the hop-
per-boy will mix it regularly with the whole.

5. If it does not keep the hopper full, turn the feed-
ing sweeper a little lower, and throw a little meal on the
top of the arm, to make it sink deeper into the meal. If
the spreading sweepers discharge their loads too soon,
and do not trail the meal all around the circle, turn them
a little lower ; if they do not discharge, but keep too full,
raise them a little.

342 UTILITY OF THE IMPROVEMENTS. [Chap.*.
CHAPTER IV.

ART. 101.

Of the utility of these inventions and improvements.

DR. WISTAR, of Philadelphia, has discovered and
proved by many experiments, (which he communicated
to the American Philosophical Society, and which they
have published in the 3d volume of their Transactions,)
that cold is one principal agent in causing moisture to
evaporate from bodies ; and the fact is evident from daily
observation, viz. that it is the different degrees of heat
and cold, between the air and bodies, that causes them
to cast off or contract moisture.

1st. We see in all sudden transitions from an extreme
cold air to a warm, that the walls of houses, stones,
ground, and every thing that retains cold, contracts
moisture ; and it certainly has the same effect on meal.

2. In all sudden changes from warm to cold, every
thing casts off its moisture; for instance, what great
quantities of water will disappear from the ground, in
one cold night ; this is the reason why meal being warm
gets so dry in cold weather, and bolts so free ; whereas
it is always harder to bolt when there is a change from
cold to warm.

3. If you warm a razor, or a glass, warmer than your
breath, neither of them will be sullied by it.

4. Fill a glass bottle with cold water in a warm day,
and wipe it dry, and there will be presently seen on its
outside large drops, collected from the moisture of the
air, though the bottle still continues full.

From these instances, it is evident, that the meal
should be spread as thin as possible, and be kept in
motion from the moment it leaves the stones, until it is
cold, that it may have a fair opportunit}^ of casting off
its moisture, which will be done more effectually in that
time, than can possibly be effected in warm weather, in

Chap. 4.] UTILITY OF THE IMPROVEMENTS. 243

anv reasonable time, after it has grown cold in a heap and
retained its moisture ; and there is no time for insects to
deposit their eggs, that may in time breed the worms,
that are often found in the heart of barrels of flour well
packed, and by the moisture being cast out more effec-
tually, it will not be so apt to sour. Therefore one great
advantage is, that the meal is better prepared for boltings
packin^^ and keepings in much less time.

2. They do the work to much greater perfection^ by
cleaning the grain and screenings more effectually, hoist-
ing and bolting over great part of the flour, and grinding
and bolting over the middlings, all at one operation, mix-
ing those parts that are to be mixed, and separating such
as are to be separated, more effectually.

3. They save much meal from being wasted^ if they be
well constructed, because there is no necessity of tramp-
ling in it, which trails it wherever we walk, nor shoveling
it about to raise a dust that flies away, &:c. This article
of saving will soon pay the first cost of building, and keep
them in repair afterwards.

4. They afford more room than they take up, because
the whole of the meal-loft tliat heretofore was little
enough to cool the meal on, may now be spared for other
uses, except the circle described by the hopper-boy: and
the wheat garners may be filled from one story to an-
other, up to the crane spout, above the collar-beams : so
that a small part of the house will hold a quantity of
wheat, and it may be drawn from the bottom into the
elevator as wanted.

5. They tend to dispatch business, by finishing as they
go ; so that there is not as much time expended in grind-
ing over middlings, which w ill not employ the power of
the mill, nor in cleaning and grinding the screenings,
they being cleaned every few days, and mixed with the
wheat ; and as the labour is easier, the miller can keep
the stones in better order, and more regularly and steady
at work, especially in the night time, when they fre-
quently stop for want of help, whereas one man, would
be sufficient to attend six pair of stones running (in one
house) well attended by machinery.

244 UTILITY OF THE IMPROVEMENTS. [Chap. 4.

6. They last a long time with but little expense of re-
pair^ because their motions are slow and easy.

7. They hoist the grain and meal with less power ^ and
disturb the motion of the mill much less than the old way,
because the descending strap balances the ascending one,
so that there is no more power used, than to hoist the
grain or meal itself; whereas in the old way for every 3
bushels of wheat, which fills a 4 bushel tub with meal,
the tub has to be hoisted, the weight of which is equal
to a bushel of wheat, consequently the power used, is as
3 for the elevator to 4 for the tubs, which is one fourth
less with elevators than tubs ; besides the weight of 4
bushels of \vheat, thrown at once on the wheel, always
checks the motion, before the tub is up ; the stone
sinks a little, and the mill is put out of tune every tubfull,
which makes a great difference in a year's grinding; this
is worthy of notice when the water is scarce.

8. 77?^^ save a great expense of attenda?ice. One half
of the hands that were formerly required are now suf-
ficient, and their labour is easier. Formerly one hand
was required for every 10 barrels of flour that the mill
made daily ; now one for every 20 barrels is sufficient.
A mill that made 40 barrels a day, required four men and
a boy ; two men are now sufficient.

Two mens' wages, at 7 dolls, each, per month, 168 dolls.
Boarding &c. for do. at 15/. per year, - 80

One boy's board, clothing, &c. - - 50

298

There appears a saving of 298 dollars a year, in the
article of wages and board, in one double mill.

In support of what is here said, I add the following
certificates.

WE do certify, that we have erected Oliver Evanses
new invented mode of elevating, conveying, and cool-
ing meal, &c. As far as we have experienced, we have
found them to answer a valuable purpose, well worthy
the attention of any person concerned in merchant, or

Chap.4.] UTILITY OF THE IMPROVEMENTS. 245

even extensive countiy mills, who wishes to lessen the
labour and expense of manufacturing wheat into flour.

JOHN ELLICOTT,
JONATHAN ELLICOTT,
GEORGE ELLICOTT,
NATHANIEL ELLICOTT.

Ellicott's mills, Baltimore county, state?
of Maryland, August 4, 1790. S

II.

WE, the subscribers, do hereby certify, that we have
introduced Oliver Evans's improvements into our mills
at Brandy wine, and have found them to answer, as re-
presented to us by a plate and description ; also to be
a great saving of waste, labour and expense, and not
subject to get out of order. We therefore recommend
them as well worthy the attention of those concerned in
manufacturing grain into flour.

JOSEPH TATNALL,
THOMAS LEA.
SAMUEL HOLLINGS WORTH,
THOMAS SHALLCROSS^
CYRUS NEWLIN.
Brandywine -mills, 3d ?
month 28th, ir91. 5

III.

WE do certify, that we have used Oliver Evans's
machinery for the space of two years, in our mills, at
Petersburg, in Virginia, consisting of three water-wheels,
and three pair of stones ; and we judge that they have
been, and will continue to be, a saving of 300 dollars
per year.

N. ELLICOTT & Co.

February 20, 1794.

IV.

WE do certify, that we have used Oliver Evans's
patent machinery in our mills at Manchester, in the
state of Virginia, consisting of three water-wheels, and
three pair of stones, for the space of one year, and we
judge upon fair calculations that they are a saving to us
of 300 dollars per annum.

NICHOLSON & TAYLOR.

246 BILLS OF MATERIALS. [Chap. 5.

Many more to the same purpose might be added, but
these may suffice.

Supposing the reader is now fully convinced of the
utility of these improvements, I proceed to give the fol-
lowing bills of materials.

CHAPTER V.

BILLS OF MATERIALS TO BE PROVIDED FOR BUILDING AND
CONSTRUCTING THE MACHINERY.

ART. 103.

For a Wheat- Elevator 4<2> feet high^ with a Strap 4 inches

wide.

Three sides of good, firm, white harness-leather.

220 feet of inch pine, or other boards that are dry, of
about 12| inches wide, for the cases; these are to be
dressed as follows:

86 feet in length, 7 inches wide, for the top and bottom.

86 feet in length, 5 inches wide, with the edges truly
squared, for the side boards.

A quantity of inch boards for the garners, as they may
be wanted.

Sheet-iron or a good butt of willow wood, for the buck-
ets.

2000 tacks, 14 and 16 ounce size, the largest about half
an inch long, for the buckets.

31b of 8d. and lib. of lOd. nails, for the cases.

2 dozen of large wood screws (but nails will do) for pul-
ley-cases.

16 feet of 2 inch plank for pulleys.

16 feet of ditto, for cog wheels, and dry pine scantling
4 1 by 4 1, or 5 by 5 inches, to give it motion.

Smithes Bill of Iron.

1 double gudgeon 3 4 inch, (such as fig, 6, plate VI.) 5
inches between the shoulders, 3| inches between the
holes, the necks, or gudgeon-part, 3 inches.

Chap. S.-] BILLS OF MATERIALS. 247

1 small gudgeon, of the common size, 3-4 inch thick.

1 gudgeon an inch thick, (fig. 7,) neck 3^ tang. 10 in-
ches, t') be next the upper pulley.

2 small bands, 4| inches from the outsides.

1 harness-buckle, 4 inches from the outsides, with 2

tongues, of the form of fig. 12.
Add whatever more may be wanting for the gears, that

are for giving it motion.

I^or a Meal- Elevator Ai^ Feet high. Strap 3| Inches wide,
and a Conveyer for two pair of Stones.

S70 feet of dry pine, or other inch boards, most of them
Hi or 12 inches wide, of any length, that they may
suit to be dressed for the case boards, as follows :

86 feet in length, 6| inches wide, for tops and bottoms
of the cases.

86 feet in length, 4| inches wide, for the side boards^
truly squared at the edges.

The back board of the conveyer trough 15 inches, bot-
tom do. H inches, and front 13 inches wide.

Some 2 inch plank for the pulleys and cog-wheels.

Scantling for conveyers 6 by 6, or 5 1 by 5 1 inches, of
dry pine or yellow poplar ; (prefer light wood) pine
for shafts, 4| by ^l or 5 by 5 inches.

Si sides of good, pliant- harness-leather.

1500 of 14 ounce tacks.

A good, clean butt of willow for buckets, unless the
pieces that are left, that are too small for the wheat-
buckets, will make the meal buckets.

41b. of 8d. and lib. of lOd. nails.

2 dozen of large wood screws (nails will do) for the pul-
ley-cases.

Smithes Bill of Iron.

1 double gudgeon, (such as fig. 4, Plate VI,) 1| inch
thick, 7| inches between the necks, 3| between the
key-holes, the necks 1 1 inch long, and the tenons at
each end of the same length, exacdy square, that the
socket may fit every way alike.

2 sockets, one for each tenon, such as appears on one
end of fig. 4. The distance between tlie outside of

248 BILLS OF MATERIALS. [Ghap. 5.

the straps with the nails in, must be 5| inches ; fig.
5 is an end view of it, and the band that drives over
it at the end of the shaft, as they appear on the end of
the conveyer.

2 small 3-4 inch gudgeons for the other ends of the con-
veyers.

4 thin bands 5| inches from the outsides, for the con-
veyers.

1 gudgeon an inch thick, neck 3^ inches, and tang. 10
inches, for the shaft in the upper pulley and next to it ;
but if a gudgeon be put through the pulley, let it be
of the form of fig. 6, with a tenon and socket at one
end, like fig. 4.

-1 harness-buckle, 3| inches from the outsides, with two
tongues ; such as fig. 12, pi. 6.
Add whatever more small gudgeons and bands may

be necessary for giving motion.

For a Hopper-Boy^

1 piece of dry, hard, clean, pine scantling, 4<| by 4|
inches, and 10 feet long, for the upright shaft.

1 piece of dry poplar, soft pine, or other soft light wood,
not Subject to crack and split in working, 8 by 2|
inches, 15 or 16 feet long, for the flight arms.

Some 2 inch plank for wheels to give it motion, and
scantling 4^ by 4| inches for the shafts.

60 flights 6 inches long, 3 inches wide, and 12 inch at
one, and 1-4 at the other edge, thinner at the fore than
hind end, that they may drive in tight like a dovetail
wedge. These may be made out of green hard maple,
split from sap to heart, and set to dry.

Half a common bed-cord, for a leading line, and balance
rope.

Smithes BjM of Iron.

1 stay-iron, C F E, plate VII, fig. 12. The height from
the top of the ring F, to the bottom of the feet C E, is
15 inches ; distance of the points of the feet C E 24
inches ; size of the legs 1-2 by 3-4 inch ; size of the
ring F J by 1-4 inches, round and smooth inside ; 4
inches diameter, tlie inside corners rounded off", to

Chap. 5-.] MILL FOR HULLING RICE, &c. 249

keep it from cutting the shaft; there must be two little

loops or eyes, one in each quarter, for the balance rope

to be hung to either that may suit best.
2 screws (with thumb-burrs that are turned by the thumb

and fingers) 1-4 of an inch thick, and 3 inches long^

for the feet of the stay-iron.
2 do. for the end flights, 3| inches long, rounded 1|

inch next the head, and square 1^ inch next the screw,

the round part thickest.
2 do. for the end sweepers, 6| inches long, rounded 1

inch next the head, 1-4 inch thick.
2 do. for the hopper sweepers, 8| inches long and 1-4

inch thick, (long nails with rivet heads will do.)
1 step-gudgeon (fig. 15), 2^ inches long below the ring,

and tang 9 inches, 3-4 inch thick.
1 plate 4 by 4, and 1-8 inch thick, for the step-gudgeoil

to pass through, (fig. 14.)
1 band for the step-gudgeon, 3| inches diameter; frona

the outsides it has to pass through the stay-iron.
1 gudgeon and band, for the top of the shaft, gudgeon

3-4 inch, band 4 inches diameter from the outsides.

The smith can, by the book, easily understand how
to make these irons; and the reader may, from these
bills of materials, make a rough estimate of the whole
expense, which he will find very low compared with
their utility.

ART. 103.
A MILL FOR CLEANING AND HULLING RICE.

Plate X, fig. 2. The rice brought to the mill in boats,
is to be emptied into the hopper 1, out of which it is
conveyed, by the conveyer, into the elevator at S, which
elevates it into the garner 3 ; on the third floor it de-
scends into the gamer 4, that hangs over the stones 5,
and supplies them regularly. The stones are to be
dressed with a few deep furrows, with but little draught,
and picked full of large holes ; they must be set more
than the length of the grain apart. The hoop should be

I i

250 MILL FOR HULLING RICE, &c. [Chap. 5

lined inside with atrong sheet-iron and if punched full
of holes it will do better. The grain is kept under the
stone as long as necessary, by causing it to rise some
distance up the hoop, to get out through a hole, which
is to be made higher or lower by a gatej sliding in the
bottom of it.

The principle by which the grain is hulled, is that of
rubbing them against one another with great force, be-
tween the stones, by which means they hull one another
without being broke by the stones, near as much as by
the usual way.* As it passes through the stones b, it
should fall into a rolling-screen or shaking-sieve 6, made
of wire, with such meshes as will let out, at the head, all
the sand and dust, which may be let run through the
floor into the water, if convenient ; and to let the rice
and most of the heavy chaff fall through into the con-
veyer, which will convey it into the elevator at 2. The
light chaff, &c. that does not pass through the sieve, will
fall out at the tail, and if useless may also run into the
water and float away. There may be a fan put on the
spindle, above the trundle, to make a light blast, to blow
out the light chaff and dust, which should be conveyed
out through the \A'all ; and this fan may supercede the
necessity of the shaking-sieve. The grain and heavy
chaff are elevated into garner 7, thence it descends into
garner 8, and passes through the stones 9, which are to
be fixed and dressed the same way as the others, and
are only to rub the grain harder ; the sharpness on the
outside of the chaff (which nature seems to have pro-
vided for the purpose), will cut off all the inside hull
from the grain, and leave it perfectly clean ; then, as it
falls from these stones it passes through the wind of the
fan 10, fixed on the spindle of the stones 9, which will
blow out the chaff and dust, and drop them in the room
21 ; the wind should escape through the wall. There

* By trying many experiments, and with much labour, striving to invent
a new machine fornibbine: the dust off the grains of wheat, and breaking
thf lumps of dust mixed with wheat that is trod on the ground; and for
shelling off' the white caps, breaking the rotten, fly-eaten, and smut grams,
and to bleak the jiarlic, he I discovered this principle; which I afterwards
used Willi a common pair of burr mill-stones, properly dressed for grind-
ing wheat, and always found ii to succeed well, without breaking any good
grains, grinding the white caps to fine dust.

Chap. 5.] MILL FOR HULLING RICE, &c. 251

is a regulating board that moves on a joint at 21, so as
to take all the grain into the conveyer, which will con-
vey into the elevator at 11, which elevates it into the
gamer IS, to pass through the rolling-screen 13, which
should have wire of 3 sized meshes ; first, to take out
the dust, to fall into a part 17, by itself; second, the
small rice into an apartment 16 ; the whole grains fall
into gamer 14?, perfectly clean, and are drawn into bar-
rels at 15. The fan 18 blows out the dust, and lodges
it in the room 1 9, and the wind passes out at 20 5 the
head rice falls at the tail of the screen, and runs into the
hopper of the stones 5, to go through the whole opera-
tion again. Thus the whole is completely done by the
water, by the help of the machinery from the boat, until
ready to put into the barrel, without the least manual
labour.

Perhaps it may be necessary to make a few fuiTows
in the edge of the stone, slanting, at an angle of about
30 degrees with a perpendicular line, these furrows will
throw up the grain next the stone, on the top of that in
the hoop, which will change its position continually, by
which means it will be better cleaned ; but this may
probably be done without.

PART IV.

THE

YOUNG MILLER'S GUIDE;

CONTAINING

THE WHOLE PROCESS

OF THE

ART OF MANUFACTURING GRAIN INTO FLOUR;

EXPLAIJ^ED, IJV ALL ITS BRAjYCHES,

ACCORDING TO THE MOST IMPROVED PLANS PRACTISED IN

THE BEST MERCHANT AND FLOUR MILLS

IN AMERICA.

CONTENTS OF PART IV.

Cmaf. I. — The principles of grinding, and rules for
draughting the furrows of mill- stones.

Chap. II. — Directions for furrowing and hanging a new
pair of burr-stones ready for grinding, and keeping
them in good face, for sharpening them and grinding
to the right fineness ; so as to clean the bran well,
and make but little coarse flour.

Chap. III. — Of Garlic, — with directions for grinding
wheat mixed with it, and dressing the stones suitable
thereto.

Chap. IV. — Of grinding the middlings, and other coarse
flour over again, to make the best profit of them.

Chap. V. — Of the quality of stones to suit the quality
of the wheat.

Chap. VI. — Of bolting-reels and cloths, with directions
for bolting and inspecting flour.

Chap. VII. — Of the duty of the miller, in keeping the
business in order.

Peculiar accidents by which mills are subject to take
fire.

Of improving mill-seats.

Ti!t

YOUNG MILLER'S GUIDE,

PART THE FOURTH

CHAPTER I.

ART. 104.

THE PRIN"CIPLES OP GRINDING EXPLAINED, WITH SOME OB-
SERVATIONS ON LAYING OUT THE FURROWS IN THE STONES,
WITH A PROPER DRAUGHT.

THE end we have in view, in grinding the grain, is,
to reduce it to such a degree of fineness, as is found by
experience to make the best bread, and to put it in
SMch a state, that the flour may be most eflfectually sepa-
rated from the bran or skin of the grain, by means of
sifting or bohing ; and it has been proved by experience,
that to grind the grain fine with dull mill- stones, will not
answer said purpose well, because it kills or destroys that
lively quality of the grain, that causes it to ferment and
raise in the baking ; it also makes the meal so clammy,
that it sticks to the cloth, and chokes up the meshes in
bolting. Hence, it appears, that it should be made fine
with as little pressure as possible ; and it is evident, that
this cannot be done without sharp instruments. Let us
suppose we undertake to operate on one single grain, I
think it seems reasonable that we should first cut it into
several pieces, with a sharp instrument, to put it in a
state suitable for being passed between two planes, in
order to be reduced to one regular fineness. The planes

K k

258 PRINCIPLES OF GRINDING. [Chap, i

should have on their faces a number of little sharp edges,
to scrape off the meal from the bran, and be set at such
a distance as to reduce the meal to the required fineness,
and no finer, so that no part can escape unground. The
same rules or principles will serve for a quantity that will
serve for one grain.

Therefore, to prepare the stones for grinding to the
greatest perfection, we may conclude that their faces
must be put in such order, that they will first cut the
grain into several pieces, and then pass it between them,
in such a manner, that none can escape without being
ground to a certain degree of fineness, and at the same
time scrape the meal off clean from the bran or skin.

1. The best way that I have yet found to effect this
is, (after the stones are faced with the staff" and the pick,)
to grind a few quarts of sharp fine sand; this will face
them to fit each other so exactly, that no meal can pass
between them without being ground ; it is also the best
way of sharpening all the litde edges on the face, that
are formed by the pores of the stone, (but instead of
sand, w^ater may be used, the stones then face each
other) so that they will scrape the meal off" of the bran,
without too much pressure being applied. But as the
meal will not pass from the centre to the periphery or
verge of the stones, soon enough, without some assist-
ance, there must be a number of furrows, to assist it in
its egress ; and these furrows must be set with such a
draught, that the meal will not pass too far along them
at once, without passing over the land or plane, lest it
should get out unground. They should also be of suf-
ficient depths, to admit air enough to pass through the
stones to carry out the heat generated by the friction of
grinding; but if they have too much draught, they will
not bear to be deep, for the meal will escape along them
unground. These furrows ought to be made sharp at
the feather edge (which is the hinder edge of the fur-
row, and the foremost edge of the land), which serves
the purpose of cutting down tlie grain; they should be
more numerous near the centre, because there the office
of the stone is to cut the grain, and near the periphery
tlieir office is (that of the two planes) to reduce the flour

Chap. 1.] PRINCIPLES OF GRINDING. 259

to its required fineness, and scFape the bran clean by the
edp^es, formed by the numerous little pores with which
the burr stone abounds. However, we must consider,
that it is not best to have the stones too sharp near the
eye, because they then cut the bran too fine. The stones
incline to keep open near the eye, unless they are too
close. If they are porous (near the eye) and will keep
open without picking, they will always be a little dull,
which will flatten the bran, without cutting it too much.
Again, if they be soft next the eye, they will keep too
open, and that part of the stone will be nearly useless.
Therefore they should be very hard aud porous.

It is also necessary, that we dress the face of the stone
in such a form, as to allow room- for the grain or meal,
ill every stage of its passage between the stones. In
order to understand this, let us conceive the stream of
wheat, entering the eye of the stone, to be about the
thickness of a man's finger, but instantly spreading every
■way over the whole face of the stone ; therefore this
stream must get thinner, as it approaches the periphery
(where it would be thinner than a fine hair, if it did not
pass slower as it becomes finer, and if the stones were
not kept apart by the bran), for this reason, the stones
must be dressed so, that they will not touch at the cen-
tre, within about a 16th or 20th part of an inch, but to
get closer gradually, till within about 10 or \2 inches
from the verge of the stone, proportioned to the diameter,
and from that part out they must fit nicely together.
This close part is called the flouring of the stone. The
furrows should be deep near the centre, to admit wheat
in its chopped state, and the air, which tends to keep the
stones cool.*

• It is asserted by some (and I believe, not without reason) that it is ab-
solutely necessary to have a bridge-tree that shall have a degree of el.sti-
city, which gives the stone a tremulous motion up and down, and therefore
effects a trituration more completely, making more lively flour ih;'n it would
do, supposmg the bridge-tree to he a solid immoveable rock- But what is
the proper degree of elasticity, or size of a bridge tree, suitable to the
weight of the stooe, I know not; not having experif-nced this matter suffi-
ciently to give an opinion on it; but I am inclined to think that this is ai>
error.

One disadvantage in having a very elastic bridge-tree is, when the stones
run empty, tiiey come together with more force, and heat quicker; and if
once made red hot, it totally destroys the good sharp quality of the burr,
as far as the heat penetrates.

260 DRAUGHT OF MILL-STONES. [Chap. 1.,

ART. 105.

OP THE DRAUGHT NECESSARY TO BE GIVEN TO THE FUR-
ROWS OF MILL-STONES

From these principles and ideas, and the laws of cen-
tral forces, explained art. 13, I form my judgment of the
proper draught of the furrows, and the manner of dress,
in which I find but few of the best millers to agree ;
some prefer one kind, and some another, which shows
that this necessary part of the miller's art is not yet
generally well understood. In order that this matter
may be more fully discussed and better understood, I
have constructed fig. 3, plate XL AB represents the
eight quarter, CD the twelve quarter, and EA the cen-
tral dress. Now we observe that in the eight quarter
dress, the short furrows at F have about five times as
much draught as the long ones, and cross one another
like a pair of shears, opened so wide that they will drive
all before them, and cut nothing ; and if these furrows
be deep they will drive out the meal as soon as it gets
into them, and thereby make much coarse meal, such
as middlings and ship stuff or carnel ; the twelve quarter
dress appears to be better ; but the short furrows at G
have about four times as much draught as the long
ones, the advantage of which I cannot yet see, because
if we have once found the draught that is right for one
furrow, so as to cause the meal to pass through the
stone in a proper time, it appears reasonable that the
draught of every other furrow should be equal to it.

In the central dress EA the furrows have all one
draught, and if we could once determine how much is
necessary exacdy, then we might expect to be right, and
I presume we will find it to be in a certain proportion to
the size and velocity of the stone ; because the centri-
fugal force that the circular motion of the stones gives
the meal, has a tendency to move it outward, and this
force will be in inverse proportion to the diameter of
the stones, their velocities being the samt^ by the 4'th
law of circular motion. E e is a furrow of the running
stone, and we may see by the figure, that the furrows
cross one another at the centre in a much greater angle

Chap. 1.] DRAUGHT OF MILL-STONES. 261

than near the periphery, uhich I conceive to be right,
because the centrifugal force is much less nearer the
centre than the periphery. But we must also consider,
that the grain, whole or but little broken, requires less
draught and central force to send it out, than it does
when ground fine; which shows, that we must here
differ in practice from the theories laid down in art. 13,
founded on the laws of circular motion and central forces;
because, the grain as it is ground into meal, is less affect-
ed by the central force to drive it out, therefore the an-
gles with which the furrows cross each other must be
greater than the verge or skirt of the stone, and less near
its centre than assigned by theory, and this variation from
theory can be formed only by conjecture, and ascertained,
by practice.

From the whole of my speculations on this difficult
subject, added to my observations on my own and
others' practice and experience, I attempt to form the
following rule for laying out a five foot mill-stone. See
fig. 1. PI. XL

1. Describe a circle with 3 inches, and another with 6
inches radius, round the centre of the stone.

2. Divide the 3 inches space between these two circles,
into 4 spaces, by 3 circles equi-distant, call these five
circles draught circles.

3. Divide the stone into 5 parts, by describing 4 circles
equi-distant between the eye and the verge.

4. Divide the circumference of the stone into 18 equal
parts, called quarters.

5. Then take a straight edged rule, lay one end at one
of the quarters at 6, at the verge of the stone, and the
other end at the outside draught circle, 6 inches from
the centre of the stone, and draw a line for the furrow
from the verge of the stone to the circle 5. Then
shift the rule from draught circle 6, to the draught
circle 5, and continue the furrow line towards the
centre, from circle 5 to 4 : then shift in the rule to
draught circle 4, and continue to 3; shift to 3 and
continue to 2; shift to two, and continue to one, and the
curve of the furrow is formed, as 1 — 6 in the figure.

6. To this curve form a pattern to lay out all the rest by.

262 DRAUGHT OF MILL-STONES. [Chap. 1.

The furrows with this curve will cross each other with
the following angles, shown fig. I,
at circle 1, which is the eve

of the stone at 75 degrees angle.

— 2 - - 45

— 3 - - 35

— 4 - - 31

— 5 - - 27

— 6 - - 23

These angles, I think, will do well in practice, will
grind smooth, and make but little coarse meal, &c. as
shown by the lines G r, H r, G s, H s, &c. &c.

Supposing the greatest draught circle to be 6 inches
radius, then by theory the angles would have been

at circle 1 - - 138 degrees angle,

— 2 - - 69

— 3 - - 46

— 4 - - 34,5

— 5 - - 27,5

— 6 - - 23

If the draught circle had been 5 inches radius, and
the furrows straight, the angles would then have been at

circle degrees.
1 about 180

And 6 inches from centre, as shown by ^ ..^

lines Gl, HI. 5 "

2—60
3—38
4—29
5—23
6 — 18
The angles near the centre here, are quite too great
to grind ; they will push the grain before them ; there-
fore, to remedy all these disadvantages, take the afore-
said rule, which forms the furrows, as shown at 6 — 7,
fig. 1, which is 4 of 18 qrs. H 8 represents a furrow of
the runner, showing the angles where they cross those
of the bed- stone, in every part. Here I have supposed
the exti-emes of the draught to be 6 inches for the verge,
and 3 inches for the eye of the stone, to be right for a
stone 5 feet diameter, revolving 100 times in a minute;

Chap. 1.] DRAUGHT OF MILL-STONES. 263

but of this we cannot be certain. Yet by experience
and practice the extremes may be ascertained in time
for all sizes of stones, with different velocities, no kind
of dress that I can conceive, appearing to me likely to
be brought to a truth except this, and it certainly appears
both by inspecting the figure, and reason, that it will
grind the smoothest of all the different kinds exhibited
in the plate.

The principle of grinding is partly that of shears clip-
ping. The planes of the face of the stones serving as
guides to keep the grain, &c. in the edge of the shears,
the furrows and pores, forming the edges ; if the shears
cross one another too short, they cannot cut ; this shows
that all strokes of the pick should be parallel to the
furrows.

To give two stones of different diameters the same
draught, we must make their draught circles in direct
proportion to their diameters : then the furrows of the
upper and lower stones of each size, will cross each
other with equal angles in all proportional distances,
from their centres, to their periphery : See art. 13. But
when we come to consider that the mean circles of all
stones are to have nearly equal velocities, and that their
central forces will be in inverse proportion to the diame-
ters ; we must consider, that small stones must have
much less draught than large ones, in proportion to
their diameters. See the proportion for determining the
draught, art. 13.

