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| UNIVERSITY OF MICHIGAN |
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SIQUEKS PENINSULAM AMⱭNAM
MSPICE
AHLILERFILLERISIMINIMUMITTEMMIII.
Received IN EXCHANGE
FROM
Rhode Island State
College Library
Samael B. Wright, J. W., Ph. D.
A
TREATISE
Sorm
OF
Lasising Line

MECHANICS,
THEORETICAL, PRACTICAL,
AND
DESCRIPTIVE.
BY
OLINTHUS GREGORY,
OF THE ROYAL MILITARY ACADEMY, WOOLWICH,
VOL. II.
CONTAINING
Remarks on the Nature, Construction, and Simplification of Machinery,
on Friction, Rigidity of Cords, First Movers, &c.
AND
Descriptions of many curious and useful Machines.
Talem intelligo Philosophiam naturalem, quæ now abeat in fumos
speculationum subtilium, aut sublimium; sed que efficaciter operetut, ad sub-
levandi vitæ humanæ incommoda. BACON. De Aug. Sci.
LONDON:
PRINTED FOR GEORGE KEARSLEY, FLEET-STREET;
1806.
Efeti
Dia
Library
Rhode Island State carlyc
3-7-1941
vet z
CONTENTS.
1
4
or
VOLUME II.
PRACTICAL MECHANICS:
On the Conftruction and Simplification of Machinery
On Rotatory, Rectilinear, and Reciprocating Motions
On Bevel-Geer, and Proportioning the Number of Teeth
On Uniformity and Smoothness of Motion
On the Operation and Ufe of a Fly
On Friction and the Stiffness of Cords, with the Experiments
of Vince, Coulumb, &c.
Page
2
12
17
An Example of the Power of the Capftan, allowing for Fric-
tion and the Rigidity of Cords
42
On Water as a Mover of Machinery ·
44
On Wind as a Mover of Machinerÿ, with Smeaton's Rules
relative to Wind-mills
46
On the Strength of fired Gunpowder
52
On Steam as a Mover of Machinery, with the Reſults of
Bettancourt and Dalton
54
On Animal Strength, Men
65
Herfes
68
DESCRIPTIONS OF MACHINES.
Air-pump, by Mendleſſöhn
80
Atwood's Machine for variable Motions
84
Balance, Hydrostatic Balance, Danish Balance
91-100
Balance of a Watch
100
Bark-mill
103
42
5
ir
CONTENTS.
Barker's Mill
Page
106
Barometers of various kinds
Beer-drawing Machine
Bellows for Forges
Bramah's Hydrostatic Prefs
The Camel
Capftan
112 et feq.
117
117
120
122
124
Cellar Crane
124
Centrifugal Pump
125
Chimney-cleansing Machines
125
Churn
129
Clocks
130
Treatifes on Clocks and Clock-making, &e.
140
Gaining, and Coining-mill
$46
Beam Compaffes, by Walton
149
Condenser
150
Condenser of Forces, by Prony
151
Crab for Artillery
153
Cranes of various Kinds, and a lowering Regulater, by
Hardie
Crane, or Syphon, with an Account of Clofe's Apparatus të
154 et seq.
raife Water above its Level
165
Cylinders, boring of, for Steam-engines
168
Ellipfograph
169.
Engine to let down great Weights
170
File-cutting Machine
171
Fire-escape
173
Fire-engines
175
Writings on Fire-extinguiſhers
179
Flax-mill
182
Flour-mill, with Tables
184
Fly
195
}
Foot-mills
196
Forcer, temporary, by Trevithack
196
CONTENTS,
Page
Gibbet of a Crane
Gimbals
Glazier's Vice
Gravimeter, by Guyton
Hand-mills
Heart-wheel
Hydraulic Engines, the Tympanum
$197
198
109
199
202
203
204
De la Faye's Wheel
the Noria
the Perfian Wheel
204
206
206
Chain Pumps, Paternofter Work, &c. 208
Hero's Fountain
209
Darwin's Engine:
210.
Hungarian Machine
210
Bofwell's Improvement of Ditto
214
the Spiral Pump at Zurich
216
Defaguliers's Drawer and Bucket
223.
Sarjeant's Machine
-224
Dearborn's Pump-engine
226
Catalogue of Treatifes reſpecting
228
Hygrometers of various Kinds
231 et feq.
Jack to raife Loads
235
Smoke-jack and Kitchen-jack.
237
Joints, univerfal
237
Kneading-mill
237
Lathe
239
Lens-grinding Machine
..239
Lever, univerfal
·240·
Loading and unloading Goods, Machine for
241.
Locks
242
Mangle
243
Machine at Marly
&
244
Mill and Bolter, for Families
248
Mills, Account of Treatifes relative to
250
vi
CONTENTS.
Page
Muller, Concave
253
Qii-mill
254
Ordnance Boring, Machine for
262
Parallel Motions, Contrivances for
264
Pendulums of various Kinds
267
Penstock
273
Pile-engines, Vauloue's and Bunce's
274-276
Pipe-borer
276
Planet-wheel
278
Preſſure-engines
Prefs, Binder's, Printing, Rolling, &c.
Pulleys, White's, Garnett's, &c.
Pumps, a great Variety, with Remarks on Piſtons, Valves,
&c
Pyrometers, by Muschenbroek, Graham, Wedgwood, &c.
Ramfden's Machine for dividing Inſtruments
279
283
286
288 et feq.
306
311
Reverſing of Motions, Contrivances for
320
Ratatory. Apparatus, Woolf's
323
Saw-mills, by Mr. Smart and others
324
Scapements, various
329 et feq.
Screw, Archimedes's
343
:
352
Shoemakers' Implement
Steam-engines, by Savary, Newcomen, Blakey, Gainsborough,
Watt, Hornblower, Cartwright, Murray, Bettancourt,
Woolf, &c.
Steelyard, by Paul of Geneva
353-405
405
Steelyards to afcertain Human Strength
411
Stream-weaſurers
412
Surface-planer, &c. by Bramah
415
Teeth of Wheels, &c. Formation of
422
Telegraphs, by Hooke, Amontons, Chappe, &t.
434
Thermometers, of various Kinds
442 et fege
Thrashing Machines
458
Tide-mills
462
CONTENTS.
vii
Page
Turning Apparatus, by Maudflay
47
Teeth-cutting Apparatus, by Maudflay
47!
Turning Apparatus, by Smart
475
Watch, Repeating ditto
477
480
Watchman's Noctuary, or Labourer's Regulator
Water-mills, Undershot, Overfbot, Floating, &c.
Weighing Machines for Carriages
483
Weighing Apparatus for Goods, by Hardie
Wheels without Cogs
Wind-mills, by Verrier, Beatfon, &c.
Wipers, their beft Forms
Yarn-mill
493
496
498
499
508
511
}
1
MECHANICS
7.
I.
Remarks on Machinery in General.
MECHANICS, according to the original import of the word,
treats of the energy of Machines: and theſe machines are no-
thing more than organa, or tools, interpofed between the work-
man or natural agent and the taſk to be accompliſhed, in order
to render that work capable of being performed, which under
the limits and circumftances propofed would have been difficult,
if not impoffible, without the intervention of fome of theſe con-
trivances.
•
45
Machines are interpoſed, as was remarked (art. 379. vol. 1.),
chiefly for three reaſons. 1. To accommodate the direction of
the moving force, to that of the reſiſtance which is to be over-
come. 2. To render a power which has a fixed and certain
velocity efficacious in performing work with a different ve-
locity. 3. To enable a natural power, having a certain de
terminate intenſity, to balance or to overcome another power or
obſtacle, whoſe intenſity or reſiſtance is greater. Each of theſe
purpoſes may be accompliſhed in different ways: i. e. either by
machines which have a motion round ſome fixed and ſupported
point, as the lever, the pulley, and the wheel and axle; or by
thoſe which, inſtead of being fupported by a fixed point, about
which they move, furniſh to the refiftance, or body to be moved,
a ſolid path, along which it is impelled, as the inclined plane,
the wedge, and the fcrew. Compound machines are peculiar
combinations of theſe fix, of which we have treated individually
in the firſt book of our firſt volume: fome remarks likewife
upon their combination have been given in Book I. Chap. IV.
art. 161. and Book II. Chap. VI. And we have treated of the
ftrength of the materials of which machines may be compofed, in
Book I. Chap. V. Such farther obfervations as appear neceffary
to complete a theoretical and practical knowledge of Machinery
in general, previous to our alphabetical deſcription of particular
machines, will now be prefented to the ſtudent.
VOL. II.
B
་་
:
N
MECHANICS.
1
2. Simplicity in the conſtruction of machines cannot be too
warmly recommended to the young engineer: for multiplicity
of parts and of motions increaſes the expence of erection,
augments the friction, and multiplies the danger of failure by
the bending or by the inaccurate adjuſtment of the parts. In
confequence of the effects of friction (of which we ſhall ſpeak
more fully, art. 24, &c.), it is well known to all engaged in the
practice of mechanics, that by no combination of wheels, or
levers, or other powers, can one weight be made to move an-
other with a greater or even an equal momentum: and by the
multiplication of wheels, levers, &c. the effect of the machine,
inſtead of being increaſed, is diminiſhed in proportion to the
augmented friction of the moving parts. Hence it follows that
in practice, effect is loft by mechanical combination, but gained
by fimplification; and that the most perfect machine is that
which operates by the feweft moving parts. In order to con-
trive a fimple machine to be theoretically equivalent in power to
a complex one, the following rule may be obferved: Conſtruct
the various parts of the fimpler machine fo that the velocity of
the impelled point (art. 365.) fhall be to that of the working
point, in the fame ratio as they are in the compound machine;
then will the effects of theſe two machines be the fame, fo far as
depends upon pure theory: but in practice the fimpler will be
the more efficacious, in confequence of the diminution of
friction.
3. For an example, fuppofe the compound machine fig. 1.
pl. II. were to be propofed, in order that a more fimple one
might be conftructed to perform the fame work. Let CA, the
lever to which the power is applied, be 10 feet, DE five feet in
diameter, EF=2 feet, HI= 3 feet, GH = 5 feet, and KL=
I foot, the latter being the cylinder on which the rope raiſing
the weight W folds. Now the diameter of the circle defcribed
by the
power at A is 20 feet: and to find the diameter of the
circle whofe circumference is equal to the ſpace paffed over by
W in one revolution of the lever CA, reduce the following frac-
tion, viz. X
}
DE GH KL
X = 2/3/18 × 1/2 × 3 = of 2 AC; confe
2 AC EF HI
5
20
5
24
5
24
24
quently the velocity of the weight is of that of the power.
And hence, if upon the vertical axis CM (fig. 2. pl. II.) a wheel
be fixed the diameter kl of which is equal to 4 feet (that is,
of 2 AC), the weight W will be raiſed the fame height by the
fimple as by the compound machine, at every revolution of the
power A. So that, the fimple machine ACM kl, will be at
leaft equal in effect to the compound one ACMDEFGHIKL,
and the wheels DE, EF, GH, HI, and KL, are extraneous, and
probably prejudicial.
Simplification of Machinery.
3
4. For another example take the following, In the common
wheel and axle, the advantage gained is in the ratio of the radius
of the winch to that of the barrel: fo that when it is propofed to
increaſe that advantage, either the handle muſt be lengthened,
or the diameter of the axle diminiſhed; neither of which, how-
ever, is practicable beyond certain limits, becauſe the handle
might be too long for convenient management, or the axle too
flender to ſupport the load: in ſuch caſes it is ufual to annex
another wheel and pinion, or a tackle of pulleys. But the fol-
lowing conftruction is greatly preferable. In fig. 7. pl. I. the
part A of the barrel is larger than the part B, and the rope
which paffes under the pulley C and fuftains the weight D is
wound upon each in contrary directions. Whenever, therefore,
the handle EF is turned, fo as to gather the rope upon the larger
cylinder, it will be given off by the fmaller: and for every turn
of the larger, or its correfpondent portion of rope wound up,
there will be given off a portion of rope anfwering to the circum-
ference of the fmaller. Confequently, the quantity of unwound
rope will be lefs after fuch a turn, by a portion equal to the
difference between the circumferences of the two cylinders;
and the weight D will be raiſed through half that ſpace.
Whence, fince the radii of circles are as their circumferences,
we may uſe this analogy:
As the radius of the winch,
To half the difference of the radii of the cylinders;
So is the weight,
To the power balancing it.
In fig. 8. is exhibited a fimple capftan in which the fame con-
trivance is adopted. Here, if the upper barrel A were 17 inches
diameter, and the lower B 16 inches, the pulley C being alfo
16 inches diameter; it will be obvious that this fimple capftan
will be equivalent to an ordinary capftan of the fame length of
bar EF, and diameter of barrel B, combined with a 16-fold
tackle of pulleys; and at the ſame time free from the great lofs
by friction and bending of ropes, which would abſorb at leaſt a
third of the power of a 16-fold tackle.
One peculiar advantage of this engine is, that the half differ-
ence of the radii of A and B may be diminiſhed ad libitum, with-
out weakening the cylinder, increafing the friction, or requiring
any rapid curvature of the rope. This windlafs has likewife the
peculiar property of holding the weight at any part of its rife
or fall without needing a ratchet wheel and catch. Its only
practical diſadvantage, that a great quantity of rope muſt be
ufed to produce a moderate change in the poſition of the
weight; but the quantity of rope will be much leſs than what
is requiſite for an equivalent tackle of pulleys. This ingenious
B 2
4
MECHANICS.
{
contrivance is generally afcribed to the celebrated George
Eckhardt; and he probably invented it without knowing that
it had been uſed elſewhere: but we have ſeen a figure, from
which our figure 8. is merely a copy, in fome Chineſe drawings
of nearly a century old.
5. The methods of communicating motion from one thing to
another, or from one point to another, are almoſt infinitely di-
verſified: fo that it will not be expected that they fhould all be
defcribed here. It is manifeſt that the communication of mo-
tion will in different circumſtances be better effected by means
of one ſimple machine (or, as they are ufually called, mecha-
nical power), than by another; and much of the ſkill of the
engineer confifts in chooſing the inftrument moſt proper for the
purpoſe propofed and the fame will be the caſe with regard to
more complex machines. In fome inftances a fimple lever, or
a fimple unbent cord, will anſwer better than any combination:
in others it may be highly advantageous to ufe a combination of
levers acting upon each other, by means of fo many fulcra; and
by theſe the direction may be changed at pleaſure: in others, as
when motion is communicated to a ſeries of wheels and axles in
fucceffion, it may be effected by a rope running in grooves
round one wheel and the fucceeding axle; or by what was de-
ſcribed in vol. I. art. 246. under the name of tooth and pinion
work in others again, by a barrel and winch with an endleſs
fcrew, And many other contrivances will readily fuggeft them-
felves to an ingenious artiſt.
6. But fuch fimple methods cannot always be adopted. Thus
when it is required by means of a rotatory motion to produce a reci-
procating one, as the alternate motion of the piftons of pumps,
for example; one of the following contrivances may be uſed.
To a vertical ſhaft as AP (fig. 6. pl. II.) fix a large horizontal
wheel MOIL, the lower part of which is indented in waves
MSO, OQI, &c. of which the conftituent arches are either
circular or parabolic. On a convenient point D of an upright
poſt as a centre of motion, let a lever EDC move; one end of
it carrying the moveable vertical wheel CR, in fize properly
adjuſted to the waves of the horizontal wheel; the other EF
being a circular arc to which is applied the chain EG of the
pump. Then whilft the great wheel is turned by the lever NA
from O towards I, the wave Q preffes down the wheel QR,
and raiſes the end E of the lever, and thus draws up the water
in the pump G. But when the deepeſt part O of the wave is
paft the higheſt part of the wheel CR, the wheel riſes up into
the hollow S, and ſo the chain EG defcends till the next wave
raiſes it again. Thus the paffage of every wave by the wheel
CR caufes a ftroke of the pump. If the number of waves be
odd, and another pump wheel and lever be placed diametrically
Reciprocating and Rotatory Motions.
oppoſite on the other fide of the great wheel; then thefe two
levers acting by turns, will keep the motion tolerably uniform,
and the power at N will have nearly a uniform action. The
wheel CR is introduced for the fake of ſoftening the friction :
but it muſt be carefully adjuſted to the magnitude of the waves,
or elſe the motion will be hobbling and irregular. On this ac-
count the following method of obtaining a reciprocating motion
is more uſual.
Inftead of making the axis AB (fig. 3. pl. II.) in one con-
tinued ſtraight line, let it be bent at right angles in the points
d, e, f, g, h, &c. fo that the portions ef, gh, fhall be parallel
to AB, and in the courſe of a rotation of the lantern or trundle
EF, they will defcribe cylindrical furfaces: if, then, piftons and
their handles Ib, Ib, be hung upon the cranks I, I, as the ro-
tatory motion of the trundle EF (when worked by another
wheel) proceeds, the piſtons are alternately forced up and down
in the pumps; and thus make one complete ftroke of each
pump for every turn of the lantern. It will be adviſable to place
pulleys or rollers at a, b, a, b, for the handles or chains to work
againft, when the obliquity of the motion of the cranks I, I,
carries them out of the vertical poſition.
Other methods of obtaining reciprocating by means of cir
cular motions may be feen under the articles Air-pump and
Saw-mill.
7. To produce a rotatory motion by means of a reciprocating one.
Suppoſe it is required to give to the wheel SVTO (fig. 4. pl. II.)
a rotatory motion about the centre C. In the plane of the
wheel, attach to a fixed point F as a centre of motion a lever
FQ, which may move freely up and down: let a pin be fixed
in the wheel as at R; and let an inflexible bar QR hang upon
the pin at R at one end, while the other end is attached to the
lever FQ by a ſtirrup; the motion being quite eafy at both ends.
Then, while the point Q is raiſed upwards the bar pulls up-
wards the pin R, and fo continues to do until the points Q, R,
and C, fall in a right line; at that time the effort of the bar to
turn the wheel is nothing; but the wheel by its anterior rotation
has acquired a quantity of motion which will carry it on in the
ſame direction, till by the downward motion of the extremity
Qof the lever, the bar begins to push forward the pin to which
it is attached: thus the motion is continued till the points Q,
C, and R, are again in a right line, R being now the fartheft
from Q: in this pofition the bar has no tendency to move the
wheel along; but here the effort of momentum continues the
motion, as before, till the bar begins to draw the point R up-
wards. And thus a reciprocating motion of the lever FR gives
a complete rotation to the wheel; and the velocity of the cir-
MECHANICS.
cumference of the wheel may be made as rapid as we pleafe,
by making the diſtance CR ſo much the ſmaller in compariſon of
CV. If the lever FQ be below the wheel, the general effect
will be the fame, but the particular circumſtances of the motion
will fucceed each other in a contrary order. In practice it is
common to ſubſtitute for the pin at R the handle of a bent
winch, as repreſented by the dotted lines in the figure. It is not
abfolutely neceffary that the lever and wheel fhould be in the
fame plane; but deviations from it are not often to be recom-
mended, except in fmall machinery, fuch as a common fpin-
ning wheel worked by the feet, &c. When it is not required to
have a complete rotation of the wheel, for every afcent and
deſcent of the lever FQ, we may change the relation of the two
motions in any proportion, by the intervention of tooth and
pinion work.
8. To defcribe a rectilinear reciprocating motion, by means of an
angular or circular reciprocating motion. Let it be propofed, for
example, to move the end F of the beam FH to and fro in the
line EC. Fix a beam AB (fig. 9. pl. I.) perpendicularly to the
given line EC, and cut in that beam a groove CD equal in length
to the beam FH: let the end H of the beam FH be confined by
a pin to run along the groove CD; and let two other pins be
fixed, one at G the middle point of the beam FH, the other at
C the lower point where the reciprocating motion of the point F
terminates: take an iron bar CG equal in length to half FH,
and let it move upon the pins C and G as joints. Then while
the end G of the bar or guide CG moves through the quadrantal
arc Lg GK; the point H of the beam will ſlide along the groove
from Ď to C, and the point F along the line CE from C to E:
and when the guide returns from K by G to L, the end F of
the beam will return along the line EC. For, when CG=GF
=GH, ſuppoſing a line drawn from C to F, the angle FGC⇒
GCH+GHC=2 GCH; and CGH GCF+GFC2 GCF.
Hence we have 2 GCF + 2 GCH = FGC + HGC = 2 right
angles, and confequently GCF+GCH=HCF=1 right angle:
that is, the point F falls in a right line drawn through C at right
angles to CD. And when FH is in any other poſition, as ƒh,
the fame may be fhewn.
-
9. To communicate motion in any direction by wheels, and to con-
Struct the wheels for that purpoſe. This may be done by placing
the wheels fo that their fhafts or axles thall be inclined in
given angles, as reprefented in figs. 1 and 7. pl. III. And in
this cafe the wheels are ſeldom portions of cylinders, but moſt
commonly portions of cones. When the wheels do not make
an angle of 90°, the adjuſtment of the ſhape and magnitude of
the conic fruftums which conſtitute the wheels, is known among
Bevel Geer
millwrights by the name of bevel-geer work; a concife account
of which is here added. If two cones A and B (fig. 2. pl. III),
whoſe ſurfaces always touch in a right line, as a e, revolve on
their axes ab, ac, rolling the one upon the other; and if the
bafes and altitudes of thefe cones be equal, they will perform
complete revolutions in one and the fame time. For fince the
bafes and altitudes are equal, circles on either cone parallel to
the baſe, and at equal diſtances from the vertex, as the diſtances
a 2, a 2, for instance, will be equal: and therefore while the
furfaces of the cones roll one upon another, every point in the
circumference of one of theſe circles will be brought fuccef-
fively into contact with a correſponding point on the circum-
ference of the other, and they will both have revolved in an
equal time. The fame will hold of the correſponding circles
at any other equal diſtances from the vertex, a 1, a 3, a 4, &c.
and confequently the two cones will form their rotations in
equal times.
Again, if the cone ade (fig. 3. pl. III.) have the diameter
of its baſe double that of the cone adf while their ſlant heights
are the fame; and if thefe two cones turn on their axes a c, ab,
their ſurfaces during the rotation always touching one another
in a right line; then, fince the circumference of the baſe de is
double that of the baſe df, and the circumference of every cir-
cular ſection parallel to the former baſe, double that of every
correfponding ſection parallel to the latter bafe, it follows that
when the cone afd has performed one rotation, the cone a dé
will have made but half a rotation, The times of rotation
being in the ratio of their baſes.
In like manner, if the cone aed, (fig. 4. pl. III.) have the
diameter of its bafe, to the diameter of the bafe of a df, as m
ton, the flant heights being the fame; and if theſe cones turn
upon their axes a c, ab, their furfaces being always in contact
in ſome right line as a d; then will the time of a complete ro-
tation of the cone aed, be to the time of rotation of a df, as
m to n; and confequently the number of rotations of the former
cone to the number of rotations of the latter in any given time,
as n to m. And if theſe cones were fluted, the flutes diverging
continually from the apex a to the baſe they would become co-
nical wheels, and conftitute bevel-geer.
10. Thus, if Bb and B d (fig. 5. pl. III.) be the bafes of two
cones turning on their axes, having teeth cut in them diverging
from the common vertex A to thoſe baſes, fuch teeth will work
freely into one another from one end to the other: but, as fuch
teeth would be very difficult of adjuſtment towards the point A,
and becauſe in practice the two axes could not both be properly
8
MECHANICS.
fixed to one and the fame point; it is neceffary to cut off a
portion, as AFE, from the upper part of both cones, and apply
the axles to the lower parts in the fame manner as in common
wheels. The great advantages of theſe conical wheels are, that
their teeth may be made of any breadth, according to the ſtreſs
they are to ſuſtain; and that the friction will be fmall in com-
pariſon of that occafioned by most other methods of com-
municating motion in oblique directions.
yg
{
11. Now, to determine the dimenfions of two conical wheels to
communicate motion in any oblique angle, the following graphic method
may be uſed. Suppoſe ab (fig. 6. pl. III.) to reprefent the fhaft
or axle of one wheel, and de the axle of another wheel, the
angle x in which they interfect each other being equal to the
angle in which the motion is propoſed to be communicated: let
it be required for the ſhaft de to revolve m times while the ſhaft
a b revolves n times; and let the line i i be drawn parallel to de
at a diſtance equal to the radius of the baſe of the wheel whoſe
axle is de. Then draw a line k k parallel to a b, and at a diſtance
from it, which ſhall be to the diſtance y h as m to n through
the point of interfection of the lines firft propofed, and y the
interfection of the two lines ii, kk, refpectively parallel to the
two former, draw the line xy w, which will be the pitch line of
the two conical wheels, or the line in which the teeth of thoſe
wheels act upon one another; and gy, hy will reprefent the
exterior radii of the wheels, which will work one againſt the
other after the manner fhewn in fig. 7. where the correfpond-
ing parts are marked by the fame letters. A third ſhaft and
wheel may eaſily be applied to communicate motion in a dif-
ferent direction from either of the former: as the ſhaft and
wheel rstu in fig. 7.
·
I
It is manifeft from what is done above, that this is nothing
more than to divide an angle bxh into two parts whoſe fines
fhall have a given ratio of m to n: a well-known problem,
which folved algebraically gives the theorem, 2 fin. 4 g xy=
2 fin. gxh. m+n• (Simpſon's Select Exerciſes, pa. 138.). Sə
that all which is required here may be eaſily calculated by the
common rules of plane trigonometry; and thus the accuracy of
the conſtruction may be eſtabliſhed.
m
12. Univerſal joints (invented by Dr. Hooke) are fometimes
ufed to communicate motion obliquely, inftead of conical
wheels. Fig. 8. pl. III. repreſents a ſingle univerfal joint which
may be employed where the angle does not exceed 40 degrees,
and when the fhafts are to move with equal velocity. The
fhafts A and B being both connected with a crofs, will move on
Uniformity and Smoothneſs of Motion.
1
the rounds at the points CE and DF, and thus if the fhaft A is
turned round, the ſhaft B will likewife turn with a fimilar mo-
tion in its reſpective pofition.
The double univerfal joint (fig. 9. pl. III.) conveys motion in
different directions when the angle is between 50 and go de-
grees. It is at liberty to move on the rounds at the points G,
H, I, K, connected with the fhaft B; alfo on the points L, M,
N, T, connected with the ſhaft A: thus the two fhafts are
fo connected that one cannot turn without caufing the other to
turn likewiſe. Theſe joints may be conſtructed by a crofs of
iron, or with four pins faftened at right angles upon the circum-
ference of a hoop or of a folid ball: they are of great uſe in
cotton-mills, where the tumbling fhafts are continued to a great
diſtance from the moving power: for by applying a univerfal
joint, the fhafts may be cut into convenient lengths, and ſo be
enabled to overcome a greater reſiſtance.
13. When the number of teeth in each of two wheels is given, and
the diameter of one of them, the diameter of the other fhould be fo
found that one wheel may drive the other without ſhaking: and for
this purpoſe there will be a different proportion of diameters or
of radii, according to the number of teeth which are to be in
contact. Let ADE, BDF (fig. 1o. pl. III.) reprefent por-
tions of the wheels, C the point where the teeth ought first to
come into contact: draw CD perpendicular to AB the right line
joining the centres of the wheels; and if this be reckoned the
radius, CB will be the fecant of the angle DCB, and AC the
fecant of the angle DCA. Confequently, CB: CA :: fecant
DCB: fecant DCA :: cofec. DBC: cofec. DAC. But, the
number of teeth in each wheel being given, the angles DBC,
DAC, vary as half the number of teeth in contact. Therefore,
divide the arch of the femicircle, or 180 degrees, by half the
number of teeth in each wheel, and proportion the radii of the
wheel to the cofecants of the quotients, or of double, or of treble
the quotients, according to the depth of the wheels running,
viz. according as they are to have two, four, or fix teeth, in
contact; fo fhall the motion be regular and free from fhaking.
In art. 147. of the firft volume, we defcribed the beſt forms
for the teeth of wheels: in many cafes, however, a ſmall de-
viation from thefe perfect forms is not of great importance.
But in caſes where the utmost accuracy is required, as in the
pallets of clocks and watches, the form of the teeth muſt be
carefully attended to.
14. To regulate any motion and make it uniform, one of the moſt
obvious methods it that by means of a pendulum and fcapement.
Thus, (fig. 5. pl. II.) as the pendulum AB vibrates, it cauſes
EFG to vibrate alfo, about the axis FG: whilft the pendulum
vibrates towards D a tooth of the wheel KL goes of the pallet
10
MECHANICS.
I, and another catches the pallet H: and when the pendulum
returns towards C, it draws the pallet H off the tooth, and an-
other catches the pallet I; and fo on alternately. So that, at
every vibration of the pendulum, a tooth goes off one or other
of the pallets: and, as the vibrations of the pendulum are ifo-
chronous, the teeth move from the pallets uniformly, the whole
rotation of the wheel KL is made regularly, and by reafon of the
connection of the teeth and pinions the defcent of W is uni-
form, which would otherwiſe have been accelerated.
15. Profeffor Robifon has given fome general obfervations on
the conſtruction of machines, and on the regulating of their
motions, which appear highly worthy of the reader's attention,
and are therefore extracted, as below.
"When heavy ſtampers are to be raiſed, in order to drop on
the matters to be pounded, the wipers by which they are lifted
ſhould be made of fuch a form, that the ſtamper may be raiſed
by a uniform preffure, or with a motion almoſt perfectly uni-
form. If this is not attended to, and the wiper is only a pin
ſticking out from the axis, the ftamper is forced into motion at
once. This occafions violent jolts to the machine, and great
ſtrains on its moving parts and their points of fupport; whereas
when they are gradually lifted, the inequality of defultory motion
is never felt at the impelled point of the machine. We have
ſeen piſtons moved by means of a double rack on the pifton-rod.
A half wheel takes hold of one rack, and raiſes it to the required
height. The moment the half wheel has quitted that fide of
the rack, it lays hold of the other fide, and forces the piſton
down again. This is propofed as a great improvement; cor-
recting the unequable motion of the piston moved in the com-
mon way by a crank. But it is far inferior to the crank motion.
It occafions fuch abrupt changes of motion, that the machine is
fhaken by jolts. Indeed if the movement were accurately ex-
ecuted, the machine would be ſhaken to pieces, if the parts did
not give way by bending and yielding. Accordingly, we have
always obferved that this motion foon failed, and was changed
for one that was more ſmooth. A judicious engineer will avoid
all fuch fudden changes of motion, eſpecially in any ponderous
part of a machine.
When ſeveral ſtampers, piftons, or other reciprocal movers,
are to be raiſed and depreffed, common fenfe teaches us to
diftribute their times of action in a uniform manner, ſo that the
machine may always be equally loaded with work. When this
is done, and the obfervations in the preceding paragraph attended
to, thé machine may be made to move almoſt as ſmoothly as if
there were no reciprocations in it. Nothing fhews the ingenuity
of the author more than the artful yet fimple and effectual con-
trivances for obviating thoſe difficulties that unavoidably ariſe
Uniformity and Smoothness of Motion.
11
from the very nature of the work that must be performed by
the machine, and of the power employed.
16. There is alſo great room for ingenuity and good choice
in the management of the moving power, when it is ſuch as
cannot immediately produce the kind of motion required for
effecting the purpofe. We mentioned the converfion of the
continued rotation of an axis into the reciprocating motion of a
pifton, and the improvement which was thought to have been
made on the common and obvious contrivance of a crank, by
fubftituting a double rack on the pifton-rod, and the incon-
venience ariſing from the jolts occafioned by this change. We
have ſeen a great forge, where the engineer, in order to avoid
the ſame inconvenience arifing from the abrupt motion given to
the great fledge hammer of feven hundred weight, refifting with
a five-fold momentum, formed the wipers into ſpirals, which
communicated motion to the hammer almoſt without any jolt
whatever; but the refult was, that the hammer rofe no higher
than it had been raiſed in contact with the wiper, and then
fell on the iron bloom with very little effect. The cauſe
of its inefficiency was not gueffed at; but it was removed, and
wipers of the common form were put in place of the ſpirals.
In this operation, the rapid motion of the hammer is abfolutely
neceffary. It is not enough to lift it up; it must be toffed up,
fo as to fly higher than the wiper lifts it, and to ftrike with great
force the strong oaken fpring which is placed in its way. It
compreffes this ſpring, and is reflected by it with a confiderable
velocity, fo as to hit the iron as if it had fallen from a great
height. Had it been allowed to fly to that height, it would have
fallen upon the iron with fomewhat more force (becauſe no
oaken ſpring is perfectly elaftic); but this would have required
more than twice the time.
17. In employing a power which of neceffity reciprocates, to
drive machinery which requires a continuous motion (as in ap-
plying the ſteam engine to a cotton or a grist mill), there alſo
occur great difficulties. The neceffity of reciprocation in the
firſt mover waſtes much power; becauſe the inftrument which
communicates fuch an enormous force muſt be extremely
ſtrong, and be well fupported. The impelling power is wafted
in imparting, and afterwards deftroying, a vast quantity of
motion in the working beam. The fkilful engineer will attend
to this, and do his utmost to procure the neceffary ſtrength of
this firſt mover, without making it a vaſt load of inert matter.
He will alſo remark, that all the ftrains on it, and on its
fupports, are changing their directions in every ftroke. This
requires particular attention to the manner of fupporting it. If
we obferve the ſteam engines which have been long erected,
J
12
MECHANICS.
we ſee that they have uniformly fhaken the building to pieces.
This has been owing to the ignorance or inattention of the en-
gineer in this particular. They are much more judiciouſly.
erected now, experience having taught the moft ignorant that
no building can withstand their defultory and oppofite jolts,
and that the great movements muſt be ſupported by a frame-
work independent of the building of maſonry which contains
it *.
The engineer will alſo remark, that when a fingle-ſtroke
fteam engine is made to turn a mill, all the communications of
motion change the direction of their preffure twice every ſtroke.
During the working ſtroke of the beam, one fide of the teeth of
the intervening wheels is preffing the machinery forward; but
during the returning ftroke, the machinery, already in motion,
is dragging the beam, and the wheels are acting with the other
fide of the teeth. This occafions a rattling at every change,
and makes it proper to faſhion both fides of the teeth with the
fame care.
It will frequently conduce to the good performance of an en-
gine, to make the action of the refifting work unequable, accom-
modated to the inequalities of the impelling power. This will
produce a more uniform motion in machines in which the mo-
mentum of inertia is inconſiderable. There are ſome beautiful
fpecimens of this kind of adjuſtment in the mechaniſm of ani-
mal bodies.
18. It is very cuſtomary to add what is called a FLY to ma-
chines. This is a heavy diſk or hoop, or other mafs of matter
balanced on its axis, and fo connected with the machinery as to
turn briſkly round with it. This may be done with the view of
rendering the motion of the whole more regular, notwithſtanding
unavoidable inequalities of the accelerating forces, or of the
reſiſtances occafioned by the work. It becomes a REGULATOR.
Suppoſe the refiftance extremely unequal, and the impelling
power perfectly conftant; as when a bucket wheel is employed
to work one pump. When the piston has ended its working
ſtroke, and while it is going down the barrel, the power of the
wheel being ſcarcely oppofed, it accelerates the whole machine,
and the piſton arrives at the bottom of the barrel with a confi-
derable velocity. But in the rifing again, the wheel is oppofed
* The gudgeons of a water-wheel ſhould never reft on the wall of the
building. It shakes it; and if fet up foon after the building has been
erected, it prevents the mortar from taking firm bond; perhaps by fhat-
tering the calcareous cryſtals as they form. When the engineer is obliged
to reft the gudgeons in this way, they fhould be ſupported by a block of
oak laid a little hollow. This foftens all tremors, like fprings of a wheel
carriage. This practice would be very ſerviceable in many other parts of
the conſtruction.
1
Operation and Use of a Fly.
13
+
•
by the column of water now preffing on the pifton. This im-
mediately retards the wheel; and when the pifton has reached
the top of the barrel, all the acceleration is undone, and is to
begin again. The motion of fuch a machine is very hobbling: but
the fuperplus of accelerating force at the beginning of a return-
ing ftroke will not make fuch a change in the motion of the
machine if we connect the fly with it. For the accelerating
momentum is a determinate quantity. Therefore, if the radius.
of the fly be great, this momentum will be attained by com-
municating a ſmall angular motion to the machine. The mo-
mentum of the fly is as the fquare of its radius; therefore it re-
fifts acceleration in this proportion; and although the overplus
of power generates the fame momentum of rotation in the
whole machine as before, it makes but a ſmall addition to its
velocity. If the diameter of the fly be doubled, the augmenta-
tion of rotation will be reduced to one-fourth. Thus, by
giving a rapid motion to a fmall quantity of matter, the great
acceleration during the returning ftroke of the pifton is pre-
vented. This acceleration continues, however, during the whole
of the returning ftroke, and at the end of it the machine has
acquired its greateſt velocity. Now the working ftroke begins,
and the overplus of power is at an end. The machine ac-
celerates no more; but if the power is juft in equilibrio with
the reſiſtance, it keeps the velocity which it has acquired, and
is ſtill more accelerated during the next returning ſtroke. But
now, at the beginning of the fubfequent working ftroke, there
is an overplus of refiftance, and a retardation begins, and con-
tinues during the whole rife of the piſton; but it is confiderable
in compariſon of what it would have been without the fly; for
the fly, retaining its acquired momentum, drags forward the
reft of the machine, aiding the impelling power of the wheel.
It does this by all the communications taking into each other
in the oppofite direction. The teeth of the intervening wheels
are heard to drop from their former contact on one fide, to a
contact on the other. By confidering this procefs with at-
tention, we eaſily perceive that, in a few ftrokes, the overplus of
power during the returning ftroke comes to be ſo adjuſted to
the deficiency during the working ſtroke, that the accelerations
and retardations exactly deſtroy each other, and every fucceeding
ftroke is made with the fame velocity, and an equal number of
ſtrokes is made in every fucceeding minute. Thus the machine
acquires a general uniformity with periodical inequalities. It is
plain, that by fufficiently enlarging either the diameter or the
weight of the fly, the irregularity of the motion may be rendered
as ſmall as we pleaſe. It is much better to enlarge the diameter.
This preferves the friction more moderate, and the pivot wears
14
MECHANICS.
lefs. For thefe reafons, a fly is in general a confiderable improve-
ment in machinery, by equalifing many exertions that are na-
turally very irregular. Thus, a man working at a common
windlafs exerts a very irregular preffure on the winch. In one
of his pofitions in each turn he can exert a force of near 70
pounds without fatigue, but in another he cannot exert above
25; nor muſt he be loaded with much above this in general.
But if a large fly be connected properly with the windlaſs, he
will act with equal eaſe and ſpeed againſt 30 pounds.
This regulating power of the fly is without bounds, and may
be uſed to render uniform a motion produced by the moſt de-
fultory and irregular power. It is thus that the moſt regular
motion is given to mills that are driven by a fingle-ſtroke ſteam
engine, where for two or even three feconds there is no force
preffing round the mill. The communication is made through
a maffive fly of very great diameter, whirling with great ra-
pidity. As foon as the impulfe ceaſes, the fly, continuing its
motion, urges round the whole machinery with almoft unabated
ſpeed. At this inftant all the teeth, and all the joints, between
the fly and the firſt mover, are heard to catch in the oppofite
direction.
If any permanent change fhould happen in the impelling
power, or in the refiftance, the fly makes no obftacle to its pro-
ducing its full effect on the machine; and it will be obſerved to
accelerate or retard uniformly, till a new general ſpeed is ac-
quired exactly correfponding with this new power and re-
fiftance.
19. Many machines include in their conſtruction movements
which are equivalent with this intentional regulator. A flour
mill, for example, cannot be better regulated than by its mil-
ſtone; but in the Albion mills, a heavy fly was added with great
propriety; for if the mills had been regulated by their milftones.
only, then at every change of ftroke in the fteam engine, the
whole train of communications between the beam, which is the
first mover, and the regulating milftone, which is the very laft
mover, would take in the oppofite direction. Although each
drop in the teeth and joints be but a trifle, the whole, added
together, would make a confiderable jolt. This is avoided by a
regulator immediately adjoining to the beam. This continually
preffes the working machinery in one direction. So judiciouſly
were the movements of that noble machine contrived, and fo
nicely were they executed, that not the leaft noiſe was heard,
nor the flighteſt tremor felt in the building.
20. Mr. Valoué's beautiful pile engine employed at Weft-
miniſter Bridge is another remarkable inftance of the regulating
power of a fly. When the ram is dropped, and its follower
Operation and Uſe of a Fly.
1.5
difengaged immediately after it, the horfes would inſtantly
tumble down, becauſe the load, againſt which they had been
ftraining hard, is at once taken off; but the gin is connected
with a very large fly, which checks any remarkable acceleration,
allowing the horſes to lean on it during the deſcent of the load;
after which their draught recommences immediately. The
fpindles, cards, and bobbins, of a cotton mill, are alſo a fort of
flies. Indeed all bulky machines of the rotative kind tend to
preferve their motion with fome degree of fleadineſs, and their
great momentum of inertia is as ufeful in this reſpect as it is
prejudicial to the acceleration or any reciprocation when
wanted.
21. There is another kind of regulating fly, confiſting of
wings whirled briſkly round till the refiftance of the air prevents
any great acceleration. This is a very bad one for a working
machine, for it produces its effect by really wafting a part of the
moving power. Frequently it employs a very great and un-
known part of it, and robs the proprietor of much work. It
ſhould never be introduced into any machine employed in ma-
nufactures.
22. Some rare cafes occur where a very different regulator is
required: where a certain determined velocity is found neceffary.
In this caſe the machine is furniſhed, at its extreme mover, with
a conical pendulum, confifting of two heavy balls hanging by rods,
which move in very nice and ſteady joints at the top of a vertical
axis. It is well known, that when this axis turns round, with
an angular velocity fuited to the length of thoſe pendulums, the
time of a revolution is determined. Thus, if the length of each
pendulum be 393 inches, the axis will make a revolution in two
feconds very nearly. If we attempt to force it more ſwiftly
round, the balls will recede a little from the axis, but it employs
as long time for a revolution as before; and we cannot make it
turn ſwifter, unleſs the impelling power be increaſed beyond all
probability; in which cafe the pendulum will fly out from the
centre till the rods are horizontal, after which every increaſe of
power will accelerate the machine very fenfibly. Watt and
Boulton have applied this contrivance with great ingenuity to
their ſteam engines, when they are employed for driving ma-
chinery for manufactures which have a very changeable refift-
ance, and where a certain ſpeed cannot be much departed from
without great inconvenience. They have connected this recefs
of the balls from the axis (which gives immediate indication of
an increaſe of power or a diminution of refiftance) with the
cock which admits the fteam to the working cylinder. The
balls flying out cauſe the cock to cloſe a little, and diminiſh
16
MECHANICS..
the ſupply of ſteam. The impelling power diminiſhes the next
moment, and the balls again approach the axis, and the rota-
tion goes on as before, although there may have occurred a very
great exceſs or deficiency of power.
23. A fly is fometimes employed for a very different purpoſe
from that of a regulator of motion-it is employed as a collector of
power. Suppofe all refiftance removed from the working point
of a machine furnifhed with a very large or heavy fly imme-
diately connected with the working point. When a fmall force
is applied to the impelled point of this machine, motion will
begin in the machine, and the fly begin to turn. Continue to
prefs uniformly, and the machine will accelerate. This may be
continued till the fly has acquired a very rapid motion. If at
this moment a refifting body be applied to the working point, it
will be acted on with very great force; for the fly has now ac-
cumulated in its circumference a very great momentum.
If a
body were expofed immediately to the action of this circum-
ference, it would be violently ſtruck. Much more will it be ſo,
if the body be expoſed to the action of the working point, which
perhaps makes one turn while the fly makes a hundred. It will
exert a hundred times more force there (very nearly) than at its
own circumference. All the motion which has been accu-
mulated on the fly during the whole progrefs of its acceleration
is exerted in an inftant at the working point, multiplied by the
momentum depending on the proportion of the parts of the ma-
chine. It is thus that the coining prefs performs its office; nay,
it is thus that the blackſmith forges a bar of iron. Swinging the
great fledge hammer round his head, and urging it with force
the whole way, this accumulated motion is at once extinguiſhed
by impact on the iron. It is thus alſo we drive a nail, &c. This
accumulating power of a fly has occafioned many to imagine that a
fly really adds power or mechanical force to an engine; and, not
underſtanding on what its efficacy depends, they often place the
fly in a fituation where it only adds a uſeleſs burden to the ma-
chine. It fhould always be made to move with rapidity. If in-
tended for a mere regulator, it ſhould be near the firſt mover: and
if it be intended to accumulate force in the working point, it
fhould not be far feparated from it. In a certain fenfe, a fly may
be faid to add power to a machine, becauſe by accumulating into
the exertion of one moment the exertions of many, we can ſome-
times overcome an obſtacle that we never could have balanced
by the ſame machine unaided by the fly. And it is this ac-
cumulation of force which gives fuch an appearance of power
to fome of our first movers. See Supplement, Encyclopædią,
Britan. art. Machinery.
Friction.
17
On Friction, and the Stiffneſs of Ropes.
24. Moſt of the propofitions laid down in the firſt volume of
this work have been conducted upon the fuppofition that all
bodies are perfectly fmooth, that they flide over one another
without any friction, and that cords and ropes are perfectly
flexible. But fince there is no fuch thing as perfect ſmoothneſs
in bodies, no machine can move without a mutual rubbing of
its parts, at all points of communication: and when we con-
fider the mode of operation of the teeth of wheel work, the
wipers and lifts, the gudgeons of the different axes, &c. we
ſhall ſee that friction, by which we mean the refiſtance a body
meets with from the furface on which it moves, has confider-
able effect in retarding the motion of machines, or gives oc-
cafion for the exertion of much more power in order that the
machine may move with the requifite velocity. Indeed in many
machines, as poliſhing mills, grinding mills, boring and fawing
mills, the ultimate task performed is either friction or very
much reſembles it. So that fome knowledge of the nature of
friction ſeems abfolutely neceffary, to enable us to apply the
principles of the fimple theory to any uſeful practical purpoſe.
25. Much attention has, therefore, been paid to this fubject
by many ingenious men; but as yet their labours have not
greatly added to the ftock of knowledge as to the real nature of
friction and although fome ingenious theories have been de-
duced from the experiments which have already been made,
they reft upon very limited hypotheſes, and are of little, if any,
actual utility. This being our opinion, the reader will not
expect a minute expofition of the theory in this place. We
fhall merely preſent a ſingle propofition, which tends to an
obvious practical purpofe, and does not require the admiffion
of more than one new principle, viz. that the friction varies
nearly as the preſſure.
PROP. A power which moves a body along a horizontal plane, acts
with the greatest advantage when the line of direction makes an
angle of about 181 with the plane. Let B (fig. 2. pl. I.) be the
body which is to be moved along the horizontal plane BC, by
a given power eſtimated in quantity and direction by BA. Demit
the perpendicular AC; and let the given line AB=1=radius,
AC fine ABC=x, BC= √ √ the force moving the
body horizontally. The power by its oblique action diminiſhes
the preffure of the weight on the horizontal plane in the ratio
of 1: *, therefore B x=that part of the preffure which is taken
off, and the actual preffure-B-Bx. Let friction be
VOL. II.
1
18
MECHANICS.
112
th part of the weight or preffure: that is, let it be=B-
*Bx.
2
n
Then the force requifite to move B horizontally muſt
be equal to the horizontal force diminiſhed by friction, or =
m
B (1 − x²) * — — B+™ Bx. This is to be a minimum, or its
.
n
n
fluxion
m
Bxx
m
B-(1-2)
=o: hence we find x=
=
//
(m² + n²) /
= fine
of the angle ABC. And if, as has been concluded from many ex-
I
periments,=, then will x= =fine of 18° 26' nearly.
If the plane along which the body is to be moved be in-
clined to the horizon, the fine of the angle which the line of di-
rection or traction of the power makes with the plane, when it
acts with the greateſt advantage, will be nearly
C
being
+9cbeing
the cofine of the angle of elevation to radius=unity.
26. The principle affumed in the inveſtigation above is, how-
ever, by no means general in its application: as there are many
circumſtances which modify the operation of friction, and cauſe
deviations from this law. Thefe circumftances will be beſt
learnt by reflecting upon fome of the experiments which have
been made relative to the friction of bodies in motion. Of
ſuch experiments we fhall firſt deſcribe thoſe of Mr. Profeffor
Vince, which were conducted with great care and ingenuity,
and led to fome important refults. The object of this phi
lofopher was to determine the following queftions:
1. Whether friction be a uniformly retarding force?
2. What is the quantity of friction?
3. Whether the friction varies in proportion to the preffure or
weight?
4. Whether the friction be the fame on whichever of its fur-
faces a body moves?
(1.) With refpect to the firſt of theſe queſtions, the author
truly obſerves, that if friction be a uniform force, the difference
between it and the given force of the moving power employed to
overcome it muſt alſo be uniform; and that therefore the moving
power, if it be a body defcending by its own weight, muft de-
foend with a uniformly accelerated velocity, juft as when there
was no friction. The fpaces deſcribed from the beginning of
the motion will indeed be diminiſhed in any given time on ae
Friction.
19
count of the friction; but ftill they muſt be to each other as the
ſquares of the times employed.
(2.) A plane was therefore adjuſted parallel to the horizon,
at the extremity of which was placed a pulley, which could be
elevated or depreffed, in order to render the ſtring which con-
nected the body and the moving force parallel to the plane. A
fcale accurately divided was placed by the fide of the pulley per-
pendicular to the horizon, by the fide of which the moving
force defcended; upon the ſcale was placed a moveable ſtage,
which could be adjuſted to the ſpace through which the moving
force defcended in any given time; which time was meaſured
by a well-regulated pendulum clock vibrating ſeconds. Every
thing being thus prepared, the following experiments were made
to aſcertain the law of friction.
(3.) Exp. 1. A body was placed upon the horizontal plane,
and a moving force applied, which, from repeated trials, was
found to defcend 524 inches in 4"; for by the beat of the clock,
and the found of the moving force when it arrived at the ſtage,
the ſpace could be very accurately adjuſted to the time: the
ſtage was then removed to that point to which the moving force
would defcend in 3", upon fuppofition, that the fpaces de-
ſcribed by the moving power were as the ſquares of the times;
and the ſpace was found to agree very accurately with the
time: the ftage was then removed to that point to which the
moving force ought to deſcend in 2″, upon the fame fuppofition,
and the defcent was found to agree exactly with the time:
laftly, the ſtage was adjuſted to that point to which the moving
force ought to defcend in 1', upon the ſame ſuppoſition, and
the ſpace was obferved to agree with the time. Now, in
order to find whether a difference in the time of deſcent could
be obſerved by removing the ſtage a little above and below the
pofitions which correfponded to the above times, the experiment
was tried, and the deſcent was always found too foon in the
former, and too late in the latter cafe; by which the author
was affured, that the ſpaces first mentioned correfponded exactly
to the times. And, for the greater certainty, each deſcent was
repeated eight or ten times; and every caution uſed in this ex-
periment was alſo made uſe of in all the following.
Exp. 2. A fecond body was laid upon the horizontal plane,
and a moving force applied which deſcended 414 inches in 3
the ftage was then adjuſted to the ſpace correſponding to 2
upon fuppofition that the ſpaces defcended through were as the
fquares of the times, and it was found to agree accurately with
the time; the ſtage was then adjuſted to the space correfpond-
ing to ", upon the fame fuppofition; and it was found to agrée
with the time.
Exp. 3. A third body was laid upon the horizontal plane, and

C 2
20
MECHANICS.
!
:
a moving force applied, which deſcended 59§ inches in
4"; the
ftage was then adjuſted to the fpace correfponding to 3", upon
ſuppoſition that the ſpaces defcended through were as the fquares
of the times, and it was found to agree with the time; the ftage
was then adjuſted to the ſpace correfponding to 2", upon the
fame fuppofition, and it was found to agree with the time; the
ſtage was then adjuſted to the ſpace correfponding to 1", and
was found to agree with the time.
I
Exp. 4. A fourth body was then taken and laid upon the ho-
rizontal plane, and a moving force applied, which deſcended
55 inches in 4"; the ftage was then adjufted to the ſpace
through which it ought to defcend in 3″, upon fuppofition that
the ſpaces defcended through were as the fquares of the times,
and it was found to agree with the time; the ſtage was then
adjuſted to the ſpace correfponding to 2", upon the ſame ſup-
pofition, and was found to agree with the time; laſtly, the ſtage
was adjuſted to the fpace correfponding to 1", and it was
found to agree exactly with the time.
Befides thefe experiments, a great number of others were
made with hard bodies, or thoſe whofe parts fo firmly cohered
as not to be moved inter fe by the friction; and in each expe-
ment, bodies of very different degrees of friction were chofen,
and the reſults all agreed with thoſe related above; it was
therefore concluded, that the friction of hard bodies in motion is
a uniformly retarding force.
But to determine whether the fame was true for bodies when
covered with cloth, woollen, &c. experiments were made in
order to aſcertain it; when it was found in all caſes, that the
retarding force increaſed with the velocity; but, upon covering
bodies with paper, the confequences were found to agree with
thoſe related above.
(4.) Having proved that the retarding force of all hard bodies
arifing from friction is uniform, the quantity of friction, con-
fidered as equivalent to a weight without inertia drawing the
body on the horizontal plane backwards, or acting contrary to
the moving force, may be immediately deduced from the foregoing
experiments. For let M=the moving force expreffed by its
weight; F-the friction; W=the weight of the body upon the
horizontal plane; S=the ſpace through which the moving force
defcended in the time t expreffed in feconds; r=16 feet;
then the whole accelerative force (the force of gravity being
unity) will be
; hence, by the laws of uniformly accele-
rated motions,
M-F
M+W
M F
M+W
I
xr²=S, conſequently FM-M+W × s,
r ta
To exemplify this, let us take the cafe of the laſt experiment,
Friction.
21
where M=7, W=25%, S=47% feet, t=4"; hence F=7-
32 × 4½-6.417; confequently the friction was to the weight
16 × 16
of the rubbing body as 6.4167 to 25.75. And the great ac-
curacy of determining the friction by this method is manifeſt
from hence, that if an error of 1 inch had been made in the
defcent (and experiments carefully made may always determine
the ſpace to a much greater exactnefs) it would not have affect-
ed the conclufion part of the whole.
I
(5.) We come in the next place to determine, whether fric-
tion, cæteris paribus, varies in proportion to the weight or pref-
fure. Now if the whole quantity of the friction of a body,
meaſured by a weight without inertia equivalent to the friction
drawing the body backwards, increafes in proportion to its
weight, it is manifeft, that the retardation of the velocity of the
body arising from the friction will not be altered; for the re-
Quantity of friction
tardation varies as Quantity of matter; hence, if a body be put in
motion upon the horizontal plane by any moving force, if both
the weight of the body and the moving force be increaſed in
the fame ratio, the acceleration arifing from that moving force
will remain the fame, becauſe the accelerative force varies, as
the moving force divided by the whole quantity of matter, and
both are increaſed in the fame ratio; and if the quantity of
friction increaſes alſo as the weight, then the retardation arif-
ing from the friction will, from what has been ſaid, remain the
fame, and therefore the whole acceleration of the body will not
be altered; confequently the body ought, upon this fuppofition,
ftill to defcribe the fame ſpace in the fame time. Hence, by
obſerving the ſpaces defcribed in the fame time, when both the
body and the moving force are increaſed in the ſame ratio, we
may determine whether the friction increaſes in proportion to
the weight. The following experiments were therefore made
in order to afcertain this matter.
Exp. 1. A body weighing 10 oz. by a moving force of 4 oz.
deſcribed in 2″ a fpace of 51 inches; by loading the body with
10 oz. and the moving force with 4 oz. it defcribed 56 inches
in 2"; and by loading the body again with 10 oz. and the
moving force with 4 oz. it defcribed 63 inches in 2″.
of
Exp. 2. A body whofe weight was 16 oz. by a moving force
5 oz. defcribed a ſpace of 49 inches in 3"; and by loading
the body with 64 oz. and the moving force with 20 oz. the
ſpace deſcribed in the fame time was 64 inches.
Exp. 3. A body weighing 6 oz. by a moving force of 24 oz.
deſcribed 28 inches in 2"; and by loading the body with 24 oz.
22
MECHANICS.
L
and the moving force with 10 oz. the ſpace defcribed in the
fame time was 54 inches.
Exp. 4. A body weighing 8 oz. by a moving force of 4 oz.
deſcribed 33 inches in 2"; and by loading the body with 8 oz.
and the moving force with 4 oz. the ſpace deſcribed in the
fame time was 47 inches.
I
Exp. 5. A body whoſe weight was 9 oz. by a moving force
of 4 oz. deſcribed 48 inches in 2'; and by loading the body
with 9 oz. and the moving force with 4 oz. the ſpace deſcribed
in the fame time was 60 inches.
Exp. 6. A body weighing 10 oz. by a moving force of
3 oz. deſcribed 20 inches in 2"; by loading the body with 10
oz. and the moving force with 3 oz. the ſpace deſcribed in the
fame time was 31 inches; and by loading the body again with
30 oz. and the moving force with 9 oz. the ſpace deſcribed was
34 inches in 2".
From theſe experiments, and many others which it is not ne-
ceffary here to relate, it appears, that the ſpace deſcribed is
always increaſed by increafing the weight of the body and the
accelerative force in the fame ratio; and as the acceleration
arifing from the moving force continued the fame, it is manifeft,
that the retardation arifing from the friction muſt have been di-
miniſhed, for the whole accelerative force muſt have been increafed
on account of the increaſe of the ſpace defcribed in the fame
time; and hence (as the retardation from friction varies as
Quantity of friction) the quantity of friction increaſes in a lefs ratio than
Quantity of
the quantity of matter or weight of the body.
(6.) We come now to the last thing which it was propoſed to
determine, that is, whether the friction varies by varying the
furface on which the body moves. Let us call two of the
furfaces A and a, the former being the greater, and the latter the
leſs. Now the weight on every given part of a is as much
greater than the weight on an equal part of A, as A is greater
than a; if therefore the friction was in proportion to the
weight, cæteris paribus, it is manifeft, that the friction on a
would be equal to the friction on A, the whole friction being,
upon fuch a fuppofition, as the weight on any given part of each
furface multiplied into the number of fuch parts or into the
whole area, which products, from the proportion above, are
equal. But from the laſt experiments it has been proved, that
the friction on any given ſurface increaſes in a lefs ratio than the
weight; confequently the friction on any given part of a has a
lefs ratio to the friction on an equal part of A than A has to a,
and hence the friction on a is lefs than the friction on A, that
is, the ſmalleſt ſurface has always the leaſt friction.
Friction.
23
As this conclufion is contrary to the generally received opi-
nion, Mr. Vince though it proper to confirm it by a fet of ex-
periments made with different bodies of exactly the fame degree
· of roughneſs on their two furfaces.
Exp. 1. A body was taken whoſe flat furface was to its edge
as 22: 9, and with the fame moving force the body deſcribed on
its flat fide 33 inches in 2″, and on its edge 47 inches in the
fame time.
Exp. 2. A fecond body was taken whoſe flat ſurface was to its
edge as 32:3, and with the fame moving force it deferibed on
its flat fide 32 inches in 2", and on its edge it defcribed 374
inches in the fame time.
Exp. 3. He took another body and covered one of its ſurfaces,
whofe length was 9 inches, with a fine rough paper, and by apply-
ing a moving force, it deſcribed 25 inches in 2″; he then took off
fome paper from the middle, leaving only of an inch at the
two ends, and with the fame moving force it defcribed 40
inches in the fame time.
Exp. 4. Another body was taken which had one of its fur-
faces, whofe length was 9 inches, covered with a fine rough
paper, and by applying a moving force it defcribed 42 inches in
2″; fome of the paper was then taken off from the middle,
leaving only 1 inches at the two ends, and with the fame
moving force it deſcribed 54 inches in 2"; he then took off
more paper, leaving only of an inch at the two ends, and the
body then deſcribed, by the fame moving force, 60 inches in the
fame time.
In the two laft experiments the paper which was taken off
the ſurface was laid on the body, that its weight might not be
altered.
Exp. 5. A body was taken whoſe flat ſurface was to its edge
as 30: 17; the flat fide was laid upon the horizontal plane, at
moving force was applied, and the ftage was fixed in order to
ftop the moving force, in confequence of which the body
would then go on with the velocity acquired until the fric-
tion had deſtroyed all its motion; when it appeared from a
mean of 12 trials that the body moved, after its acceleration
ceaſed, 53 inches before it ſtopped. The edge was then applied,
and the moving force defcended through the fame ſpace; and
it was found, from a mean of the fame number of trials, that
the ſpace deſcribed was 7 inches before the body loft all its
motion, after it ceafed to be accelerated.
Exp. 6. Another body was then taken whofe flat furface was
to its edge as 60: 19, and by proceeding as before, on the flat
ſurface it deſcribed, at a mean of 12 trials, 5 inches, and on
24
MECHANICS.
the edge 6 inches, before it ſtopped, after the acceleration
ceafed.
Exp. 7. Another body was taken whoſe flat ſurface was to its
edge as 26: 3, and the ſpaces defcribed on theſe two ſurfaces,
after the acceleration ended, were, at a mean of ten trials, 43 and
7 inches refpectively.
From all theſe different experiments its appears, that the
ſmalleſt ſurface had always the leaſt friction, which agrees with
the conſequence deduced from the confideration that the friction
does not increaſe in ſo great a ratio as the weight; we may
therefore conclude, that the friction of a body does not continue the
fame when it has different furfaces applied to the plane on which it
moves, but that the smallest furface will have the leaft friction.
To the experiments inſtituted by Mr. Ferguſon and others, from
which conclufions have been drawn fo different from thefe, this
author makes the following objections: It was their object to
find what moving force would just put a body at reft in motion;
and having, as they thought, found it, they thence concluded,
that the accelerative force was then equal to the friction. But
it is manifeft, as Mr. Vince obferves, that any force which will
put a body in motion must be greater than the force which
oppoſes its motion, otherwiſe it could not overcome it; and
hencé, if there were no other objection than this, it is evident,
that the friction could not be very accurately. obtained: but
there is another objection, which totally deſtroys the experiment
fo far as it tends to fhew the quantity of friction, which is the
ftrong coheſion of the body to the plane when it lies at reft;
and this is confirmed by the following experiments. ft, A
body of 122 oz. was laid upon an horizontal plane, and then
loaded with a weight of 8lb. and fuch a moving force was ap-
plied as would, when the body was juſt put in motion, continue
that motion without any acceleration; in which caſe the fric-
tion muſt be juſt equal to the accelerative force. The body
was then ſtopped, when it appeared, that the ſame moving force
which had kept the body in motion before would not put it in
motion, and it was found neceffary to take off 4 oz. from the
body before the fame moving force would put it in motion;
it appears, therefore, that this body, when laid upon the
plane at reft, acquired a very strong cohefion to it. 2dly,
a body whoſe weight was 16 oz. was laid at reft upon the hori-
zontal plane, and it was found that a moving force of 6 oz.
would just put it in motion; but that a moving force of 4 oz.
would, when it was just put in motion, continue that motion
without any acceleration, and therefore the accelerative force
muſt then have been equal to the friction, and not when the
moving force of 6 oz. was applied.
Friction.
25
I
39
From theſe experiments therefore it appears, how very con-
fiderable the coheſion was in proportion to the friction when
the body was in motion; it being, in the latter caſe, almoſt,
and in the former it was found to be very nearly equal to the
whole triction. All the conclufions therefore deduced from the
experiments, which have been inftituted to determine the fric-
tion from the force neceffary to put a body in motion (and
very few have been deſcribed but upon fuch a principle), have
manifeftly been totally falfe; as fuch experiments only fhew the
refiftance which arifes from the coheſion and friction conjointly.
Mr. Vince concludes this part of the ſubject with a remark
upon art. 5. "It appears (fays he) from all the experiments.
which I have made, that the proportion of the increaſe of the
friction to the increaſe of the weight was different in all the
different bodies which were made ufe of; no general rule there-
fore can be eſtabliſhed to determine this for all bodies, and the
experiments which I have hitherto made have not been fufficient
to determine it for the fame body."
Such are the refults of Mr. Vince's ingenious experiments.
He founds upon them a theory which the curious reader may
perufe in the Philofophical Tranfactions, Vol. 75. or Nos. 65. 66.
of Tilloch's Philofophical Magazine, but which is not inferted
here, as it does not feem readily applicable to any practical
cafes.
27. An ingenious engineer, Mr. John Southern of Bir-
mingham, made a feries of experiments upon mills uſed for
turning grindstones, with a view of corroborating Mr. Vince's
poſition that Friction is a uniform retarding force. And theſe
experiments are the more worthy of notice as they were made
on heavy machinery, with confiderable variation of velocity of
the rubbing ſurface, and great ſpaces rubbed over: the weight
which caufed the friction being upwards of 33 cwt., the velocity
of the rubbing furfaces 4 feet per fecond at the greateſt, and
the length of furface rubbed over about 1000 feet at a medium.
Theſe experiments feem to confirm the opinion that friction is
a uniform reſiſtance, at leaſt where the rubbing ſurface moves
with a velocity of from 9 inches to 4 feet per fecond; and Mr.
Southern concludes from them, that in favourable cafes it does
not exceed the fortieth part of the pressure or weight that oc-
cafions it.
The experiments from which thefe inferences are deduced,
are defcribed in No. 66 of the Philofophical Magazine juft re-
ferred to.
28. M. Coulumb has an extenfive paper on the fubject of Fric-
tion, in vol. 10. "Des Memoires des Savants étrangers ;" where
he deſcribes his experiments at conſiderable length, and deduces
+
:
1
j
26
MECHANICS.
from them an elaborate theory. We cannot here enter into the
detail of all theſe experiments: but ſhall merely ſtate M. Cou-
lumb's principal refults.
This gentleman's conclufions are widely different from Mr.
Vince's in one important particular: for he afferts that (cateris
paribus) the friction is proportional to the preſſure. The mean
ratios of friction to preffure, given by M. Coulumb's expe-
riments for different kinds of wood, are as follow, the preffure
being denoted by unity.
Oak againſt oak
Oak againſt fir
Fir againſt fir
Elm againſt elm
•
•
0'43
0.65
0.56
0'47
the friction being made in the direction of the threads or fibres
of the wood. But when the friction is made across the grain
of the wood, or ſo that the direction of the fibres forms a right
angle with that of the motion, the friction is lefs than in the
former caſe, but ſtill in a conſtant ratio to the preffure; the re-
fults being then as below:
Oak againſt fir
Fir againſt fir
Elm againſt elm
0.158
0.167
Ο ΙΟΟ
Theſe ratios are conftant quantities, not depending upon the ve-
locities, except in the cafe of elm when the preffures are very
fmall, for then the friction increaſes fenfibly with the velocity.
M. Coulumb gives the following general ſummary.
“(1.) The friction of wood ſliding over wood (both being
dry) oppoſes after a fufficient time of quiefcence a refiftance
proportional to the preffure; that refiftance fenfibly increafing
in the firſt inſtants of repoſe: but after fome minutes it uſually
arrives at its maximum or its limit.
"(2.) When wood glides dry over wood with any velocity
whatever, the friction is ftill proportional to the preffure; but
its intenfity is much leſs than that which is experienced in de-
taching the furfaces after fome minutes of reft: it has been
found, for example, that the force neceffary to detach and
produce a fliding motion in two furfaces of oak after fome
minutes of quiefcence, is to that neceffary to overcome the fric-
tion when the furfaces have obtained any degree of velocity
whatever, nearly as 9 to 2.
(3.) The friction of metals fliding over metals, without
oiling, is alſo proportional to the preffures; but its intenſity is
the fame, whether the furfaces are detached after having been
any time in repofe, or whether they preferve any uniform ve-
locity whatever.
“(4.) Heterogeneous furfaces, ſuch as woods and metals ſlid-
A
Friction.
27
ing the one over the other, without oiled furfaces, give for their
friction reſults very different from the preceding ones: for the
intensity of their friction relatively to the time of repofe in-
creaſes flowly, and does not attain its limit till after four or five
days, and ſometimes more; inftead of which, in metals the limit is
attained in an inftant, and in wood in a few minutes: this
augmentation is even fo flow that the refiftance due to the
friction in infenfible velocities is almoſt the ſame as that which
we muſt furmount in moving or detaching the furfaces after
three or four feconds of reft. And this is not all: in wood
gliding unoiled over wood, and in metals fliding over metals,
the velocity has very little influence upon the friction; but
here the friction increafes very fenfibly in proportion as the
velocities are augmented; in fuch manner that the friction in-
creafs nearly according to an arithmetical progreffion, when
the velocities increaſe in a geometrical progreffion."
The ratio of the friction to the preffure (1) when oak was
made to flide over iron, was found, from forty experiments, to
be as here ftted: when the velocity was almoft infenfible,
*0894, -773, 0785, and 0736: when the velocity was about
a foot per fecond, 1698, 1722, 1817, and 1573-
29. When metals flide upon wood done over with greaſe,
the friction. fays M. Coulumb, "appears much foftened, and
we may produce infenfible velocities with degrees of traction
lefs confiderable than in all the other fpecies of friction; but
when the velocities have been a little augmented, we have
found that the friction increaſes greatly with refpect to the
velocity, as was the caſe when we made unoiled metals flide
upon wood; and we have, for the relation of the augmentation
of velocities and the degree of traction which produced that
augmentation, nearly the fame law with that we fought to de-
termine in the friction of metals fliding dry upon wood: but if
the greaſing be not renewed at each experiment, it coagulates,
changes its nature, and the friction fucceffively augments."
"When the furfaces are done over with tallow, the ratio of
the friction to the preffure is greater under preffures of about
50 pounds, than under greater preffures.
ず
​"With coatings (enduits, plafters) of cart-greafe the friction
is never less than of the preffure. Its refiftance depends upon
the confiftence of the coating, and the friction augments fen-
fibly as this coating is fofter. When the furfaces are done over
with tallow, and are of great extent, the friction corrupts or
changes the nature of the tallow, and augments fenfibly as we
continue the motion without renewing the coating: yet it is
always found less than of the preffure. But when the tallow
is diffolved to an oil, this effect is lefs fenfible."
vy B
28
MECHANICS.
"
M. Coulumb's experiments on the friction of axes will be
deſcribed farther on.
On comparing the reſults of Mr. Vince's experiments with
thofe of M. Coulumb's, already referred to, it will be ſeen that
our knowledge on this branch of the ſubject is very far from
being fo certain and fatisfactory as is defirable. We may,
however, now deduce a few practical inferences from the
preceding articles.
(1.) Friction is diminiſhed by making the furfaces fmooth which
move upon each other. But there is a limit to this ſmoothneſs:
for the furfaces may be fo highly polished as to render the at-
traction of coheſion very ſenſible.
(2.) Friction is diminiſhed by anointing the rubbing ſurfaces
with fome unctuous matter. Thus, in wood acting against
wood, olive oil reduces the friction to nearly its half, and
metals oiled have leſs friction than when poliſhed.
(3.) Friction is diminiſhed by diminiſhing the furfaces in
contact. But this has a limit: for if the moving ſurface be very
thin, and the other ſoft, the former will plough a groove in the
latter, and thus have the friction increaſed.
(4.) Friction is diminiſhed by difpofing the parts of a ma-
chine in ſuch a manner, that the ratio of the velocity of the
parts which rub againſt each other to the velocity of the power,
may be as fmall as poffible.
(5.) Friction is greatly diminiſhed by cauſing the body to roll
inftead of fliding along the furface. This is in fact a diftinct
fpecies of friction, and will come under confideration more
fully foon.
(6.) Hence in machines, left the friction fhould employ a
great part of the power, care is to be taken that no part of the
machine flide along another if it can be avoided; but rather that
the parts fhould roll or turn upon each other. With this view
it will be proper to lay the axes of cylinders, &c. not in a groove
or concave matrix, as uſual, but upon a horizontal bar with two
vertical pieces to keep fuch axes from rolling off, or, between
little wheels called friction wheels, moveable on their refpective
axes: for, by this contrivance the friction is transferred from
the circumference of thoſe wheels to their pivcts. And in like
manner the friction may be ftill farther diminiſhed by making
the axes of thoſe wheels reft upon other friction wheels that
turn round with them. For the fame reaſon friction balls or
rollers have been placed within the naves of carriage wheels
s;
and lately a Mr. Garnett had a patent for an improved manner
of applying friction-wheels to any axis, as of carriages, blocks,
pulleys, fcale-beams, &c. in which the enclofed wheels or
rollers are kept always at the ſame diſtance by connecting rods
or bars.
Stiffness of Cords:
29
-
(7.) Friction is diminiſhed by cauſing the ſurface of one kind
of ſubſtance to run not upon the fame kind of matter, but a
furface of another material equally polished. Thus, pivots of
fteel meet with lefs friction when they flide in grooves of copper,
than when the grooves are of ſteel alfo.
(8.) As to friction in the mechanical powers: 1. The fimple
lever has no fuch refiſtance, unleſs the place of the fulcrum is
changed during the operation. 2. In the wheel and axle, the
friction on the axis is nearly as the weight upon it, the diameter
of the axis, and the angular velocity. This fort of friction,
however, is very fmall. 3. The friction of the pulley is very
confiderable when the fheaves rub againſt the blocks. 4. There
is alſo very great friction in the ſcrew: if the fcrew has a ſquare
thread it will raiſe a weight more eaſily than one with a tri-
angular thread: but in most if not all fcrews the friction is
equal to the power. 5. In the inclined plane the friction varies
according as the body rolls or flides; the friction in the latter
cafe being far the greateft. 6. In the wedge the friction is at
leaſt equal to the power, fince the wedge retains any poſition it
is driven into.
30. Since cords and ropes are not perfectly flexible, it be-
comes neceffary in eftimating the advantages of pulleys, cap-
ftans, &c. to make fome allowance for this want of flexibility:
in this caſe we may have recourſe to a theory which is far more
fatisfactory than any which has yet been invented with regard
to friction, and which accords far better with experiment. The
moſt uſeful formulæ may be deduced in a very ſmall compaſs.
Thus, let AC=CB=r, the radius of a pulley (fig. 3. pl. I.)
and two weights W and Q in equilibrio: if W fhould prevail,
it is obvious that the cord DQ becomes in the upper part bent
fo as to fit to the groove of the pulley, and in the lower part
bent inwards fo as to fall into the vertical b W: if the cord be
tolerably flexible, the curving is pretty regular from B almoſt
down to W: but if the cord be very rigid, BEW and ADQ
are found to be nearly ftraight lines, but neither of them ver-
tical; the weight Q being found to hang vertically below ſome
point as a, making a greater than CA, and the weight W
hanging below fome point b where Cb is lefs than CB. So that
as the arm of the lever at which one of the forces act is be-
come greater, and that of the other leſs than r, the condition
of equilibrium is no longer W=Q
When the cord is only moderately rigid, as in moſt practical
cafes, the diſtance Bb is always found fo extremely ſmall that
it may be fafely neglected in the difcuffion; that is, we need in
ſuch caſes pay no regard to the want of flexibility in the part
BEW correfponding to the weight W which is fuppofed to pre-
•
30
MECHANICS.
vail; but merely enquire into that of the part ADQ by which
the other weight is fufpended. Hence, if we put Aa=q, the
condition of equilibrium will be expreffed thus:
Wr=Q (r-+-g).
From this it refults, that if W-Q be the magnitude by which
we ſhould augment the power, that it may be on the point of
prevailing; and if we have regard to the fiffneſs of the cord,
this magnitude will be W-Q-Q
Confequently, to in-
troduce the confideration of the stiffness of the cord employed in a ma-
chine, we have only to fuppofe that the arm of the lever at which the
refiftance acts is greater than it really is, by a determinate quantity q.
It remains, then, to afcertain this quantity 9: in order to
which, it may be obſerved that a cord refifts, on two accounts,
the efforts which are made to bend it. The firft is due to the
tenfion of the cord, and is proportional to it, it will therefore
be=bQ; the ſecond is due to its warping or twifting, and we
may repreſent by a the force employed to overcome it. Here.
a and b are, as is manifeft, variable coefficients. Thus, for one
and the fame cord a+bQ_may repreſent the force required to
bend it: but, if the cord be changed, the diameter d will be
different, and we may conclude that, cæteris paribus, the force
which muſt be employed will be proportional to a certain power
n of d; for the force neceffary to bend a cord will increaſe with
its diameter: this power will decreaſe on the contrary with the
dn
radius r of the pulley; therefore (a+bQ) may repreſent the
force neceffary to overcome the ſtiffneſs of the cord; ʼn being as
yet an indeterminate quantity. This value being the augment-
ation which muſt be given to the force or weight W that it
may be on the point of prevailing over the refiftance Q, muſt,
from what is before ſhewn, be equal to Q. Thus we have
dn
d" (a+bQ)=Qq, or q = = (a+b Q)
(A).
This equation, it is true, is only furniſhed by general con-
fiderations, and not by a rigorous inveſtigation: it contains,
moreover, the unknown coefficients n, a, and b, varying for dif-
ferent cords. But there is a fimple method of finding theſe co-
efficients, and of affuring ourfelves that the expreffion is fuf-
ficiently exact in practice.
31. Chooſe any cord, and after bending it along the groove
of a pulley, as the cord QDABEW (fig. 3.), attach to it two
equal weights, and augment one of them till it is just on the
t
Rigidity of Cords.
31
point of prevailing fo as to give motion to the ſyſtem, marking
the difference of the weights. Make a fimilar experiment four
times, taking as many different values of W and of Q, alfo of r:
fo fhall there be obtained four values of W-Q, that is to ſay,
dn
of (a+bQ), which will furniſh four equations. Putting e,
ጕ
f, g, h, thefe values, and denoting by r, r', r'", "", the feveral
radii of the pullies, and Q, Q, Q", Q", the weights employed
in their turns, we ſhall have
dn
e= (a+bQ)
r
dn
8 = = = (a+bQ').
go!!
dn
ƒ===(a+bQ')
dn
b ====== (a+bQ"")
Of theſe equations the three first ferve to diſcover the values of
n, a, and b; and the laſt enables us to affure ourſelves whether
the formula (A) has the accuracy we wish.
32. As to experiments on the rigidity of ropes and cords, we
know none of any great importance and extent befides thoſe of
M. Coulumb. Thefe experiments were made with two kinds
of apparatus, one contrived by M. Amontons, the other by M.
Coulumb himſelf: the experiments made by means of one in-
ftrument corroborated the reſults of thoſe made by the other :
but we ſhall here merely deſcribe the experiments by means of
M. Coulumb's apparatus, which we prefer becauſe it was con-
trived to aſcertain at the fame time that kind of friction which
is occafioned by the rolling of cylinders upon horizontal
planes.
The apparatus confifts of two treffels of 6 feet in height, and
fufficiently folid and firm, on which there are laid two pieces of
fquared wood; upon theſe two pieces of wood are fixed two
rulers of oak well planed, DD, D' D' (fig. 4. pl. I. nos. 1. 2.),
and poliſhed with a little fiſh-ſkin: then two cylinders of
lignum vitæ are procured, one of 6 inches diameter, the other
of two inches; together with feveral cylinders of elm from 2
to 12 inches in diameter.
Theſe things prepared, in order first to find the friction of the
rollers, they are laid horizontally upon the two rulers of oak,
and croffing their directions perpendicularly, as repreſented in
fig, 4. no. 2. the rulers being in a perfectly horizontal poſition:
then fufpend on each fide of the roller in ufe a weight of 50lbs.
with very fine and flexible packthread; or indeed by means of
feveral fuch threads diftributed over the roller, and charged
each with 50 lbs. on each fide, produce upon the rulers any de
terminate preffure; and afcertain by the aid of little counter-
32
MECHANICS.
weights fufpended alternately on the different fides of the roller
what will be the force neceffary to give it a motion barely.
fenfible.
The friction of the rollers being eftimated by the preceding
method, it will be eaſy to allow for it, when inftead of the very
flexible packthread, the cords or ropes of which the ſtiffneſs is
to be determined are fubftituted. And this new determination
will be made in the fame manner as with reſpect to the naſcent
friction by fufpending the little weights alternately on each fide
of the roller, fo that they fhall give it a motion juft perceptible.
It is obvious to remark that this method of eftimating the
effects of the rigidity of cords will furniſh reſults directly ap-
plicable to the preceding formula: for the weights which pro-
duce the very ſmall motion in the cylinders will be precifely
equal to the augmentation of the refiftance arifing from the
ftiffneſs of the cord, eftimated in the direction of that portion
of the cord to which the reſiſtance is applied that repreſents the
uſeful effect of the machine.
33. We ſhall firſt exhibit the refults of M. Coulumb's ex-
periments, on the ſecond ſpecies of friction, produced by rollers
of lignum vitæ of 6 and of 2 inches diameter.

Charge of the rollers,
their weight being]
comprised.
Weights which produce an extremely slow motion, the
diameter of the rollers being
100 lb.
500
1000
6 inches
0.6
3'0
6'0
2 inches
1.6
9'4
18.0
From this table M. Coulumb infers that the friction of cy-
linders which roll upon horizontal planes, is directly as the
preffures, and inverfely as the diameters of the rollers. He
alfo found that greafing the furfaces did not here cauſe any
fenfible diminution in the friction.
Note. The foot and the pound ſpoken of throughout theſe
experiments are thofe of the ancient Paris ftandard: we have
not reduced them to English meaſures, fince the deductions
founded upon the experiments does not render this neceffary.
2
Rollers of elm produced a friction of about the greater
than lignum vitæ. And under fmall preffures the friction was
rather greater than would refult from the law of friction being
proportional to the preffure.
34. We fhall next preſent the reſults of M. Coulumb's ex-
periments upon the rigidity of cords, and different rollers be-
tween 2 and 12 inches in diameter: the deduction for the
friction is ſtated in the table, and a comparative column exhibits
the rigidity deduced from the experiments made with the ap-
Rigidity of Cords.
33
paratus of Amontons. The cords were of three kinds: No. 1,
of 6 threads in a yarn, or 2 in a ftrand, the circumference 12
lines, and weight of a foot in length 4 drams. No. 2, of 15
threads in a yarn, or 5 in a ftrand, circumference 20 lines,
weight of a foot in length 12 drams. No. 3, of 30 threads
in a yarn, or 10 in a ftrand, circumference 28 lines, weight of a
foot in length 24 drams.
Kinds of
the rulers Friction
Stiffness of the Cord.
No. of experiments. |
Cords
used in
wood:
diameter
and
the expe-
riments.
weight of
Weights
hung on
each side
the roller
Addition.
weight
to sur-
Total
charge of
mount
friction of
roller and
which
support
of the
Valued
by Cou-
roller.
lumb's
the
in lbs.
the
Valued
by Amon-
tons' ap-
stiffness
appa-
paratus.
rollers.
roller.
ratus.
of cords.
Elm
Cord
No. 3. of
100
5 lbs.
315
1'5
3.5
4.4
12 inches
I
30 threads
diameter,
300
II
721
3.6
7'4
10'4
in a yarn.
weight
IIO lbs.
500
20
1130
5.6
14'4
16.4
Elm
6 inches
2
Idem.
diameter,
200
18
443
weight
25 lbs.
Guiacum
6 inches
3
Idem.
diameter,
200
16
466
2.8
13.2
14.8
weight
50 lbs.
Guiacum
2 inches
25
II
651
Idem.
4
diameter,
weight
200
52
456/1/
4 lbs.
Cord
Guiacum
25
I
IOI
No. 2. of
6 inches
100
6
256
15 threads diameter,
200
II
461
2.8
8.2
7.6
in a yarn.
weight
500
24
i074
6.4
17:6
17.8
50 lbs.
Cord
No. 1. of
100
Idem.
6 threads
200
36
30
253
456
2.7
3.3
3.I
in a yarn.
From this table it will be ſeen that the method of Amontons
and that of Coulumb furniſh nearly the fame refults: M.
Coulumb aſcribes the differences where greateſt to the circum-
ftance of the cords having been more ufed previous to their
being taken for one kind of experiment than for the other.
$5. M. Coulumb, before he commenced the experiments
upon the friction of axes, cauſed the pulley to turn on its axis
during ſuch a time and with ſuch a velocity as was neceſſary to
VOL. II.
D
t

34
MECHANICS..
enable the furfaces in contact to acquire all the polish and
glibnefs of which they were fufceptible. The chief object held
in view in the experiments of which we now ſpeak was to de-
termine the friction of the axes of machines in motion. M.
Coulumb therefore caufed the fufpended weights to run over a
ſpace of 6 feet, and to meaſure ſeparately by half feconds the time
employed to run over the first three feet, and that occupied
in running over the laſt three feet. The following table con-
tains the reſults of experiments on the friction of axes of iron
in boxes of copper: the axis ufed was 19 lines in diameter,
and had a play of 12 lines in the copper box, the pulley was
144 lines in diameter, and weighed 14 pounds.

!
1
}
}
36
MECHANICS.

Weight
Weight
Addi-
Fric-
Ratio
No. of
experi-
ments.
hung
tional
Kind of cord Kind of greas-
used.
used to
Jon each
weight
Motion of the
weight suspended
Pres-
tion
of fric-
sure on
reduc.
tion to
ing.
bend
side of
to move
on each side of the
the
to
the
the cord.
over the the
the
pulley.
axis.
surface
pres-
pulley. pulley. pulley.
of axis.
sure.
Very flexi-
ble thread of
Friction with-
O'O
103
6
Slow and irregular.
226
42
0.186
3 lines cir-
out-greasing.
cumference,
10.5
Slow and irregular.
424
65
0.153
Cord No. 1.
The first 3 ft. fallen
of 6 threads
Idem.
1'5
200
13.5
thro' in 6", the last
in a yarn.
3 in 3″.
21
Slow but continual.
825
130
0'156
The first 3 feet de-
28
scribed in 5″5, the
3
Idem,
Idem.
3'0
400
39
last three in 2"5.
First 3 ft. described
in 3", the last 3 in
I{".
Very flexi-
2.5
Slow but continual.
216.5 17.5
0·08x
ble thread,
tallow.
O'O
100
The first 3 feet de-
of 2 lines cir-
6
cumference.
Cord No. I.
6.5
5
of 6 threads
Idem.
1'5
200
in a yarn.
10'0
scribed in 3″5, the
last 3 in 1"5.
Slow but continual.
The first 3 feet, de-
scribed in 3"-5, the
420
36 0'086
last 3 in 1"5.
13
Slow and continual.
827
72
24
0°087
The first 3 feet, de-
6
Idem.
Idem.
3.0
400
18
scribed in 5″-5, the
last 3 in 2"
first 3 feet in 3",
24
last 3 feet in 2".
Table of Friction, &c. continued.
፣

་
Thread of 2
lines in cir-
cumference.
Cart grease.
8
Idem.
Idem.
9
Idem.
Idem.
៖ ៖ ៖
100
150
Cord No. 1.
IO
of 6 threads
Idem.
IOO
8 58 5
2'5
Slow and continual.
117
17'5
· 0.15
3.7
Idem.
218
26
0'119'
5'7
Idem.
320
40.
O'125
4.3
Slow and uncertain.
218
26
0.119
9
first 3 feet in 3",
in a yarn.
last 3 feet in 1½".
8.5
Uncertain,
422
50
0.118
II
Idem.
Idem.
1'5
200
14
first 3 feet in 4″,
last 3 feet in 2".
20
all 6 feet in 3"5.
17
Uncertain.
831
101
O'121
12
Idem.
Idem.
3'0
400
22
28
The cart
first 3 feet in 6″·5,
last 3 feet in 2" 5.
first 3 feet in 4",
last 3 feet in 1"5.
From
200
to
1200
lbs.
0'127
>
13
14
x5
grease of prec.
exp. wiped,
the pores of
the metal re-
mained unc-
tuous.
The surface
fresh done
with oil.
The greasing
not renewed of
a long time,
though the
machine bad
been much
used.
1
វ
i
O'127
0'133
0*133
38
MECHANICS.
The weights employed to bend the cord, and which are con-
tained in the 4th column, were calculated from the tenfions ex-
preffed in the 5th column, by means of the formulæ already
given, and the refults of fome previous experiments. Thefe
weights being fubtracted from thofe of the 6th column, which
put the fyftem in motion, leave the weights employed in over-
coming the friction. Thefe latter weights acting at a di-
ſtance from the centre of rotation equal to the fum of the radii
of the pulley and the cord; the friction which is exerted upon
the axis, and which in the cafe of a very flow motion may be
confidered as making an equilibrium with thoſe weights, is
therefore equal to the product of thoſe weights into the ratio
of the fum of the radii of the pulley and the cord, to the radius
of the axis, which ratio is very nearly 7 to 1, when the weight
fufpended by a thin packthread, and nearly 72 to 1, when
it is fufpended by the cord No. 1. From theſe confidera-
tions the 9th column was calculated. The weights compriſed
in the 8th column are compofed, 1. Of the weight of the
pulley or cylinder; 2. Double the correfponding weight in the
5th column; 3. The weights contained in the 6th column; for
the fum of thefe evidently compofe the preffure upon the axis.
Hence, to find the ratio of the friction to the preffure, as ex-
preffed in the 10th column, it is only neceffary to divide any
number in the 9th column by the correfponding one in the 8th.
36. When it is proper to have regard to the velocity of the
weight, to afcertain the effort which furmounts the friction and
the ſtiffneſs of the cord, we may obſerve at once that in this caſe
the motion is nearly a uniformly accelerated motion, fince the firſt
3 feet are deſcribed in a time about double that employed in
running over the laft 3 feet. It remains, therefore, to learn what
part w of the additional weight ftated in the 6th column, which
we call w, was employed in accelerating the motion of the ſuf-
pended weight; for the other part of the additional weight,
w', is manifeftly that which furmounts the friction and
the ſtiffneſs of the cords. Now t being the time of the whole
deſcent, the accelerating force which has place is equal to 2X6;
viz. w
tz
and, naming W the total fum of the weight hanging upon the
pulley compriſing in it 7 pounds for the inertia of the pulley,
which weighed 14 pounds, and g the accelerating force of gra-
vity, the mafs put in motion will be
maſs by the accelerating force will be
W
g'
and the product of that
2 X 6 W
g ta
; which being fub-
tracted from the additional weight which put the pulley in mo-
\
Stiffness of Cords.
39.
tion, gives the quantity w-w', or the part of the weight w em-
ployed to overcome the ſtiffneſs of the cord and the friction.
It appears from the 7th, 8th, 9th, 10th, 11th, and 12th ex-
periments, that the friction of axes of iron in boxes or cheeks of
copper is much lefs foftened by the cart-greafe than by tallow.
37. M. Coulumb has likewife endeavoured to afcertain the
friction of axes of rotation made of the different kinds of wood
which are commonly found in rotatory machines. To render
the friction more fenfible he uſed pulleys of 12 inches mounted
upon axes of 3 inches; fometimes the axes were immoveable,
at others they moved, but in both cafes the friction was the
fame the proper precautions were adopted to ſmoothen the fur-
faces in contact, and thence to avoid the uncertainty and irre-
gularity which might otherwife have attended the refults.
Kinds of wood uſed in the experiments.
Ratio of
friction
to pressure.
Axis of holm-oak, box of lignum vitae, coated with 0·038
tallow
Ditto the coating wiped, the furface remaining oily
Axis and box as before, but uſed ſeveral times with-
out having the coating refreſhed
'}
Axis of holm-oak, box of elm, coated with tallow.
Ditto both axis and box wiped, furfaces remaining oily
Axis of boxtree, box of lignum vitæ, coated with tallow
Ditto the coating wiped, the furfaces remaining oily
Axis of boxtree, box of elm
Ditto the coating wiped off
Axis of iron, box of lignum vitæ, the coating wiped
off, and the pulley turned for ſome time
d'oб
: 0°06
d'o8
0.03
0'05
0043
007
0'035
-0.05
0.0.5
The velocity does not appear to influence the friction in any
fenfible manner, except in the firft inſtants of motion: and in
every caſe the friction is leaft, not when the ſurfaces are
plaſtered over, but when they are merely oily.
38. The experiments on the ſtiffneſs of cords defcribed (art.
34) were made in cafes of motions nearly infenfible; but M.
Coulumb enquired whether with a finite velocity the refulting
effect of the ſtiffneſs of the cord were augmented or diminiſhed.
For this purpoſe he took a pulley and box of copper, and an
axis of iron done over with tallow the diameter of the pulley
was 144 lines, and that of the axis 20 lines; and the cord was
one of 30 threads to a yarn, or No. 3. of which the ſtiffneſs
with refpect to infenfible velocities was determined by ſome of
the foregoing experiments. The enfuing table fhews the re-
fults of the experiments: the weights were made to run over a
diftance of 6 feet, and the times of defcribing the firſt three and
the laſt three feet were meaſured by a half-fecond pendulum.
+
40
MECHANICS.

Weight
No. of hung
experi-on each
ments. side the
Addi- Part of
tional wt. to
weight over-
to
come
1
move friction
pulley.
the and ri-
pulley. gidity.
• Motion of the
weights hung upon
the pulley..
[Weight] Stiffness | Stiffness
acting
Pres- at ex-
of the
cord
sure on tremity deduced
the of pul- from the
axis in ley, ba- weights
3.
lancing which
the
move the
of the
cord esti
mated
from its
tension
and for-
mer ex-
friction pulley. perimts.
7.5 lbs. 75 lbs.
Slow and continued 221 lbs. 2.6lbs.
4'9 lbs.
4'0 lbs.
'first 3 feet in 3
I
roolbs.
12
7.6
last 3 feet in 1"
15
first 3 feet in 2″
7.6
last 3 in 14"
II
II
Slow and uncertain 425 4'9
6.1
6.6
99
first 3 feet in 6"
15
12.9
2
200
last 3 in 3"
first 3 feet in 31"
19
12.2
last 3 in 14"
20.5 20'5
Slow and uncertain 834 -9'7
10.8
11.8
S
3
'first 3 feet in 6"
24
19'9
3
400
last 3 in 3"
3x
17.6
first 3 feet in 3″
last 3 in 2"
31°5
31.5
Doubtful and conti. 1235
14.5 17.0
17.0
4
600
137
first 3 feet in 6″
31'5
last 3 in 3½"
7
:
It appeared in the table (art. 34.) that to bend the cord
no. 3. of 30 threads in a yarn, about a roller of 12 inches di-
ameter, and with a tenfion of 500lbs, would require a weight
of 14 4 lbs of which weight the conftant part due to the
fabrication of the cord is about 1'4 lbs: this value may be
retained; but it will be here proper to deduce the part due to
the tenfion of the cord by the quintal to (14°4 −1·4)
13=2.6lbs. From theſe data the laſt column to the right of
the above table was computed.
典
​ड
39. To complete the object of the experiments it is neceſſary
to have the ſtiffneſs of the cord without afferting any thing à
priori on the values which had been previously found for fuch
rigidity. To this end M. Coulumb has eſtimated the friction
of the axis from its charge and the experiments of art. 35;
where it appeared that this friction was independent of its
velocity and equal to o'087 of the preffure. This friction
which is exerted at the furface of the axis being computed, and
the radius of the axis being to the diſtance between the centre
of rotation and the middle of the cord as 1 to 75, it will be
eafy to calculate the weight which acting in the vertical di-
rection of the middle of the cord may be in equilibrium with
the friction in each experiment; and theſe weights are con-
tained in the ſeventh column. Subtracting theſe weights from
f
Stiffness of Cords.
41
the additional weights contained in the third column, namely
thoſe which put the pulley in motion, we have in the caſe of a
very flow motion the values of the weights which juſt ſurmount
the ſtiffneſs of the cord; theſe weights are compriſed in the 8th
column, and differ but little from thoſe calculated immediately
and contained in the 9th column.
8 12
40. Now to know if the greater or lefs velocity of the
weight fufpended upon the pulley has any influence upon
the reſiſtance due to the ſtiffneſs of the cord, we muft in
the cafe of the motion calculate what portion of the ad-
ditional weight hung upon the pulley is employed in over-
coming the friction and the rigidity of the cord. Here the
formula of a preceding article has its application, w'=2X6w :for,
the time occupied by the weight in deſcribing the laſt three feet
being nearly the half of that employed in defcribing the firſt
three feet, the motion may be confidered as uniformly accele-
rated, and the quantities w-w', which refult, and are con-
tained in the 4th column, differ but little, as is manifeft, from
the weights employed to overcome the friction and the ſtiffneſs
of the cords, in the cafe of an extremely flow motion. And,
as it appeared from the preceding experiments that the friction
was independent of the velocity, or that it oppoſed the fame
refiſtance to the motion in the different trials for each ex-
periment; it hence follows that the reſiſtance arifing from the
stiffness of the cord was likewife conſtant in the fame trials, and
depended not upon the velocity, at least in any fuch fenfible manner
as to merit our regard in computing the powers of machines.
41. The invariableneſs of the refiſtance occafioned by the
ftiffness of cords, under different velocity, appears alfo imme-
diately from the refults compriſed in the 5th column of the
table, which, as before obferved, proves that the motions were
nearly uniformly accelerated. And from this property it fol-
lows, that there is always a conftant part of the weight or
power employed in furmounting the friction and the ſtiffneſs of
the cords.
"Nevertheleſs," adds M. Coulumb, " it muſt be acknow-
ledged, that it is not ftrictly true, that the augmentation of ve-
locity does not augment the refiftance due to the rigidity of
cordage. This augmentation appears eſpecially perceptible
when the cords are ftretched with weights or by forces that are
under 100 pounds. I have eſtimated, by many trials, that in
fuch caſes a velocity of 8 feet per fecond would increafe by
nearly a pound the refiftance occafioned by the ſtiffneſs of our
cord of 30 threads in a yarn : but this augmentation of refiſtance
feems to be a conftant quantity for the fame degree of velocity,
1
42
MECHANICS.
whatever the tenfion may be; in fuch fort that it ceaſes to be
perceptible under great tenfions, and that there are but very
few circumſtances in which it may not be neglected in practice:
this augmentation with regard to the velocity appears, befides,
much greater in new than in old cords, and in tarred cords.
than in thoſe which are white or untarred””
42. M. Coulumb deduces from theſe experiments the follow-
ing general conclufions :
(1.) That with refpect to practice, in all rotatory machines
the ratio of the preffure to the friction may always be fuppofed
conſtant, and that the influence of the velocity is too ſmall to
need our regard.
(2.) That the refiſtance which must be overcome to bend a
cord over a roller or pulley is reprefented by a formula com-
poſed of two terms; the firft is a conſtant quantity independent
a dn
of the tenfion, and of the form (art. 31.) where a is a con-
T
ftant quantity determined by experience, d" is a power of the
diameter d of the cord, and the radius of the roller; the
b dn
fecond term is Q, where b is a conſtant quantity, d, n, and r,
T
as before, and Q the tenfion of the cord. Thus the complete
Q_the
dn
formula expreffing the ſtiffneſs of the cord is (a+bQ). The
power ʼn varies according to the flexibility of the cord, but is
ufually about 1'7 or 1-8, or the refiftance is nearly proportional
to the fquare of the diameter of the cord: when the cord is
much uſed n decreaſes to 1.5 or even 1.4. The following is a
fummary of refults.
of 30 threads in a yarn
White
Cord,
Sof
-15
6
Tarred
Cord,
12
of 30 threads in a yarn
-15
6
15
lbs.
dn
-b. 100 = 9°0
dn
a=4.2
•
=1°2
=0°2
=6·6.
= 5'1
= 2.2
=2.0
=0°4
=11:6
= 56
= 24
be
43. Our knowledge of the nature of the friction of axes, and
ſtiffneſs of cords, though confeffedly very imperfect, may
introduced into the computation of the power of machines: this
may be illuftrated by an example of a capftan or windlafs,
where the general formula for an equilibrium will be this:
r2
PR=QR'+ √i+};
+dr (a+bQ)
where P reprefents the power, and the other letters as below,
1
The Capftan, allowing for Friction, &c.
43
The weight to be elevated, is
Q=1000 lbs.
The radius of the axis or pivot, which is of iron, is
r=2 inches.
This axis turns in a box of copper: the radius of the cylinder
about which the cord is rolled, is
R'10 inches.
The arm of the capftan, or the radius, or diſtance at which the
men exert their force, is
R=10 feet 120 inches.
The pivots are ſuppoſed to have been plaſtered with tallow ſome
time, and the inftrument often uſed, till the ratio of the fric-
tion to the preffure is reduced to that of experiment 15 in the
table of article 35. whence we have that ratio, or
f=0*133, and +7:5851.
ff
The cord is fuppofed tarred, and of 120 threads in a yarn,
which will fupport 12 or 14000 lbs. without breaking. Now
a tarred cord of 30 threads in a yarn requires a conſtant effort
equivalent to 6·6 lbs. to bend it about a roller of 2 inches radius,
and an effort proportional to the tenſion, of 11.6 lbs. for a quin-
tal, or 116 lbs. for 1000 lbs. Here the radius of the cylinder
being 10 inches, we muſt, firſt ſuppoſing the cords equal, diminiſh
theſe efforts in the ratio of 10 to 2, viz. make their fum
(66+116) for fooo lbs., and = (6·6+8x116) for 8000.
And as the cord is of 120 threads in a yarn inſtead of 30, we
muſt increaſe the laſt refult, in the ratio of 30 to 120, fo fhall
we have × (6·64·928)=7477 for the effort which will fur-
mount the ſtiffneſs of the cord, that is
?
dn
R'
2
To
(a+bQ)=747*7.
And fince R'10, we have d" (a+bQ)=7477-
2
To
Thefe values being fubftituted in the general formula it be-
comes
PX 120 (8000 x 10)+
8000 X 2
7.5851
+7477.
P=666·6+1.7°577+62·3=746.5 lbs.
or,
It will be neceffary therefore to diſtribute at the extremities of
the bars of the capftan efforts whofe fum fhall be equivalent to
746.5 lbs.: that is, if a man makes an effort balancing 25 lbs.,
30 men will be required to move the weight of 8000 lbs. Had
there been no friction and were the cords perfectly flexible, the
8000
force neceffary would have been only or 666 6, lefs than
12
the other by almoſt 80 pounds, a difference which is more than
equivalent to the force of three men. So that in this example
મ
44
MECHANICS.
the friction and rigidity of the cord, require an increaſe of be-
tween an 8th and a 9th of the whole power which would other-
wife have been requifite,
This, however, we wish to be received only as an approxima-
tion. The details which have been here entered into will, we
truft, be found of fome utility in directing the practice, and
may furniſh ſome hints to thoſe who have time and inclina-
tion to adopt other feries of well-conducted experiments;
and thus fupply theſe moſt important defiderata in practical
mechanics.
On the Energy of First Movers.
44. The confideration of the abfolute and relative forces of
different kinds of first movers is of too great confequence in the
application of mechanics to be entirely omitted in this perform-
ance: we fhall, therefore, prefent the reader with fome ob-
fervations and tables refpecting the chief claffes of powers ufed
to drive machinery, viz. water, air, fteam, gunpowder, and
animal exertion.
Water is generally made to operate upon machines by means
of its momentum when in motion: but it may alſo be uſed,
and that as a very powerful mover, when acting by its preffure
merely. In the theory of hydroftatics (art. 387.) we ex-
plained the principle of the hydroftatical paradox, in which it
is afferted that any quantity of water or other fluid may be
made to fupport any other quantity or any weight however
great, and indeed to raise the greater weight until it reaches
fuch a height as enfures the equilibrium. Thus in the hydro-
ſtatic bellows the weight of a few ounces of water is made to
raiſe ſeveral hundred pounds. And in like manner Otto Gue-
ricke of Magdeburg made a child balance, and even overcome,
the pull exerted by the emperor's fix coach horfes, merely by
fucking the air from beneath a pifton. This great power de-
pends upon the fundamental property of fluids, that they prefs
equally in all directions. Mr. Bramah, an ironmonger in Pic-
cadilly, has lately obtained a patent for a machine acting as a
prefs on this principle of the quaqua verfum preffure of fluids:
A pifton of of an inch diameter forces water into a cylinder
of 12 inches diameter, and by this intervention raiſes the piſton
of the cylinder: ſo that a boy acting with a fourth part of his.
ftrength on the ſmall pifton by means of a lever can raiſe about
94080 lbs. or 42 tons preffing on the great piſton; the increaſe
of power being as I to 4 x 12 or 1 to 2304. This contrivance
will be more minutely explained under the article Bramah's-ma-
chine, in the alphabetical part of this volume.

4
First Movers.
45
45. As to the effect of water in motion, it will manifeftly depend
upon the quantity of fluid and its velocity jointly. When the
water runs through a notch or an orifice of a regular form fituated
in the bottom or fide of a refervoir, the quantity diſcharged in any
given time may be determined by the rules laid down for thoſe
purpoſes in vol. 1. Book IV. If s² be the area of any plane ex-
pofed to the action of a current of water, and the velocity per
fecond with which the fluid ſtrikes the plane, then will the force
of the fluid be equivalent to the weight of a volume of water
expreſſed by, where g repreſents 32% feet, on the ſup-
2 g
บ
pofition that the water ſtrikes the plane dire&ly: but if the fluid
ftrike the plane obliquely and I repreſent the angle of incid-
ence, the force will be equivalent to the weight of the column
22 52
2 g
fin.2 I. Or, fince a cubic foot of water weighs 62 lbs
6240²sk
averd. if v and s be expreffed in feet we ſhall have 2 g
fin. I =971502 fin.² I v² s² lbs. averd. for the equivalent
weight, which becomes barely 971502v's² lbs. when the plane
is directly oppofed to the fluid.
46. In the determination of the velocity of the ſtream it will
be neceffary either to aſcertain the height h through which the
water has fallen freely, as from the end of a ſpout, when √√2gh,
or nearly 8 h, will fhew the velocity, b being in feet; or when
the water iffues through an orifice in the bottom or ſide of a
refervoir, to have recourſe to Chap. 1 and 2. Book IV. vol. I.
before referred to. If the ftream be ample without much fall,
fuch as muſt neceffarily be applied to move an underfhot wheel
by its impulfe, the power will be determinable from the ve-
locity of the water and the quantity which paffes through the
fection of its bed. Dr. Defaguliers, in his Experimental Phi-
lofophy, vol. II. pa. 419. gives the following eafy method of
afcertaining theſe data: Obferve a place where the banks of the
river are fteep and nearly parallel, fo as to make a kind of
trough, for the water to run through, and by taking the depth
at various places in croffing make a true fection of the river.
Stretch a ftring at right angles over it, and at a ſmall diſtance
another parallel to the firft. Then take an apple, an orange,
or other ſmall ball, juft fo much lighter than water as to fwim in
it, and throw it into the water above the ftrings. Obferve when
it comes under the firft ftring, by means of a half fecond pen-
dulum, a ftop watch, or any other proper inftrument; and ob-
ferve likewife when it arrives at the fecond ftring. By this
means the velocity of the upper furface, which in practice may
46
MECHANICS.

generally be taken for that of the whole, will be obtained. And
the fection of the river at the ſecond ſtring muſt be aſcertained
by taking various depths, as before. If this fection be the fame
as the former, it may be taken for the mean fection: if not,
add both together, and take half the fum for the mean fec-
tion. Then the area of the mean fection in ſquare feet being
multiplied by the diftance between the ftrings in feet, will give
the contents of the water in folid feet, which paffed from one
ftring to the other during the time of obfervation; and this by
the rule of three may be adapted to any other portion of time.
Suppofe, for example, the time were 12", and the hourly expen-
diture of water were required, the proportion would be, as
12": 3600" :: the number of cubic feet between the two
ftrings: the hourly expenditure in cubic feet. If the mere ve-
locity be required with reference to any fixed interval of time,
a fimilar proportion will give it, only obferving to take, inſtead
of the folid content or capacity in the third term, the diſtance
between the two ftrings.
The operation may often be greatly abridged by taking notice
of the arrival of the floating body oppofite two ſtations on the
fhore, eſpecially when it is not convenient to ftretch a ftring
acroſs. An arch of a bridge is a good ſtation for an expe-
riment of this kind, becauſe it affords a very regular fection
and two fixed points of obfervation: and in fome inſtances the
fea practice of heaving the log may be advantageous. Where a
time-piece is not at hand, the obferver may eaſily conſtruct a
half-feconds or quarter-feconds pendulum: the former may be
made by fufpending a ſmall round (not flat) button, or other
ſpherical weight, by a thread looped over a pin of fuch a length
that the diſtance from the point of fufpenfion to the centre of
the weight fhall be 9.8 inches: the quarter-feconds pendulum
muſt be a fourth of this length. If, by obfervations at ſeveral
ſtations above and below any particular point of the river, the
velocity does not appear to vary, the ſection of the river in all
that ſpace may be confidered as uniform; and it will not be
neceffary to determine more than one fection by actual meaſure-
ment.
47. The effect of underſhot and overfhot wheels has been
very variouſly ſtated by different authors; the moſt valuable and
correct obfervations are thofe of Mr. Smeaton, an abſtract of
which was given in Chap. 4. Book IV. vol. I. The numerous
practical remarks and experiments related in that chapter and
the fecond chapter of the fame book, will render it unneceffary
for us now to dwell longer upon the effects of water as a mover
of machinery.
48. AIR is the next natural mover we propoſe to confider.
And this like water may be regarded either as at reft, or in mo
Air as a Mover of Machinery.
47
}
tion. The preffure of the atmoſphere in a medium ftate is
equivalent to the weight of 14 or 15 lbs. averdupois on a
ſquare inch; and this preffure will fupport, and, by means of a
fucking pump, raife water to the height of about 33 feet; it
fupports mercury in the barometer at the height of 28 to 32
inches.
།
The denfity of air is, at a medium, about 833 times leſs than
that of water: if we take round numbers and reckon 800 to `I
for the ratio of the denfities, and put s² for the ſurface on which
the wind ſtrikes, v for the velocity with which it moves, and I
for the angle of incidence, then the force of the wind will be
equal to the weight of a volume of water expreſſed by go
72 st
2g
fin. 'I=0012144 v² s² fin.² I lbs. averdupois.
I
This formula, however, is only an approximation, and would
lead to confiderable errors when the velocities are great: on
this ſubject we have treated pretty fully in art. 554, &c. Book V.
vol. I. where the tables of Dr. Hutton, Mr. Roufe, &c. are
exhibited: the following is Mr. Roufe's table of velocity and
correfponding force in the form it was originally given by Mr.
Smeaton; but the form in which it is thrown in art. 554 is
more uſeful.
Velocity of the
Wind.
Miles! feet in
1