It is very necessary that the true draught of the fur-
rows, should be determined to suit the velocity of the
stone: because the centrifugal force of the meal will
vary, as the squares of the velocity of the stone, by the
5th law of circular motion. But the error of the draught
may be corrected, in some measure, by the depth of the
furrows. The less the draught, the deeper the furrow ;
and the greater the draught, the shallower must the fur-
row be to prevent the meal from escaping unground.
But if the furrows be too shallow, there will not a suf-
ficient quantity of air pass through the stones to keep
them cool. But in the central dress the furrows meet
so near together that they cut the stone too much away

264 OF FACING MILL-STONES. [Oap. 2.

at the centre, unless they are made too narrow ; there-
fore, I prefer what is called the quarter dress ; but divid-
ed into so many quarters, that there will be little differ-
ence between the draught of the furrows ; suppose 18
quarters in a 5 foot stone; then each quarter takes up
about 10| inches of the circumference of the stone ;
which suits to be divided into about 4 furrows and 4
lands, if the stone be close ; but if it be open, 2 or 3
furrows to each quarter will be enough. This rule will
give 4 feet 6 inch stones, 16 ; and 5 feet 6 inch stones,
2t ; and 6 feet stones, 23 quarters. But the number of
quarters is not so particular, but better more than less. If
the quarters be few, the disadvantage of the short furrows
crossing at too great an angle, and throwing out the meal
too coarse, may be remedied, by making the land widest
next the verge, thereby turning the furrows towards the
centre, when they will have less draught, as in the quar-
ter H I, fig. 3.

CHAPTER II.

Directions for Jacing a pair of new burr stones, laying out
the furrows, hanging them for grinding, and for keeping
them in good face ; picking and sharpening them; for
grinding to the right fineness, so as to clean the bran
'well, and make but little middlings, ^c.

ART. 106.
OP FACING MILLSTONES.

THE burr mill-stones are generally left in such face
by the maker, that the miller need not spend much la-
bour and time on them with picks, before he may hang,
and grind water or dry sand, with them, because he can
make much better speed by tliis method. After they
have ground a quantity, that may be judged sufficient,
they must be taken up, and the red staff tiied over their

Chap. 2.] OF FACING MILL-STONES. 265

faces,* and if it touches in circles, the red parts should
be well cracked with picks, then put them to grind a
small quantity of water or sand again ; after this take
them up, and try the staft' on them, picking off the red
parts as before, and repeat this operation, until the staff
will touch nearly alike all the way across, and until the
stone comes to a face in every part, that the quality
thereof may plainly appear ; then, with a red or black
line proceed to lay out the furrows, in the manner deter-
mined upon, from the observations already laid down in
ch. I. But here we must observe that the edges do the
grinding, and that the quantity ground will be in propor-
tion to the number of edges that are to do it. After
having a fair view of the face and quality of the stone,
■we can judge of the number of furrows most suitable,
observing, that where the stone is most open and porous,
few furrows will be wanted ; but where it is close and
smooth, the furrows ought to be more numerous, and
both tfiey and the lands narrow, (about 1 and 1-8 of an
inch wide) that they may form the more edges, to per-
form the grinding. The furrows, at the back, should
be made nearly the* depth of the thickness of a grain of
wheat, but sloped up to a feather edge, not deeper than
the thickness of a finger-nail ;t this edge is to be made
as sharp as possible, which cannot be done without a
very sharp, hard pick. When the furrows are all made,
try the red staff over them, and if it touches near the

• The red staff is longer than the diameter of the stones, and three in-
ches thick on the edge, which is made perfectly straight, on which is rub-
bed red clay, mixed with water; which shows the highest parts of the
faces of the stones, when rubbed over them, by leavinij the red on those
high parts.

t For the form of the bottom of the furrow, see plate XI. fig. 3. The
curve line e b shows the bottom, b the feather edge, and e the back part.
If the bottom had been made square at the back as at e, the grain would
lay in the corner, and by the centrifugal force, would work out along the
furrows without passing over the lands, and part would escape unground.
The back edge must be sloped for two reasons ; 1st, that the meal may be
pushed on to the feather edge ; 2d, that the furrow may grow narrower, as
the face of the stones wears away, to give liberty to sharpen the feather
edge, without making the furrows too wide. Fig. 5. represents the face
of wo stones, working together, the runner moving from a to d. When
the furrows are right over one another as at a, there is room for a grain of
wheat; when they move to the position of b, it is flattened, and at c, is
clipped in two by the feather edges, and the lands or planes operate on it
asatd-

L I

266 OF HANGING MILL-STONES. [Chap. 2,

centre, the marks must be quite taken off about a foot
next to it, but observing to crack lighter the farther from
it, so that when the stones are laid together, they will not
touch at the centre, by about one twentieth part of an
inch, and close gradually, so as to touch and fit exactly,
for about 10 or 12 inches from the verge. If the stones
be now well hung, having the facing and furrowing neatly
done, they will be found in the most excellent order for
8;rinding wheat, that they can possibly be put in, because
they are in good face, fitting so neatly together, that the
wheat cannot escape unground, and all the edges being
at their sharpest, so that the grain can be ground into
flour, with the least pressure possible.

ART. 107.

OF HANGING MILL STONES.

•

If the stone have a balance-ryne it is an easy matter
to hang it, for we have only to set the spindle perpendi-
cular to the face of the bed-stone ; ^\hich is done by
fastening a staff on the cock-head of the spindle, so that
the end may reach to the edge of the stone, and be near
the face. In this end we put a piece of whale-bone or
quill, so as to touch the stone, that, when one turns the
trundle-head, the quill will move round the edge of the
stone, and when it is made to touch alike all the way-
round, by altering the wedges of the bridge, the stone
may be laid down and it will be ready hung;* but if we
have a stiff-ryne, it will be much more difficult, because
we have not only to fix the spindle perpendicular to the

* But here we must observe, whether tbe stone be of a true balance, as
It hangs on the cock head, and if not, it must be truly balanced, b} running
le;'d into the 1 ghiesi side- This ought to be carefully attended to by the
maker, because the s'one may be made to b; lance truly v.'hen at resi ; yet,
if every opposite p irt does not balance each other truly, the stone may
be greatly out of balance when in motion, aithoMt^h truly balanced when at
rest; and this is the reason why the hush of some stones cannot be kept
tight hut a few hours, while others Will keep t gtr several months, the
spindles being good, and stones balaiu ed when at rest- The reason why a
stone that is balanced at rest, will sometimes not be balanced in motion, is,
that if the upper side be heaviest on one side, sind the lowest side be hea-
viest on the other side of the centre, the stone may balance al res', yet,
when set in motion, the heaviest parts draw o\it\iards most by the centrifu-
sjal force, which v/ill put the stone out ol balance while in motion ; and if

Chap. 2.] OF HANGING MILL-STONES. 26r

face of the bed-stone, but we must set the face of the
runner perpendicular to the spindle, and all this must be
done to the greatest exactness, because the ryne being
stiff, will not give way to suffer the runner to form itself
to the bed-stone, as will the balance-ryne.

The bed of the ryne being first carefully cleaned out,
the ryne is put into it and tied, until the stone is laid
down on the cock-head ; then u e find the part that hangs
lowest, and, by putting the hand thereon, we press the
stone down a little, turning it about at the same time,
and observing, whether the lowest part touches the bed-
stone equally all the way round ; if it does not, it is
adjusted by altering the wedges of the bridge-tree, until
it touches equally, and then the spindle will stand per-
pendicular to the face of the bed-stone. Then, to set
the face of the runner perpendicular or square to the
spindle, we stand in one place, turning the stone, and
pressing on it at every horn of the ryne, as it passes, and
observing whether the runner will touch the bed-stone
equally, at every horn, which, if it does not, we strike
with an iron bar on the horn, that bears the stone high-
est, which, by its jarring, will setde itself better into its
bed, and thereby let the stone down a little in that part ;
but if this be not sufficient there must be paper put on
the top of the horn, that lets the stone too low ; observ-
ing to mark the high horns, that when the stone is taken
up, a little may be taken off the bed, and the ryne will
soon become so neatly bedded, that the stone will hang
very easily. But I have ever found the bridge to be a
little out of place, or in other words the spindle moved
a little from its true perpendicular position, with respect
to the face of the bed-stone, at every time the stone is

the stone be not round, the parts farthest from the centre will have ths
greatest centrifugal force, because the centrifugal force is as the square of
the distance from the centre. The neck of the spindle wll wear nest the
lonfrest side, and get bush loose ; and this argues in favour of a stiff ryne.
The best method that I have heard of for hanging siones with stiff horned
rynes, appears to be as follows- Fix a screw to each horn to regulate by,
which is done thus — after the horns are bedded, sink under each horn a
strong burr, through which the screw is to pass from the back of the stone,
and fasten them in with lead ; ihen, after the siont- is laid down, put in the
acrews from the top of the stone, screwing them till the points bear tight
on the horn : then proceed to hang the stone, which is very easily done,
by turninij the screws.

268 OF REGULATING THE FEED, &c. [Chap. 2.

taken up ; which is a great objection to the stifF horn
ryne ; for if the spindle be but very little out of place, the
stones cannot come together equally; whereas if it be
considerably out of place with a balance ryne, it will be
little or no injury to the grinding, because the running
stone has liberty to form itself to the bed- stone.

ART. 108.
OF REGULATING THE FEED AND WATER IN GRINDING.

The stone being well hung, proceed to grind, and
when all things are ready, draw as much water as is
judged to be sufficient ; then observe the motion of the
stone, by the noise of the damsel, and feel the meal ; and
if it be too coarse, and the motion too slow, give less feed,
and she Mill grind finer, and the motion will be quicker ;
if it grind too coarse yet, lower the stone ; then if the
motion be too slow draw a little more water ; but if the
meal feel to be too low ground, and the motion right,
raise the stone a litde, and give a litde more feed. If the
motion and feed be too great, and the meal be ground too
low, shut oif part of the water.

But if the motion be too slow, and feed be to small,
draw more water.

To regulate the grinding to suit the quantity of water,
the following rule is set in verse, that it may be more
easily remembered.*

RULE.

If the motion be too great,
Then add a little feed and weight;
But if the motion be too slow,
Less feed and weight will let her go.

But here the miller must remember, that there is a
certain portion of feed that the stones will bear and grind

* The miller should, by many experiments, find the quantity of water
that best suits his mill, aid have a mark made on the stafF by which he
draws the gate, that he may draw a suitable quantity at once.

Chap.2.] OF REGULATING THE FEED, &c. 269

well; which will be in proportion to the size, velocity
and sharpness of them, and if this be exceeded, there
%vill be a loss by not having the grinding well done.
But no rule can be laid down, to ascertain this portion of
feed ; it must be attained by practice ;* as must also the
art of judging of the right fineness. I may, however, lay
down such rules and directions as may be of some as-
sistance to the young beginner.

ART. 109.
RULE FOR JUDGING OF GOOD GRINDING.

Catch your hand full of the meal as it falls from the
stones, and feel it lightly between your fingers and
thumb ; and if it feels smooth and not oily or clammy,
and wiU not stick much to the hand, it shows it to be
fine enough, and the stones to be sharp. If there be no
lumps to be felt larger than the rest, but all of one fine-
ness, it shows the stones to be well faced, and the fur-
rows to have not too much draught, as none has escaped
unground.

But if the meal feels very smooth and oily, and sticks
much to the hand, it shows it to be too low ground, hard
pressed and the stones dull.

But if it feels part oily, and part coarse and lumpy,
and will stick much to the hand, it shows that the stones
have too much feed ; or, that they are dull, and badly
faced, or have some furrows that have too much draught ;
or are too deep, or perhaps too steep at the back edge,
as part has escaped unground, and part too much pressed
and low.

Catch your hand full, and holding the palm up, shut
it briskly ; if the greatest quantity of the meal fly out and
escape between your fingers, it shows it to be in a fine
and lively state, the stones sharp, the bran thin, and will
bolt well : But the greater the quantity that stays in the
hand, the more it shows the reverse.

* If the stones be over-fed, it is not possible that the bran should be
■well cleaned, because the sharp edges on ilit- face of ihe stone, tliai is
made for the purpose of scraping the bran clean, is kepi from it by the
quantity of meal that is between the stones.

270 OF REGULATING THE FEED, &c. [Chap. 2.

Catch a hand full of meal in a sieve, and sift the meal
clean out of the bran ; then feel it, and if it feels soft and
springing, or elastic, and also feels thin, with but little
sticking to the inside of the bran, and no pieces found
much thicker than the rest, will show the stones to be
shar[), and the grinding well done.*

But if it is broad and stiff, and the inside white, it is a
sure sign that the stones are dull or overfed. If you find
some parts that are much thicker and harder than the rest,
such as almost half or quarter grains, it shoAvs that there
are some furrows that have too much draught, or are too
deep or steep, at the back edge ; else, that you are grind-
ing with less feed than the depth of the fun-ows, and ve-
locity of the stone will bear.

ART. 110.
OF DRESSING AND SHARPENING THE STONES WHEN DULL

When the stones get dull they must be taken up, that
they may be sharpened ; to do this in the best manner,
we must be provided with sharp hard picks, with which
the feather edge of the furrows are to be dressed as sharp
as possible ; which cannot be done with soft or dull
picks. The bottoms of the furrows are likewise to be
dre'-sed, to keep them of the proper depth ; but here the
dull picks may be used.f The straight staff must now
also be run over the face carefully, and if there be any
parts harder or higher than the rest, the red will be left
on them ; which must be cracked lightly, with many
cracks, to make them wear as fast as the softer parts, in
order to keep the face good. These cracks do also form

• Instead of a sieve, you may take a shovel and hold the point near the
stream of meal, and it will catch part of the bran, with but little meal mix-
ed with it; whicli may be separated by tossing it from one hand to the
other, Wiping^ the hand at each toss.

f To prevent the steel from striking your fingers, take a piece of lea-
ther about 5 by 6 inches square, make a hole through the middle, and put
the handle of the pick through it, keeping it between your hands and the
pick, uiakiufj a loop in the lower edge, through which put one of your fiu-
gers, to keep up the lower part from the stone.

Oiap.2.] DEGREE OF FINENESS FOR FLOUR. 271

edges that help to clean the bran ; and the harder and
closer the stone, the more numerous are they to be. They
are to be made with a very sharp pick, parallel to the
furrows ; and the damper the grain, the more the stone
is to be cracked, and the drier and harder, the smoother
must the face be. The hard smooth places which glaze,
may be made to wear more evenly, by striking them,
either with a smooth or rough faced hammer many light
strokes, until a dust begins to appear, which frets the
flinty part, and makes it softer and sharper. The stone
will never be in the best order for cleaning the bran,
without first grinding a little sand, to sharpen all the little
edges formed by the pores of the stone ; the same sand
may be used several times. The stones may be sharpened
without being taken up, or even stopped, viz. take half
a pint of sand, and hold the shoe from knocking, to let
them run empty ; then pour in the sand, and this will
take the glaze off the face, and whet up the edges so
that they will grind considerably better : this ought to
be often done.*

Some are in the practice of letting stones run for
months without being dressed ; but I am well convinced
that those who dress them well twice a week, are well
paid for their trouble.

ART. 111.

OP THE MOST PROPER DEGREE OF FINENESS FOR FLOUR.

As to the most proper degree of fineness for flour,
millers differ in their opinion ; but a great majority, and
many of the longest experience, and best judgment,

• But care should be taken to prevent the sand from getting mixed with
the meal ; it sliould be caiciied in some vessel, the stone being suffered to
run quite empty; the sm^ll quantity thut will remain in the stone will not
injure the Bour But I do not wish to encourage a lazy miller, to neglect
taking «ip the stone.

When stones are first set to grind, they incline to raise, and grind coarser
for a considerable time, the true reason of which is difficult to assign.
Some attribute it to the expansion of the metal in the spindle ; it has been
suggested to me, that it is the steam, or the rarification of the air, by the
heal produced by the action of the stones, which, not having a perfectly free
passage to escape, bears up a part of the weight of the stone ; and this
catise will increase, until the stones are heated to the greatest degree.

272 DEGREE OF FINENESS FOR FLOUR. [Chap. 2.

agree in this ; that, if the flour be made very fine, it will
be killed (as it is termed) ; so that it will not raise, or
ferment so well in baking; but I have heard several
millers of good judgment, give it as their opinion, that
flour cannot be made too fine, if ground with sharp clean
stones; provided they are not suffered to rub against
each other ; and some of those millers do actually re-
duce almost all the meal they get out of the wheat into
superfine flour ; by which means they have but two
kinds, viz. superfine flour, and horse feed, which is what
is left after the flour is made, and is not fit to make even
tlie coarsest kind of ship-bread.

I have tried the following experiment, viz. I contrived
to catch as much of the dust of flour that was floating
about in the mill, as made a large loaf of bread, which
was raised with the same yeast, and baked in the same
oven, with other loaves, that were made out of the most
lively meal ; when the loaf made of tlie dust of the flour
was equally light, and as good, if not better than any of
the others ; it being the moistest, and pleasantest tasted,
though made of flour that felt like oil, it being so very
fine.

I therefore conclude, that it is not the degree of fine-
ness that destroys the life of the flour, but the degree of
pressure applied on it in grinding ; and that flour may
be reduced to the greatest degree of fineness, without
injuring the quality ; provided, it be done with sharp
clean stones, and little pressure.*

• It might be difficult to assij^n the true reason why pressure or heat
has such an effect on flour, as to destroy that life or principle, that causes
it to ferment and raise in the baking — Bui we may form a few conjectures.

Q'lery, may not this life be that vegetative quality that causes the grain
to grow, seeing it is a fact known by experience, that if the grain be dam-
aged, either by wet op heating in a heap so as to destroy its vegetation, that
the flour that is made thereof will not bake well ? And I presume, that if
grain be heated by any means, so as to destroy its vegetative quality, it will
not make flour that will have an easy fermentation ; and it is probable, that
this degree of heat is generated by the act of grinding when great pressure
is applied, which cannot be avoided if the stones be dull.

But again, if we consider that most bodies are in part composed of air,
which is in a solid and fixed state, and constitutes a proportional part of
their weight, and this proportion is diflTerent in different species of matter,
from 1-16 to 1-2, and in one species of wheat has been found, by experi-
ments, to be 1-5 of its whole weight ; that is, 121b. of fixt d air in 60ib. or
one bushel of wheat. Now this air is roused into action two ways, viz. by
fermentation and by heat, and as fast as it is roused, it instantly leaves the

Chap. 3.] OF GARLIC, &c. 273

CHAPTER III.

ART. 112.

OF G\RLTC, WITH DIRECTIQNS FOR GRINDING WHEAT MIXED
THKRKWITH; AND FOR DRESSING THE STONES SUITABLE
THERKTO.

IN many parts of America there is a species of onion
called garlic, that grows spontaneously with the wheat.
It bears a head resembling a seed onion, which contains
a number of grains about the size of a grain of wheat,
but somewhat lighter.* It is of a glutinous substance,
which very soon adheres to the stone (in grinding) in
such a manner as to blunt the edges, that they will not
grind to any degree of perfection. Therefore, as often
as the stones become dull, we are obliged to take the

body, and expands itself into about a million times more space than it fill-
ed before, in the form of a dense body. See Martm's Philosopiiy. New-
cider contains a large portion of this fixed air, whch flies off by fermenta-
tion, leaving the cast consider, bly emptied; and as soon as the fixed air
is all gone, the fermentation ceases-

Query, Is not this fixed air the very soul of vegetation and fermentation,
and may not the degree of heat generated by grinding witli great pressure,
set it in motion and cause it to leave the floir, thereby not only destroying
its life, but greatly lessening its weight, to the great loss of the miller;
who, although he expects by hard squeezmg to gain profit, sustains loss ?
As a confirmation of this hypotliesis, we may observe, that many experi-
ments have been made, by weighing a quantity of wheat carefully, before
it was ground, and then weighing every thing that it made in manufactur-
ing, and we have found it to be lacking in weight from 1 to 5 lb. per b .sh-
el : which could not be accounted tor any way better, than supposing the
loss to be occasioned by the escape of the fixed air. Therefore, I con-
cltide, that the stones ought to rtvohe slow and be kept sharp; and the
larijer they are, the slower will they require to go, and the lighter may tfiey
press ihe grain, and yet grind a sufficient quantity, and make the bes' fiour.

* The complete separation ot this garlic from the wheat, is so difficult,
that it has hitherto baffl.,-d all our art. Those grains that are larger, and
those that are smaller, can be separated by screens ; and those that are
much lighter, may be blown out by fans ; but those that are of the same
size, and nearly of the same weight, cannot be separated without putting
the wheat in water, where the wheat will sink, and the garbc swim. But
this method is too tedious tor the miller to practise, except it be once a
year, to clean up the headings, or the like, rc'ther than lose the wheat that
is mixed with the garlic, which cannot be otherwise sufHcifntly separated.
Great care should be tak'^n by the farmers to prevent this troublesome
thing from getting root in their farms, which, if it does, it will be almost
impossible ever to root it out again; because it propagates by both seed
and root, and is very hardy.

M m •

274 OF GARLIC, &c. [Chap. 3.

runner up, and wash the glaze off with water, scrubbing
the faces with stiff brushes, and drying up the water
with cloths or sponges ; this laborious operation must
be repeated twice, or perhaps four times, in 24 hours ;
if there be about 10 grains of garlic in a handful of
wheat.

To put the stones in the best order to grind garlicky
wheat, they must be cracked roughly all over the face ;
and dressed more open about the eye, that they may not
break the grains of garlic too suddenly, but gradually
giving the glutinous substance of the garlic more time to
incorporate itself with the meal, that it may not adhere
to the stone. The rougher the face, the longer will the
stones grind, because the longer will the garlic be in fill-
ing all the edges.

The best method that I have yet discovered for manu-
facturing garlicky wheat, is as follows, viz.

First, clean it over several times, in order to take out
all the garlic that can be got out by the machinery,
(which is easily done if you have a wheat elevator well
fixed, as directed in art. 94, plate IX.) then chop or half
grind it, which will break the garlic, (it being softer than
the wheat) the moisture of which, will so diffuse itself
through the chopped wheat, that it will not injure the
stones so much, in the second o:rindin2:. Bv this means
a considerable quantity can be ground, without taking
up the stones. The chopping may be done at the rate
of 15 or 20 bushels in an hour ; and with but little trou-
ble or loss of time ; provided there be a meal-elevator
that will hoist it up to the meal-loft, from whence it may
descend to the hopper by spouts, to be ground a second
time; when it will grind faster than if it had not been
chopped. Great care should be taken, that it be not
chopped so fine that it will not feed by the knocking of
the shoe ; (which would make it very troublesome) as
likewise, that it be not too coarse, lest the garlic be not
sufficiently broken. If the chopped grain could lay a
considerable time, that the garlic may dry, it would
grind much better.

But although every precaution be taken, if there be
much garlic in the wheat, the bran will not be well

Chap. 4] OF GRINDING MIDDLINGS, &c. 275

cleaned ; besides, there will be much coarse meal made ;
such as middlings, and stuff; which will require to be
ground over again, in order to make the most profit of
the grain : this I shall tieat of in the next chapter.*

CHAPTER IV.

ART. 113.

OF GRINDING OVER THE MIDDLINGS, STUFF AND BRAN, OR
SHORTS, IF NECESSARY; TO MAKE THE MOST OF THEM.

ALTHOUGH we grind the grain in the best man-
ner we possibly can, so as to make any reasonable de-
spatch ; yet there will appear in the bolting, a species of
coarse meal, called middlings; and stuff, a quality be-
tween superfine and shorts; which will contain a por-
tion of the best part of the grain : but in this coarse state
they will make very coarse bread ; consequently, will
command but a low price. For which reason it is often-
times more profitable to tlie miller to grind and bolt such
over again, and make them into superfine flour, and
fine middlings ; this may easily be done by proper ma-
nagement.

The middlings are generally hoisted by tubs, and laid
in a convenient place on the floor, in the meal-loft, near
the hopper-boy, until there is a large quantity gathered :
when the first good opportunity offers it is bolted over,
without any bran or .shorts mixed with it, in order to
tkke out all that is already fine enough ; which will pass
through the superfine cloth. The middlings will pass
through the middlings' cloth, and will then be round
and lively, and in a state fit for grinding ; being freed
from the fine part that would have prevented it from
feeding freely. The small specks of bran that were
before mixed with it, being lighter than the rich round

• Timothy Kirk, of York Town, (Pennsylvania,) has communicated to
me an invention of his, an improved fun, for cleaning wheal, the principle
of whrch is, to blow the prain twice with one blast of wmd ; whicli, with,
some further improvemenis, appears lo offer fair to effect a complete sepa-
ration of the garlic from the wheat, and every other substance that is light-
er than the grain.

276 OF GRINDING MIDDLINGS, &c. [Chap. 4.

part, will not pass through the middlings' cloth, but will
pass on to the stuff's cloth. The middlings will, by this
means, be richer than before ; and when made fine, may
be mixed with the ground meal, and bolted into super-
fine flour.

The middlings may now be put into the hanging
garner, over the hopper of the stones ; out of \\ hich it
will run into the hopper, and keep it full, as does the
wheat, provided the garner be rightly constructed, and
a hole, about 6 by 6 inches made for it to issue out at.
There must be a rod put through the bar that supports
the upper end of the damsel, the lovier end of which
must reach into the eye of the stone, near to the bottom,
and on one side thereof, to prevent the meal from stick-
ing in the eye, w hich if it does it will not feed. The hole
in the bottom of the hopper must not be less than four
inches square. Things being thus prepared, and the
stones being sharp and clean, and nicely hung, draw a
small quantity of water, (for meal does not require above
one-tenth part that grain does) taking great care to avoid
pressure, because the bran is not between the stones
now to prevent their coming too close together. If you
lay on as much weight as when grinding grain, the flour
will be killed. But if the stones be well hung, and it be
pressed lightly, the flour will be lively, and will make
much better bread, without being bolted, than it would
before it was ground. As fast as it is ground, it may be
elevated and bolted ; but a little bran m ill now be neces-
sary to keep the cloth open ; and all that passes thnjugh
the superfine cloth in this operation, may be mixed with
what passed through in the first bolting of the middlings :
and be hoisted up, and mixed (by the hopper-boy) regu-
larly with the ground meal, and. bolted into superfine
flour, as directed art. 89.*

The stuff, which is a degree coarser than middlings,
if it . be too poor for ship bread, and too rich to feed

• But all this trouble and loss of time may be saved by a little simple
machinery of late in\ention, that will cost but a few dollars, viz. As the
middlings fall by th. first bolting-, let them be conveyed into tlie eye of the
stone, and ground with the wheat, us directed art. 89, plate VHI.; by which
means, the wliole thereof may be made into snpeifine flour, wi'honi any
loss of time, or danger of being too hard pressed for want of the bran
to keep the stones apart. This mode I first introduced, and several others
have since adopted it with approbation.

Chap. 5.] QUALITY OF MILL-STONES, &c. Q77

cattle on, is to be ground over in the same manner as
the middlings. But if it be mixed with fine flour, (as it
sometimes is,) so that it will not feed freely, it must be
bolted over first; this will take out the fine flour, and
also the fine specks of bran, which being lightest, will
come through the cloth last. When it is bolted, the
part that passes through the middlings' and stuff''s parts
of the cloth, are to be mixed and ground together; by
which means the rich particles will be reduced to flour;
and w hen bolted will pass through the finer cloths, and
will make tolerable good bread. What passes through
the middlings' cloth, will make but indifferent ship-bread,
and w hat passes through the ship-stuff''s cloth, will be
what is called brown-stuft', roughings, or horse-feed.

The bran and shorts seldom are worth the trouble of
grinding over, unless the stones have been very dull ; or
the grinding been but slightly performed ; or the wheat
very garlicky. For this purpose the stones are to be
very sharp, and more water and pressure is here required,
than in grinding grain. The flour that is made there-
of, is generally of an indifferent quality, being made of
that part of the grain that lies next the skin, and great
part thereof, being the skin itself, cut fine.*

CHAPTER V.

ART. 414.

OF THE QUALITY OF MILL STONES, TO SUIT THE QUALITY OF
THE WHEAT.

IT has been found by experience, that different quali-
ties of wheat require different qualities of stones, to grind
to the best perfection.

• But the merchant miller is to consider, that there is a certain degree
of closeness or perfection that he is to aim at in maniifacturini^, which will
yield him the maximum, or j^reitest profit possihle, in a given time. And
this degree of care and perfecion will vary with the prict-s of wheat and
flour, so that what would yield the greatest profit at one time, would sink
money at another ; because, if the difference of the prices of wheat and
flour be but little, then we must make the grain yield the must possible,
to obtain any profit Bit if the price of flour be much above that of the
wheat, then we had best make the greatest despatch, even if we should
not do it so well, in order that the greater quantity may be done while

srs QUALITY OF MILL-STQNES, &c. [Chap. S.

Although there be several species of wheat, of differ-
ent qualities ; yet with respect to the grinding, we may
take notice of but the three following qualities, viz.

1'. The dry and hard.

2. The damp and soft.

3. Wheat that is mixed with garlic.
When the grain that is to be ground to dry and hard,

such as is raised on

high.

and clay lands; threshed in

other prices last ; whereas, if we were to make such a despatch when the
price of flour was but little above that of wheat, we would sink money.

A TABLE

Showing the product of a bushel of wheat of different weights and quali-
ties, ascertained by experiments in grinding parcels.

Tail

Bead

Screen.

Weighi

Super-

flour &

st<.flr,

ings and

per
bushel.

fine
flour.

mid-
dlings.

Ship
Stuff.

shortS)
&bran.

loss in
grind-

Proof,
lb.

Quality of the grain-

lb.

ing,
lb.

59,5

38,5

3,68

2,5

13,1

1,72

59,5

White wheat clean.

40,23

3,65

2,12

Do. do well cleaned.

38,7

3,6

1,61

8,52

7,57

Red do- not well do-

39,7

5,68

2,4

9,54^

3,68

White do mixt with
green garlic.

35.81

1,85

7,86

5,48

White do. very clean.

59,25

35,26

4,4

1,47

11,33

6,79

59,25

Red do. with some
cockle Stlight grains.

If the screenings had been accurately weighed, and the loss in weight
occasioned by the grinding ascertained, this table would have been more
interesting. A loss of weight does take place bythe evaporation of the mois-
ture by the heat of the stones in the operation.

The author having conceived that if a complete separation of the skin of
the wheat from the flour could be eff*ected, and the flour reduced to a suf-
ficient degree of fineness, it might all pass for superfine flour. After hav-
ing made the experiments in the table, he made such improvements in tlie
manufacture by dressing the miil-siones to grind smooth, and by means of
the machinery which he invented, returning the middlings into the eye of
the stone» to be ground over with the wheat, and elevating the tail flour to
the hopper-boy to be bolted over again, &c. &c. That in making his last
2000 barrels of superfine flour he left no middlings nor ship-stuff" but what
was too poor for any kind of bread, exceptmg some small quantities « hich
were retained in the mill, and the flour passed the inspection with credit.
Others have since pursued the same prmciples and put them more fully and
completely in operation. Thus the manufacture of flour has arrived nearly
to a state of perfection, and those millers who had faith to believe, have
for fourteen years past been enjoying themselves, seeing the machinery of
their mills perform all the laborious parts of the work, and have been sell-
ing and eating good superfine flour ; while those who had not, have been
toiling, sweating, and doing the labour that the power of the water which
move's their mills might have done, and have been selling and eating mid-
dlings and ship-stuff".

Chap. 5.] QUALITY OF MILL-STONES, &c. 279

barns, and kept dry ;* the stones for grinding such
wheat, should be of that quahty of the burr, that is call-
ed close and hard, with few large pores ; in order that
they may have more face. The grain being brittle and
easy broken into pieces, requires more face or plane
parts (spoken of in art. 104,) to reduce it to the requir-
ed fineness, without cutting the skin too much.

When the grain that is to be ground is a little damp
and soft, such as is raised on a light, sandy soil, tread
out on the ground, and carried in the holds of ships to
market, which tends to increase the dampness, the
stones are required to be more open, porous, and sharp,
because the grain is tough, difficult to be broke into
pieces, and requires more sharpness, and less face (or
plane surface) to reduce it to the required fineness. f
See art. 104.

When there is more or less of the garlic, or wild
onion, (mentioned art. 111.) mixed with the wheat, the
stones will require to be open, porous and sharp ; be-
cause the glutinous substance of the garlic adheres to
the face of the stones, and blunts the edges ; by which
means little can be ground, before the stones get so dull
that they will require to be taken up, and sharpened ;
and the more porous and sharp the stones are, the longer
will they run, and the more will they grind, without
getting dull. There is a quality of the burr stone which
I shall for distinction call a mellow or soft qualit}% very
diiferent from the hard and flinty ; these are not so sub-
ject to glaze on their face, and it is found by experience
that stones of this quality will grind at one dressing

* Such wheat as is produced by the mountainous and clay lands of the
country distant from the sea and tide waters, is jjenerally of a brownish
colour, the grain appearing flinty, and sometimes the inside a little trans-
parent, when cut by a sharp knife. This transparent kmd of wheat is ge-
nerally heavy, and of a thin skin, and will make as white flour, and as much
of it, as the whitest grain.

f Such is the wheat thai is raised in all the low, level, and sandy lands,
of countries near the sea and tide waters of America, where it is customa-
ry to tread out their wheat on the ground by horses, and if sometimes gets
wet by rain and dew, and the dampness of the ground- This grain is na-
turally of af a irer colour, and softer ; and when bioken, the inside is white,
which siiows ii to be nearer a state of pulverisation, and is more easily re-
duced to flour, and will not bear as mu'h prrssure as the grain that is
raised on high and clay lands, or such, thatwh^n broken, appears solid and
transparent

280 OF BOLTING-REELS AND CLOTHS. [Chap. 6.

three or four times as much grain, mixed with garlic, as
those of a hard quahty.* See art. 111.

CHAPTER VI.

ART. 115.

OP BOLTIKG -REELS, AND CLOTHS ; WITH DIRECTIONS FOR
BOLIING AND INSPECTING THE FLOUR-

THE effect we wish to produce by sifting, or bolting,
is to separate the different qualities of flour from each
other ; and from the skin, shorts, or bran. For this rea-
son, let us consider the most rational means that we can
use to attain this end.

Queries concerning Bolting.

1. Suppose that we try a sieve, the meshes of which
are so large, as to let all the bran and meal through :
now it is evident, that we could never attain the end
proposed by the use thereof.

2. Suppose we try a finer sieve, that will let all the

* It is very difficult to convey my ideas of the quality of the stones to
the reader, for want of something to measure or compare their degree of
porosity or closeness, hardness or softness with- The knowledge of these
diffc-reni qualities is only to be attained by practice and experience; hut I
m..y observe, that there is no need of any pores in the stone to be larger in
diameter than the length of a grain of wheat, for whatever they are larger,
is so much loss of the face, because it is the edges that do the grinding;
thert- f )re, all larjije pores in stones are a disadvantage. The greater the
number of pores in the stone, (so as to leave a sufficient quantity of touch-
ing surfaces, to reduce the flour to a sufficient degree of fineness) the bet-
ter.

Mill-stone makers ought to be acquainted with the true principles on
which grinding is perform<-d, and with the art of manufacturing grain into
flour, that they may be judges of the quality of the stones suitable to the
quality of the wheat, of different parts of the country; also, of the best
manner of disposing of the different pieces of stone, of different qualities,
in the same mill si one, according to the office of the several parts, from the
centre to the verge of the stone. See art- 104-

Mill stones are generally but very carelessly and slightly made, whereas,
they should be made with the greatest care and to the greatest nicety. The
ri'nner must be balanced exactly on its centre, and every corresponding
opposite part of it shouhl be of equal weight, or else the spindle will not
keep tight m the bush : (see art. 107) and if it is to be hung on a balance
ryne, it should be put in at the formation of the stone, which should be
oicely balanced thereon.

But above all, the q>alityof the stone should be most attended to, that
no piece of un unsuitable quality for the rest, be put in ; it being known to
mos experienced millers, that they had better give a high price for an ex-
traordinary good pair, than to have an indifferent pair for nothing.

Chap. 6.] OF BOLTING-KEELS AND CLOTHS. 281

meal through, but none of the bran : but by this we can-
not separate the different qualities of flour.

3. We provide as many sieves of the different degrees
of fineness, as we intend to make different qualities of
flour ; and which, for distinction, we name — Superfine,
Middlings, and Carnel.

The superfine sieve, of meshes so fine as to let through
the superfine flour, but none of the middlings : the mid-
dlings' sieve, so fine as to let the middlings pass through,
but none of the camel : the carnel sieve, so fine as to let
none of the shorts or bran pass through.

Now it is evident, that if we would continue the ope-
ration long enough, with each sieve, beginning with the
superfine, that we might effect a complete separation.*
But if we do not continue the operation a sufficient length
of time, with each sieve, the separation will not be com-
plete. For part of the superfine will be left, and will
pass through with the middlings, and part of the mid-
dlings with the carnel, and part of the carnel with the
shorts ; and this would be a laborious and tedious work,
if performed by the hand.

To facilitate this business, many have been the im-
provements ; amongst which the circular sieve, or bolt-
ing-reel, is one of the foremost ; and which was, at first,
turned and fed by hand ; though afterwards contrived
to be turned by water.

But many have been the errors in the application of
this machine, either by having the cloths too coarse, by
which means the middlings and small pieces of bran will
pass through with the superfine flour, and part of the
carnel with the middlings : or by having the cloths too
short, when they are fine enough, so that the operation
cannot be continued a sufficient time to take all the
superfine out, before it reaches the middlings' cloth, and
all the middlings, before it reaches the carnel cloth.

The late improvements made on bolting, seem to be
wholly as follows, viz.

• This metUod I have been informed is practised in England ; they have
several bolting^ cloths of difFereni degrees of fineness for the same ivel.
They first put on the fine one, and piss the meal chrout^h. whi h taktrs out
the superfine flour; they then take off ihe superfine cloth, md put on 'he
next degree of fineness, which takes out the common fin • floup; and so on
through the lifferent <legTees, the cloths having drawl ng-strings at each end
for drawing the ends close.

N n

282 OF INSPECTING FLOUR. [Chap. 6,

1. By using finer cloths — but they were found to
clog, or choke up, when put on small reels of 22 inches
diameter.

S. By enlarging the diameter of the reels to 271
inches, which gives the meal greater distance to fall, and
causes it to strike harder against the cloth, which keeps
it open.

3. By lengthening the cloths, that the operation may
be continued a sufficient length of time.

4. By bolting a greater part of the flour over again,
than was done formerly.

The meal, as it is ground, must be hoisted to the meal-
loft, where it is spread thin, and often stirred, that it may
cool and dry, to prepare it for bolting. After it is bolted,
the tail-flour, or that part of the superfine that falls last,
and which is too full of specks of bran to pass for super-
fine flour, is to be hoisted up again, and mixed with the
ground meal, to be bolted over again. This hoisting,
spreading, mixing, and attending the bolting hoppers, in
merchant- mills, creates a great deal of hard labour, if
done by hand ; and is never completely done at last : but
all this, and much more of the labour of mills, can now
be done by machinery, moved by water. See part. 3.
Of Inspecting Flour.

The miller must by some means attain a knowledge
of the standard quality, passable in the markets.

He holds a clean piece of board under the bolt, mov-
ing it from head to tail, so as to catch a proportional
quantity all the way, as far as is taken for superfine : then,
having smoothed it well, by pressing an even surface on
it, to make the specks and colour more plainly appear ;
if it be not good enough, turn a little more of the tail to
to be bolted over.

If the flour appears darker than expected, from the
quality of the grain, it shows the grinding to be high,
and bolting too near ; because the finer the flour, the
whiter its colour.*

* This appears reasonable, when we consider, that many dark coloured
and transparent substances (while in a solid state) when pulverised, be-
come white, and their whiteness is proportionate to the dei^ree of pulveri-
sation ; for instance, salt, alum, and many kinds of stone, and particularly
slate. — Ice pulverised is as white as snow, transparent wheat makes the
whitest flour.

Chap. 7.] THE MILLER'S DUTY. 283

But this mode requires good light ; therefore, the best
way is for the miller to observe to what degree of poor-
ness he may reduce his tail Hour, or middlings, so as to
be safe ; by which he may judge with much more safety
in the night. But the quality of the tail flour, middlings,
&:c. will gready vary in different mills ; for those that
have the late improvements for bolting over the tail flour,
grinding over the middlings, &c. can make nearly all
into superfine.

Whereas, those that have them not — the quality that
remains next to superfine, is common, or fine flour ; then
rich middlings, ship-stuff, &c. Those who have expe-
rience will conceive the difference in the profits. If the
flour feels soft, dead, and oily, yet white, it shows the
stones to have been dull, and too much pressure used. If
it appear li\'ely, yet dark coloured, and too full of very
fine specks, it shows the stones to have been too rough,
sharp, and that it was ground high and bolted too close.

CHAPTER VIL

Directions for keeping the Mill^ and the business of it^ in
good order.

ART. 116.

THE DUTY OF THE MILLER.

THE mill is supposed to be completely finished for
merchant work, on the new plan ; supplied with a stock of
grain, flour casks, nails, brushes, picks, shovels, scales,
weights, &c. when the millers enter on their duty.

If there be two of them capable of standing watch, or
taking charge of the mill, the time is generally divided
as follows : In the day time they both attend to business,
but one of them has the chief direction : The night is
divided into two watches, the first of which ends at one
o'clock in the morning ; when the master miller should
enter on his watch, and continue till morning ; that he
may be ready to direct other hands to their business
early. The first thing he should do, when his watch
begins, is to see whether the stones are grinding-, and the
cloths bolting, well.

284 THE MILLER'S DUTY. [Chap. 7.

And 2dly, to review all the moving gudgeons of the
mill, to see whether any of them want grease, Sslc. that
he may know what care may be necessary for them dur-
ing his watch ; for want of this the gudgeons often run
dry, and heat, which brings on heavy losses of time and
repairs ; for when they heat, they get a little loose, and
the stones they run on crack, after which they cannot be
kept cool. He should also see what quantity of grain is
over the stones, and if there be not enough to supply
them till morning, set the cleaning machines in motion.

All things being set right, his duty is very easy — he
has only to see the machinery, the grinding, and bolting,
once in an hour; he has therefore plenty of time to
amuse himself in reading. Sec. rather than going to
sleep, which is not safe.

Early in the morning, all the floors should be swept,
and the flour dust collected. The casks nailed, weighed,
marked and branded, and the packing began, that it may
be completed in the forepart of the day ; by this means,
should any unforeseen thing occur, there will be spare
time. Besides, to leave the packing till the afternoon,
is a lazy practice, and keeps the business out of order.

When the stones are to be sharpened, every thing
necessary should be prepared before the mill is stopped,
(especially if there be but one pair of stones to a water-
wheel) that as little time as possible may be lost : the
picks made right sharp, not less than 12 in number.
Things being ready, take up the stone ; set one hand to
each, and dress them as soon as possible, that they may
be set to work again , not forgetting to grease the gears,
and spindle foot.

In die after part of the day, a sufficient quantity of grain
is cleaned down, to supply the stones the whole night ;
because it is best to have nothing to do in the night, more
than to attend to the grinding, bolting, gudgeons, &c.

ART. 117.

PECULIAR ACCIDENTS BY WFUCH MILLS ARE SUBJECT TO
CATCH FIRE.

1. There being many moving parts in a mill, if any
piece of timber fall, and lay on any moving wheel, or

Chap.7.] ON IMPROVING OF MILL-SEATS. 285

shaft, and the velocity and pressure be great, it will ge-
nerate fire, and perhaps consume the mill.

S. Many people use wooden candlesticks, that may be
set on a cask, bench, or the floor, and forgetting them, the
candle bums down, sets the stick, cask, &c. on fire, which
perhaps may not be seen until the mill is in a flame.

3. Careless millers sometimes stick a candle to a cask,
or post, and forget it, until it burns a hole in the post, or
sets the cask on fire.

4. Great quantities of grain sometimes bend the floor
so as to press the head blocks against the top of the
upright shafts, and generate fire : (unless the head blocks
have room to rise as the floor settles) mill-wrights should
consider this, and be careful to guard against it as they
build.

5. Branding irons, carelessly laid down, when hot,
and left, might set something on fire.

6. I have heard of bran falling from the tail of a bolt,
round a shaft, the friction of which burnt the shaft off".

7. The foot of the mill-stone spindle, and gudgeons,
frequently heat, and set the bridge- tree or shaft on fire.
It is probable, that from such causes mills have taken
fire, when no person could discover how.

ART. 118.

OBSERVATIONS ON IMPROVING OF MILL SEATS.

I may end this part with a few observations on im-
proving mill- seats. The improving of a mill-seat at
1000/. expense, is an undertaking worthy of mature de-
liberation, as wrong steps may increase it to 1100/. and
the improvement be incomplete: whereas, right steps
may reduce it to 900/. and perfect them.

Strange as it may appear, yet it is a real fact, that those
who have least experience in the milling business, gene-
rally build the best and completest mills. The reasons
are evident —

The experienced man is bound to old systems; he re-
lies on his own judgment in laying all his plans; whereas.

The unexperienced man, being conscious of his defi-
ciency, is at liberty; perfectly free from all prejudice,
to call on all his experienced friends, and to collect all
the improvements that are extant.

286 ON IMPROVING OF MILL-SEATS. [Chap.r.

A merchant who knows but little of the miller's ait,
or of the structure or mechanism of mills, is naturally
led to the following steps, viz.

He calls several of the most experienced millers and
mill-wrights, to view the seat separately, and point out
the spot for the mill-house, dam, &c. and notes their
reasonings in favour of their opinion. The first perhaps
fixes on a pretty level spot for the mill-house, and a cer-
tain rock, that nature seems to have prepared, to support
the breast of the dam, and an easy place to dig the race,
mill-seat, &c.

The second passes by these places without noticing
them ; explores the stream to the boundary line ; fixes on
another place, the only one he thinks appointed by nature
for building a lasting dam, the foundation a solid rock,
that cannot be undermined by the tumbling water; fixing
on a rugged spot for the seat of the house : assigning for
his reasons, that the whole fall must be taken in, that all
may be right at a future day. He is then informed of the
opinion of the other, against which he gives substantial
reasons.

The mill-wright, carpenter and mason, that are to un-
dertake the building, are now called together, to view the
seat, fix on the spot for the house, dam, &c. After their
opinion and reasons are heard, they are informed of the
opinion and reasons of the others, all are joined together,
and the places are fixed on. They are then desired to
make out a complete draught of the plan for the house,
&c. and to spare no pains to plan all for the best ; but
alter and improve on paper, till all appear to meet right,
in the simplest and most convenient manner; (a week
may be thus well spent) making out complete bills of
every piece of timber, quantity of boards, stone, lime,
&c. bill of iron work, number of wheels, their diame-
ters, number of cogs, &c. &c. in the whole work. Each
person can then make out his charge, and the costs can
be counted nearly. Every species of materials may be
contracted for, to be delivered in due time : then the
' work goes on regularly without disappointment, and when
done, the improvements are complete, and 100/. out of
1000/. at least saved by such steps.

PART V.

THE

PRACTICAL MILL-WRIGHT;

CONTAIlSriNG

INSTRUCTIONS FOR BUILDING MILLS,

WITH

ALL THEIR PROPORTIONS j

SUITABLE

TO ALL FJLLS OF FROM THREE TO THIRTY-SIX FEET.

Received from Thomas Ellicott,

Mill-fVright.

CONTENTS OF PART V.

T^he Preface explains the Plate containing the new im-
provements.

ART. 1. Of undershot mills — directions for laying on
the water.

Art. 2. Draught of a forebay, with directions for mak-
ing them durable.

Art. 3. Principles and practical experiments, to deter-
mine the proper motion for undershot wheels.

A table for gearing undershot wheels, suited to all falls,
from 3 to 20 feet.

Art. 4. Of breast mills, with directions for proportioning
and gearing them, to give the stone the right motion.

Art. 5. Of pitch-back mills, do. do.

Art. 6. Of overshot mills, and their dimensions.

Art. 7. Of the proper motion for overshot mills.

Art. 8. Of gearing the water-wheel to the mill-stones,
to give them the proper motion.

Art. 9. Rules for finding the diameter of the pitch circles.

Table of all the proportions for overshot mills, suitable
for all falls, from 15 to 36 feet ; for 4 and 4; feet 6
inches, and 5 and 5 feet 6 inch stones, diameter.

Art. 10. Directions for constructing undershot wheels,
for dressing shafts.
, for laying out mortises for arms,
for putting in gudgeons,
for constructing cog-wheels,
for making sills, spurs, and head
blocks.

Art. 16. Of the best time for cutting cogs, and method
of seasoning them.

Art. 17. Of shanking, putting in, and dressing off the
cogs.

Art. 18. Of the little cog-wheel and shaft.

Art.

11.

do.

Art.

12.

do.

Art.

13.

do.

Art.

14.

do.

Art.

15.

do.

a90 CONTENTS.

Art. 19. Directions for making wallowers and trundles.

Art. 20. do. for fixing the head blocks, and hang-
ing the wheels.

Art. 21. Directions for sinking the balance ryne.

Art. 22. do. for bridging the spindle.

Art. S3. do. for making the crane and lighter-
staff.

Art. 24. do. for making a hoop for the mill-
stones.

Art. 25. do. for grinding sand to face the stones.

Art. 26. do. for laying out the furrows in new
stones.

Art. 27. do. for making a hopper, shoe and feeder.

Art. 28. do. for making bolting chests and reels.

Art. 29. do. for setting bolts to go by water.

Art. 30. do. for making bolting wheels.

Art. 31. or roUing-screens.

Art. S2 OF fans.

Art. 33. Of the shaking sieve.

Art. 34. Of the use of draughting to build mills by.

Art. 35. Directions for draughting and planning mills.

Art. 36. Bills of bcanding for a mill.

Art. 37. Bills of iron work for do.

Art. 38. Explanation of the plates.

Art. 39. Of saw- mills, with a table of the dimensions of
flutter-wheels, to suit all heads from 6 to 30 feet.

Art. 40. Of fulling-mills.

TO THE READER.

I BEING requested by Oliver Evans, to assist
iiim in completing his book, entitled, The Young
Mill- Wright and Miller's Guide, have thought pro-
per to give the reader a short history of the rise
and progress of merchant mills, towards their pre-
sent state of perfection, since the beginning of my
time.

It is now upwards of 38 years since I first be-
gan mill-wrighting: I followed it very constantly for
about ten years, making it niy particular study.
Several of my brothers being also mill-wrights, we
kept in company, and were often called to different
parts of this and the adjacent states, to build mills
of the first rates, in their day. Some of them en-
tered into the manufacturing line; but I continued
at mill-wrighting, and other business connected
therewith ; such as roUing-screens, and fans, and
making them to go by water, in merchant and
grist-mills ; also farmer's fans, for cleaning grainy
being one of* the first, 1 believe, that made these

• .Mr- Ellicolt observed that he was sorry the words (one of) hftU been
left out, therefore they were put in by Mr. Rvans.

:29a TO THE READER.

things in America: but for several years past,
have done but little else than build mills, or
draught to build by.

When I first began the business, mills were at
a low ebb in this country ; neither burr-stones,
nor rolling-screens being used ; and but few of
the best merchant mills had a fan. Many carried
the meal on their backs, and bolted it by hand,
even for merchant work ; and I have frequent-
ly heard, that a little before my beginning the
business, it had been customary, in many in-
stances, to have the bolting mill some distance
from the grinding mill, and there bolted by hand.
It was counted extraordinary when they got their
bolting to go by water : after this, fans by hand,
and standing-screens, took place; then burr-stones,
rolling-screens, and superfine bolting cloths, with
a nuniber of other improvements. Some of the
latest are, the elevators, hopper-boys, ^c; invent-
ed by Oliver Evans, late of Delaware, though now
of Philadelphia.

Being very desirous to improve in the art of
building mills, and manufacturing grain into flour,
I have frequently went a considerable distance to
see new improvements, and have often searched
the book-stores in expectation of finding books
that might instruct me, but never found any which
was of use to me in that respect, more than to
learn the ancient names of some parts of the mills;
for although they had been wrote by men of con-
siderable learnicg, in other respects ; yet, as they

TO THE READER. S93

had never been mill-wrights themselves, they had
neither practical, nor experimental knowledge to
direct them in the work. For instance, see the
mill-wright's table, in Ferguson's Lectures, page
79^ where the cog-wheel is to have i27 cogs,
about 15 i-2 feet diameter; trundle, 6 staves, and
stones 6 feet: And in Imison's Introduction to
Useful Knowledge, page 31, the water-wheel is to
be 18 feet, cog-wheel S54 cogs, about 31 feet di-
ameter, much higher tlian the water-wheel ; staves
in the trundle (5, and stones 4 l-S feet. Besides^
some liave asserted, that water applied on an un-
dershot wheel, will do 6 times as much as if ap-
plied on an overshot ; others, that if apphed on an
overshot it will do 10 times as much as an under-
shot, the quantity and falls being equal ; many
other parts of their theories are equally wrong
in practice. So that what knowledge I have gain-
ed, has been by steady attention to the improve-
ments of our own country : I have wondered, that
no person of practical knowledge in the art, has
yet attempted to write a treatise on it, seeing it is
a subject worthy attention, and such a book so
much wanted. The manufacturing of our own
country produce, in the most saving, expeditious,
and best manner, I have thought, is a subject wor-
thv the attention of the legislatures. Mills are
often laid under heavy taxes, being supposed to
be very profitable ; but if all the spare wheat was
to be shipped, where would the miller's profit be?
But to return to the subject : I have often thought,

S94 TO THE READER.

that if I could spare time, I would write a small
treatise on mill-wrighting myself, (thinking it would
be of much use to young mill-wrights,) but fearing
I was not equal to the task, I was ready to give it
up; but on further consideration, I called on Tho-
mas Dobson, printer of the Encyclopedia, and ask-
ed him if he would accept of a small treatise on
mill-wrighting; he said Oliver Evans had been
there a few days before, and proposed such a
work, which 1 thought would save me the trouble.
But some time afterwards, the said Evans, apphed
to me, requesting my assistance in his under-
taking ; this I was the more willing to do, having
built several mills with his additional improve-
ments, and draughted several others ; and without
which improvements, I think a mill cannot now
be said to be complete. By them the manufac-
ture of grain into flour, is carried on by water
with very little hand labour, and much less waste,
either in small or large business. And I do be-
lieve, that taking a large quantity of wheat toge-
ther, that we can make 2 or 3 lbs. more out of a
bushel by the new, than by the old way, although
ft be equally well ground ; because it is so much
more completely bolted, and v/ith less waste. In
the old way, the wheat is weighed and carried up
one or two pair of stairs, and thrown into garners j
the bags often having holes in, it is spilt and tram-
pled under foot ; several pounds being frequently
lost in receiving a small quantity ; and when it is
taken from these garners, and carried to the roll-

TO THE READER. S95

iiig-screens, some is again wasted, and as it is
ground, it is shoveled into tubs, a dust is raised,
and some spilt and trampled on ; it is then hoist-
ed, and spread, and tossed about with shovels, over
a large floor, raked and turned to cool, and shov-
eled up again, and put into the bolting hopper ; all
which occasions great labour, besides being spilt
and trampled over the mill, which occasions a con-
siderable waste. Besides these disadvantages,
there are others in attending the bolting hoppers ;
being often let run empty, then filled too hard,
so that they choke, which occasions the flour to be
very unevenly bolted ; sometimes too poor, and
at other times too rich, which is a considerable
loss ; and when the flour is bolted, it is much
finer at the head than tiie tail of the cloths ; the
fine goes through first, and has to be mixed by
hand, with shovels or rakes ; and this labour is
often neglected or only half done ; by this means,
part of the flour will be condemned for being too
poor, and the rest above the standard quality.
The hoisting of the tail flour, mixing it with bran,
by hand, and bolting it over, is attended with so
much labour, that it is seldom done to perfection.
In the new way, all these inconveniences and
disadvantages are completely provided against :
See plate XXII ; which is a representation of the
machinery, as they are applied in the whole pro-
cess of the manufacture, taking the grain from the
ship or wagon, and passing it through the whole
process by water, until it is completely manufac-
tured into superfine flour. As they are applied

^96 TO THE READElt.

in a mill of my planning and draughting, now in
actual practice, built on Occoquam river, in Virgi-
nia, with 3 water-wheels, and 6 pair of stones.

If the wheat comes by water to the mill in the
ship Z, it is measured and poured into the hopper
A, and thence conveyed into the elevator at B,
which elevates it, and drops it into the conveyer
C D, which conveys it along under the joists of
the second floor, and drops it into the hopper gar-
ner at D, out of w^hich it is conveyed into the main
wheat elevator at E, which carries it up into the
peak of the roof, and delivers it into the rolling-
screen at F, which (in this plan) is above the col-
lar beams, out of which it falls into the hopper G,
thence into the short elevator at H, which conveys
it up into the fan I, from whence it runs down
slanting into the middle of the long conveyer at j,
that runs towards both ends of the mill, and con-
veys the grain, as cleaned, into any garner KKK
KKK, over all the stones, which is done by shift-
ing a board under the fan to guide the grain to
either side of the cog-wheel j, and although each
of these garners should contain 2000 bushels of
wheat, over each pair of stones, 12000 bushels in
6 garners, yet nearly all may be ground out with-
out handling it, and feed the stones more even and
regular than it is possible to do in the old way.
As it is ground by the several pairs of stones, the
meal falls into th'^ meal conveyer at M M M, and
is conveyed into the common meal elevator at N,
which raises it to O, from thence runs down the
hopper-boy at P, which spreads and cools it over

TO THE READER. 297

a circle of 10 or 15 feet diameter, and (if thought
best) will raise over it, and form a heap two or
three feet high, perhaps tliirty barrels of flour or
more at a time, which may be bolted down at
pleasuie. When it is bolting, the hopper-boy
gathers it into the bolting hoppers at Q, and at-
tends them more regularly than is ever done by
hand. As it is bolted, the conveyer R, in the bot-
tom of the superfine chest, conveys the superfine
flour to a hole through the floor at S, into the
packing chest, which mixes it completely. Out
of the packing chest it is filled into the barrel at T,
weighed in the scale U, packed at W by water,
headed at X, and rolled to the door Y, then low-
ered down by a rope and windlas into the ship
again at Z.

If the wheat comes to the mill by land, in the
wagon 7, it is emptied from the bags into a spout
that is in the wall, and it runs in the scale 8, which
is large enough to hold a wagon load, and as it is
weighed it is (by drawing a gate at bottom) let run
into the garner D, out of which it is conveyed
into the elevator at E. and so through the same
process as before.

As much of the tail of the superfine reels 37
as we think will not pass inspection, we suffer to
pass on into the short elevator, (by shutting the
gates at the bottom of the conveyer next the ele-
vator, and opening one further towards the other
end.) The rubblings. which fall at the tail of said

reels, is also hoisted into the bolting hoppers of

298 TO THE READER.

the sifting reel 39, which is covered with a fine
cloth, to take out all the fine flour dust, which
will stick to the hran, in warm dannp weather, and
all that passes through it is conveyed hy the con-
veyer 40, into the elevator 41, which elevates it
go high tliat it will run fi-eely into the hopper-boy
at O, and is bolted over again with the ground
meal. The rubbhngs that fall at the tail of the
sifting reel 39, fall into the hopper of the mid-
dlings' reel 42 ; and the bran falls at the tail into
the lower story. Thus you have it in your power
either by day or night, without any hand labour
except to shift the sliders, or some such trifle, to
make your flour to suit the standard quahty ; and
the most superfine possible made out of the grain,
and finished complete at one operation.

These improvements are a curiosity worthy the
notice of the philosopher and statesman, to see
with what harmony the whole machinery works
in all their different operations.

But to conclude, agreeably to request I attempt
to show the method of making and putting water
on the several kinds of water-wheels commonly
used, with their dimensions, ^c. suited to falls and
heads from 3 to 36 feet; and have calculated ta-
bles for gearing them to mill-stones; and made
draughts* of several water-wheels with their fore-
bays and manner of putting on the water, ^c.

THOMAS ELLICOIT.

* All my drauEfhts are taken from a scale of 8 feet to an inch, except
nl. V. which is 4 feet to an inch

THE

PRACTICAL MILLWRIGHT

ART. 1.
OF UNDERSHOT MILLS.