Perpendi-
cular force
onone fquare
foot, in
in one
one
averdupois
hour.
fecond.
pounds.
I
I'47
*005
2
2'93
*020
3
4°40
*044
4
5.87
*079
5
7*33
*123
10
14.67
*492
1 2
no
15
20
22'00
1'107
29'34 1'968
25
36.67
3'075
30 44'01
4'429
35
51.34
6.027
40
58.68
7-873
45
66.01
9*963
50
73.35
12.300
60
88.02 17.715
80
117.36
31'490
TOO
146'70
49°200
48
MECHANICS.
49. As it is not eaſy to obferve the true velocity of the wind,
and thence determine its force, ſeveral philofophers have in-
vented inſtruments called Anemometers or wind gages, by
which the force of the wind may be afcertained independent of
its velocity. M. Bouguer contrived a very fimple inſtrument
for this purpoſe: it is a hollow tube AABB (fig. 5. pl. I.) in
which a ſpiral ſpring CD is fixed, that may be more or lefs
compreffed by a rod FSD paffing through a hole within the
tube at AA. Having obferved to what degree different forces
or given weights are capable of compreffing the ſpiral, put di-
vifions upon the rod in fuch a manner that the mark obferved
at S in all poſitions of that rod fhall indicate the weight requifite
to force the ſpring into the correfponding poſition CD. After-
wards join perpendicularly to this rod at F a plane ſurface EFE
of a given area, either greater or leſs, as may be judged proper:
then nothing more is neceffary than to oppofe this inftrument
to the wind, in order that it may ftrike the furface in the direc-
tions VE, VE, parallel to that of the rod; and the mark at S
will fhew the weight to which the wind is equivalent. It will
then be eaſy to reduce any obſerved force to a volume of water
equivalent to it in energy; and fo in all caſes afcertain the mag-
nitude of the force which the wind exerts.
50. The moſt uſual method of applying wind as a mover of
machinery is in the conftruction of windmills for different
purpoſes, in which the wind produces its effect by impulſe upon
the fails. In theſe machines, therefore, whatever varieties there
may be in the internal structure, there are certain rules with
regard to the pofition, fhape, and magnitude of the fails, which
will bring them into the beſt ſtate for the action of the wind,
and the production of uſeful effect. Theſe particulars have
been confidered much at large by Mr. Smeaton: for this purpoſe
he conſtructed a machine of which a particular deſcription is
given in the Philofophical Tranſactions, vol. 51. By means of
a determinate weight it carried round an axis with an horizontal
arm, upon which were four ſmall moveable fails. Thus the
fails met with a conftant and equable blaſt of air; and as they
moved round, a ftring with a weight affixed to it was wound
about their axis, and thus fhowed what kind of fize or con-
ftruction of fails anſwered the purpoſe beft. With this ma-
chine a great number of experiments were made; the reſults
of which were as follow:
(1.) The fails fet at the angle with the axis, propoſed as the
beſt by M. Parent and others, viz. 55°, was found to be the
worst proportion of any that was tried.
(2.) When the angle of the fails with the axis was increaſed
from 72° to 75°, the power was augmented in the proportion
Wind as a Mover of Machinery.
49
of 31 to 45; and this is the angle moſt commonly in ufe when
the fails are planes. See art. 547. vol. I.
(3.) Were nothing more requifite than to cauſe the fails to
acquire a certain degree of velocity by the wind, the pofition
recommended by M. Parent would be the beft. But if the fails
are intended with given dimenfions to produce the greateſt
effects poffible in a given time, we muſt, if planes are made
ufe of, confine our angle within the limits of 72 and 75 degrees.
(4.) The variation of a degree or two, when the angle is near
the beft, is but of little confequence.
(5.) When the wind falls upon concave fails it is an advan-
tage to the power of the whole, though each part feparately
taken fhould not be difpofed of to the beft advantage.
(6.) From ſeveral experiments on a large fcale, Mr. Smeaton
has found the following angles to anfwer as well as any.
The
radius is ſuppoſed to be divided into fix parts; and th, reckon-
ing from the centre, is called 1, the extremity being denoted 6.
N°
Angle with
that axis.
1
72°
2
71
3
72
4
74
Angle with
the plane of
motion.
18°
19
5
6
772
83
18 middle
16
12
7 extremity.
(7.) Having thus obtained the best method of weathering the
fails, i. e. the moſt advantageous manner in which they can be
placed, our author's next care was to try what advantage could
be derived from an increaſe of ſurface upon the fame radius.
The refult was, that a broader fail requires a larger angle; and
when the fail is broader at the extremity than near the centre,
the figure is more advantageous than that of a parallelogram.
The figure and proportion of enlarged fails, which our author
determines to be moſt advantageous on a large fcale, is that
where the extreme bar is one-third of the radius or whip (as
the workmen call it), and is divided by the whip in the pro-
portion of 3 to 5. The triangular or loading fail is covered
with board from the point downward of its height, the reft as
uſual with cloth. The angles above mentioned are likewife
the moſt proper for enlarged fails; it being found in practice,
that the fails ſhould rather be too little than too much expoſed
to the dire& action of the wind.
Some have imagined, that the more fail the greater would be
the power of the windmill, and have therefore propofed to fill up
the whole area; and by making each fail a fector of an ellipfis,
VOL. II.
E
50
MECHANICS.
according to M. Parent's method, to intercept the whole cy-
linder of wind, in order to produce the greateſt effect poffible.
From our author's experiments, however, it appeared, that
when the furface of all the fails exceeded feven-eights of the area,
the effect was rather diminished than augmented. Hence he
concludes, that when the whole cylinder of wind is intercepted,
it cannot then produce the greateſt effect for want of proper
interftices to escape.
"It is certainly defirable (fays Mr. Smeaton), that the fails
of windmills ſhould be as fhort as poffible; but it is equally
defirable, that the quantity of cloth fhould be the leaft that
may be, to avoid damage by fudden fqualls of wind. The beft
ſtructure, therefore, for large mills, is that where the quantity
of cloth is the greatest in a given circle that can be on this
condition, that the effect holds out in proportion to the quan-
tity of cloth; for otherwife the effect can be augmented in a
given degree by a leffer increaſe of cloth upon a larger radius
than would be required if the cloth was increafed upon the
fame radius.”
(8.) The ratios between the velocities of windmill fails un-
loaded, and when loaded to their maximum, turned out very
different in different experiments; but the moſt common propor-
tion was as 3 to 2. In general it happened that where the power
was greateft, whether by an enlargement of the furface of the fails
or an increaſed velocity of the wind, the fecond term of the
ratio was diminiſhed.
(9.) The ratios between the leaft load that would ſtop the
fails and the maximum with which they would turn, were con-
fined betwixt that of 10 to 8 and 10 to 9; being at a medium
about 10 to 8.3, and 10 to 9, or about 6 to 5; though on the
whole it appeared, that where the angle of the fails or quantity
of cloth was greateſt, the ſecond term of the ratio was lefs.
(10.) The velocity of windmill fails, whether unloaded or
loaded, fo as to produce a maximum, is nearly as the velocity`
of the wind, their ſhape and poſition being the fame. On this
fubject Mr. Ferguſon remarks, that it is almost incredible to
think with what velocity the tips of the fails move when acted
upon by a moderate wind. He has feveral times counted the
number of revolutions made by the fails in 10 or 15 minutes ;
and, from the length of the arms from tip to tip, has computed,
that if an hoop of the fame fize was to run upon plain ground
with an equal velocity, it would go upwards of 30 miles in an
hour.
(11.) The load at the maximum is nearly, but fomewhat lefs
than, as the fquare of the velocity of the wind; the shape, and
pofition of the fails being the fame.
Smeaton's Rules for Windmills
51
(12.) The effects of the fame fails at a maximum are nearly,
but fomewhat lefs than, as the cubes of the velocity of the
wind.
(13.) The load of the fame fails at a maximum is nearly as
the fquares, and the effect as the cubes of their number of turns
in a given time.
(14.) When fails are loaded fo as to produce a maximum at
a given velocity, and the velocity of the wind increaſes, the
load continuing the fame; then the increaſe of effect, when
the increaſe of the velocity of the wind is fmall, will be nearly
as the fquares of thefe velocities: but when the velocity of the
wind is double, the effects will be nearly as 10 to 27; and when
the velocities compared are more than double of that where
the given load produces a maximum, the effects increaſe nearly
In a fimple ratio of the velocity of the wind. Hence our author
concludes, that windmills, fuch as the different fpecies for
draining water, &c. lofe much of their effect by acting againſt
one invariable oppofition.
(15.) In fails of a fimilar figure and pofition, the number of
turns in a given time will be reciprocally as the radius or length
of the fail.
(16.) The load at a maximum that fails of a fimilar figure and
pofition will overcome, at a given diftance from the centre of
motion, will be as the cube of the radius.
(17.) The effects of fails of fimilar poſition and figure are as
the fquare of the radius. Hence augmenting the length of the
fail without augmenting the quantity of cloth, does not increaſe
the power; becauſe what is gained by length of the lever is
loft by the flowneſs of the motion. Hence alfo, if the fails are
increaſed in length, the breadth remaining the fame the effect
will be as the radius.
(18.) The velocity of the extremities of the Dutch fails, as
well as of the enlarged fails, either unloaded or even when
loaded to a maximum, is confiderably greater than that of the
wind itſelf. This appears plainly from the obfervations of
Mr. Ferguſon, already related, concerning the velocity of fails.
(19.) From many obfervations of the comparative effects of
fails of various kinds, Mr. Smeaton concludes, that the enlarged
fails are fuperior to thofe of the Dutch conftruction.
(20.) He alfo makes ſeveral juſt remarks upon thoſe wind-
mills which are acted upon by the direct impulfe of the wind
againſt fails fixed to a vertical fhaft: his objections have, we
believe, been juftified in every inftance by the inferior efficacy
of theſe horizontal mills.
"The diſadvantage of horizontal windmills (fays he) does not
confiſt in this, that each fail, when directly oppofed to the wind, is
I 2
£9
MECHANICS.
capable of a lefs power than an oblique one of the fame di-
menſions; but that in an horizontal windmill little more than
one fail can be acting at once: whereas in the common wind-
mill, all the four act together; and therefore, fuppofing each
vane of an horizontal windmill to be of the ſame ſize with that
of a vertical one, it is manifeſt that the power of a vertical mill
will be four times as great as that of an horizontal one, let the
number of vanes be what they will. This difadvantage arifes
from the nature of the thing; but if we confider the further
diſadvantage that arifes from the difficulty of getting the fails
back again againſt the winds, &c. we need not wonder if this
kind of mill is in reality found to have not above one-eighth or
one-tenth of the power of the common fort; as has appeared
in fome attempts of this kind.”
51. Another first mover, of whofe effects it may be proper
to give fome account, is fired gunpowder. Theſe effects are too
violent and fudden to allow of their being applied to many
practical purpoſes (the chief ufe of gunpowder being in the
difcharge of balls and fhells from guns and mortars); but they
are fo prodigious and extraordinary, and are fo important in
the art of war, that it may be naturally expected we ſhould
give ſome eſtimate of them in this place.
Now to underſtand the force of gunpowder it must be
confidered that whether it be fired in a vacuum or in air, it
produces by its explofion a permanently elastic fluid: and it
appears from experiment that the elaſticity or preffure of the
fluid produced by this firing of gunpowder is, cateris paribus,
directly as its denfity.
•
To determine the elaſticity and quantity of this fluid, pro-
duced from the exploſion of a given quantity of gunpowder,
Mr. Robins premifes, that the elafticity increaſes by heat, and
diminiſhes by cold, in the fame manner as that of the air; and
that the denſity of this fluid, and confequently its weight, is the
fame with the weight of an equal bulk of air, having the fame
elaſticity and the fame temperature. From theſe principles,
and from the experiments by which they are eſtabliſhed (for a
detail of which we muſt refer to the book itfelf), he concludes
that the fluid produced by the firing of gunpowder is nearly
of the weight of the generating powder itself; and that the
volume or bulk of this air or fluid, when expanded to the rarity of
common atmoſpheric air, is about 244 times the bulk of the
faid generating powder.-Count Saluce, in his Mifcel. Phil.
Mathem. Soc. Priv. Taurin. p. 125, makes the proportion as
222 to 1; which he fays agrees with the computation of Meffrs.
Haukfbee, Amontons, and Belidor.
3
Hence it appears, that any quantity of powder fired in any
Strength of Fired Gunpowder.
53
confined ſpace, which it adequately fills, exerts at the inftant
of its exploſion againſt the fides of the veſſel containing it, and
the bodies it impels before it, a force at leaft 244 times greater
than the elaſticity of common air, or, which is the fame thing,
than the preffure of the atmoſphere; and this without con-
fidering the great addition arifing from the violent degree of
heat with which it is endued at that time; the quantity of
which augmentation is the next head of Mr. Robins's enquiry.
He determines that the elasticity of the air is augmented in a
proportion fomewhat greater than that of 4 to 1, when heated
to the extremeft heat of red-hot iron; and fuppofing that the
flame of fired gunpowder is not of a lefs degree of heat, in-
creafing the former number a little more than 4 times, makes
nearly 1000; which fhews that the elaſticity of the flame, at the
moment of exploſion, is about Icoo times ftronger than the
elaſticity of common air, or than the preffure of the atmoſphere.
But, from the height of the barometer, it is known that the
preffure of the atmoſphere upon every fquare inch is on a
medium 143 lb; and therefore 1000 times this, or 14750 lb.
is the force or preffure of the flame of gunpowder, at the mo-
ment of exploſion, upon a fquare inch, which is very nearly
equivalent to 6 tons and a half.
This great force, however, diminiſhes as the fluid dilates itſelf,
and in that proportion, viz. in proportion to the ſpace it oc-
cupies, it being only half the ftrength when it occupies a double
ſpace, one-third the ſtrength when triple the ſpace, and ſo on.
Mr. Robins further fuppofes the degree of heat above men-
tioned to be a kind of medium heat; but that in the caſe of
large quantities of powder the heat will be higher, and in very
fmall quantities lower; and that therefore in the former cafe
the force will be ſomewhat more, and in the latter fomewhat
lefs, than 1000 times the force of the atmoſphere.
He further found that the ftrength of powder is the fame in
all variations in the denfity of the atmoſphere: but that the
moiſture of the air has a great effect upon it; for the fame
quantity which in a dry feaſon would diſcharge a bullet with a
velocity of 1700 feet in one fecond, will not in damp weather
give it a velocity of more than 12 or 1300 feet in a fecond, or
even lefs, if the powder be bad, and negligently kept. Robins's
Tracts, vol. 1, p. 101, &c. Further, as there is a certain
quantity of water which, when mixed with powder, will pre-
vent its firing at all, it cannot be doubted but every degree of
moiſture muſt abate the violence of the exploſion; and hence
the effects of damp powder are not difficult to account for.
The velocity of expanfion of the flame of gunpowder, when
fired in a piece of artillery, without either bullet or other body
$4
MECHANICS.
before it, is prodigiouſly great, viz. 7000 feet per fecond, or
upwards, as appears from the experiments of Mr. Robins. But
M. Bernoulli and M. Euler fufpect it is ftill much greater.
And Dr. Hutton ſuſpects it may not be leſs, at the moment of
exploſion, than 4 times as much.
It is this prodigious celerity of expanſion of the flame of fired
gunpowder which is its peculiar excellence, and the circum-
ftance in which it fo eminently furpaffes all other inventions,
either ancient or modern; for as to the momentum of theſe
projectiles only, many of the warlike machines of the ancients
produced this in a degree far furpaffing that of our heavieſt
cannon fhot or fhells; but the great celerity given to theſe
bodies cannot be approached with facility by any other means
than the exploſion of powder.
52. Since the important invention of the Steam-engine
another ſpecies of firſt movers has come under the confideration
of the mechanical inveſtigator, namely, fuch as ariſe from the
volatiliſation of different fluids. Of theſe the one moſt com-
monly choſen is the STEAM raiſed from hot water, which is an
elaſtic fluid, and which when raiſed with the ordinary heat of
boiling water is almoſt 3000 times rarer than water, or more than
3 times rarer than air, and then has its elafticity equal to that of
the common atmoſpheric air: by great heat it has been found
that the ſteam may be expanded into 14000 times the ſpace of
water, and then exerts a force of nearly 5 times the preffure of
the atmoſphere: and there is no reaſon to fuppofe this is the
limit: indeed fome accidents which have happened prove clearly
that the elaſtic force of fteam may at leaft equal that of gun-
powder.
Σ
The obfervations on the different degrees of temperature
acquired by water in boiling, under different preffures of the
atmoſphere, and the formation of the vapour from water under
the receiver of an air-pump, when with the common tem-
peratures the preffure is diminiſhed to a certain degree, fhew
clearly that the expanfive force of vapour or ſteam is different
in the different temperatures, and that in general it increaſes in
a variable ratio as the temperature is raiſed. Previous to de-
fcribing the method which has been adopted to meaſure the
force of team under different temperatures, it will be proper to
defcribe briefly the method by which the Chemifts account for
the production of aeriform fluids.
53. The term Caloric is uſed to denote the cauſe, whatever
it may be, of heat, and of the phenomena which accompany
heat: it is now almoft univerfally admitted to be a highly elaſtic
fluid. Every body is, according to its nature, capable of con-
taining under a given volume a certain quantity of caloric,
Elaftic Force of Steam.
$5
either greater or leſs: this property was firft obferved by Dr.
Black, and the Engliſh chemiſts deſignated it by the term Ca-
pacity of a body to contain the matter of heat. Profeffor Wilcke
and M. Lavoifier firſt made ufe of the term ſpecific caloric, de-
noting by it the quantity of caloric refpectively neceffary to
elevate to the fame number of degrees the temperature of fe-
veral bodies of equal weight.
Subſtances volatiliſed and reduced to gas or aeriform fluids,
are nothing elſe than ordinary folid or fluid bodies which by
ſome circumſtance are found fuperabundantly combined with
caloric, in ſuch a manner that the conftituent particles of thefe
bodies are feparated the one from the other, by a quantity of
ambient caloric much more confiderable than that which fur-
rounds the fame particles in the natural ſtate of the bodies.
The extreme elaſticity of the caloric the effect of which is aug-
mented by its condenfation, and the weakening of the reci-
procal attraction or of the coheſion of the particles of the bodies
(a weakening or diminution produced by the increaſed diſtance
of thoſe particles) concur to diminiſh the denſity of the bodies
in ſuch a manner that they become reduced to an aeriform
state.
54. As to the elaſticity of gaſeous fluids thus formed, it ap-
pears in great meaſure to be produced by the elaſticity of ca-
loric itſelf, which, when bodies are reduced to the gafeous ftate,
occupy a very great part of their volume. This eminent elaſti-
city of caloric tends continually to produce expanfion; on the
other hand, this fluid, by a particular deftination of nature, is
more or lefs diffeminated between the molecule of all bodies,
in fuch fort that we may ſay with M. Lavoifier that even in the
folid ftate theſe molecule do not touch, but, as it were, ſwim
in the caloric at a certain diſtance from each other. There
muſt, therefore, be a perpetual conteſt between the expanſive
force of caloric which tends to diffeminate the molecule, and
the coheſive attraction of the molecule which tends to join
them together. From the reciprocal intenfity of theſe two
powers refults the folid and liquid ftates of bodies: thus, water
only differs from ice by the greater or lefs condenſation of ca-
loric, which permits more or leſs of the molecule of the liquid
to yield to the effect of their attraction or reciprocal coheſion.
When fubftances pafs from the liquid to the aeriform ftate,
there is a third power to combine with the expanfive effort of
caloric, and the aggregative or attractive effort of the mole-
culæ ; namely, the preffure of the atmoſphere, or of any elaftic
fluid whatever which compreffes the fluid, and oppoſes itſelf to
the ſeparation of its parts. This third power has a certain in-
duence alfo upon the paffage from the folid to the fluid ftate,
56
MECHANICS.
but it is moſt frequently (in this caſe) very ſmall, and even
evaneſcent in compariſon of the refiftance arifing from the
mutual coheſion of the molecule. The contrary effect has
place in the courſe of the paffage from the liquid to the gafeous
or aeriform ſtate; the coheſion of the fluid molecule being ex-
tremely fmall, the elaſticity of the caloric has fcarcely any thing
to furmount to produce volatilisation befides the preffure of the
atmoſphere, or gas which actually compreffes it.
55. Hence it reſults that the fame liquid under different
preffures ought to volatilife at different temperatures. M.
Lavoifier proved the truth of this refult, by placing ether under
the receiver of an air-pump and producing volatiliſation ſolely
by taking off a part of the preffure of the atmoſphere. See
Chymie, tome I. pa. 9. And we know by many experiments of
M. Deluc and others, that water boils the more fpeedily as it
is lefs preffed by the weight of the atmoſphere.
Lavoifier notices a curious confequence of what has been
here faid; which is, that if our planet revolved upon its axis
with ſuch a velocity as to leffen the preffure of the atmoſphere,
or if the temperature of the air were raiſed, then ſeveral fluids
which we now fee under a liquid ftate would only exiſt in the
aeriform ſtate; for example, if under the temperature of ſum-
mer the preffure of the atmoſphere were only equivalent to 20
or 24 inches of the barometrical tube, that preffure would not
retain ether in the fluid ftate, it would be changed into gas;
and the like would happen, if while the preffure of the air was
equivalent to 28 or 30 inches of the mercury the habitual tem-
perature were 105 or 110 degrees on Fahrenheit's ſcale.
56. The principles which have been here exhibited are fuf-
ficient for the underſtanding of all which relates to the action
of water or other fluids reduced to vapour. Now, it has ap-
peared from frequent experiments that water heated in common
air volatiliſes at 80° of Reaumur's thermometer, or 212° of
Fahrenheit's, the height of the barometer being 28 French, or
29.0 Engliſh inches: and fpirits of wine under a like preffure
volatilifes at between 63° and 64° of Reaumur, or nearly 175°
of Fahrenheit. The expanfive force of the vapour muft, there-
fore, in both thefe cafes, according to the principles juſt ex-
plained, be meaſured by a column of mercury of 28 French,
or 29.9 Engliſh inches, in like manner as fuch a column meaſures
the preffure of the atmoſphere, or the elaſticity of common air.
And at any more elevated temperatures the elaftic force of the
vapour will furpaſs the preffure of the atmoſphere by a quantity
which has a certain relation with the excefs of the temperaturę
above thoſe juſt ſtated.
57. Till lately there was wanting on this important fubject a
Elaftic Force of Steam.
ST
ſeries of exact and direct experiments by means of which, having
given the temperature of the heated fluid, the expanſive force of
the fteam rifing from it might be known, and vicè verfa. There
was likewiſe wanting an analytical theorem expreffing the re-
lation between the temperature of the heated fluid and the
preffure with which the force of the fteam was in equilibrio.
Theſe defiderata have, however, been lately ſupplied by M.
Bettancourt, an ingenious Spanish philofopher, after a method
which we ſhall now conciſely explain.
58. M. Bettancourt's apparatus confifts of a copper veffel or
boiler, with its cover firmly foldered on: this cover has three
orifices which cloſe up with fcrews: at the firſt the water or
other fluid is put in and out; through the fecond paffes the
ſtem of a thermometer which has the whole of its ſcale or gra-
duations above the veffel, and its ball within, where it is im-
merſed either in the fluid or in the fteam according to the dif-
ferent circumſtances; through the third hole paffes a tube,
making a communication between the cavity of the boiler and
one branch of an inverted fyphon, which contains mercury,
and acts as a barometer for meaſuring the preffure of the elaſtic
vapour within the boiler. In the fide of the veſſel there is
fourth hole into which is inferted a tube with a turncock, mak-
ing a communication with the receiver of an air-pump, in order
to extract the air from the boiler and to prevent its return.
The apparatus being prepared in good order, and diftilled
water introduced into the boiler at the firſt hole, and then ſtop-
ped, as well as the end of the inverted fyphon or barometer,
M. Bettancourt furrounded the boiler with ice, to lower the
temperature of the water to the freezing point, and then, hav-
ing extracted all the air from the boiler by means of the air-
pump, the difference between the columns of mercury in the
two branches of the barometer fhewed the meaſure of the elaſtic
force of the vapour arifing from the water in that temperature.
Then lighting the fire below the boiler, he gradually raiſed the
temperature of the water from o to 110° of Reaumur's ther-
mometer, that is, from 32° to 279° of Fahrenheit's thermo-
meter; and for each degree of elevation in the temperature he
obferved the height of the mercurial column which meaſured
the elasticity or preffure of the vapour.
Thefe experiments were repeated various times and with dif
ferent quantities of water in the veffel; their reſults were ar-
ranged in different columns for the fake of compariſon, and it
appeared that the preffures for different temperatures agreed
yery nearly, however much the quantity of fluid in the veffel
was varied. It was alfo feen that the increaſe in the expanfive
force of the vapour is at firſt very flow; but increaſes gradually
$8
MECHANICS.
unto the higher temperatures, where the increaſe becomes very
rapid, as will be obvious from an examination of the tables in
fome of the following pages.
59. To exprefs the relation between the degrees of tem-
perature of the vapour and its elaftic force, this philofopher
employs a method fuggeſted hy M. Prony, which confifts in
imagining the heights of the columns of mercury meaſuring the
expansive force to reprefent the ordinates of a curve, and the
degrees of heat the correſponding abfciffæ of that curve; making
the ordinates equal to the fum of feveral logarithmic ones which
contain two indeterminates, and afcertaining thefe quantities in
fuch manner that the curve may agree with a tolerable number
of obfervations taken throughout the whole extent of the change
of temperature, from the lowest to the highest extreme of the
experiments. Then a formula or equation to a curve is in-
veſtigated, and when the curve correfponding to that equation
is conftructed, if it coincide (with the exception of a few
trifling anomalies) with the curve conftructed by the refults of
the experiments, the formula may be looked upon as correct,
and furniſhing a true analytical reprefentation of the pheno-
mena. This was done by M. Bettancourt, and the curve con-
ftructed from his equation has a point of inflexion at about the
102° of Reaumur, as it ought to have, becauſe the ſecond dif-
ferences of the barometrical meaſures of the elaftic force be-
came negative at that temperature.
60. In a fimilar manner M. Bettancourt made experiments on
the ſtrength of the vapour from alcohol or fpirit of wine; con-
structing the curve and deducing the requifite analytical formula.
This curve had likewiſe a point of inflexion at about 88 of
Reaumur, the fecond differences in the table of barometrical
meaſures becoming then negative. From a compariſon of the
experiments on the vapour of water with thofe on the vapour of
alcohol, a remarkable conclufion was derived: for it appeared
that, after the first 20° of Reaumur, the ftrength of the va-
pour of fpirit of wine was to that of the vapour of water,
nearly in the fame conflant ratio of 23 to 10, or 7 to 3, for
any one and the fame degree of heat. Thus, at the tempe-
rature of 40° of Reaumur, the strength of the ſteam of water
is measured by 2.9711 Paris inches in the barometer, and that
of vapour of alcohol by 6·9770, the latter being about 23 times
the former.
61. The equations to the curve of temperature and preffure,
denoting the relation between the abfciffe and ordinates, or be-
tween the temperature and the elafticity of the vapour, as given
by M. Bettancourt, were of the following form.
Elaftic Force of Steam.
89
a. For water, y
pe tax µé táx
e
μtax µ'+xx
e
20.0
e
ox-§. o'x-g'
te
+e
dx-g
- A.
2. alcohol, y=e te
Where y repreſents the height of the column of mercury which
meaſures the expanfive force, x the correfponding degrees of
Reaumur's thermometer, and the other letters certain values
which are affigned to them in the inveſtigation.
62. But M. Prony, in the 2d volume of his Architecture Hy-
draulique, has thrown theſe equations into a rather more con-
venient form, though analogous to thofe of Bettancourt. His
formula for the vapour of water is this,
X
GIV
y = μ, §, " + ", e,, * +μ * +
The method which he followed confifted in fatisfying the refults
between o° and 80°, by means of the two firft terms, and to
interpolate by means of the other two, the differences between
the obferved values, and thofe computed by the two firſt terms,
from 80° up to 110°. In this manner he fucceeded to exprefs
fo exactly the obſervations in their whole extent, that the curves
of the calculus and the experiments were only diſtinguiſhable
the one from the other by fuch little anomalies, as were ma-
nifeftly the effect of fome trifling though inevitable errors in
the obſervations, and in the graduations of the ſcales in the ap-
paratus. He afterwards employed an equation of three terms,
giving to the different coefficients the following values:
§, 1*172805
§₁=1'047773
S-1028189
μ₁ = ~ o'¯¯Ò¯Ñ072460407
th
+0.8648188803
-0.8648181057
•
log. §, =0.0692259
log. =0'0202661
Ç'll
log. 00120736
log. 78601007
μ,
log. μT-936927 I
log. T-9369248
Subſtituting theſe ſeveral values in the equation
y = μ, B, * + μ, Su
20
it ſatisfies not only the numbers employed in its formation, but
all the intermediate obfervations, as may be concluded from the
following table, which exhibits to every 10 degrees of Reau-
mur's thermometer the barometrical refults both of obfervation.
and the calculus.
40
MECHANICS.

Tempe-
Preſſures given by
Ano-
rature.
malies.
Experim. Calculus.
O
0'00 in.
0'00 in.
o'00 in.
ΙΟ
0*15
0°24
20
0.65
0.69
+0·09
+0:04
30
1.52
1°51
Ο ΟΙ
40
2.92
2.95
+0.03
50
5'35
5'42
+0:07
бо
9'95
9.62
-0.33
70
16.90
16.57
-0.33
80
28.00
27.92
·0·08
90
46.40
45.87
-0°53
100
71.80
7194
+0.14
IIO 98.00
98.36
+0:36
The anomalies are generally much more minute than in the
formulæ of four terms: we may therefore regard the equation
juft preceding the table, which is more fimple than that of Bet-
tancourt, as reprefenting the phenomena and meaſuring the
effects of the expanfive force of the ſteam of water with all de-
firable accuracy. M. Prony remarks, that the ſmallneſs of the
coefficient μ, will allow the term, or to be neglected in reckon-
ing between o° and 80°; and thus from the temperature of ice
up to that of boiling water, the equation of two terms alone
will fuffice, that is to ſay....y μ,, §₁, x + μ,,, },!,
"
63. M. Prony's equation for the vapour of alcohol compriſes
5 terms originally: but in moſt cafes three of thoſe terms will
give refults fufficiently accurate. The numeral values of the
coefficients are as below:
}, = 1'11424
R₁ = 1'05714
Lu= '79943
0.0021293
fle,
μ₁ =+ 0°9116186
log. 19027776
log. f
log. g,
f.
0'04697771
002413079
f
=
log.,
5-3282330
log.,
T-9598132
"
μιν
Hiv
+ 0.2097778
11192671
•
log.μ-3217595
Theſe numbers cauſe the experiments and calculus to co-
incide very nearly, when introduced into the equation
X
I
y=µ, gx + v,,, §,,x + μ,,, ļ,, * +μv•
The magnitude of the anomalies will be feen by inspecting
the following table.
Elafticity of Vapour of Water and Alcohol.
61

Tempe-
rature.
Preffures given by
Experim. Calculus.
Ano-
malies.
•
o'o in.
o'oo in.
O'00
10
0'47
0'45
-0'02
20
1.52
1.56
+0.04
30
3'49
3'54
+0.05
40
6.90
6.97
+0.07
50
13.05
12'93
- O'12
бо
23.65
23.05
-0°50
7༠
39°30
39'31
+00:
80
63.80
$4.35
+0.55
90 98.00
98.28
+0.28
1
Thus the formula for the vapour of ſpirit of wine is found as
fimple as that for the vapour of water, without ceafing to re-
preſent the experiments with all defirable exactneſs. But more
than this, we may retrench one of the variable terms; for in
the first degree has no greater value than o∙18, and
when x is 2, 3, or any other poſitive value, this third term may
be ſafely neglected. The equation therefore is reduced to
JC
y=μ, 1,
y = μ, gx + μ, ç, * +μiv;
a form much more fimple than Bettancourt's original equation,
and indeed more ſimple than Prony's improved equation for the
vapour of water.
64. To fave the trouble of inveſtigating the ftrength of the
vapour by theſe formula for every feparate cafe that may occur,
we add a table (calculated from thefe principles) in which the
ftrength of the vapour both of water and of ſpirit of wine is
ſhewn for every degree of Reaumur's thermometer up to 110°,
or for every 24 degrees of Fahrenheit, from 32 to 280°: the
ſtrengths are expreffed, not in Engliſh or in French inches upon
the barometer, but in terms whoſe unit is the medium preſſure
of the atmoſphere, fuppofing that medium equivalent to 29'9
Engliſh, or 28 French inches of mercury. The preffure upon
a ſquare inch in pounds averdupois correfponding to any tem-
perature may be found by multiplying the correfponding num-
ber taken from the table by 14'75: and the preffure for any in-
termediate degree of Fahrenheit may be found pretty nearly,
by proportioning, as is uſual in tables of Logarithms, &c.
62
MECHANICS.

Degrees
of
Thermometer.
Pressure in terms of At-
mospheric Pressure.
Vapour
Vapour
Degrees
of
Thermometer.
Pressure in terms of
Atmospheric Pressure.
Vapour Vapour
of
of
of
of
Reau. Fahr.
Water.
Alcohol.
Reau. Fahr.
Water.
Alcohol.
Ham+mo zoo ao
I
34
2
36/2/2
3
38/
mich mica maha
·00063.
·00015
56
18
*27481
•65864
*00124
*00074
57
160
*29076
•69671
*00192
*00171
58
7
162플
​*30650
·73673
4
41
•00267
*00299
59
164
*32525
•77167
434
·0037.1
*00449
60
167
*34386
•82337
45/
⚫00433
·00641 61
169
•36345
•86946
7
474
·00539
•00849
62
171
*38249
'91467
50
·006 ZI
στο 8ο
63
1732
*40572
*96587
9
52
*00740
01333
64
176
*42849
I'0231
544
00823
01608 65
1784
*45245
1·0795
II
564
·00971
•01832 66
1804
*47765
1.1385
12
59
•01085
·02163
67
1824
*50414 I'2004
13
614
⚫01221
·02514
68
185
*53199
1.2652
14.
631/2
01384
*02884 69
187
*56126
I'3330
15
654
01521
·03276 70
1891/
*59203
1*4038
16
68
·01706
*03689
71
191
•62436
1*4778
17
70/1
•c1860
*04126 72
194
•65832
1*5552
18
72
*02046
*04588 73
1961
•69403
1·6359
19
744
*02244
·05076 74
198
**74589
I'7199
20
77
*02454
*0559!
75
2.00
·77096
1·8075
21
794
*02677
·06136 76
22
23
24
25*
:
26
60 00 00 00 00:
83弄
​86
884
90
222
27
·924
28
95
136∞ ON 5
814
02914
c6711
77
·03165
*07319
78
81 8
203
81236
1·8985
2054
·85.588
1'9932
2072/2
*96214
2.0855
03432
·07961
79 209
*94957
2.1895
*03715
•08641
80
112
*1·0000
2·2983
*04014
*09358
81
214
1'0519
2.4074
*04331
•10116
82
21641
I'1064
2.5177
*04667
*10917
83
218
I'1634
2·6345
29
97
05023
∙11763
84
223
1'2232
2.7527
30
99
·05364
•12657
85
2234
1.2851
2.8739
3r
101
·05833
•13603
86
225 //
1*3500
2.9977
32
104
'06219
'1460 I
87
227条
​1'4177
3.1236
33
сб
*06668
*15656.
88
230
1.4872
3*2548
34
108
*07136
•16771
89
2.324
1.5618
3.3806
2 mm og en
35
FIO
·07634
*17949
90
2341/
1.6382
3'5099
37
38
160 200
36 ∙113
•08159
*19193
91 2363
1-7176
1154
*c87₤4
201;1
92
239
1*8003
1172
*09302 *21893
93
241
1·8851
39
40
4I
1194
122
1241
*09921
*23366 94
2431
1'9733
•10011
*24921
95
245
2'0643
'11266 ·26557 96
248
2*1579
42
126 1/2
•11994
•28289
97
250
2.2539
43
1284
•12762
*30120
98
252 1/2
2*3527
44
131
*13573
*32054
99
254章
​2.4533
1334
•14428
*34098.
100
257
2'5554
13512
*15329
•36256
101
2594
2.6587
47
137
•16279
•38538
102
261
2·7628
48
140
*17281
*40931
103
2634
2.8667
49
142
18338
*43500
104
266
2.9735
50
144
*19447
*46193
105
268
3'0711
51 1463
•20609
*49036 106
270/1
3'1691
52
149
•21855
*52043
107
272 3°2631
53
•23155
*55218 108
275
3°3505
54
1534
*24524
•58571 109
2774
3.4299
55
1553
•25228
•62117
IIO
2792
35127
Vapour of Water and Alcohol.
63
- Several curious and in fome refpects uſeful confequences
might be deduced from theſe experiments and theorems. M.
Bettancourt fhews for inftance, that the effect of ſteam engines
muft, in general, be greater in winter than in fummer, owing
to the different degrees of temperature in the water of injection.
And from the greatly fuperior ftrength of the vapour of fpirit
of wine over that of water, he argues that, by trying other
fluids, fome may be found, not very expenfive, whofe vapour
may be fo much ftronger than that of water, with the fame
degree of heat, that it may be fubftituted inſtead of water in
the boilers of ſteam engines, to the great faving in the expence
of fuel: nay, he even afferts, that fpirit of wine itſelf might
thus be employed in a machine of a particular conſtruction,
which, with the fame quantity of fuel, and without any in-
creaſe of expence in other things, fhall produce an effect far
fuperior to what is obtained from the fteam of water. Another
uſe of theſe reſearches ſuggeſted by M. Bettancourt is, to mea-
fure the height of mountains by means of a thermometer im-
merfed in boiling water; which he thinks may be done with a
precifion equal, if not fuperior, to that of the barometer. But`
this, being foreign to our preſent enquiries, cannot be entered
upon here: a comparison of the refults of this method with
fome deduced from the more cuftomary procefs may be feen in
Dr. Hutton's Dictionary, vol. II. pa, 756, to which fuch as
are defirous of further information on this point are referred.
65. Our ingenious countryman Mr. Dalton, of Mancheſter,
is of opinion that M. Bettancourt's deductions are not quite ac-
curate. His chief error confifls in having affumed the force of
vapour from water of 32° (Fahrenheit) to be nothing; which
makes his numbers eflentially wrong at that point and in all the
lower parts of the fcale: and in the higher part, or that which
is above 212°, the force is determined too much; owing, as
Mr. Dalton apprehends, to a quantity of air, which being dif
engaged from the water by heat and mixing with the ſteam, in-
creaſes the clafticity.
Mr. Dalton's first experiments with ſpirit of wine led him
to adopt the fame conclufion as M. Bettancourt, with refpect to
the conftant ratio between the force of the vapour from this
ſpirit and that from water and inferred the fame with regard
to the vapour from other fluids. But, on purſuing the ſubject,
he concluded that this principle was not true, either with re-
ſpect to ſpirit of wine or any other liquid. His experiments
upon fix different liquids agree in eſtabliſhing as a general law,
"That the variation of the force of vapour from all liquids is the
" fame for the fame variation of temperature, reckoning from vapour
"of any groen force: thus, affuming a force equal to thirty inches
ર
}
MECHANICS.

#C
" of mercury as the ſtandard, it being the force of vapour from
any liquid boiling in the open air, we find aqueous vapour
lofes half its force by a diminution of 30 degrees of tem-
perature: fo does the vapour of any other liquid lofe half its
"force by diminiſhing its temperature 30 degrees below that
" in which it boils; and the like for any other increment or de-
"crement of heat. This being the cafe, it becomes unneceffary
" to give diſtinct tables of the force of vapour from different
"liquids, as one and the fame table is fufficient for all."
The experiments on which this conclufion refts, are related
in the fifth volume of the Manchester Memoirs: they may alſo
be feen in the 6th volume of the New Series of Mr. Nicholſon's
Journal. Mr. Dalton has calculated a table of the force of
vapour of water from the temperature of 40° below zero of Fah-
renheit, to 325° above it. From this table we have extracted the
following; in which we have, as before, reduced the force to
the medium preffure of the atmoſphere for the meaſuring unit,
that the ſmall differences in the reſults of the Engliſh and the
Spaniſh philofopher may be the more readily traced.

Tempe- Force of
rature aqueous
on Fahr. Vapour.
Tempe- Force of
rature aqueous
on Fahr. Vapour.
80°
*0333
212° I'000
90
*0453
220
1*166
100
·0620
230
I'391
110
*0843
240
1·655
120
*II10
250
I'940
130
*1446
260
2.257
140 *1913
270
2.595
150
*2473
280
2.958
160
'3153
290
3'337
170
*4043
३००
3.727
180
*5050
310
4'117
190
·6333
315
4'309
200 ·7880
320
4'500
210
*9613
325
4.690
66. There remains for us to conſider another kind of mover
of machinery, which is ANIMAL EXERTION, and which is of
fo fluctuating a nature that it is not eaſy to ſubject it to any
eftimate. Phyfical caufes muft affect both the magnitude and
duration of the efforts either of man or beaſt, and befides this,

Animal Strength-Men.
65
the ftrength of man is confiderably influenced by his moral
habits. The various combinations of theſe different cauſes have
occafioned a variety of eſtimates of animal labour to be ad-
vanced by different authors.
In the first volume of this work (art. 378.) we ftated the
average force of a man at reft to be 70 lbs., and his utmoſt
walking velocity when unloaded to be about 6 feet per fecond;
and we thence inferred that a man would produce the greateſt
momentum when drawing 314 lbs. along a horizontal plane
with a velocity of 2 feet per fecond. But this is not the moſt
advantageous way of applying human ſtrength.
67. Dr. Defaguliers afferts, that a man can raiſe of water or
any other weight about 550 lbs., or one hogfhead (weight of
the veffel included), 10 feet high in a minute: this ſtatement,
though he ſays it will hold good for 6 hours, appears from his
own facts to be too high; and is certainly fuch as could not be
continued one day after another. Mr. Smeaton conſiders this
work as the effort of haſte or diſtreſs; and reports that 6 good
Engliſh labourers will be required to raiſe 21141 folid feet of
fea water to the height of four feet in four hours: in this cafe
the men will raiſe a very little more than 6 cubic feet of freſh
water each to the height of 10 feet in a minute. Now the
hogfhead containing about 8 cubic feet, Smeaton's allowance
of work proves lefs than that of Defaguliers in the ratio of 6 to
8 or 3 to 44 And as his good English labourers who can
work at this rate are eſtimated by him to be equal to a double
fet of common men picked up at random, it ſeems proper to
ſtate that, with the probabilities of voluntary interruption, and
other incidents, a man's work for feveral fucceffive days ought
not to be valued at more than half a hogfhead raiſed 10 feet
high in a minute. Smeaton likewiſe ſtates, that 2 ordinary
horfes will do the work in three hours and twenty minutes,
which amounts to little more than two hogfheads and a half
raiſed 10 feet high in a minute. So that, if theſe ſtatements be
accurate, one horſe will do the work of five men.
I
2
68. Mr. Emerſon affirms, that a man of ordinary ſtrength
turning a roller by the handle can act for a whole day againſt
a refiftance equal to 30 pounds weight; and if he works 10
hours a day he will raiſe a weight of 30 lbs. through 34 feet in
a fecond of time; or, if the weight be greater, he will raife it-
to a proportionally lefs height. If two men work at a windlaſs
or roller, they caif more eaſily draw up 70 lbs. than one man
can 30 lbs.; provided the elbow of one of the handles be at
right angles to that of the other. Men ufed to hear loads, ſuch
as porters, will carry from 150 lbs. to 200 or 250 lbs. according
to their ſtrength. A man cannot well draw more than 70 lbs.
VOL. II.
F
66
MECHANICS.
or 80 lbs. horizontally: and he cannot thruft with a greater
force acting horizontally at the height of his ſhoulders than 27
or 30 lbs. But one of the most advantageous ways in which a
man can exert his force is to fit and pull towards him nearly
horizontally, as in the action of rowing.
69. M. Coulumb communicated to the French National
Inftitute the refults of various experiments on the quantity of
action which men can afford by their daily work, according to
the different manners in which they employ their ftrength. In
the firſt place he examined the quantity of action which men
can produce when, during a day, they mount a ſet of ſteps or
ſtairs, either with or without a burthen. He found that the
quantity of action of a man who mounts without a burthen,
having only his own body to raife, is double that of a man
loaded with a weight of 68 kilogrammes, or 223 lbs. aver-
dupois*, both continuing at work for a day. Hence it appears
how much, with equal fatigue and time, the total or abfolute
effort may obtain different values by varying the combinations
of effort and velocity.
But the word effect here denotes the total quantity of labour
employed to raiſe, not only the burthen, but the man himſelf;
and, as Coulumb obferves, what is of the greateſt importance
to confider is the useful effect, that is to ſay, the total effect, de-
`ducting the value which reprefents the transference of the
weight of the man's body. This total effect is the greateſt
poffible when the man afcends without a burthen; but the
ufeful effect is then nothing: it is alſo nothing if the man be ſa
much loaded as to be fcarcely capable of moving: and confe-
quently there exifts between theſe two limits a value of the
load fuch that the uſeful effect is a maximum. M. Coulumb
ſuppoſes that the lofs of quantity of action is proportional to
the load (an hypothefis which experience confirms), whence he
obtains an equation which, treated according to the rules of
maxima and minima, gives 53 kilogrammes (1734 lbs. averd.)
for the weight with which the man ought to be loaded, in order
to produce during one day, by aſcending ſtairs, the greateſt
uſeful effect: the quantity of action which refults from this
determination has for its value 56 kilogrammes (1833 lbs. averd.)
raiſed through one kilometre, or nearly 1094 yards. But this
method of working is attended with a lofs of three-fourths of
the total action of men, and confequently coſts four times as
much as work in which, after having mounted a fet of ſteps
without any burthen, the man fhould fuffer himſelf to fall by
any means, ſo as to raiſe a weight nearly equal to that of his
own body.
* The kilogramme is = 22966 grs. — 3'28 lbs. averd.
Animal Strength-Men.
67
From an examination of the work of men walking on a ho-
rizontal path, with or without a load, M. Coulumb concludes
that the greateft quantity of action takes place when the men
walk being loaded; and is to that of men walking under a
load of 58 kilogrammes (1904 lbs. averd.) nearly as 7 to 4.
The weight which a man ought to carry in order to produce
the greateſt uſeful effect, namely, that effect in which the quan-
tity of action relative to the carrying his own weight is de-
ducted from the total effect, is 50'4 kilogrammes, or 165.3 lbs.
averdupois.
•
There is a particular caſe which always obtains with reſpect
to burthens carried in towns, viz. that in which the men, after
having carried their load, return unloaded for a new burthen.
The weight they ſhould carry in this cafe, to produce the greateſt
effect, is 61 25 kilogrammes (2007 lbs. averd.). The quantity
of uſeful action in this cafe compared with that of a man who
walks freely and without a load is nearly as 1 to 5, or, in other
words, he employs to pure lofs of his power. By.caufing a
man to mount a fet of fteps freely and without burthen, his
quantity of action is at leaſt double of what he affords in any
other method of employing his ftrength.
When men labour in cultivating the ground, the whole quan-
tity afforded by one during a day amounts to 100 kilogrammes
elevated to one kilometer, that is, 328 lbs. raiſed 1094 yards.
M. Coulumb comparing this work with that of men employed
to carry burthens up an aſcent of ſteps, or at the pile-engine,
finds a lofs of about part only of the quantity of action
which may be neglected in refearches of this kind.
2
In eftimating mean refults we ſhould not determine from
experiments of ſhort duration, nor fhould we make any de-
ductions from the exertions of men of more than ordinary
ftrength. The mean refults have likewiſe a relation to climate.
"I have cauſed," fays M. Coulumb, "extenſive works to be
executed by the troops at Martinico, where the thermometer
(of Reaumur) is feldom lower than 20° (77° of Fahrenheit).
Ì have executed works of the fame kind by the troops in
· France: and I can affirm that under the fourteenth degree of
latitude, where men are almoſt always covered with perfpira-
tion, they are not capable of performing half the work they
could perform in our climate*." Bulletin de la Soc. Philomath,
No. 16.