FIG. 1, plate XIII, represents an undershot wheel 18
feet diameter, with 3 feet total head and fall. It should
be 2 feet^ide for every foot the mill-stones are in dia-
meter ; tnat is, 8 feet between the shrouds for a -^ feet,
and 10 feet wide for a 5 feet stone. It should have three
sets of arms and shrouds, on account of its great width.
Its shaft should be at least 26 inches diameter. It re-
qtSires 12 arms, 18 feet long, 3| inches thick, by 9
wide; and S4 shrouds, 7| feet long, 10 inches deep, by
3 thick, and 32 floats 15 inches wide. Note, it may be
geared the same as an overshot wheel, of equal diame-
ter. Fig. 2 represents the forebay, with its sills, posts,
sluice and fall : I have in this case allowed 1 foot fall
and 2 feet head. *

Fig. 3 represents an undershot wheel, 18 feet diame-
ter, with 7 ^eet head and fall. It should be as wide be-
tween the shrouds as the stone is in diameter. Its shaft
should be 2 feet diameter. Requires 8 arms 18 feet
long, 3| of an inch thick, by 9 wide. And 16 shrouds,
7i feet long, 10 inches deep, by 3 thick. Note, it may
be geared the same as an overshot wheel 13 feet diame-
ter, because their revolutions per minute will be nearly
equal.

Fig. 4 represents the forebay, sluice, and fall, the head
and fall about equal.

300 OF UNDERSHOT MILLS.

Fig. 5 represents an undershot wheel, 12 feet diame-
ter, with 15 feet total head and fall. It should be 6
inches wide for every foot the stone is in diameter. Its
shaft 30 inches diameter. Requires 6 arms 12 feet long,
3 by 8 inches; and IS shrouds, 6| feet long, 2{ inches
thick, and 8 deep. It suits well to be geared to a 5
feet stone with single gears, 60 cogs in the cog-wheel,
and 16 rounds in the trundle; to a 4| feet stone, with
62 cogs and 15 rounds ; and, to a 4 feet stone, with 64
cogs and 14 rounds. These gears will do well till the
fall is reduced to 12 feet, only the wheel must be less as
the falls are less, so as to make the same number of re-
volutions in a minute; but this wheel requires more
water than a breast-mill, with the same fall.

Fig. 6 is the forebay, gate, shute and fall. Forebays
should be wide proportionable to the quantity of water
they are to convey to the wheels; and should stand 8 or
10 feet in the bank, and be firmly joined, to prevent the
water from breaking through; which it will c<^|ainly d9,
unless thev be well secured.

, ART. 2.

DIRECTIONS FOR MAKING FOREBAYS.

The best way that I know for making these kind of
forebays, is shown in plate XVII, fig. 7. Make a number
of solid frames, consisting of a sill, two posts, and a cap
each; set them cross-wise, (afB.shown in the figure) 2|
or 3 feet apart; to these the plank are to be spiked, for
there should be no sills lengthwise, as the water is apt to
find its way along them. The frame at the head next
the water, and one 6 or SlTeet downwards in the bank,
should extend <t or 5 feet 6n each side of the forebay in
the bank; and be planked in front to prevent the water
and vermin from working round. Both of the sills of
these long frames should be well secured, by driving
down plank edge to edge, like piles, -along the upper
side, from end to end.

The sills being settled on good foundations, the earth

OF UNDERSHOT MILLS, 301

or gravel must be rammed well on all sides, full to the
top of the sills. Then lay the bottom with good sound
plank, well jointed and spiked to the sills. Lay your
shute, extending the upper end a little above the point
of the gate when full drawn, to guide the water in a right
direction to the wheel. Plank the head to its proper
height, minding to leave a suitable shiice, to guide the
water smoothly down. Fix the gate in an upright posi-
tion — hang the wheel and finish it off ready for letting on
the water.

A rack must be made to keep oif the floating trash that
would break the floats and buckets of undershot, breast,
and pitch-back wheels, and injure the gates. See it at
the head of forebay, fig. 7, plate XVIL This is done by
setting a frame 3 feet in front of the forebaj^, and laying a
sill 2 feet in front of it, for the bottom of the rack ; in it
the staves are put, made of laths, set edgewise with the
stream, 2 inches apart, their upper ends nailed to the cap
of the last frame, which causes them to lean down stream.
The bottom of the race must be planked between the
forebay and rack, to prevent the w^ter from making a
hole by tumbling through the rack when choked; and
the side^ be planked outside the posts to keep up the
banks. This rack must be dotible as long as the forebay
is wide, or els» the Xvater will not come fast enough
through it to keep the head up ; for the head is the spring
of motion of an undershot mill.

ART. 3.

jof the principle of undershot mills.

They difler from all others in principle, because the
water loses all its force by the first stroke against the
floats; and the time this force is spending, is in propor-
tion to the difference of the velocities of the wheel and
water, and the distance of the floats. Other mills have
the weight of the water after the force of the head is
spent, and will continue to move ; but an undershot will
stop as soon as the head is spent, as they depend not on

S02 OF UNDERSHOT MILLS.

the weight. They should be geared so, that when the
stone goes with a proper motion, they will not run too
fast with the water, so as not to receive its force ; nor too
slow, so as to lose its power by rebounding and dashing
over the buckets. This matter requires very close at-
tention, and has puzzled our mechanical philosophers to
find it out by theory. They give us for a rule, that the
wheel must move just 1-3 the velocity of the water: per-
haps this may suit where the head is not much higher
than the float- boards, but I am fully convinced it will not
suit high heads.

Experiments for determining the proper Motion for Un^
dershot Wheels.

I drew a full sluice of water on an undershot wheel
with 15 feet head and fall, and counted its revolutions
per minute ; then geared it to a mill-stone, set it to work
properly, and again counted its revolutions, and the differ-
ence was not more than one-fourth slower. I believe,
that if I had checked the motion of the wheel to be
equal 1-3 the motion of the water, that the water would
have rebounded and flew up to the shaft. Hence I
conclude, that the motion of the water must not be
checked by the wheel more than 1-3, nor less than 1-4;
else it will lose in power; for although the wheel will
carry a greater load with the slow, than swift motion, yet
it will not produce so great effect, its motion being too
slow. And again, if the motion be too swift, the load
or resistance it will overcome will be so much less, that
its effect will be lessened also. I conclude, that about
2-3 the velocity of the water is the proper motion for
undershot wheels, the water will then spend all its force
in the distance of two float-boards ; notwithstanding the
learned authors have asserted it to be but 1-3. To
confute them, suppose tlie floats 12 inches, and the co-
lumn of water striking them, 8 inches deep; then, if
2-3 of the motion of this column be checked, it must
instantly become 24 inches deep, and rebound against
the backs of the floats, and the wheel would be wal-
lowing in this dead water; whereas, when 1-3 of its
motion is checked, it becomes only \.% inches deep, and
runs off" from the wheel smooth and livelv.

OF UNDERSHOT WHEELS.

303

Directions for gearing Undershot Wheels^ 18 feet diame-
ter, where the head is above 3 and under 8 feet, ivith
double gears ; counting the head from the point where
the water strikes the floats.

1. For 3 feet head and 18 feet wheel, see 18 feet wheel
in the overshot table.

2. For 3 feet 8 inches head, see 17 feet wheel in said
table.

3. For 4 feet 4 inches head, see 16 feet wheel in do.

4. For 5 feet head, see 15 feet wheel in do.

5. For 5 feet 8 inches head, see l^ feet wheel in do.

6. For 6 feet 4 inches head, see 13 feet wheel in do.

7. For 7 feet head, see 12 feet wheel in do.

jAe revolutions of the wheels will be nearly equal -;
th#cfore the gears may be the same.

The following table is calculated to suit for any sized
stone, from 4 to 6 feet diameter ; different sized water-
wheels from 12 to 18 feet diameter, and different heads
from 8 to 20 feet above the point it strikes the floats.
And to make 5 feet stones revolve 88 times ; 4 feet 6
inch stones 97 times ; and 4 feet stones 106 times in a
minute, when the water-wheel moves 2-3 the velocity of
the striking water.

MILL-WRIGHT'S TABLE FOR UNDERSHOT MILLS— SINGLE
GEARED.

Velocit
tcrpe
feet.

Velocit
ter-wl
nnte i

llevolu
water-

^ z

^ 3

■z

■ ~ ft

llevolu
mill-s
of t
wheel

.. 9.

3 3
n n

n o

i "

- V;

= o^

n :- C.

"w *"*

7^ ''

O "5

en ^ r— *-•

" n

-> -n

S-''

3 ^

-^ 1 o

■ ^ o

7i 3

-5 -

;, c_

■ n ° o

3 ''

5' ~

£.2-

— ' ^

^■3 c;

3 ^

~ c.

^ -■

o=s

-^"'

'^ s

— c

ft O

= 5

^ o* o

ft "^

re —

r- <^

•■: '^

3 -^.

•^ Ti

P -5 -*5

5 o

-■t

If.

•a -

it; ~
-5 a

? a

~ CB

ft Oi

7 n n

1360

9U6

3 3-4

1448

965

23 1-2

37-8

1521

1014

23 1-7

3 6-7

1595

1061

22 3-4

334

1666

1111

22 1.4

3 7-8

1735

1157

231-7

3 3.4

18U0

1200

323

1863

1242

24 4-5

31-2

1924

1283

25 2-3

3 3-8

1983

1322

3 3-4

2041

1361

25 2-3

33 8

2097

1398

3 3-4

2H2

1435

25 1-2

o .-> o

8 1 9

504 OF BREAST-WHEELS.

Note that there is nearly 60 cogs in the cog-wheel, in
the foregoing table, and 60 inches is the diameter of a 5
feet stone ; therefore, it will do without sensible error, to
put 1 cog more in the wheel for every inch that the stone
is less than 60 inches diameter, down to 4 feet; the ti'un-
dle head and water-wheel the same.

And for every 3 inches that the stone is larger than
60 inches in diameter, put 1 round more in the trundle,
and the motion of the stone will be nearly right up to 6
feet diameter.

ART. 4.

OFBREAST-WHEELS, ^(

Breast Vvheels differ but little in their structure or mo-
tion from overshots, excepting only, the water passes
under instead of over them, and they must be wider in
proportion as their fall is less.

Fig. 1, plate XIV, represents a low^ breast with 8 feet
head and fall. It should be 9 inches wide for every foot
of the diameter of the stone. Such wheels are generally
18 feet diameter; the number and dimensions of their parts
being as follows : 8 arms 18 feet long, 3 1-4 by 9 inches;
16 shrouds 8 feet long, 2 1-2 by 9 inches ; 56 buckets ;
and shaft, 2 feet diameter.

Fig. 2. shows the forebay, water-gate, and fall, and
manner of striking on the water.

Fig. 3. is a middling breast-wheel 18 feet diameter,
with 12 feet head and fall. It should be 8 inches wide
for every foot the stone is in diameter.

Fig. 4. shov. s the forebay, gate and fall, and manner of
striking on the water.

Fig. 5. and 6. is a high breast-wheel, 16 feet diameter,
with 3 feet head in the forebay, and 10 feet fall. It
should be 7 inches wide for every foot the stone is in
diameter. The number and dimensions of its parts are,
6 arms 16 feet long, 3 1-4 by 9 inches ; 12 shrouds 8
feet 6 inches long, 2| by 8 or 9 inches deep, and 48
buckets.

QF PITCH-BACK WHEELS, &c. 305

ART. 5.

OF PITCH-BACK WHEELS;

Pitch back wheels are constructed exactly similar to
breast- wheels, only the water is struck on them higher.
Fig. 1, plate XV, is a wheel 18 feet diameter, with 3 feet
head in the penstock, and 16 feet fall below it. It should
be 6 inches wide for every foot of the diameter of the
stone.

Fig. 2 shows the trunk, penstock, gate, and fall, the
gate sliding on the bottom of the penstock, and drawn by
the lever A, turning on a roller. This wheel is much
recommended by some mechanical philosophers, for the
saj^g of water ; but I do not join them in opinion, but
think that an overshot with an equal head and fall, is
fully equal in power; besides the saving of the expense of
so high a wheel and fall, that are difficult to be kept in
order.

ART. 6.

OF OVERSHOT WHEELS.

Overshot wheels receive their water on tlie top, being-
moved by its weight ; and are much to be recommended
where there is fall enough for them. Fig. 3 represents
one 18 feet diameter, which should be about 6 inches
wide for every foot the stone is in diameter. It should
hang 8 or 9 inches clear of the tail water, because they
draw it under them. The head in the penstock should
be generally about 3 feet, which will spout the water
about 1-3 faster than the wheel moves. Let the shute
have about 3 inches fall, and direct the water into the
wheel at the centre of its top.

I have calculated a table for gearing overshot wheels,
which will equally well suit any of the others of equal
diameter, that have equal heads above the point where
the water strikes the wheel.

a06 OF OVERSHOT WHEELS.

Dimensions of this wheel, 8 arms 18 feet long, 3 by 9
inches ; 16 shrouds 7 feet 9 inches long, 2| by 7, or S
inches ; 56 buckets, and shaft, 24? inches diameter.

Fig. 4 represents the penstock and trunk, &c. the
water being let on the v\ heel by drawing the gate G.

Fig. 1 and 2 plate XVI, represents a low overshot 12
feet diameter, which should be in width equal to the dia-
meter of the stone. Its parts and dimensions are, 6 arms
12 feet long, 3f by 9 inches ; 12 shrouds 6| feet long,
2 1 by 8 inches ; shaft 22 inches diameter, and 30
buckets.

Fig. 3 represents a very high overshot 30 feet diameter,
which should be 3| inches wide for every foot of the
diameter of the stone. Its parts and dimensions are, 6
main arms, 30 feet long, 3| inches thick, 10 inches ^jde
at the shaft, and 6 at the end; 12 short arms 14 wet
long, of equal dimensions ; which are framed into the
main arms near the shaft, as in the figure ; for if they
were all put through the shaft, they would make it too
weak. The shaft should be 27 inches diameter, the
wheel being very heavy and bearing a great load. Such
high wheels require but little water.

ART. 7.
OF THE MOTION OF OVERSHOT WHEELS.

After trying many experiments, I concluded that the
circumiference of overshot wheels geared to mill-stones,
grinding to the best advantage, should move 530 feet in
a minute ; and that of the stones 1375 feet in the same
time ; that is, ivhile the wheel moves 12, the stone moves
30 inches, in the proportion of 2 to 5.

Then, to find how often the wheel we propose to make
w^ill revolve in a minute, take the following steps : 1st,
Find the circumference of the wheel by multiplying the
diameter by 32, and dividing by 7, thus :

OF GEARING.

sor

Suppose the diameter to be 16 feet,"1
then 16 multiplied by 22, produces I
332; which, divided by 7, quotes [
50 2-7 for the circumference. J

By which we divide 550, the distance^
the wheel moves in a minute, and it j
quotes 11, for the revolutions of the >
wheel per minute, casting off the frac- j
tion 2-7, it being small. J

To find the revolutions of the stone ^
per minute, 4? feet 6 inches (or 54 I
inches) diameter, multiply 51 inches I
by^, and divide by 7, and it quotes '
16T5-7 (say 170) inches, the circum-
ference of the stone.

By which divide 1375 feet, or 16500
inches, the distance the skirt of the
stone should move in a minute, and .
it quotes 97; the revolutions of a [
stone per minute, 4 1-S feet diame
ter.

To find how often the stone revolves"]
for once of the water wheel, divide 97,
the revolutions of the stone, by 11, the >
revolutions of the wheel, and it quotes |
8 9-il, (say 9 times.) J

7 )352
50 2T

5(0)5510
11 times,

108

7) 1188

16y 5T

17lO)1650iO(9/
153
120
119

11)97(89-11
88

ART. 8.
OP GEARING.

Now if the mill was to be single geared, 99 cogs and
11 rounds, would give the stone the right motion, but
the cog-wheel would be too large, and trundle too small,
therefore it must be double geared.

308

OF GEARING.

8441, not quite

25
15

125

375

528

264

375)3168(8168-375
3000
168

Suppose we choose 66 cogs in the
big cog-wheel and 48 in the httle one,
and 25 rounds in the wallower, and 15
in the trundle.

Then, to find the revolutions of the
stone for one of the \Aater- wheel, mul- y
tiply the cog-wheels together, and the
wallower and trundle together, and
divide one product by the other, and it
will quote the answer,
8 1 revolutions instead of 9

Therefore we must make another proposition — Consi-
dering which of the wheels we had best alter, and wish-
ing not to alter the big cog-wheel nor trundle, we put
one round less in the wallower, and two cogs more imthe
little cog-wheel, and multiplying and dividing as before,
we find the stone vvill turn 9 1-6 times for once of the
water-wheel, which is as near as we can get. The mill
now stands thus, a 16 foot overshot wheel, that will re-
volve 11 times in a minute, geared to a stone 4 l-2> feet
diameter; the big cog-wheel 66 cogs, 4 12 inches from
centre to centre of the cogs; (which we call the pitch of
the gear) little cog-wheel 50 cogs 4| pitch; wallower 2^
rounds, 4| pitch, and trundle 15 rounds, 4^ inches
pitch.

ART. 9.
RULES FOR FINDING THE DIAMETER OF THE PITCH CIRCLES.

To find the diameter of the pitch "|
circle, that the cogs stand in, multiply I
the number of cogs by the pitch, |
which gives the circumference; which, I
multiplied by 7, and divided by 22, f
gives the diameter in inches; which,
divided by 12, reduces it to feet and
inches thus :

_4|

264

297

22)2079(94^ in.
198

99
88
11

RULES FOR FINDING THE DIAMETER, &c. 309

For the cos^-wheel of 66 cogs, 4| pitch, we find to be 7

feet 10 1 1 -S3 inches, the diameter of the pitch circle ; to

which I add 8 inches, for the outside of the cogs, makes 8

feet 6| inches, the diameter from out to out.

By the same rules I find the diameters of the pitch

circles of the other wheels, to be as follows, viz.

ft. in.

Little coar- wheel 50 coffs, 40 t ^n m oo
.,^vr &'2C 5 71 10-22 p. cir.

mches pitch, ^ z i

I add for the outside of the circle, 7|

Total diameter from out to out 6 3

Wallower 24 rounds 41 inches 7 o n o >« ^ <nr^

rftch, S 2 113-4 4-22

Acid for outsides, 3 18-22 do.

Total diameter from the outsides, 3 3

Trundle head 15 rounds 4| inch 7 . 8^ ^ 22 d

pitch, 3 "^ '

Add for outsides, S| 19 32

Total diameter for the outsides, 111

Thus we have completed the calculations for one mill,
with a 16 feet overshot water-wheel, and stones 41 feet
diameter. By the same rules we may calculate for wheels
of all sizes from 12 to 30 feet, and stones from 4 to 6
feet diameter, and may form tables that may be of great
use to many, even to master- workmen that understand
©alculating well in despatching of business, in laying out
work for their apprentices and other hands, getting out
timber, &c. but more especially to those who are not
learned in arithmetic sufficient to calculate, I beinar from
long experience highly sensible of the need of such a
table, have therefore undertaken the arduous task.

310 EXPLANATION OF THE TABLES.

MILL- WRIGHTS' TABLES,

Calculated to suit overshot water-wheels with suitable
heads above them, of all sizes from IS to 30 feet diame-
ter, the velocity of their circumferences being about 550
feet per minute, showing the number of cogs and rounds
in all the wheels, double gear, to give the circumference
of the stone a velocity of 1375 feet per minute, also the
diameter of their pitch circles, the diameter of the out-
sides, and revolutions of the water-wheel and stones per
minute.

For particulars see what is written over the head of
each table. Table I, is to suit a 4 feet stone, table II, a
41, table III, a 5 feet, and table IV, a 5| feet stone.

N. B. If the stones should be an inch or two biggeiior
less than those above described, make use of the table
that comes nearest to it, and likewise for the water-wheels.
For further particulars see draughting mills.

Use of the folio-wing Tables.

Having levelled your mill-seat and found the total fall,
after making due allowances for the fall in the races, and
below the wheel, suppose there is SI feet 9 inches, and
the mill- stones are 4 feet diameter, then look in table I,
(which is for 4 feet stones) column 3, for the fall that is
nearest yours, and you find it in the 7th example : and
against it in column 8, is the head proper to be above the
wheel 3 feet, in column 4 is 18 feet, for the diameter of
the wheel, &c. for all the proportions of the gears to make
a steady moving mill, the stones to revolve 106 times in
a minute.*

• The following tables are calculated to give the stones the revolution
per minute mentioned in them, as near as any suitable numberof cogs and
rounds would permit, which motion 1 find is 8 or 10 revolutions per minute
slower than proposed by Evans in his table;— his motion may do best in
cases where 'here is plenty of power and steady work on one kind of gram ;
but in country mills, where they are continually changing from one kind
to another, and often starting and stopping, I presume a slow motion will
work most regular. His table bemg calculated for only one size of mill-
stones, and mine for four, if any choose his motion, look for the width of
the water-wheel, number of cogs, and rounds and size of the wheels to
suit them, in the next example following, keeping to my table in other re-
spects, and you will have his motion nearly-

TABLES, &c.

311

TABLE I. For Overshot Mills with Stones 4 feet Diameter, to revolve 106
times in a minute, pitch of the gear of great cog wheel and wallowers
4i inches, and of lesser cog wheel and trundle 4i inches.

1-1

O Ol

5 "i 1

-•c 2.'

p'
3

o
re" ^

cr? 3
t n

& 5

n
M

if?

ft "3 r-

re
T (ft

2 c

2.1
2 ^

re 3q

2 "5.

I2.

I-
o-o.

DO "^

? i '

re "'•
* crs)

• ft ft

3 ->

re ?

2 T

en rV
re O

-J 3"

re re

re->

- *

ft t9

I« f?

*••

re
re

So"

re
re aq

I2.

re T
re o_
10 re"
• »

rt 2-

* re

p,
5"

■ &
n
re

U* "^

^-5

-1

t'c. in.

f i.

feet.

f. i.

f. in.

f. i

f. i.

*15,3

2,6

=." r^^

7,10 5
5,4 87

8,6.5
6,0.5

25
15

2,11.75
1,833

3,3
1,11.33

16,4

2,7

^A%

8,233
5,4 87

8,10.33
6,0.5

25
15

2,1175
1,8.33

3,3
1.11.33

12.5

17,5

2,8

2.« ffs

8,2 33
5,4.87

8,10 33
6,0.5

26
15

3,125
1,8.33

3,5.25
1,1133

18,6

2,9

^.-^ Is

8,2.33
5,7.5

8,10.33
6,3

25
15

2,1175
1,833

3,3
1,11.33

11.5

19,7

2,10

2 4 r^2

'''^ \ 52

8,7.25
5,10.33

9,3
6,6

26
15

3,1.25
1,8 33

3,5.25
1,11.33

20,8

2.11

2.3 r.^

8,7.25
5,10.33

9,3
6,6

25
14

2.1175
1.7

3,3
1,10

10.5

21,9

3,0

2.^ |S

8.7.25
5.10.33

9,3
6.5

24
14

2,10 33
1.7

3,1.5
1,10

22,10

3.1

^>^ 1^5^

8,11.33
5,10.33

9,7.33
6,6

24
14

2,10.33
1,7

3,1.5
1.10

9.66

23,11

3,2

2.0 r^^

8,11.33
5,10.33

9,7.33
6,6

23
14

2,9
1,7

3,0
1,10

9 25

25,1

3,4

^.^^ U^

9,35
5,10.33

9,115
6,6

24
14

2,1033
1,7

3.1.5
1,10

8.87

26,3

3,6

^10 rs

9,3.5
5,1033

9,115
6,6

23
14

2,9
1.7

3,0
1,10

27,5

3,8

^.^ L^^

9,3.5
6,1

9,11.5
6,8.5

23
14

2,9
1,7

3,0
1,10

825

28,7

3,10

^.B f^l

9,8
6,1

10,4
6,8.5

23
14

2,9
1.7

3,0
1.10

29,9

4,0

-^ U^

9,8
6,3 75

10,4
6,11.25

23
14

2,9
1,7

3.0
1,10

7.75

30,11

4,2

l.« f5^^

10,0.25
6,3.75

10,8 25
6,11.25

23
14

2,9
1,7

3,0
1,10

7.5

32,1

4,4

15 r-^

10,0 25

10.8.25

2,9

3,0

6.75

6,6 25

7,175

',7

1.10

OOyO

4.6

14 r^^

'.* J 5f

10,0.25

10,8.25

2,9

3,0

6.66

6,3 75

6,11.25

1,5.25

1,8.25

34,6

4,9

13 r^

10,0.25

10,8.25

2.7 5

2,10.5

6.5

^'•^ V.56

6,3.75

6,1125

1.5.25

1,8.25

35,9

5,9

1.2

C87
t56

10,5
6 3 75

11 1
6,1125

22
13

2.7.5
1,5 25

2,10 5
1,825

6 25

31?

TABLES, &c.

TABLE II. For Overshot Mills with Stones 4 feet 6 inches Diameter, to
revolve 99 times in a minute, pitch of the gems 4A inches and 4i in-
ches.

2; c

»;

^' O X

—

c 75 5

.re

- -5p

a 3

? 3

fii

ft
re

— 2.

? re

-3 £
re _.

S3 ~j

*.- -T

n _
t c

2 c_

n _

re o

—

n "^

re"H.

3- =

-a
1 -

to >-•

Zl re

c a,

3 i
re ^

3 "■

2 "

~' £

5 ft
=-75

« i-

to j:"

IT 5.

• re

-D_

05 ^

!■«

"* ^

? a-

'* s.

■< "

?r"^

r- »5

o d

— 2

= 2.

^2.

" «

-^ re
or p

f ^

2 «

o! re

5" r

^»

«5

—

r _o

• c_

►1

ft. in.

M il .

K-ei

ft. in.

ft. m.

ft -n

ft. in.

ft. PI.

7,10.5

8,6.5

1
3,1.25 ;3.4.25

15,3

2,6

5,4 87

6,0 5

1,833 1,11.33

16,4

2,7

3.^ 1^^

7,10 5
5,4.87

8.65
6,05

25
15

2,11.75'3,3
1,8.33 |l, 11.33

12.5

17,5

2,8

W {%

8,2.33
5.4 87

8.10 33
6,0.5

^6
15

3,1.25
1.8 33

3.4.25
1,11.33

18,6

2,9

3.0 ^^^

8.2.33
5,4 87

8,10.3,?
6,0.5

25
15

2,1175!3,3
1,833 !l.ll.5

115

19,7

2,10

^••0 {^2

8,2.33
5,7.87

8,10.53
6,3

25
15

2,11.75 3,3
1,8.33 1,11.5

20,8

2.11

^.s {S

8.7.25
5,10,33

9.3
6,6

26
15

3,125 3.4.25
i,833 1.115

l0 5

21,9

3,0

'.^ ^^^

8,725
5.10.33

9.3
6,6

25
14

2,11.75 3,3
1.7 1,11.5

22.10

3,1

'■* ^i

8,7.25
5,10.33

9,3
6,6

24
14

2.10 33 3,2 5
1,7 1.115

9.5

2,3 ^52

8,11.33

9.7.33

2.10.33 3,2.5 „ 1

23,11

3,2

5,10 33

6,6

1,7

1,11.5 ''

25,1

3,4

,. Ill

8,11.33
5,1033

9,7.33
6.6

23
14

2.9
1,7 ^^

.3,0 ' s
1,115 ^-^^

26,3

3,6

^A III

9,3.5
5,10.33

9,11.5
6,6

24
14

2,10.333,2.5 n-

1,7 ;i,ii.5 ^-^^

27,5

3.8

.,0 {g

9,3.5
5,10.33

9,11.5
6,6

23
14

2,9

1,7

3,0 ocr

1,11.5 "-^

28,7

3,10

-." v^

9,3.5
6.1

9,11.5
6,8.5

2-
14

2,9
1,7

3,0 a
1,11.5 **

29,9

4,0

MO ffl

9.8
6,1

10,4
6,8.5

23
14

2,y
1,7

^•^ 7 75
1,115 '^^

30,11

4,2

'.^ f.^J

9,8
6,3-25

10,4
6,11.25

2;i
14

2,9

1.7

3.U 7,
1,11.5 ^^

32,1

4.4

'.3 Ce

10.0 25
6,3 25

10.825
6.11.25

2,-">
14

2,9
1,7

1,115 ^'^

33,3

4,6

'.« {^^

10.0-25
6,625

10.8 25
7.125

23
14

2.9
1,7

3'^ 6 66
1,115 °-^^

■■= {It

10,025

10,8.25

.^ T

2,9

3,0 .^

34.6

4,9

6,3-25

6,1125

I 5.25 1,825 "" /

>.^ ir^

10.0 75

10.825

2,7.5 12,10 5 .,, J

35,9

5,0

6,325

6,11.25

13 i.5 2 5:l.b25 - "•' |

TABLES, &c.

313

TABLE III. Stones 5 feet Diameter, to revolve 86 times in a minute, the
pilch of the gears 4^ and 4^ incheS'

Zii

T> 3

< 3

<
O

■»5

-1

5 01

•a 5

— 2-

? 5

3 in

— o

2 o

q S.

n
-J O

"»»

T ZT -

" *

"Z. ^

o .■

O "^

ft -»i

f^ "^

c *

Bl -»J

a'o

» n ?

1 re

29 -^

^ ~

= 8

3 -

5-H.

S CO

s "*•

• n> 't

ifc

.^ IT

-«

? T

"^ «

O 3R

^ i

M *"

i* 3-

3
n

3 ~
cr ;^.

O O

n 3

3- j:

'5 t-
O -

r" f»

r -:
n

rti -!

o
=? 2.

3 O

C- n'

P -i
-» re

° n

».

2 (^
2, w

:?»

n
^

(0 ft

s- X

-■5

-»5

ft in.

r u

r,e

ft.WI.

fi. .n.

r Ml.

It in.

ft. til.

15.3

2,6

*.» |48

7,6.12
5,4.87

8.2.12
6.0.5

26
16

3,1.25
1,9 66

3,4.25
2.4.25

16,4

2,7

3.>0 J-

7.10.5
5,4.87

8.6.5
6,0 5

26
16

3,125
1,9 66

3,4.25
2,4.25

12.5

17.5

2,8

3.B ft^

7,10.5
5,4.87

8.6.5
6.0.5

25
15

2,11.75
1,8 33

3,3
1.11.33

18,6

2,9

^■^ ^^^

8,2 33
5,4 87

8,10 33
6,0.5

26
15

3,125
1,8.33

3,4.25
1,11.33

11.5

19,7

2,10

- A ?69
^'4 |48

8,2 33
5,4.87

8,10.3o
6,0 5

25
15

2,11.75
1,8.33

3,3
1.11.5

20,8

2.11

3.2 {f.