* In the preceding account of the effects of human exertion, fince the
profeffed object was to ftate the mean refults of regular and uniform la-
bour, we have taken no notice either of feats of extraordináry ftrength,
or of fuch as were in appearance fuch, while in reality they were the ef
fect of contrivance and ſkill, and might have been performed by almoſt
F 2
68
MECHANICS.
70. Among quadrupeds the moſt uſeful as a firſt mover of
machinery is the horse. The ſtrength of this animal is pro-
any men who had fufficient knowledge of the ſubject to exert their
ftrength under ſimilar circumſtances. But as it may be expected that
fome notice fhould be taken of fuch matters, we fhall throw into this
note a few remarks which have formerly been made in reference to them.
M. de la Hire, in an Examination of the Force of Men, given in the Me-
moirs of the Academy of Sciences for 1699, fays, "There are men
whoſe ſpirits flow fo abundantly and ſo ſwiftly into their muſcles, that
they exert three or four times more ftrength than others do; and this
ſeems to me to be the natural reafon of the furpriſing ftrength that we
fee in fome men who carry and raiſe weights which two or three ordinary
men can hardly fuftain, though theſe men be fometimes but of a moderate
ſtature, and rather appear weak than ftrong. There was a man in this
country a little while ago, who would carry a very large anvil, and of
whom were reported ſeveral wonderful feats of ftrength. But I faw an-
other at Venice, who was but a lad, and did not ſeem able to carry above
40 or 50 lbs. with all poſſible advantages; yet this young fellow, ſtanding
upon a table, raiſed from the earth, and ſuſtained off the ground, an aſs,
by means of a broad girt, which, going under the creature's belly, was
hung upon two hooks that were faftened to a plat of ſmall cords coming
down in treffes from the hair on each fide of the lad's head, which were
in no great quantity. And all this great force depended only upon the muf-
cles of the fhoulders and thofe of the loins: for he ftooped at firft whilſt the
hooks were faſtened to the girt, and then raiſed himſelf, and lifted up the
afs from the ground, bearing with his hands upon his knees. He raiſed
alſo in the fame manner other weights that feemed heavier, and uſed to
fay he did with more eaſe, becauſe the afs kicked and ftruggled when
firft lifted from the ground."
Dr. Defaguliers, in fome annotations upon De la Hire's paper, fays,
"What he attributes here to the muscles of the loins was really per-
formed by the extenfors of the legs; for the young man's ftooping with
his hands upon his knees was not with his body forwards and his knees
ftiff, but his body upright and his knees bent, fo as to bring the two
cords with which he lifted to be in the fame plane with his ancles and
the heads of his thigh bones; by which means the line of direction of
the man and the whole weight came between the ſtrongeſt part of his two
feet, which are the ſupports: then as he extended his legs he raiſed him-
felf, without changing the line of direction. That this muſt have been
the manner I am pretty well affured of, by not only obferving thoſe that
perform ſuch feats, but having often tried it myſelf. As for the muſcles
of the loins, they are incapable of that ſtrain, being above 6 times weaker
than the extenfors of the legs; at leaſt I found them fo in myſelf.
"About the year 1716, having the honour of fhewing a great many
experiments to his late majeſty king George the firft, his majeſty was
defirous to know whether there was any fallacy in thoſe feats of ſtrength
that had been ſhewn half a year before, by a man, who ſeemed by his
make to be no ftronger than other men: upon this I had a frame of
wood made to ftand in (and to reft my hands upon), and with a girdle
and chain lifted an iron cylinder made uſe of to roll the garden, fuftain-
ing it eaſily when once it was up. Some noblemen and gentlemen who
were preſent tried the experiment afterwards, and lifted the roller; ſome
with more eaſe, and fome with more difficulty, than I had done. This
roller weighed 1900lbs. as the gardener told us. Afterwards I tried to
lift 300 lbs, with my hands, (viz, two pails with 159 lbs. of quickfilver
Animal Strength-Horfes.
€9
bably about fix times that of a man. Defaguliers ftates the
proportion as 5 to 1; coinciding with the deductions of Smea-
in each), which I did indeed raiſe from the ground, but ſtrained my back
fo as to feel it three or four days: which fhews that, in the fame
perſon, the muſcles of the loins (which exerted their force in this laſt
experiment) are more then fix times weaker than the extenfors of the
legs: for I felt no inconveniency from raifing the iron roller."
During the time occupied in printing the fecond volume of Dr.
Defaguliers's Philoſophy, a man of great natural ſtrength exhibited him-
felf in London: of this man the doctor gives an account, from which the
following is extracted :
"Thomas Topham, born in London, and now about 31 years of age,
five feet ten inches high, with mufcles very hard and prominent, was
brought up a carpenter, which trade he practifed till within theſe fix or
feven years that he has fhewed feats of ftrength: but he is entirely igno-
rant of any art to make his ſtrength more ſurprifing. Nay, fometimes he
does things which become more difficult by his diſadvantageous fituation;
attempting, and often doing, what he hears other ſtrong men have done,
without making uſe of the ſame advantages.
"About fix years ago he pulled againſt a horfe, fitting upon the
ground with his feet againſt two ftumps driven into the ground, but
without the advantages which might have been attained by placing him-
ſelf in a proper fituation; the horſe, however, was not able to move him,
and he thought he was in the right poſture for drawing againſt a horſe :
but when, in the fame pofture, he attempted to draw againſt two horſes,
he was pulled out of his place by being lifted up, and had one of his
knees ſtruck againſt the ſtumps, which fhattered it ſo, that, even to this
day, the patella, or knee pan, is fo looſe, that the ligaments of it ſeem
either to be broken or quite relaxed, which has taken away moſt of the
ftrength of that leg."
66
The exploits which Dr. Defaguliers ſaw him perform were theſe :
1. By the ſtrength of his fingers (only rubbed in coal aſhes to keep
them from flipping,) he rolled up a very ſtrong and large pewter diſh.
2. He broke ſeven or eight ſhort and ſtrong pieces of tobacco-pipe
with the force of his middle finger, having laid them on the firſt and third
finger.
66
3. Having thruſt in under his garter the bowl of a ſtrong tobacco-
pipe, his legs being bent, he broke it to pieces by the tendons of his
hams, without altering the bending of his leg.
<<
4. He broke fuch another bowl between his firſt and ſecond finger,
by preffing his fingers together fideways.
5. He lifted a table fix feet long, which had half a hundred weight
hanging at the end of it, with his teeth, and held it in an horizontal
pofition for a confiderable time. It is true the feet of the table reſted
againft his knees; but, as the length of the table was much greater than
its height, that performance required a great ſtrength to be exerted by
the mufcles of his loins, thofe of his neck, the maffeter and temporal
(mufcles of the jaws), befides a good ſet of teeth.
"6. He took an iron kitchen poker, about a yard long, and three
inches in circumference, and, holding it in his right hand, he ftruck upon
his bare left arm, between the elbow and the wrift, till he bent the poker
nearly to a right angle.
66 7. He took fuch another poker, and holding the ends of it in his
hands, and the middle againſt the back of his neck, he brought both ends
of it together before him; and, what was yet more difficult, he pulled it
1
1
70
MECHANICS.
ton, before mentioned. The French authors commonly reckon
7 men for 1 horſe. As a mean between theſe, we took, in
almoſt ſtraight again: becauſe the muſcles which feparate the arms
horizontally from each other are not ſo ſtrong as thofe that bring them
together.
"8. He broke a rope of about two inches in circumference, which
was in part wound about a cylinder of four inches diameter, having
faſtened the other end of it to ftraps that went over his fhoulders. But
he exerted more force to do this than any other of his feats, from his
awkwardneſs in going about it; for the rope yielded and ſtretched as he
ſtood upon the cylinder, fo that when the extenfors of the legs and thighs
had done their office in bringing his legs, and thighs ftraight, he was
forced to raiſe his heels from their bearings, and uſe other muſcles that
are weaker. But if the rope had been ſo fixed that the part to be broken
had been ſhort, it would have been broken with four times lefs difficulty.
9. I have feen him lift a rolling ftone of about 800 lbs. with his
hands only, ſtanding in a frame above it, and taking hold of a chain that
was faſtened to it. By this, I reckon he may be almoſt as ſtrong again
as thoſe who are generally reckoned the ftrongeft men, they generally
lifting no more than 400lbs. in that manner. The weakest men who
are in health, and not too fat, lift about 125 lbs. having about half the
ftrength of the ſtrongeſt.
"N. B. This fort of comparifon is chiefly in relation to the muſcles
of the loins; becaufe in doing this one muft ftoop forwards a little.
We muſt alſo add the weight of the body to the weight lifted. So that
if the weakest man's body weigh 150 lbs. that added to 125 lbs. makes
the whole weight lifted by him to be 275 lbs. Then if the ftronger man's
body weighs alfo 150 lbs. the whole weight lifted by him will be 550 lbs.
that is 400 lbs. and the 150 lbs. which his body weighs. Topham weighs
about 200lbs. which, added to the 800 lbs. that he lifts, makes 1000 lbs.
But he ought to lift 900 lbs. befides the weight of his body, to be as
ftrong again as a man of 150 lbs. weight who can lift 400 lbs.'
Again: About thirty years ago one Joyce, a Kentish man, famous
for his great ſtrength, fhewed feveral feats in London and the country,
which fo much furpriſed the ſpectators, that he was by moſt people
called the fecond Sampfon. But though the poftures which he had learnt
to put his body into, and found out by practice without any mechanical
theory, were fuch as would make a man of common ftrength do fuch
feats as would appear furpriſing to every one who did not know the
advantage of thofe pofitions of the body; yet nobody then attempted
to draw againſt horſes, or raiſe great weights, or to do any other thing in
imitation of him: because, as he was very strong in the arms, and
grafped thofe that tried his 'ftrength that way fo hard that they were
obliged immediately to defire him to defift, his other feats (wherein his
manner of acting was chiefly owing to the mechanical advantage gained
by the pofition of his body,) were entirely attributed to his extraordinary
ftrength.
"But when he had been gone out of England, or had ceaſed to fhew
his performances for eight or ten years, men of ordinary ſtrength found
out the way of making fuch advantage of the fame poftures as Joyce had
put him£lf into as to paſs for men of more than common ftrength, by
drawing againſt horfes, breaking ropes, lifting vaft weights, &c. (though
they could in none of the poftures really perform fo much as Joyce,
yet they did enough to amaze and amuſe, and get a great deal of money),
fo that every two or three years we had a new ſecond Sampfon.
Animal Strength-Horfes.
71
art. 378. vol. I. the proportion of 6 to 1, and ſtated the ſtrength
of a horfe as equivalent to 420 lbs. at a dead pull. But the pro-
portion is by no means conftant, for it varies greatly according
to the different kinds of work. Thus the worst way of apply-
ing the ftrength of a horfe is to make him carry a weight up at
fteep hill; while the organization of a man fits him very well
for this kind of labour: hence, three men climbing up fuch a
hill with a weight of 100 lbs. each will proceed fafter than a
horſe with a load of 300 lbs. This, we believe, was firſt ob-
ſerved by M. de la Hiré.
We are not acquainted with any feries of experiments which
have been made with a view of determining the weights horfes
can carry when moving up floping roads, making given angles
with the horizon: but, fortunately, this deficiency is not of
much confequence, becauſe the carrying of weights is far from
the beſt manner of employing the ftrength of a horſe. It is
known, however, that, in general, a horfe loaded with a man and
his equipage, weighing altogether about 2 cwt. may, without
being forced, travel, in 7 or 8 hours, the diſtance of 43000
yards, or nearly 25 miles, upon a good road. When a horfe
travels day after day without ceffation, either the weight he
carries or the diftance paffed over muft undergo fome diminu
tion, as well as the time actually employed in travelling: but we
do not pretend to affign a mean value in this place.
"About fifteen years ago a German of middle fize, and but ordinary
ftrength, fhewed himſelf at the Blue Pofts, in the Haymarket, and, by the
contrivances above-mentioned, paffed for a man of uncommon ftrength,
and got confiderable fums of money by the daily concourſe of ſpectators.
After having feen him once, I gueſſed at his manner of impofing upon
the multitude; and being refolved to be fully fatisfied in the matter, I
took four very curious perfons with me to fee him again, viz. the lord
marquis of Tullibardin, Dr. Alexander Stuart, Dr. Pringle, and a mecha-
nical workman who uſed to affift me in my courfes of experiments.
We placed ourſelves in fuch manner round the operator, as to be able
to obferve nicely all that he did; and found it fo practicable, that
we performed feveral of his feats that evening by ourfelves, and after-
wards I did the moſt of the reít, as I had a frame to fit in to draw, and
another to ſtand in and lift great weights, together with a proper girdle
and hooks. I likewife fhewed fome of the experiments before the Royal
Society; and ever fince at my experimental lectures I explain the
reafon of fuch performances, and take any perſon of ordinary ftrength
that has a mind to try, who can eafily do all that the German above-
mentioned uſed to do, without any danger or extraordinary ſtraining,
by making uſe of my apparatus for that purpoſe.'
The Doctor then proceeds to explain the principles on which thefe
achievements depended, and illuſtrates his poſitions by various diagrams.
He likewiſe deſcribes fome contrivances to determine the ſtrength which
men exert in different ways; for an account of the chief of which, the
reader may turn to the article STEELYARD, to aſcertain the Strength of
Men, in a fubfequent part of this volume.
+
72
MECHANICS.
!
!
71. In the Memoirs of the French Academy for 1703, are
inferted the comparative obfervations of M. Amontons, on the
velocity of men and of horſes; in which he ſtates the velocity
of a horfe loaded with a man and walking to be rather more
than 54 feet per fecond, or 3 miles per hour, and when going a
moderate trot with the fame weight to be about 8 feet per
ſecond, or about 6 miles per hour. Thefe velocities, however,
are ſomewhat lefs than what might have been taken for the mean
velocities.
72. But the best way of applying the ftrength of horfes is to
make them draw weights in carriages, &c. To this kind of
labour, therefore, the enquiries of experimentaliſts ſhould be
directed. A horfe put into harneſs and making an effort to
draw bends himſelf forward, inclines his legs, and brings his
breaſt nearer to the earth; and this fo much the more as the
effort is the more confiderable. So that when a horſe is em-
ployed in drawing, his effort will depend, in fome meaſure, both
upon his own weight and that which he carries on his back.
Indeed it is highly uſeful to load the back of a drawing horſe
to a certain extent; though this, on a flight confideration,
might be thought to augment unneceffarily the fatigue of the
animal: but it muſt be confidered that the mafs with which the
horfe is charged vertically is added in part to the effort which
he makes in the direction of traction, and thus difpenfes with
the neceffity of his inclining fo much forward as he muſt other-
wife do; and may, therefore, under this point of view, relieve
the draught more than to compenfate for the additional fatigue,
occafioned by the vertical preffure. Carmen, and waggoners in
general, are well aware of this, and are commonly very careful
to diſpoſe of the load in ſuch a manner that the fhafts fhall
throw a due proportion of the weight on the back of the ſhaft
horfe.
73. The beſt diſpoſition of the traces during the time a horſe
is drawing is to be perpendicular to the pofition of the collar
upon his breaſt and ſhoulders: when the horſe ſtands at eaſe,
this pofition of the traces is rather inclined upwards from the
direction of the road; but when he leans forward to draw the
load, the traces fhould then become nearly parallel to the plane
over which the carriage is to be drawn; or, if he be employed in
drawing a fledge, or any thing without wheels, the inclination of
the traces to the road, fuppofing it to be horizontal, ſhould
(from what we obferved when treating of friction) be about
1810.
74. From the preceding obſervations it will be eaſy in moſt
cafes to adapt the fize of the wheels to that of the animal which
is to draw in the fhafts, fo that when he leans forward to his
Animal Strength-Horſes.
73
work the traces may be nearly parallel to the road, whether
that road be horizontal or not: always recollecting that, if
there be any variation from the parallel pofition, it muſt be
rather inclining upwards than downwards; as the former will
fomewhat diminish the friction, while the latter, inſtead of
raifing the wheels from any hollow into which they may fall,
will tend to draw them down lower, and much increaſe the
labour of the animal.
75. When ſeveral horſes are harneffed one before another,
fo that they may all draw at the fame load, and the flope on
which they are drawing changes, as from DA to AB (fig. 6.
pl. I.), the effort of the horſe which draws along the road AB
is decompofed into two parts, of which one tends to pull up
the load, the other to pull down the horſe which is in the fhafts
and is drawing along the ſlope DA. This latter compofant is
always greater as the traces of the foremoſt horſe are the
longer; and it may be worth while to find its values, and its
augmentation with regard to an increaſe in the length of the
traces. To this end let EA' be the height above AD of the
breaſt of the horſe which draws in the ſhafts near the point A,
and let ER and ER' be two different lengths of the traces;
the breaſt of the horſe when harneffed to either of theſe traces
being at the fame diſtance from the plane AB', that is, BR=
B'R' EA'. Take EF-EF' to reprefent the effort of the horſe
in the direction of the trace; draw E q parallel to DA, EQ
perpendicular to BA produced, Eg parallel to AB, and Fq,
Fq, perpendicular to E q. The effort which tends to pull the
horſe down whoſe breaſt is at E is reprefented by Fq, when the
breaſt of the other horfe is at R, and by F'q' when it is at R';
and q E, q'E are the correſponding efforts tending to raiſe the
load along the flope DA. Make EA'=RB=R'B'=a, ER=λ,
ER'=', angle A'EQ=q Eg= ſupplem. DAB=s, and EF=
EF=4. Then, when the trace ER is uſed, the effort which
tends to pull down the fhaft horfe when he just reaches the
fummit of the flope will be . fin. 7 EF fin. (q Eg-
7.
FEg), and the effort tending to raiſe the load will be = cofin.
(q Eg-FE g). In like manner, when the foremoſt horfe
draws by the trace ER', the effort tending to pull down the
fhaft horfe will be reprefented by o fin. (9 Eg'-F'Eg'), and
that which tends to draw up the carriage by cofin. (q Eg'
and fin. FEg=
R g
FEg). Now we have fin. FEg=ER'
R' g
ER'
R g
ER
$
But Rg=BREQ=a-a cofin. s=a (I
cofin.). Recollecting, therefore, that the angles FEg, F'Eg,
74
MECHANICS.
are always ſo ſmall that the arcs differ very little from the fines,
we have FE g=
a (1-cosin, s)
a(1-cosin.s)
and FEg'-
እ
: thefe
values being fubſtituted in the preceding expreffions, give
a
(1) ...Fq=0
• Fq=4 fin. (s — ª (1—cosin. s)).
(2) ... F'q'=q fin. (s
(3) ... E q=9 cofin. (s
λ
a (1-cosin.
a (1-cosin.
λ
(4) ……..Eq'=ø
……. E q'=q cofin. (s—ª (1 — cosin. s.))
a — —
λ'
Suppoſe, for example, that AB is horizontal, and that the
afcent DA is ſuch that for every fix feet, as CN in a horizontal
plane, the vertical riſe NA ſhall be one foot: this flope is too
steep for any common road, but may be fometimes met with in
afcents from ftone quarries, &c. In this cafe the angle s will
be nearly 9° 28′, which, expreffed in decimal parts of the ra-
dius, gives s=0'16522, and cofin. s=0'98638. Let the effort
=200 lb., a=34 feet, λ = 8 feet, and λ=12 feet. Then
thall we have,
(1) ... Fq=200 fin. (0·16522—3′5 (1−0·98638))
8.
=200 fin. 9° 7′ 29″=31716 lbs.
(2) –
... F'q'=200 fin. (0·16522 — 3'5 (1—0′98638)
(3)
(4)
12
=200 fin. 9° 14′ 29″=32.25 lbs.
Eq=200 cofin. 9° 7′ 29″17747 lbs.
Eq=200 cofin. 9° 14′ 29″ 197 404 lbs.
Hence it appears, that the horſe whofe breaft is at E is
pulled downwards by the other horſe, with a force equivalent
to about 32lbs: this weight is fmall for a horſe that is not
fatigued; but we ſhould confider, that when drawing up a ſteep
road the animal's ftrength is much weakened, fo that it may
be obliged to yield to a very ſmall effort. A lengthening of
four feet to a trace of eight feet will produce an augmentation
of 32.25-31716=0.534 lbs. in the effort which tends to pull
the fhaft horfe down, and a diminution of 197°47—197°404=
0*066 lbs. in the effort which raifes the load up the hill. Thefe
quantities are not confiderable; but it appeared deſirable to
explain the method of afcertaining their magnitude. And it
may be added, that when a horſe pulls for only a ſhort time, as
a few minutes, he will often exert a force equivalent to 500 or
600 lbs.: in which cafe, the tendency to pull down a ſhaft
horfe rifing a hill would be thrice as much as we have ſtated
`Animal Strength-Horſes.
773
*
it above: a force againſt which no horfe could ftand in ſuch a
difadvantageous pofition.
•
76. When a horfe is made to move in a circular path, as is
often practifed in mills and other machines moved by horſes, it
will be neceffary to give the circle which the animal has to
walk round, the greateft diameter that will comport with
the local and other conditions to which the motion muſt be
ſubjected. It is obvious, indeed, that, fince a rectilinear mo-
tion is the moſt eaſy for the horſe, the leſs the line in which he
moves is curved, with the greater facility he will walk over it,
and the lefs he need recline from a vertical pofition: and be-
fides this, with equal velocity the centrifugal force will be leſs
in the greateſt circle, which will proportionally diminiſh the
friction of the cylindrical part of the trunnions, and the labour
of moving the machine. And, further, the greater the dia-
meter of the horſe-walk, the nearer the chord of the circle in
which the horſe draws is. to coincidence with the tangent,
which is the moſt advantageous pofition of the line of traction.
On theſe accounts it is that, although a horſe may draw in a
circular walk of 18 feet diameter, yet in general it is advifeable
that the diameter of fuch a walk fhould not be leſs than 25 or
30 feet; and in many inftances 40 feet would be preferable to
either.
:
77. It has been ftated by Defaguliers (vol. I. pa. 251) and
fome others, that a horfe employed daily in drawing nearly
horizontally can move, during eight hours in the day, about
200 lbs. at the rate of 24 miles per hour, or 33 feet per fecond.
If the weight be augmented to about 240 or 250 lbs., the horſe
cannot work more than fix hours a day, and that with a leſs
velocity. And, in both cafes, if he carry fome weight, he
will draw better than if he carried none (art. 72.) M. Sau-
veur eſtimates the mean effort of a horſe at 175 French, or
189 averd. pounds, with a velocity of rather more than three
feet per fecond and this agrees very nearly with our deduć-
tion in art. 378. vol. I. But all thefe are probably too high
to be continued for eight hours, day after day; for in our in-
veſtigation juſt referred to we affumed 10 feet per fecond, as
the utmoſt walking velocity of a horſe; a velocity which we
conceive no horſe would be able to continue long. In another
place Defaguliers ftates the mean work of a horfe as equivalent
to the raiſing a hogfhead full of water (or 550 lbs.) 50 feet high
in a minute. But Mr. Smeaton, to whofe authority much is
due, afferts, from a number of experiments, that the greateſt
effect is the raiſing 550 lbs. forty feet high in a minute. And,
from fome experiments made by the Society for the Encourage-
1
"B
MECHANICS.
ment of Arts, under the direction of their late able fecretary,
Mr. Samuel Moore, it was concluded, that à horſe moving at
the rate of three miles an hour can exert a force of 80 lbs.
Unluckily, we are not fufficiently acquainted with the nature
of the experiments and obſervations from which theſe deduc-
tions were made to inftitute an accurate compariſon of their
refults. Neither of them ought to exprefs what a horſe can
draw upon a carriage; becauſe in that cafe friction only is to
be overcome (after the load is once put into motion); ſo that a
middling horſe, well applied to a cart, will often draw much
more than 1000 lbs. The proper eſtimate would be that which
meaſures the weight which a horſe would draw up out of a
well; the animal acting by a horizontal line of traction turned
into the vertical direction by a fimple pulley, or roller, whoſe
friction fhould be reduced as much as poflible. It would, in-
deed, be far the beft, in all the inftances of experiments, to
uſe no fuch combinations of machinery as would make the ve-
locity of the load or weight different from that of the animal:-
we could then readily compare the different reſults by means
of the expreffion M∞ (W-V)², or Mx (W – V)³ (art. 378.
vol. I.), where V repreſents the velocity in feet per fecond
with which the animal moves the maſs M, and W his greateſt
walking velocity, or that in which he can move no weight but
his own.
Thus might we obtain a mean eſtimate of the ani-
mal's ftrength at any one velocity, and could thence infer his
maximum of uſeful effort; namely, that when V is nearly
W. As to the abfolute power of the animal, it might be in-
ferred in any cafe of railing a weight with his own velocity,
by means of the formula =(M+H) V+Mgt, where M and
Vare as before, H the weight of the horfe, its power, g=
32% feet the meafure of the force of gravity, and t the time
in feconds during which the animal continues his uniform
exertion.
78. It follows, from what has been faid, and from the con-
fideration of the ftrengths of horſes variouſly employed, fuch
as waggon horfes, dray horfes, plough horfes, heavy horfes,
light coach horfes, &c. that what is called "horse-power" is of
fo fluctuating and indefinite a nature, that it is perfectly ridi-
culous to affume it as a common meaſure, by which the force
of ſteam-engines and other machines fhould be appreciated,
In most of the deductions which have been hitherto made we
apprehend there may be fomething of temporary effort and
we think, on the whole, that about 70 lbs., at three miles an
hour, or 43 feet per fecond, may be a fair eftimate for the
regular work of ftout London cart horſes; though we would
Animal Strength-Horfes.
77
infer, with Mr. Nicholſon, "that the animal can double his
"ftrength for a fhort time, fuch as 10 minutes, without re-
ceiving any injury from the exertion.”
દ
Thus have we preſented a view of the moſt uſeful and cor-
rect information we have been able to collect, on the different
energies of firſt movers: what is here done is not ſo ſatisfactory
as might be wifhed; but our knowledge on many of thefe
points muſt remain imperfect, till freſh light is diffuſed over it
by the diligent and able enquiries of future obfervers.
:
{
•
:
DESCRIPTIONS
1
OF
MACHINES:
ALPHABETICALLY ARRANGED.
AIR-PUMP is a machine by means of which the air may be
exhauſted out of proper veffels, fo as to make what is popularly
called a vacuum, but which is, in fact, only a very high de-
gree of rarefaction.
The invention of this noble inftrument, to which the prefent
age is indebted for ſo many admirable diſcoveries, is afcribed to
Otto de Guericke, a conful of Magdeburg, who exhibited his
first public experiments with his pump before the emperor and
the ftates of Germany at the breaking up of the imperial diet.
at Ratiſbon, in the year 1654. Guericke, indifferent about
the folitary poffeffion of an invention which afforded fuch en-
tertainment to the numerous perfons who, from time to time,
witneffed his experiments, gave a minute defcription of all his
pneumatic apparatus to Gafper Schottus, profeffor of mathe-
matics at Wirtemberg, who publifhed it, with the conſent of
the inventor, with an account of fome of its performances,
first in 1657, in his Mechanica Hydraulico-pneumatica; and
then, in 1664, in his Technica Curiofa. Guericke's own ac-
count was not publiſhed till 1672.
About the time of Guericke's invention the foundations
of the Royal Society of London were laid. Boyle, Wren,
Brounker, Wallis, and other learned men, held frequent
meetings at Oxford, in which accounts were received and re-
lated of all important advances in the ftudy of nature; and
many experiments were exhibited. The refearches of Galileo,
Torricelli, and Paſcal, concerning the preffure of the air, had
80
MACHINES.
}
:
greatly engaged their attention, and thus prepared them for the
invention of Guericke. Mr. Boyle, in particular, as foon as
he heard what had been accompliſhed by the philofopher of
Magdeburg, and before any defcription of his machine had
been publiſhed, fet about the conftruction of one, to anſwer
the fame purpoſes; and fucceeded in the attempt: though he
frankly acknowledges that it was but ſeldom, and with great
difficulty, that he could produce an extreme degree of rare-
faction; fuch as it appeared, from the account of Schottus,
was obtained by means of Guericke's machine.
Boyle's inftrument was fomewhat improved by Hawkſbee,
and further by Martin; with fome flight modifications to par-
ticular views, it ſtill remains the moſt approved form. The
air-pump we defcribed in art. 521. vol. I. is only fo far va-
ried from Hawkfbee's improvement of Boyle's original con-
trivance, as to render it more portable. The machine, in its
primitive ſtate, is deſcribed in the article Pneumatics, English
Encyclopædia; where, alfo, the fucceffive improvements of
Smeaton, Cuthbertſon, &c. are defcribed at large.
Many other ingenious attempts have been made, during the
laſt ten or twelve years, to improve the mechaniſm of the air-
pump; to deſcribe a fourth part of which would extend this
article to more than its due length. Juftice, however, to the
authors of theſe improvements, as well as a defire to gratify
the reader, induces us to refer to Nicholfon's Journal, vols. I
and II. 4to. for deſcriptions of the air-pumps invented by meff.
Prince, Sadler, Little, sir G. Mackenzie, &c. and to Mr.
Vince's Hydrostatics for an account of the pump uſed by that
gentleman in his lectures.
Notwithſtanding the many improvements which have fuc-
ceffively followed each other in the conftruction of the air-
pump, it was ftill, however, defirable that it ſhould be further
fimplified in its mechaniſm, while it poffeffed the fame advan-
tages as attended thoſe of more complicated ftructure. Cuth-
bertſon, Haas, and fome others, have fo contrived their inftru-
ments, that their mechanical power, and not the preffure of
air, ſhould open the valves: but, although the air-pumps in-
vented by theſe gentlemen are exceedingly ingenious, they are
in ſome reſpects fo complex, that it must be very difficult for
many perſons who poffefs thefe inftruments to clean them, or
to keep them in proper order for experiments.
Mr. N. Mendleffohn, a mathematical inftrument-maker, of
Surrey-ſtreet, Black-friars, having reflected upon the difficul
ties juft alluded to, was led to the conſtruction of a more
fimple air-pump, which is capable of being put together in leſs
Air-pump.
81
than half an hour, whenever it is cleared, and requires that
operation very ſeldom. He has rejected the tube which, in
common air-pumps, leads from the valves to the receiver, toge-
ther with the cock that ferves to fhut this pipe: the receiver is
placed immediately upon the valves, theſe being put on the top
of the cylinders, which, confequently, required the rackwork
and pinion being underneath, and inverted the whole inftru-
ment. See the drawing, pl. IV. where AB and CD reprefent
the two cylinders of glafs ground and poliſhed infide. E and F
are the two valves that allow the cylinders to communicate with
the receiver O through two very fhort canals AB and CD (fig. 2:
plate IV.) and the cock G. Two other valves that open into
the atmoſphere are within the covers i and k, as may be ſeen in
fig. 1, where e reprefents one of them. MN is the receiver-
plate of glafs ground flat; PQ_a barometer-guage, upon the
plan of the firft Torricellian tube, as the eafieft to conſtruct
and the moſt infallible in its effects. It will be found to be.
here quite out of the way, fecure from being broke by accident,
and the moſt in fight. HK and IL are two brafs pillars that
ſupport the whole. RSVW the ufual rackwork, having a
double winch Im, which, upon trial, will be found preferable
to a fingle one.
It will now be neceffary to fhew how this pump acts, in
which it will be fufficient to explain the action of one cylinder,
becauſe the other is in all parts like it. E is a conical metallic
valve, from which a canal goes through the cock G up to the
receiver, as is feen in fig. 1 and 2, where all the parts aré
marked with the fame letters. ET is a fteel rod going through
a leather box in the piton U. The top of this rod is fixed to
the valve E, and its bottom part flides in a ſmall hole with an
allowance of o'i inch up and downward, confequently the valve
E can move no further. When the piſton deſcends, it firſt
opens the valve by puſhing the rod to the bottom of the hole.
Then it flides down along the rod ET, and the air from the
receiver has now free access to the cylinder. When the piſton
returns it lifts the rod ET, and thus fhuts up the valve. Then
the piſton flides again along the rod up to the top of the cylin
der, condenſing the air above it, which air, by the leaft con-
denfation, opens a velve e, fig. 2, and eſcapes freely into the
atmoſphere. This laft valve has neither fpring nor additional
weight to fhut it, but fhuts by its own weight (about a quarter
of an ounce) as foon as the piſton is arrived to the top of the
cylinder.
The cylinders are made of glaſs, and the piſtons of tin, fo well
fitted as to be air-tight, without the interpofition of any leathers.
VOL. II.
G
32
MACHINES.
1
The friction of theſe two bodies is fmall beyond expectation,
a fufficient proof that they will be durable. They poffefs the
further advantage of being capable of ftanding for even fix
months, after which time they will ſerve without being cleaned
or repaired, becauſe they are not liable to be corroded by the
oil which they contain, an inconvenience too general in brafs
cylinders. After all, if the preſent pump fhould want cleaning,
it is an eafy operation to take off the top piece g h, by unfcrew-
ing the nuts H and I, when this piece, with all the apparatus
upon it, will come off. Then each cylinder may very eaſily be
flid off from the pifton, wiped out and replaced, after having
greaſed it infide with a little of the cleaneft fweet oil: the top
is then to be put again in its place, and the two nuts H and I
being ſcrewed upon it, the inftrument is ready. Neither racks
nor pinion need to be taken out of their places, the cylinders
ſtanding above them.
The cock is conftructed fo, that, being in the fituation re-
prefented in fig. 1, the communication is open between the
cylinders, the receiver, and the barometer-guage, and, by a
quarter of a revolution, the cylinders are excluded, the receiver
and guage being ftill left in communication. A little ſtopper
in fig. 2, ground into the cock, being open, air is admitted to
the receiver, if required.
The receiver-plate is of glaſs ground flat, as was mentioned
before this will be found preferable to brafs, becauſe cleaner,
and never corroded by acids or water; it will befides often
prove very convenient in making electrical experiments in the
vacuum.
The whole inftrument is fixed upon a mahogany-table,
which ferves as a ſtand for it.
Mr. Mendelsſhon concludes his deſcription by obſerving that
"neither the employing of glaſs cylinders, nor the method of
opening the valves, is new; but, for aught he knows, this is the
firft inftrument of the kind ever executed: and the idea of
putting the valves at top, and thus fimplifying the inftrument,
feems to have eſcaped the attention of the eminent artiſts, both
here and abroad, as, to my beſt knowledge, it has never been
done or deſcribed any where. The metallic piftons, without
leathering, muſt certainly add to the durability, and diminiſh
the great labour that ufually attends working an air-pump."
Nicholson's Journal, New Series, No. 39.
Mr. Vream, who was Dr. Defaguliers's operator for philofo-
phical machines, made fuch an alteration in Hawkfbee's air-
pump, as produced the alternate reciprocating motion of the
piftons, without turning the handle to and fro :while the handle
turns conſtantly one way in its operation, a crank by means of
Rigidity of Cords.
33
No. of experiments. |
Cords
used in
and
weight of
Weights
hung on
each side
the roller
Addition.
weight
to sur-
mount、
friction of
the
in lbs.
rollers.
roller and
stiffness
of cords.
I
páratus of Amontons. The cords were of three kinds : No. 1,
of 6 threads in a yarn, or 2 in a ſtrand, the circumference 12
lines, and weight of a foot in length 4 drams. No. 2, of 15
threads in a yarn, or 5 in a ftrand, circumference 20 lines,
weight of a foot in length 12 drams. No. 3, of 30 threads.
in a yarn, or 10 in a ftrand, circumference 28 lines, weight of a
foot in length 24½ drams.

the expe-
riments.
Kinds of
wood:
diameter
the rulers Friction
Stiffness ofthe Cord.t
Valued
by Cou
Valued
by Amon-
lumb's
tons' ap-
appa-
paratus.
ratus.
Total
charge of
which
support
of the
roller.
the
roller.
Elm
100
Cord
5 lbs.
315
1.5
3.5
44
12 inches
No. 3. of
I
30 threads
diameter,
300
II
721
3.6
7'4
10'4
in a yarn.
weight
IIO lbs.
500
20
1130
5.6
14.4
16.4
Elm
6 inches
2
Idem.
diameter,
200
18
443
weight
25 lbs.
Guiacum
6 inches
3
Idem.
diameter,
200
16
466
2.8
13.2
14.8
weight
J
50 lbs.
Guiacum
2 inches
25
II
65/1/2
Idem.
4
diameter,
weight
200
52
456/1/
4 lbs.
Cord
Guiacum
25
No. 2. of
6 inches
璟
​IOI
100
6
5
15 threads
diameter,
256
200
II
461
2.8
8.2
7.6
in a yarn.
weight
500
24
1074
6.4
17:6
17.8
50lbs.
Cord
No. I. of
100
6 threads
Idem.
200
36
253
456
2'7
3.3
3'x
?
in a yarn.
From this table it will be feen that the method of Amontons
and that of Coulumb furniſh nearly the fame refults: M.
Coulumb aſcribes the differences where greateſt to the circum-
ftance of the cords having been more uſed previous to their
being taken for one kind of experiment than for the other.
35. M. Coulumb, before he commenced the experiments
upon the friction of axes, caufed the pulley to turn on its axis
during ſuch a time and with ſuch a velocity as was neceſſary to
VOL. II.
D
34
MECHANICS..
:
enable the furfaces in contact to acquire all the polish and
glibnefs of which they were fufceptible. The chief object held
in view in the experiments of which we now fpeak was to de-
termine the friction of the axes of machines in motion. M.
Coulumb therefore caufed the fufpended weights to run over a
ſpace of 6 feet, and to meaſure ſeparately by half feconds the time
employed to run over the first three feet, and that occupied
in running over the last three feet. The following table con-
tains the reſults of experiments on the friction of axes of iron
in boxes of copper: the axis ufed was 19 lines in diameter,
and had a play of 12 lines in the copper box, the pulley was
144 lines in diameter, and weighed 14 pounds.

}
!
:
1
:
36
MECHANICS.

Weight
Weight
Addi-
Fric-
Ratio
No. of
hung
tional
experi-
Kind ofcord
used.
Kind of greas-
ing.
used to
Jon each
weight
Motion of the
weight suspended
Pres-
sure on
tion
reduc.
of fric-
tion to
ments.
bend
the cord.
over the
side of
the
to move
the
on each side of the
pulley.
the
to
the
axis.
surface
pres-
pulley. pulley. | pulley.
of axis.
sure.
Very flexi-
ble thread of
Friction with-
O'O
3 lines cir-
out greasing.
103
6
Slow and irregular.
226
42
0.186
cumference,
10'5
Slow and irregular.
424
65
0.153
Cord No. 1.
The first 3 ft. fallen
of 6 threads
Idem.
1'5
200
13'5
thro' in 6", the last
in a yarn.
3 in 3".
21
Slow but continual.
825
130
0.156
The first 3 feet de-
28
scribed in 5″5, the
3
Idems
Idem.
3'0
400
last three in 2″5.
First 3 ft. described
39
in 3", the last 3 in
Very flexi-
I{".
2.5
Slow but continual.
216.5
17'5
0'081
ble thread,
tallow.
O'O
100
The first 3 feet de-
of 2 lines cir-
6
scribed in 3″5, the
cumference.
last 3 in 1"5.
Cord No. 1.
6.5
Slow but continual.
420
·36
0'086
of 6 threads
Idem.
1'5
200
in a yarn.
10'0
13
6
Idem.
Idem.
3'0
400
18
24
t3
The first 3 feet, de-
scribed in 3″.5, the
last 3 in 1"5.
Slow and continual.
The first 3 feet, de-
scribed in 5″.5, the
last 3 in 2".
first 3 feet in
last 3 feet in
"
827
25
0*087
3″
Table of Friction, &c. continued.
་
Thread of 2
lines in cir-
cumference.
Cart grease.
IO
∞ a a
8
Idem.
Idem.
9
Idem.
Idem.
៖ ៖ ៖
O'O
O'O
100
O'O
58 55
2.5
Slow and continual.
117
1.7°5
0.15
Idem.
218
26
0.119
3'7
ldem.
5'7
320
40.
O'125
Slow and uncertain.
218
26
0.119
Cord No. I.
4.3
of 6 threads
Idem.
0'7
100
9
first 3 feet in 3",
in a yarn.
last 3 feet in 1½".
8.5
Uncertain.
422
50
0.118
Idem.
Idem.
1'5
200
14
first 3 feet in 4″,
last 3 feet in 2".
20
all 6 feet in 3″5.
17
Uncertain.
831
IOI
O'121
12
Idem.
Idem.
3.0
400
22
28
The cart
grease of prec.
first 3 feet in 6"·5,
last 3 feet in 2"*5.
first 3 feet in 4″,
last 3 feet in 1"5.
From
200
to
1200
lbs.
0.127
13
14
15,
exp. wiped,
the pores of
the metal re-
mained unc-
tuous.
The surface
fresh done
with oil.
The greasing
not renewed of
a long time,
though the
machine had
been much
used.
O'127
O'133
O'133
38
MECHANICS.
The weights employed to bend the cord, and which are con-
tained in the 4th column, were calculated from the tenfions ex-
preffed in the 5th column, by means of the formulæ already
given, and the refults of fome previous experiments. Thefe
weights being fubtracted from thoſe of the 6th column, which
put the fyftem in motion, leave the weights employed in over-
coming the friction. Thefe latter weights acting at a di-
ſtance from the centre of rotation equal to the ſum of the radii
of the pulley and the cord; the friction which is exerted upon
the axis, and which in the cafe of a very flow motion may be
confidered as making an equilibrium with thoſe weights, is
therefore equal to the product of thoſe weights into the ratio
of the fum of the radii of the pulley and the cord, to the radius
of the axis, which ratio is very nearly 7 to 1, when the weight
is fufpended by a thin packthread, and nearly 72 to 1, when
it is fufpended by the cord No. 1. From theſe confidera-
tions the 9th column was calculated. The weights compriſed
in the 8th column are compofed, 1. Of the weight of the
pulley or cylinder; 2. Double the correfponding weight in the
5th column; 3. The weights contained in the 6th column; for
the fum of thefe evidently compofe the preffure upon the axis.
Hence, to find the ratio of the friction to the preffure, as ex-
preffed in the 10th column, it is only neceffary to divide any
number in the 9th column by the correfponding one in the 8th.
36. When it is proper to have regard to the velocity of the
weight, to afcertain the effort which furmounts the friction and
the ſtiffneſs of the cord, we may obſerve at once that in this caſe
the motion is nearly a uniformly accelerated motion, fince the firſt
3 feet are deſcribed in a time about double that employed in
running over the laft 3 feet. It remains, therefore, to learn what
part w of the additional weight ftated in the 6th column, which
we call w, was employed in accelerating the motion of the ſuſ-
pended weight; for the other part of the additional weight,
viz. ww', is manifeftly that which furmounts the friction and
the ſtiffneſs of the cords. Now t being the time of the whole
defcent, the accelerating force which has place is equal to 2x6;
tz
and, naming W the total fum of the weight hanging upon the
pulley compriſing in it 7 pounds for the inertia of the pulley,
which weighed 14 pounds, and g the accelerating force of gra-
vity, the mafs put in motion will be
mafs by the accelerating force will be
W
g'
•
and the product of that
2 X 6 W
& 12
; which being fub-
tracted from the additional weight which put the pulley in mo-
Stiffness of Cords.
39.
tion, gives the quantity w-w', or the part of the weight w em-
ployed to overcome the ſtiffneſs of the cord and the friction.
It appears from the 7th, 8th, 9th, 10th, 11th, and 12th ex-
periments, that the friction of axes of iron in boxes or cheeks of
copper is much lefs foftened by the cart-greafe than by tallow.
37. M. Coulumb has likewiſe endeavoured to afcertain the
friction of axes of rotation made of the different kinds of wood
which are commonly found in rotatory machines. To render
the friction more ſenſible he uſed pulleys of 12 inches mounted
upon axes of 3 inches; fometimes the axes were immoveable,
at others they moved, but in both cafes the friction was the
fame the proper precautions were adopted to fmoothen the fur-
faces in contact, and thence to avoid the uncertainty and irre-
gularity which might otherwife have attended the refults.
Kinds of wood used in the experiments.
Axis of holm-oak, box of lignum vitæ, coated with
tallow
Ditto the coating wiped, the furface remaining oily
Axis and box as before, but uſed ſeveral times with-
out having the coating refreſhed
Ratio of
friction
to pressure.
}
Axis of holm-oak, box of elm, coated with tallow
Ditto both axis and box wiped, furfaces remaining oily
Axis of boxtree, box of lignum vitæ, coated with tallow
Ditto the coating wiped, the furfaces remaining oily
Axis of boxtree, box of elm
Ditto the coating wiped off.
Axis of iron, box of lignum vitae, the coating wiped
off, and the pulley turned for fome time
0.038
d'oб
: 0°06
d'o8
0°03
0'05
0.043
007
0.035
0.05
0.05
The velocity does not appear to influence the friction in any
fenfible manner, except in the firſt inſtants of motion: and in
every caſe the friction is leaft, not when the furfaces are
plaſtered over, but when they are merely oily.
38. The experiments on the ſtiffneſs of cords defcribed (art.
34) were made in cafes of motions nearly infenfible; but M.
Coulumb enquired whether with a finite velocity the refulting
effect of the ſtiffneſs of the cord were augmented or diminifhed.
For this purpoſe he took a pulley and box of copper, and an
axis of iron done over with tallow: the diameter of the pulley
was 144 lines, and that of the axis 20 lines; and the cord was
one of 30 threads to a yarn, or No. 3. of which the ſtiffneſs
with respect to infenfible velocities was determined by ſome of
the foregoing experiments. The enfuing table fhews the re-
fults of the experiments: the weights were made to run over a
diſtance of 6 feet, and the times of defcribing the first three and
the last three feet were meaſured by a half-fecond pendulum.
篮
​40
MECHANICS.

Weight Stiffness | Stiffness
acting
of the
Addi-Part of
Weight
No. of hung
experi-jon each
ments. side the
to
come
tional wt. to
weight over-
'Motion of the
weights hung upon
the pulley.
the
Pres- at ex-
sure on tremity deduced
axis inley, ba- weights
cord
of the
cord esti-
mated
of pul- from the
from its
tension
move friction
)3.
lancing which
and for-
pulley.
the land ri-
the
move the
mer ex-
pulley.gidity.
friction pulley.
perimts.
75 lbs. 7.5 lbs.
Slow and continued 221 lbs. 2.6lbs.
4'9 lbs.
4'0 lbs.
Sfirst 3 feet in 3'
Ioolbs.
12
7.6
last 3 feet in 1½"
15
7.6
Sfirst 3 feet in 2″
last 3 in 1½"
II
II
Slow and uncertain 425 49
6.1
6.6
first 3 feet in 6″
15
12.9
2
200
last 3 in 3"
first 3 feet in 31"
19
12.2
last 3 in 14″
20.5 20'5
|
24
3
400
19'9
{ first
Slow and uncertain 8349'7
10.8
11.8
f first 3 feet in 6"
last 3 in 3"
31
17.6
{ last 3 in 2
first 3 feet in 3″
(315 31.5
Doubtful and conti. 1235
14.5 17.0
17.0
4
600
first 3 feet in 6"
37
31.5
last 3 in 3½"
It appeared in the table (art. 34.) that to bend the cord
no.. 3. of 30 threads in a yarn, about a roller of 12 inches di-
ameter, and with a tenfion of 500lbs, would require a weight
of 14'4 lbs of which weight the conftant part due to the
fabrication of the cord is about 14 lbs: this value may be
retained; but it will be here proper to deduce the part due to
the tenfion of the cord by the quintal to (144-14)=
×13=2.6lbs. From theſe data the laſt column to the right of
the above table was computed.
ड
39. To complete the object of the experiments it is neceſſary
to have the ſtiffneſs of the cord without afferting any thing à
priori on the values which had been previouſly found for fuch
rigidity. To this end M. Coulumb has eſtimated the friction
of the axis from its charge and the experiments of art. 35;
where it appeared that this friction was independent of its
velocity and equal to o'087 of the preffure. This friction
which is exerted at the furface of the axis being computed, and
the radius of the axis being to the diſtance between the centre
of rotation and the middle of the cord as 1 to 75, it will be
eafy to calculate the weight which acting in the vertical di-
rection of the middle of the cord may be in equilibrium with
the friction in each experiment; and thefe weights are con-
tained in the feventh column. Subtracting theſe weights from
Stiffness of Cords.
41
•
the additional weights contained in the third column, namely
thoſe which put the pulley in motion, we have in the cafe of a
very flow motion the values of the weights which juſt ſurmount
the ſtiffneſs of the cord; theſe weights are compriſed in the 8th
column, and differ but little from thofe calculated immediately
and contained in the 9th column.
40. Now to know if the greater or lefs velocity of the
weight ſuſpended upon the pulley has any influence upon
the refiſtance due to the ſtiffneſs of the cord, we muſt in
the cafe of the motion calculate what portion of the ad-
ditional weight hung upon the pulley is employed in over-
coming the friction and the rigidity of the cord. Here the
formula of a preceding article has its application, w’= :for,
2X6W
812
the time occupied by the weight in defcribing the laſt three feet
being nearly the half of that employed in defcribing the firſt
three feet, the motion may be confidered as uniformly accele-
rated, and the quantities w-w', which refult, and are con-
tained in the 4th column, differ but little, as is manifeft, from
the weights employed to overcome the friction and the ſtiffneſs
of the cords, in the cafe of an extremely flow motion. And,
as it appeared from the preceding experiments that the friction
was independent of the velocity, or that it oppoſed the fame
refiſtance to the motion in the different trials for each ex-
periment; it hence follows that the reſiſtance arifing from the
ſtiffneſs of the cord was likewife conftant in the fame trials, and
depended not upon the velocity, at least in any fuch fenfible manner
as to merit our regard in computing the powers of machines.
41. The invariablenefs of the refiftance occafioned by the
ſtiffneſs of cords, under different velocity, appears alfo imme-
diately from the refults compriſed in the 5th column of the
table, which, as before obferved, proves that the motions were
nearly uniformly accelerated. And from this property it fol-
lows, that there is always a conftant part of the weight or
power employed in furmounting the friction and the ſtiffneſs of
the cords.
"Nevertheleſs," adds M. Coulumb, "it muſt be acknow-
ledged, that it is not ftrictly true, that the augmentation of ve-
locity does not augment the refiftance due to the rigidity of
cordage. This augmentation appears eſpecially perceptible
when the cords are ſtretched with weights or by forces that are
under 100 pounds. I have eſtimated, by many trials, that in
fuch caſes a velocity of 8 feet per fecond would increafe by
nearly a pound the reſiſtance occafioned by the ſtiffneſs of our
cord of 30 threads in a yarn : but this augmentation of refiſtance
feems to be a conftant quantity for the fame degree of velocity,
42
MECHANICS.
whatever the tenfion may be; in fuch fort that it ceaſes to be
perceptible under great tenfions, and that there are but very
few circumftances in which it may not be neglected in practice:
this augmentation with regard to the velocity appears, befides,
much greater in new than in old cords, and in tarred cords
than in thoſe which are white or untarred"”
42. M. Coulumb deduces from theſe experiments the follow-
ing general conclufions :
(1.) That with refpect to practice, in all rotatory machines
the ratio of the preffure to the friction may always be ſuppoſed
conftant, and that the influence of the velocity is too ſmall to
need our regard.
(2.) That the refiſtance which must be overcome to bend a
cord over a roller or pulley is repreſented by a formula com-
poſed of two terms; the firft is a conſtant quantity independent
a dr
of the tenſion, and of the form (art. 31.) where a is a con-
T
α
ftant quantity determined by experience, d" is a power of the
diameter d of the cord, and the radius of the roller; the
b dn
fecond term is Q, where b is a conſtant quantity, d, n, and r,
T
as before, and Q the tenfion of the cord. Thus the complete
dn
formula expreffing the ſtiffneſs of the cord is (a+bQ). The
power n varies according to the flexibility of the cord, but is
ufually about 1'7 or 1·8, or the refiftance is nearly proportional
to the fquare of the diameter of the cord: when the cord is
much uſed n decreaſes to 1.5 or even 1.4. The following is a
fummary of reſults.
White
Cord,
Tarred
Cord,
of 30 threads in a yarn
Sof
-15
6
of 30 threads in a yarn
-15
lbs.
dn
a=4.2
•
7
=1°2
=0°2
=6·6.
=2'0
=0.4
dn
-b. 100 = 9°0
= 5°1
=2.2
=11:6
= 5'6
= 24
43. Our knowledge of the nature of the friction of axes, and
ſtiffneſs of cords, though confeffedly very imperfect, may be
introduced into the computation of the power of machines: this
may be illuftrated by an example of a capftan or windlafs,
where the general formula for an equilibrium will be this :
r 2
PR=QR'+
Wit
+d" (a+bQ)
where P reprefents the power, and the other letters as below,
The Capftan, allowing for Friction, &c.
43
The weight to be elevated, is
Q=1000 lbs.
The radius of the axis or pivot, which is of iron, is
r=2 inches.
This axis turns in a box of copper: the radius of the cylinder
about which the cord is rolled, is
R'10 inches.
The arm of the capftan, or the radius, or diftance at which the
men exert their force, is
R=10 feet 120 inches.
=
The pivots are ſuppoſed to have been plaſtered with tallow fome
time, and the inftrument often uſed, till the ratio of the fric-
tion to the preffure is reduced to that of experiment 15 in the
table of article 35. whence we have that ratio, or
ƒ=0'133, and √1+4=7:5351.
ff
The cord is fuppofed tarred, and of 120 threads in a yarn,
which will fupport 12 or 14000 lbs. without breaking. Now
a tarred cord of 30 threads in a yarn requires a conſtant effort
equivalent to 6·6 lbs. to bend it about a roller of 2 inches radius,
and an effort proportional to the tenfion, of 116 lbs. for a quin-
tal, or 116lbs. for 1000 lbs. Here the radius of the cylinder
being 10 inches, we muſt, firſt ſuppofing the cords equal, diminiſh
theſe efforts in the ratio of 10 to 2, viz. make their fum
78
(66+116) for rooo lbs., and (6'6+8x116) for 8000.
And as the cord is of 120 threads in a yarn inftead of 30, we
muft increaſe the laſt reſult, in the ratio of 30 to 120, fo fhall
we have × (6·6+·928)=7477 for the effort which will fur-
mount the ſtiffneſs of the cord, that is
dn
R'
=
2
ΤΟ
(a+bQ)=747°7-
And fince R'10, we have d" (a+bQ)=7477-
2
Thefe values being fubftituted in the general formula it be-
comes
Px 120=(8000 × 10) +
8000X 2
7.5851
+7477.
or,
It will be neceffary therefore to diftribute at the extremities of
the bars of the capftan efforts whofe fum fhall be equivalent to
746.5 lbs.: that is, if a man makes an effort balancing 25 lbs.,
30 men will be required to move the weight of 8000 lbs. Had
there been no friction and were the cords perfectly flexible, the
P=666·6+1.7*577+62·3=746'5 lbs.
8000
force neceffary would have been only or 666 6, lefs than
12
the other by almoſt 80 pounds, a difference which is more than
equivalent to the force of three men. So that in this example
1
MECHANICS.
44
the friction and rigidity of the cord, require an increaſe of be-
tween an 8th and a 9th of the whole power which would other-
wife have been requifite,
This, however, we wish to be received only as an approxima-
tion. The details which have been here entered into will, we
truſt, be found of fome utility in directing the practice, and
may furniſh ſome hints to thoſe who have time and inclina-
tion to adopt other ſeries of well-conducted experiments;
and thus fupply theſe moſt important defiderata in practical
mechanics.
On the Energy of First Movers.
44. The confideration of the abfolute and relative forces of
different kinds of firſt movers is of too great confequence in the
application of mechanics to be entirely omitted in this perform-
ance: we fhall, therefore, prefent the reader with fome ob-
fervations and tables refpecting the chief claffes of powers ufed
to drive machinery, viz. water, air, fteam, gunpowder, and
animal exertion.
Water is generally made to operate upon machines by means
of its momentum when in motion: but it may alſo be uſed,
and that as a very powerful mover, when acting by its preffure
merely. In the theory of hydroftatics (art. 387.) we ex-
plained the principle of the hydroſtatical paradox, in which it
is afferted that any quantity of water or other fluid may be
made to fupport any other quantity or any weight however
great, and indeed to raise the greater weight until it reaches
fuch a height as enfures the equilibrium. Thus in the hydro-
ftatic bellows the weight of a few ounces of water is made to
raiſe ſeveral hundred pounds. And in like manner Otto Gue-
ricke of Magdeburg made a child balance, and even overcome,
the pull exerted by the emperor's fix coach horſes, merely by
fucking the air from beneath a pifton. This great power de-
pends upon the fundamental property of fluids, that they prefs
equally in all directions. Mr. Bramah, an ironmonger in Pic-
cadilly, has lately obtained a patent for a machine acting as a
prefs on this principle of the quaqua verfum preffure of fluids:
A pifton of of an inch diameter forces water into a cylinder
of 12 inches diameter, and by this intervention raiſes the pifton
of the cylinder: fo that a boy acting with a fourth part of his.
ſtrength on the ſmall pifton by means of a lever can raife about
94080 lbs. or 42 tons preffing on the great piſton; the increaſe
of power being as I to 4× 122 or 1 to 2304. This contrivance
will be more minutely explained under the article Bramah's-ma- '
chine, in the alphabetical part of this volume.

First Movers.
45
#
45. As to the effect of water in motion, it will manifeftly depend
upon the quantity of fluid and its velocity jointly. When the
water runs through a notch or an orifice of a regular form fituated
in the bottom or fide of a reſervoir, the quantity difcharged in any
given time may be determined by the rules laid down for thoſe
purpoſes in vol. 1. Book IV. If s² be the area of any plane ex-
poſed to the action of a current of water, and v the velocity per
fecond with which the fluid ſtrikes the plane, then will the force
of the fluid be equivalent to the weight of a volume of water
expreffed by where g repreſents 32% feet, on the fup-
pofition that the water ſtrikes the plane directly: but if the fluid
ftrike the plane obliquely and I reprefent the angle of incid-
ence, the force will be equivalent to the weight of the coluinn
Or, fince a cubic foot of water weighs 62 lbs
22 32
2 g
fin. I.
2
v2 sz
2 g
averd. if v and s be expreffed in feet we fhall have
2
62 ½ v²sk
28
fin.² I =971502 fin. I v² ² lbs. averd. for the equivalent
weight, which becomes barely 971502v's² lbs. when the plane
is directly oppofed to the fluid.
46. In the determination of the velocity of the ſtream it will
be neceffary either to afcertain the height b through which the
water has fallen freely, as from the end of a ſpout, when √2 gh,
or nearly 8 h, will fhew the velocity, h being in feet; or when
the water iſſues through an orifice in the bottom or fide of a
refervoir, to have recourſe to Chap. 1 and 2. Book IV. vol. I.
before referred to. If the ſtream be ample without much fall,
ſuch as muſt neceffarily be applied to move an underſhot wheel
by its impulfe, the power will be determinable from the ve-
locity of the water and the quantity which paffes through the
fection of its bed. Dr. Defaguliers, in his Experimental Phi-
lofophy, vol. II. pa. 419. gives the following eafy method of
afcertaining thefe data: Obferve a place where the banks of the
river are fteep and nearly parallel, fo as to make a kind of
trough, for the water to run through, and by taking the depth
at various places in croffing make a true fection of the river.
Stretch a ftring at right angles over it, and at a ſmall diſtance.
another parallel to the firft. Then take an apple, an orange,
or other ſmall ball, juft fo much lighter than water as to fwim in
it, and throw it into the water above the ftrings. Obferve when
it comes under the firft ftring, by means of a half fecond pen-
dulum, a ftop watch, or any other proper inftrument; and ob-
ferve likewife when it arrives at the ſecond ſtring. By this
means the velocity of the upper furface, which in practice may
46
MECHANICS.

generally be taken for that of the whole, will be obtained. And
the fection of the river at the fecond ſtring must be afcertained
by taking various depths, as before. If this fection be the fame
as the former, it may be taken for the mean ſection: if not,
add both together, and take half the fum for the mean fec-
tion. Then the area of the mean fection in fquare feet being
multiplied by the diſtance between the ftrings in feet, will give
the contents of the water in folid feet, which paffed from one
ftring to the other during the time of obfervation; and this by
the rule of three may be adapted to any other portion of time.
Suppofe, for example, the time were 12", and the hourly expen-
diture of water were required, the proportion would be, as
12": 3600" :: the number of cubic feet between the two
ftrings: the hourly expenditure in cubic feet. If the mere ve-
locity be required with reference to any fixed interval of time,
a fimilar proportion will give it, only obferving to take, inſtead
of the folid content or capacity in the third term, the diſtance
between the two ftrings.
The operation may often be greatly abridged by taking notice
of the arrival of the floating body oppofite two ſtations on the
fhore, eſpecially when it is not convenient to ftretch a ftring
acrofs. An arch of a bridge is a good ftation for an expe-
riment of this kind, becauſe it affords a very regular ſection
and two fixed points of obfervation: and in fome inſtances the
fea practice of heaving the log may be advantageous. Where a
time-piece is not at hand, the obferver may eaſily conftruct a
half-feconds or quarter-feconds pendulum: the former may be
made by fufpending a ſmall round (not flat) button, or other
fpherical weight, by a thread looped over a pin of fuch a length
that the diſtance from the point of ſuſpenſion to the centre of
the weight ſhall be 9.8 inches: the quarter-feconds pendulum
muſt be a fourth of this length. If, by obfervations at ſeveral
ſtations above and below any particular point of the river, the
velocity does not appear to vary, the fection of the river in all
that ſpace may be confidered as uniform; and it will not be
neceffary to determine more than one fection by actual meaſure-
ment.
47. The effect of underſhot and overſhot wheels has been
very variouſly ſtated by different authors; the moſt valuable and
correct obfervations are thofe of Mr. Smeaton, an abftract of
which was given in Chap. 4. Book IV. vol. I. The numerous
practical remarks and experiments related in that chapter and
the ſecond chapter of the fame book, will render it unneceffary
for us now to dwell longer upon the effects of water as a mover
of machinery.
48. AIR is the next natural mover we propofe to confider.
And this like water may be regarded either as at reft, or in mo-
Air as a Mover of Machinery.
41
}
tion. The preffure of the atmoſphere in a medium ſtate is
equivalent to the weight of 14 or 15 lbs. averdupois on a
fquare inch; and this preffure will ſupport, and, by means of a
fucking pump, raife water to the height of about 33 feet; it
fupports mercury in the barometer at the height of 28 to 32
inches.
The denſity of air is, at a medium, about 833 times leſs than
that of water: if we take round numbers and reckon 800 to I
for the ratio of the denfities, and put s² for the ſurface on which
the wind ftrikes, v for the velocity with which it moves, and I
for the angle of incidence, then the force of the wind will be
equal to the weight of a volume of water expreſſed by ·
fin. 2 I='0012144 vs fin. I lbs. averdupois.
2g
I
This formula, however, is only an approximation, and would
lead to confiderable errors when the velocities are great: on
this ſubject we have treated pretty fully in art. 554, &c. Book V.
vol. I. where the tables of Dr. Hutton, Mr. Roufe, &c. are
exhibited: the following is Mr. Roufe's table of velocity and
correſponding force in the form it was originally given by Mr.
Smeaton; but the form in which it is thrown in art. 554 is
more uſeful.

Velocity of the| Perpendi-
Wind.
cular force
on one fquare
Miles] feet in
foot, in
in one
one
averdupois
hour.
fecond.
pounds.
I
1'47
*005
2
293
*020
3
4'40
044
4
5.87
*079
5
7*33-
123
10
14'67
*492
15
22'00
I'107
20
29'34
1'968
25 36.67
3'075
30
44'01
4'429
35
51'34
6.027
40
58.68
7.873
4
45
66.01 9'963
50
73.35
12.300
60
88.02 177715
80
117.36
31'490
100
146.70
49°200
43
MECHANICS.
49. As it is not eaſy to obferve the true velocity of the wind,
and thence determine its force, feveral philofophers have in-
vented inftruments called Anemometers or wind gages, by
which the force of the wind may be aſcertained independent of
its velocity. M. Bouguer contrived a very fimple inftrument
for this purpoſe: it is a hollow tube AABB (fig. 5. pl. I.) in
which a fpiral ſpring CD is fixed, that may be more or lefs
compreffed by a rod FSD paffing through a hole within the
tube at AA. Having obferved to what degree different forces
or given weights are capable of compreffing the ſpiral, put di-
vifions upon the rod in fuch a manner that the mark obſerved
at S in all pofitions of that rod fhall indicate the weight requifite
to force the ſpring into the correſponding pofition CD. After-
wards join perpendicularly to this rod at F a plane furface EFE
of a given area, either greater or lefs, as may be judged proper:
then nothing more is neceffary than to oppoſe this inftrument
to the wind, in order that it may ſtrike the ſurface in the direc-
tions VE, VE, parallel to that of the rod; and the mark at S
will fhew the weight to which the wind is equivalent. It will
then be eaſy to reduce any obferved force to a volume of water
equivalent to it in energy; and ſo in all caſes aſcertain the
nitude of the force which the wind exerts.
mag-
50. The moſt ufual method of applying wind as a mover of
machinery is in the conftruction of windmills for different
purpoſes, in which the wind produces its effect by impulfe upon
the fails. In theſe machines, therefore, whatever varieties there
may be in the internal ſtructure, there are certain rules with
regard to the pofition, fhape, and magnitude of the fails, which
will bring them into the beſt ſtate for the action of the wind,
and the production of uſeful effect. Theſe particulars have
been confidered much at large by Mr. Smeaton: for this purpoſe
he conſtructed a machine of which a particular deſcription is
given in the Philoſophical Tranſactions, vol. 51. By means of
a determinate weight it carried round an axis with an horizontal
arm, upon which were four ſmall moveable fails. Thus the
fails met with a conftant and equable blaſt of air; and as they
moved round, a ftring with a weight affixed to it was wound
about, their axis, and thus fhowed what kind of fize or con-
ftruction of fails anſwered the purpoſe beſt. With this ma-
chine a great number of experiments were made; the reſults
of which were as follow:
(1.) The fails fet at the angle with the axis, propofed as the
beſt by M. Parent and others, viz. 55°, was found to be the
worst proportion of any that was tried.
(2.) When the angle of the fails with the axis was increaſed
from 72° to 75°, the power was augmented in the proportion
Wind as a Mover of Machinery.
49
of 31 to 45; and this is the angle moſt commonly in ufe when
the fails are planes. See art. 547. vol. I.
(3.) Were nothing more requifite than to cauſe the fails to
acquire a certain degree of velocity by the wind, the pofition
recommended by M. Parent would be the beſt. But if the fails
are intended with given dimenfions to produce the greateſt
effects poffible in a given time, we muft, if planes are made
ufe of, confine our angle within the limits of 72 and 75 degrees.
(4.) The variation of a degree or two, when the angle is near
the beft, is but of little confequence.
(5.) When the wind falls upon concave fails it is an advan-
tage to the power of the whole, though each part feparately
taken fhould not be difpofed of to the beſt advantage.
(6.) From ſeveral experiments on a large fcale, Mr. Smeaton
has found the following angles to anfwer as well as any. The
radius is ſuppoſed to be divided into fix parts; and th, reckon-
ing from the centre, is called 1, the extremity being denoted 6.
N°
Angle with
that axis.
72°
Angle with
the plane of
motion.
18°
2
3
71
72
4
5
74
77/1/2
83
19
18 middle
16
121
7 extremity.
(7.) Having thus obtained the beſt method of weathering the
fails, i. e. the moſt advantageous manner in which they can be
placed, our author's next care was to try what advantage could
be derived from an increaſe of ſurface upon the fame radius.
The refult was, that a broader fail requires a larger angle; and
when the fail is broader at the extremity than near the centre,
the figure is more advantageous than that of a parallelogram.
The figure and proportion of enlarged fails, which our author
determines to be moſt advantageous on a large fcale, is that
where the extreme bar is one-third of the radius or whip (as
the workmen call it), and is divided by the whip in the pro-
portion of 3 to 5. The triangular or loading fail is covered
with board from the point downward of its height, the reſt as
uſual with cloth. The angles above mentioned are likewiſe
the moſt proper for enlarged fails; it being found in practice,
that the fails fhould rather be too little than too much expoſed
to the dire& action of the wind.
Some have imagined, that the more fail the greater would be
the power of the windmill, and have therefore propofed to fill up
the whole area; and by making each fail a ſector of an ellipfis,
VOL. II.
50
MECHANICS.
according to M. Patent's method, to intercept the whole cy
linder of wind, in order to produce the greateft effect poffible.
From our author's experiments, however, it appeared, that
when the ſurface of all the fails exceeded ſeven-eights of the area,
the effect was rather diminiſhed than augmented. Hence he
concludes, that when the whole cylinder of wind is intercepted,
it cannot then produce the greateſt effect for want of proper
interſtices to escape.
"It is certainly defirable (fays Mr. Smeaton), that the fails
of windmills ſhould be as fhort as poffible; but it is equally
defirable, that the quantity of cloth fhould be the leaft that
may be, to avoid damage by fudden fqualls of wind. The beft
ftructure, therefore, for large mills, is that where the quantity
of cloth is the greatest in a given circle that can be on this
condition, that the effect holds out in proportion to the quan-
tity of cloth; for otherwife the effect can be augmented in a
given degree by a leffer increaſe of cloth upon a larger radius
than would be required if the cloth was increafed upon the
fame radius."
:
(8.) The ratios between the velocities of windmill fails un-
loaded, and when loaded to their maximum, turned out very
different in different experiments; but the moſt common propor-
tion was as 3 to 2. In general it happened that where the power
was greateft, whether by an enlargement of the furface of the fails
or an increaſed velocity of the wind, the fecond term of the
ratio was diminiſhed.
(9.) The ratios between the leaft load that would ftop the
fails and the maximum with which they would turn, were con-
fined betwixt that of 10 to 8 and 10 to 9; being at a medium
about 10 to 8.3, and 10 to 9, or about 6 to 5; though on the
whole it appeared, that where the angle of the fails or quantity
of cloth was greateft, the ſecond term of the ratio was lefs.
(10.) The velocity of windmill fails, whether unloaded or
loaded, fo as to produce a maximum, is nearly as the velocity`
of the wind, their ſhape and pofition being the fame. On this
fubject Mr. Fergufon remarks, that it is almost incredible to
think with what velocity the tips of the fails move when acted
upon by a moderate wind. He has feveral times counted the
number of revolutions made by the fails in 10 or 15 minutes;
and, from the length of the arms from tip to tip, has computed,
that if an hoop of the fame fize was to run upon plain ground
with an equal velocity, it would go upwards of 30 miles in an
hour.
(11.) The load at the maximum is nearly, but fomewhat leſs
than, as the fquare of the velocity of the wind; the shape and
pofition of the fails being the fame.
Smeaton's Rules for Windmills
51
(12.) The effects of the fame fails at a maximum are nearly,
but fomewhat lefs than, as the cubes of the velocity of the
wind.
(13.) The load of the fame fails at a maximum is nearly as
the fquares, and the effect as the cubes of their number of turns
in a given time.
(14.) When fails are loaded fo as to produce a maximum at
a given velocity, and the velocity of the wind increaſes, the
load continuing the fame; then the increaſe of effect, when
the increaſe of the velocity of the wind is fmall, will be nearly
as the fquares of thefe velocities: but when the velocity of the
wind is double, the effects will be nearly as 10 to 27; and when
the velocities compared are more than double of that where
the given load produces a maximum, the effects increafe nearly
In a fimple ratio of the velocity of the wind. Hence our author
concludes, that windmills, fuch as the different fpecies for
draining water, &c. lofe much of their effect by acting againſt
one invariable oppofition.
(15.) In fails of a fimilar figure and poſition, the number of
turns in a given time will be reciprocally as the radius or length
of the fail.
(16.) The load at a maximum that fails of a fimilar figure and
pofition will overcome, at a given diſtance from the centre of
motion, will be as the cube of the radius.
(17.) The effects of fails of fimilar pofition and figure are as
the fquare of the radius. Hence augmenting the length of the
fail without augmenting the quantity of cloth, does not increaſe
the power; becauſe what is gained by length of the lever is
loft by the flowneſs of the motion. Hence alfo, if the fails are
increafed in length, the breadth remaining the fame the effect
will be as the radius.
(18.) The velocity of the extremities of the Dutch fails, as
well as of the enlarged fails, either unloaded or even when
loaded to a maximum, is confiderably greater than that of the
wind itſelf. This appears plainly from the obſervations of
Mr. Ferguſon, already related, concerning the velocity of fails.
(19.) From many obfervations of the comparative effects of
fails of various kinds, Mr. Smeaton concludes, that the enlarged
fails are fuperior to thofe of the Dutch conſtruction.
(20.) He alfo makes ſeveral juſt remarks upon thoſe wind-
mills which are acted upon by the direct impulfe of the wind
againſt fails fixed to a vertical fhaft: his objections have, we
believe, been juftified in every inftance by the inferior efficacy
of thefe horizontal mills.
"The diſadvantage of horizontal windmills (fays he) does not
confiſt in this, that each fail, when directly oppofed to the wind, is
I 2
£9
MECHANICS.
capable of a lefs power than an oblique one of the fame di-
menſions; but that in an horizontal windmill little more than
one fail can be acting at once: whereas in the common wind-
mill, all the four act together; and therefore, fuppofing each
vane of an horizontal windmill to be of the ſame ſize with that
of a vertical one, it is manifeſt that the power of a vertical mill
will be four times as great as that of an horizontal one, let the
number of vanes be what they will. This difadvantage arifes
from the nature of the thing; but if we confider the further
diſadvantage that arifes from the difficulty of getting the fails
back again against the winds, &c. we need not wonder if this
kind of mill is in reality found to have not above one-eighth or
one-tenth of the power of the common fort; as has appeared
in fome attempts of this kind.”
51. Another firſt mover, of whofe effects it may be proper
to give fome account, is fired gunpowder. Thefe effects are too
violent and fudden to allow of their being applied to many
practical purpoſes (the chief uſe of gunpowder being in the
diſcharge of balls and ſhells from guns and mortars); but they
are fo prodigious and extraordinary, and are fo important in
the art of war, that it may be naturally expected we ſhould
give ſome eſtimate of them in this place.
Now to underſtand the force of gunpowder it must be
confidered that whether it be fired in a vacuum or in air, it
produces by its exploſion a permanently elaſtic fluid: and it
appears from experiment that the elasticity or preffure of the
fluid produced by this firing of gunpowder is, cæteris paribus,
directly as its denfity.
To determine the elaſticity and quantity of this fluid, pro-
duced from the exploſion of a given quantity of gunpowder,
Mr. Robins premifes, that the elafticity increaſes by heat, and
diminiſhes by cold, in the fame manner as that of the air; and
that the denfity of this fluid, and confequently its weight, is the
fame with the weight of an equal bulk of air, having the fame.
elaſticity and the fame temperature. From theſe principles,
and from the experiments by which they are eſtabliſhed (for a
detail of which we must refer to the book itſelf), he concludes
that the fluid produced by the firing of gunpowder is nearly
of the weight of the generating powder itſelf; and that the
volume or bulk of this air or fluid, when expanded to the rarity of
common atmoſpheric air, is about 244 times the bulk of the
faid generating powder.-Count Saluce, in his Mifcel. Phil.
Mathem. Soc. Priv. Taurin. p. 125, makes the proportion as
222 to 1; which he fays agrees with the computation of Meffrs.
Haukſbee, Amontons, and Belidor.
To
Hence it appears, that any quantity of powder fired in any
Strength of Fired Gunpowder.
53
confined ſpace, which it adequately fills, exerts at the inftant
of its explofion againſt the fides of the veſſel containing it, and
the bodies it impels before it, a force at leaft 244 times greater
than the elaſticity of common air, or, which is the fame thing,
than the preffure of the atmoſphere; and this without con-
fidering the great addition arifing from the violent degree of
heat with which it is endued at that time; the quantity of
which augmentation is the next head of Mr. Robins's enquiry.
He determines that the elafticity of the air is augmented in a
proportion fomewhat greater than that of 4 to 1, when heated
to the extremeft heat of red-hot iron; and fuppofing that the
flame of fired gunpowder is not of a lefs degree of heat, in-
creaſing the former number a little more than 4 times, makes
nearly 1000; which fhews that the elafticity of the flame, at the
moment of exploſion, is about Icoo times ftronger than the
elaſticity of common air, or than the preffure of the atmoſphere.
But, from the height of the barometer, it is known that the
preffure of the atmoſphere upon every fquare inch is on a
medium 143 lb; and therefore 1000 times this, or 14750 lb.
is the force or preffure of the flame of gunpowder, at the mo-
ment of exploſion, upon a fquare inch, which is very nearly
equivalent to 6 tons and a half.
This great force, however, diminiſhes as the fluid dilates itſelf,
and in that proportion, viz. in proportion to the ſpace it oc-
cupies, it being only half the ftrength when it occupies a double
ſpace, one-third the ftrength when triple the ſpace, and ſo on.
Mr. Robins further fuppofes the degree of heat above men-
tioned to be a kind of medium heat; but that in the caſe of
large quantities of powder the heat will be higher, and in very
fmall quantities lower; and that therefore in the former cafe
the force will be ſomewhat more, and in the latter fomewhat
lefs, than 1000 times the force of the atmoſphere.
He further found that the ftrength of powder is the fame in
all variations in the density of the atmoſphere: but that the
moiſture of the air has a great effect upon it; for the fame
quantity which in a dry feaſon would diſcharge a bullet with a
velocity of 1700 feet in one fecond, will not in damp weather
give it a velocity of more than 12 or 1300 feet in a fecond, or
even lefs, if the powder be bad, and negligently kept. Robins's
Tracts, vol. 1, p. 101, &c. Further, as there is a certain
quantity of water which, when mixed with powder, will pre-
vent its firing at all, it cannot be doubted but every degree of
moiſture muſt abate the violence of the exploſion; and hence
the effects of damp powder are not difficult to account for.
The velocity of expanſion of the flame of gunpowder, when
fired in a piece of artillery, without either bullet or other body
$4
MECHANICS.
[
before it, is prodigiously great, viz. 7000 feet per fecond, or
upwards, as appears from the experiments of Mr. Robins. But
M. Bernoulli and M. Euler fufpect it is still much greater.
And Dr. Hutton fufpects it may not be leſs, at the moment of
exploſion, than 4 times as much.
It is this prodigious celerity of expanſion of the flame of fired
gunpowder which is its peculiar excellence, and the circum-
ftance in which it ſo eminently furpaffes all other inventions,
either ancient or modern: for as to the momentum of theſe
projectiles only, many of the warlike machines of the ancients.
produced this in a degree far furpaffing that of our heaviest
cannon fhot or fhells; but the great celerity given to theſe
bodies cannot be approached with facility by any other means
than the exploſion of powder.
52. Since the important invention of the Steam-engine
another ſpecies of firft movers has come under the confideration
of the mechanical inveſtigator, namely, fuch as ariſe from the
volatiliſation of different fluids. Of theſe the one moſt com,
monly choſen is the STEAM raiſed from hot water, which is an
elaſtic fluid, and which when raiſed with the ordinary heat of
boiling water is almoſt 3000 times rarer than water, or more than
3 times rarer than air, and then has its elaſticity equal to that of
the common atmoſpheric air: by great heat it has been found
that the ſteam may be expanded into 14000 times the ſpace of
water, and then exerts a force of nearly 5 times the preffure of
the atmoſphere: and there is no reaſon to ſuppoſe this is the
limit: indeed fome accidents which have happened prove clearly
that the elaſtic force of fteam may at leaft equal that of gun-
powder.
The obfervations on the different degrees of temperature
acquired by water in boiling, under different preffures of the
atmoſphere, and the formation of the vapour from water under
the receiver of an air-pump, when with the common tem-
peratures the preffure is diminiſhed to a certain degree, fhew
clearly that the expanfive force of vapour or fteam is different
in the different temperatures, and that in general it increaſes in
a variable ratio as the temperature is raifed. Previous to de-
fcribing the method which has been adopted to meaſure the
force of fteam under different temperatures, it will be proper to
deſcribe briefly the method by which the Chemifts account for
the production of aeriform fluids.
53. The term Caloric is uſed to denote the cauſe, whatever
it may be, of heat, and of the phenomena which accompany
heat: it is now almoft univerfally admitted to be a highly elaſtic
fluid. Every body is, according to its nature, capable of con-
taining under a given volume a certain quantity of caloric,
Elaftic Force of Steam.
$5
LA
either greater or lefs: this property was firft obferved by Dr.
Black, and the Engliſh chemiſts deſignated it by the term Ca-
pacity of a body to contain the matter of heat. Profeffor Wilcke
and M. Lavoifier firſt made ufe of the term fpecific caloric, de-
noting by it the quantity of caloric reſpectively neceffary to
elevate to the fame number of degrees the temperature of fe-
veral bodies of equal weight.
Subſtances volatiliſed and reduced to gas or aeriform fluids,
are nothing elſe than ordinary folid or fluid bodies which by
fome circumſtance are found fuperabundantly combined with
caloric, in fuch a manner that the conftituent particles of thefe
bodies are feparated the one from the other, by a quantity of
ambient caloric much more confiderable than that which fur-
rounds the fame particles in the natural ſtate of the bodies.
The extreme elafticity of the caloric the effect of which is aug-
mented by its condenfation, and the weakening of the reci-
procal attraction or of the coheſion of the particles of the bodies
(a weakening or diminution produced by the increaſed diſtance
of thoſe particles) concur to diminiſh the density of the bodies
in ſuch a manner that they become reduced to an aeriform
state.
54. As to the elaſticity of gaſeous fluids thus formed, it ap-
pears in great meaſure to be produced by the elaſticity of ca-
loric itſelf, which, when bodies are reduced to the gafeous ſtate,
occupy a very great part of their volume. This eminent elaſti-
city of caloric tends continually to produce expanfion; on the
other hand, this fluid, by a particular deftination of nature, is
more or lefs diffeminated between the moleculæ of all bodies,
in fuch fort that we may fay with M. Lavoifier that even in the
ſolid ſtate theſe moleculæ do not touch, but, as it were, fwim
in the caloric at a certain diſtance from each other. There
muſt, therefore, be a perpetual conteſt between the expanſive
force of caloric which tends to diffeminate the moleculæ, and
the coheſive attraction of the molecule which tends to join
them together. From the reciprocal intenfity of theſe two
powers refults the folid and liquid ftates of bodies: thus, water
only differs from ice by the greater or lefs condenfation of ca-
loric, which permits more or lefs of the molecule of the liquid
to yield to the effect of their attraction or reciprocal coheſion.
When fubftances pafs from the liquid to the aeriform ſtate,
there is a third power to combine with the expanfive effort of
caloric, and the aggregative or attractive effort of the mole-
cula; namely, the preffure of the atmoſphere, or of any elaftic
fluid whatever which compreffes the fluid, and oppofes itfelf to
the ſeparation of its parts. This third power has a certain in-
Auence alfo upon the paffage from the folid to the fluid ſtate,
:
56
MECHANICS.
but it is moſt frequently (in this cafe) very ſmall, and even
evanefcent in compariſon of the refiftance arifing from the
mutual coheſion of the molecule. The contrary effect has
place in the courſe of the paffage from the liquid to the gafeous
or aeriform ſtate; the coheſion of the fluid molecule being ex-
tremely ſmall, the elaſticity of the caloric has ſcarcely any thing
to furmount to produce volatilisation befides the preffure of the
atmoſphere, or gas which actually compreffes it.
•
55. Hence it reſults that the fame liquid under different
preffures ought to volatilife at different temperatures. M.
Lavoifier proved the truth of this refult, by placing ether under
the receiver of an air-pump and producing volatiliſation ſolely
by taking off a part of the preffure of the atmoſphere. See
Chymie, tome I. pa. 9. And we know by many experiments of
M. Deluc and others, that water boils the more fpeedily as it
is lefs preffed by the weight of the atmoſphere.
Lavoifier notices a curious confequence of what has been
here faid; which is, that if our planet revolved upon its axis
with fuch a velocity as to leffen the preffure of the atmoſphere,
or if the temperature of the air were raiſed, then feveral fluids
which we now fee under a liquid ftate would only exiſt in the
aeriform ſtate; for example, if under the temperature of fum-
mer the preffure of the atmoſphere were only equivalent to 20
or 24 inches of the barometrical tube, that preffure would not
retain ether in the fluid ftate, it would be changed into gas;
and the like would happen, if while the preffure of the air was
equivalent to 28 or 30 inches of the mercury the habitual tem-
perature were 105 or 110 degrees on Fahrenheit's fcale.
56. The principles which have been here exhibited are fuf-
ficient for the underſtanding of all which relates to the action
of water or other fluids reduced to vapour. Now, it has ap-
peared from frequent experiments that water heated in common
air volatiliſes at 80° of Reaumur's thermometer, or 212° of
Fahrenheit's, the height of the barometer being 28 French, or
29.0 Engliſh inches: and fpirits of wine under a like preffure
volatilifes at between 63° and 64° of Reaumur, or nearly 175°
of Fahrenheit. The expanfive force of the vapour muft, there-
fore, in both theſe cafes, according to the principles juft ex-
plained, be meaſured by a column of mercury of 28 French,
or 29.9 Engliſh inches, in like manner as fuch a column meaſures
the preffure of the atmoſphere, or the elafticity of common air.
And at any more elevated temperatures the elaſtic force of the
vapour will furpaſs the preffure of the atmoſphere by a quantity
which has a certain relation with the excefs of the temperaturę
above thoſe juſt ſtated.
57. Till lately there was wanting on this important fubject a
Elaftic Force of Steam.
ST
feries of exact and direct experiments by means of which, having
given the temperature of the heated fluid, the expanfive force of
the ſteam rifing from it might be known, and vicè verfa. There
was likewife wanting an analytical theorem expreffing the re-
lation between the temperature of the heated fluid and the
preffure with which the force of the fteam was in equilibrio.
Theſe defiderata have, however, been lately fupplied by M.
Bettancourt, an ingenious Spaniſh philoſopher, after a method
which we ſhall now conciſely explain.
58. M. Bettancourt's apparatus confifts of a copper veffel or
boiler, with its cover firmly foldered on: this cover has three
orifices which cloſe up with fcrews: at the firſt the water or
other fluid is put in and out; through the fecond paffes the
ſtem of a thermometer which has the whole of its ſcale or
gra-
duations above the veffel, and its ball within, where it is im-
merfed either in the fluid or in the fteam according to the dif-
ferent circumſtances; through the third hole paffes a tube,
making a communication between the cavity of the boiler and
one branch of an inverted fyphon, which contains mercury,
and acts as a barometer for meaſuring the preffure of the elaſtic
vapour within the boiler. In the fide of the veffel there is a
fourth hole into which is inſerted a tube with a turncock, mak-
ing a communication with the receiver of an air-pump, in order
to extract the air from the boiler and to prevent its return.
The apparatus being prepared in good order, and diftilled
water introduced into the boiler at the firſt hole, and then ſtop-
ped, as well as the end of the inverted fyphon or barometer,
M. Bettancourt ſurrounded the boiler with ice, to lower the
temperature of the water to the freezing point, and then, hav-
ing extracted all the air from the boiler by means of the air-
pump, the difference between the columns of mercury in the
two branches of the barometer ſhewed the meaſure of the elaſtic
force of the vapour arifing from the water in that temperature.
Then lighting the fire below the boiler, he gradually raiſed the
temperature of the water from o to 110° of Reaumur's ther-
mometer, that is, from 32° to 279° of Fahrenheit's thermo-
meter; and for each degree of elevation in the temperature he
obſerved the height of the mercurial column which meaſured
the elaſticity or preffure of the vapour.
Thefe experiments were repeated various times and with dif
ferent quantities of water in the veffel; their refults were ar-
ranged in different columns for the fake of compariſon, and it
appeared that the preffures for different temperatures agreed
very nearly, however much the quantity of fluid in the veffel
was varied. It was alſo ſeen that the increaſe in the expanſive
force of the vapour is at firſt very flow; but increaſes gradually
\
•
58
MECHANICS.
unto the higher temperatures, where the increaſe becomes very
rapid, as will be obvious from an examination of the tables in
fome of the following pages.
59. To exprefs the relation between the degrees of tem-
perature of the vapour and its elaftic force, this philofopher
employs a method fuggeſted by M. Prony, which confifts in
imagining the heights of the columns of mercury meaſuring the
expanfive force to reprefent the ordinates of a curve, and the
degrees of heat the correfponding abfciffe of that curve; making
the ordinates equal to the fum of feveral logarithmic ones which
contain two indeterminates, and afcertaining thefe quantities in
fuch manner that the curve may agree with a tolerable number
of obfervations taken throughout the whole extent of the change
of temperature, from the lowest to the higheſt extreme of the
experiments. Then a formula or equation to a curve is in-
veſtigated, and when the curve correfponding to that equation
is conftructed, if it coincide (with the exception of a few
trifling anomalies) with the curve conftructed by the refults of
the experiments, the formula may be looked upon as correct,
and furniſhing a true analytical repreſentation of the pheno-
This was done by M. Bettancourt, and the curve con-
ftructed from his equation has a point of inflexion at about the
102° of Reaumur, as it ought to have, becauſe the ſecond dif-
ferences of the barometrical meaſures of the elaftic force be-
came negative at that temperature.
mena.
of
60. In a fimilar manner M. Bettancourt made experiments on
the ſtrength of the vapour from alcohol or fpirit of wine; con-
ftructing the curve and deducing the requifite analytical formula.
This curve had likewife a point of inflexion at about 88 of
Reaumur, the fecond differences in the table of barometrical
meaſures becoming then negative. From a compariſon of the
experiments on the vapour of water with thoſe on the vapour
alcohol, a remarkable conclufion was derived: for it appeared
that, after the first 20° of Reaumur, the ftrength of the va-
pour of fpirit of wine was to that of the vapour of water,
nearly in the fame conflant ratio of 23 to 10, or 7 to 3, for
any one and the fame degree of heat. Thus, at the tempe-
rature of 40° of Reaumur, the strength of the fteam of water
is meaſured by 2.9711 Paris inches in the barometer, and that
of vapour of alcohol by 6·9770, the latter being about 24 times
the former.
61. The equations to the curve of temperature and preffure,
denoting the relation between the abfciffe and ordinates, or be-
tween the temperature and the elafticity of the vapour, as given
by M. Bettancourt, were of the following form.
Elaftic Force of Steam.
39
:
1. For water, y
=
pe tax µé' táx
μtax μétáx
e
σ
e
**
o'x - g'
te
dx-g'
te
- A.
2. - alcohol, y=e te
Where y repreſents the height of the column of mercury which
meaſures the expanfive force, x the correfponding degrees of
Reaumur's thermometer, and the other letters certain values
which are affigned to them in the inveſtigation.
62. But M. Prony, in the 2d volume of his Architecture Hy-
draulique, has thrown theſe equations into a rather more con-
venient form, though analogous to thofe of Bettancourt. His
formula for the vapour of water is this,
X
y = μ, §, " + ", c₁ * + * + LIV *
///
The method which he followed confifted in fatisfying the reſults
between o° and 80°, by means of the two firft terms, and to
interpolate by means of the other two, the differences between
the obferved values, and thoſe computed by the two firſt terms,
from 80° up to 110°. In this manner he fucceeded to exprefs
fo exactly the obſervations in their whole extent, that the curves
of the calculus and the experiments were only diſtinguiſhable
the one from the other by fuch little anomalies, as were ma-
nifeftly the effect of fome trifling though inevitable errors in
the obſervations, and in the graduations of the ſcales in the ap-
paratus. He afterwards employed an equation of three terms,
giving to the different coefficients the following values:
P₁ =1'172805
{₁ = 1'047773
Lui
μ₁ = -0.00000072460407
де
#11
1*028189
+0·8648188803
−0·8648181057
• log. g, =0·0692259
log.
00202661
log.P00120736
log.
7-8601007
•
log.
μ,
T9369271
log.
1-9369248
2,
Subſtituting theſe ſeveral values in the equation
y = μ, §," + μ, §,, " + 1,
it fatisfies not only the numbers employed in its formation, but
all the intermediate obfervations, as may be concluded from the
following table, which exhibits to every 10 degrees of Reau-
mur's thermometer the barometrical reſults both of obſervation .
and the calculus.
40
MECHANICS.

Tempe-
Preffures given by
Ano-
rature.
Experim. Calculus.
malies.
O
O'00 in.
0'00 in.
o'oo in.
ΙΟ
0.15
0°24
20
0.65
0.69
+0:09
+0.04
30
1.52
1°51
Ο ΟΙ
40
2.92
2.95
+0·03
50
5'35
5'42
+0.07
бо
9'95
9.62
-0.33
70
16.90
16.57
-0.33
80
28.00
27'92
-0·08
90
46.40
45.87
-0°53
100
71.80
7194
+0.14
IIO
98.00
98.36
+0:36
The anomalies are generally much more minute than in the
formulæ of four terms: we may therefore regard the equation
juft preceding the table, which is more fimple than that of Bet-
tancourt, as repreſenting the phenomena and meaſuring the
effects of the expanfive force of the ſteam of water with all de-
firable accuracy. M. Prony remarks, that the fmallneſs of the
coefficient, will allow the term p, pa to be neglected in reckon-
ing between 0 and 80°; and thus from the temperature of ice
up to that of boiling water, the equation of two terms alone
will fuffice, that is to fay • ;=μ,, &₁, x + μ,
" "
".
63. M. Prony's equation for the vapour of alcohol compriſes
5 terms originally: but in moft cafes three of thoſe terms will
give refults fufficiently accurate. The numeral values of the
coefficients are as below:
g, = 1'11424
P₁ = 1'05714
} = 0*79943
file,
0.0021293
μ, +0.9116186
ار صلاح
P₁ =+ 0·2097778
μιν
H₁ == 1'1192671
log. f
log. f
0.04697771
=0'02413079
log.
=
T9027776
log.μ,
3-3282330
log. u,,
19598132
log.
M
13217595
Theſe numbers cauſe the experiments and calculus to co-
incide very nearly, when introduced into the equation
y = μ, ex + ~,, §,,x +μ,,, ļ,, * +μ...
ད་•
The magnitude of the anomalies will be feen by inſpecting
the following table.
Elafticity of Vapour of Water and Alcohol.
61

Preffures given by
Tempe-
rature.
Experim. Calculus.
Ano-
malies.
•
o'o. in.
o'co in.
0'00
10
0'47
0'45
-0'02
20
1'52
1'56
+0:04
30
3'49
3'54.
+0:05
40
6.90
6.97
+0.07
50
13.05
12.93
O'12
бо
23.65
23.05
-0.50
70 39°30 39'31
+ooi
80
63.80
64.35
+0.55
90 98.00
98.28
+0.28
Thus the formula for the vapour of ſpirit of wine is found as
fimple as that for the vapour of water, without ceafing to re-
preſent the experiments with all defirable exactnefs. But more
than this, we may retrench one of the variable terms; for in
the first degree has no greater value than o 18, and
μ,,, Bui
when x is 2, 3, or any other pofitive value, this third term may
be fafely neglected. The equation therefore is reduced to
y = μ, gx + μ, §,,x +μiv;
a form much more fimple than Bettancourt's original equation,
and indeed more fimple than Prony's improved equation for the
vapour of water.
64. To fave the trouble of inveftigating the ſtrength of the
vapour by theſe formula for every ſeparate cafe that may occur,
we add a table (calculated from theſe principles) in which the
ftrength of the vapour both of water and of fpirit of wine is
fhewn for every degree of Reaumur's thermometer up to 110°,
or for every 24 degrees of Fahrenheit, from 32 to 280°: the
ſtrengths are expreffed, not in Engliſh or in French inches upon
the barometer, but in terms whofe unit is the medium preffure
of the atmoſphere, fuppofing that medium equivalent to 29′9
Engliſh, or 28 French inches of mercury. The preffure upon
a fquare inch in pounds averdupois correfponding to any tem-
perature may be found by multiplying the correfponding num-
ber taken from the table by 14'75 and the preffure for any in-
termediate degree of Fahrenheit may be found pretty nearly,
by proportioning, as is uſual in tables of Logarithms, &c.
62
MECHANICS.

Pressure in terms of At-
Pressure in terms of
Degrees
of
Thermometer.
mospheric Pressure.
Vapour
Vapour
Degrees
of
Thermometer.
Atmospheric Pressure.
Vapour Vapour
of
of
of
of
Reau. Falır.
Water.
Alcohol.
Reau. Fabr.
Water.
Alcohol.
I
Her✡ 5g 20 a
2
3
4
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361
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Vapour of Water and Alcohol.
63
I
r
- Several curious and in fome refpects uſeful confequences
might be deduced from theſe experiments and theorems. M.
Bettancourt fhews for inftance, that the effect of ſteam engines
muft, in general, be greater in winter than in fummer, owing
to the different degrees of temperature in the water of injection.
And from the greatly ſuperior ſtrength of the vapour of fpirit
of wine over that of water, he argues that, by trying other
fluids, fome may be found, not very expenfive, whofe vapour
may be fo much stronger than that of water, with the fame
degree of heat, that it may be fubftituted inftead of water in
the boilers of ſteam engines, to the great faving in the expence
of fuel: nay, he even aflerts, that fpirit of wine itſelf might
thus be employed in a machine of a particular conftruction,
which, with the fame quantity of fuel, and without any in-
creaſe of expence in other things, fhall produce an effect far
fuperior to what is obtained from the fteam of water. Another
ufe of theſe reſearches fuggefted by M. Bettancourt is, to mea-
fure the height of mountains by means of a thermometer im-
merſed in boiling water; which he thinks may be done with a
preciſion equal, if not fuperior, to that of the barometer. But
this, being foreign to our preſent enquiries, cannot be entered
upon here: a compariſon of the refults of this method with
fome deduced from the more cuftomary procefs may be feen in
Dr. Hutton's Dictionary, vol. II. pa, 756, to which fuch as
are defirous of further information on this point are referred.
65. Our ingenious countryman Mr. Dalton, of Mancheſter,
is of opinion that M. Bettancourt's deductions are not quite ac-
curate. His chief error confifls in having affumed the force of
vapour from water of 32° (Fahrenheit) to be nothing; which
makes his numbers effentially wrong at that point and in all the
lower parts of the ſcale: and in the higher part, or that which
is above 212°, the force is determined too much; owing, as
Mr. Dalton apprehends, to a quantity of air, which being dif
engaged from the water by heat and mixing with the ſteam, in-
creaſes the clafticity.
Mr. Dalton's first experiments with ſpirit of wine led him
to adopt the fame conclufion as M. Bettancourt, with refpect to
the conftant ratio between the force of the vapour from this
fpirit and that from water and inferred the fame with regard
to the vapour from other fluids. But, on purſuing the ſubject,
he concluded that this principle was not true, either with re-
ſpect to ſpirit of wine or any other liquid. His experiments
upon fix different liquids agree in eſtabliſhing as a general law,
That the variation of the force of vapour from all liquids is the
* fame for the fame variation of temperature, reckoning from vapour
"of any given force: thus, affuming a force equal to thirty inches
1
1
**
MECHANICS.
" of mercury as the ftandard, it being the force of vapour from
any liquid boiling in the open air, we find aqueous vapour
lofes half its force by a diminution of 30 degrees of tem-
હૃદ
"perature: fo does the vapour of any other liquid loſe half its
"force by diminiſhing its temperature 30 degrees below that
" in which it boils; and the like for any other increment or de-
"crement of heat. This being the cafe, it becomes unneceffary
"to give diſtinct tables of the force of vapour from different
liquids, as one and the fame table is fufficient for all.”
The experiments on which this conclufion refts, are related
in the fifth volume of the Manchester Memoirs: they may alfo
Be feen in the 6th volume of the New Series of Mr. Nicholſon's
Journal. Mr. Dalton has calculated a table of the force of
vapour of water from the temperature of 40° below zero of Fah-
renheit, to 325° above it. From this table we have extracted the
following; in which we have, as before, reduced the force to
the medium preffure of the atmoſphere for the meaſuring unit,
that the ſmall differences in the reſults of the Engliſh and the
Spaniſh philofopher may be the more readily traced.

Tempe-Force of
rature aqueous
Tempe- Force of
rature aqueous
on Fahr. Vapour. on Fahr. Vapour.
80°
*0333
212° 1'000
୨ଦ
*0453
220
1*166
100
·0620
230
1.391
110
*0843
240
1·655
120
'II10
250
I'940
130
1446
260
2.257
140
*1913
270
2.595
150
*2473
280
2.958
160
'3153
290
3.337
170
*4043
300
3°727
180
:
·5050
310
4'117
190
•6333
315 4'309
200 *7880
320 4'500
21@
*9613
325
4.690
66. There remains for us to confider another kind of mover
of machinery, which is ANIMAL EXERTION, and which is of
fo fluctuating a nature that it is not eaſy to ſubject it to any
eftimate. Phyfical caufes muft affect both the magnitude and
duration of the efforts either of man or beaſt, and beſides this,