8,233
5,7.3

8,10.33
6,3

25
15

2,11.75

1,8.33

3,3
1.115

105

21,9

3.0

3.0 1^^

8.7.25
5,10,33

9.3
6,6

26
15

3,1.25
1,833

3,4.25
1,11.33

22,10

3.1

07'^

8,7 25

5,10.3.;

9.3
6.6

25
14

2,11.75
1,7

3,3
1,11.5

9 66

23,11

3,2

^■« p.^

8.7.25
5,1033

9,3
6,6

24
14

2,1033
1.7

3'^^ 9 25
1,11.5 ^'^^

25,1

3,4

2<^ J^^

8,11 33
5,10.33

9.7.33
6,6

J4
14

2,10 333,2.5
1.7 1,11.5

8 87

26,3

3,6

- Vsi

8,11.33
5,10.33

9,7.33
6,6

23
14

2.9
1.7

3,0
1.11.5

8.5

27,5

3,8

^■^ m

9,3.5

5,10.33

9,11.5
6,6

24
14

2.10.33
1,7

3.2.33
1,11.5

8.25

28,7

3,10

^■^ III

9,35
5,10 33

9.11.5
6,6

2.9
1.7

3,0
1,11.5

29,9

4,0

^■= m

9,3 5
6,1

9,11.5
6.8.5

23
14

2,9
1.7

3,0
1,115

7.75

30 11

4.2

2.0 ^?l

9,8
6,1

10,4
6,8 5

23
14

2,9
1.7

3,0
1,11.5

32.1

4,4

M. c^

9.8
6,3 25

10,4
6.1125

23
14

2.9
1.7

3,0
1.11.5

6.33

33,3

4,6

'.' Oa

10,0 25
6,3 25

10,8 25
6,1125

23
14

2.9
1.7

3,0
1,115

6.66

34,6

4.9

••' {%

10.0.25
6,6.25

10.8 25
7.125

23
14

2.9
1.7

?;?i.5 «^

35.9

5.0

•.<= i^J

10.0.25
6.3 25

10,8 25
6.1125

23
13

2,9
1,5.25

n.s ^-^^

j^ r

314,

TABLES, &c.

TABLE IV. For Overshot Mills with Stones 5 feet 6 inches Diameter, to
revolve 80 times in a minute, pitch of the gears 4| inches and 4i in
cbes.

o o 2

H
1^

.-5

-^ -^ 6-

' 3

Q-

S ^

^ 3

tfi

M O

p ft

'^ n
p -J

3 CO

n
1
ce

o ->

V £■

3 1'

= B'c

ft* as

= £.

CO J3

-J 01

IT o

= 2,

s-g.

1 O

s-i

5-^

ft
»4

f^l

O CO

-3

O V

o s

3 3

ce -*s
3 ^

— ■ n --
-3 w ^

2 7

rr-

O vq

— 3-
1 "

=1 ^

3 —

p 6:

ill

o re

re
2.

=r o

2. (D

zr
n
n

§0

CO n>

V! c

o o

o
a

f. i.

o
3

fe^-t.

r. I.

d
3

ft. in.

f. m.

f. 1.

f 1.

15,3

2,6

4g r60 7,6 75
*'° 1 48' 5,8 75

8,2.75
6,4 25

26
16

3,3.25
1,11

3,6-25

2,2

16,4

2.7

,. 1 63i 7,1112
*'* 1 48! 5,8 75

8,7.12

6,425

26
16

3,3 25
1,11

3,6.25
2,2

125

ir,5

*■= JS

8,3 75
5,875

8,1175

6,4 25

26
16

3,3.25
1,11

3,6.25
2,2

18,6

2.9

^.» U^

8.3.75
5,8,75

8,1175
6,4 25

26
15

3,3 25
1.9 5

3,6.25
2.0.5

11.5

i9.r

2,10

o 1f^ ^69

^.10 [48

8,8 33
5,8.75

9,4.33
6,4.25

26
15

3 3 25
1,9.5

3,6.25
2.0-5

20,8

2.11

-ft 1 69

8,8 33
5,8.75

9,4.33
6 4 25

25
1)

3,175
1,95

3,4-75
2,0.5

10.5

21,9

3,0

^.« f??

8,8.33
5,115

9,4 33
62 5

25
15

3,1 75
1,95

3,4.75
2,0.5

22,10 3,1

^■* Is

9.0.75
6,2.5

9,8 75
6,10

26
14

3,325
1,8

3,625
1,11

9.66

23,11 3,2

^•^ f^2

9,0.75
6,2.5

9,8.75
6,10

25
14

3 175
1,8

3,4-75
1,11

9 25

25,1 '3,4

=.» U^

9,0 75
6,2.5

9,8 75
6,10

24
14

3.0 75
1,8

3,3-75
1,11

8.12

26,3

3,6

''in r

9,5.33

10,1.33

3,075

3375

^,iu 1 ^2

6,2.5

6,10

1,8

1,11

27,5

3,8

2>3 Ui

9,5.33

6.2.5

10,1.33
6,10

23
14

2,10.75
1,8

3,1.75
1,11

825

28,7

3,10

^>« r^^

9,10.5
6,2.5

10,6
6,10

24
14

3,U.75
1,8

3,3.75
1.11

29,9

4,0

2.^ Is

9,10 5
6,25

10,6
6,10

23
14

2,10.75
1,8

3,1.75
1.11

7.75

30,11

4.2

9 r78

■''^ J 54

9,10 5
6,5.33

10,6
7,1

23
14

2,10 75
1,8

3,175
1,11

7.5

32.1

4,4

^0 r^

10,2.5

10,10.5

2,10.75

3,175

6.75

~'^ 1 54

6,5.33

7,1

1.8

1,11

33,3

4,6

■." j?J

10,2 5
6,8

10,10 5

7.:is

23
14

2,10.75
1,8

3,1-75
1,11

6.66

34,6

4,9

■.'» Is

10,7
6,8

11,3
7,3.5

23
14

2,1075
1,8

3,1,75
1,11

6.5

35,9

5,0

■.^ f^J

1U,7
6,11

113

7,6.5

23
14

2,10.75
1,8

3,1.75
1,11

6.25

OF CONSTRUCTim; WHEELS. 315

ART. 10.

V)IRECtlONS FOR CONSTRUCTING UNDERSHOT WHEELS, SUCH
AS FIG 1, PLATE XHI.

1. Dress the arms straight and square on all sides, and
find the centre of each ; divide each into 4- equal parts on
the side square centre scribe, and gauge them from the
upper side across each point, on both sides, 6 inches each
way from the centre.

S. Set up a truckle or centre-post, for a centre to frame
the wheel on, in a level place of ground, and set a stake
to keep up each end of the arms level with the truckle,
of convenient height to work on.

3. Lay the first arm with its centre on the centre of the
truckle, and take a square notch out of the upper side 3-4
of its depth, wide enough to receive the 2d arm.

4. Make a square notch in the lower edge of the 2d
arm, 1-4 of its depth, and lay it in the other, and they
will joint standing square across each other.

5. Lay the 3d arm just equi-distant between the others,
and scribe the lower arms by the side of the upper, and
the lower edge of the upper by the sides of the lower
arms. Then, take the upper arm off" and strike the
square scribes, taking out the lower half of the 3d arm,
and the upper half of the lower arms, and fit and lay them
together.

6. Lay the 4th arm on the others, and scribe as direct-
ed before ; then take 3-4 of the lower edge of the 4? h
arm, and 1-4 out of the upper edge of the others, and
lay them together, and they will be locked together in
the depth of one.

7. Make a sweep-staff with a gimblet hole for the
centre at one end, which must be set by a gimblet in the
centre of the arms. Measure from this hole half the di-
ameter of the wheel, making a hole there, and another the
depth of the *jhrouds towards the centre, making each
edge of this sweep at the end next the shrouds, straight
towards the centre hole, to scribe the ends of the shrouds
by.

8. Circle both edges of the shrouds by the sweep,

316 OF CONSTRUCTING WHEELS.

dress them to width and thickness, lay out the laps 5
inches long, set a gauge to a little more than 1-3 their
thickness, gauge all their ends for the laps from the out-
sides, cut them all out but the last, that it may be made
a little longer, or shorter, as may suit to make the wheel
the right diameter ; sweep a circle on the arms to lay the
shrouds to, while fitting them, put a small draw-pin in the
middle of each lap, to draw the joints close, strike a true
circle for both inside and outside the shrouds, and one

1 1-2 inch from the inside, where the arms are to be let in.

9. Divide the circle into 8 equal parts, coming as
near the middle of each shroud as possible ; strike a
scribe across each to lay out the notch by, that is to be
cut by 1 1 inch deep, to let in the arm at the bottom of
"where it is to be forked to take in the remainder of the
shroud. Strike a scribe on the arms with the same sweep
that the stroke on the shrouds for the notches was struck
with.

10. Scribe square down each side of the arms, at the
bottom of where they are to be forked ; make a gauge
to fit the arms, so wide as just to take in the shrouds, and
leave 1 1 inch of wood outside of the mortise ; bore 1 or

2 holes through each end of the arms to draw-pin the
shrouds to the arms when hung; mark all the arms and
shrouds to their places, and take them apart.

11- Fork the arms, put them together again, and put
the shrouds into the arms; drawbore them, but not too
much, which would be worse than too little ; take the
shrouds apart again, turn them the other side up, and
draw the joints together with the pins, and lay out the
notches for 4 floats between each arm, 32 in all, large
enough for admitting keys to keep them fast, but allow-
ing them to drive in when any thing gets under the
wheel. The ends of the floats must be dovetailed a little
into the shrouds ; when one side is framed, frame the
other to fellow it. This done, the wheel is ready to hang,
but remember to face the shrouds between the arms with
inch boards, nailed on with strong nails, to keep the
wheel firm together.

OF CONSTRUCTING WHEELS. 317

ART. 11.

DIRECTIONS FOR DRESSING SHAFTS, 5tc.

The shaft for a water-wheel with 8 arms should be
16 square, or 16 sided, about 2 feet diameter, the tree
to make it being 2 feet 3 inches at the top end. When
cut down saw it off square at each end and roll it on
level skids, and if it be not straight, lay the rounding
side down and view it, to find the spot for the centre at
each end. Set the big compasses to half its diameter,
and sweep a circle at each end, plumb a line across each
centre, and at each side at the circle, striking chalk lines
over the plumb lines at each side from end to end, and
•dress the sides plumb to these lines ; turn it down on
one side, setting it level ; plumb, line, and dress off the
sides to a 4 square ; set it exactly on one corner, and
plumb, line, and dress off the corner to 8 square. In the
same manner dress it to 16 square.

To cut it square off to its exact length, stick a peg in
the centre of each end, take a long square (that may be
made of boards) lay it along the corner, the short end
against the end of the peg, mark on the square where
the shaft is to be cut, and mark the shaft by it at every
corner line, from mark to mark ; then cut it off to the
lines, and it will be truly square.

ART. 12.

TO LAY OUT THE MORTISES FOF THE ARMS.

Find the centre of the shaft at each end, and strike a
circle, plumb a line through the centre at each end to be
in the middle of two of the sides ; make another scribe
square across it, divide the distance equally between
them, so as to divide the circle into 8 equal parts, and
strike a line from each of them, from end to end, in the
middle of the sides ; measure from the top end about
3 feet, and mark for the arm of the water-wheel, and
the width of the wheel, and make another mark. Take

318 OF CONSTRUCTING WHEELS.

a straight edge 10 feet pole, and put the end even with
the end of the shaft, and mark on it even with the marks
on the shaft, and by these marks measure for the arm
at ever}- corner, marking and lining all the way round.
Then take the uppermost arms of each rim, and by them
lay out the mortises, about half an inch longer than they
are wide, which is to leave key room ; set the compasses
a little more than half the thickness of the arms, and
set one foot in the centre line at the end of the mortise,
striking a scribe each way for to lay out the width by ;
this done, lay out 2 more on the opposite side, to com-
plete the mortises through the shaft. Lay out 2 more
square across the first, one quarter the width of the arm,
longer inward, towards the middle of the wheel. Take
notice which way the locks of the arms wind, whether
to right or left, and lay out the third mortises to suit,
else it will be a chance whether they suit or not : these
must be half the width of the arms, longer inwards.

The 4th set of mortises must be | longer inwards than
the width of the arms ; the mortises should be made
rather hollowing than rounding, that the arms may slip
in easily and stand fair.

If there be three (which are called 6) arms to the cog-
wheel, but 1 of them can be put through the sides of the
shaft fairly ; therefore, to lay out the mortises, divide the
end of the shaft anew, into but 6 equal parts, by striking
a circle on each end ; and without altering the compasses,
step from one of the old lines, six steps round the circle,
and from these points strike chalk lines, and they will be
the middle of the mortises, which may be laid out as
before, minding which way the arms lock, and making
2 of the mortises 1-3 longer than the width of the arm,
extending 1 on one side, and the other on the other side
of the middle arm.

If there be but 2 (called 4) arms in the cog-wheel,
(which will do where the number of cogs do not exceed
60) they will pass fairly through the sides, whether the
shaft be 12 or 16 sided. One of these must be made
one half longer than the width of the arms, to give room
to put the arm in.

OF CONSTRUCTING WHEELS. -319

ART. 13.
TO PUT IN THE GUDGEONS.

Strike a circle on the ends of the shaft to let on the end
bands ; make a circle all round 2 1-2 feet from each end,
and saw a notch all round half an inch deep. Lay out a
square round the centres the size of the gudgeons, near
the neck ; lay the gudgeons straight on the shaft, and
scribe round them for their mortises ; let them down
within 1-8 of an inch of being in the centre. Dress off
the ends to suit the bands ; make 3 keys of good season-
ed white oak, to fill each mortise above the gudgeons,
to key them in, those next to the gudgeons to be 3 i-i
inches deep at their inner end, and 11-2 inch at their
outer end, the wedge or driviug key 3 inches at the head,
and 6 inches longer than the mortise, that it may be cut
off if it batters in driving ; the piece next the band so
wide as to rise half an inch above the shaft, when all are
laid in. Then take out all the keys and put on the
bands, and make 8 or 12 iron wedges about 4 inches
long by 2 wide, 1-3 inch thick at the end, not much ta-
pered except half an inch at the small end, on one side
next the wood ; drive them in on each side the gudgeon
exceeding hard at a proper distance with a set. Then
put in the k6ys again, and lay a piece of iron under each
band between it and the key 6 inches long, half an inch
thick in the middle, and tapering off at the ends ; then
grease the keys well with tallow and drive it well with
a heavy sledge : after this drive an iron wedge half an
inch from the two sides of each gudgeon 5 inches long,
near half an inch thick, and as wide as tl^e gudgeon.

ART. 14.

OF COG-WHEELS.

The great face cog-wheels require 8 (called 6) arms,
if the number of cogs exceed 54, if less 4 will do. We

320 OF CONSTRUCTING WHEELS.

find by the table, example 43, that the cog-wheel must
have 69 cogs, with 4 1-2 inches pitch, the diameter of
its pitch circle 8 feet 2 1-3 inches, and of its outsides 8
feet 10 1-3 inches. It requires 3 arms 9 feet long, 14
by 3 3-4 inches ; 12 cants 6 1-2 feet long, 16 by 4 in-
ches. See it represented plate XVII, fig. 1.

To frame it, dress and lock the arms together, as fig.
6) as directed art. 10, only mind to leave 1-3 of each
arm uncut, and to lock them the right way to suit the
winding ©f the mortises in the shaft, which is best found
by putting a strip of board in the middle mortise, and
supposing it to be the arm, mark which way it should
be cut, then apply the board to the arm, and mark it.
The arms being laid on a truckle as directed art. 10,
triake a sweep the sides directing to the centre, 2 feet
from the out end to scribe by ; measure on the sweep
half the diameter of the wheel, and by it circle out the
back edges of the cants, all of one width in the mid-
dle ; dress them, keeping the best faces for the face side
of the wheel ; make a circle on the arms 1-2 an inch
larger than the diameter of the wheel, laying 3 of the
cants with their ends on the arms at this circle at equal
distance apart. Lay the other three on the top of them,
so as to lap equally, scribe them both under and top,
and gauge all for the laps from the face side ; dress
them out and lay them together, and joint them close ;
draw-pin them by an inch pin near their inside corners :
this makes one half of the wheel shown fig. 5. Raise
the centre level with that half, strike a circle near the
outside and find the centre of one of the cants ; then,
with the sweep that described the circle, step on the cir-
cle 6 steps, beginning at the middle of the cant, and these
steps will show the middle of all the cants or places for the
arms. Make a scribe from the centre across each; strike
another circle exactly at the corners, to place the corners
of the next half by, and another about 2| inches farther
out than the inside of the widest part of the cant, to let the
arms in by ; lay on three of the upper cants, the widest
part over the narrowest part of the lower half, the inside
to be at the point where the corner circle crosses the cen-
tre lines. Saw off the ends at the centre scribes, and fit

OF CONSTRUCTING WHEELS. 321

them down to their places, doing the same with the rest.
Lay them all on, and joint their ends together ; draw pin
them to the lower half by inch pins, 2 inches from their
inmost edges, and 9 inches from their ends. Raise the
centre level with the wheel; plane a litde of the rough off
the face, and strike the pitch circle and another 4 inches
inside for the width of the face; strike another very neav
it, in which drive a chisel half an inch deep all round,
and strike lines with chalk in the middle of the edge of
the upper cants, and cut out of the solid half of the up-
per cants, which raises the face ; divide the pitch circle
into 69 equal parts, 4| inches pitch, beginning and
ending in a joint; strike two other circles each 2 1-2
inches from the pitch circle, and strike central scribes
between the cogs, and where they cross the circles put
in pins, as many as there are cogs, half on each circle;
find the lowest part on the face, and make the centre le-
vel Mith it; look across in another place square with
the first, and make it level with the centre also ; then
make the face straight from these 4? places, and it will
be true.

Strike the pitch circle, and divide it over again, and one
of each side of it, 1 inch distance for the cog mortises;
sweep the outside of the wheel and inside of the face, and
two circles 3-4 of an inch from them, to dress off the cor-
ners ; strike a circle of two inches diameter on the centre
of each cog, and with the sweep strike central scribes
at each side of these circles for the cog mortises ; bore
and mortise half through ; turn the wheel, dress and mor-
tise the back side, leaving the arms from under it ; strike
a circle on the face edge of the arms, equal in diameter
to that struck on the face of the half wheel, to let them
in by; saw in square and take out 4| inches, and let
them into the back of the wheel 11-4 inch deep, and
bore a hole 11-2 inch into each arm, to pin it to the
wheel.

Strike a circle on the arms one inch less than the dia-
meter of the shaft, make a key 8 inches long. If thick,
3 1 at the butt, and 2| inches at the top end, and by it lay
out the mortises ; two on each side of the shaft, in each
arm to hang the wheel by.

s s

gl2 OF SILLS, SPUR-BLOCKS, &c.

ART. 15.

OF SILLS, SPUR-BLOCKS, AND HEAD-BLOCKS.

See a side view of them in plates XIII, XIV, XV, and
XVI, and a top view of them with their keys at the end
of the shaft, plate XVIII. The sills are generally 12
inches square. Lay them on the wall as firm as possible^
and one 3 feet farther out, on these lay the spurs, which
are 5 feet long, 7 by 7 inches, 3 feet apart, notched and
pinned to the sills ; on these are set the head-blocks, 14 by
12 inches, 5 feet long, let down with a dove-tail shoulder
between the spurs, to support keys to move it endways,
and let 2 inches into the spurs with room for keys, to move
it sideways, and hold it to its place ; see fig. 33 and 34*,
plate XVIII. The ends of the shaft are let 2 inches into
the head- blocks, to throw the weight more on the centre.

Provide two stones 5 or 6 inches square, very hard
and clear of grit, for the gudgeons to run on, let them
into the head-blocks, put the cog-wheel into its place,
and then put in the shaft on the head-blocks in its place.

Put in the cog-wheel arm, lock them together and pin
the wheel to them ; then hang the wheel first by the keys,
to make it truly round, and then by side wedges, to
make it true in face ; turn the wheel, and make two cir-
cles one on each side of the cog-mortises, half an inch
from them, so that the head of the cogs may stand be-
tween them equally.

ART. 16,

OF COGS; THE BEST TIVIE FOR CUTTING, AND WAY OF SEA-
SONING THEM.

They should be cut 14 inches long, 3 1-4 inches
square, when the sap runs at its fullest, which should be
done at least a year before they are used, that they may
dry without cracking. If either hickory or white-oak is
cut when the bnrk is set, they will worm-eat, and if
dried hastily, will crack ; to prevent which, boil them

* OF COGS. 32^

and dry them slowly, or soak them in water, a year, (SO
years in mud and fresh water would not hurt them ;)
when they are taken out they should be put in a hay-
Ynow under the hay, which when foddered away they
will dry without cracking ; but this often takes too long
time. I have discovered the following method of dry-
ing them in a few days without cracking : I have a malt-
kiln with a floor of laths two inches apart. I shank the
cogs, hang them shank downwards, between the laths
cover them with a hair-cloth, make a wood fire, and the
smoke preserves them from cracking. Some dry them
in an oven, which ruins them. Boards, planks, or
scantling are best dried in a kiln, covered so as to keep
the smoke amongst them. Instead of a malt kiln, dig
a cave in the side of a hill, 6 feet deep, 5 or 6 feet wide,
with a post in each corner with plates on them, on
which lay laths on edge, and pile the cogs on end near-
ly perpendicular, so that the smoke can pass freely
through or amongst them. Cover slighdy with boards
and earth, make a slow fire and close up the sides, and
renew the fire once a day for 12 or 15 days, they will
dry without cracking. Experienced by James Dellet,
Mill-wright.

ART. 17.

OF SHANKING, PUTTING IN, AND DRESSING OFF COGS.

Straighten one of the heart sides for the shank, make a
pattern, the head 4 and shank 10 inches long, and 2 inches
wide at the head, 1| at the point; lay it on the cog,
scribe the shank and shoulders for the head, saw in and
dress off the sides ; make another pattern of the shank,
without the head, to scribe the sides and dress off the
backs by, laying it even with the face, which is to have no
shoulder ; take great care in dressing them off, that thq
axe does not strike the shoulder, if it does it will crack
there in drying (if they be green) ; fit and drive them in
the mortises exceeding tight, with their shoulders fore-
most when at work. When the cogs are all in, fix two

324 OF THE LITTLE COG WHEEL AND SHAFT

pieces of scantling for rests, to scribe the cogs by, one
across the cog-pit near the cogs, another in front of them,
fix them firm. Hold a pointed tool on the rest, and
scribe for the length of the cogs b}^ turning the wheel,
and saw them off 3| inches long ; then move the rest
close to them, and fix it firm ; find the pitch circle on
the end of the cogs, and by turning the wheel describe
it there.

Describe another | of an inch outside thereof, to set
the compass in to describe the face of the cogs by, and
another at each side of the cogs to dress them to their
width : then pitch the cogs by dividing them equally, so
that in stepping round, the compasses may end in the
point wiiere they began ; describe a circle in some par-
ticular place with the pitch that it may not be lost ; these
points must be as near as possible, of a proper distance
for the centre from the back of the cogs ; find the cog
that this point comes nearest to the back, and set the
compasses from that point to the back of the cog, and
with this distance set off the backs of all the cogs equal-
ly, on the circle 1-4 of an inch outside of the pitch cir-
cle, and from these points last made, set off the thick-
ness of the cogs, which should be 2 1-8 inches in this
case.

Then describe the face and back of the cogs by setting
the compasses in the hindmost point of one cog, and
sweeping over the foremost point of another for the face,
and in the foremost point of one, sweeping over the hind-
most of the other, for the back part ; dress them ofi" on
all sides, tapering about 1-8 of an inch in an inch dis-
tance, try them by a gauge to make them all alike, take
a little of the corners off, and they are finished.

ART. 18.
OF THE LITTLE COG-WHEEL AND SHAFT.

The process of making this is similar to that of the big
cop;- wheel- Its dimensions we find by the table, and the
same example 43, to be 52 cogs, 4 1-4 pitch. Diameter
of pitch circle 5 feet 10 1-3 inches, and from out to out
6 feet 6 inches.

OF WALLOWERS AND TRUNDLES. 325

It requires 3 arms 6 feet 6 inches long, 11 by 3|
inches; 8 cants f> feet 6 inches, 17 by 3| inches. See
it, plate XVII, fig. 4.

Of the Shaft.

Dress it 8 feet long, 14 by 14 square, and describe a
circle on each end 14 inches diameter; strike two lines
through the centre parallel to the sides, and divide the
quarters into 4 equal parts each ; strike lines across the
centre at each part at the end of these lines ; strike chalk
lines from end to end to hew off the corners by, and it
will be 8 square ; lay out the mortises for the arms, put
on the bands, and put in the gudgeons, as with the big
shaft.

ART. 19.
DIRECTIONS FOR MAKING WALLOWERS AND TRUNDLE^.

By example 43 in the table, the wallower is to have
26 rounds 4| pitch. Diameter of its pitch circle is 3
feet 1| inch, and 3 feet 4| inches from outsides: see
fig. 3. plate XVII. Its head should be 3^ inches thick,
doweled truly together, or made double with plank cross-
ing each other. Make the bands three inches wide, 1-6
of an inch evenly drawn; the heads must be made to
suit the bands, by setting the compasses so that they
will step round the inside of the band in 6 steps; with
this distance sweep the head, allowing about 1-16 of an
inch outside in dressing to make such a large band tiojht.
Make them hot alike all round with a chip fire, which
swells the iron; put them on the head while hot, and
cool them with water to keep them from burning the
wood too much, but not too fast lest they snap : the same
for hooping all kinds of heads.

Dress the head fair after banded, and sti-ike the pitch
circle and divide it by the same pitch of the cogs ; bore
the holes for the rounds with an auger at least 1 1 inch ;
make the roimds of the best wood 2 3-8 inches diame-

m OF HANGING WHEELS, he.

ter, and 1 1 inches between the shoulders, the tenons 4
inches, to fit the holes loosely until within 1 inch of the
shoulder, then drive tight. Make the mortises for the
shaft in the heads, with notches for the keys to hang it
by. When the rounds are ajl drove in to the shoulders,
observe whether they stand straight, if not, they may be
set fair by putting the wedges nearest to one side of the
tenon, so that the strongest part may incline to draw them
straight : this should be done with both heads.

ART. 20.

OF FIXING THE HEAD BLOCKS AND HANGING THE WHEELS.

The head blocks for the wallower shaft, are shown in
plate XVIII. Number 19 is one called a spur, 6 feet
long and 15 inches deep, one end of which at 19 is let
one inch into the top of the husk-sill, which sill is 1| inch
above the floor, the other end tenoned strongly into a
strong post 14 by 14 inches, 12 or 14 feet long, standing
near the cog- wheel on a sill in the bottom of the cog- pit;
the top is tenoned into the husk-plank; these are called
the tomkin posts. The other head-blocks appear at 20
and 38. In these large head-blocks there are small ones
let in, that are 3 feet long and 6 inches square, with a
stone in each for the gudgeons to run on. That one in
the spur 19 is made to slide, to put the wallower out and
in gear by a lever screwed to its side.

Lay the centre of the little shaft level with the big
one, so as to put the wallower to gear 2-3 the thickness
of the rounds deep into the cog-wheel; put the shaft
into its place and hang the wallower, and gauge the
rounds to equal distance where the cogs take. Hang the
cog-wheel, put in the cogs, make the trundle as directed
for the wallower. See plate XVII, fig. 4.

ART. Si.
DIRECTIONS FOR PUTTING IN THE BALANCERYNE.

Lay it in the eye of the stone, and fix it truly in the
centre ; to do which make a sweep by putting a long pin

OF SINKING THE BALANCE-RYNE. S2?

through the end to reach into and fit the pivot hole in
the balance ryne ; by repeated trials on the opposite sides
fix it in the centre ; then make a particular mark on the
sweep and others to suit it on the stone, scribe round
the horns, and with picks and chisels sink the mortises
to their proper depth, trying by the sweep if it be in the
centre, by the particular marks made for the purpose.
Put in the spindle with the foot upwards and the driver
on its place, while one holds it plumb. Set the driver
over two of the horns, if it has four, but between them
if it has but two. When the neck is exactly in the cen-
tre of the stone, scribe round the horns of the driver,
and let it into the stone, nearly to the balance, if it has
four horns. Put the top of the spindle in the pivot-hole
to try whether the mortses let it down freely on both
sides.

Make a tram to set the spindle square by, as follows :
take a piece of board, cut a notch in one side, at one
end, and hang it on the top of the spindle, by a little peg
in the shoulder of the notch, to go in the hole in the
foot to keep it on, let the other end reach down to the
edge of the stone, take another piece, circle out one end
to fit the spindle neck, and make the other end fast to
the lower end of the hanging piece near the stone, so as
to play round level with the face of the stone, resting on
the centre-hole in the foot, and against the neck, put a
bit of quill through the end of the level piece, that will
touch tlie edge of the stone as it plays round. Make
litde wedges and drive them in behind the horns of the
driver, to keep both ends at once close to the sides of
the mortises they bear against when at work, keeping
the pivot or cock-head in its hole in the balance, try the
tram gently round, and mark where the quill touches the
stone first, and dress off" the bearing sides of the mortises
for the driver until it will touch equally round, giving
the driver liberty to move endways and sideways to let
the stone rock an inch any way. The ryne and driver
must be sunk 3-4 of an inch below the face of the stone.
Then hang the trundle firmly and truly on the spindle,
put it in its place to gear in the little cog-wheel.

'S28 OF BRIDGING THE SPINDLE, &c.

ART. S2.

TO BRIDGE THE SPINDLE.

Make a little tram of a piece of lath, 3 inches wide at
one end, and 1 inch at the other, make a mortise in the
wide end, and put it on the cock-head, and a piece of
quill in the small end, to play round the face of the stone :
then, while one turns the trundle, another observes where
the quill touches first, and alters the keys of the bridge-
tree, driving the spindle-foot toward the part the quill
touches, until it touches equally all round. Case the
stone neatly round within 2 inches of the face-.

ART. 23.
OF THE CRANE AND LIGHTER-STAFF.