Animal Strength-Men.
65
the ftrength of man is confiderably influenced by his moral
habits. The various combinations of theſe different cauſes have
occafioned a variety of eſtimates of animal labour to be ad-
vanced by different authors.
In the first volume of this work (art. 378.) we fſtated the
average force of a man at reft to be 70 lbs., and his utmoſt
walking velocity when unloaded to be about 6 feet per fecond;
and we thence inferred that a man would produce the greateſt
momentum when drawing 31 lbs. along a horizontal plane
with a velocity of 2 feet per fecond. But this is not the moſt
advantageous way of applying human ſtrength.
67. Dr. Defaguliers afferts, that a man can raife of water or
any other weight about 550 lbs., or one hogfhead (weight of
the veffel included), 10 feet high in a minute: this ftatement,
though he ſays it will hold good for 6 hours, appears from his
own facts to be too high; and is certainly fuch as could not be
continued one day after another. Mr. Smeaton confiders this
work as the effort of haſte or diſtreſs; and reports that 6 good
Engliſh labourers will be required to raiſe 21141 folid feet of
fea water to the height of four feet in four hours: in this cafe
the men will raiſe a very little more than 6 cubic feet of freſh
water each to the height of 10 feet in a minute. Now the
hogfhead containing about 84 cubic feet, Smeaton's` allowance.
of work proves leſs than that of Defaguliers in the ratio of 6 to
82 or 3 to 44. And as his good English labourers who can
work at this rate are eſtimated by him to be equal to a double
fet of common men picked up at random, it ſeems proper to
ſtate that, with the probabilities of voluntary interruption, and
other incidents, a man's work for feveral fucceffive days ought
not to be valued at more than half a hogfhead raiſed 10 feet
high in a minute. Smeaton likewife ftates, that 2 ordinary
horfes will do the work in three hours and twenty minutes,
which amounts to little more than two hogfheads and a half
raiſed 10 feet high in a minute. So that, if theſe ſtatements be
accurate, one horſe will do the work of five men.
68. Mr. Emerſon affirms, that a man of ordinary ftrength
turning a roller by the handle can act for a whole day againſt
a refiſtance equal to 30 pounds weight; and if he works 10
hours a day he will raife a weight of 30 lbs. through 34 feet in
a fecond of time; or, if the weight be greater, he will raife it
to a proportionally lefs height. If two men work at a windlafs
or roller, they can more eafily draw up 70 lbs. than one man
can 30 lbs.; provided the elbow of one of the handles be at
right angles to that of the other. Men uſed to bear loads, fuch
as porters, will carry from 150 lbs. to 200 or 250 lbs. according
to their ſtrength. A man cannot well draw more than 70 lbs.
VOL. II.
F
66
MECHANICS.
or 80 lbs. horizontally: and he cannot thruft with a greater
force acting horizontally at the height of his ſhoulders than 27
or 30 lbs. But one of the moſt advantageous ways in which a
man can exert his force is to fit and pull towards him nearly
horizontally, as in the action of rowing.
69. M. Coulumb communicated to the French National
Inſtitute the refults of various experiments on the quantity of
action which men can afford by their daily work, according to
the different manners in which they employ their ftrength. In
the firſt place he examined the quantity of action which men
can produce when, during a day, they mount a fet of ſteps or
tairs, either with or without a burthen. He found that the
quantity of action of a man who mounts without a burthen,
having only his own body to raiſe, is double that of a man
loaded with a weight of 68 kilogrammes, or 223 lbs. aver-
dupois*, both continuing at work for a day. Hence it appears
how much, with equal fatigue and time, the total or abfolute
effort may obtain different values by varying the combinations
of effort and velocity.
But the word effect here denotes the total quantity of labour
employed to raife, not only the burthen, but the man himſelf
and, as Coulumb obferves, what is of the greateſt importance
to confider is the uſeful effect, that is to fay, the total effect, de-
ducting the value which reprefents the transference of the
weight of the man's body. This total effect is the greateſt
poffible when the man afcends without a burthen; but the
useful effect is then nothing: it is alfo nothing if the man be fa
much loaded as to be ſcarcely capable of moving: and confe-
quently there exifts between thefe two limits a value of the
load fuch that the uſeful effect is a maximum. M. Coulumb
fuppofes that the lofs of quantity of action is proportional to
the load (an hypothefis which experience confirms), whence he
obtains an equation which, treated according to the rules of
maxima and minima, gives 53 kilogrammes (1734 lbs. averd.)
for the weight with which the man ought to be loaded, in order
to produce during one day, by afcending ftairs, the greateſt
uſeful effect: the quantity of action which reſults from this
determination has for its value 56 kilogrammes (1833 lbs. averd.)
raiſed through one kilometre, or nearly 1094 yards. But this
method of working is attended with a lofs of three-fourths of
the total action of men, and conſequently coſts four times as
much as work in which, after having mounted a fet of ſteps
without any burthen, the man fhould ſuffer himſelf to fall by
any means, ſo as to raiſe a weight nearly equal to that of his
own body.
* The kilogramme is 22966 grs. =
3°28 lbs. averd.
Animal Strength—Men.
67
►
From an examination of the work of men walking on a ho-
rizontal path, with or without a load, M. Coulumb concludes
that the greateſt quantity of action takes place when the men
walk being loaded; and is to that of men walking under a
load of 58 kilogrammes (190 lbs. averd.) nearly as 7 to 4.
The weight which a man ought to carry in order to produce
the greateſt uſeful effect, namely, that effect in which the quan-
tity of action relative to the carrying his own weight is de-
ducted from the total effect, is 50'4 kilogrammes, or 165.3 lbs.
averdupois.
There is a particular caſe which always obtains with reſpect
to burthens carried in towns, viz. that in which the men, after
having carried their load, return unloaded for a new burthen.
The weight they ſhould carry in this cafe, to produce the greateſt
effect, is 61.25 kilogrammes (2007 lbs. averd.). The quantity
of uſeful action in this cafe compared with that of a man who
walks freely and without a load is nearly as 1 to 5, or, in other
words, he employs to pure lofs of his power. By .caufing a
man to mount a fet of ſteps freely and without burthen, his
quantity of action is at leaſt double of what he affords in any
other method of employing his ftrength.
When men labour in cultivating the ground, the whole quan-
tity afforded by one during a day amounts to 100 kilogrammes
elevated to one kilometer, that is, 328 lbs. raiſed 1094 yards.
M. Coulumb comparing this work with that of men employed
to carry burthens up an aſcent of ſteps, or at the pile-engine,
finds a lofs of about part only of the quantity of action
which may be neglected in refearches of this kind.
20
In eftimating mean refults we ſhould not determine from
experiments of ſhort duration, nor ſhould we make any de-
ductions from the exertions of men of more than ordinary
.ftrength. The mean reſults have likewiſe a relation to climate.
"I have cauſed," fays M. Coulumb, "extenfive works to be
executed by the troops at Martinico, where the thermometer
(of Reaumur) is feldom lower than 20° (77° of Fahrenheit).
Ì have executed works of the fame kind by the troops in
France: and I can affirm that under the fourteenth degree of
latitude, where men are almoſt always covered with perfpira-
tion, they are not capable of performing half the work they
could perform in our climate*, Bulletin de la Soc. Philomath,
No. 16.
* In the preceding account of the effects of human exertion, fince the
profeſſed object was to ſtate the mean refults of regular and uniform la-
bour, we have taken no notice either of feats of extraordináry ſtrength,
or of ſuch as were in appearance fuch, while in reality they were the ef-
fect of contrivance and ſkill, and might have been performed by almoſt
F 2
1
65
MECHANICS.
70. Among quadrupeds the moſt uſeful as a firſt mover of
machinery is the horse. The ftrength of this animal is pro-
any men who had fufficient knowledge of the fubject to exert their
ſtrength under fimilar circumſtances. But as it may be expected that
fome notice ſhould be taken of fuch matters, we fhall throw into this
note a few remarks which have formerly been made in reference to them.
M. de la Hire, in an Examination of the Force of Men, given in the Me-
moirs of the Academy of Sciences for 1699, fays, "There are men
whofe fpirits flow fo abundantly and ſo ſwiftly into their muſcles, that
they exert three or four times more ftrength than others do; and this
ſeems to me to be the natural reaſon of the ſurpriſing ſtrength that we
fee in ſome men who carry and raiſe weights which two or three ordinary
men can hardly ſuſtain, though theſe men be ſometimes but of a moderate
ftature, and rather appear weak than ftrong. There was a man in this
country a little while ago, who would carry a very large anvil, and of
whom were reported ſeveral wonderful feats of ftrength. But I ſaw an-
other at Venice, who was but a lad, and did not ſeem able to carry above
40 or 50 lbs. with all poffible advantages; yet this young fellow, ftanding
upon a table, raiſed from the earth, and fuftained off the ground, an aſs,
by means of a broad girt, which, going under the creature's belly, was
hung upon two hooks that were faſtened to a plat of ſmall cords coming
down in treffes from the hair on each fide of the lad's head, which were
in no great quantity. And all this great force depended only upon the muſ-
cles of the shoulders and thoſe of the loins: for he ſtooped at firft whilft the
hooks were faſtened to the girt, and then raiſed himſelf, and lifted up the
afs from the ground, bearing with his hands upon his knees. He raiſed
alſo in the fame manner other weights that ſeemed heavier, and uſed to
fay he did with more eaſe, becauſe the afs kicked and ſtruggled when
firft lifted from the ground."
Dr. Defaguliers, in fome annotations upon De la Hire's paper, fays,
"What he attributes here to the muscles of the loins was really per-
formed by the extenfors of the legs; for the young man's ftooping with
his hands upon his knees was not with his body forwards and his knees
ftiff, but his body upright and his knees bent, ſo as to bring the two
cords with which he lifted to be in the fame plane with his ancles and
the heads of his thigh bones; by which means the line of direction of
the man and the whole weight came between the ſtrongeſt part of his two
feet, which are the fupports: then as he extended his legs he raiſed him-
felf, without changing the line of direction. That this muſt have been
the manner I am pretty well affured of, by not only obſerving thoſe that
perform ſuch feats, but having often tried it myſelf. As for the muſcles
of the loins, they are incapable of that ſtrain, being above 6 times weaker
than the extenfors of the legs; at least I found them fo in myſelf.
"About the year 1716, having the honour of fhewing a great many
experiments to his late majefty king George the firft, his majefty was
defirous to know whether there was any fallacy in thofe feats of strength
that had been fhewn half a year before, by a man, who feemed by his
make to be no ftronger than other men: upon this I had a frame of
wood made to ftand in (and to reft my hands upon), and with a girdle
and chain lifted an iron cylinder made uſe of to roll the garden, fuftain-
ing it eaſily when once it was up. Some noblemen and gentlemen who
were preſent tried the experiment afterwards, and lifted the roller; fome
with more eafe, and fome with more difficulty, than I had done. This
roller weighed 1900lbs. as the gardener told us. Afterwards I tried to
lift 300 lbs. with my hands, (viz. two pails with 150 lbs. of quickfilyer
Animal Strength—Horfes.
€9
bably about fix times that of a man. Defaguliers ſtates the
proportion as 5 to 1; coinciding with the deductions of Smea-
in each), which I did indeed raiſe from the ground, but ſtrained my back
fo as to feel it three or four days: which fhews that, in the fame
perſon, the muſcles of the loins (which exerted their force in this laſt
experiment) are more then fix times weaker than the extenfors of the
legs: for I felt no inconveniency from raifing the iron roller."
During the time occupied in printing the fecond volume of Dr.
Defaguliers's Philoſophy, a man of great natural ſtrength exhibited him-
felf in London: of this man the doctor gives an account, from which the
following is extracted:
"Thomas Topham, born in London, and now about 31 years of age,
five feet ten inches high, with mufcles very hard and prominent, was
brought up a carpenter, which trade he practiſed till within theſe fix or
feven years that he has fhewed feats of ftrength: but he is entirely igno-
rant of any art to make his ſtrength more ſurpriſing. Nay, fometimes he
does things which become more difficult by his difadvantageous fituation;
attempting, and often doing, what he hears other ſtrong men have done,
without making ufe of the fame advantages.
"About fix years ago he pulled againſt a horfe, fitting upon the
ground with his feet againſt two ſtumps driven into the ground, but
without the advantages which might have been attained by placing him-
ſelf in a proper fituation; the horſe, however, was not able to move him,
and he thought he was in the right pofture for drawing againſt a horfe
but when, in the fame poſture, he attempted to draw againſt two horſes,
he was pulled out of his place by being lifted up, and had one of his
knees ftruck againſt the ſtumps, which fhattered it fo, that, even to this
day, the patella, or knee pan, is fo looſe, that the ligaments of it ſeem
either to be broken or quite relaxed, which has taken away moſt of the
ſtrength of that leg."
The exploits which Dr. Defaguliers faw him perform were theſe :
1. By the ſtrength of his fingers (only rubbed in coal aſhes to keep
them from flipping,) he rolled up a very ſtrong and large pewter diſh.
2. He broke feven or eight fhort and ftrong pieces of tobacco-pipe
with the force of his middle finger, having laid them on the firſt and third
finger.
3. Having thruſt in under his garter the bowl of a ſtrong tobacco-
pipe, his legs being bent, he broke it to pieces by the tendons of his
hams, without altering the bending of his leg.
66
4. He broke fuch another bowl between his firſt and ſecond finger,
by preffing his fingers together fideways.
5. He lifted a table fix feet long, which had half a hundred weight
hanging at the end of it, with his teeth, and held it in an horizontal
pofition for a confiderable time. It is true the feet of the table reſted
against his knees; but, as the length of the table was much greater than
its height, that performance required a great ſtrength to be exerted by
the mufcles of his loins, thofe of his neck, the maffeter and temporal
(muſcles of the jaws), befides a good ſet of teeth.
"6. He took an iron kitchen poker, about a yard long, and three
inches in circumference, and, holding it in his right hand, he ſtruck upon
his bare left arm, between the elbow and the wrift, till he bent the poker
nearly to a right angle.
66
7. He took fuch another poker, and holding the ends of it in his
hands, and the middle againſt the back of his neck, he brought both ends
of it together before him; and, what was yet more difficult, he pulled it
70
MECHANICS.
{
ton, before mentioned. The French authors commonly reckon
7 men for 1 horfe. As a mean between thefe, we took, in
almoſt ſtraight again: becauſe the mufcles which feparate the arms
horizontally from each other are not ſo ſtrong as thoſe that bring them
together.
"8. He broke a rope of about two inches in circumference, which
was in part wound about a cylinder of four inches diameter, having
faſtened the other end of it to ftraps that went over his fhoulders. But
he exerted more force to do this than any other of his feats, from his
awkwardneſs in going about it; for the rope yielded and ſtretched as he
ftood upon the cylinder, fo that when the extenfors of the legs and thighs
had done their office in bringing his legs, and thighs ftraight, he was
forced to raiſe his heels from their bearings, and ufe other muſcles that
are weaker. But if the rope had been fo fixed that the part to be broken
had been ſhort, it would have been broken with four times lefs difficulty.
9. I have ſeen him lift a rolling ftone of about 800 lbs. with his
hands only, ftanding in a frame above it, and taking hold of a chain that
was faftened to it. By this, I reckon he may be almoft as ftrong again
as thoſe who are generally reckoned the ftrongeft men, they generally
lifting no more than 4c0lbs. in that manner. The weakest men who
are in health, and not too fat, lift about 125 lbs, having about half the
ftrength of the ſtrongeſt.
"N. B. This fort of compariſon is chiefly in relation to the muſcles
of the loins; becaufe in doing this one muft ftoop forwards a little,
We muſt alſo add the weight of the body to the weight lifted. So that
if the weakest man's body weigh 150 lbs. that added to 125 lbs. makes
the whole weight lifted by him to be 275 lbs. Then if the ftronger man's
body weighs alfo 150 lbs. the whole weight lifted by him will be 550 lbs.
that is 400 lbs. and the 150 lbs. which his body weighs. Topham weighs
about 200lbs. which, added to the 800 lbs. that he lifts, makes 1000 lbs:
But he ought to lift 900 lbs. befides the weight of his body, to be as
ftrong again as a man of 150 lbs. weight who can lift 400 lbs.”
"C
Again: About thirty years ago one Joyce, a Kentish man, famous
for his great ftrength, fhewed feveral feats in London and the country,
which fo much ſurpriſed the ſpectators, that he was by moſt people
called the ſecond Sampfon. But though the poſtures which he had learnt
to put his body into, and found out by practice without any mechanical
theory, were fuch as would make a man of common ftrength do fuch
feats as would appear furprifing to every one who did not know the
advantage of thoſe poſitions of the body; yet nobody then attempted
to draw againſt horſes, or raiſe great weights, or to do any other thing in
imitation of him: because, as he was very, ftrong in the arms, and
grafped thofe that tried his 'ftrength that way fo hard that they were
obliged immediately to defire him to defift, his other feats (wherein his
manner of acting was chiefly owing to the mechanical advantage gained
by the pofition of his body,) were entirely attributed to his extraordinary
ftrength.
"But when he had been gone out of England, or had ceaſed to fhew
his performances for eight or ten years, men of ordinary ſtrength found
out the way of making fuch advantage of the fame poftures as Joyce had
put himself into as to pafs for men of more than common ftrength, by
drawing againſt horſes, breaking ropes, lifting vaſt weights, &c. (though
they could in none of the poftures really perform fo much as Joyce,
yet they did enough to amaze and amufe, and get a great deal of money),
fo that every two or three years we had a new ſecond Sampfon.
Animal Strength-Horfes.
71
J
art. 378. vol. I. the proportion of 6 to 1, and ſtated the ſtrength
of a horſe as equivalent to 420 lbs. at a dead pull. But the pro-
portion is by no means conftant, for it varies greatly according
to the different kinds of work. Thus the worſt way of apply-
ing the ſtrength of a horfe is to make him carry a weight up a
fteep hill; while the organization of a man fits him very well.
for this kind of labour: hence, three men climbing up ſuch a
hill with a weight of 100 lbs. each will proceed faſter than a
horſe with a load of 300 lbs. This, we believe, was firft ob-
ferved by M. de la Hire.
We are not acquainted with any ſeries of experiments which
have been made with a view of determining the weights horſes
can carry when moving up floping roads, making given angles
with the horizon: but, fortunately, this deficiency is not of
much confequence, becauſe the carrying of weights is far from
the beſt manner of employing the ftrength of a horſe. It is
known, however, that, in general, a horfe loaded with a man and
his equipage, weighing altogether about 2 cwt. may, without
being forced, travel, in 7 or 8 hours, the diſtance of 43000
yards, or nearly 25 miles, upon a good road. When a horfe
travels day after day without ceffation, either the weight he
carries or the diftance paffed over muft undergo fome diminu
tion, as well as the time actually employed in travelling: but we
do not pretend to affign a mean value in this place.
"About fifteen years ago a German of middle fize, and but ordinary
ftrength, fhewed himſelf at the Blue Pofts, in the Haymarket, and, by the
contrivances above-mentioned, paffed for a man of uncommon ftrength,
and got confiderable fums of money by the daily concourſe of ſpectators.
After having feen him once, I gueffed at his manner of impofing upon
the multitude; and being refolved to be fully fatisfied in the matter, I
took four very curious perfons with me to fee him again, viz. the lord
marquis of Tullibardin, Dr. Alexander Stuart, Dr. Pringle, and a mecha-
nical workman who uſed to affift me in my courfes of experiments.
We
e placed ourſelves in fuch manner round the operator, as to be able
to obſerve nicely all that he did; and found it fo practicable, that
we performed feveral of his feats that evening by ourſelves, and after-
wards I did the moſt of the reſt, as I had a frame to fit in to draw, and
another to ſtand in and lift great weights, together with a proper girdle
and hooks. I likewiſe fhewed fome of the experiments before the Royal
Society; and ever fince at my experimental lectures I explain the
reafon of ſuch performances, and take any perfon of ordinary ſtrength
that has a mind to try, who can eafily do all that the German above-
mentioned uſed to do, without any danger or extraordinary training,
by making uſe of my apparatus for that purpoſe.'
The Doctor then proceeds to explain the principles on which thefe
achievements depended, and illuftrates his pofitions by various diagrams.
He likewiſe deſcribes ſome contrivances to determine the ſtrength which
men exert in different ways; for an account, of the chief of which, the
reader may turn to the article STEELYARD, to ascertain the Strength of
Men, in a fubfequent part of this volume.
72
MECHANICS.
1
:
71. In the Memoirs of the French Academy for 1703, are
inferted the comparative obfervations of M. Amontons, on the
velocity of men and of horſes; in which he ſtates the velocity
of a horſe loaded with a man and walking to be rather more
than 54 feet per fecond, or 3 miles per hour, and when going a
moderate trot with the fame weight to be about 8 feet per
fecond, or about 6 miles per hour. Theſe velocities, however,
are ſomewhat less than what might have been taken for the mean
velocities.
72. But the beſt way of applying the ftrength of horfes is to
make them draw weights in carriages, &c. To this kind of
labour, therefore, the enquiries of experimentalifts fhould be
directed. A horfe put into harneſs and making an effort to
draw bends himſelf forward, inclines his legs, and brings his
breaſt nearer to the earth; and this fo much the more as the
effort is the more confiderable. So that when a horſe is em-
ployed in drawing, his effort will depend,fin ſome meaſure, both
upon his own weight and that which he carries on his back.
Indeed it is highly uſeful to load the back of a drawing horſe
to a certain extent; though this, on a flight confideration,
might be thought to augment unneceffarily the fatigue of the
animal: but it muſt be confidered that the mafs with which the
horfe is charged vertically is added in part to the effort which
he makes in the direction of traction, and thus difpenfes with
the neceffity of his inclining ſo much forward as he muſt other-
wife do; and may, therefore, under this point of view, relieve
the draught more than to compenfate for the additional fatigue,
occafioned by the vertical preffure. Carmen, and waggoners in
general, are well aware of this, and are commonly very careful
to diſpoſe of the load in fuch a manner that the fhafts fhall
throw a due proportion of the weight on the back of the ſhaft
horfe.
73. The beſt difpofition of the traces during the time a horſe
is drawing is to be perpendicular to the pofition of the collar
upon his breaſt and ſhoulders: when the horſe ſtands at eaſe,
this pofition of the traces is rather inclined upwards from the
direction of the road; but when he leans forward to draw the
load, the traces fhould then become nearly parallel to the plane
over which the carriage is to be drawn; or, if he be employed in
drawing a fledge, or any thing without wheels, the inclination of
the traces to the road, fuppofing it to be horizontal, fhould
(from what we obferved when treating of friction) be about
1810.
74. From the preceding obfervations it will be eaſy in moſt
cafes to adapt the fize of the wheels to that of the animal which
is to draw in the shafts, fo that when he leans forward to his
Animal Strength-Horfes.
73
[
work the traces may be nearly parallel to the road, whether
that road be horizontal or not: always recollecting that, if
there be any variation from the parallel pofition, it muſt be
rather inclining upwards than downwards; as the former will
fomewhat diminish the friction, while the latter, inftead of
raifing the wheels from any hollow into which they may fall,
will tend to draw them down lower, and much increaſe the
labour of the animal.
9,
75. When feveral horfes are harneffed one before another,
fo that they may all draw at the fame load, and the flope on
which they are drawing changes, as from DA to AB (fig. 6.
pl. I.), the effort of the horſe which draws along the road AB
is decompofed into two parts, of which one tends to pull up
the load, the other to pull down the horſe which is in the ſhafts
and is drawing along the flope DA. This latter compofant is
always greater as the traces of the foremoſt horſe are the
longer; and it may be worth while to find its values, and its
augmentation with regard to an increaſe in the length of the
traces. To this end let EA' be the height above ÅD of the
breaſt of the horſe which draws in the fhafts near the point A,
and let ER and ER' be two different lengths of the traces;
the breaſt of the horſe when harneffed to either of theſe traces
being at the fame diſtance from the plane AB', that is, BR=
B'R' EA. Take EF-EF' to reprefent the effort of the horfe
in the direction of the trace; draw E q' parallel to DA, EQ
perpendicular to BA produced, Eg parallel to AB, and F
Fq, perpendicular to Eq. The effort which tends to pull the
horſe down whoſe breaſt is at E is reprefented by Fq, when the
breaſt of the other horfe is at R, and by F'q' when it is at R';
and q E, q' E are the correſponding efforts tending to raiſe the
load along the flope DA. Make EA'=RB=R'B'=a, ER=λ,
ER'=', angle A'EQ=q Eg= fupplem. DAB=s, and EF=
EF'. Then, when the trace ER is ufed, the effort which
tends to pull down the ſhaft horfe when he juſt reaches the
fummit of the flope will be. fin. q EF-4 fin. (q Eg-
FEg), and the effort tending to raiſe the load will be cofin.
(qEg-FE g). In like manner, when the foremoft horſe
draws by the trace ER', the effort tending to pull down the
fhaft horfe will be reprefented by ₫ fin. (q Eg' — F’E g'), and
that which tends to draw up the carriage by p cofin. (q Eg'.
FEg). Now we have fin. FEg= ER and fin. FEg=
But Rg=BREQ=a-a cofin. s=a (1—
R'g'
ER'
R g
ER'
1
R. g
cofin.). Recollecting, therefore, that the angles FE g, F'Eg,
74
MECHANICS.
are'always ſo ſmall that the arcs differ very little from the fines,
we have FE g=
a (1-cosin. s)
a(1-cosin.s)
and F'Eg'=
: theſe
values being ſubſtituted in the preceding expreffions, give
(1) …..Fq=4 fin. (s—a (1-cosin. s)).
(2) ... F'q'=q fin. (s
-s)
(3) ... E q= cofin. (s-
λ
a (1-cosin.
λ'
a (1-cosin.
(s_ª (1—0
(4) …….Eq'=4 cofin. (s
• 5.)).
a (1-cosin. s.)
λ'
Suppofe, for example, that AB is horizontal, and that the
afcent DA is ſuch that for every fix feet, as CN in a horizontal ·
plane, the vertical rife NA fhall be one foot: this flope is too
steep for any common road, but may be ſometimes met with in
afcents from ftone quarries, &c. In this cafe the angle s will
be nearly 9° 28', which, expreffed in decimal parts of the ra-
dius, gives so'16522, and cofin. so'98638. Let the effort
=2c0lb., a=34 feet, λ = 8 feet, and λ=12 feet. Then
fhall we have,
(1) ...
••• Fq=200 fin. (0*16522—3′5 (1—098638))
=200 fin. 9° 7' 29"=31716 lbs.
(2) ……. –
F'q'=200 fin. (0·16522 — 3'5 (5—098638)
(3)
(4)
12
=200 fin. 9° 14′ 29″=32.25 lbs.
Eq=200 cofin. 9° 7′ 29″177°47 lbs.
Eq=200 cofin. 9° 14′ 29″-197 404 lbs.
Hence it appears, that the horſe whofe breaſt is at E is
pulled downwards by the other horſe, with a force equivalent
to about 32lbs: this weight is fmall for a horſe that is not
fatigued; but we ſhould confider, that when drawing up a ſteep
road the animal's ftrength is much weakened, fo that it may
be obliged to yield to a very fmall effort. A lengthening of
four feet to a trace of eight feet will produce an augmentation
of 32.25-31716=0'534 lbs. in the effort which tends to pull
the fhaft horfe down, and a diminution of 19747-197°404=
o*066 lbs. in the effort which raifes the load up the hill. Thefe
quantities are not confiderable; but it appeared defirable to
explain the method of afcertaining their magnitude. And it
may be added, that when a horfe pulls for only a fhort time, as
a few minutes, he will often exert a force equivalent to 500 or
600 lbs.: in which cafe, the tendency to pull down a ſhaft
horfe rifing a hill would be thrice as much as we have ſtated
`Animal Strength-Horfes.
773
it above: a force against which no horfe could ſtand in ſuch a
difadvantageous poſition.
}
ཟ
76. When a horſe is made to move in a circular path, as is
often practifed in mills and other machines moved by horſes, it
will be neceffary to give the circle which the animal has to
walk round, the greateft diameter that will comport with
the local and other conditions to which the motion muſt be
fubjected. It is obvious, indeed, that, fince a rectilinear mo-
tion is the moſt eaſy for the horſe, the leſs the line în which he
moves is curved, with the greater facility he will walk over it,
and the lefs he need recline from a vertical pofition: and be-
fides this, with equal velocity the centrifugal force will be lefs
in the greateſt circle, which will proportionally diminiſh the
friction of the cylindrical part of the trunnions, and the labour
of moving the machine. And, further, the greater the dia-
meter of the horſe-walk, the nearer the chord of the circle in
which the horſe draws is to coincidence with the tangent,
which is the moſt advantageous pofition of the line of traction.
On theſe accounts it is that, although a horfe may draw in a
circular walk of 18 feet diameter, yet in general it is adviſeable
that the diameter of fuch a walk fhould not be leſs than 25 or
30 feet; and in many inſtances 40 feet would be preferable to
either.
77. It has been ftated by Defaguliers (vol. I. pa. 251) and
fome others, that a horfe employed daily in drawing nearly
horizontally can move, during eight hours in the day, about
200 lbs. at the rate of 24 miles per hour, or 33 feet per fecond.
If the weight be augmented to about 240 or 250 lbs., the horfe
cannot work more than fix hours a day, and that with a leſs
velocity. And, in both cafes, if he carry fome weight, he
will draw better than if he carried none (art. 72.) M. Sau-
veur eſtimates the mean effort of a horſe at 175 French, or
189 averd. pounds, with a velocity of rather more than three
feet per fecond: and this agrees very nearly with our deduc-
tion in art. 378. vol. I. But all theſe are probably too high
to be continued for eight hours, day after day; for in our in-
veſtigation juſt referred to we affumed 10 feet per fecond, as
the utmoſt walking velocity of a horfe; a velocity which we
conceive no horſe would be able to continue long. In another
place Defaguliers ftates the mean work of a horſe as equivalent
to the raiſing a hogfhead full of water (or 550 lbs.) 50 feet high
in a minute. But Mr. Smeaton, to whofe authority much is
due, afferts, from a number of experiments, that the greateſt
effect is the raifing 550 lbs. forty feet high in a minute. And,
from fome experiments made by the Society for the Encourage-
1
76
MECHANICS.
ment of Arts, under the direction of their late able fecretary,
Mr. Samuel Moore, it was concluded, that a horſe moving at
the rate of three miles an hour can exert a force of 80 lbs.
Unluckily, we are not fufficiently acquainted with the nature
of the experiments and obfervations from which theſe deduc-
tions were made to inſtitute an accurate compariſon of their
refults. Neither of them ought to exprefs what a horſe can
draw upon a carriage; becauſe in that cafe friction only is to
be overcome (after the load is once put into motion); ſo that a
middling horſe, well applied to a cart, will often draw much
more than 1000 lbs. The proper eſtimate would be that which
meaſures the weight which a horfe would draw up out of a
well; the animal acting by a horizontal line of traction turned
into the vertical direction by a fimple pulley, or roller, whoſe
friction fhould be reduced as much as poflible. It would, in-
deed, be far the beft, in all the inftances of experiments, to
uſe no fuch combinations of machinery as would make the ve-
locity of the load or weight different from that of the animal:
we could then readily compare the different reſults by means
of the expreffion M∞ (W− V)², or M∞ (W – V)³ (art. 378.
vol. I.), where V reprefents the velocity in feet per fecond
with which the animal moves the maſs M, and W his greateſt
walking velocity, or that in which he can move no weight but
his own. Thus might we obtain a mean eſtimate of the ani-
mal's ftrength at any one velocity, and could thence infer his
maximum of uſeful effort; namely, that when V is nearly
W. As to the abfolute power of the animal, it might be in-
ferred in any cafe of raifing a weight with his own velocity,
by means of the formula (M+H) V+Mgt, where M and
V are as before, H the weight of the horfe, its power, g=
32 feet the meaſure of the force of gravity, and t the time
in feconds during which the animal continues his uniform
exertion.
78. It follows, from what has been ſaid, and from the con-
fideration of the ſtrengths of horſes variouſly employed, fuch
as waggon horfes, dray horfes, plough horfes, heavy horfes,
light coach horfes, &c. that what is called "horſe-pcaver" is of
fo fluctuating and indefinite a nature, that it is perfectly ridi-
culous to affume it as a common meaſure, by which the force
of fteam-engines and other machines fhould be appreciated,
In moſt of the deductions which have been hitherto made we
apprehend there may be fomething of temporary effort: and
we think, on the whole, that about 70 lbs., at three miles an
hour, or 4 feet per fecond, may be a fair eſtimate for the
regular work of ftout London cart horfes; though we would
Animal Strength-Horfes.
77
infer, with Mr. Nicholfon, "that the animal can double his
"ſtrength for a fhort time, ſuch as 10 minutes, without re-
"ceiving any injury from the exertion.”
Thus have we preſented a view of the moſt uſeful and cor-
rect information we have been able to collect, on the different
energies of firſt movers: what is here done is not fo fatisfactory
.as might be wifhed; but our knowledge on many of theſe
points muſt remain imperfect, till freſh light is diffuſed over it
by the diligent and able enquiries of future obſervers.
*
1.
$
DESCRIPTIONS
OF
MACHINES:
ALPHABETICALLY ARRANGED.
AIR-PUMP is a machine by means of which the air may be
exhauſted out of proper veffels, fo as to make what is popularly
called a vacuum, but which is, in fact, only a very high de-
gree of rarefaction.
The invention of this noble inftrument, to which the prefent
age is indebted for fo many admirable diſcoveries, is afcribed to
Otto de Guericke, a conful of Magdeburg, who exhibited his
first public experiments with his pump before the emperor and
the fates of Germany at the breaking up of the imperial diet
at Ratisbon, in the year 1654. Guericke, indifferent about
the folitary poffeffion of an invention which afforded fuch en-
tertainment to the numerous perfons who, from time to time,
witneſſed his experiments, gave a minute defcription of all his
pneumatic apparatus to Gafper Schottus, profeffor of mathe-
matics at Wirtemberg, who publifhed it, with the confent of
the inventor, with an account of fome of its performances,
firft in 1657, in his Mechanica Hydraulico-pneumatica; and
then, in 1664, in his Technica Curiofa. Guericke's own ac-
count was not publifhed till 1672.
About the time of Guericke's invention the foundations
of the Royal Society of London were laid. Boyle, Wren,
. Brounker, Wallis, and other learned men, held frequent
meetings at Oxford, in which accounts were received and re-
lated of all important advances in the ftudy of nature; and
many experiments were exhibited. The refearches of Galileo,
Torricelli, and Paſcal, concerning the preffure of the air, had
1
80
MACHINES.
greatly engaged their attention, and thus prepared them for the
invention of Guericke. Mr. Boyle, in particular, as foon as
he heard what had been accompliſhed by the philofopher of
Magdeburg, and before any defcription of his machine had
been publiſhed, fet about the conftruction of one, to anſwer
the fame purpoſes; and fucceeded in the attempt: though he
frankly acknowledges that it was but feldom, and with great
difficulty, that he could produce an extreme degree of rare-
faction; fuch as it appeared, from the account of Schottus,
was obtained by means of Guericke's machine.
Boyle's inftrument was fomewhat improved by Hawkfbee,
and further by Martin; with fome flight modifications to par-
ticular views, it ftill remains the moſt approved form. The
air-pump we defcribed in art. 521. vol. I. is only ſo far va-
ried from Hawkfbee's improvement of Boyle's original con-
trivance, as to render it more portable. The machine, in its
primitive ſtate, is defcribed in the article Pneumatics, English
Encyclopædia; where, alfo, the fucceffive improvements of
Smeaton, Cuthbertfon, &c. are defcribed at large.
Many other ingenious attempts have been made, during the
laft ten or twelve years, to improve the mechaniſm of the air-
pump; to deſcribe a fourth part of which would extend this
article to more than its due length. Juftice, however, to the
authors of theſe improvements, as well as a defire to gratify
the reader, induces us to refer to Nicholfon's Journal, vols. I
and II. 4to. for deſcriptions of the air-pumps invented by meff.
Prince, Sadler, Little, sir G. Mackenzie, &c. and to Mr.
Vince's Hydroſtatics for an account of the pump uſed by that
gentleman in his lectures.
Notwithſtanding the many improvements which have fuc-
ceffively followed each other in the conftruction of the air-
pump, it was ftill, however, defirable that it fhould be further
fimplified in its mechaniſm, while it poffeffed the fame advan-
tages as attended thofe of more complicated ftructure. Cuth-
bertſon, Haas, and ſome others, have fo contrived their inftru-
ments, that their mechanical power, and not the preffure of
air, fhould open the valves: but, although the air-pumps in-
vented by theſe gentlemen are exceedingly ingenious, they are
in ſome reſpects fo complex, that it must be very difficult for
many perfons who poffefs thefe inftruments to clean them, or
to keep them in proper order for experiments.
Mr. N. Mendleffohn, a mathematical inftrument-maker, of
Surrey-ſtreet, Black-friars, having reflected upon the difficul
ties juft alluded to, was led to the conſtruction of a more
fimple air-pump, which is capable of being put together in lefs
Air-pump.
81
than half an hour, whenever it is cleaned, and requires that
operation very feldom. He has rejected the tube which, in
common air-pumps, leads from the valves to the receiver, toge
ther with the cock that ſerves to ſhut this pipe: the receiver is
placed immediately upon the valves, theſe being put on the top
of the cylinders, which, confequently, required the rackwork
and pinion being underneath, and inverted the whole inftru-
ment. See the drawing, pl. IV. where AB and CD reprefent
the two cylinders of glaſs ground and poliſhed infide.. E and F
are the two valves that allow the cylinders to communicate with
the receiver O through two very ſhort canals AB and CD (fig. 2:
plate IV.) and the cock G. Two other valves that open into
the atmoſphere are within the covers i and k, as may be ſeen in
fig. 1, where e reprefents one of them. MN is the receiver-
plate of glafs ground flat; PQ a barometer-guage, upon the
plan of the firft Torricellian tube, as the eafieft to conftruct
and the moſt infallible in its effects. It will be found to be.
here quite out of the way, fecure from being broke by accident,
and the moſt in fight. HK and IL are two brafs pillars that
ſupport the whole. RSVW the ufual rackwork, having a
double winch Im, which, upon trial, will be found preferable
to a ſingle one.
It will now be neceffary to fhew how this pump acts, in
which it will be ſufficient to explain the action of one cylinder,
becauſe the other is in all parts like it. E is a conical metallic
valve, from which a canal goes through the cock G up to the
receiver, as is feen in fig. 1 and 2, where all the parts are
marked with the fame letters. ET is a fteel rod going through
a leather box in the piton U. The top of this rod is fixed to
the valve E, and its bottom part flides in a ſmall hole with an
allowance of 0.1 inch up and downward, confequently the valve
E can move no further. When the piſton deſcends, it firft
opens the valve by pushing the rod to the bottom of the hole.
Then it flides down along the rod ET, and the air from the
receiver has now free acceſs to the cylinder. When the piſton
returns it lifts the rod ET, and thus fhuts up the valve. Then
the pifton flides again along the rod up to the top of the cylin
der, condenfing the air above it, which air, by the leaft con-
denſation, opens a velve e, fig. 2, and eſcapes freely into the
atmoſphere. This laft valve has neither fpring nor additional
weight to fhut it, but fhuts by its own weight (about a quarter
of an ounce) as ſoon as the pifton is arrived to the top of the
cylinder.
The cylinders are made of glaſs, and the pistons of tin, fo well
fitted as to be air-tight, without the interpofition of any leathers.
VOL. II.
G
{
82
MACHINES.
The friction of theſe two bodies is fmall beyond expectation,
a fufficient proof that they will be durable. They poffefs the
further advantage of being capable of ſtanding for even fix
months, after which time they will ferve without being cleaned
or repaired, becauſe they are not liable to be corroded by the
oil which they contain, an inconvenience too general in brafs
cylinders. After all, if the prefent pump fhould want cleaning,
it is an eaſy operation to take off the top piece gb, by unſcrew-
ing the nuts H and I, when this piece, with all the apparatus
upon it, will come off. Then each cylinder may very eaſily be
flid off from the pifton, wiped out and replaced, after having
greaſed it infide with a little of the cleaneft fweet oil: the top
is then to be put again in its place, and the two nuts H and I
being ſcrewed upon it, the inftrument is ready. Neither racks
nor pinion need to be taken out of their places, the cylinders
ſtanding above them.
The cock is conftructed fo, that, being in the fituation re-
preſented in fig. 1, the communication is open between the
cylinders, the receiver, and the barometer-guage, and, by a
quarter of a revolution, the cylinders are excluded, the receiver
and guage being ftill left in communication, A little ftopper
in fig. 2, ground into the cock, being open, air is admitted to
the receiver, if required.
The receiver-plate is of glaſs ground flat, as was mentioned
before this will be found preferable to brafs, becauſe cleaner,
and never corroded by acids or water; it will beſides often
prove very convenient in making electrical experiments in the
vacuum.
The whole inftrument is fixed upon a mahogany-table,
which ferves as a ſtand for it.
Mr. Mendelsfhon concludes his defcription by obferving that
"neither the employing of glaſs cylinders, nor the method of
opening the valves, is new; but, for aught he knows, this is the
firft inftrument of the kind ever executed: and the idea of
putting the valves at top, and thus fimplifying the inftrument,
feems to have eſcaped the attention of the eminent artiſts, both
here and abroad, as, to my beſt knowledge, it has never been
done or deſcribed any where. The metallic piftons, without
leathering, muſt certainly add to the durability, and diminiſh
the great labour that ufually attends working an air-pump."
Nicholfon's Journal, New Series, No. 39.
Mr. Vream, who was Dr. Defaguliers's operator for philofo-
phical machines, made fuch an alteration in Hawkfbee's air-
pump, as produced the alternate reciprocating motion of the
piftons, without turning the handle to and fro :while the handle
turns conftantly one way in its operation, a crank by means of
Air-pump.
two leading pieces, gives the wheel that moves the racks a
motion of about two-thirds (or more when required) of its
circumference, every time the crank goes round. The advan-
tages which Mr. Vream thought would refult from this altera-
tion, he deſcribes in the following words: "I hope I have
improved Mr. Hawkfbee's pump by a contrivance whereby
in turning the winch quite round the emboli, or piſtons, are
alternately raiſed and depreffed; whereas in Mr. Hawkfbee's
way, the moving of the hand backward and forward is not
only more troublefome, but ſhakes the pump; becauſe it is
required to preſs the barrel hard againſt the bottom piece under
the barrels, to diſcharge the water from the valves at every ſtroke.
Befides if the pump ſhould at any time happen to leak, when an
experiment ſhould be made in hafte; you may exhauſt ſo faſt
this way as to make your experiment without being at the trou-
ble to pull the pump to pieces, in order to make it tight, except
in fuch cafes as require the recipient to be perfectly exhauſted."
Fig. 11. pl. III. will fhew in what this improvement of Mr.
Vream's confiſts. The axis DB on which the crank A a b and
handle BF turn, is perpendicular to the plane of the wheel WE
which moves the racks S,T: two leaders N,N, of equal length,
are hung by one end upon the crank A a, and by the other
upon the two ends of a pin I which paffes through the wheel at
a ſuitable diſtance from the centre. While the crank is rifing
the pin I is raiſed from its pofition in the figure to fome higher
point, as R, thus caufing the wheel to turn upon its centre E,
and raiſe the rack S, while it depreffes the rack T: afterwards,
while the crank is defcending through the other half of its revo-
lution, the pin is puſhed back again from R to I, the wheel E
turns the contrary way, the rack T is raifed, and S depreffed.
So the racks are alternately raiſed and depreffed as the circular
motion of the handle F carries round the crank A a. The radius.
a b of the crank muſt be rather leſs than the diſtance EI of the
pin I from the centre of the wheel, in order to enſure the alter-
nate motion of the piftons: and the more extenſive the motion
of theſe is required to be with refpect to the motion of the
crank, the more muſt the radius of the wheel EW exceed the
diſtance EI.
This contrivance, however ingenious, has been ſeldom applied
to air-pumps; probably becaufe there is a confiderable variation
of requifite moving force in the different parts of the revolution
of the crank; a variation which may produce jolts in the motion.
But this inequality of force upon the crank, being occafioned by
the variable obliquity in the pofition of the leaders N,N, may
be much reduced by making the diſtances a b, EI, as ſmall as
G 2
84
MACHINES.
•
•
can be conveniently, with refpect to the length aI of the
leaders.
ANEMOMETER. See art. 49. of the introductory part
of this volume.
ATWOOD'S MACHINE, the name which is now commonly
applied to the ingenious apparatus invented by Mr. Atwood of
Trinity college, Cambridge, to illuftrate the doctrines of ac-
celerated motion. This machine has been found to anſwer the
purpoſe far more completely than any other; fubjecting to ex-
perimental examination, the quantity of matter moved, the
meaſure of the force which moves it, the ſpace deſcribed from
quiefcence, the time of deſcription, and the velocity acquired.
The theory of this inftrument depends upon the principles ex-
hibited in art. 267. vol. i. But we ſhall here give ſo much of
the theory and deſcription as ſeems neceffary to fhew its nature
and uſe, chiefly in the words of the ingenious inventor.
1. Of the mass moved.-In order to obferve the effects of the
moving force, which is the object of any experiment, the inter-
ference of all other forces ſhould be prevented: the quantity of
matter moved, therefore, confidering it before any impelling
force has been applied, fhould be without weight; for although
it be impoffible to abſtract the natural gravity or weight from
any fubftance whatever, yet the weight may be fo counteracted
as to be of no fenfible effect in experiments. Thus in the in-
ftrument conſtructed to illuftrate this fubject experimentally,
A, B, fig. 1. pl. V. reprefent two equal weights affixed to the
extremities of a very fine and flexible filk line: this line is
ſtretched over a wheel or fixed pulley abcd, moveable round an
horizontal axis: the two weights A, B, being preciſely equal
and acting againſt each other, remain in equilibrio; and when
the leaft weight is fuperadded to either (ſetting aſide the effects
of friction), it will preponderate. When AB are fet in motion
by the action of any weight m, the fum A+B+m would confti-
tute the whole mafs moved, but for the inertia of the materials
which must neceffarily be uſed in the communication of mo-
tion: theſe materials confift of, 1. The wheel abcd, over which
the line fuſtaining A and B paffes. 2. The four friction-
wheels, on which the axle of the wheel abcd refts: the uſe of
theſe wheels is to prevent the lofs of motion, which would be
occafioned by the friction of the axle if it revolved on an im-
moveable furface. 3. The line by which the bodies A and B
are connected, fo as when fet in motion to move with equal
velocities. The weight and inertia of the line are too ſmall to
have fenfible effect on the experiments; but the inertia of the
other materials juſt mentioned conftitute a confiderable propor-
Atwood's Machine.
85
tion of the mafs moved, and muſt be taken into account. Since
when A and B are put in motion, they muft neceffarily move
with a velocity equal to that of the circumference of the wheel
abcd, to which the line is applied; it follows, that if the whole
mafs of the wheels were accumulated in this circumference,
its inertia would be truly eſtimated by the quantity of matter
moved; but fince the parts of the wheels move with different
velocities, their effects in refifting the communication of mo-
tion to A and B by their inertia will be different; thofe parts
which are furtheft from the axis refifting more than thoſe which
revolve nearer in a duplicate proportion of thoſe diſtances. If
the figures of the wheels were regular, from knowing their
weights and figures, the diſtances of their centres of gyration
from their axes of motion would become known, and confe-
quently an equivalent weight, which being accumulated uni-
formly in the circumference abcd, would exert an inertia equal
to that of the wheels in their conftructed form. But as the
figures are wholly irregular, recourſe muſt be had to experi-
ment, to affign that equivalent quantity of matter, which being
accumulated uniformly in the circumference of the wheel abcd,
would refift the communication of motion to A in the fame
manner as the wheels.
In order to afcertain the inertia of the wheel abcd, with that
of the friction-wheels, the weights AB being removed, the fol-
lowing experiment was made. A weight of thirty grains was
affixed to a filk line (the weight of which was not fo much as
4th of a grain, and confequently too inconfiderable to have fen
fible effect in the experiment); this line being wound about
the wheel abcd, the weight 30 grains by defcending from reft
communicated motion to the wheel, and by many trials was
obferved to defcribe a ſpace of about 38 inches in 3 feconds.
From thefe data the equivalent mafs or inertia of the wheels
will be known from this rule:
Let a weight P (fig. 2.) be applied to communicate mo-
tion to a fyftem of bodies by means of a very flender and
flexible line going round the wheel SLDIM, through the
centre of which the axis paffes (G being the common centre of
gravity, R the centre of gravity of the matter contained in
this line, and O the centre of ofcillation). Let this weight
defcend from reft through any convenient ſpace s inches, and
let the obferved time of its defcent be t feconds;. then if I be
the ſpace through which bodies defcend freely by gravity in
one fecond, the equivalent weight fought =
PX 121.
-P. See art. 314. vol. i.
WX SRX SO
SD2
86
MACHINES.
Here we have p=30 grains, t = 3 feconds, /=193 inches,
s = 38.5 inches; and
or 24 ounces.
PXR
P=
S
30X9X 193
385
30=1323 grains
This is the inertia equivalent to that of the wheel abcd, and
the friction wheels together: for the rule extends to the eſti-
mation of the inertia of the maſs contained in all the wheels.
The reſiſtance to motion therefore arifing from the wheels'
inertia, will be the fame as if they were abfolutely removed, and
a maſs of 22 ounces were uniformly accumulated in the cir-
cumference of the wheel abcd. This being premiſed, let the
boxes A and B, fig. 1. be replaced, being fufpended by the filk
line over the wheel or pulley abcd, and balancing each other:
ſuppoſe that any weight m be added to A ſo that it fhall defcend,
the exact quantity of matter moved, during the deſcent of the
weight A, will be aſcertained, for the whole maſs will be A+
B + m + 23 oz.
:
In order to avoid troubleſome computations in adjuſting the
quantities of matter moved and the moving forces, fome deter-
minate weight of convenient magnitude may be affumed as
a ftandard, to which all the others are referred. This ftandard
weight in the fubfequent experiments is of an ounce, and is,
repreſented by the letter m. The inertia of the wheels being
therefore = 22 ounces, will be denoted by II m. A and B
are two boxes conftructed ſo as to contain different quantities
of matter, according as the experiment may require them to be
varied: the weight of each box, including the hook to which it
is fufpended, = 1 oz. or according to the preceding eftimation,
the weight of each box will be denoted by 6 m; thefe boxes
contain fuch weights as are repreſented by fig. 3. each of which
weighs an ounce, fo as to be equivalent to 4 m; other weights of
— oz. = 2m, 1=m, and aliquot parts of m, fuch as, m, may be
alſo included in the boxes, according to the conditions of the
different experiments hereafter deſcribed.
If
4 oz. or 19 m, be included in either box, this, with the.
weight of the box itſelf, will be 25 m; fo that when the weights
A and B, each being 25 m, are balanced in the manner above
repreſented, their whole maſs will be 50 m, which being added
to the inertia of the wheels 11 m, the fum will be 61 m. More-
over, three circular weights, ſuch as that which is reprefented
at fig. 4. are conftructed; each of which 4oz. or m: if one
of theſe be added to A and one to B, the whole mafs will now
become 63 m, perfectly in equilibrio, and moveable by the leaſt .
weight added to either (fetting afide the effects of friction), in
the fame manner precifely as if the fame weight or force were
Atwood's Machine.
87
:
applied to communicate motion to the mafs 63, exifting in
free ſpace and without gravity.
2. The moving force. Since the natural weight or gravity of
any given fubftance is conftant, and the exact quantity of it
eaſily eſtimated, it will be convenient here to apply a weight to
the mafs A as a moving force: thus, when the fyftem confifts
of a maſs = 63 m, according to the preceding deſcription, the
whole being perfectly balanced, let a weight 4 oz. or m, ſuch as
is repreſented in fig. 5. be applied on the mafs A; this will
communicate motion to the whole fyftem: by adding a quantity
of matter m to the former mafs 63 m, the whole quantity of
matter moved will now become 64 m; and the moving force
being=m, this will give the force which accelerates the defcent
of A= › or part of the accelerating force by which the
m
647
I
64
bodies defcend freely towards the earth's furface.
By the preceding conftruction, the moving force may be
altered without altering the mafs moved: for fuppofe the three
weights m, two of which are placed on A, and one on B to be
removed, then will A balance B. If the weights 3 m be all
placed on A, the moving force will now become 3 m, and the
mafs moved 64 m as before, and the force which accelerates
the deſcent of A=33 parts of the force by which gravity
3m
64m 64
accelerates bodies in their free defcent to the furface.
I
2
Suppoſe it were required to make the moving force 2m, the
mafs moved continuing the fame. In order to effect this, let
the three weights, each of which=m, be removed; A and
B will balance each other; and the whole mafs will be 61 m:
let m, fig. 5. be added to A, and m to B, the equilibrium will
ftill be preſerved, and the mafs moved will be 62 m; now let
2 m be added to A, the moving force will be 2 m, and the mafs
moved 64 m, as before; wherefore the force of acceleration
32 2 part of the acceleration of gravity. Thefe alterations in
the moving force may be made with great eafe and convenience
in the more obvious and elementary experiments, there being no
neceffity for altering the contents of the boxes A and B but
the proportion and abfolute quantities of the moving force and
maſs moved may be of any affigned magnitude, according to the
conditions of the propofition to be illuftrated.
I
3. Of the space defcribed. The body A fig. 1. deſcends in a
vertical line; and a fcale about 64 inches in length graduated
into inches and tenths of an inch is adjusted vertically, and fo
placed that the defcending weight A may fall in the middle of a
fquare ftage, fixed to receive it at the end of the deſcent: the
beginning of the deſcent is eſtimated from o on the ſcale, when
88
MACHINES,
the bottom of the box A is on a level with o. The defcent of
A is terminated when the bottom of the box ftrikes the ftage,
which may be fixed at different diftances from the point o; fo
that by altering the pofition of the ftage, the ſpace deſcribed
from quiefcence may be of any given magnitude leſs than 64
inches.
4. The time of motion is obferved by the beats of a pendulum,
which vibrates feconds; and the experiments, intended to illuf-
trate the elementary propofitions, may be eafily fo conftructed
that the time of motion ſhall be a whole number of ſeconds: the
eſtimation of the time, therefore, admits of confiderable exact-
hefs, provided the obſerver takes care to let the bottom of the
box A begin its defcent preciſely at any beat of the pendulum;
then the coincidence of the ftroke of the box againſt the ſtage,
and the beat of the pendulum at the end of the time of motion,
will ſhew how nearly the experiment and the theory agree to-
gether. There might be various mechanical devices thought of
for letting the weight A begin its deſcent at the inftant of a beat
of the pendulum W: let the bottom of the box A, when at o
on the ſcale, reft on a flat rod, held in the hand horizontally, its
extremity being coincident with o, by attending to the beats of
the pendulum; and with a little practice the rod which ſupports
the box A may be removed at the moment the pendulum beats,
ſo that the deſcent of A fhall commence at the fame inſtant.
5. Of the velocity acquired. It remains only to defcribe in
what manner the velocity acquired by the defcending weight
A, at any given point of the fpace through which it has de-
fcended, is made evident to the fenfes. The velocity of A's
deſcent being continually accelerated, will be the fame in no
two points of the fpace defcribed. This is occafioned by the
conftant action of the moving force; and fince the velocity of
A at any inftant is meaſured by the ſpace which would be de
fcribed by it, moving uniformly for a given time with the ve
locity it had acquired at that inſtant, this meaſure cannot be ex-
perimentally obtained, except by removing the force by which
the defcending body's acceleration was caufed.
I
In order to fhew in what manner this is affected practically,
let us again fuppofe the boxes A and B = 25 m each, fo as to-
gether to be 50 m; this, with the wheel's inertia 11 m, will
make 61 m; now let m, fig. 3. be added to A, and an equal
weight m to B, thefe bodies will balance each other, and the
whole maſs will be 63 m. If a weight m be added to A, motion
will be communicated, the moving force being m, and the maſs
moved 64 m. In eftimating the moving force, the circular weight
m was made uſe of as a moving force: but for the preſent
purpoſe of fhewing the velocity acquired, it will be convenient
•
Atwood's Machine.
to uſe a flat rod, the weight of which is alfom. Let the bottom
of the box A be placed on a level with o on the ſcale, the whole
mafs being as deſcribed above =63 m, perfectly balanced in
equilibrio. Now let the rod, the weight of which = m, be
placed on the upper furface of A; this body will deſcend along
the ſcale preciſely in the fame manner as when the moving
force was applied in the form of a circular weight. Suppoſe
the maſs A, fig. 6, to have defcended by conftant acceleration
of force of m, for any given time, or through a given ſpace:
let a circular frame be fo affixed to the fcale, contiguous to
which the weight defcends, that A may pafs centrally through
it, and that this circular frame may intercept the rod m, by
which the body A has been accelerated from quieſcence. After
the moving force m has been intercepted at the end of the given
•fpace or time, there will be no force operating on any part of
the fyftem which can accelerate or retard its motion: this being
the cafe, the weight A, the inftant after m has been removed,
muſt proceed uniformly with the velocity which it hadacquired
that inftant: in the fubfequent part of its deſcent, the velocity,
being uniform, will be meaſured by the ſpace deſcribed in any
convenient number of feconds.
Other uses of the inftrument it is needleſs to deſcribe particu-
larly, but it may not be improper to mention fome of them;
fuch as the experimental eftimation of the velocities communi-
cated by the impact of bodies elaſtic and non-elaſtic; the quantity
of refiftance oppoſed by fluids, as well as for various other pur-
pofes. Thefe ufes we fhall not infift on; but the properties of
retarded motion being a part of the preſent ſubject, it may be
neceffary to fhew in what manner the motion of bodies refifted
by conftant forces are reduced to experiment by means of the
inftrument above defcribed, with as great eaſe and precifion as
the properties of bodies uniformly accelerated. A fingle in-
ſtance will be fufficient: Thus, fuppofe the mafs contained in
the weights A and B, fig. 6, and the wheels to be 61 m, when
perfectly in equilibrio; let a circular weight m be applied to B,
and let two long weights or rods, each = m, be applied to A,
then will A defcend by the action of the moving force m, the
maſs moved being 64 m: fuppofe that when it has defcribed
any given ſpace by conftant acceleration, the two rods m are in-
tercepted by the circular frame above deſcribed, while A is de-
fcending through it, the velocity acquired by that defcent is
known; and when the two rods are intercepted, the weight
A will begin to move on with the velocity acquired, being now
retarded by the conftant force m; and fince the maſs moved is
62 m, it follows, that the force of retardation will be part of
I
हर
90.
MACHINES.
that force whereby gravity retards bodies thrown perpendicularly
upwards. The weight A will therefore proceed along the gradu-
ated fcale in its defcent with an uniformly retarded motion, and
the ſpace defcribed, times of motion, and velocities deftroyed
by the refifling force, will be fubject to the ſame meaſures as in
the examples of accelerated motion above defcribed.
In the foregoing defcriptions, two fuppofitions have been
affumed, neither of which is mathematically true: but it may
be eaſily fhewn that they are fo in a phyfical fenfe; the errors
occafioned by them in practice being infenfible.
1. The force which communicates motion to the fyftem has
been affumed conftant; which will be true only on a fuppofition
that the line, at the extremities of which the weights A and B,
fig. 1. are affixed, is without weight. In order to make it
evident that the line's weight and inertia are of no fenfible
effect, let a cafe be referred to, wherein the body A defcends
through 48 inches from reft by the action of the moving force
297, when the maſs moved is 64 m; the time wherein A defcribes
48 inches is increaſed by the effects of the line's weight by no
more than 7th parts of a fecond: the time of defcent being
3.9896 feconds, when the ſtring's weight is not confidered, and
the time when the ftring's weight is taken into account=4.0208
feconds; the difference between which is wholly infenfible by
obfervation.
2. The bodies have alſo been fuppofed to move in vacuo,
whereas the air's refiftance will have fome effect in retarding
their motion: but as the greateſt velocity communicated in
thefe experiments cannot much exceed that of about 26 inches
in a fecond (fuppofe the limit 26.2845), and the cylindrical
boxes being about 1 inches in diameter, the air's refiftance can
never increaſe the time of defcent in fo great proportion as that
of 240: 241; its effects therefore will be infenfible in experiment.
I
2
The effects of friction are almoſt wholly removed by the
friction wheels; for when the furfaces are well polifhed and
free from duft, &c. if the weights A and B be balanced in per-
fect equilibrio, and the whole mafs confifts of 63 m, according
to the example already defcribed, a weight of 1 grain, or at
moft 2 grains, being added either to A or B, will communicate
motion to the whole; which fhews that the effects of friction
will not be fo great as a weight of 1 or 2 grains. In fome
cafes, however, efpecially in experiments relating to retarded
motion, the effects of friction become fenfible; but may be very
readily and exactly removed by adding a fmall weight of 1.5 or 2
grains to the defcending body, taking care that the weight added
is fuch as is in the leaft degree ſmaller than that which is juft
+
Balance.
91
fufficient to ſet the whole in motion, when A and B are equal,
and balance each other before the moving force is applied.
Atwood on Motion, p. 316.
BALANCE, as diftinguiſhed from the Steelyard, is a lever
with equal arms, whofe fulcrum or centre of motion is fituated
immediately above the centre of gravity of the beam, when hori-
zontal: it is uſed chiefly in determining the equality or differ-
ence in the weights of different bodies.
Some remarks on the nature of the balance were made when
we treated of the lever in the firſt volume; where alſo we
fhewed how to correct the deception occafioned by a falfe
balance in addition to what was there ftated, we fſhall now
preſent a few fuch obſervations as may be moſt ſerviceable in
directing the accurate conftruction of this inftrument.
1. The axis of motion of the balance fhould be above the
centre of gravity of the beam.
2. A flender index, or tongue (as it is called), paffes through
the centres of gravity and motion of the beam, perpendicular
to its axis by this index the horizontal pofition of the beam,
when loaded, in the compariſon of weights, is determined.
3. When the balance unloaded is quiefcent, and therefore
horizontal, if the index which paffes through the fulcrum be
directed to any fixed point; and again when the balance is re-
verſed, it be directed to the fame fixed point; it is in the right
line which joins the centre of gravity and the fulcrum.
By this means the poſition of the index is adjuſted.
4. The perpendicular diſtances of the points of application of
the weights to be compared, from the right line which joins the
centres of gravity and of motion, ſhould be equal, that is, the
arms of the balance ought to be equal.
5. The points of application from which the weights are ſuſ-
pended, ſhould be in the fame right line perpendicular to the
line joining the centres of gravity and of motion.
6. The nearer the right line joining the points of application
is to the centre of motion, the larger vibrations of the balance,
and a more fenfible effect, will be produced.
7. If the centre of motion be fituated below the line joining
the points of application, the beam, when loaded with equal
weights, will overſet, reft in any pofition, or equilibrate, accord-
ing to the weight.
8. When two given weights, fufpended from the arms of a
balance, are in equilibrio, if theſe weights when transferred to
the oppofite ſcales be ftill in equilibrio, the arms of the balance
are equal.
9. The various adjustments of the balance are theſe: 1ft.
equal weights are readily found, whatever be the ſtate of the
$
02
MACHINES.
1
balance; for, if they reduce the beam to the fame pofition,
when fucceffively applied to the fame arm, they muſt be equal:
then if theſe equal weights tranfpoſed do not diſturb the poſition
of the beam, the arms are equal. 2dly. If unequal weights
tranfpofed produce equal deflections of the beam, the points of
fufpenfion are in the fame right lines, perpendicular to that
which joins the centre of gravity and motion; and therefore
the line joining theſe points will be horizontal when the beam
hangs freely. 3dly. Let the index be directed to any fixed point,
then the beam being reverſed, if it ftill pafs through the fame
point, the index is perpendicular to the axis of the beam.
10. The equilibrium of the balance will be affected by the
tongue, unless it be continued below the centre of motion, fo
that the momenta on both fides may be equal and oppoſite.
11. Minute differences of weight. are rendered more dif-
cernible by diminishing the friction upon the axis, as by fufpend-
ing it in a fork with fprings, &c.
Indeed when balances are required for accurate philofophical
purpoſes, much caution is requifite in the various parts of the
conftruction, and many peculiar contrivances have been adopt-
ed: fome of the beſt of theſe are given in the following article.
Hydrostatic BALANCE, is an inftrument contrived to determine
accurately the fpecific gravity of both folid and fluid bodies.
One of the moft ingenious forms of this balance is exhibited in
fg. 5. pl. VI. where VCG is the ſtand or pillar, which is to be
fixed in a table. From the top A hangs by two filk ftrings the
horizontal bar BB, from which is fufpended by a ring i the
fine beam of a balance b; which is prevented from defcending
too low on either fide by the gently fpringing piece tx y z, fixed
on the ſupport M. The harneſs is annulated at o, to fhew dif
tinctly the perpendicular pofition of the examen, by the finall
pointed index fixed above it.
The ftrings by which the balance is fufpended, pafling over
two pulleys, one on each fide the piece at A, go down to the
bottom on the other fide, and are hung over the hook at v; which
hook, by means of a ſcrew P, is moveable to about the diſtance
of an inch and a quarter backward and forward, and therefore
the balance may be raiſed or depreffed fo much. But if a
greater elevation or depreffion be required, the fliding piece
which carries the fcrew P, is readily removed to any part of the
fquare brafs rod VK, and fixed by means of a fcrew.
The motion of the balance being thus adjuſted, the reſt of
the apparatus is as follows: HH is a ſmall board fixed upon the
piece D, under the fcales d and e, and is moveable up and down
in a low flit in the pillar above C, and faſtened at any part by a
fcrew behind. From the point in the middle of the bottom of
Hydrostatic Balance.
93
each ſcale hangs, by a fine hook, a brafs wire a d, and ar: theſe
pafs through two holes m, m, in the table. To the wire ad is
fufpended a curious cylindric wire rs, perforated at each end
for that purpoſe: this wire rs is covered with paper graduated
by equal divifions, and is about five inches long.
In the corner of the board at E is fixed a brafs tube, on which
a round wire h l is ſo adapted as to move neither too tight nor
too freely, by its flat head I. Upon the lower part of this
moves another tube Q, which has fufficient friction to make it
remain in any pofition required: to this is fixed an index T,
moving horizontally when the wire bl is turned about, and
may therefore be eaſily ſet to the graduated wire rs. From the
lower end of the wire rs hangs a weight L; and from that a
wire pn, with a ſmall braſs ball g about one fourth of an inch
diameter. On the other fide from the wire a c hangs a large
glafs bubble R, by a horfe-hair.
Now, let us fuppofe the weight L taken away, and the wire
p n fufpended from s: and on the other fide let the bubble R
be taken away, and a weight, as F, fufpended at c in its room.
This weight F we fuppofe to be fufficient to keep the ſeveral
parts hanging from the other fcale in equilibrium; at the fame
time that the middle point of the wire pn is at the ſurface of
the water in the veffel O. The wire pn is to be of ſuch a ſize
that the length of one inch ſhall weigh four grains.
Now it is evident, fince braſs is about eight times heavier
than water, that for every inch the wire finks in the water, it
will become half a grain lighter; and half a grain heavier for
every inch it riſes out of the water: confequently, by finking
two inches below the middle point, or rifing two inches above
it, the wire will become in effect one grain lighter or heavier.
If, therefore, when the middle point is at the furface of the
water in equilibrio, the index T be fet to the middle point of
the graduated wire r s, and the diſtance of r and of s from the
index be each reckoned to contain 100 equal parts; then, if in
weighing bodies the weight is required to the hundredth part of
a grain, it may be eafily obtained by proceeding thus:-Let the
body to be weighed be placed in the fcale e; and let this be fo
determined that one grain more fhall be too much, and one
grain leſs too little. Then the balance being moved gently
up or down by the fcrew P till the equilibrium be nicely
fhewn at o, if the index T be at the middle point of the wire
rs, it fhews that the weights put into the ſcale e are juſt equal
to the weight of the body.
But if the index T ftand nearer to r than to s, as ſuppoſe 36
of the 100 parts, it fhews the number of grains in the fcale e
were leſs than equal to the weight of the body in ſcale d, by 36
94
MACHINES.
hundredths of a grain: and if, on the other hand, the index had
ftood at the divifion 36 below the middle point of rs, then would
the grains in the ſcale e indicate more than the real weight in d
by 36 hundredths of a grain.
Inftead of putting the body in the ſcale d as before, let it be
appended with the weight F at the hook c by a horſe-hair, as at
R, fuppofing the veffel of water were away; then obſerve the
equilibrium, and as it hangs, let it be immerfed in the water of
the veffet O, and it will become much lighter; the number of
grains and parts of grains, determined as before, required to
reftore the equilibrium, will fhew the weight of water equal in
bulk to the body immerfed.
In practice, the wire p n ſhould be oiled, and then wiped as
clean as poffible; enough will remain to prevent the water ad-
hering to it. The balance ought to be raiſed very gently, and
when brought to an equilibrium fhould be gently agitated, to
fee whether it will return to the equilibrium again.
For the defcription of M. Paul's accurate fteelyard to anſwer
the fame purpoſes, ſee the article STEELYARD.
M. Prony, of whom we have often had occaſion to ſpeak,
has invented a ſtand or fupport for balances of all dimenfions,
which is calculated to render the operations for which thefe
inſtruments are uſed, more expeditious and convenient, without
diminiſhing their accuracy. His account is publiſhed in the
Annales de Chimie, xxxvi. 50.
"Several experiments," fays he, "in which I was engaged
during the courfe of the laft winter, put me under the neceflity
of contriving a fupport which might be applied promifcuously
to every kind of balance, whether provided with a fufpending
handle or not, and which, without detriment to its accuracy,
ſhould afford me commodious means of fucceffively raifing and
lowering it. It is well known how embarraſſing and laborious
the operation of weighing is, when performed with balances
fupported by the hand; though this is often only the ſmalleſt in-
convenience with which their uſe is attended.
"Various artiſts have contrived fupports, commodious in
their uſe, and ingenious in their principle; but as each of theſe
fupports can only be adapted to a fingle balance, they become
fo expenfive as to be out of the reach of the majority of artifts
and experimentalifts. I think, therefore, I fhall do them an
acceptable fervice by publiſhing, in compliance with the re-
queft of feveral eminent chemifts, the defcription of a fupport,
which, befides the advantage of being adapted for all kinds of
balances, poffeffes that of being conſtructed, at a ſmall expenfe,
either in wood or metal.
"A triangular foot of brafs A a, a, a (figs. 1. and 2. plate
Hydrostatic Balance.
95
VI. reprefenting the elevation and fection of my apparatus), has
its three extremities a, a, a, firmly fcrewed down upon a table
or horizontal plane. Into the part A of this foot is ſcrewed a
cylindrical rod A B, which may be of any arbitrary length: it
may even be convenient to have two of theſe of different lengths,
in order that they may be changed, when we wish to employ
the machine for very large balances. Thoſe which I have made
ufe of are, the one half a metre, and the other one metre (39′4
inches) in length.
"A vertical pulley, P, is placed at the top of the ſtem A B,
in fuch a manner that the fame vertical plane paffes through the
axis of the rod, and through the horizontal axis of the pulley;
the block or collar CD of this pulley has at its lower part a tube
CB, into which enters, with a gentle friction, the fuperior ex-
tremity of the rod AB; a fcrew, E, ferves to keep the pulley in a
fixed pofition.
"Another pulley, P, is fixed at the bottom of the rod AB, in
fuch a pofition that the tangent of the pulleys P and P is parallel
to the axis of the rod AB.
I
"A cord Ktp HGPF, to the end of which is fufpended on
the outſide of the vertical table K a ſmall weight k, paffes
through a hole t made in the foot a, rolls over the pulleys p and
P, and is attached at F to a piece m m¹ n q, which has the form
of a fork, and to which are fufpended (as I fhall fhortly explain)
the balance, the weights, and the fubftances that are to be
weighed. Fm is a button, which being fcrewed at the top of
the fork, receives the end of the cord, and by means of a knot
made on it fuftains the fork.
"The tail or handle of this fork is of a priſmatic form at the
part m'n; this prifmatic part enters a groove ƒ ƒ made at the ex-
tremity N of the horizontal piece NO, ſo that it can ſlide freely
in this groove either upwards or downwards, its courfe being
however limited at m', where it is ſtopped by the enlarged handle
of the fork, and at n by the greater width produced by the fepa-
ration of the two branches of the fork.
"The piece NO, which is hollow, and interfected at O by
the ſtem AB, can flide along and turn round this ftem: when it
is brought to its proper height, it is fecured by means of the
ſcrew V, and it is then neceffary, firſt, that it ſhould be at ſuch
a height that, when the ſtop m refts on the fide of the groove ƒƒ,
or when NO can move no further down, the ſcale of the balance
ſhall be in contact with the table or horizontal plane, in order
that we may afterwards be able to raiſe it the whole height of
ƒn; ſecondly, that the cord FF be in one and the fame vertical
plane with HG.
96.
MACHINES.
"The groove at N ought to be fituated in fuch a manner
that the axis of the prifmatic part of the tail of the fork, and
the cord FF', fhall always be in the fame verticle plane, or in a
parallel line with the axis of the ftem AB.
"Theſe difpofitions being made, let us imagine the two
branches n g of the fork to be perforated with holes of different
diameters, in order to receive horizontal pins (gg) of different
fizes; and we ſhall have all that is requifite for the ordinary
operations of weighing, performed in the air with balances,
the beams of which are fufpended from above.
"In fact, whatever kind of balance we ufe, we are to intro-
duce the extremity of its ſuſpending handle into the fork nq,
and infert into the round hole, which the handle of the balance
always has at its fuperior extremity, any one of the pins that
will enter with cafe; we then apply the piece ON in fuch a
manner as to fulfil the conditions above laid down for the
pofition of this piece; after which, it is to be fixed by the
fcrew V. This being done, the ſcales of the balance are to
be charged, which being in contact with the table, or horizontal
plane, can have no motion. When the ſcales are charged, we
lay. hold of the fmall ball k, and draw the cord which fufpends
it fo as to raiſe the balance very flowly: if the ſcales be not in
equilibrio, the cord is to be loofened till they reft again upon
the table, and fo fucceffively.
"A counterpoife, Q, fufpended to the cord FG, ought to
preferve the equilibrium with the weight of the balance. By
means of this precaution, it comes to paſs, that the common
centre of gravity of all the forces fupported by the pulley P,
falls in all cafes upon the axis of the ftem AB, which thus has
no tendency to bend.
“If we wiſh now to uſe a hydroftatic balance, we adapt to
the ſtem AB a ſmall board ON, fig. 3. which, by means of a
cylindrical hole at O, may flide along the rod AB, and be fixed
at any arbitrary height by a ſcrew at V. Another piece, or board,
K' K', is placed upon V'N', in fuch a manner that the holes
TT correfpond with the centre of the fcales, under which are
placed the hooks intended for holding the ſubſtances ſuſpended
in the water, and K' K' is fixed upon V¹ N' by means of
fcrews V¹.
I
"Theſe arrangements being made, let the piece N' O¹and
the board K'K', be placed in fuch a manner that, first, the
whole height of the balance be placed between this piece and
the board, and that the ſcales LL be in contact with the board
K¹K, their centres correfponding with holes made in TT
Secondly, that K'K' be fufficiently elevated to enable us to
འ
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}
Hydrostatic Balance.
place under it the veffels WW, filled with water, and cont
veniently to immerfe, in one of thefe veffels, the fubftances
which we wiſh to weigh hydroſtatically.
"According to the common practice, thefe fubftances are
fufpended by a very thin wire; but by placing. after my method,
two veffels, and fufpending to the two ſcales wires of equal
diameter, the one of which fupports the ſubſtance that is to be
weighed, and the other merely in part immerfed, the magnitude
of the diameter will have no influence upon the accuracy of the
operation; for, let us fuppofe the apparatus to be adjuſted in
fuch a manner that at firſt the two wires were in equilibrio
with each other (which may eaſily be obtained by varying the
height of the water in the veffels), theſe two wires will ſtill be
in equilibrio, when the beam FF¹, being elevated, will remain
in its horizontal pofition: whence it follows, that if one of the
wires have fufpended from it a fubftance immerfed in the water,
and we place in the oppoſite ſcale, and confequently out of the
water, a weight adequate to keep the equilibrium with the im-
merſed ſubſtance, for a horizontal pofition of the beam, the
equilibrium will ſtill be maintained, whatever may be the eleva-
tion or depreffion of the beam, provided it continue in a hori
zontal pofition; for the lengths of the wires, either above or
below the furface of the water, being equal, the difference be-
tween the ſpecific weight of the water and that of the metal
will operate equally upon both extremities of the beam. It is
evident that this advantage will not be obtained if we employ
only the wire to which the fubftance is fufpended, and that the
equilibrium, eſtabliſhed for a certain elevation and a horizontal
poſition of the beam, will not apply to other elevations of the
beam by preferving it in the horizontal pofition.
"It is to be remarked, that my method compenfates not
only for the exceſs of the ſpecific weight of the wires over that
of the water, but alſo for that which depends upon the adheſion
of the fluid to the wires, and the covering of water which they
carry along with them.
"All that has been faid hitherto applies only to balances
that are provided with ſuſpending handles; but, in order to
render this fupport abfolutely univerfal in its ufe, it was necef-
fary that it ſhould be poffible to adapt it to a beam which had
nothing but its centres; for which purpoſe I contrived an ap-
paratus, which is fufpended, like thofe of a common balance,
to the fork n q, and which may receive the centres of any
beam. The engraved plates of my machine reprefent it pro-
vided with this apparatus, the conftruction of which is as
follows.
A
"A piece ♪♪ has a fcrewed hole bored into it at sinto
VOL. II.
H
MACHINES.
which the fcrew dd is inferted half its length. Another hole,
made at is, in a perpendicular direction to the firft, receives the
pin g g, to which all the inferior apparatus is fufpended. This
hole s fupplies the place of that which is found at the upper ex-
tremity of the fufpending handle of balances.
"The two other vertical pieces r, r, fig. 4, have at their upper
part cylindrical holes not fcrewed, in which the ſcrew dd can
turn freely. Theſe ſuperior parts are placed at an arbitrary di
ftance, and retained in their fituation by means of four nut-ſcrews
u, u, u, u, each of the pieces being faftened between two of
thefe nut-ſcrews. A cylindrical rod bb traverfes the inferior
parts of thefe pieces rr, and is fixed there by means of nut-
fcrews, in fuch a manner that the fuperior and inferior points of
the pieces rr are invariably at the fame diſtance.
"Each of theſe pieces r r has, upon the furface which is per-
pendicular to the direction of dd and bh, a groove e e, and a cir-
cular aperture X, having at its lower part a fmall bracket of
poliſhed ſteel a a, intended to ſupport one of the centres of the
beam. Into the upper part of the grooves e e a rule e' e' is in-
troduced, which must enter with tightnefs, and which, with the
pieces d d and bh, give ſuch a ſolidity to the apparatus, that the
adjuſtment of its parts cannot be in the ſmalleſt degree de-
ranged. The remainder of the groove, which is not occupied
by e' e', ought to be of a length fomewhat greater than that of
the largeſt cock or index adapted to the beams which we ſhall
have to uſe.
"The method of uſing the apparatus which I have juſt de-
fcribed is very fimple. The beam which we intend to em-
ploy is placed between the two branches rr, which are re-
moved from each other till the centres can be brought oppofite
to the circular holes X; the pieces r, r, are then brought to-
gether in fuch a manner that the centres enter theſe holes X,
and fo as ftill to leave fome room for motion between theſe
pieces and the body of the beam, in order that the oſcillations.
of the balance may be perfectly free. The pieces r, r, are
brought parallel with each other, and the adjustment of the
apparatus is rendered perfectly firm, by means of nut-fcrews,
by the ſmall cylindrical rod bh, and by the rule e' e'. The
apparatus being adjuſted in this manner, it is fufpended to the
fork nq, by inferting the pin g g into the hole s, and the
balance is uſed in the manner that has already been explained.
We know the equilibrium to be eſtabliſhed, and the beam to
be horizontal, when the index y y divides the breadth of the
fpace e e into two equal parts; but, in order to aſcertain the
circumftance with greater accuracy, I have attached to the rule
e' e' a plummet e' i', by means of which we may diftinguiſh the