Make a crane for taking up and putting down the stone,
with a screw and bale. See it represented in Evans's
part, pi. XI. fig. 2 and 3. Set the post out of the way as
much as possible, let it be 9 by 6 inches in the middle, the
arm 9 by 6, brace 6 by 4, make a hole plumb over the
spindle, for the screw, put an iron washer on the arm
under the female screw, nail it fast, the screw should be
above half the diameter of the stone, in the worm, and
10 inches below it, the bale to touch only at the ends to
give the stone liberty to turn, the pins to be 7 inches long,
11-8 thick, the bale to be 2| inches wide in the middle,
and 1| inch wide at the end ; all of the best iron, for
if either of them break the danger would be great. The
holes in the stone should be nearest the upper side of
it. Raise the runner by the crane, screw and bale, turn
it and lay it down, with the horns of the driving ryne in
their right places, as marked, it being down, as appears
in pi. XXI. fig. 9. Make the lighter-staff C C to raise
and lower the stone in grinding, about 6 feet long, 3|
by 21 inches at the large end, and 2 inches square at
the small end, with a knob on the upper side. Make a
mortise through the butt end for the bray-iron to pass

OF MAKING A HOOP FOR THE MILL-STONE. 329

throus^h, which goes into a mortise 4 inches deep in the
end of the bray at b, and fastened with a pin; it may be
2 inches wide, half an inch thick, a plain bar with one
hole at the lower end, and 5 or 6 at the upper end, set in
a staggering position. This lighter is fixed in front of the
meal-beam, at a proper height to be handy to raise or
lower at pleasure ; a weight of 4 lb. is hung to the end of
it by a strap, that laps two or tliree times round, and the
other end fastened to the post below, that keeps it in its
place. Play the lighter up and down, and observe whe-
ther the stone rises and falls flat on the bed-stone, if it
does, draw a litde water, and let the stone move gently
round, then see that all things be right, and draw a little,
more water, let the stone run at a middling rate, and
grind the faces a few minutes.

ART. S4.
DIRECTIONS FOR MAKING A HOOP FOR THE MILL STONE.

Take a white pine or poplar board, 8 inches longer
than will go round the stone, and 2 inches wider than
the top of the stone is high, dress it smooth, and gauge
it one inch thick, run a gauge mark 1-6 of an inch from
the outside, divide the length into 52 parts, and saw as
many saw- gates square across the inside to the gauge -
line. Take a board of equal width, 1 foot long, nail one
half of it on the outside at one end of the hoop, lay it
in water a day or two to soak, or sprinkle the outside
well an hour or two with hot water. Bend it round so
that the ends meet, and nail the other end to the short
board, put sticks across inside in every direction to press
out the parts that bend least, and make it truly round.
Make a cover for the hoop, such as is represented in
plate XIX, fig. 23, 8 square inside, and 1 inch outside
the hoop. It consists of 8 pieces lapped over one ano-
ther, the black lines showing the joints as they appear
when made, the dotted lines the under parts of the laps.
Describe it on the floor, and make a pattern to make all

T t

330 OF FACING STONES, Sec.

the rest by ; dress all the laps, fit and nail them to,8jether
b}' the circle on the floor, and then nail it on the h>')p;
put the hoop over the stone and scribe it to fit the floor
in its place.

ART. 25.

OF GRINDING SAND TO F'\CE THR STONES.

Lay boards over the hoop to keep the dust from fly-
ing, and take a bushel or two of dry, clean, sharp sand,
teem it gently in the eye, while the stones move at a
moderate rate, continuing to grind for an hour or two ;
then take up the stones, sweep them clean, and pick the
smoothest hardest places, and lay the stone down again,
and grind more sand as before, turning off" the back, (if
it be a bun-) taking great care that the chisel does not
catch ; take up the stone again, and make a red staff", i»
length the diameter of the stone, 3 by 2 1 inches, paint it
with red paint and water, and rub it over the face of the
stones in all directions, the red will be left on the highest
and hardest parts, which must be pecked down, making
the bed-stone perfectly plain, and the runner a little con-
cave about 1-6 of an inch at the eye, and lessening gra-
dually to about 8 inches from the skirt. If they be close
and have much face they need not touch or flour so far,
as if they are open and have but little face; those things
are left to the judgment of the mill-wright and miller.

ART. 26.

DIRECTIOXS FOR LAYING OUT THE FURROWS IN THE
STONES, &c.

If they be five feet in diameter, divide the skirt into
16 equal parts, called quarters, if 6 feet, into 18, if 7
feet, into 20 quarters. Make two strips of board, one
an inch, and the other 2 inches v\ ide : stand with your
face to the eye, and if the stone turns to the right when
at work, lay the strip at one of the quarter divisions, and
the other at the left hand side close to the eye, and mark

OF FURROWING STONES. 331

with a flat pointed spike for a master furrow ; they all
are laid out the same way in both stones, for when their
faces are together, the furrows should cross each other like
shears in the best position for cutting cloth. Then, hav-
ing not less than 6 good picks, proceed to pick out all
the master furrows, making the edge next the skirt and
the end next the eye the deepest, the feather edge not
half so deep as the back.

When all the master furrows are picked out, lay the
broad strip next to the feather edges of all the furrows,
and mark the head lands of the short furrows, then lay
the same strip next the back edges, and mark for the
lands, and lay the narrow strip, and mark for the fur-
rows, and so on mark out all the lands and furrows,
minding not to cross the head lands, but leaving it be-
tween the master furrows and the short ones of each
quarter. But if they be close country stones, lay out
both furrows and land with the narrow strip.

The neck of the spindle must not be wedged too tight
else it will burn loose ; bridge the spindle again ; put a
collar round the spindle neck, but under it put a piece
of an old stocking, with tallow rolled up in it, about a
finger thick ; tack it close round the neck ; put a piece
of stiff leather about 6 inches diameter on the cock-head
under the driver, to turn with the spindle and drive off
the grain, &c. from the neck ; grease the neck with tal-
low every time the stone is up.

Lay the stone down and turn off the back smooth,
and grind more sand. Stop the mill ; raise the stone a
little, and balance it truly with weight laid on the light-
est side. Take lead equal to this weight, melt it, and
run it into a hole made in the same place in the plaister,
largest at bottom to keep it in, fill the hole with plaister,
take up the runner again, try the staff over them, and if
in good face give them a nice dressing, and lay them
down to grind wheat.

^2 OF THE HOPPER, SHOE, AND FEEDER.

ART. S7.

DIRECTIONS FOR MAKING A HOPPER, SHOE, AND FEEDER.

The dimension of the hopper of a common mill is 4
feel at the top, and 2 feet deep, the hole in the bottom 3
inches square, with a sliding gate in the bottom of the
front to lessen it at pleasure : the shoe 10 inches long,
and 5 wide in the bottom, of good sound oak. The side
7 or 8 inches deep at the hinder end, 3 inches at the
foremost end, 6 inches longer than the bottom at the
fore end, slanting more than the hopper behind, so that
it may ha\ e liberty to hang down 3 or 4 inches at the
fore end, which is hung by a strap called the feeding-
string, passing over the fore end of the hopper-frame,
and lapping round a pin in front of the meal-beam, that
will turn by the hand, called the feeding- screw.

The feeder is a piece of wood turned in a lathe, about
20 inches long, 3 inches diameter in the middle against
the shoe, tapered oft' to 1| inches at the top ; the lower
end is banded and a forked iron drove in it, that spans
over the ryne fitting into notches made on each side, to
receive it, right above the spindle, and turns with it ; the
upper end running in a hole in a piece across the hop-
per-frame. In the large part next the shoe are set 6
iron knockers, 7 inches long, half an inch diameter, with
a tang at each end, turned square to drive into the wood,
these knock against, and shake tlie shoe, and thereby
shake in the grain regularly.

Then put grain into the hopper, draw water on the
mill, regulate the feed by turning the feed-screw, until
the stream falling into the eye of the stone, is propor-
tioned to the size thereof, or the power of the mill. Here
ends the mill-wright's work, with respect to grinding,
and the miller takes charge thereof.

ART. S8.
OF BOLTING CHESTS AND REELS.

Bolting-chests and reels are of different lengths, accord-
ing to the use they are for. Common country chests (a

OF BOLTING-CHESTS AND REELS. 333

top view of one of which is shown, pi. VIL fig. 9,) are
commonly about 10 feet long, 3 feet wide, and 7 feet -t
inches high, with a post in each corner, the bottom 3 feet
from the floor, with a board 18 inches wide, set slanting
in the back side, to cast the meal forward in the chest,
to make it easily taken up ; the door of the whole length
of the chest, and two feet wide, the bottom side board
below the door 16 inches wide.

The shaft of the reel equal in length with the chest, 4j
inches diameter, 6 square, two bands on each end, 3 1-4)
and 3 3-4 diameter, gudgeons 13 inches long, 7-8 of an
inch diameter ; 8 inches in the shaft, round g 1-2 inches
at the neck, with a tenon for a socket or handle, six ribs
112 inch deep, 1 1-8 inch thick, half an inch shorter at
the tail, and 1 1-S inch at the head, than the shaft, to leave
room for the meal to be spouted in at the head, and the
bran to fall at the tail ; four sets of arms, that is, 12 of
them, 11-3 inch wide, and 5-8 thick. The diameter of
the reel from out to out of the ribs, is one-third part of
the double width of the cloth. A round wheel of inch
boards, and diameter equal to the outside of the ribs, 4|
inches wide, measuring from the outside towards the
centre, (which is taken out) is to be framed, to the head
of the reel, to keep the meal from falling out at the head
unbolted. Put a hoop 4| inches wide, and ^ thick, round
the tail, to fasten the cloth to. The cloth is sewed two
widths of it together, to reach round the reel ; putting a
strip of sti'ong linen 7 inches wide, at the head, and 5
inches at the tail of the cloth, to fasten it to the reel by.
Paste a strip of linen, soft paper, or shammy leather
(which is the best) 1 § inch wide on each rib, to keep the
cloth from fretting. Then put the cloth on the reel tight,
and sew or nail it to the tail, and stretch it lengthways as
hard as it will bear, nailing it to the head.

N. B. 6 yards of cloth covers a 10 feet reel.

Bolting-reels for merchant, are generally longer than
for country, work, every part should be stronger in pro-
portion as necessary. They are best when made to suit
the wide cloths. The socket gudgeons at the head should

334 OF SETTING BOLTS TO GO BY WATER.

be much stronger, they being apt to wear out, and trou-
blesome to repair.

The bolting hopper is made through the floor above
the chest, IS inches square at the upper and 10 inches
at the lower end; the foremost side 5 inches and the back
side 7 inches from the top of the chest.

The shoe 2 feet long at the bottom of the side pieces,
slanting: to suit the hopper at the hinder end, set 4 inches
h'8:her at the Hinder than the fore end, the botto.n 17
inches long and 10 inches wide. There should be a bow
of iron riveted to the fore end to rest on the top of the
knocking wheel, fixed on the socket gudgeon at the head
of the chest, which is 10 inches diameter, 2 inches thick,
with 6 half rounds cut out of its circuniference by way
of knockers, to strike against the bow, and lift the shoe |
of an inch every stroke to shake in the meal.

ART. 29.

OP SETTING BOLTS TO GO BY WATER.

The bolting reels are set to go by water as follows :
Make a bridge 6 by 4 inches, and 4 inches longer than
the distance of the tomkin posts, described art. 20; set
it between them on rests fastened into them, 10 inches
below the cogs of the cog-wheel, and the centre of it
half the diameter of the spur-wheel in front of them; on
this bridge is set the step gudgeon, of an upright shaft,
with a spur-wheel of 16 or 18 cogs to gear into the cog-
wheel. Fix a head-block to the joists of the 3d floor for
the upper end of this shaft, put the wheel 28, plate VII,
on it; hang another head-block to the joists of the 2d
floor near the corner of the mill at 6, for the step of the
short upright shaft that is to be fixed there, to turn the
reels 1 and 9. Hang another head-block to the joists
of the 3d floor for the upper end of the said short up-
rip^ht, and fix also head-blocks for the short shaft at the
head of the reels, so that the centres of all these shafts
will meet. Then fix a hanging post in the corner 5, for

OF MAKING BOLTING WHEELS. 53-3;

'die gudgeon of the long horizontal shaft 27 — 5 to run in.
After the head-blocks are all fixed, then measure the
length of each shaft, and make them as follows, viz.

The upright shaft 5^ inches for common mills, but
if for merchant-work, with Evans's elevators, &c. added,
make it larger 6 or 7 inches ; the horizontal shaft 21 — 5
and all the other 5 inhes diameter. Put a socket-gud-
geon in the middle of the long shafts to keep them steady;
make them 8 or 16 square, except at the end where the
v\ heels are hung, where they must be 4* square. Band
their ends, put in the gudgeons, put them in their proper
places in the head-blocks, to mark where the wheels are
to be put on them.

ART. 30.

OF MAKING BOLTING WHEELS.

Make the spur-wheel for the first upright with a 4|
inch plank, the pitch of the cogs the same as the cog-
wheel, into which it is to work, put two bands 3-4 of an
inch wide, one on each side of the cogs, and a rivet be-
tween each cog to keep the wheel from splitting.

To proportion the cogs in the wheels to give the bolts
the right motion, ihe common way is —

Hang the spur-wheel and set the stones to grind with
a proper motion, and count the revolutions of the upright
shaft in a minute, and compare its revolutions with the
revolutions that a bolt should have, which is about 2>& re-
volutions in a minute. If the upright goes 1-6 more, put
1-6 less in the first driving-wheel than in the leader, sup-
pose 15 in the driver then 18 in the leader: but if their
difference be more (say one half) there must be a differ-
ence in the next two wheels ; observing, that if the mo-
tion of the upright shaft be greater than the bolt should
be, then the driving- ^vheel must be proportionably less
than the leader; but if it be slower, then the driver must
be greater in proportion. The common size of bolting
wheels is from 14 to 20 cogs; if less than 14 the head-
blocks will be too near the shafts.

336 OF ROLLING-SCREENS.

Common bolting wheels should be made of plank at
least 3 inches thick, well seasoned, and are best to be as-
wide as the diameter of the wheel, and banded with bands
near as wide as the thickness of the wheel, made gene-
rally of rolled iron, about 1-8 of an inch thick. Some
make them of two inch plank, crossed, and no bands :
but this proves no saving, as they are apt to go to pieces
in a few years. For hooping wheels see art. 1 9, and for
finding the diameter of the pitch circle see art. 9. The
wheels are generally two inches more in diameter than
the pitch circle if banded; but if not, they should be
more. The pitch or distance of the cogs are different, if
to turn 1 or 2 bolts 3| inches, but if more S| : but if
much heavy work, they should not be less than 3 inches.
Their cogs are half the pitch in thickness, the shank to
drive tight in an inch auger hole.

When the mortises are made for the shafts in the head,
and notches for the keys to hang them, drive the cogs in
and pin their shanks at the back side, and cut them off
half an inch from the wheel.

Hang the wheels on the shafts so that they will gear a
proper depth, about 2-3 the thickness of the cogs ; dress
all the cogs to equal distance by a gauge ; then put the
shafts in their places, the wheels gearing properly, and the
head-blocks all secure, set them in motion by water.
Bolting reals should turn to drop the meal on the back
side of the chest, as it will then hold more, and will not
cast out the meal when the door is opened.

ART. 31.

OF ROLLING SCREENS.

These are circular sieves moved by water, and are
particularly useful in cleaning wheat for merchant work.
They are of different constructions.

1st. Those of one coat of wire with a screw in them.

2d. Those of two coats, the inner one nailed to 6 ribs,
the outer one having a screw between it and the inner
one.

3. Those of a single coat and no screw.

OF FANS. 33^

The first kind answers well in some, but not in all
eases, because they must turn a certain number of times
before the wheat can get out, and the grain has not so
good an opportunity of separating, there being nothing
to change its position, it floats a considerable way with
the same grains uppermost.

The double kind are better because they may be short-
er and take up less room ; and worse, for being more
difficult to be kept clean.

The 3d kind has this advantage ; we can keep the
grain in it a longer or shorter time at pleasure, by raising
or lowering the tail end, and is also tossed about more ;
but they must be longer. They are generally 9 or 10
feet long, 2 feet 4 inches diameter, if to clean for two or
three pair of stones, but if for more, they should be lar-
ger accordingly: will clean for from one to six pair of
stones. They are made 6 square, with 6 ribs, which
lie flatwise, the outer corners taken off to leave the edge
I of an inch thick ; the inner corners so as to bring it
nearly to sharp edges, the wire work nailed on with i'i
ounce tacks.

They are generally moved by the same upright shaft
that moves the bolts, by a wheel on its upper end with
two sets of cogs : those that strike downwards gearing
into a wheel striking upwards that turns a laying shaft,
with two pulleys on the other end, one of 24 inches dia-
meter, to turn a fan with quick motion, the other 8 inches,
over which passes a strap to a pulley 24 inches diameter,
on the gudgeon of the rolling screen, to reduce its mo-
tion to about 15 revolutions in a minute. See pi. XIX.
fig. 23. This may do for mills in the small way, but
where they are in perfection for merchant- work, with
elevators, &c. and have to clean wheat for 2, 3, or 4 pair
of stones, they should be moved by cogs.

ART. 32.

OF FANS.

The Dutch fan is a machine of great use for blowing
the dust and other light stufi:' from among the wheat ;

u u

338 OF THE SHAKING SIEVE.

there are various sorts of them ; those that are only for
blowing the wheat, as it falls from the rolling-screen, are
generally about 15 inches long, and 14 inches wide in
the wings, and have no riddle or screen in them.

To give it motion, put a pulley 7 inches diameter on
its axle for a band to run on, from the pulley on the shaft
that moves the screen of 24 inches diameter, to give it a
swift motion; when the band is slack it slips a little on the
small pulley, and the motion is slow ; but vi hen tight the
motion is quicker ; by this the blast is regulated.

Some use Dutch fans complete, with riddle and screen
under the rolling screen for merchant- work, and again
use the fan alone for country-work.

The wings of those, which are the common farmers
wind- mills or fans, are 18 inches long, and 20 inches
wide, but in mills they are set in motion with a pulley
instead of a cog-wheel and wallower.

ART. 33.

OP THE SHAKING SIEVE.

They are of considerable use in country mills, to sift
indian meal, separating it into several degrees of fineness
if required, and take the hulls out of buckwheat meal,
that are apt to cut the bolting- cloth, and the dust out of
the grain, if rubbed before ground; and are sometimes
used to clean wheat or screenings instead of rolling
screens.

If they are for sifting meal they are 3 feet 6 inches long,
9 inches wide, 3| inches deep; see it plate VI. fig. 16.
The wire-work is 3 feet long, 8 inches wide : across the
bottom of the tail end is a board 6 inches wide, to the top
of V hich the wire is tacked, and then this board and wire
tacked to the bottom of the frame, leaving an opening at
the tail end for the bran to fall into the box 17, the meal
falling into the meal-trough 15, the head-piece should be
strong to hold the iron bow at 15, through which passes
the lever that shakes the sieve, in the following manner :
Take two pieces of hard wood 15 inches long, and as wide

OF THE USE OF DRAUGHTING MILLS. 339

as the spindle, and so thick that when one is put on each
side just above the trundle, it will make it I^ inch
thicker than the spindle is wide. The corners of these
are taken off to a half round, and they are tied to the
spindle with a small strong cord. These are for to strike
against the lever that works on a pin near its centre,
which is fastened to the sieve, and shakes it as the trun-
dle goes round ; see it represented plate XVIII. This
lever must always be put to the contrary side of the spin-
dle, that it is of the meal- spout, else it will draw the meal
to the upper end of the sieve : there must be a spring
fixed to the sieve to draw it forward as often as it is
driven back. It must hang on straps and be fixed so as
to be easily set to any descent required, oy means of a
roller in form of the feeding screw, only longer, round
which the strap w-inds.

Having now given directions for making and putting
to work, all the machinery of one of the completest of
the old fashioned gi'ist-mills, that may do merchant-
work in the small way as represented by plates XVIII,
XIX, XX, XXI; but not to near so much advantage as
with the late and new improvements, which are shown
by plate X.

ART. 34.

OP THE USE OF DRAUGHTING TO BUILD MILLS BY, &c.

Perhaps some are of opinion that draughts are useless
pictures of things, serving only to please the fancy. This
is not what I intend by them; but to give the reader true
ideas of the machines, &c. described, or to be made.
They are all drawn on a small scale of 1-8 of an inch for
a foot, in order to suit the size of the book, except plate
XVII, which is quarter of an inch for a foot, and this
scale I recommend, as most buildings will come on the
size of a common sheet of paper.

N. B. Plate XXIV, was made after the above direc-
tions, and has its explanations to suit it.

The great use of draughting mills, &c. to build by, is
by conveying our ideas more plain, than is possible to
be done by writing or words, which may be miscon-

340 OF PLANNING AND DRAUGHTING MILLS.

strued or forgotten; but a draught well drawn, speaks
for itself, when once understood by the artist; who, by
applying his dividers to the draught and to the scale,
iinds the length, breadth and height of the building, or
the dimensions of any piece of timber, and its place in
the building, &c.

By the draught, the bills of scantling, boards, rafters,
laths, shingles, &c. &c. are known and made out; it
should show every wheel, shaft, and machine, and their
places. By it we can find whether the house is suffi-
cient to contain all the works that are necessary to carry
on the business ; the builder or owner understands what
he is about, and carries on cheerfully without errof ; it
directs the mason where to put the windows, doors,
navel-holes, the inner walls, &c. whereas, if there be no
draught, every thing goes on, as it were, in the dark ;
much time is lost and errors are committed to the loss
of many pounds. I have heard a man say, he believed
his mill was 500/. better, by having employed an expe-
rienced artist, to draw him a draught to build it by.
And I know by experience the great utility of them.
Every master builder ought, at least, to understand
them.

ART. 35.
DIRECTIONS FOR PLANNING AND DRAUGHTING MILLS.

1st. If it be a new seat, view the ground where the
dam is to be, and where the mill-house is to stand, and
determine on the height of the top of the water in the
head-race where it is taken out of the stream ; and level
from it for the lower side of the race down to the seat of
the mill-house, and mark the level of the water in the
dam there.

2d. Begin where the tail-race is to empty into the
stream, and level from the top of the water up to the
mill-seat, noticing the depth thereof in places as you pass
along, which will be of use in digging it out.

Then find the total fall, allowing 1 inch to a rod for fall
in the races, but if they are very wide and long, less will do.

OF PLANNING AND DRAUGHTING MILLS 341

Then, supposing the fall to be 21 feet 9 inches, which
is sufficient for an overshot mill, and the stream too
light for an undershot, consider well what size stone
will suit, for I do not recommend a large stone to a
weak, nor a small one to a strong stream. I have pro-
posed stones 4 feet diameter for light, and 4',6 for mid-
dling, and 5 or 5 feet 6 inches diameter for heavy-
streams. Suppose you determine on stones 4 feet, then
look in table I, (which is for stones of that size) column
2, fur the fall that is nearest 21 feet 9 inches, your fall,
and you find it in the 7tb example. Column 3 contains
the head of water over the wheel 3 feet; 4th, the diame-
ter of the wheel 18 feet; 5th, its width, 2 feet 2 inches,
&c. for all the proportions to make the stone revolve 106
times in a minute.

Having determined on the size of the wheels and size
of the house, heights of the stories to suit the wheels,
and machinery it is to contain, and business to be carried
on therein, proceed to draw a ground plan of the house,
such as plate XVIII, which is 32 by 55 feet. See the
description of tlie plate. And for the second story, as
plate XIX, &c. for the 3d, 4th and 5th floors, if required,
taking care to plan every thing for the best, and so as
not to clash one with another.

Draw an end view, as plate XX, and a side view as
plate XXI. Take the draught to the ground and stake
out the seat of the house. It is commonly best to set
that corner of an ovefshot mill that the water comes in
at farthest in the bank ; but take great care to recon-
sider and examine every thing more than once whether
it be planned for the best; because, much labour is often
lost for want of due consideration, and by setting build-
ings in, and laying foundations on wrong places. This
done, you may from the draughts make out the bills of
scantling and iron work.

342 BILLS OF SCANTLING.

ART. 36.

BILLS OF SCANTLING FOR A MILL, 32 BY 55 FEET, 3 STORIES
HIGH, SUCH AS DESCRIBED PLA1 ES XVIII, XIX, XX, AND
XXI. THE WALLS OF MASON WORK.

For the Jirst Floor,

5 sills, S9 feet long, 8 by 12 inches, to lay on the walls
for the joists to lay on.

48 joists, 10 feet long, 4 by 9 inches; all of timber that
will last well in damp places.

For the second Floor.
2 posts, 9 feet long, IS by 12 inches.
2 girders, 30 feet long, 14 by 16 do.
48 joists, 10 feet long, 4- by 9 do.

For the Floor over the Water-house,

1 cross girder, 30 feet long, 12 by 14 inches, for one
end of the joists to lay on.

2 posts to support the girder, 12 feet long, 12 by 12
inches.

16 joists, 13 feet long, 4 by 9 inches; all of good white-
oak or other timber that will last in damp places.

For the third Floor. '
4 posts, 9 feet long, 12 by 12 inches, to support the

girders.
2 girder-posts, 7 feet long, 12 by 12 inches, to stand on

the water-house.
2 girders, 53 feet long, 14 by 16 inches.
90 joists, 10 feet long, 4 by 9 inches,
For the fourth Floor.

6 posts, 8 feet long, 10 by 10 inches, to support the
girders.

2 girders, 53 feet long, 13 by 15 inches.

31) joists, 10 feet long,' 4 by 8 do. for the middle tier of
the floor.

60 do, 12 feet do. 4 by 8, for the outside tiers, which ex-
tends 12 inches over the walls, for the rafters to stand
on.

2 plates, 54 feet long, 3 by 10 inches : these lay on the
top of the walls, and the joists on them.

BILLS OF SCANTLING. 3i^

9 raising pieces, 55 feet long, 3 by 5 inches ; these lay
on the ends of the joists for the rafters to stand on.

For the Roof.

54 rafters, 22 feet long, 3 inches thick, 6| wide at bot-
tom, and 41 at top end.
2^ collar beams, 17 feet long, 3 by 7 inches.
2760 feet of laths, running measure.
7000 shingles.

For Doors and Window- Cases.

12 pieces, 12 feet long, 6 by 6 inches, for door cases-.
36 do. 8 feet long, 5 by 5 inches for window-cases.

For the Water-House.

2 sills, 27 feet long, 12 by 12 inches.

1 do. 14 feet long, li^ by 12 do.

2 spur- blocks, 4 feet 6 inches long 7 by 7 do.
2 head-blocks, 5 feet long, 1:3 by 14 do.

4 posts, 10 feet long, 8 by 8 to bear up the penstock.

2 capsails, 9 feet long, 8 by 10, for the penstock to stand
on.

4) corners posts, 5 feet long, 4 by 6 inches, for the cor-
ners of the penstock.

For the Husk of a Mill of one Water-wheel and two Pair

of Stones.

2 sills, 24 feet long, 12 by 12 inches,

4 corner posts, 7 feet long, 12 by 14 inches.

2 front posts, 8 feet long, 8 by 13 do.

2 back posts, 8 feet do. 10 by 12 inches, to support the

back ends of the bridge-trees.
2 other back posts 8 feet long, 8 by 8 inches.
2 tomkin posts, 12 feet long, 12 by 14 do.
2 interties, 9 feet long, 12 by 12 inches, for the outer

ends of the little cog-wheel shafts to rest on.
2 top pieces, 10 feet 6 'inches long, 10 by 10 inches.
2 beams, 24 feet long, 16 by 16 inches.
2 bray-trees, 8^ feet long, 6 by 12 inches.
2 bridge-trees, 9 feet long, 10 by 10 inches.
4 plank, 8 feet long, 6 by 1 4 inches, for the stone-bearers.

344 BILLS OF SCANTLING.

20 plank 9 feet long, 4 by about 15 inches, for the tdp of
the husk.

5 head-blocks, 7 feet long, 13 by 15 inches, for the wal-
lower shafts to run on. They serve as spurs also for
the head-block for the water-wheel shaft.

For the JVater and big Cog- Wheel.

1 shaft, 18 feet long, S feet diameter.
8 arms for the water-wheel, 18 feet long, 3 by 9 inches.
16 shrouds, %\ feet long, 2 inches thick, and 8 deep.
16 face boards, 8 feet long, one inch thick, and 9 deep.
S^ bucket boards, 2 feet 4j inches long, and 17 inches

wide.
140 feet of boards, for scaling the wheel.

3 arms for the cog-wheel, 9 feet long, 4 by 14 inches.
16 cants, 6 feet long, 4 by 17 inches.

For little Cog-wheels.

% shafts 9 feet long, 14 inches diameter.

4 arms, 7 feet long, 3| by 10 inches.
16 cants, 5 feet long, 4 by 18 inches.

For JFalloxvers and Trundles.

60 feet of plank, 3| inches thick.

40 feet do. 3 inches thick, for bolting gears.

Cogs and Rounds.

SCO cogs to be split, 3 by 3, 14 inches long.

80 rounds, do. 3 by 3, 20 inches long.

160 cogs, for bolting works, 7 inches long, and 1 3-4
square : but if they be for a mill with machinery com-
plete, there must be more accordingly.

Bolting Shafts.

1 upright shaft, 14 feet long, 5| by 5| inches.

2 horizontal shafts, 17 feet long, 5 by 5 inches.
1 upright do. 13 feet long, 5 by 5 inches.

6 shafts, 10 feet long, 4 by 4 do.

BILL OF THE LARGE IRON, &c. 345

ART. 37.

BILL OF THE- LA^RGE IROXS FOR A MILL OF TWO PAIR OP

* ,.,j,;.. STONES.

3 gudgeons, S" feet 3 inches long in the shaft; neck 4|
inches long, 3 inches diameter, well steeled and turn-
ed. See plate XII, fig. 16.

S bands, 19 inches diameter inside, | thick, and 3 inchei^

wide, for the ends of the shaft.
2 do. 20 i inches inside, h an inch thick, and 3| inches

wide, for do.
2 do. 23 inches do. | an inch thick, and 2| inches wide,

for do.

4 gudgeons, 16 inches in the shaft, 3| inches long, and
2 1 inches diameter in the neck for wallower shafts :
See fig. 15, plate XXIV.

4 bands, 13 inches diameter inside, 1 an inch thick, and
2 wide, for do.

4 do. 13 inches do. ^ an inch thick and 3 wide, for do.

4 wallower bands, 3 feet 2 inches diameter inside, 3
inches wide and | of an inch thick.

4? trundle bands, 2 feet diameter inside, 3 inches wide,
and I of an inch thick.

2 spindles and rynes ; spindles 5 feet 3 inches long from
the foot to the top of the necks ; cock-heads 7 or 8
inches long above the necks ; the body of the spin-
dles SI by 2 inches ; the neck 3 inches long, and 3
inches diameter : the balance rynes proportional to the
spindles, to suit the eye of the stone, which is 9 inches
diameter. See plate XII, fig. 1, 2, 3.

2 steps for the spindles, fig. 4.

3 sets of damsel- irons, 6 knockers to each set.

3 bray-irons, 3 feet long, 1 1 inch wide, ^ an inch thick '.
being a plain bar, one hole at the lower, and 6 or 6 at
the upper end.

JBill of Iron Jor the Bolting a?id Hoisting-works in the
common JFay.

3 spur-wheel bands, 20 inches diameter from outsides,
for the bolting spur-wheel, | of an inch wide, and f
thick.

346 BILL OF IRON, &c.

2 spur-wheel bands 12 inches diameter from outsides,
for the hoisting spur-wheel.

S step gudgeons and steps, 10 inches long, l-J inch thick
in the tang, or square part ; neck 3 inches long, for the
upright shafts. See plate XXIV, fig. 5 and 6.

2 bands for do. 5 inches diameter inside, 1| wide, and
1| thick.

2 gudgeons, 9 inches tang ; neck 3 inches long, 11-8
square, for the top of the uprights.

8 bands, 4^ inches diameter inside.

1 socket gudgeon, 1 1-8 of an inch thick ; tang 12 inches
long; neck 4 inches; tenon to go into the socket 1|
inch, with a key-hole at the end. See fig. 8 and 9.

14* gudgeons, necks 2| inches, tangs 8 inches long, and
one inch square, for small shafts and one end of the
bolting -reels.

10 bands for do. 4 inches diameter inside, and 1 inch
wide.

4 socket-^nidgeons, for the 4 bolting-reels, If square;
tangs 8 inches : necks 3 inches, and tenons li inch,
with holes in the end of the tangs for rivets, to keep
them from turning : the sockets 1 inch thick at the
mortise, and 3 inches between the prongs. See fig.

8 and 9. Prongs 8 inches long and 1 wide.

8 bandis, 3| inches, and 8 do. 4 inches diameter, for the
bolting-reel shafts.

Por the Hoisting-wheels.

2 gudgeons, for the jack- wheel, neck 31 inches, and tang

9 inches long, 11-8 square.

2 bands for do. 4| inches diameter.

% gudgeons, for the hoisting- wheel, neck 3| inches, tang

9 inches long, and 1^ inch square.
2 bands, for do. 7 inches diameter.
6 bands for bolting-heads, 16 inches diameter inside,

2| wide, and 1-6 of an inch thick.
6 do. for do. 15 inches do. do.

N. B. All the gudgeons should taper a little,' as the
sizes given are their largest part. The bands for shafts
should be a little widest at the foremost side to make them
drive well ; but those for heads should be both sid es

EXPLANATION OF THE PLATES. 347

equal. — 6 picks for the stones, 8 inches long, and 1 }
wide, will be wanted.

ART. 38. ^

EXPLANATION OF THE PLATES.

PLATE XVIL

Drawn from a scale of quarter of an inch for a foot.
Fig. 1, a big cog-wheel, 8 feet 2 1-3 inches the diameter
of its pitch circle; 8 feet 10 1-3 inches from out to
out; 69 cogs, 4| inch pitch.

2, a little cog-wheel, 5 feet 10 1-3 inches the diameter
of its pitch circle, and 6 feet 6 inches from out to out,
to have 52 cogs, 4^ pitch.

3, a wallower, 3 feet 1^ inches the diameter of its pitch
circle, and 3 feet 4-^ inches from out to out ; 26 rounds,
41 pitch.

4, a trundle, 1 foot 8 1-3 inches the diameter of its pitch
circle, and 1 foot 11 1-3 inches from out to out; id
rounds, 4i inches pitch.

0, the back part of the big cog-wheel.

6, a model of locking 3 arms together.

7, the plan of a forebay, showing the sills, caps, and
where the mortises are made for the posts, with a rack
at the upper end to keep off the trash.

PLATE XVlll.— The Ground-plan of a Mill

Fig. 1 and 8, bolting-chests and reels, top view.

2 and 4, cog-wheels that turn the reels.

3, cog-wheel on the lower end of a short upright shaft.

5 and 7, places for the bran to fall into.

6, 6, 6, three gamers on the lower floor for bran.

9 and 10, posts to support the girders.

11, the lower door to load wagons, horses, &c. at.

15, the step-ladder, from the lower floor to the husk.
13, the place where the hoisting casks stand when fill-
ing,

14 and 15, the two meal-troughs and meal-spouts.

16, meal shaking sieve for indian and buck-wheat.

34d EXPLANATION OF THE PLATES.

Fig. 17, a box for the bran to fall into from the sieve.
18 and 19, the head-block, and long spur-block, for the
big shaft.

50, four posts in front of the husks, called bray posts.

51, the water and cogwheel shaft.

SS, the little cog wheel and shaft, for the lower stones.

53, the trundle for the burr stones.

54, the wallower for do.

55, the spur-wheel that turns the bolts.

56, the cog-wheel.

g7, the trundle, head wallower and bridge-tree, for

country stones.
Sc, the four back posts of the husk. -
S9, the two posts that support the cross girder.

30, the two posts that bear up the penstocks at one side.

31, the water-wheel 18 feet diameter.

33, the two posts that bear up the other side of the

penstock.
33, the head-blocks and spur-blocks, at water end.
34", a sill to keep up the outer ends.

35, the water-house door.

36, a hole in the wall for the trunk to go through.

37, the four windows of the lower story.

VLATEXlX^Second Floor,

Fig 1 and 9, a top view of the bolting-chests and reels.

2 and 10, places for bran to fall into.

3 and 8, the shafts that turn the reels.

4 and 7, wheels that turn the reels.

0, a wheel on the long shafts between the uprights.
6, a wheel on the upper end of the upright shaft.
11 and IS, two posts that bear up the girders of the third
floor.

13, the long shaft between two uprights.

14, five garners to hold toll, &c.

15, a door in the upper side of the mill-house.

16, a step-ladder from Sd to 3d floor.

17, the running burr mill-stone laid off" to- be pressed.

18, the hatchway.

19, stair- wa3% "*

EXPLANATION OF THE PLATES. 349

Fig. SO, the running country stone turned up to be
dressed.

^1, a small step-ladder from the husk, to second floor.

S3, the places where die cranes stand.

24, the pulley-wheel that turns the rolling screen.

S5 and S6, the shaft and wheel that turns the rolling-
screen and fan.

57, the wheel on the horizontal shaft to turn the bolting-
reels.

58, the wheel on the upper end of the first upright shaft.

59, a large pulley that turns the fan.

30, the pulley at the end of the rolling-screen.

31, the fan.'

35, the rolling-screen.

33, a step-ladder from the husk to the floor over the

water-house.
34? and 35, two posts that support the girders of the 3d

floor.

36, a small room for the tailings of the rolling-screen,

37, a room for the fannings.

38, do. for the screenings.

39, a small room for the dust.

40, the penstock of water.

41, a room for the miller to keep his books in.
4rS, a fire-place.

43, the upper end door.

44, ten windows in the Sd story, IS lights each.

PLATE XX.

Represents a view of the lower side of a stone mill-house
. three stories high, which plan will suit tolerably well for a
two story house, if the third story be not wanted. Part
of the wall supposed to be open, so that we have a view
of the stones, running gears, &c.

Line 1 represents the lower floor, and is nearly level
M'ith the top of the sills, of the husk and water-house.
S, 3 and 4 the second, third, and fourth floors.
5 and 6 are windows for admitting air under the lower

floor.
7 the lower door, with steps to ascend to it, which com-
monly suits best to load from.

350 EXPLANATION OF THE PLATES.

8 the arch over the tail-race for the water to run from
the wheel.

9 the water-house door, which sometimes suits better
to be at the end of the house, where it makes room to
wedge the gudgeon.

10 the end of the water-wheel shaft.

11 the big cog-wheel shaft.

12 the little cog-wheel and wallower, the trundle being
seen through the window.

13 the stones with the hopper, shoe and feeder, as fixed
for grinding.

14 the meal-trough.

We have an end view of the husk frame- — there are
thirteen windows with twelve lights each.

PLATE XXL

Represents an outside view of the water end of a mill-
house, and is to show the builders, both masons, car-
penters and mill-wrights, the height of the walls, floors,
and timbers ; places of the doors and windows, with a
view of the position of the stones and husk-timbers, sup-
posing the wall open so that we could see them.
Fig. 1, 3, 3, and 4 shows the joists of the floors.

5 represents a fish turning with the wind on an iron rod,
which does as well as a weather-cock.

6 the end of the shaft for hoisting outside of the house,
which is fixed above the collar-beams above the
doors, to suit to hoist into either of them, or either
story, at either end of the house, as may best suit.

7 the dark squares, showing the ends of the girders.

8 the joists over the water-house. ^

9 the mill- stones, with the spindles they run on, and the
ends of the bridge- trees as they rest on the brays a a.
b b shows the end of the brays, that are raised and
lowered by the levers c c, called the lighter-staflfs,
thereby raising and lowering the running stone.

10 the water-wheel and big cog-wheel.

11 the wall between the water and cog-wheel.
IS the end view of the two side walls of the house.

Plate X is explained in the Preface.

OF SAW-MILLS. 351

ART. 39.

OP SAW MILLS— THEIR UTILITY.

They are for sawing timber into all kinds of scantling,
boards, laths, &c. &c. are used to great advantage where
labour is dear. One mill, attended by one man, if in
good order, will saw more than 30 men will with whip-
saws, and much more exactly.

Construction of their Water-wheels.

They have been variously constructed ; the most sim-
ple and useful of which, where water is plenty, and above
six feet fall, is the flutter-wheel ; but where water is
scarce in some cases, and for want of sufficient head in
others, to give flutter-wheels sufficient motion, high
wheels, double geared, have been found necessary.
Flutter- wheels may be made suitable for any head above
six feet, by making them low and wide, for low heads ;
and high and narrow for high ones, so as to make about
120 revolutions, or strokes of the saw, in a minute :
but rather than double gear I would be satisfied with
100.

352

OF SAW MILLS.

A TABLE

DIAMETER OF FLUTTER WHEELS,

Prom out to outsides, and their width in the clear, stiitable to all heads,
from 6 to 30 feet.

n
o

3
n

ft.

ft. in.

2:8

5:6

2:10

5:0

2:11

4:8

3:0

4:3

3:1

4:0

3:2

3:9

3:3

3:6

3:4

• 3:3

3:5

3:0

3:6

2:9

3:7

2:6

3:8

2:4

3:9

2:2

3:10

2:0

3:11

1:10

4:0

1:9

4:1

1:8

4:2

1:7

4:3

1:6

4:4

1:5

4:5

1:4 «

4:6

1:3

4:7

1:2

4:8

1:1

4:9

1:0

N. B. The above wheels are proposed as narrow as
will well do on account of saving water ; but if there is
very plenty of it, the wheels may be made wider than
directed in the table, and the mill will be more pow-
erful.

OF SAW-MILLS. S5t

Of Gearing Saw-Mills,

Of this I shall say but little, they being expensive and
but little used. — They should be geared so as to give the
saw about 120 strokes in a minute, when at work in a
common log. The water-wheel is like that of another
mill, whether of the undershot, overshot, or breast kind ;
the cog-wheel of the spur kind, and as large as will clear
the water. The wallower commonly has 14 or 15
rounds, but so as to produce the right motion. On the
wallower shaft is a balance- n^heel, which may be of stone
or wood : this is to regulate the motion. There should
be a good head above the water-wheel to give it a lively
motion, else the mill will run heavily.

The mechanism of a complete saw-mill is such as to
produce the following effects, viz.

1. To move the saw up and down, with a sufficient
motion and power.

2. To move the log to meet the saw.

3. To stop of itself when within 3 inches of being
through the log.

4. To draw the carriage with the log back by the
power of water ready to enter again.

The mill is stopped as follows, viz. When the gate
is drawn the lever is held by a catch, and there is a trig-
ger, one end of which is within half an inch of the side
of the carriage, on which is a piece of wood an inch and
a half thick, nailed so that it will catch against the trig-
ger as the carriage moves, which throws the catch off
of the lever of the gate, and it shuts down at a prop«r
time.

Description of a Saw-mill.

Plate XXIllis an elevation and perspective view of a
saw-mill, showing the foundation, walls, frame, &c. &c.

Fig. 0. 1. the frame uncovered, 52 feet long, and 12
feet wide.

Fig 2. the lever for communicating the motion from
the saw-gate to the carriage, to move the log. It is 8 feet
long, 3 inches square, tenoned into a roller 6 inches

Y ^-

854 OF SAW-MILLS.

diameter, reaching from plate to plate, and working on
gudgeons in them ; in its lower side is framed a block 10
inches long, with a mortise in it S inches wide, its whole
length, to receive the upper end of the hand-pole, having
in it ?5everal holes for an iron pin, to join the hand-pole to
it to regulate the feed, by setting the hand-pole nearer
the centre of the roller to give less, and farther off, to
give more feed.

Fig. 3. the hand-pole or feeder, 12 feet long, and 3
inches square where it joins the block.

Fig. 4. tapering to 2 inches at the lower end, on which
is the iron hand 1 foot long, with a socket, the end of
which is flattened, steeled and hardened, and turned
down at each side half an inch, to keep it on the rag-
wheel.

Fig. 5. the rag wheel. This has four cants 4f feet
long, 17 by 3 inches in the middle, lapped together to
make the wheel 5 feet diameter, is faced between the
arms with 2 inch plank to strengthen the laps. The
cramp or ratchet-iron is put on as a hoop near 1 inch
square, with ratchet-notches cut on its outer edge, about
3 to an inch. On one side of the wheel are put 12 strong
pins, nine inches long, to tread the carriage back, when
the backing works are out of order. On the other side
are the cogs, about 56 in number, 3 inch pitch to gear
into the cog-vrheel on the top of the tub-wheel shaft, with
15 or 16 cogs. In the shaft of the rag-wheel are 6 or >
rounds, 1 1 inches long in the round part, let in near their
whole thickness, so as to be of a pitch equal to the pitch
of the cogs of the carriage, and gear into them easily : the
ends are taperetl off outside, and a bund drove on tliem at
each end, to keep them in their places.

Fig. 6. the carnage. Is a frame 4 feet W'ide from out-
sides, one side 29 feet long, 7 by 7 inches ; the other 32
feet long, 8 by 7 inches, very straight and true, the inter-
ties at each end 15 by 4 inches, strongly tenoned and
braced into the sides to keep the frame from racking.
In the under side of the largest piece are set two rows of
cogs, 2 inches between the rows, and 9 inches from the
fore side of one cog to that of another : the cogs of one

OF SAW-MILLS. 355

row between those of the other, so as to make 4| Inch
pitch, to gear into the rounds of the rag-wheel. The
cou^s are about 60 in number ; shank 7 inches long, 1
3 4f inch square ; head 2 3-4! long, 2 inches thick at the
points, and 2^ inches at the shoulder.

Fig. 7. the ways for the carriage to run on. These are
strips of plank 4| inches wide, 2 inches thick, set on
edge, let 1| inch into the top of the cross sills, of the
whole length of the mill, keyed fast on one side, made
very straight both side and edge, so that one of them will
pass easily between the rows of cogs in the carriage, and
leave no room for it to move sideways. They should be
of hard wood, well seasoned, and hollowed out between
the sills to keep the dust from lodging on them.

Fig. 8. the fender posts. The gate with the saw plays
in rabbets 2| deep and 4 inches wide, in the fender
posts, which are 13 feet long, and 12 inches square, hung
by hooked tenons, the front side of the two large cross
beams in the middle of the frame, in mortises in their up-
per sides, so that they can be moved by keys to set them
plumb. There are 3 mortises two inches square through
each post, within half an inch of the rabbets, through
which pass hooks with large heads, to keep the frame in
the rabbets : they are keyed at the back of the posts.

Fig. 9. the saw, which is 6 feet long, 7 or 8 inches
wide when nevy, hung in a frame 6 feet wide from the
outsides, 6 feet 3 inches long between the end pieces, the
lowermost of which is 14 by S inches, the upper one 12
by 3, the side pieces 5 by 3 inches, 10 feet long, all of
the best dry, hard wood. The saw is fastened in the
frame by two irons in form of staples, the lo\ver one with
two screw pins passing through the lower end, screw-
ing one leg to each side of the end piece : the legs of
the upper one are made into screws, one at each side of
the end piece, passing through a broad flat bar that rests
on the top of the end piece, with strong burrs 1 3-4 inch
square, to be turned by an iron span made to fit them.

These straps are made of flat bars, 3 feet 9 inches long,
3 inches wide, 3-4 thick before turned ; at the turn they
are 5 inches wide, square, and split, to receive the saw,

356 OF SAW-MILLS.

and tug-pins, then brought nearer together, so as to fit
the gate. The saw is stretched tight in this frame, by
the screws at the top, exactly in the middle at each end,
measuring from the outside ; the top end standing about
half an inch more forward than the bottom.

Fig. 10. the forebay of water projecting through the
upper foundation wall.

Fig. 11. the flutter- wheel. Its diameter and length ac-
cording; to the head of water, as shown in the table. The
floats i.re fastened in with keys, so that they will drive
inward, when any thing gets under them, and not break.
These wheels should be very heavy, that they may act
as a fly or balance to regulate the motion, and work more
powerfully.

Fig. 13. the crank — see it represented by a draught
from a scale of 1 foot to an inch — pi. XXIV. fig. 17.
The part in the shaft 2 feet 3 inches long, 3| by 2 inches,
neck 8 inches long 3 thick, and 12 inches from the centre
of the neck to the centre of the wrist or handle, which is
5 inches long to the key hole, and 2 inches thick.

The gudgeon at the other end of the shaft is 18 inches -
in the shaft, neck 35 long, 2| diameter.

The crank is fastened in the same way as gudgeons.
See art. 13.

Fig. 12 — 13. the pitman ; which is Si inches square
at the upper end, 4i in the middle, and 4 near the lower
end ; but 20 inches of the lower end is 4i by 5^, to hold
the boxes and key, to keep the handle of the crank
tight.

Pitman Irons of an improved Construction.

See plate XXIV. fig. 10, 11, 12, 13, 14. 18. Fig. 10.
is a plate or bar, with a hole in each end, through which
the upper ends of the lug-pins 11 — 11 pass, with a strong
burr screwed on each, they are 17 inches long, 11-8
inch square, turned at the lower end to make a round
hole 11-8 diameter, made strong round the hole.

t\g. i2. is a large flat link, through a mortise near the
lower side of the end of the saAv-frame. The lug-pins

OF SAW-MILLS. 357

pass one through each end of this link, which keeps
them close to the gate sides.

Fig. 14 is a bar of iron 2 feet long, 3| inches wide, i
inch thick, at the lower end, and 1 1-8 at the upper end.
It is split at the top and turned as the fig. to pa.ss through
the lug-pins. At fig. 13 there is a notch set in the head
of the pitman bar 14, 1 i inch long, nearly as deep as to
be in a straight line with the lower side of the side pins
made a little hollow, steeled and made very hard.

Fig. 18 is an iron plate ii inch wide, half an inch
thick in the middle, with 2 large nail-holes in each end,
and a round piece of steel welded across the middle and
hardened, made to fit the notch in the upper end of the
pitman, pi. XXVI. and draw close by the lug-pins, to the
underside of the saw-frame and nailed fast. Now, if the
bearing part of this joint be in a straight line, the lower
end of the pitman may play without friction in the joint,
because both the upper and lower parts will roll without
sliding, like the centre of a scale beam, and will not wear.
This is by far the best plan for pitman irons. The first
set I ever seen or heard of has been in my saw-mill 8
years, doing much hard work, and has not cost three
minutes to adjust them ; whereas others are frequently
very troublesome.

Fig. l-i, the tub-wheel for running the carriage back.
This is a very light whe«l, 4 feet diameter, and put in
motion by a motion of the foot or hand, at once throw-
ing it in gear with the rag-wheel, lifting off the hand and
clicks from the ratchet, and hoisting a little gate to let
water on the wheel. The moment the saw stops, the
carriage with the log begins to move gently back again.
Fig. 15, the cog-wheel on the top of the tub- wheel
shaft, with 15 or 16 cogs.

Fig. 16, the log on the carriage, sawed part through.
Fig. 17, a crank and windlas to increase power, by
which one man can draw heavy logs on the mill, and
turn them by a rope round the log and windlas.
Fig. 18, a cant hook for rolling logs.
Fig. 19, a double dog, fixed into the hindmost head-
block, used by some to hold the log.

Fig. 20, are smaller dogs to use occasionally at either
end.

358 OF A FULLING-MILL.

Fig. 21 — 22, represents the manner of shuting water
on a flutter-wheel by a long open shute, which should
not be more perpendicular than an angle of 45 degrees,
lest the water should rise from the shute and take air,,
which VA ould be a great loss of power.

Fig. 2S, represents a long, perpendicular, tight shute ;
the gate 33 is always drawn fully, and the quantity of
water regulated at the bottom by a little gate r for the
purpose. There must be air let into this shute by a tube
entering at a.* These shutes are for saving expense
where the head is great, and should be much larger at
the upper than lower end, else there will be a loss of
power.f The perpendicular ones suit best where a race
passes within 12 feet of the upper side of the mill.

OPERATION.

The sluice drawn from the penstock 10, puts the
wheel 11 in motion — the crank 13 moves the saw-gate
and saw 9 up and down, and as they r^se they lift up the
lever 2, which pushes forward the hand-pole 3, which
moves the rag-wheel 5, which gears in the cogs of the
carriage 6, and ,draws forward the log 16 to meet the
saw, as much as is proper to cut at a stroke. When it
is within 3 inches of being through the log, the cleet C,
on the side of the carriage, arrives at a trigger and lets it
fly, and the sluice-gate shuts down ; the miller instantly
draws water on the wheel 14, which runs the log gently
back, &c. &c.

ART. 40.

i
DESCRIPTION OF A FULLING-MILL.

Fig. 19, plate XXIV, is the penstock, water-gate and
spout of an overshot fulling-mill, the whole laid down
from a scale of 4 feet to an inch.

Fis;. 20, one of the 3 interties, that are framed one end
into the front side of the top of the stock-block ; the
other ends into the tops of the 3 circular pieces that

• The use of this air-tiibe is shown art. 71, page 161.
I Must be. very strong else they will burst.

OF A FULLING-MILL. 359

guide the mallets ; they are G feet long, 5 inches wide,
and 6 deep.

Fig. SI are the two mallets; they are 4" feet 3 inches
long, 21 inches wide, and 8 thick, shaped as in the
figure.

Fi^. 22 their handles, 8 feet long, 20 inches wide, and
3 thick. There is a roller passes through them, 8 inches
from the upper ends, and hang in the hindermost corner
of the stock-post. The other ends go through the mal-
lets, and have each on their underside a plate of iron
faced with steel and hardened, 2 feet long, 3 inches
wide, fastened by screw-bolts, for the tappet-blocks to
rub against while lifting the mallets.

Fig. 23 the stock-post, 7 feet long, 2 feet square at
the bottom, 15 inches thick at top, and shaped as in the
figure.

Fig. 24- the stock where the cloth is beaten, shaped
inside as in the figure, planked inside as high as the
dotted line, which planks are put in rabbets in the post^
the inside of the stock being 18 inches wide at bottom,
1 9 at top, and 2 feet deep.

Fig. 25 one of the 3 circular guides for the mallets ;
they are 6 feet long, 7 inches deep, and 5 thick; are
framed into a cross sill at bottom that joins its lower
edge to the stock-post. This sill forms part of the bot-
tom of the stock, and is 4 feet long, 20 inches wide, and
10 thick.

The sill under the stock-post is 6 feet long, 20 inches
wide, and 18 thick. The sill before the stock is 6 feet
long, and 14 inches square.

Fig. 26 the tappet-arms, 5 feet 6 inches long, 21
inches each side the shaft, 12 inches wide, and 4 thick.
Therh is a mortise through each of them 4 inches wide,
the length from shaft to tappet, for the ends of the mal-
let handles to pass through. The tappets are 4 pieces
of hard wood, 12 inches long, 5 wide, and 4 thick,
made in the form of half circles pinned to the ends of
the arms.

Fig. 27 the overshot water-wheel, similar to other mills.

Fig. 28 one of the 3 sills, 16 feet long, and 12 inches
square, with w alls under them as in the figure.

360 OF A FULLING-MILL, &c.

OPERATION.

The cloth is put in a loose heap into the stock 24;
the water being drawn on the wheel, the tappet-arms lift
the mallets alternately, which strike the under part of
the heap of cloth, and the upper part is continually fall-
ing over, and thereby turning and changing its position
under the mallets, which are of the shape in the figure,
to produce this effect.

Description oftheDrawings of the Iron-work s^PlateXXlV,

Fig. 1 is a spindle, 2 the balance-ryne, and 3 the dri-
ver, for a mill-stone. The length of the spindle from
the foot to the top of the neck is about 5 feet 3 inches ;
cock-head 8 or 9 inches from the top of the neck, which
is 3 inches long, and 3 diameter; blade or body 3| by
2 inches; foot 1| inch diameter; the neck, foot, and top
of the cock-head, steeled, turned and hardened.

Fig. % the balance-ryne, is sometimes made with 3
horns, one of which is so short as only to reach to the
top of the driver, which is let into the stone right under
it ; the other to reach near as low as the bottom of the
driver : but of late are mostly made with 2 horns only,
which may be made sufficiently fast by making it a little
wider than the eye, and let into the stone a little on each
side to keep it steady and from moving sideways. Some
choose them with four horns, which fills the eye too
much.

Fig. 3 is a driver, about 15 inches long.

Fig 4 the step for the spindle foot to run in. It is a
box 6 inches long, 4 inches wide at top, but less at bot-
tom, and 4 inches deep outsides, the sides and bottom
half an inch thick. A piece of iron 1 inch thick is fitted
to lay tight in the bottom of this box, but not welded ;
in the midle of which is welded a plug of steel 1 \ inch
square, in which is punched a hole to fit the spindle-foot
a quarter af an inch deep. The box must be tight to
hold oil.

Fig. 5 a step-gudgeon for large upright shafts, 16 inches
long and two square, steeled and turned at the toe.

Fig. 6 the step for it, similar to 4 but less proportion-
able.

OF SAW- MILLS. 36t

Fig. 7 is a gudgeon for large bolting- shafts, 13 inches
long and 1| square.

Fig. 8 a large joint-gudgeon, tang 14 inches, neck 5,
and tenon 2 inches long, 1| square.

Fig. 9 the socket part to fit the shaft, with 3 rivet<s
holes in each.

Fig. 10 — 14 — 18 pitman- irons, described art. 39.

Fig. 15 the wallo\ver gudgeon, tang 16 inches, neck
3 1 inches long, and 2-^ diameter.

Fig. 16 the water-wheel gudgeon, tang 3 feet 2 inches
long, neck 4-^ inches ditto, 3| square.

tig. 17 a saw-mill crank, described art. 39.

N. B The spindle-ryne, &c. is drawn from a scale of
2 feet to an inch, and all the other irons 1 foot to an inch.

In addition to what is said of Saw-mills, by Tho-
mas Ellicott, I add the following.

Of hanging the Saw.

First, set the fender posts as near plumb every way as possible, and the
head-blocks on which the log- is to lay, level. Put the saw right in he
middle of the gate, me^isuring from the out sides, with the upper teeth
about half an inch farther forward than the lower ones; set it by the gate
and not by a plumb line — this is to give the saw liberty to rise without
cutting, and the log room to push forward as it rises. Run the carriage
forward, so that the saw strike the block — stick up a nail, &c. there — run
it back again its full length, and standing behind the saw, set it to direct
exactly to the mark. S'retch the saw in the frame, rather most at the
edge, that it may be stifTest there. Set it to go, and hold a tool close to
one side, and observe whether it touch equally the whole length of the
stroke — try if it be square with the top of the head blocks, else it will not
make the scantling square.

Of xvhetting the Saw.

The edge of the teeth ought to be kept straight, and not suffered to
wear hollowing — the teeth seta little out, equal at each side, and the outer
corners a little longest— they will clear their way the better. Some whet
the under side of the teeth nearly level, and others a little droopmg down ;
but then it will never saw steady — will be apt to wood too much ; they
should slope a little up, but very little, to make it work steady. Try a
cut through the log, and if it comes out at the mark made to set it by, it is
shown to be right hung-

Z Z

362 OF SAW-MILLS.

Of springing Logs straight.

Some long small logs will spring so much in sawing as to spoil the
scantling, unless they can be held straight : to do which make a clamp to
bear with one end against the side of the carriage, the other end under the
log with a post up the side thereof — drive a wedge between the post and
log. and spring it straight; this will bend the carriage side — but this is no
injury.

Of moving the Logs, to the Size of the Scantling, i^c.

Make a sliding-block to slide in a rabbet in front of the main head block;
fasten the log to this with a little dog on each side, one end of which being
round, is drove into around hole, in the front side of the sliding-block, the
other flatted to drive in the log, cutting across the grain, slanting a little
out — it will draw the log tight, and stick in the better. Set a post ot hard
wood in the middle of the main block close to the sliding one, and to ex-
tend with a shoiilder over tht- slidintj one, for a wedge to be drove under
this shoulder to keep the block light. Make a mark on each block to
measure from — when the log is moved thf key is driven out. The other
end next the saw is best held by a sliding dog, part on each side of the saw
pointed like a gouge, with two .joint dogs, one on each side of the saw.

Remedy for a long Pitman.

Make it in two parts by a joint 10 feet from the crank, and a mortise
through a fixed beam, for the lower end of the upper part to play in, the
gate will work more steady, and all may be made lighter-

The feed of a saw mill ought to be regulated by a screw fixed to move
the hand-pole nearer or farther froni the centre of the roller that moves it,
which may be done as the saw arrives at a knot without stopping the mill.

END OF PART FIFTH.