7
+
"
Danish Balance
99
flightest deviations of the index from the perpendicular di
rection."
+
Danish BALANCE, is a kind of balance or fteelyard in common
ufe in many parts of the continent of Europe, and is of a very
fimple conftruction. It is thus defcribed in the Encyclopedia
Britannica (art. Steelyard): "It confifts of a batten of hard
wood, having a heavy lump K (fig. 7. pl. VI.) at one end, and a
fwivel hook b at the other. The goods to be weighed are fuf-
pended on the hook, and the whole is carried in a loop of whip-
cord F, in which it is flid backward and forward till the goods
are balanced by the weight of the other end. The weight of
the goods is eſtimated by the loop on a ſcale of divifions in
harmonic progreffion. They are marked (we prefume) by trial
with known weights."
It would feem, then, that the writer of the article, whence
the above is extracted, was not aware that the divifions on the
Daniſh balance might be effected by a method purely geo-
metrical: yet M. Roemer pointed out ſuch a method more than
a century ago, in Recueil des Machines appr. par L'Acad. Roy.
Sci. tom. I. pa. 80. It is in fubftance as follows. Let AC (figs.
7. 8.) be the diſtance between the point A from which the body
whoſe weight is to be determined is fufpended, and C the
centre of gravity of the balance when the weight W is not at-
tached to it. From the point C draw an indefinite line CD,
making any angle ACD with the line AC on which the divifions
of the balance are to be marked; and through A draw another
right line AN parallel to CD. Set off any equal distances CE,
EF, FG, GH, HI, &c. along the line CD; and upon AN. fet
off the diftance AB equal to one of the equal diſtances, as CE,
upon CD. From B as a fixed point draw lines BE, BF, BG,
BH, &c. to the ſeveral points of divifion on CD; and they will
interfect the line AC, in the points 1, 2, 3, 4, 5, &c. where the
ſubdiviſion marks ought to ftand in the balance, fig. 7. The
numbers 1, 2, 3, 4, &c. fig. 8. denote fo many times the actual
weight of the balance and its knobs, independent of the adven-
titious weight W. Thus if the unloaded balance weigh 6lbs,
the diſtances marked 1, 2, 3, 4, 5, &c. in fig. 8. would corre-
fpond to the fubdivifion marks, 6, 12, 18, 24, 30, &c. in fig. 7.
M. Roemer has not demonftrated the truth of this conftruc-
tion: but it may be eaſily fhewn thus: Let w be the weight of
the balance and knob, and W that of the body which is to be
afcertained by the inftrument. Then, when the point of fuf-
penſion is that marked 1, fig. 8. we have in the triangles AB r
ICE, the fides AB and CE equal, alfo angle BA I=1CE,
and B 1 A=E1 C; therefore thefe triangles are both equi
angular and equiláteral; confequently, A I≈ 1 C, and by the
H 2
100
MACHINES.
natures of the lever, and the centre of gravity W=w. Again, în
like manner when the point of fufpenfion is 2, the triangles AB 2,
2 CF, are equiangular; and fince FC=2 AB, we have C 2=
2 A 2, and W=2 w. So alfo the triangles AB 3, 3 CG, are
equiangular; whence becaufe CG=3 AB, C 3=3 A 3, and
W=3 w. And fo on, through the whole divifion.
This balance has been defcribed more on account of its
curioſity than actual utility: for in aſcertaining large weights
it would be extremely cumberſome and difficult to manage. In
the determination of weights not exceeding twenty or thirty
pounds, it might, however, be rendered very manageable: for it
might be about the length of an excifeman's rod, or a walking
ftick, having a knob of lead at one end; and in this caſe the
diviſions near the knob might be ſo numerous as to enable a
perſon to weigh accurately to quarters of pounds, if not to
ounces: the rod might be moved to and fro upon a chair-back,
or the edge of a treffel; and thus this inftrument might often
be more conveniently uſed than a ſpring ſteelyard.
BALANCE of a Clock or Watch, is that part which, by its motion,
regulates and determines the beats. The circular part of it is
called the rim, and its fpindle the verge; there belong to it
alſo two pallets or nuts, that play in the fangs of the crown-
wheel: in pocket watches that ſtrong ftud in which the lower
pivot of the verge plays, and in the middle of which one pivot
of the crown-wheel runs, is called the potence: the wrought
piece which covers the balance, and in which the upper pivot
of the balance plays, is the cock; and the ſmall ſpring in the
new pocket watches is called the regulator.
The motion of a balance, as well as that of a pendulum,
being reciprocating, while the preffure of the wheels is con-
ſtantly in one direction, it is obvious that ſome art must be uſed
to accommodate the one to the other. When a tooth of the
wheel has given the balance a motion in one direction, it muſt
quit it, that it may get an impulfion in the oppofite direction.
The balance or pendulum thus eſcaping from the tooth of the
wheel, or the tooth eſcaping from the balance, has given to the
general conſtruction the name of fcapement among our artiſts.
See SCAPEMEnt.
Some of the most important propofitions relative to watch
balances may be conciſely ftated as follows: 1. The balance of
a watch is analogous to the pendulum in its properties and uſe,
The ſimple balance is a circular annulus, equally heavy in all
its parts, and concentrical with the pivots of the axis on which
it is mounted. This balance is moved by a ſpiral ſpring called
the balance ſpring, the invention of Mr. Hook,
2. The pendulum requires a lefs maintaining power than
Balance of a Watch.
101
:
the balance. Hence the natural ifochroniſm of the pendulum
is leſs diſturbed by the relatively ſmall inequalities of the main-
taining power.
3. The elaftic force of the fpring which impels the circum-
ference of the balance is directly as the tenfion of the fpring;
that is, the weights neceffary to counterpoiſe a ſpiral ſpring's
elaftic force, when the balance is wound to different diftances
from the quiefcent point, are in the direct ratio of the arcs
through which it is wound.
4. The vibrations of a balance, whether through great or
fmall arcs, are performed in the fame time. For the accelerat-
ing force is directly as the diſtance from the point of qui-
efcence: hence, therefore, the motion of the balance is analo-
gous to that of a pendulum vibrating in cycloidal arches (vol. i
art. 276.)
5. The time of the vibration of a balance is the fame as if a
quantity of matter, whoſe inertia is equal to that by which the
mafs contained in the balance oppofes the communication of
motion to the circumference, defcribed a cycloid whofe length
is equal to the arc of vibration, defcribed by the circumference,
the accelerating force being equal to that of the balance,
6. The times of vibration of different balances are in a ratio
compounded of the direct fubduplicate ratios of their weights
and femidiameters, and the inverfe fubduplicate ratio of the
tenfions of the fprings, or of the weights which counterpoife
them, when wound through a given angle.
7. The times of vibration of different balances are in a ratio
compounded of the direct fimple ratio of the radii and direct
fubduplicate ratio of their weights, and the inverſe ſubduplicate
ratio of the abfolute forces of the fprings at a given tenfion.
8. Hence the abfolute force of the balance fpring, the di-
ameter and weight of the balance being the fame, is inverfely
as the fquare of the time of one vibration.
9. The abfolute force or ftrength of the balance ſpring, the
time of one vibration, and the weight of the balance being the
fame, is inverſely as the fquare of the diameter.
10. The weight of the balance, the ftrength of the ſpring
and time of vibration being the fame, is inverſely as the fquare
of the diameter.
Hence, a large balance, vibrating in the fame time with the
fame ſpring, will be much lighter than a ſmall one.
II. If the rim of the balance be always of the fame breadth
and thickneſs, fo that the weight fhall be as the radius, the
ſtrength of the ſpring muſt be as the cube of the diameter of
the balance, that the time of vibration may continue the fame,
1
102
MACHINES.
12. The momentum of the balance is increafed better by in-
creaſing its diameter than its weight.
13. The longer a detached balance continues its motion the
better.
14. The greater the number of vibrations performed by a balance
in a given time, the leſs ſuſceptible is it of external agitations.
15. Slow vibrations are, to a certain extent, preferable to
quick vibrations: but there is manifeftly a limit; for if the
vibrations be too flow, the watch will be liable to ftop.
16. A balance fhould defcribe as large arches as poffible, as
fuppofe 240°, 260°, 300°, or an entire circle.
Firſt, becauſe the momentum of the balance is thus increaſed;
and therefore the inequalities in the force of the maintaining
power bear a lefs proportion to it, and of confequence will
have lefs influence. 2dly. The balance is leſs fufceptible of ex-
ternal agitations. 3dly. A given variation in the extent of the vi-
brations produces a lefs variation in the going of the machine.
But care muſt be taken that in thefe great vibrations, the
ſpring ſhall neither touch any obftacle, nor its fpires touch
each other in contracting.
17. The time of the vibration of the balance is increaſed by
heat, and diminiſhed by cold. Firft, becauſe the length of the
fpiral fpring is increaſed by heat, and therefore its force di-
miniſhed; and the contrary by cold. 2dly. The diameter of
the balance is increaſed by heat, and therefore alfo the time of
vibration; and the contrary by cold.
18. That balance is the moft perfect which, without the
compenfation of a thermometer, is moft fubject to the influ
ence of heat and cold. Becauſe the obftructions from oil and
friction act as a compenſation to the expanſion or contraction
of the ſpring and balance; therefore that balance which is moſt
affected is moft free from the influence of oil and friction.
19. The errors in the going of a watch, arifing from the
change of temperature, may be corrected by varying the length
of the balance fpring. Nevertheleſs, as it is extremely difficult
to form an ifochronal ſpiral, any variation in its length is danger-
pus, becauſe we fhall thus probably loſe that point which de-
termines its iſochroniſm.
20. The errors in the going of a watch, occafioned by the
variation of temperature, may be corrected by varying the di-
ameter of the balance.
This may be effected by a peculiar contrivance which has
obtained the name of the expanfion balance, being compofed of
two different metals which poffefs different degrees of ex-
panfibility, as braſs and fteel, for inftance; of which two metals
Bark-mill.
103
it has been obferved, that the increaſe of dimenſions by ex-
panfion, in like elevations of temperature, is nearly as 2 to 1.
For, according to Mr. Smeaton's experiments (vol. 48, Phil.
Trans.), the correfponding expanfions of hard fteel and brafs
wire are as 147 and 232, the expanſions being occafioned by a
change from a medium temperature to that of 180° of Fahren-
heit's thermometer. One of the moſt approved conftructions
of an expanſion balance, is exhibited in plate VII. and is thus
deſcribed by Mr. Nicholſon: The outer part of the rim is braſs,
and the inner ſteel. After this compound rim is brought to its
figure by turning, it is cut through in three places, A; B, C,
which fets one end of each third part of the periphery at liberty
to move outwards, when the temperature is diminiſhed, or in-
wards when it is increaſed. D, E, F, are three fimilar and equal
maffes of metal, fitted upon the circular bars in a proper manner
to admit of their being fixed at any required diſtance from the
extremity, where the motion is moft confiderable. G, H, I, are
three ſcrews, the heads of which may be ſet nearer to, or further
from, the centre, and ferve as weights to effect the adjuſtments
for pofition and rate. The peculiar advantage of this, balance
may be explained as follows: when an increaſe of heat di-
miniſhes the elaſtic force of the pendulum fpring K, the outer
braſs rim being lengthened more than the ſteel, muſt throw the
weights D, E, F, nearer to the axis, and diminiſh the effect of
the inertia of the balance, which confequently is as fpeedily
carried through its vibration as before. And on the contrary,
when cold weather adds to the elaſtic force of the ſpring, the
fame weights are alſo thrown further out, and prevent the ac-
celeration which would have followed. The exact adjuſtment
of the weights is found by trial of the going of the machine:
if it gain by heat, the weights do more than compenfate, and
muſt be moved further from the extreme ends of the circular
compound bars; but if the gain be produced by cold, the ſpring
predominates, and the weights will accordingly require to be
fet further out.
BARK-MILL, a mill conftructed for the purpofe of grinding
and preparing bark, till it is fit for the uſe of a tanner.
Bark-mills, like moſt other mills, are worked ſometimes by
means of horſes, at others by water, and at others by wind.
One of the beſt mills we have feen deſcribed for theſe purpoſes,
is that invented by Mr. Bagnall, of Worfley in Lancaſhire: this
machine will ſerve not only to chop bark, to grind, to riddle
and pound it; but to beam, or work green hides and ſkins out
of the maftering or drench, and make them ready for the oufe
or bark liquor; to beam fheepskins and other ſkins for the
fkinner's ufe; and to ſcour and take off the bloom from tanned
104
MACHINES.
leather, when in the currying ftate. The nature and connee-
tion of the different parts of this contrivance may be under-
ſtood from the three figures on the right-hand fide of plate VII.
together with the following defcription.
Fig. 1. is a horizontal plan of the mill. Fig. 2. longitudinal
fection of it. Fig. 3. tranfverfe fection of it.
A, The water-wheel, by which the whole machinery is
¿worked.
B, The (hafts.
C, The pit-wheel, which is fixed on the water-wheel fhaft B,
and turns the upright fhaft E, by the wheel F, and works the
cutters and hammer by tapets.
D, The fpur and bevil-wheel at the top of upright ſhafts.
E, The upright ſhaft.
F, The crown-wheel, which works in the pit-wheel C.
G, The fpur-nut to turn the ftones I.
P, The beam, with knives or cutters fixed at the end to chop
or cut the bark; which bark is to be put upon the cutters or
grating i, on which the beam is to fall.
The tryal that receives the bark from the cutters i, and
conveys it into the hopper H, by which it defcends through the
fhoe J to the ftones I, where it is ground.
K, The fpout, which receives the bark from the ftones, and
conveys it into the tryal L; which tryal is wired to fift or drefs
the bark, as it defcends from the ftones I.
¿M,. The trough to receive the bark that paffes through the
tryal L.
R, The hammer, to cruſh or bruiſe the bark that falls into
the difh S, which ſaid diſh is on the incline, ſo that the hammer
keeps forcing it out of the lower fide of the faid diſh, when
bruifed.
k, A trough to receive the duſt and moſs that paffes through
the tryal Q
T, 1 he bevil-wheel, that works in the wheel D, which
works the beam-knife by a crank V at the end of the ſhaft u
W, The penetrating rod, which leads from the crank V to
the start.x
, The ſtart, which has feveral holes in it to lengthen or
fhorten the ſtroke of the beam-knife. ..
4
y,. The fhaft, to which the flide rods b, h, are fixed by the
ſtarts n,n. bal
h, The flide rod, on which the knife fis fixed; which knife
is to work the hides, &c. On the knife are two ſprings a, to
let it have a little play as it makes its ſtroke backwards and for
wards, ſo that it may not fcratch or damage the hides, &c.
Is a catch in flide-rod, which catches on the arch-head es
Bark-mill.
100
and the faid arch-head conveys the knife back without touching
the hide, and then falls back to receive the catch again.
1, The roller to take up the flide-rod b, while the hides are
fhifting on the beam b by pulling at the handle m.
b, The beam to work the hides, &c. on. Each beam has four
wheels p, p, working in a trough road g, g, and removed by the
levers c,'c. When the knife has worked the hide, &c. fuf-
ficiently in one part, the beam is then fhifted by the lever cas
far as is wanted.
d, A prefs, at the upper end of the beam, to hold the hide
faft on the beam while working.
e, An arch head, on which the ſlide-rod b catches.
ƒ, The knife fixed on the flide-rod b, to work the hides, &c.
i, Cutters or grating to receive the bark for chopping.
The beam P, with knives or cutters, may either be worked by
tapers, as defcribed, or by the bevil-wheel T, with a crank, as
a as
to cut the fame s fhears.
The knife ƒ is fixed at the bottom of the ftart, which is fixed
on the flide rod b; the bottom of the ſtart is ſplit open to
admit the knife, the width of one foot; the knife ſhould have
a gudgeon at each end, to fix in the open part of the ſtart; and
the two fprings a, a, prevent the knife from giving too much
way when working; the knife fhould be one foot long and four
or five inches broad.
The arch-head e will ſhift nearer to, or further from, the beam
, and will be fixed fo as to carry the knife back as far as is
wanted, or it may be taken away till wanted.
The roller is taken up by pulling at the handle´m, which
takes up the ſlide-rod ſo high as to give head-room under the
beam-knife. The handle may be hung upon a hook for that
purpoſe. The flide-rod will keep running upon the roller all
the time the hide is fhifting; and when the hide is fixed the
knife is put on the beam again by letting it down by the handle
m. There may be two or more knives at work on one beam at
the fame time, by having different flide-rods. There should be
two beams, fo that the workmen could be ſhifting one hide, &c.
while the other was working. The beam must be flat, and a
little on the incline. As to the breadth it does not matter; the
broader it is the lefs fhifting of the hides will be wanted, as the
levere will ſhift them as far as the width of the hide, if required.
Mr. Bagnall has formed a kind of prefs d, to let down, by a
lever, to hold the hide faſt on each fide of the knife if required,
fo that it will fuffer the knife to make its back ftroke without
pulling the hide up as it comes back. The flide-rod may be
weighted, to cauſe the knife to lay ftreſs on the hide, &c. ac-
cording to the kind and condition of the goods to be worked.
106
MACHINES.
Hides and ſkins. for the ſkinner's ufe are worked in the fame
way as for the tanners.
Scouring of tanned leather for the currier's uſe will be done
on the beam, the fame as working green hides. It is only
taking the knife away, and fixing a ſtone in the fame manner
as the knife by the faid joint, and to have a bruſh fixed to go
either before or after the ſtone. The leather will be better
fecured this way than by hand, and much fooner.
The whole machinery may be worked by water, wind, fteam,
or any other power. And that part of the machinery which
relates to the beaming part of the hides may be fixed to any
horſe bark-mill, or may be worked by a horfe or other power
feparately.
BARKER'S MILL is a kind of water-mill, invented by Dr.
Barker, which without either wheel or trundle performs the
operation of grinding corn. This mill is repreſented in fig. 3,
pl. IV. in which A is a pipe or channel that brings water from
a refervoir to the upright tube. The water runs down the
tube, and thence into the horizontal trunk C, which has equal
arms; and, laſtly, runs out through holes at d'and e, opening on
contrary fides near the ends of thofe arms. Thefe orifices d, e,
I have fliders fitted to them, ſo that their magnitude may be in-
creaſed or diminiſhed at pleaſure.
The upright ſpindle D is fixt in the bottom of the trunk,
and ſcrewed to it below by the nut g; and is fixt into the trunk
by two cross bars at f: ſo that, if the tube B and trunk C be
turned round, the fpindle D will be turned alfo.
The top of the ſpindle goes fquare into the rynd of the upper
mill-ftone H, as in common mills; and as the trunk, tube, and
ſpindle, turn round, the mill-ſtone is turned round thereby. The
lower or quiefcent mill-ftone is reprefented by I; and K is the
floor on which it reſts, in which is the hole L to let the meal run
through, and fall down into a trough which may be about M.
The hoop or cafe that goes round the mill-ftone reſts on the
floor K, and fupports the hopper, in the common way. The
lower end of the ſpindle turns in a hole in the bridge-tree GF,
which fupports the mill-ftone, tube, ſpindle, and trunk. This
tree is moveable on a pin at h, and its other end is fupported by
an iron-rod N fixed into it, the top of the rod going through
the firſt bracket O, and having a ſcrew-nut o upon it, above the
bracket. By turning this nut forward or backward, the mill-
ftone is raiſed or lowered at pleaſure.
Whilſt the tube B is kept full of water from the pipe A, and
the water continues to run out from the ends of the trunk; the
upper mill-ftone H, together with the trunk, tube, and ſpindle,
turn round. But if the holes in the trunk were ftopt, no motion
Barker's Mill.
107
would enfue; even though the tube and trunk were full of
water. For, if there were no hole in the trunk, the preffure of
the water would be equal againſt all parts of its fides within.
But when the water has free egrefs through the holes, its
preffure there is entirely removed: and the preffure againſt the
parts of the fides which are oppofite to the holes turns the
machine.
Mr. James Rumfey, an American gentleman, has rather im-
proved this machine, by conveying the water from the reſervoir,
not by a pipe as ADB, in great part of which the ſpindle turns,
but by a pipe which defcends from A, without the frame LN,
till it reaches as low, or lower, than G; and then to be convey-
ed by a curvilinear neck and collar from G to g, where it enters
the arms, as is fhewn by the dotted lines at the lower part of
the figure. A like improvement was made by M. Segner, a
German.
Moſt of the authors who have attempted to lay down the
theory of this mill have fallen into error: the moſt ingenious
theory we have yet ſeen is by Mr. Wm. Waring (given in the
American Tranfactions, vol. iii.); which, with fome fuch cor-
rections as appeared neceffary to adapt his rules to practical
purpoſes, is nearly as follows:
1. The first enquiry relates to the magnitude of the pipe which
conveys the water from the refervoir to the centre of the hori-
zontal tube ed, at g. To this end, let A = the area of the
orifice by which the water is admitted at g;
h = the perpen-
dicular height of the furface of the water in the refervoir above
g; d = the vertical depth of any horizontal ſection of the pipe
below the fame furface; S the ſurface or area of the hori-
zontal ſection of the pipe, at the depth d. Then fince the
areas in the ſeveral parts of the pipe ſhould be inverſely as the
velocities, and the velocities (art. 439, cor 2. vol. I.) are in the
fubduplicate ratio of the depths below the head, thofe areas
muſt be inverſely in the fubduplicate ratio of the depths; confe-
=V, and S = A
So that the pipe muſt
S
quently, A
h
have its bore increaſed from the level of g upwards in the ratio
√
h
d?
of 1 to
be affigned by this ratio, the water will be obftructed in its
paffage.
and if a ſection in any part be leſs than would
2. Of the initial force with which the machine commences its
motion. If we conceive the water preffing in the tube from
g
towards e, previous to the opening of the aperture, there will
manifeftly be no motion occafioned; becauſe the forces on the
oppoſite ſides of the tube balance each other, and the force
1
108
MACHINES.
A
against the end C is refifted by the fixed axle D g, or, if we
confider both arms, it is balanced by the equal force acting upon
the equal end at d, in an oppoſite direction. But if one of the
apertures, as d (its area being=a), is opened, the preffure upon
that portion of the tube is taken away, and the equal and oppofite
preffure upon an equal portion of the contrary fide of the tube,
having now nothing to keep it in equilibrio, tends to move the
arm Cg about the axis Dg: in like manner when the aperture e
(alfo=a) is opened, the preffure, which was previouſly counter-
balanced by the oppofite preffure on the orifice e, now exerts its
tendency to produce a rotatory motion about the axis Dg: fo
that combining together the effects of both theſe unbalanced
preffures, and confidering that the preffure of water upon any
point is proportional to the depth of that point below the
upper furface of the fluid, we fhall have 2 a hw, for the force
which cauſes the rotatory motion to commence; the values of a
and being taken in feet, and w repreſenting 624 lbs. avoirdupois,
the weight of a cubic foot of water. But as the velocity of
rotation increaſes, the preffure depending upon the relative
velocities of the water and the fides of the tube diminiſhes,
and confequently the power is diminiſhed, notwithſtanding what
is gained by that which we now proceed to confider.
3. The centrifugal force. This may be found in a fimilar
manner to that which was adopted when conſidering the theory
of the centrifugal pump (art. 537, vol. i.). Thus, if befides the
preceding notation we take / for the length of each arm gd,
ge, t for the time of rotation, g for 32% feet, the meaſure of the
force of gravity, and 7 for 3.141593; fince a is the fection of the
flowing water at right angles to its motion, we ſhall have, by
T
મ
proceeding as in the article juſt referred to, = the length
27212
gt z
of a column of water, whofe preffure is equal to the centrifugal
force, or
4 m² e re l²
812
= 76.70625
a 12
12
the weight of a column of
water in lbs., which is equivalent to the centrifugal force of the
fluid in both arms. And this is equivalent to the augmentation
of power at the apertures, becauſe fluids prefs equally in all
directions.
4. The inertia of the fluid greatly counteracts the effects of the
centrifugal force. The inertia of the rotatory tube with the
contained fluid would not continue to refift the moving power
after the velocity became uniform, were the fame fluid retained
in it as was in it when the motion was firſt imparted: but as
this paffes off, and there is a continual fucceffion of new matter
acquiring a motion in the direction of the rotatory, there muſt
Barker's Mill.
109
be a conftant re-action againſt the fides of the tube, equal to the
communicating force. Now this re-action is very different
from that of a fluid confined in the tube, when it begins to
move; becaufe a particle at the extremity of the tube is not to re-
ceive its whole circular motion there, but gradually acquires it
by a uniform acceleration during its paffage along the tube:
ſo that we muſt here enquire what force will give to the quantity
of water a l'w, in the time of its paffing through its reſpect-
D
ive horizontal arm, the velocity 277, in the direction of the
aperture. Managing this according to the rules given for forces
in the Dynamics, we ſhall have 12:273 alo 8·0208
X
= 19.6878
t
5
10, for the refiftance in lbs. oppoſed to each arm, ſuch refiſt-
ance being eſtimated as if accumulated at the diſtance from
the centre of motion.
I
5. Acquired velocity of the water. According to the theory of
Hydraulics, the velocity of water iffuing through an aperture at
the depth h below the upper furface of a refervoir is expreffed
by 8.0208/b, which when reduced, in conformity with the ex
periments of Boffut and others, becomes 5b very nearly; and
this is the velocity of the water paffing out of the tubes at the
commencement of the rotation. Then, as √2abw:5b::
(2 a b + 7670625): 5 √(b+38′35312) = 5
W w
= 5
'(b + ·61365 ") = v, the acquired velocity of the water.
6. Ratio of the central force to the inertia. This will be aſcer-
tained by ſubſtituting for v in the expreffion 19.6878 alu, its
value juft found; ſo that we have 98-439/(-61365 +
h) for the inertia, while the centrifugal force is meaſured by
76-70625 . Now we find that 76:706252 : 98-439 2
£12.
61365)::: 192833 (61365), or as 1; (
110
MACHINES.
',
+646) very nearly; which is the ratio of the power gained
2
by the centrifugal force to the obftruction arifing from inertia.
Whence it appears that the latter is greater than the former,
except when t=o, h=o, or /= ∞, cafes never occurring in prac-
tice; and that the longer the arms, the leſs the fall of water, and
the greater the velocity of rotation, the nearer theſe forces ap-
proach to the ratio of equality.
6. Adjustment of the parts and motion. Here it muſt be par-
ticularly obſerved, that the centrifugal force ſhould not exceed
the gravity of the water revolving in the arms gd, ge; for in
that cafe the water would be drawn into the tube fafter than it
could be naturally ſupplied at its entrance, by the velocity
proper to that depth, and of confequence a vacuum muſt be
occafioned: nor fhould the velocity of the apertures be greater
than half that of the water through them; for the apertures
being ſtill adapted in point of magnitude to the velocity, the
effluent quantity or number of acting particles is as the time,
the momentum is in the fimple ratio of the relative velocity, and
therefore (art. 472, cor. 3, vol. i.) the greateſt effect will be
produced when the velocity of the apertures is equal to half that
due to the head of water. Theſe two conditions expreffed alge-
braically will furniſh the equations,
76.70625 al² = 2 alw..
=2alw....
w.... 2 x 1 = 3/
t2
t
from which eqnations we deduce the following,
viz.
ť
Sb = 9*293451 = 15*1446 ←
{
1 = 16296 t = 1076 h
t = √613651= √06603 h
b+1:
;
Whence it appears that h, l, and t, are nearly in the conſtant
ratio of 15,94, and 1.
Still it ſhould be obſerved that while and t are preferved in
a 12
a conſtant ratio, the values of 76-70625 and of 12.273
α als
i.e. of the central force and of the inertia muſt remain the
fame: fo that the brachia may be made of any length at plea
fure (not lefs than 1076 b) if the time of revolution be taken
in a correfponding proportion, or fo that the velocity of the
apertures undergo no variation, which will be enfured by mak
ing t = √61365 1: for a double or triple radius, revolving in
a double or triple time, or with half or a third the angular
velocity, has the fame abfolute velocity at the extremity; and,
with the fame power there applied, will produce the fame effect
Hence,
+
7. The moving force and velocity of the machine, when the effect
is a maximum, may be found. For, if we put 61365 / for ť²,
Barker's Mill:
111
and 9-29345 / for %, in the expreffion /(1+1-646h) it be-
Vi
comes 1 + 3 = 2; in which caſe the refiftance of inertia is
juſt double the central force, or the gravity of the water in the
tube=125 al, which taken from the impelling force leaves 62'5
(ab+1)—125 a l=62·5 a (b−1) = 55.775 a b lbs. avoirdupois
= the real moving force, at the distance of the centres of the
apertures from the centre of motion, / being taken = 1076 h.
And by a like fubftitution the velocity + 1, becomes
21*1076 h = 2*63205 √/h, feet per fecond.
8. Area of the apertures. If A= the area of a ſection of
the race perpendicular to the direction of its motion, V = its
velocity per second, both in feet, a and b as before; then it
will be AV = 10 a
a
(b+·61365 — ) cubic feet = the quantity
of water emitted per fecond, by both apertures: hence a =
070066 AV√h, the area proper for one of the
AV
14:2722/h
apertures.
h
From the preceding inveſtigation we may deduce the follow-
ing
Eafy practical rules.
1. Make each arm of the horizontal tube, from the centre of
motion to the centre of the aperture, of any convenient length,,
not less than of the perpendicular height of the water's ſurface
above theſe centres.
2. Multiply the length of the arm in feet, by 61365, and
take the fquare root of the product for the proper time of a re-
volution in ſeconds; and adapt the other parts of the machinery
to this velocity: or,
3. If the time of a revolution be given, multiply the fquare
of this time by 16296 for the proportional length of the arm
in feet.
4. Multiply together the breadth, depth, and velocity per
fecond of the race, and divide the laft product by 14°27 times
the fquare root of the height, for the area of either aperture:
or, multiply the continual product of the breadth, depth, and
velocity, of the race, by the fquare root of the height, and by
the decimal 07; the laſt product, divided by the height, will
give the area of the aperture.
5. Multiply the area of either aperture by the height of the
head of water, and the product by 55.775 (or 56 lbs), for the
moving force, eftimated at the centres of the apertures in
pounds avoirdupois.
112
MACHINES.
6. The power and velocity at the apertures may be eafily
reduced to any part of the machinery, by well-known rules.
BAROMETER, a well-known inftrument for meaſuring the
weight or preffure of the atmoſphere, and the variations that
happen therein, in order to indicate the changes in the weather,
or the changes in vertical diftance from any point upon the
earth's furface.
We fhall here deſcribe a few of the moſt uſeful conſtructions
of the barometer, and fhall begin with
I
Σ
The Common Barometer. This is repreſented at fig. 1. plate
VII. fuch as it was invented by Torricelli. AB is a glafs tube,
of 4, or, or ½ inch wide, the more the better, and about 34
inches long, being clofe at the top A, and the open end B im-
merſed in a bafin of quickfilver CD, which is the better the
wider it is. To fill this, or any other barometer, take a clean
new glafs tube, of the dimenfions as above, and pour into it well-
purified quickfilver, with a ſmall funnel either of glaſs or paper,
in a fine continued ſtream, till it wants about half an inch or an
inch of being full; then, ftopping it cloſe with the finger, invert
it flowly, and the air in the empty part will afcend gradually
to the other end, collecting into itfelf fuch other fmall air
bubbles as unavoidably get into the tube among the mercury,
in filling it with the funnel: and thus continue to invert it fe-
veral times, turning the two ends alternately upwards, till all
the air bubbles are collected, and brought up to the open end
of the tube, and till the part filled fhall appear, without fpeck,
like a fine poliſhed ſteel rod. This done, pour in a little more
quickfilver, to fill the empty part quite full, and fo exclude all
air from the tube: then, ſtopping the orifice again with the
finger, invert the tube, and immerſe the finger and end, thus
ftopped, into a bafin of like purified quickfilver. In this
pofition withdraw the finger; fo fhall the mercury deſcend in
the tube to ſome place, as H, between 28 and 31 inches above
that in the bafin at F, as theſe are the limits between which
it always ftands in this country on the common ſurface of the
earth. Then meaſure, from the furface of the quickfilver in
the baſin at F, 28 inches to K and 31 inches to L, dividing the
ſpace between them into inches and tenths, which are marked
'on a fcale placed againſt the fide of the tube; and the tenths
are fubdivided into hundredth parts of an inch by a fliding
index carrying a vernier or nonius. Thefe 3 inches, between
28 and 31, fo divided, will anfwer for all the ordinary purpoſes
of a ſtationary or chamber barometer; but for experiments on
altitudes and depths it is proper to have the divifions carried on
a little higher up, and a great deal lower down. In the proper
filling and otherwiſe fitting up of the barometer,feveral circum-
Barometer.
113
ſtances are to be carefully noted; as, that the bore of the tube
be pretty wide, to allow the freer motion of the quickfilver,
without being impeded by an adheſion to the fides; that the
bafin below it be alfo pretty large, in order that the furface of the
mercury at F may not fenfibly rife or fall with that in the tube;
that the bottom of the tube be cut off rather obliquely, fo that
when it refts on the bottom of the bafin there may be a free
paffage for the quickfilver; and that, to have the quickſilver very
pure, it is beft to boil it in the tube, which will expel all the air
from it. This barometer is commonly fitted up in a neat ma-
hogany cafe, together with a thermometer and hygrometer.
2. As the fcale of variation is ſmall in the common baro-
meter, being not more than 3 inches, feveral contrivances have
been deviſed to enlarge the ſcale, or to render the motion of the
quickfilver more perceptible. Among the beſt of theſe is that
known by the name of Diagonal Barometer, and is repreſented
in fig. 2. where ABC is a tube hermetically fealed at C, and
immerſed in a bafin of mercury at A. This tube is perpen-
dicular from A to B, where the ſcale of variation begins; but
is there bent into the form BC, making an acute angle FBC.
This part BC extends to the higheſt limit in the ſcale of varia-
tion, viz. IC; and confequently while the mercury rifes from K
to I, in the common barometer, it will move in this from B to
C, enlarging the ſcale of variation in the proportion of BC to
FB; that is, of the diagonal to the leaft fide of the paral-
lelogram.
p
But this barometer is attended with one great inconvenience,
which leffens its utility. Quickfilver being a very heavy body,
and ſupported on the part BC, forming an inclined plane, it
muſt have a very confiderable degree of friction, which will be
increaſed in proportion as the part BC is more oblique; and
confequently the very fmall and nice variation of the air's
preffure cannot be fo accurately indicated in this as in the
common form. It alfo very often happens, from the inclina-
tion of the part BC, that the quickfilver divides into feveral
parts, and thence frequently requires the trouble of re-filling
the tube. This barometer was invented by Sir Samuel More-
land.
3. Caffini invented another kind of barometer, in order to
enlarge the ſcale of variation; an invention which was after-
wards completed by M. John Bernoulli. It confiſts of a tube
ACDF (fig. 3.) hermetically fealed at A, and bent to a right
angle at D; whence it has acquired the name of the horizontal
rectangular barometer. The mercury ftands in both the legs
from E to B; the fcale of variation from A to C is made in a
larger part; and it is evident, that in moving three inches from
VOL. II.
I
114
MACHINES.
A to C it will move through ſo many times three inches in the
ſmall leg DF as the bore of DF is lefs than the bore of AC;
whence the motion of the mercury at E muſt be extremely
fenfible. But the inconvenience here too is, that the mercury
is very apt to break off in the leg E, and alſo to run out at the
end E. Here is alſo a great degree of friction, and at the ſame
time the attraction of cohefion will, from the fmallneſs of the
bore DF, impede the free motion of the mercury.
4. The Pendant Barometer is made in another form, confiſting of
a fingle tube ſuſpended by a ſtring faſtened to the end A (fig. 4.).
This tube is of a conical or tapering form, the end A being a
little leſs than that at B. It is hermetically fealed at A, and
filled with mercury: then will the mercury fink to its common
ſtation, and admit a length of altitude CD, the fame with that
in the common barometers. But, from the conical bore of the
tube, the mercury will defcend as the air becomes lighter, till it
reaches its loweft altitude, when the mercury will ftand from
the loweſt part of the tube B to E; fo that BE = 28 inches:
and confequently the mercury will, in fuch a tube, move from
A to E, or 32 inches, if the tube be five feet long; ſo that the
ſcale AE may here be made more than 10 times greater than
that of the common barometer. The inconvenience at-
tending this barometer is, that as the tube muſt be made of a
very ſmall bore, to prevent the mercury from falling out by an
accidental ſhake, the friction and adheſion to the fides of the
tube prevent that freedom of motion neceffary to fhew a very
ſmall variation in the weight of the air.
5. Mr. Rowning had ſeveral contrivances for enlarging the fcale,
and that in any proportion whatever. One of theſe is deſcribed
in No. 427. Phil. Trans. and has now obtained the name of
Rowning's Barometer: it is repreſented at fig. 5. where ABC is
a compound tube, hermetically fealed at A, and open at C;
empty from A to D, filled with mercury from thence to B, and
thence to E with water. Here, by varying the proportions of
the two tubes AF and FC, the ſcale of variation may be changed
in any degree.
6. Dr. Hooke's Wheel Barometer was invented about 1668,
and is likewife intended to render the alterations in the ſtate of
the air more perceptible. Here the barometer tube has a large
ball AB at the top (fig. 9. pl. VII.), and is bent up at the lower
or open end, where an iron ball, G, floats on the top of the
mercury in the tube, to which is connected another ball, H, by
a cord, hanging freely over a pulley, turning an index KL about
its centre. When the mercury rifes in the part FG it raiſes the
ball, and the other ball defcends and turns the pulley with the
index round a graduated circle from N towards M and P; and
the contrary way when the quickſilver and the ball fink in the
Portable Barometer.
115
bent part of the tube. Hence the fcale is eafily enlarged ten or
twelve fold, being increaſed in proportion as the length of
the index exceeds the radius of the pulley. But then the
friction of the pulley and axis greatly obftructs the free motion
of the quickfilver. Contrivances to leffen the friction are
deſcribed in Phil. Trans. vol. 52 and 60. In Nicholſon's
Journal, No. 9, New Series, the rev. James Wilfon has
deſcribed a method of increafing the fenfibility of the baro-
meter, ad libitum, which is very ingenious; but need not be in-
ferted here: for this, and all contrivances, having the fame end
in view, are not ſuperior, but often inferior, to the common
barometer, for all philofophical purpoſes; and that for a reaſon
which admits of no reply. Their ſcale muſt be determined in
all its parts by that of the common barometer; and, therefore,
notwithſtanding their great range, they are fufceptible of no
greater accuracy than that with which the common barometer
can be obſerved and meaſured. And befides this, theſe com-
pound barometers have an additional fource of error, in the
action of cohefion, the operation of friction, &c. So that, ex-
cept (perhaps) for mere chamber purpoſes, the common con-
ftruction of the barometer, with a nonius applied to its ſcale, is
greatly preferable; and our attention ſhould be entirely directed
to its improvement and portability.
7. This leads us to ſpeak of the conſtruction of a portable Baro-
meter, which may be carried from one place to another without
being rendered unfit for ufe; and is, therefore, ready to be.
adopted at all times in the menſuration of altitudes, &c. In
this barometer the end of the tube is tied up in a leathern bag,
not quite full of mercury; which being preffed by the air
forces the mercury into the tube, and keeps its fufpended at its
height. This bag is ufually encloſed in a box, through the
bottom of which paffes a fcrew, by whofe means the mercury
may be forced up to the top of the tube, and prevented from
breaking it by daſhing againſt the top when the inftrument is
removed from one ftation to another. Mr. Patrick was, we
believe, the firſt who made a contrivance of this kind; but the
portable barometer has received various improvements fince by
M. de Luc, Sir Geo. Shuckburgh, Col. Roy, Mr. Ramfden,
and others. Fig. 8. pl. VII. repreſents this inftrument as en-
cloſed in its mahogany cafe by means of three metallic rings
b, b, b. This cafe is a hollow cone, fo fhaped within as fteadily
to contain the body of the barometer, and is divided into three
branches from a to c, forming three legs or fupports for the
inftrument when obfervations are making, and ſuſtaining it at
the part g of the cafe; by an improved kind of gimbals, as it
appears in fig. 7. in which its own weight renders it fufficiently
12
116,
MACHINES.
ſteady at any time. In the part of the frame a g where the
barometer tube appears a long flit or opening is made, ſo that
the column of mercury may be feen againſt the light, and the
vernier piece, a, brought down to coincide very nicely with the
edge of the mercury. When the inftrument is fixed in its
ftand, the fcrew, f, is to be turned to let the mercury down to its
proper pofition, and a peg at p muſt be looſened, in order that
the external air may be admitted to act upon the mercury con-
tained in the box b. The proper adjuſtment or mode of obſerv-
ing the zero or o divifion of the column of mercury is by ob-
ferving it in the tranſparent part of the box b, which has a glafs
reſervoir for the quickfilver, and an edged piece of metal at-
tached to the external part of it; with the edge of which the
mercury is to be brought into contact, by turning the fcrew f
to the right or left, as occafion requires. The vernier piece
at a, which determines the altitude of the mercurial column, is
firſt brought down by the hand to a near contact, and then
accurately adjuſted by turning the fcrew h at the top. The
divifions annexed to the tube of this inftrument may be of any
kind, or of any degree of minutenefs, according to the purpoſe it
is intended to ferve. To accommodate it to the ufe of foreigners
as well as the English, there are commonly added ſcales of both
French and Engliſh inches, with the requifite fubdivifions. It
is ufual to place the French ſcale of inches on the right fide, at
ag from 19 to 31 inches, meaſured from the zero or furface
of the mercury in the box b; each inch being divided into lines.
or 12th parts, and each line fubdivided by the vernier into 10th
parts: fo that the length of the mercurial column may be deter-
mined to the 120th part of a French inch. The other ſcale,
which is placed on the left fide of the inftrument, is divided
into 20th parts of inches, and theſe again into 25th parts by
means of the vernier; thus meaſuring to 500ths of an English
inch: and the divifions on the vernier fcale are marked double
what they really are, in order that the meaſures may be expreffed
in thouſandth parts of an inch, for the convenience of cal-
culation.
To this inftrument a thermometer is always attached, as a
neceffary appendage; being faftened to the body at c, and ſunk
into the furface of the frame to preferve it from injury: the
degrees of this thermometer are generally marked fo as to indi-
cate the divifions both of Fahrenheit's and of Reaumur's fcale.
(See THERMOMETER.) Alfo on the right-hand of theſe two ſcales
is a third, called ſcale of correction, with the words add and ſubtract
marked; thus ferving to fhew the neceffary correction of the
obferved altitude of the mercury, at any given temperature of
the air indicated by the thermometer.
Bellows.
117
Several minutiæ in the mechanical conftruction of this in-
ftrument will be more obvious from a few minutes' infpection
than by any further details here. The rules for its uſe in the
aſcertaining of altitudes may be learnt by turning to the theo-
retic part of this work: book iv.
BEAM COMPASSES. See COMPASSES.
BEER-DRAWING MACHINES are contrivances by means of
which the beer is drawn from three or four caſks at once, from
cocks ſtanding in one frame, in the bar of a tavern, or any con-
venient place above a cellar. Theſe machines are nothing elſe
than an affemblage of fmall pumps, either fucking or forcing,
whofe pipes of communication are attached to the lower parts
of the reſpective caſks from which the liquor is drawn. The
motion is given to the piſton ſometimes by levers, at others
by cranks; moft frequently, we believe, by means of a hammer-
formed lever moving in a vertical plane.
BELLOWS, an inftrument conftructed for the purpoſe of
alternately drawing and expelling air. In the common culinary
bellows the air rufhes in at a hole or holes in the bottom,
called feeders, over which is a flapping valve, and is expelled
through a conical pipe called the nozzle, by means of a kind of
mechaniſm which is too well known to need any defcription
here.
It is not the impulfive force of the blaſt that is wanted in
moſt caſes, but merely the copious ſupply of air to produce the
rapid combuſtion of imflammable matter; and the fervice would,
in general, be better performed if this could be done with mo-
derate velocities and an extended ſurface. What are called
air-furnaces, where a confiderable furface of inflammable matter
is acted on at once by the current which the mere heat of the
expended air has produced, are found more operative, in pro-
portion to the air expended, than blaft-furnaces animated by
bellows. There is, indeed, a great impulfive force required in
fome cafes; as, for blowing off the fcoriæ from the furface of
filver or copper in refining furnaces, or for keeping a clear
paffage for the air in great iron furfaces. But in general we
cannot procure this abundant fupply of air in any other way
than by giving it a great velocity by means of a great preffure
or impulfe; the air is admitted into a very large cavity, and
then forcibly expelled from it through a ſmall orifice.
The method of producing a continual blaft by a centrifugal
force has been long known, being mentioned by Agricola de
Re Metallica, lib. 6. p. 62. But the firft bellows acting upon
this principle, of which we recollect a diftinct account amongſt
the moderns, is that invented by M. Teral, in 1729, and de-
fcribed in the Recueil des Machines approuvées par L'Academic
118
MACHINES.
1
Roy. des Sciences, tome 5. This machine is reprefented in fig. 7.
pl. VIII. where AB is a cubical box, with a top rather arched :
to this box is adapted a hollow pyramidal fruftrum C, at the
extremity of which is the tube or nozzle D; the capacity of the
pyramid not being feparated from that of the box. This box
contains an arbor or ſhaft carrying vanes, as GF, pofited hori-
zontally, and which are here placed, as it were, out of the box,
that their ſhape and number may be feen. The ends of the
arbor run in a proper collar on each fide of the box, and one
end, as F, paffes through the fide of the box, and carries a pulley:
over this pulley paffes a cord or band, which alfo runs round
part of a wheel HI, fituated at ſome diſtance from the bellows,
and which is turned by the handle M. Thus it will be mani-
feft, that as this handle turns the wheel HI, it will, by means
of the band, turn the pulley F and the arbor and vanes, with a
velocity which will be to that of the wheel as the radius of the
wheel to that of the pulley. Hence the greater the diameter
of the wheel, and the lefs that of the pulley, the more rapidly will
the exterior air (which enters by ſmall holes h h, into the top of
the box) be driven by the vanes, and compreffed into the trunc-
ated pyramid c, and thence expelled at D, in a continued blaſt;
which will likewiſe be the more violent the greater the action
at the handle M. This machine, being very ſimple, is eaſily
conſtructed, and at a ſmall expence.
Another bellows, furniſhing a uniform blaft, is deſcribed in
the article PNEUMATICS, Encyclopædia Britannica, as below:
one cylinder is made to deliver its air into another cylinder,
which has a pifton exactly fitted to its bore, and loaded with a
fufficient weight. The blowing cylinder ABCD (fig. 3. pl. VIII.)
has its pifton P worked by a rod NP, connected by double
chains with the arched head of the working beam NO, moving
round a gudgeon at R. The other end O of this beam is con-
nected by the rod OP with the crank PQ of a wheel machine; or
it may be connected with the piſton of a ſteam-engine, &c. &c.
The blowing cylinder has a valve or valves E in its bottom,
opening inwards. There proceeds from it a large pipe CF,
which enters the regulating cylinder GHKI, and has a valve at
top, to prevent the air from getting back into the blowing
cylinder. It is evident that the air forced into this cylinder
muſt raiſe its piſton L, and that it muſt afterwards deſcend,
while the other pifton is rifing. It muft defcend uniformly,
and make a perfectly equable blaſt,
Obferve, that if the pifton L be at the bottom when the ma-
chine begins to work, it will be at the bottom at the end of every
ftroke, if the tuyere T emits as much air as the cylinder ABCD
furniſhes; nay, it will lie a while at the bottom; for, while it
Bellorus.
119
was rifing, air was iffuing through T. This would make an
interrupted blaft. To prevent this, the orifice T muſt be
leffened; but then there will be a furplus of air at the end of
each ſtroke, and the pifton L will rife continually, and at laft
get to the top, and allow air to eſcape. It is juſt poffible to
adjuſt circumſtances, fo that neither fhall happen. This is done
eaſier by putting a ftop in the way of the pifton, and putting a
valve on the piſton, or on the conducting pipe KST, loaded
with a weight a little fuperior to the intended elaſticity of the
air in the cylinder. Therefore, when the piſton is prevented by
the ſtop from rifing, the ſhifting valve, as it is called, is forced
open, the fuperfluous air eſcapes, and the blaft preferves its uni-
formity.
The Hydraulic Forge Bellows, of Mr. J. C. Hornblower, is a
véry ingenious contrivance, and is, therefore, defcribed here.
This invention is fhewn in plate V.
A. The plunger, or working part of the bellows, 18 inches
fquare within, which receives the air by a valve in the hinder
part opening inwards, which at the ftroke by the rockftaff E
throws it down the tube indicated by the dotted lines, which
has a valve opening into the reſervoir D, whence it is led to the
tuyere by the pipe P. Length of the plunger 20 inches, ſtroke
nine inches. Diameter of P three inches; of the nozzle o‘6.
The whole is placed in a pit or ciſtern, having water fuffici-
ent to riſe to the lower end of the tube where the valve hangs;
this tube is the only communication between the upper part and
the reſervoir D: when as much water is poured in round the
working part, over the waſh-boards, as will rife within five inches.
of the upper edge of them, the bellows is ready for uſe. The
little frame-work ferves to keep it from rifing, and affords a
convenient fupport for the balance and the rockftaff. The
area of the pit or ciftern ought to be at leaſt twice as much as
that of the plunger A.
•
Mr. Hornblower mentions a very ſtriking difference between
the effect of this bellows and a common leathered 30-inch
bellows in the fame ſhop. The leathered bellows throws con-
fiderably more air to the fire, and its nozzle compared with
this is as 73 to 60 in diameter, but it does not produce fo
great an effect in bringing on the heat, and the voice of this is
fo great as almoft to drown that of the common one.
only difference in other refpects is, that in the hydraulic bellows
the pipe goes underground for about eight feet, and the conduct-
ing pipe of the other comes down about the fame diſtance from
the fhop above. Nicholson's four. N. S. vol. I.
BORING of Cylinders, Ordnance, Wooden Pipes, &c,
See CYLINDERS, ORDNANCE, and PIPES.
The
120
MACHINES.
1
BRAMAH'S MACHINE, Bramah's Hydrostatic Prefs, &c.—
names which are now commonly given to the contrivances of
Mr. Bramah of Piccadilly, by which he applied the quaqua
verfum preffure of fluids as a very powerful agent in many
kinds of machinery requiring motion and force. Theſe con-
trivances (for which Mr. Bramah took out a patent in March
1796) confift in the application of water, or other denfe fluids,
to various engines, fo as, in fome inftances, to cauſe them to
act with immenfe force; in others, to communicate the motion
and powers of one part of a machine to ſome other part of the
fame machine; and, laftly, to communicate the motion and
force of one machine to another, where their local fituations
preclude the application of all other methods of connection.
The firſt and moſt material part of this invention will be
clearly underſtood by an inſpection of fig. 4. pl. IX. where "A
is a cylinder of iron, or other materials, fufficiently ſtrong, and
bored perfectly ſmooth and cylindrical; into which is fitted the
piſton B, which must be made perfectly water-tight, by leather
or other materials, as ufed in pump-making. The bottom of
the cylinder muſt alſo be made fufficiently ftrong with the other
part of the furface, to be capable of refifting the greateſt force
or ſtrain that may at any time be required. In the bottom of
the cylinder is inferted the end of the tube C; the aperture of
which communicates with the infide of the cylinder, under the
piſton B, where it is ſhut with the ſmall valve D, the fame as
the fuction-pipe of a common pump. The other end of the
tube C communicates with the ſmall forcing-pump or injector
E, by means of which water or other denfe fluids can be forced
or injected into the cylinder A, under the piſton B. Now,
ſuppoſe the diameter of the cylinder A to be 12 inches, and the
diameter of the pifton of the fmall pump or injector E only
one quarter of an inch, the proportion between the two furfaces
or ends of the faid piftons will be as I to 2304; and ſuppoſing
the intermediate ſpace between them to be filled with water or
other denſe fluid capable of fufficient refiftance, the force of
one piſton will act on the other juſt in the above proportion,
viz. as I is to 2304. Suppofe the fmall pifton in the injector
to be forced down when in the act of pumping or injecting
water into the cylinder A, with the power of 20 cwt. which
could eaſily be done by the lever H; the piſton B would then
be moved up with a force equal to 20 cwt. multiplied by 2304.
Thus is conſtructed a hydro-mechanical engine, whereby a
weight amounting to 2304 tons can be raiſed by a fimple lever,
through equal ſpace, in much lefs time than could be done by
any apparatus conftructed on the known principles of me-
chanics; and it may be proper to obferve, that the effect of all
•
1
Bramal's Prefs, c.
121
other mechanical combinations is counteracted by an accumu-
lated complication of parts, which renders them incapable of
being uſefully extended beyond a certain degree; but in ma-
chines acted upon or conftructed on this principle every dif-
ficulty of this kind is obviated, and their power fubject to no
finite reftraint. To prove this, it will be only neceffary to remark,
that the force of any machine acting upon this principle can be
increaſed ad infinitum, either by extending the proportion be-
tween the diameter of the injector and the cylinder A, or by
applying greater power to the lever H.
Fig. 5. reprefents the fection of an engine, by which very
wonderful effects may be produced inftantaneouſly by means of
compreffed air. AA is a cylinder, with the pifton B fitting
air-tight, in the fame manner as deſcribed in fig. 4. C is a
globular veffel made of copper, iron, or other ftrong materials,
capable of refifting immenfe force, fimilar to thofe of air-guns.
D is a ſtrong tube of ſmall bore, in which is the ſtop-cock E.
One of the ends of this tube communicates with the cylinder
under the piſton B, and the other with the globe C. Now,
ſuppoſe the cylinder A to be the fame diameter as that in fig. 4.
and the tube D equal to one quarter of an inch diameter, which
is the fame as the injector fig. 4.: then, ſuppoſe that air is in-
jected into the globe C (by the common method), till it preffes
againſt the cock E with a force equal to 20 cwt. which can
eafily be done; the confequence will be, that when the cock E
is opened the pifton B will be moved in the cylinder AA with
a power or force equal to 2304 tons; and it is obvious, as in the
cafe fig. 4. that any other unlimited degree of force may be ac-
quired by machines or engines thus conftructed.
"Fig. 6. is a fection, merely to fhew how the power and
motion of one machine may, by means of fluids, be transferred
or communicated to another, let their diſtance and local fituation
be what they may.
A and B are two ſmall tubes, ſmooth
and cylindrical; in the infide of each of which is a piſton, made
water and air-tight, as in figs. 4. and 5. CC is a tube conveyed
under ground, or otherwife, from the bottom of one cylinder to
the other, to form a communication between them, notwith-
ftanding their diſtance be ever fo great; this tube being filled
with water or other fluid, until it touch the bottom of the piſton;
then, by depreffing the piſton A, the pifton B will be raiſed.
The fame effect will be produced vice verfa: thus bells may
be rung, wheels turned, or other machinery put invifibly in
motion, by a power being applied to either.
"Fig. 7. is a fection, fhewing another inftance of communi-
cating the action and force of one machine to another; and how
water may be raiſed out of wells of any depth, and at any di-
1
122
MACHINES.
ftance from the place where the operating power is applied.
A is a cylinder of any required dimenfions, in which is the
working pifton B, as in the foregoing examples: into the bottom
of this cylinder is inferted the tube C, which may be of lefs
bore than the cylinder A. This tube is continued, in any re-
quired direction, down to the pump cylinder D, fuppoſed to be
fixed in the deep well EE, and forms a junction therewith above
the piſton F; which pifton has a rod G, working through the
ftuffing-box, as is uſual in a common pump. To this rod G is
connected, over a pulley or otherwiſe, a weight H, fufficient to
overbalance the weight of the water in the tube C, and to raiſe
the piſton F when the pifton B is lifted: thus, fuppofe the
pifton B is drawn up by its rod, there will be a vacuum made
in the pump cylinder D, below the pifton F; this vacuum will
be filled with water through the fuction pipe, by the preffure of
the atmoſphere, as in all pumps fixed in air. The return of the
pifton B, by being preffed downwards in the cylinder A, will
make a ſtroke of the pifton in the pump cylinder D, which may
be repeated in the ufual way by the motion of the piſton B, and
the action of the water in the tube C. The rod G of the piſton
F, and the weight H, are not neceffary in wells of a depth where
the atmoſphere will overbalance the water in the fuction of the
pump cylinder D, and that in the tube C. The fmall tube and
cock in the cistern I are for the purpofe of charging the tube C."
By theſe means it is obvious moft commodious machines
of prodigious power, and fufceptible of the greateſt ſtrength,
may readily be formed. If the fame multiplication of power
be attempted by toothed wheels, pinions, and racks, it is fcarcely
poffible to give ſtrength enough to the teeth of the racks, and
the machine becomes very cumberſome and, of great expence.
But Mr. Bramah's machine may be made abundantly ſtrong in
very_fmall compafs. It only requires very accurate execution.
Mr. Bramah, however, is greatly miſtaken when he publiſhes it
as the diſcovery of a new mechanic power. The principle on
which it depends has been well known for nearly two centuries;
and it is matter of ſurpriſe that it has never before been applied
to any uſeful practical purpoſe.
CAMEL is the name given to a machine employed by the
Dutch for carrying veffels heavily laden over the fand-banks in
the Zuyder-Zee. In that fea, oppofite to the mouth of the
river Y, about fix miles from the city of Amfterdam, there are
two fand-banks, between which is a paffage called the Pampus,
fufficiently deep for ſmall veffels, but not for thoſe which are
large and heavily laden. On this account fhips which are out-
ward bound take in before the city only a ſmall part of their
cargo, receiving the reft when they have got through the Pam
The Camel.
123
:
pus. And thofe that are homeward bound muft, in a great
meaſure, unload before they enter it. For this reafon the goods
are put into lighters, and in theſe tranſported to the warehouſes
of the merchants in the city; and the large veffels are then
made faſt to boats, by means of ropes, and in that manner
towed through the paffage to their ſtations.
Though meafures were adopted fo early as the middle of the
fixteenth century, by forbidding ballaft to be thrown into the
Pampus, to prevent the further accumulation of ſand in this
paffage, that inconvenience increaſed ſo much from other cauſes
as to occafion ftill greater obftruction to trade; and it at length
became impoffible for fhips of war, and others heavily laden, to
get through it. About the year 1672 no other remedy was
known than that of making faft to the bottoms of fhips large.
chefts filled with water, which was afterwards pumped out; fo
that the ſhips were buoyed up, and rendered fufficiently light to
paſs the ſhallow. By this method, which was attended with
the utmoſt difficulty, the Dutch carried out their numerous
fleet to ſea in the abovementioned year. This plan, however,
gave rife ſoon after to the invention of the camel, by which the
labour was rendered eafier.
The camel confifts of two half fhips, conftructed in fuch
a manner that they can be applied below water, on each fide of
the hull of a large veffel. On the deck of each part of the
camel are a great many horizontal windlaffes, from which ropes
proceed through apertures in the one half, and, being carried
under the keel of the veffel, enter fimilar apertures in the
other, from which they are conveyed to the windlaffes on its
deck. When they are to be uſed, as much water as may be
neceffary is ſuffered to run into them; all the ropes are caft
loofe, the veffel is conducted between them, and large beams
are placed horizontally through the port-holes of the veſſel,
with their ends refting on the camel on each fide. When the
ropes are made faſt, ſo that the fhip is fecured between the two
parts of the camel, the water is pumped from them; by which
means they rife, and raiſe the ſhip along with them. Each half
of the camel is often about 127 feet in length; the breadth at
one end is 22, and at the other 13. The hold is divided into
ſeveral compartments, that the machine may be kept in equili-
brio while the water is flowing into it. An Eaft-India fhip that
draws 15 feet of water can, by the help of the camel, be made
to draw only 11; and the heaviest fhips of war, of 90 or 100
guns, can be fo lightened as to pafs, without obftruction, all the
fand-banks of the Zuydee-Zee.
Leupold, in chap. 6. of his Theatrum Machinarum, publiſhed
124
MACHINES.
in 1725, at Leipfick, deſcribes this machine under the head Bef
chreibung der fe genannten Camele zu Amfterdam, womit die befrach-
ten Schiffe über dem Pampus gebracht werden, and fays it was in-
vented by Cornelius Meyer, a Dutch engineer. But the Dutch
writers almoſt unanimouſly aſcribe this invention to a citizen of
Amfterdam, called Meuves Meindertſzoon Bakker.
+
As ſhips built in the Neiva cannot be conveyed into harbour,
on account of the fand-banks formed by the current of that
river, camels are employed alfo by the Ruffians, to carry ſhips
over theſe fhoals: and they have them of various fizes. Ber-
noulli faw one, each half of which was 217 feet long, and 36
broad. Camels are uſed likewife at Venice. An engraving of
the camel may be ſeen in L'Art de batir les Vaiffeaux, Amfter-
dam, 1719, 4to. vol. ii. pa. 93.
CANALS, motion of water in. See STREAM.
CAPSTAN, a large maffy column, ſhaped like a truncated
cone, placed perpendicularly on the deck of a fhip, and turned
by levers or bars, which pafs through holes pierced in its upper
extremity; ferving, by means of a cable which winds round
the barrel, to draw up burdens faftened to the end of the cable.
The power of this machine in its fimpleſt ſtate is manifeſtly re-
ducible to that of the axis in peritrochio. There is frequently
attached to it a tackle of pulleys, but the ingenious contrivance
deſcribed in art. 4 of the introductory part of this volume is far
preferable.
CELLAR CRANE, a machine reprefented in fig. 6. pl. VI.;
and is very uſeful to wine-merchants, brewers, &c. in drawing
up and letting down caſks full of wine, beer, &c. It faves the
trouble and inconvenience of horſes, and in many places can be
uſed where horſes could not. AA are two wooden props, about
6 feet in height, and jointed together like a ruler at B. They
are connected to each other by an iron round bar C, and
wooden bar at the bottom D. The iron prongs EE faſten the
uprights ſteadily to the edge of the cellar; F is the axis round
which two ropes are coiled, the ends of which are faſtened to
the two clamps GG. On the axis F is fixed the iron wheel
H, of 3 feet in diameter: in the teeth of this works the pinion I,
of about 6 or 7 inches in diameter, and is turned by the handle
at K.
It is evident, by a bare inſpection of the figure, that when the
two ropes are flipt over the ends upon the barrel, either at
the top or bottom of the cellar, by turning of the winch K to-
wards or from you, the barrel can be fafely and expeditiously
taken out or lowered down. When the crane is done with it
shuts up, by unscrewing the nut at B, taking the wheel and axis.
Chimney Cleanfers.
125
away out of the loops at L, and folding the fides at A together,
like a jointed rule; it may then be taken away in the cart or
dray, or taken in the men's hands.
CENTRIFUGAL PUMP, a very curious machine, invented
by Mr. Erskine, for raifing water by means of a centrifugal force
combined with the preffure of the atmoſphere. It confifts of a
large tube of copper, &c. in the form of a crofs, which is
placed perpendicularly in the water, and refts at the bottom on a
pivot. At the upper part of the tube is an horizontal cog-
wheel, which touches the cogs of another in a vertical poſi-
tion; ſo that by the help of a double winch the whole machine
is moved round with very great velocity. Near the bottom of
the perpendicular part of the tube is a valve opening upwards;
and near the two extremities, but on the contrary fide of the
arms or croſs part of the tube, are two other valves opening out-
wards. Theſe two valves are, by the affiftance of fprings, kept
ſhut till the machine is put in motion, when the centrifugal ve-
locity of the water forces them open, and diſcharges itſelf into
a ciſtern or refervoir placed there for that purpoſe. On the
upper part of the arms are two holes, which are cloſed by pieces
fcrewed into the metal of the tube. Before the machine can
work thoſe holes muſt be opened, and water poured in through
them, till the whole tube be full; by this means all the air will
be forced out of the machine, and the water fupported in the
tube by means of the valve at the bottom. The tube being
thus filled with water, and the holes clofed by the fcrew-caps,
it is turned round by means of the winch, when the water in
the arms of the tube acquires a centrifugal force, opens the
valves near the extremities of the arms, and flies out with a ve-
locity nearly equal to that of the extremities of the faid arms.
The theory of this pump may be ſeen in arts. 537, 538, of our
firft volume.
CHIMNEY CLEANSING MACHINES have been lately invented,
in order, as far as poffible, to diminiſh the number of infant vic-
tims of a filthy and difgufting operation, performed under the
infpection of unfeeling mafters. Thoſe who have long viewed
the wretchedneſs to which many of the children are expoſed
who are ſtill employed in climbing chimneys, will be happy to
hear of any contrivances which have a tendency to leffen their
fufferings: we therefore mention here two machines which
have been deviſed for the purpoſe of fweeping chimneys; either
of which may, we doubt not, be made ufe of with confiderable
fuccefs.
The firft is that invented by Mr. George Smart, of Ord-
nance-wharf, Westminster-bridge. Its principal parts are the
bruſh, the rods for raifing the bruth, and the cord for connect.