APPENDIX,

CONTAINING,

Rules for Discovermg New Improvements ^

EXEMPLIFIED IN IMPROVING

THE ART OF CLEANING AND HULLING RICE,

WARMING ROOMS,

AND

VENTING SMOKE BY CHIMNEYS, §c.

The True Paths to Inventions.

NECESSITY IS called the mother of Inventions— but upon inquiry we
shall fi id, that Rt-ason and Expt-rimem bring them forth— For aimo-.! all
invent ons have been discovered by such steps as the following; which
aaay be taken as a

RULE.

STEP I. Is to investigate the fundamental principles of the theory, and
process ot the art or manufacture we wish to improve-

II. To consider what is the best plan in theory that can be deduced
from, or founded on those principles to produce the effVct we desire-
Ill. Consider whether the theory is already put in practice to the best
advantage; and what are the imperfections or disadvantages of the com-
mon process improved, and what plans are likely to succeed

IV Make experiments m practice to 'ry any plans that these speculative
reasonings may propose, or lead to — Any ingenious artist, taking the fore-
going steps. Will probably be led to improvements on his own art : for we
see by daily experience, that every an may be improved. It will, how-
ever, be in vain to attenipi improvements unless the mind be freed from
prejudice, in favour of established plans.

EXAMPLE I,

Take the Art of cleaning Grain by fVind.

BY THE RULE-
STEP I What are the principles on which the art is founded ? Bodies^
falling through resisiing mediums, their velocities are as their specific
gravities ; consequently the farmer they tall the greater will be their dis«
tance ; on this principle a separation can be effected-

364 APPENDIX.

II. what is the best plan in theory ? First, make a current of air for the
grain to tall throu^ch, as deep as possible ; then the lighiest will be carried
farthest, and the separation be more complete at the end of the tall- Se-
condly, cause the gran with the chaff, &c. to fall in a narrow line across
the ciirrt-nt, that the lighi parts may- nicirt no obsiruciion from the ht-avjr
in being carried forward- Third!), fix a movea'-lt- hoard edgewise to se-
parate between the good clean gra'h, and light grain, &c. F nr'hly, cause
the s^me blast to blow the grain several tiiiies, and thereby effect a com-
plete separation at one opt-raiion.

Ill- Is this theory in practice already ? what are the disadvantages of the
common process ? We find that the f.-»rmers' common fans drop the grain
in a line 15 niclies wide, to fall through a <iirrt-ni of air about 8 inches
deep, fins. e id of tailing in a Ime half an inch wide, through a current tliree
feet deep ) So that it requires a very sirong blast even to blow ou' 'he
chaff; but garlic, light grains, &c- cannot be got out, they meet so much
obs' ruction trom tlie heavy grams- It h:is to undergo iwo or three opera-
tions; so that the practice appears no way equal to theory; and appears
absurd when tried by the scale of re.>son.

IV. The fourth step is to construct a fan to put the tbeory in priictlce,
to try the experiment.* See Art. 83.

EXAMPLE II.

Take the Art of Distillation.

STEP I. The principles on wh'ch this art is founded are, evaporation
and condensation. The liquid being heated, ihe spirit it contains being
most oily and lightest, evaporates fiist into steam, which being condensed
again into liquid, by cold, is the spirits.

II. The best plan in theory for effecting this, appears as follows: the fire
should be applied to the still so as to spend the greatest part of its heat
possible, to heat the liquid. Secondly, the steam should be conveyed int»
a metal vessel of any form that may sui best; which is to be immersed in
cold water, to condense the steam; and in order to keep the condenser
cold, there shoi-ld be a stream of water continually entering the bottom
and flowing over the top of the condensing tub, the steam should have no
free passage out of the condenser, else the strongest part of the liquor may
escape.

Ill- Is this theory already p'tt in practice, and what are the disadvan-
tages of the common process ?— 1st Greatest part of the heat escapes up
the chimney. 2d. It is almost impossible to kef-p the grounds froni burn-
ing in the still. 3dly. The fire cannot be reguL.ted to keejAhe still from
boding over ; therefore we are obliged to run slow: to remedy these dis-
advantages — First, to lessen the fuel, apply the fire as much to the surface
of the still as possible Enclose the fire by a wall of clay that will not con-
vey the heat awa\ so fast as s'one ; let m as little a'r as possibly can be
made to keep the fire biiriiing ; for the air carries away the heat of the fii-e.
Secondly, to keep the grounds from bmning, immerse 'he still with the
liquor into a vessel of water, joining their tops together, then by applying
the fire to heat the water in the outside vessel the grounds v.ill not burn,

• This, Timothy Kirk, carpenter, of York-town, is about to do, and
ckiims the invention of the application of the samp blast several times, so
as to clean the grain completely ai one operation ; and if the plans are well
executed will no doubt excel all others vet made.

APPENDIX. 56*

and by regulating the heat of the outside vessel the still may be kept from
boiling over.

IV. A still of this structure was made by Colonel Alexander Anderson^
of Philadelphia, and the experinnent tried ; but the water in the outside
vessel boiled, and being open, the heat escaped thereby> and '.he liquor in
the still could not be made to boil — this appeared to defeat the scheme.
B'lt considering that by enclosing the water in a ti^ht vessel, so that the
steam could not escape, and that by compressure the heat might be in-
creased, and it passed to the liquor in the sliU, which now boiled as well
as if ihe fire had been immediaiely applied to the still. Again, by fixing
a valve to be loaded so as to let the sfeam escape, when arrived to such a
degree of heat as to be near boiling over, then the stili could not be iDade
to boil over at all.

Thus was an improvement produced, by which he can despatch business
in the ratio of 2 to 1, expei.ding fuel in the ratio of 2 to 2^, to produce
equal quantities of liquor. — We may bring forward another improvement
by considering, that, as we know by experience that compressure above
the weight of the atmosphere, keeps the stt^amfrom rising from the water,
till heated to a certain degree above the boiling heat. We may hence con-
clude that a compressure less than the atmosphere, will suffer it to rise
wiih a degree less than boiling heat, which suggests the expediency of tak-
ing off the pressure of the atmosphere from the liquor in the still, by which
means we shall expend less fuel, and the heat need never be so great as to
burn the grounds, which may be done by putting the end of the worm into
a light globular vessel of meial> and a cock between it and the condenser;
then inject steam from a small boiler, and expel all the air out of this ves-
sel; turn the cock and it will run into the condenser and be condensed.
By repeating this, a vacuum may be easily made, and kept up in the worm
and top of the still, and the spirits will probably come ofT with half the
heal ard fuel usually expended.

Th:s is aboijt to be put in practice to try the experiment. Proved to be
an error : much more heat is required to bring off the quantity of spirits.
See my woik on Steam Engines.

EXAMPLE.

Take the Art of Venting Smoke from Roo772S by Chimneys.

STEP I. The principles are: — Heat, by repelling the particles of air to
a greater distance, being lighter titan cold, will rise above it, forming a
current upwards, with a velocity proportional lo the degree and quantity
of heat, and size of ihe tube or funnel of the chimney, throu h which it as-
cends, and with u power proportional to its perpendicular height, which
power to ascend will always be equal to the difference of the weight of a.
column of rarefied air of the size ut the smallest part of the chimney, and
a column of common air of eqial size and height-

II. What is the best plan in theory for venting smoke, that can be found-
ed on these principles ?

1st. The size of the chimney must be proportioned to the size and close-
ness of the room and size of the fire ; because, if the chimney be immense-
ly large and 'he fire small, there <Aill be no current upwards. And again,
if the fire be large, and the chimney too small, the smoke cannot be all
vented by it, more air being noce^sai y to supply the fire than can find vent
up the chimney, it must spread in the room again, which after passing
through the fire and being burnt is suffocating.

a66 APPENDIX.

2d. The narrowest place in the chimney must be next the fire, and ia
front of it, so that the smoke would have to pass under it to get into the
room : the current will there be greatest, and will draw up the smoke
briskly-

3d, The chimney must be perfectly tight, so as to admit no air but at
the bottom.

Ill- The errors in chimneys in common practice are,

1st- In making them widest at bottom.
• 2d Too large for the size and closeness of the room.

3d. In not building them high enough above the wind whirling' over the
tops of houses, that blow down them.

4th. By letting in air any where near the bottom, destroys the current
of it at bottom.

IV. The cures directed by the principles and theory are,

1st. If the chimney smoke on account of being too large for the size and
closeness of the room, open a door or a wmdow, and make a large fire.
But if this be too expensive, make the chimney less at the bottom — its
size at the top will not be much injury, but will weaken the power of as-
cent, by giving the smoke time to cool before it leaves the chimney: the
room may be as tight, and fire as small as you please, if the chimm-y be in
proportion*

2d. If it be small at the top and large at the bottom, there is no cure but
to lessen it at the bottom.

3d. If it be too small, which is seldom the case, stop up the chimney
and use a stove — it will be large enouj^^h to vent all the air that can pass
through a two inch hole, which is large enough to kindle the fire in a
stove-* The chimneys built to put these theories in practice I believe are
every vxhere found to answer the purpose. See Franklin's letters on
smoky chimneys.

EXAMPLE IV.

Take the Art of Warming Rooms by Fire.

STEP I. The principles of fire are too mysterious to be investigated
here -, but the effects are,

1st. The fire ratifies the air in the room, which gives us the sensation
of heat or warmth.

2d. The warmest part being lightest, rises to the uppermost part of the
room, and will ascend through holes (if there be any) to the room above,
making it warmer than the one in which the fire is.

3d. If the chimney be open the warm air will fly up it first, leaving the
room empty, the cold air will then rush in at all crevices to supply its
place, which keeps the room cold.

II. Considering these principles, what is the best plan in theory for
warming rooms ?

1st. We must contrive to apply the fire to spend all its heat, to warm the
air as it comes in the room-

2d. To retain the warm air in the room, and let the coldest out first to
obtain a ventilation.

3d. Make the fire in a lower room, conducting the heat through the floor

• The quantity of fuel necessary to warm a room, will ever be in propor-
tion to the quantity of air that ascends the chimney.

APPENDIX. 367

into the upper one, and leaving another hole for the cold air to descend to
the li/wer rf)()m

4ih M.iktr the roonn perfectly tight so as to admit no cold air, but all
warmed js it comes m.

5'h By stopping up the chimney to lei no warm air escape up it, but
what is absoliUfly ne.:essary to kindle thefiie — a hole of two square inch-
es will be sufficient for a very large room.

6rh. The fire may be kindled, by a current of air brought from wlhout,
noi using uny of the air already warmed. If this theory, which is found-"
ed on true principles and reason, be compared with common practice, the
errors will appear— ihe disadvantaj^es of which may be evaded.

III. I had a stove consM-ucted to put this theory as fjlly in practice as
possible, and have found all 'o answer according to theory.

The operation and effects are as follows, viz.

1st. It applies the fire to warm the air as it enters the room, and admits
a full and fresh supply, rendering the room mod' ra'ely warm ihroughnut.

2d. It effectual y prevents the cold air from p:essing in at the clunks or
crevices, but causes a small current to pass ou'wards.

3d. It conveys the coldest air out of the room first, conseqiiently,

4th. It is a complete ventilator, thereby renderir.g the irxirti healihy.

5th. The fire m;iy be supplied (in very cold wi a>li(-r) by a current of air
from without, that dOfS not communic.-te with the warm air in the room.

6th. Warm air may be ret-ined in the room any lengt of time, at plea-
sure ; circulating through the stove, the coldest entering first to be warm-
ed over again *

7th. It will bake, roast, and boil equally well with the common ten plate
stove, as it has a capacious oven.

8'h. In consequence of these philosophical improvements, it requires not
more than half the usual quantity of fuel.

Description of the Philosophical and Ventilating Stove.

It consists either of three cylindric or square parts, the greatest sur-
rounding the least. See plate X. fig. 1. SF is a perspective view hereof
in a square form, supposed open at one side : the fire is put in at F, in the
least part which comiiiunicates with the space next the outside, wliei e i he
smoke passes to the pipe 1 — 5. The middle part is about two mclit-s U ss
than the o-'tside part, leaving a large space between it and above ihe in-
ner part for an oven, in which the air is warmed, being brought m by a pipe
B D between the joists of ll.e floor, from a hole in the w all ai B, ns ng mto
the stove at U, in'o the space -ind oven sunocnding the fire, which air is
again surrounded by the smoke, giving the fire a fuil a .ion to waim it,
and ascending into tiie room by ihe pipe 2- K brings air from itit p pa
DB to blow the fire. II is a view of the front end piate, show.ng the fire
and oven doors I is a view of the back end, the plate bein,, off, tlif. uark
sqiare shows the space for the fire, and the light part the air space vur-
rounding the fire» the dark outside space the smoke surrounding the air;
these are drawn on a larger scale. The stove consists of 15 plates, 12 of
which join one end against the front plate H.

To apply 'his stove to the best advantage, suppose fig- 1, pla e X. to re-
present a three or four story house, two rooms on a floor — set ihe stove SF

• This application was suggested to me by Isaac Garret son, of York-
town, on his viewing the stove and considering its principles whilst I had
it m^tng.

368 APPENDIX.

in the partition on the lower floor, half in each room ; pass the emoke pipe
throui^h all the stories: make the room very close ; let no air enter but
what comf s in by the pipes A B or CC through the wall at A and G, that it
may be the more pure, and pass through the stove and be warmed. But
to convey it to any room, and take as m>ich heal as possible with it, there
must be an airpipe surrounding the smoke-pipe, with a valve to open at
every floor. Suppose we wish to warm the rooms No. 3 — 6, we open the
valves, and the warm air enters, ascends to the upper part, depresses the
cold air, and ii we open the holes a — c it will descend the pipes, and enter
the stove to be warmed again : this may be done in very cold weather. The
higher the room above the stove, the more powerfully will the warm air as-
cend and expel the cold air. But if the room requires to be ventilated,
the air must be prevented from descending, by shutting the little gate 2 or 5,
and drawing 1 or 6, and giving it liberty to ascend and escape at A or G — or
up the chimney, letting it m close at the hearth. If the warm air be con-
veyed under the floor, as between 5 — 6, and let rise in several places, with
a v.ilve at each, it would be extremely convenient and pleasant ; or above
the floor as at 4 — several persons might set i.heir feet on it to warm. The
rooms will be moderately warm throughout — a person will not be sensible
of ihe coldness of the weather.

One larije stove of this construction may be made to warm a whale
house, ventilate the rooms at pleasure, bake bread, meat, &c.

These principles and improvements ought to be considered and provid-
ed for in bulding.

EXAMPLE V.

Take the Art of Hulling and Cleaning Rice,

STEP I. The principles on which this art may be founded will appear
by taking a handful of rough rice, and rubbing it hard between the hands

the hulls will be broken off, ;<nd by continuing the operation the sharp

text: re of the outside of the hull (which through a magnifying glass ap-
peavs like a sharp fine file, and no doubt is designed by nature for the puijj
pose) will cut off the inside hull, the chaff being blown out, will leave the
rice perfectly clean, without breaking any of the grains.

11 What is the best plan in theory for effecting this ? — See the plan pro-
posed, represented plate X fig 2 — explained art. 103.

Ill- The disadvantages of the old process are known to those who have
it to dO'

EXAMPLE VL

To Save Ships from Sinking at Sea.

STEP I- The principles on which ships float, is the difference of their
specific gravities from that of the water, bulk for bulk— sinking only to
displace water equal in weight to the ship; therefore, they sink deeper in
fresh than salt water. If we can calculate the cubic feet a ship displaces
when empty it will show her weight, and subtracting that from what she
di places when loaded, shows the weight of her load, each cubic foot of
frtsh water being 62,5lb. If an empty rum hogshead weigh 62,51b. and
measure 15 cubic feet, it will require 875 lb. to sink it. A vessel of iron.

APPENDIX. 369

&c. filled with air, so large as to make its whole bulk lighter than so much
water, will float, but if the air be let out and filled with water, will sink.
Hence we may conclude that ships, loaded with any thing that will float.
Will not sink, if filled with water; but if loaded with any thing specifically
heax'ler th^n water, will sink as soon as filled.

II This appears to be the true theory — How is it to be put in practice,
in case a ship springs a leak, that gains on the pumps ?

III. The mariner who understands well the above principles and theory,
will be led to the following steps.

1st. To cast overboard such things as will not float, and carefully to re-
serve every thing that will float, for by them the ship may be at last buoy-
ed up.

2d. Empty every cask or thing that can be made water-tight, and put
them in the hold and fasten them down under the water, filling the vacan-
cies between them with billets of wood; even the spars and masts may be
cut up for this purpose In desperate cases, which will fill the hold with air
and light matter, and as soon as the water inside is level with that outside,
no more will enter. If every hogshead buoy up 8751b. they will be a great
help to buoy up the ship, (but care must be taken not to put the empty
casks too low, which wo'dd overset the ship) and she will float, although
half her bottom be torn off. Mariners, for want of this knowledge, often
leave their ships too soon, taking to their boat, altliough the ship is much
the safest, and does not sink for a long time after being abandoned — not
considering, although the water gain on their pumps at first, they may be
able to hold way with it when risen to a certain height in the hold, be-
cause the velocity with which it will enter, will be in proportion to the
square root of the diflference between the level of the water inside and out-
Bide — added to this, the fuller the ship the easier the pumps will work,
tberetore they ought not to be too soen discouraged.

EXAMPLE VII.

Take the Art of Preserving Fruits, Liquor s, ^c. from
Putrefaction and Fermentation.

STEP I. What are the principles of putrefaction and fermentation ? By
experiments with the air-pump it has been discovered that apples, cher-
ries, &c. put in a tight vessel, having the air pumped out, wdl keep their
natural fresh bloom for a long time- Again, by repeated experiments it
is proved things frozen will neither putrify nor ferment while in that state.
Hence we may conclude that air and heat are the principles or moving
causes of putrefaction and fermentation.

II. What plans in theory are most likely to succeed ? By removing the
causes we may expert to evade the effect-

1. Suppose a cistern m a cellar be made on the side of a hill, and sup-
plied by a spring of cold water running in at the top, that can be drawn off"
at the bottom at pleasure. If apples, &c. be put in tight vessels, and the
air pumped out, and beer, cider, &c. be put m this cistern, and immersed
in water, will they putrify or ferment I May not the experiment succeed
in an ice-house, and fruits be conveyed from one country to another in glass
or metal vessels made for the purpose, with the air pumped out and her-
metically sealed.

In support of this hypothesis, a neighbour of mine told me, he filled a
rum hogshead in the fall full of apples at the bung, bunged it tight, and in

3 A

370 APPENDIX.

the spring found them all sound ; another, when a hoy, buried a hollow ^in
bee hive full ot apples, trampled the earth tight about tliem, opened tliem
when the wheat bei^an to npen, and found them all sound, but leaving
thenn, returned in a day or two, and found them all rotten*

I^or those who Bead to have Leisure.

BY the right use of Natural Philosophy and Reason, aided by Experi-
nienis, m:^ny im|)rovements might be made thai would add much to the
conveniences and comforts of lite- But the great obstacle is the expense
of experiments, in reducing theory to practice, which tiew will risk- For
when a man attempts to m^ike any improvements, he is sure to be ridiculed
until he succeeds, and then the invention is often depreciated — Dr. Frank-
lin said— that "a man's useful inventions subject him to insult, robbery,
and abuse" — but this I have as yet experienced only from two or three in-
dividuals from whom it was least to be expected- I am firmly persuaded,
that if, in iuy country, the small sum of ■ dollars annually, was aa->

signed to red <ce to practice probable iheonts, the arts would rise in im-
provement beyond any precedent that history can evince; and the power
and wealth of the nation in pi-oportion — For a long list of inventions la
theory might be given, that offer fair to be very useful in practice, that lie
dormant until the inventor can make experiments with convenience, to re-
duce them to practice — many of which, no doubt, will die with the inven-
tors.

Sensible of the expense, time, labour, and thought, that this (though
small) work has cost me, and hoping it may be well received by, and prove
serviceable to, my country — 1 wail to see its fate ; and feel joy in being
ready to say — FINIS.

• Much contained In this Appendix is to be found in different authors;
and several things, which I thought bad originated with myself, have been
treated of by Dr- Franklin.

APPENDIX. S7l

COMMUNICATION.

The following Essay on Saw-Mills^ &c. I receiv-
ed from William French, Mill-wright^ Bur-
lington county^ (JVew Jersey.) si?ice I concluded,
and fearing I may not have another opportunity,
I publish it,

SAW-MILLS have been much improved in this state, for low.heads»
Mills wi'h two saws, with not more than 7 feet head and fall, have sawed
5 and 6 hundred thousand feet o> board:>, plunk, and scantlmg, in one year.
If (he w^-ter be put on the wheel in a proper manner, and the wh el of a
proper size, (as by the following table) the sa« will strike between 100
and 130 strokes in a minute : see fig. I, plate XIV- The lower edge of the
breasi-beam B to be 3 4 the height of the wheel, and one inch 'o a toot,
slanting up stream, fastened to the penstock-pos's wuti screw-bolts, (see
post A) circled out to s'lit the wheel C; the tall D circled to soit the
wheel and extended to F, 2 inches above the lower edge of the breast-
beam, or higher, according to the size of the throat or slnice E. with a
shuttle or gate sliding on FE, shutting against the breast-beam B: then
4 buckets 0'>t of 9 will be acted on by the water- The method of fasten-
ing thf buckets or floats is, to step them in starts mortised in ibe sh^fi-^
see start G— 4 buckets in a wheel 4^ inches wide, see them numbered
1, 2, &c.

Fig. 2, is the go-back, a tub-wheel. Its common size is from 4^ to 6 feet
diameter, with 16 buckets- The water is brought on it by tlie trunk H.
The bucket I is made with a long tenon so as to fasten it with a pin al the
top of the wheel

TABLE

Of the Dimensions of Flutter-wheels.

Head 12 feet-

Bucket 5 feet.

Wheel 3 feet.

Throat 1 3-4 inch

512

2 18

61-2

2 10 inches

21 4

2 9

212

71-2

2 8

314

2 7 p.

312

2 6

3 3 4'

N'. B. The crank about 11 inches, but varies to suit the timber.

372 APPENDIX.

The Pile Engine.

Fig-. 3, a simple machine for driving piles in soft bottoms for setting
mill-walls or dams on. It consists of a frame 6 or 7 feet square, of scani-
linef, 4 by 5 inches, with 2 upright posts 2 inches apart, 10 or 12 tee« high,
3 bj 3 Inches, braced from top to bottom of the frame, with a cap on 'op 2
feet long, 6 by 8 inches, with a pulley in its middle, for a ropp to bend over
fastened to a block I, called a tup, which has 2 pieces 4 inches wide be-
tween the uprights, with a piece of 2 inch plank T, 6 inche< wide, fr;inied
on the ends, so as to slide up and down the upright posts S- This machme
is worked by 4 or 6 men, drawing the tup up by the sticks fastened to the
end of the rope K, and letting it fall on th. pde L : they can strike 30 or
10 strokes by the swing of their arms in a minute-

Of building Dams on Soft Foundations.

The best method is to lay 3 sills across stream, and frame cross sills in
them up and down stream, setting the main mudsills on round pdes, and
pile them with 2 inch plank, well jointed and drove close together edge
to edge, from one to the oilier end- By taking one corner off the lower
end of the plank will cause it to keep a close joint at boliom, and by driv-
ing an iron dog in the mud-sill, and a wooden wedge to keep it close at
the top end will hold it to its place when the tup strikes- Ii is necessary
to pile the outside cross sills also in some bottoms, and to have wings to run
10 or 12 feet into the bank at each side; and the wing-posts 2 or 3 feet
higher than the posts of the dam, where the water falls over, planked to
the top NN, and filled with dirt to the plaie O.

Fig. 4, IS a front view of the breast of the t'mbling dam-
Fig. 5, is a side view of the frame of the tumbling dam, on its piling a b
c d e and f g h is the end of the mud sills. The posts k are framed into
the main mud-sills with a hook tenon, leaning down stream 6 inches in 7
feet, supported by the braces 1 1, framed in the cross sills I; the cross sills
I to run 25 feet up and down stream, and be well planked over ; and the
breast-posts to be planked to the top (see P, fig- 4,) and filled with dirt on
the upper side, within 12 or 18 inches of the plate O ; (sei:- Q, fig. 5,) slant-
ing to cover tlie up stream ends of the sills 3 or 4 feet deep : R represents
the water.

When the heads are high it is best to plank the braces for the water to
run down, but if low, it may fall perpendicularly on the sheeting.

I THINK it my duty to embrace this opportunity, once more to at-
tempt at drawing the attention of my fellow-citizens, to the most ruinous
error tliat the supreme legislature of my country has commiited, viz The
laws do not protect the inventors of useful improvements in the arts, in the
exclusive enjoyment of the fruits of their labour, for a s.fficient length of
time, nor afford them any adequate compensation, but make them common

APPENDIX. 373

to all at the end of 14 years ; a time barely sufficifeht to mature (in this
country) any useful improvement. The consequence is, the inventor is de-
luded by the name of a patent, and his hopes raised by the accounts he has
heard of the success of inventors in England, and he makes great exertions
and sacrifices to mature, and introduce into use, his improvements; but
just us he begins to receive compensation his patent expires, his sanguine
hopes are all blasted, he finds himself ruined, and conceives that he has
been robbed by law, is thrown into despair, and tempted to deem the pre-
cious gift of God (rendering him useful to his country) as a curse; his chil-
dren that n»ay receive the same gift, bury their talents to shun the danger.
Thanks to the Divine Disposer of Events, I have narrowly escaped the
worst part of this general fate, having had prudence sufficient to suppress
(with murh difficulty) my great desire of putting into operation the many
useful improvements and discoveries that opened clearly on my mind, so
far as to attend to carrying on some regular business for the support of my
family, and defrslying the expense of my experiments, at the same time
that my mind was principally employed in the investigation of principles,
and inventing useful improvements. I am however free to declare, that
all my study, labour, and time expended during the most vigorous half of
my life, in making new inventions, &c. I account as lost to myself and fa-
mily, excepting the time, &c. expended in compiling and publishing this
work, the exclusive right of selling which, is by law secured to me for a
second term of 14 years. Two years ago I totally relinquished all pursuit
of new improvements, and there is nothing more irksome to me at present,
than »o be troubled with the description of any proposed new improve-
ments, or to be asked for my opinion or advice concerning them ; and
I do request the reader, to refrain from intruding in the least on my
time in that way, either by written or verbal commnnications, and I do
further declare that I do verily believe, that had the laws been such as to
ensure adequate compensation, I could in the time already past, have in-
vented and introduced into use other improvements that would have prov-
ed ten times as beneficial to my country, as all those which I have accom-
plished ; but I have been forced to bury my talent with disgust ; and have
bound in a bundle the drawings and specifications of my inventions, which
I have discovered and matured, ready for putting into operation, at the ex-
pense of the most intense study and labour of the mind, resolving never to
open them, until the laws make it my interest, or their own, to do so; be-
cause a patent in this country is not yet worth the expense of obtaining
it.

If I did believe that these declarations would only tend to damp the ar-
dour of the American genius, far would it be from me to make them> (in
this I may indeed have erred :) but looking forward to futurity I contem-
plate a contrary effect; (worse the case cannot be made — the ardour of all
prudent men has long ago been sufficiently damped, to prevent them from
engaging in such pursuits.) >Joihing but such a statement of real facts, in
plain truth, will rouse the attention of our legislators to a revision of the
laws, so as to protect inventors, as well as other classes of the community,
in the enjoyment of the fruits of their labours, for a sufficient length of
time, to remunerate them for their time and labour, and reward them for
their perseverance and ingfenuily, in proportion to the benefits they render
their country; which alone can inspire them with renewed hope, and give
new spring to genius ; for it is absurd to suppose that any prudent man
will labour for property which he must surrender by law, often before he
can fully acquire it, or that expensive experiments should be made with-
out hopes of reward. But if congress will extend the patent term to a pe-
riod that will ensure adequate compensation, and change the present road
to rtiin and disgrace, (in which none but the imprudent will walk,) to a
path leading to wealth and honour, they will soon see many prudent, inge-

3/4 APPENDIX.

nious men walking therein ; and the arts will improve with a progress more
raptd than hitlierto known in any country, and arrive *' a greater de^^ree of
perfection in half a century, than in a thousand years under the present
discouraging system of lepal robbery. Then, mstead of discoveries tjemg
suppressed, they wdl be put in operation, and the good people will receive
tile benefits.

I wish not to be understood to have relinquished the pirsuit of improve-
ments on the business I may follow, or in ♦he application o'' my new prin-
ciple to steam rngmes, which I have patentedr; no, this 'oven'ion is already
accomplish, d, and lam striving to make the hest of it during my patent
term — 1 make steam engines which will work with a power of lOOI'-s to
the inch area of the work piston ; one of eight inches diameter to carry a
load of 5000 ib. when required in extraordinary cases. This is ihv ■ nly
principle whcb will apply to propel boats against the current of the Mis-
sissippi by steam, and it may be much improved on in its application for
that purpose ; ali attempts without it will fad to be useful, because 'here
is no other principle in nature left, that will serve as a substitute. When
those improvements shall be made in the application of this principle, and
shall be put in full operation to navigate that great commercial river, then
will the absurdityof that penurious system, which has ftl.-eadykept backthis
great and useful discovery for upwards of twenty years, mos^ glarin .ly ap-
pear. Let a calculator si down to conpute the anniial btnefits iha w-U
arise to the people, and he will be astonished at the many m llionsof dol-
lars that will appear as ihe result. This calculation I refrain from slating,
because I believe, chat most of my readers would supi>ose me deranged.
The truth will not bear to be told m this case, even lo those whose local
situation is such, that they would be raosi bei'efi'ted

For a full explanation ot my improvt ment on steam engines, see my new
work, entitled, "The .\bortion of the Young Ste<m Engineer's Guide.**
Price 125 cents. I am well prepared to construct stea.ii engines, on short
notice for those who may want them: they will serve as a substitute for
water falls, with great advantage, where fuel is pi' nty. I have established
works for the purpose, consisting of an iron foundry, ste^m engineer's
shop, mould maker's shop, steam mill for turning and boring heavy iron
work, and a blacksmith's shop, all connected: Also, a m'U-sion manufac-
tory'— and am prepared to execute all orders th^t I may receive in either
of the above lines, especially for ensfine and mill-woi ks, of either cast or
wrought iron- Apply at Mars's Works, Philadelphia.

THE END.

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