126
MACHINES.
"
ing the whole together. The brush confifts of four fan-ſhaped
or wing-like portions, which are hung upon hinges, in order
that in aſcending the chimney the bruſh may take up as little
ſpace as poffible, and in defcending may ſpread out and ſweep
the fides of the flue: this bruſh is prevented from falling down
into its contracted form by a contrivance exactly like that which
is made uſe for umbrellas. The ſubſtance made uſe of in ge-
neral for the bruſh is what is called whisk. The rods are hol-
low tubes, with a metal focket at the lower end; fome of the
fockets have screws in them, for the purpoſe of confining the
cord, and preventing the rods from feparating. The upper
ends of the rods are now made without ferrules, and are rather
tapered, which allows of a small motion within the fockets.
Each rod is about 2 feet long. The cord runs from the top
of the brush through all the rods, and when drawn tight keeps
the whole of the machine together.
Method of using the machine. Having firſt aſcertained, by
looking up the chimney, what courſe the flue immediately takes,
the cloth is then to be fixed before the fire-place, with the hori-
zontal bar, and the fides to be clofed with two upright bars.
The next part of the operation is to introduce, through the
opening in the cloth, the brufh in its contracted form: this
opening is then to be buttoned or tied up, to prevent the foot
coming into the apartments; then one of the rods is to be paffed
up the cord into the focket, on the lower end of the rod which
fupports the bruſh; the other rods are in like manner, one by
one in fucceffion, to be brought up, until the brush is raiſed
fomewhat above the top of the chimney, obferving to keep the
cord conſtantly tight; and when thoſe rods which have a ſcrew
in the focket are brought up they are to be placed on the pur-
chaſe, when the cord is to be put round the pulley and drawn
very tight, and fcrewed down, by which all the rods above will
be firmly connected together, and the whole may be confidered
one long flexible rod.
When the operator thinks that the brush is near the top of
the chimney he fhould move it up and down, as he will then
find the bruſh, if out, stop, in returning, on the top of the pot
or chimney.
When it is known to be out the machine is to be pulled
down: in doing which the edges of the bruſh, ftriking againſt
the top of the chimney, will cauſe it to expand; and there being
a fpring to prevent its contracting again, it will ſweep the foot
down before it: the whisk being long and elaftic, makes the
bruſh capable of filling flues of different diameters. In draw-
ing down the machine the perſon fhould grafp with his left
hand the rod immediately above that which he is feparating
1
Chimney Cleanfers.
127
with his right hand, otherwife he may chance to have thofe
above loofen and flide down the cord, which will render the
operation unpleaſant and difficult: the rods, as they are brought
down, are to be laid carefully one by one in as small a compafs
as they conveniently can be, that they may not dirt the apart-
ments: with a little attention they may be placed like a bundle
of ſticks, fide by fide, in very little compafs. When the bruſh
is quite down it is to be fhaken within-fide the cloth, then the
ſpring muſt be puſhed in, and the bruſh which was expanded
will flap down into the ſtate it went up.
If, as fometimes happens, there is any difficulty found in
drawing the bruſh into the upper part of the chimney, the rods
muſt be thruſt up again ſomewhat higher, in order to alter the
direction, then carefully drawn down. It will be proper to let
the cloth remain a ſhort time up (where great cleanlineſs is re-
quired), in order to let the finer particles of foot fubfide with-
in it.
For extinguiſhing a chimney on fire a coarſe cloth is to be
tied over the bruſh and dipped into water, then paffed up as
above directed.
It is now nearly three years fince this machine was invented,
and its uſe has been attended with very confiderable ſuccess; for
it appears that there is ſcarcely one chimney in a hundred in the
vicinity of the metropolis but what may be properly ſwept by
it. The following perfons have undertaken to fweep chimneys
with Mr. Smart's machines, at the uſual prices :-Thomas Bad-
ger, chimney-sweeper, No. 2, Whalebone-court, oppofite Token-
houſe-yard, Great Bell-alley, Coleman-ftreet.-John Bedford,
chimney-fweeper, 56, Swallow-street, Piccadilly.-Thomas
Murless, chimney-fweeper, Bell-yard, near the Bridge, Hack-
ney.-Richard Page, chimney-fweeper, 23, Colonnade, near
Guildford-street, Foundling-hofpital.-George Smart, 15, Great
Bell-alley, Coleman-street; and at his timber yard, Pratt's-place,
Camden-town; and at Ordnance-wharf, Weftminfter-bridge.-
Thomas Taylor, 9, Well's-ftreet, Oxford-road.-George Turner
and James Laver, Walthamſtow.-Thomas Wood, 36, Poland-
ftreet, Oxford-road.
Another machine for the fame benevolent purpoſe has been
invented by Mr. J. C. Hornblower, engineer, Eaft-place, City-
road: The apparatus is 'simply this: a veffel into which air is
condenſed communicates with a tube charged with ſmall gra-
vel, which being blown up the chimney brings down the foot.
The body of the machine is made of copper, of about 3
pound to the fquare foot, and its capacity is about three cylin-
drical feet. In the middle of the cover, which is foldered on,
is a ſyringe or condenſer, having its handle above the cover.
128
MACHINES.
On one fide of the cover is inferted a crooked pipe, having a
valve opening inward in its inner or lower end, the ftem of
which comes up through the pipe, and terminates with a but-
ton. The pipe is continued by a flexible leather one, to which
is united a tube of tin plate. This latter tube has a croſs bar of
tin plate, fixed edgewife in the bottom or breach of the tube
which detaches from the leather pipe, ſomewhat like a piſtol
barrel, leaving a piece of tube about fix inches remaining to the
leather pipe, into the bottom of which this cafe bar is fixed,
and ferves to receive a charge of ſmall gravel, having a piece of
paper firft laid on the croſs-bar; the other part of the tube is
then to be replaced, and the air-veffel fuppofed to be full, the
valve is preffed down by a little lever accompanying the ma-
chine, and its contents are difcharged into the fhaft of the
chimney; and if there is any fuch quantity of foot as really
needs fweeping away, it will come down.
The veffel contains nearly three cylindrical feet, and we can
crowd three atmoſpheres of air into it, in which cafe there
will be 42 lbs. per inch ſquare, at round numbers, preffing
againſt the charge in the tube, or rather againſt the valve, the
tube being 24 inch diameter, which amounts to 168 lbs. for
the whole area. This air will all be diſcharged in one fecond,
the mean velocity of which may be fairly reckoned at 50 feet,
in that time having impetus in itſelf fufficient to carry away
any foot of conſequence in a chimney of 100 feet high; but
when we take into the account the charge of gravel, being
alternately incident and reflected on all fides of the chimney,
we need not fear to affirm that it is perfectly applicable to its
intention.
To render it as univerfal as poffible there muſt be another
tube, to be occafionally ufed, when the fide of the chimney
near the fire place is gathered over, in order to bring the throat
of the flue over the fire: or it ſhould be in ſeveral pieces, to
conform to the height of this gathering, and in this caſe the
charge muſt be at the upper fiffure, and the pipe ftayed as per-
pendicularly as can be conveniently done; for which purpoſe
there is a piece made to fix on the pipe, having two ſtems,
which, if put in the bearing fide of the pipe, will keep it up-
right and in the crater of the flue. The machine thus con-
ftructed is to be laid on a little truck, and tranfported from
houſe to houſe, with a gallon of gravel to begin with; becauſe,
until it has obtained the good opinion of the public, it would
not be neceflary to attempt fuch regulations as would after-
wards be deemed requifite to facilitate the operation.
The inventor of this condenfing machine, in a letter on the
ſubject in Nicholſon's Journal, N. S. No. 28, has made ſome
Churn.
129
ingenious obfervations on the peculiarity of its conftruction,
and what he thinks its advantages, compared with the machine
previouſly deſcribed in this article.-" One circumſtance," fays
he, "prefents itſelf, by which the air machine muſt have a de-
cided preference over the brushes; which is this, you must
know the height of the chimney, and adapt the length of the
rods to that height, or elſe you will not know when you are in
the flue or out of it. Whereas, my machine knows no neces-
fity for fuch a punctilio; all that is neceffary being only to give
fo many fhocks of the condenfer to a chimney of two ftories,
and fo many to one of three, and ſo on. And again, thefe
brushes in the very outſet of trial made with them are ſubject
to accidents, and will moſt affuredly wear out very faſt. What
muſt become of thoſe whalebone rods when the fewing is rub-
bed through in paffing up and down againſt the projections of
unceremonious bricks and mortar? What repairs will they not
be ſubject to in the courſe of one day's action? Whereas the
air machine will fweep a hundred chimneys, and be repaired
for two-pence; it wanting only a little oil in the condenfer."
Our readers will decide for themſelves, from the preceding
deſcriptions, which contrivancé deferves the preference. We
are gratified in having an opportunity of ſpeaking of both,
deeming that a laudable endeavour which is intended to recom-
mend to the public the uſe of one or other of two machines
well calculated for the purpoſe of performing a moft difagree-
able and ſometimes dangerous operation; thereby relieving a de-
graded clafs of our fpecies from very inhuman treatment, and
reſtoring them to their rank in civil fociety.
CHUCK, UNIVERSAL. See TURNING
CHURN, a well-known veffel in which butter, by long and
violent agitation, is feparated from the ferous part of the milk.
The inferiority of the churns in common ufe has induced
feveral ingenious mechanics to exert their ſkill in contriving
others that would render the procefs of making butter lefs tedi-
ous and expenfive. Of theſe, one of the most valuable is
Mr. William Bowler's improved churn, with which the Society
for the Encouragement of Arts, &c. were fo well fatisfied as to
preſent the inventor with thirty guineas. As it renders the
operation of churning far lefs fatiguing; and has, befides, fome
peculiar advantages, we thall fubjoin a deſcription.
This churn is of the barrel kind; being a cylinder 18 inches
in diameter, and 9 wide; the fides are of wood, and the rim a
tin plate, which has two openings, one 8 inches in length, and
4 in width, through which the cream is poured into the churn,
and the hand introduced for cleaning it; the other a ſhort pipe,
one inch in diameter, by which the butter-milk runs out of the

VOL. II.
K
}
130
¡
MACHINES.
churn when the operation is finiſhed. The firſt of theſe open-
ings has a wooden cover, fastened down by two fcrews; and
the other a cork fitted to it, while the butter is churning. There
is further, near the larger opening, a ſmall vent-hole with a peg,
to admit the paffage of any air that may be diſcharged from the
cream at the beginning of the operation. An axle alfo paffes
through the churn, terminating in two gudgeons, on which it.
hangs; its lower part being immerfed in a trough, in order to
hold occafionally either hot or cold water, according to the fea
fon of the year. On the infide of the rim are four projecting
pieces of wood, with holes, ferving to agitate the cream by the
motion of the churn. This movement is cauſed by a pendulum
3 feet 6 inches long, that has an iron bob weighing 10 lbs. and
at its upper end a turning pulley 10 inches in diameter, from
which a rope goes twice round another pulley about 3 inches in
diameter fixed on the axis of the churn, which it caufes to
make a partial revolution by each vibration of the pendulum.
There are likewiſe fliding covers to the machinery, and ans
other to the water trough; in order, when hot water is uſed,
to ſecure the ſteam, and keep the cream in a proper degree of
warmth. The motion of the pendulum is given, and con
tinued, by means of a wooden rod about 3 feet 9 inches in
length, which turns on a pin 3 inches above the bob of the pen-
dulum. If there be a tranfverfe handle at the upper end of
this wooden rod a boy may give motion to the churn, with great
facility, even while fitting; the action being then much like
that of rowing, one of the moſt advantageous methods of ap-
plying human force...

+
AA, fig. 8, pl. XII, is the body. B, an opening by which the
cream is put in. C, the cover of the large opening: the fmall
hole on the oppofite fide of the churn cannot be fhewn in this
view. D, the gudgeon on which the body of the churn hangs
E, the upper or larger pully. F, the fmaller pulley fixed on
the axis or gudgeon of the churn. GG, the rod of the pen
dulum hanging from the upper pulley E. H, the bob of the
pendulum. II, the handle, moveable on a pin at a, by which
the pendulum is moved to and fro, making a traverſe in form
of the dotted line KK. L, the trough for the hot or cold
water. M, a projecting piece of wood, with a fhoulder, by
which the handle I is fupported when the churn is not at
work.
CLOCK, a machine now conftructed in fuch a manner, and fo
regulated by the uniform motion of a pendulum, as to meaſure
time, and all its fubdivifions, with great exactnefs. Before the
invention of the pendulum a balance, not unlike the fly of a
kitchen-jack, was ufed inftead of it. Clocks were at firft called


Clocks
131
25
nocturnal dials, to diſtinguiſh them from fun-dials," whic
fhewed the hour by the fhadow of the fun bon is and agri
The invention of clocks with wheels is aferibed to Pacificus,
archdeacon of Verona, in the 9th century, on the credit of an
epitaph quoted by Ughelli, and borrowed by him from Panvi-
nius. Others attribute the invention to Boethius, about the
year $10.
Mr. Derham, however, makes clock-work of a much older
rate; ranking Archimedes's ſphere, mentioned by Claudian,
and that of Pofidonius, mentioned by Cicero, among machines
of this kind: not that either their form or ufe was the fame
with thoſe of ours, but that they had their motion from ſome
hidden weights or ſprings, with wheels or pulleys, or fome fuch
clockwork principle.
1
In the Difquifitiones Monaftica of Benedictus Haëften, pub™
liſhed in the year 1644, he ſays, that clocks were invented by
Silvefter the 4th, a monk of his order, about the year 998, ası
Dithmarus and Bozius have fhewn; for before that time they
had nothing but fun-dials and clepfydræ to fhew the hour.-
Conrade Gefner, in his Epitome, page 604, fays, that Richard
Wallingford, an Engliſh abbot of St. Albans, who flourished in
the year 1326, made a wonderful clock by a moft excellent art,
the like of which could not be produced by all Europe:-Moreri,
under the word Horologe du Palais, fays, that Charles the Fifth,
called the wife king of France, ordered at Paris the firſt large
clock to be made by Henry de Vie, whom he fent for from
Germany, and ſet it upon the tower of his palace in the year
1372.John Froiffart, in his Hiftoire & Chronique, vol. 2, chap.
28, fays, the duke of Bourgogne had a clock which founded
the hour, taken away from the city of Courtray in the year
1382: and the ſame thing is faid by William Paraðîn in his
Annals de Bourgogne.
Clock-makers were firft Introduced into England in 1368,
when Edward the Third granted a licence for three artifts to
come over from Delft, in Holland, and practife their-occupation
in this country.
$
לוג
V
The water-clocks or clepfydræ, and fun-dials, have both a
much better claim to antiquity The French annals mention
one of the former kind, fent by Aaron, king of Perfia, to Charle
magne, about the year 807, which it would feem bore fome rez
femblance to the modern clocks: it was of brafs, and fhewed
the hours by 12 little balls of the fame metal, which at the end
of each hour fell upon a bell, and made a found. There were
alſo figures of 12 cavaliers, which at the end of each hour came
out through certain apertures or windows in the fide of the
clock, and fut them again, &e.
K 2
132
MACHINES.
7
+
The invention of pendulum clocks is owing to the happy
induſtry of the laft age; and the honour of that discovery is
diſputed between Galileo and Huygens. The latter, who
wrote an excellent volume on the ſubject, declares it was firſt
put in practice in the year 1657, and the deſcription of it print-
ed in 1658. Becher, De Nova Temporis dimetiendi Theoria, anno
1680, contends for Galileo; and relates, though at fecond-
hand, the whole hiftory of the invention; adding, that one
Trefler, clock-maker to the father of the then grand-duke of
Tuſcany, made the firſt pendulum clock at Florence under the
direction of Galileo Galilei, a pattern of which was brought
to Holland. And the Academy del Cimento fays exprefsly,
that the application of the pendulum to the movement of a
clock was firſt propoſed by Galileo, and put in practice by his
ſon Vincenzo Galilei in 1649. But whoever may have been
the inventor, it is certain that the invention never flouriſhed
till it came into the hands of Huygens, who infifts on it that, if
ever Galileo thought of fuch a thing, he never brought it to
any degree of perfection. The firſt pendulum clock made in
England was in the year 1662, by one Fromantil, a Dutchman.
After this brief ſketch of the hiftory of clocks, which may be
interefling to ſome of our readers, we ſhall give a deſcription of
a modern clock according to the most approved conftruction.
The firſt figure of plate VIII. is a profile of fuch a clock; P is
a weight which is fufpended by a cord that winds about the
cylinder or barrel C, which is fixed upon the axis a, a; the
pivots b, b, go into holes made in the plates TS, TS, in which
they turn freely. Thefe plates are made of brafs or iron,
and are connected by means of four pillars, Z, Z; the whole
together being called the frame. The weight P, if not re-
ftrained, would neceffarily turn the barrel C, with an uniformly
accelerating motion, in the fame manner as if the weight were
falling freely. But the barrel is furniſhed with a ratchet-wheel,
K, K, the right fide of whofe teeth ftrikes against the click,
which is fixed with a fcrew to the wheel DD, as repreſented
in fig. 2; ſo that the action of the weight is communicated to
the wheel DD, the teeth of which act upon the teeth of the
fmall wheel d, which turns upon the pivots c, c. The commu-
nication or action of one wheel with another is called the pitch-
ing; a fmall wheel like d is called a pinion, and its teeth are
called leaves of the pinion. Several things are requiſite to form
a good pitching, the advantages of which are obvious in all ma-
chinery where teeth and pinions are employed. The teeth and
pinion-leaves fhould be of a proper fhape, and perfectly equal
among themſelves: the fize alfo of the pinion fhould be of
juſt proportion to the wheel acting into it.
Clocks.
133
1
The wheel EE is fixed upon the axis of the pinion d; and
the motion communicated to the wheel DD by the weight is
tranſmitted to the pinion d, confequently to the wheel EE, as
likewife to the pinion e and wheel FF, which moves the pinion
f, upon the axis of which the crown or balance wheel ĠH is
fixed. The pivots of the pinion ƒ play in holes of the plates
LM, which are fixed horizontally to the plates TS. In a word,
the motion begun by the weight is tranfmitted from the wheel
GH to the palettes IK, and by means of the fork UX rivetted
on the palettes, communicates motion to the pendulum AB,
which is fufpended upon the hook A. The pendulum AB de-
ſcribes, round the point A, an arc of a circle alternately going
and returning. If, then, the pendulum be once put in motion
by a puſh of the hand, the weight of the pendulum at B will
make it return upon itſelf, and it will continue to go alternately
backward and forward till the refiftance of the air upon the
pendulum, and the friction at the point of fufpenfion at A,
deſtroys the original impreffed force. But as at 'every vibra-
tion of the pendulum the teeth of the balance-wheel GH act ſo
upon the palettes IK (the pivots upon the axis of theſe palettes
play in two holes of the potence s t), that after one tooth Ḥ
has communicated motion to the palette K, that tooth efcapes;
then the oppofite tooth G acts upon the palette I, and eſcapes
in the fame manner; and thus each tooth of the wheel eſcapes
the palettes IK, after having communicated their motion to the
palettes in fuch a manner that the pendulum, inſtead of being
ſtopped, continues to move. The wheel EE revolves in an
hour; the pivot c of this wheel paffes through the plate, and is
continued to r; upon the pivot is a wheel NN, with a long
focket faſtened in the centre; upon the extremity of this focket
r, the minute-hand is fixed. The wheel NN acts upon the
wheel O; the pinion of which p acts upon the wheel
gg,
fixed
upon a focket which turns along with the wheel N. This
wheel gg makes its revolution in 12 hours, upon the focket of
which the hour-hand is fixed.
From the above deſcription it is eaſy to fee, 1. That the
weight P turns all the wheels, and at the fame time continues
the motion of the pendulum. 2. That the quickness of the
motion of the wheels is determined by that of the pendulum.
3. That the wheels point out the parts of time divided by the
uniform motion of the pendulum.
When the cord upon which the weight is fufpended is en-
tirely run down from off the barrel, it is wound up again by
means of a key, which goes on at the fquare end of the arbor at
Q by turning it in a contrary direction from that in which the
weight defcends. For this purpoſe the inclined fide of the
134
MACHINES.
teeth of the wheel K (fig. 2.) removes the click C, fo that the
ratchet-wheel R turns while the wheel D is at reft; but as
foon as the cord is wound up, the click falls in between the
teeth of the wheel D, and the right fide of the teeth again act
upon the end of the click, which obliges the wheel D to turn
along with the barrel; and the fpring A keeps the click be-
tween the teeth of the ratchet wheel R.
·
+
We fhall now explain how time is meaſured by the motion
of the pendulum; and how the wheel E, upon the axis of
which the minute-hand is fixed, makes but one precife revòlu-
tion in an hour. The vibrations of a pendulum are performed
in a fhorter or longer time in proportion to the length of the
pendulum itfelf. A pendulum of 39 inches in length makes
3600 vibrations in an hour: i. e. each vibration is performed in a
Tecond of time, and for that reafon it is called a fecond pendulum.
But a pendulum of 93 inches makes 200 vibrations in an
hour, or two vibrations in a fecond of time, and is called á half-
Second pendulum. Hence, in conftructing a wheel whofe revo-
lution must be performed in a given time, the time of the vibra-
tions of the pendulum which regulates its motion must be con-
fidered, Suppofing, then, that the pendulum AB makes 7200
vibrations in an hour, let us confider how the wheel E fhall
take up an hour in making one revolution. This entirely de-
pends on the number of teeth in the wheels and pinions. If
the balance-wheel confifts of 30 teeth, it will turn once in the
time that the pendulum makes 6e vibrations: for at every turn
of the wheel the ſame tooth acts once on the palette I, and
once on the palette K, which occafions two ſeparate vibrations
in the pendulum; and the wheel having 30 teeth it occafions
twice 30, or 60 vibrations. Confequently this wheel muſt per-
form 120 revolutions in an hour; becauſe 60 vibrations, which
it occafions at every revolution, are contained 120 times in
7200, the number of vibrations performed by the pendulum in
an hour. Now, in order to determine the number of teeth
for the wheels E F, and their pinions ef, it muſt be remarked
"that one revolution of the wheel E muft turn the pinion e as
many times as the number of teeth in the pinion is contained
“in the number of teeth in the wheel. Thus, if the wheel E
contains 72 teeth, and the pinione 6, the pinion will make 12
revolutions in the time that the wheel makes 1 for each tooth
of the wheel drives forward a tooth of the pinion, and when the
6 teeth of the pinion are moved, a complete revolution is per-
formed; but the wheel E has by that time only advanced 16
teeth, and has ftill 66 to advance before its révolution be com-
pleted, which will occafion 1 more revolutions of the pinion.
For the fame reafon the wheel F having 60 teeth, and the
..

3 Clocks.
135
心
​pinion f6, the pinion will make 10 revolutions while the wheel
performs 1. Now the wheel F being turned by the pinion e
makes 12 revolutions for one of the wheel E; and the pinion f
makes to revolutions for one of the wheel F;-confequently the
pinion fperforms 10 times 1-2, or-120, revolutions in the time the
wheel E performs one. But the wheel G, which is turned by
the pinion f, occafions 60 vibrations in the pendulum each time
it turns round; confequently the wheel G occafions. 60 times
120, or 7200, vibrations of the pendulum while the wheel E
performs one revolution; but 7200, is the number of vibrations
made by the pendulum in an hour, and confequently the wheel
E performs but one revolution in an hour; and fo of the rest.
From this reafoning it is eafy to diſcover how a clock may be
made to go for any length of time without being wound up.
1. By increafing the number of the teeth in the wheels. 2. By
diminishing the number of teeth in the pinions. 3. By increaf
ing the length of the cord that fufpends the weight. 4. By
increafing the length of the pendulum. And, 5. By adding to
the number of wheels and pinions. But in proportion as the
time is augmented, if the weight continues the fame, the force
which it communicates to the laft wheel GH will be dimi
nifhed.

#
It only remains to take notice of the number of teeth in the
wheels which turn the hour and minute-hands. The wheel E
performs one revolution in an hour; the wheel N N, which is
turned by the axis of the wheel E, muft likewife make only one
revolution in the fame time; and the minute-hand is fixed
to the focket of this wheel. The wheel N has 30 teeth, and
acts upon the wheel O, which has likewife 30 teeth, and the
fame diameter; confequently the wheel O takes one hour to a
revolution: now the wheel O carries the pinion p, which has
6 teeth, and which acts upon the wheel qq of 72 teeth; con-
fequently the pinion p makes 12 revolutions while the wheel
4.9
makes one, and of courſe the wheel qq takes 12 hours to, one
revolution and upon the focket of this wheel the hour-hand is
fixed. Much that has been faid here, concerning revolutions
of wheels, &c. is equally applicable to watches as to clocks.
But it is time to fpeak of the ftriking part; in which,
indeed, as well as the other part of a clock, there is room for
great variety and choice in the conftruction. The wheels
ufually compofing this part are, the great or firft wheel, which
is moved by the weight or fpring at the barrel, in fixteen or
thirty-hour clocks, this has ufually pins, and is called the pin-
wheel in eight-day pieces the fecond wheel is commonly the
pin-wheel, or ſtriking-wheel, which is moved by the former
ede nás naar od gairí i basqw adi noen vond von
T
136
MACHINES.
•
Next to the ſtriking-wheel is the detent-wheel, or hoop-wheel,
having a hoop almoſt round it, wherein is a vacancy at which
the clock locks. The next is the third or fourth wheel, accord-
ing to its diſtance from the reft, called the warning-wheel. The
laft is the flying pinion, with a fly or fan, to gather air, and fo
bridle the rapidity of the clock's motion. To thefe muft be
added the pinion of report; which drives round the locking-
wheel, called alfo the count-wheel; ordinarily with eleven notches
in it, unequally diftant, to make the clock ftrike the hours.
Befides the wheels, to the clock part belongs the rash or ratch;
a kind of wheel with twelve large fangs, running concentrical
to the dial-wheel, and ferving to lift up the detents every hour
and make the clock ftrike: the detents or ftops, which being
lifted up and let fall, lock and unlock the clock in ſtriking;-
the hammer, which ftrikes the bell; the hammer-tails, by
which the striking pins draw back the hammers; latches, where-
by the work is lifted up and unlocked; and lifting-pieces which
lift up and unlock the detents.
In the year 1803 the Society for the Encouragement of Arts,
&c. prefented to Mr. John Prior of Nefsfield, Yorkshire, a
reward of 30 guineas, on account of his contrivance for the
Striking part of an eight-day clock. As this invention is likely
to be uſeful, we fhall defcribe it here. It confifts of a wheel
and fly, with fix turns of a ſpiral line, cut upon the wheel for
the purpoſe of counting the hours. The pins below this ſpiral
elevate the hammer, and thofe above are for the uſe of the de-
tent. This fingle wheel ferves the purpoſe of count-wheel, pin-
wheel, detent-wheel, and the fly-wheel, and has fix revolutions
in ftriking the 12 hours. If we fuppofe a train of wheels and
pinions uſed in other ftriking parts to be made without error,
and that the wheels and pinions would turn each other without
ſhake or play: then, allowing the above fuppofition to be true
(though every mechanic knows it is not), Mr. Prior's ftrik-
ing part would be found fix times fuperior to others, in ftrik-
ing the hours 1, 2, 5, 7, 10, 11; twelve times fuperior in
ſtriking 4, 6, 8; and eighteen times, in ftriking 3, 9, and 12.
In ftriking 2, the inventor purpoſely made an imperfection
equal to the ſpace of three teeth of the wheel; and, in ſtriking
3, an imperfection of nine or ten teeth; and yet both theſe
hours are ftruck perfectly correct. The flies in clocks turn
round, at a mean, about fixty times for every knock of the
hammer, but this turns round only three times for the fame pur-
pofe; and ſuppoſe the pivots were of equal diameters, the in-
fluence of oil on them would be as the number of revolutions
in each. It would be better for clocks if they gave no warning
Curious Clocks.
137
at all, but the fnail-piece to raife a weight fomewhat fimilar
to the model Mr. P fent for the infpection of that refpectable
Society.
Reference to Mr. PRIOR's Striking Part of his Clock.
Plate X. fig. 1. A, the large wheel, on the face of which
are funk or cut the fix turns of a ſpiral.
B, the fingle worm fcrew, which acts on the above wheel,
and moves the fly C.
D, the ſpiral work of the wheel A. The black ſpots fhew
the grooves into which the detents drop on ftriking the hour.
E, the groove into which the locking-piece F drops when it
ftrikes one, and from which place it proceeds to the outward
parts of the ſpiral in the progreffive hours, being thrown out by
a lifting piece H at each hour: the upper detent G being pump-
ed off with the locking piece F, from the pins in the wheel A.
In ftriking the hour of twelve, the locking-piece, having
arrived at the outer fpiral at H, rifes up an inclined plane, and
drops by its own weight to the inner circle, in which the hour
one is to be ftruck, and proceeds on in a progreffive motion
through the different hours till it comes again to twelve.
I. the hammer-work made in the common way, which is
worked by thirteen pins on the face of the ſpiral.
Fig. 2.-K, the thirteen pins on the face of the ſpiral, which
work the hammer-work.
L, the outer pins, which lock the detent.
M, the pump-fpring to the detent.
For other information reſpecting clockwork, fee the articles
BALANCE, PENDULUM, and SCAPEMENT, in this volume.
Some very fimple contrivances for clocks, by Mr. Ferguſon,
and Dr. Franklin, may be ſeen in Ferguſon's Select Exercifes.
In the fourth century an artiſt named James Dondi con-
ſtructed a clock for the city of Padua, which was long confidered
as the wonder of that period. Befides indicating the hours, it
repreſented the motion of the fun, moon, and planets, as well
as pointed out the different feſtivals of the year. On this ac-
count Dondi obtained the furname of Horologio, which became
that of his pofterity. A little time after, William Zelander
conftructed for the fame city a clock ftill more complex; which
was repaired in the fixteenth century by Janellus Turrianus, the
mechanift of Charles V.
·
But the clocks of the cathedrals of Straſburgh and of Lyons,
are much more celebrated. That of Strafburgh was the work
of Conrad Daſypodius, a mathematician of that city, who finiſh-
ed it about 1573. The face of the baſement of this clock ex-
hibits three dial-plates; one of which is round, and confifts of.
138
MACHINES.

feveral concentric circles, the two interior ones of which per-
form their revolutions in a year, and ferve to mark the days of
the year, the feſtivals and other circumstances of the calendar.
The two lateral dial-plates are fquare, and ferve to indicate the
eclipfes both of the fun and the moon. Above the middle dial-
plate, and in the attic space of the basement, the days of the week
are reprefented by different divinities, fuppofed to prefide over
the planets from which their common appellations are derived.
The divinity of the current day appears in a car rolling over the
clouds, and at midnight retires to give place to the fucceeding
one. Before the bafement is feen a globe, borne on the wings
of a pelican, around which the fun and moon revolved; and
which in that manner reprefented the motion of theſe planets:
but this part of the machine, as well as feveral others, has been
deranged for a long time,. The ornamental turret, above this
bafement, exhibits chiefly a large dial in the form of an aſtrolabe;
which thews the annual motion of the fun and moon through the
ecliptic, the hours of the day, &c. The phafes of the moon are
feen alfo marked out on a particular dial-plate above. This work is
remarkable alfo for a confiderable affemblage of bells and figures,
which perform different motions. Above the dial-plate laft
mentioned, for example, the four ages of man are reprefented
by fymbolical figures: one paffes every quarter of an hour, and
marks the quarter by ftriking on fmall bells thefe figures are
followed by Death, who is expelled by Jefus Chriftrifen from
the grave; who, however, permits it to found the hour, in
order to warn man that time is on, the wing. Two ſmall angels
perform movements alfa; one ftriking a bell with a fceptre,
while the other turns an, hour-glafs at the expiration of an hour.
In the last place, this work was decorated with various animals,
which emitted founds fimilar to their natural voices; but none
of them now remains, except the cock, which crows immedi
ately before the hour, ftrikes, firft ftretching out its neck and
clapping its wings. Indeed it is to be regretted that a great
part of this machine is now entirely deranged,

{
A
The clock of the cathedral of Lyons is of lefs fize than that
of Strafburgh, but is not inferior to it in the variety of its move
ments; it has the advantage alfo of being in a good condition.
It is the work of Lippius de Bafle, and was exceedingly well res
paired in the last century by an ingenious, clock-maker of Lyons
named Nouriffon. Like that of Strafburgh, it exhibits on differ
ent dial-plates the annual and diurnal progrefs of the fun and
moon, the days of the year, their length, and the whole calendar,
Civil as well as ecclefiaftic. The days of the week are indicated
by fymbols more analogous to the place where the clock is
erected; the hours are announced by the crowing Jofua cock,
E
Treatifes on Clockwork.
139
three times repeated after it has clapped its wings, and made
various other movements. When the cock has done crowing,
angels appear, who, by ftriking various bells, perform the air of
a hymn; the annunciation of the Virgin is reprefented alſo by
-moving figures, and by the deſcent of a dove from the clouds;
and after this mechanical exhibition the hour ſtrikes. On one
of the fides of the clock is feen an oval dial-plate, where the
hours and minutes are indicated by means of an index, which
lengthens or contracts itſelf, according to the length of the femi-
diameter of the ellipfis over which it moves.
A very curious clock, the work of Martinot, a celebrated
clock-maker of the feventeenth century, was formerly to be
ſeen in the royal apartments at Verfailles. Before it ftruck the
hour, two cocks on the corners of a ſmall edifice crowed alter-
nately, clapping their wings: foon after two lateral doors of the
edifice opened, at which appeared two figures bearing cymbals,
beat upon by a kind of guards with clubs. When theſe figures
had retired, the centre door was thrown open, and a pedeſtal,
fupporting an equeftrian ftatue of Louis XIV. iffued from it,
while a group of clouds feparating, gave a paffage to a figure of
Fame, which came and hovered over the ftatue. An air was
then performed by bells: after which the two figures re-entered;
the two guards raiſed up their clubs, which they had lowered as
if out of refpect for the preſence of the king, and the hour was
then ſtruck-
While, however, we have thought it right to defcribe thefe
ingenious performances of foreign artiſts, we must not neglect
to mention the equally ingenious workmanship of fome of our
own countrymen. We now refer to two clocks made by Eng-
lith artifls, as a prefent from the East-India company to the
emperor of China. Thefe two clocks are in the form of chariots,
in each of which a lady is placed in a fine attitude, leaning her
right hand upon a part of the chariot, under which appears a
clock of curious workmanſhip, little larger than a fhilling, that
ftrikes and repeats, and goes for eight days. Upon the lady's
finger fits a bird, finely modelled, and fet with diamonds and
rubies, with its wings expanded in a flying pofture, and actually
flutters for a confiderable time on touching a diamond button
below it: the body of the bird, in which are contained part of
the wheels that animate it as it were, is less than the 16th part of
an inch. The lady holds in her left-hand a golden tube little
thicker than a large pin, on the top of which is a fmall round
box, to which is fixed a circular ornament not larger than a
fixpence, fet with diamonds, which goes round in near three
hours in a conftant regular motion. Over the lady's head is a
double cumbrella, fupported by a ſmall fluted pillar not thicker
140
MACHINES.
than a quill, and under the larger of which a bell is fixed, at a
confiderable diftance from the clock, with which it feems to
have no connection; but from which a communication is fe-
cretly conveyed to a hammer, that regularly ſtrikes the hour,
and repeats the fame at pleaſure, by touching a diamond button
fixed to the clock below. At the feet of the lady is a golden
dog.
As the ſubject of clock and watch making is very important,
we think the following copious catalogue of the chief writings
relating to it, both in theory and practice, may be acceptable
and beneficial to many of our readers.
Carmen de aftronomico horologio argentoratenfi, fcriptum a
M. Nicodemo Frifchlino Balingenfi, academiæ Tubingenfis pro-
feffore. A. D. 1575·
Defcriptio brevis et fuccincta horologii rariffimi æque ac pre-
tiofiffimi, ab ingeniofiffimo mechanico Jo. Davide Lieberkühn
conftructi. 1576.
Conradi Dafypodii heron mechanicus. Ejufdem horologii
aftronomici, &c. 1580.
Brevis defcriptio artificiofi novi et aftronomici automati
horologii, cujus fimile ante hac non exftitit; inventi primum
ftudio et induftria M. Jacobi Cunonis. 1581.
Traité de géométrie et d'horologiographie pratique, par
Jean Bullant. 1602.
Horologium aftronomicum Upfalienfe, cujus artificiofiffima
ftructura, analyfis, et ufus, &c. Auctore Laurent. Fornelio,
1630.
Fo. Sarazini horographum catholicum feu univerfale, quo
omnia horologia fciotherica defcribuntur. 1630.
Le nouveau fciatère pour fabriquer d'horloges. 1633.
Athanafii Kircheri ars magnis lucis et umbræ. 1646.
Johannis Baptifta Trotta novum horologium nocturnam e
ftellis. 1651.
Chriftiani Hugenii a Zulichem Conft. F. horologium,
1658.
[It was in this elegant little piece that Huygens firſt treated of
the regulation of time by the pendulum; and on this he entered
more at large in his celebrated work, Horologium ofcillatorium.]
A narrative concerning the fuccefs of pendulum watches at
fea for finding the longitude, by Major Holmes. Phil. Trans.
No. 1. 1665.
Antonio Tempera l'horologio giufto utiliffimo a naviganti. 1668.
Chr. Hugenii Zulechemii Conft. F. horologium ofcillatorium,
five de motu pendulorum ad horologia aptato demonſtrationes
geometricæ. Parisüs. 1673.
I. S. Horological dialogues, in three parts; fhewing the
Treatifes on Clockwork.
141
nature, uſe, and right managing of clocks and watches: with an
appendix, containing Mr. Oughtred's method for calculating of
numbers. 1675.
Very exact portable watches, by Mr. Huygens. Phil,
Trans. No. 112. A. D. 1675-
M. Leibnitz on his portable watches. Phil. Trans. No. 113.
A. D. 1675.
Compendium horologico-fciotericum et geometricum. Chr.
Zuicker. 1675.
Factum de M. l'abbé de Hautefeuille touchant les pendules
de poche, contre Mr. Huyghens. 1675.
M. Campani de Alimenis horologium folo naturæ motu atque
ingenio, &c. 1677.
Traité d'horologiographie du père de la Magdeleine. 1680.
D. I. I. Becheri, de nova temporis dimetiendi ratione, et ac-
curata horologiorum conftructione, theoria et experientia, Lon-
dini. 1680.
Horologia fcioterica prælibata ad delineandum - ſciotericôn
declinationis, folaris quantum indies eft perceptibilis, per N.
Hanbury. Lond. 1683.
Horologium horologiorum defcriptum et explicatum, ab
Joanne Bartholo. Fichelli. Venetiis. 1685.
Henrici Coetfii Arnhemienfis horologiographia plana, feu
methodus in fuperficiebus planis omnia horologiorum genera
defcribenda methodus. Lugd. Batav. 1689.
Horological difquifitions. A work very neceflary for all
that would underſtand the true way of rightly managing clocks
and watches. By John Smidt, C. M. 1694.
The artificial clock-maker, a treatiſe of watch and clöck-
work, by W. D. [W. Derham.] 1696.
[This ufeful little work has gone through many editions. It
was tranflated into the German language in 1708, and into the
French in 1731.]
Remarques fur la conftruction des horloges à pendule, par
M. de la Hire, mem. R. Acad. 1700, pa. 161.
De la figure des fusées des horloges à reffort, par M.Va-
rignon, mem. R. Acad. 1702, pa. 122. Mécan.
The invention of making clocks to keep time with the fun's
apparent motion afferted by W. J. Williamfon. Phil. Trans.
No. 363.
•
Regle artificielle du tems pour aprendre la divifion naturelle
et artificielle du tems, et connoitre toutes fortes d'horloges et de
montres, et la maniere de s'en fervir adroitement, par H. S. de
Londres. Imprimé à Vienne. 1714.
This curious work, the author Henry Sully, went through
various editions in different languages.] .
142
MACHINES.
Conftruction d'un horloge qui marque le tems vrai avec le
moyen. Par M. de la Hire. mem. R. Acad. 1717.
Horologiographie pratique, ou la manière de faire des horloges
à poids et les montres, par le religieux Auguſtin P. B. à
Rouen. 1719.

الله
Defeription d'une grande et merveilleufe horloge portative
en pèndule, la plus admirable et furprenante que aye jamais para
au monde: digne de l'admiration des beaux efprits: étant l'uni-
que au monde de fon efpèce; nouvelle parachevée par l'in
venteur, qui eſt le Sr. T. Paftre, ci-devant marchand fabriquant
en bas de foye et laine, à la ville de Nimes en Languedoc. 1721.
Conſtruction nouvelle de trois montres portatives d'un
nouveau balancier en forme de croix, qui fait les oſcillations des
péndules très-petites, &c. par M. de Hautefeuille. 1722.
Deſcription d'une horloge d'une nouvelle invention pour la
juſte meſure du tems fur mer, par Sully. 1726.
A contrivance to avoid the irregularities in a clock's motion,
occafioned by the action of heat and cold on the pendulum rod, by
Mr. George Graham, watchmaker, F. R. S. Phil. Trans. No. 392.
A. D. 1726.
Traité général des horloges, par le père Dom Jacques-Alex-
andre. 1734-
Moyens de conftruire un pendule qui ne peut s'alonger par
la chaleur ni fe racourcir par le froid, par M. Caffini, mem. R.
Acad, 174!.
Traité de l'horlogerie mechanique et pratique, approuvé par
l'Académie Royal des Sciences, par M. Thiout l'aine. 1741.
[Much alfo on the fubjects of pendulums, fcapements, &c.
may be feen in the account of machines et inventions approuvées
par l'Acad. Roy. des Sciences. vol. 1 to 5.]
Job. George Hartmanns Klein-Uhrmachers zu Jena nöthiger
Unterricht von Verbefferung der Sackuhren, durch den waager
echten Stand, Berechnung, Aufarbeitung, Beurtheilung, Ge-
brauch, Stellung, Kennzeichen und Probirung derfelben. 1752.
Traité d'horlogerie, par M. 7. A. le Paute. 1755-
Difcours fur l'horlogerie, et expofition d'une nouvelle mé
chanique de pendule, approuvée par Mefs. de l'Académie Roy.
des Sci. par le fieur Mazurier. 1756.
Jul. Le Roy anweifung die einfachen fowohl als Repe-
tiruhren wohl einzurichten und zu gebrauchen. Drefden. 1759.
L'art de conduire et de régler les pendules et les montres,
&c. par M. Ferdinand Berthoud. 1759.
Molitor's anweiſung, wie Geh-, Schlag-, Repetir-, und Sackuh-
ren richtig berechnet, probirt und traktirt werden. Frankfurt
am Mayn. 1762.
Effai fur l'horlogerie, dans lequel on traite de cet art relative

Treatifeson-Clockawork.
143.
ment à l'ufage civil, à l'aftronomie, et à la navigation, en établif
fent des principes confirmés par l'experience, par Fer. Berthoud.
Bertligyd
1763.
Elements of clock and watch work, by, Alexander Cumming.
1766.
An account of the going of Mr. Harriſon's watch at the
Royal Obfervatory from May 5th, 1766, to March 4th, 1797-
Together with the original obfervations and calculations of the
fame. By the rev. Nevil Mafkelyne, aftronomer, royal, &c.
1767.
Principles of Mr. Harrifon's time-keeper, with plates of the
fame, publiſhed by order of the commiffioners of jongitude.
1767.
Remarks on a pamphlet lately publiſhed by the reverend
Mr. Mafkelyne, by Mr. Harrison. 1798,
A defeription concerning fuch mechanifm as will afford a
nice or true menfuration of time, by John Harrison. 1775 £
Effay de la montre marine de M. le Roy, mem, Roy. Acad.
1767.
Relation du voyage de M. Caſſini, fils, fait par ordre du roi,
pour examiner les montres marines de M. le Roy, laine, mem.
Roy. Acad. 1769.
Suite du précis fur les montres marines, avec un fupplement
au mémoire fur la meilleure maniere de mefurer le tems au mer
par M. le Roy, à Leyd.
1776.

Recherches fur le vrai moyen de perfectionner les pendules à
fecondes, deſtinés à indiquer les équations journalières du foleil,
&c. par le fieur Ridereau. 1770
A
1, sdi ro che Juja.
On the going of Mr. Arnold's pocket chronometer made on
a new conſtruction, by Dr. N. Majkelyne, 1770 buah
Defcription nouvelle de la cathédrale de Strasbourg, et de fa
fameufe tour, par M. Jofeph Schweighaeufer. 179YŰ
D'une montre particulière, nommée almanach en montre, ou
montre à la Jablonowiky, par M. Paffament, 1776. tet, dapaid
"Steph. Ramaufki experimenta circa longitudinem penduli
fimplicis minuta, fecunda, Kolae et Archangelopoli ofcillantis.
Nov. Com, Acad. Petrop, 1775me
a
Traité des horloges marines, contenant la théorie, la con
ftruction, la main-d'œuvre de ces machines, et la manière de
des
les éprouver, pour parvenir par leur moyen à la rectification, des
cartes marines et à la determination des longitudes, &c, par
M. Ferdinand Berthoud. 1773, et 1793
Eclairciffemens, fur d'invention, la théorie, la conftruction, et
les épreuves des nouvelles machines proposées en France pour la
détermination des longitudes en mer par 'le mefure du tems,
par M. Ferd. Berthoud, 177365 Scienc
Rapport fait à l'Académie des Sciences par Meffrs. Montigni

144
MACHINES.
et Vaucanfon, fur un nouvel échappement à détente, imaginé et
préfenté par M. Platier, horloger et méchanicien de S. A. S.
Monfeigneur le Prince de Conti. 1774.
Leonh. Euler, de oſcillationibus minimis penduli quotcunque
pondufculis onufti. Nov. Com. Acad. Petrop. 1775.
Leonh. Euler, de motu oſcillatorio binarum lancium ex libra
fufpenfarum. Nov. Com. Ac. Petrop. 1775.
Dan. Bernoulli commentatio phyfico-mechanica, &c. Nov.
Com. Acad. Petrop. 1775-
Reflexions fur l'échappement, par M. de la Grange, mem.
Acad. Berlin.
1777.
Dan. Bernoulli fpecimen philofophicum de compenfationibus
horologicis et veriori menfuria temporis. Act. Acad. Imp.
Petrop. 1777.
Lettre de M. Magellan à M. le chevalier de Bory, de l'Aca-
démie Royale des Sciences, rélativement à la montre marine.
de M. Mudge, éleve du célébre Graham, et l'un des plus habiles
horlogers de ce fiècle.
[This is inferted in Rozier's Obfervations fur la phyfique, fur
l'hiſtoire naturelle, et fur les arts, tom. xi. 1778.]
Abraham Gotthelf Käftner, über die Aenderung des Ganges
der Pendeluhren un Sommer und Winter. Gottingen. 1778.
Various papers relative to the contrivances in watch-work,
by François Arlaud, François Callet, &c. in the Mémoires de la
fociété établie à Genève pour l'encouragement des arts et de
l'agriculture, tom. i. ii. &c. 1778.
Leonhard Euler de motu ofcillatorio pendulorum ex filo tenſo
dependentium. A&t. Acad. Imp. Petrop. 1779.
Defcription d'une machine pour refendre plufieurs roues
d'horlogerie en même temps, inventée par M. Pingeron, capitaine
de l'artillerie, &c. 1780.
Balancier de pendule à fecondes d'une nouvelle conftruc-
tion, par le fieur Grenier. Rouen. 1780.
L'art de faire les refforts de montres, fuivi de la manière de
faire les petits refforts de répétitions et des refforts fpiraux, par
W. Blakey. Amfterdam. 1780.
A letter from Mr. Chriftian Mayer, aftronomer to the elector
palatine, to Mr. N. N. on the going of a new pendulum clock,
made by Mr. John Arnold, and ſet up in the elector's obferva-
tory at Manheim. (Tranflated from the German.) London,
Becket.

1781.
Der neue engliſche Uhrmacher, oder vollständige Anweis
fung alle Geh-, Schlag-, und Repetiruhren richtig zu berechnen
und gehörig zufammenzufetzen, nebft der Befchreibung einer
Univerfal-Sonnenuhr, mit nöthigen Kupfern, &c. 1781.
Extrait d'une lettre de M. L. H. Magellan à un de fes amis
de Paris, ſur la préférence des grand arcs de vibration pour le
Treatises on Clockwork.
145

régularité des pendules aftronomiques, avec la defcription d'us
echappement libre, pour des petites pendules à demifecondes
qui battent des fecondes entières. [This is inferted in tom.
XX. of Rozier's Obfervations, &c. 1782.]
Nic. Fufs Determinatio motuum penduli compofiti bifili ex
primis mechanicæ principiis petita. Nov. Act. Petrop. tom. I.
1783.
Leonh. Euler De motu oſcillatorio, &c. Nov. Act. Petrop
tom. I. 1786.
Three regiſters of a pocket chronometer, by count de Brühl.
1785.
Mémoire fur l'horlogerie; contenant une nouvelle conftruc
tion des montres fimples et à repetition à roues de rencontre,
approuvées par l'Acad. Roy. des Sciences. Par Heffen. 1785.-
Der felbftlehrende uhrmacher, oder genugthuende anweifung,
alle ſchlag-, geh-, repetir-, und fonnen-uhren richtig zu ber-
echnen, nebft allen vortheilen, auf die neuefte und einfachfte
art fie zu verfertigen ohne einen weitern mündlichen unterricht
nöthig zu haben. Von einem Freunde der Künfte. 1786.
Deſcription of the two-part chime-clock invented by Robert
Sampfon. Tranfactions of the Society for the Encouragement
of Arts, &c. for 1786, vol. iv. [Defcriptions of many other in-
genious inventions of Engliſh artiſts may likewife be found in
the different volumes of the Tranfactions of this reſpectable and
uſeful ſociety.]
An account and deſcriptions of three pendulums invented and
conftructed by John Crofthwaite. Trans. Roy. Iriſh. Acad.
1788.
Horlogerie pratique à l'ufage des apprentifs et des amateurs.
par M. Vioniaux, à Toulouſe. 1788.
Tratado general y matematico de la reloxeria, que comprende
el modo ex hacer reloxes de todas claffes, y del de faberlos com-
poner y arreglar por dificiles que fean; acompanado de los
elementos neceffarios para ella. Su autor Em. de Cercella é
Icoaga. Madrid. 1789.
Sopra la teoria de pendoli e fulla legge della forza centripeta
proporzionale alla femplice diftanza del centro e fulla fua appli-
cazione alla dottrina de' pendoli; difcorfi del fign. Gregoria
Fontana. Pavia. 1789.
Whitehurst's Verfuch durch zeitmeffung unveränderliche
maſſe zu erhalten; uberſetzt von J. H. Wiedmann. Nürnberg.
1790.
Differtation fur l'horlogerie, par Fr. Huet. 1791.
Tratado methodico de la reloxeria fimple; efcr. por Ph. y Pl
Chaboft. Madrid. 1791.

VOL. II.
146
MACHINES.
}
Der uhrmacher, &c. von J. G. Geissler. 1793-1799.
Account of a new pendulum, by Geo. Fordyce, M. D. F.R.S.
Phil. Trans. 1794. Part I.
Inveſtigations, founded on the theory of motion, for determin-
ing the times of vibrations of watch balances, by Geo. Atwood,
F.R.S. Phil. Trans. 1794. Part. I.
Beytrag zur zeitmeſs kunft fur freunde und liebhaber von
uhrwerken aller art. Von Friedrich Auguft Schmidt. Leipzig.
1797.
Suite du traité des montres à longitudes, &c. par F. Ber-
thoud. 1797.
Verfuch einer gefchichte der entſtlehung und fortſchritte
der theoretiſch-praktiſchen uhrmacherkunft. Von Joh. Heinr.
Mortitz Poppe. Gottingen. 1797.
Theoretisch-praktiſches worterbuch der uhrmakerkunft, &c.
Von 7. H. M. Poppe. 1799-1800. Leipzig.
Ausführliche gefchichte der theoretisch-praktiſchen uhr-
macherkunft, &c. Von f. H. M. Poppe. Leipzig. 1801.
[The two latter are deemed to be very valuable performances.]
The article WATCHWORK in the Supplement to the Encyclo-
pædia Britannica, and different parts of Nicholſon's Philofophical
Journal, and Tilloch's Philofophical Magazine, contain much
ufeful information on the fubjects of pendulums, fcapements, &c.
COINAGE, or COINING, the art or act of making money.
Coining is either performed by the hammer or the mill. The
first method is now little uſed in Europe, eſpecially in England,
France, &c. though the only one known till the year 1553,
when a new machine, or coining mill, invented by an engraver,
one Antoine Brucher, was firſt tried in the French king's palace
at Paris, for the coining of counters: though fome attribute the
invention of the mill to Varin, a famous engraver, who, in
reality, was no more than an improver of it; and others to
Aubry Olivier, who had only the inſpection of it.
The mill has met with various fate fince its first invention;
being now uſed, and again laid by, and the hammer refumed;
but it has at length got that footing, by the neatneſs and perfec-
tion of the fpecies ftruck with it, that there appears no great
probability of its ever being again diſuſed.
In either kind of coining, the pieces of metal are ſtamped or
ftruck with a fort of punchions or dyes, wherein are engraven
the prince's effigies, with the arms, legend, &c.
: Coining by the mill, or milled money. The bars or plates being
taken out of the mould, and ſcraped and bruſhed, are paffed
feveral times through a mill, to flatten them further, and bring
them to the just thickneſs of the' fpecies to be coined; with

Coining Prefs, &c.
147
this difference, however, that the plates of gold are heated again
in a furnace, and quenched in water, before they undergo the
mill;
which foftens and renders them more ductile: whereas .
thofe of filver paſs the mill juſt as they are, without any heating;
and when afterwards they are heated they are left to cool again
of themſelves, without water.
The plates, whether gold, filver, or copper, thus reduced as
near as poffible to their thickneſs, are cut into round pieces,
called blanks or planchets, near the fize of the intended fpecies,
with a cutting inftrument faſtened to the lower extremity of an
arbor, whoſe upper end is formed into a ſcrew; which, being
turned by an iron handle, turns the arbor, and lets the fteel,
well ſharpened, in form of a punch-cutter, fall on the plates; and
thus is a piece punched out.
Theſe pieces are now given to be adjuſted, and brought by
filing, or rafping, to the weight of the ftandard, whereby they
are to be regulated: and what remains of the plate between the
circles is melted again, under the denomination of ſizel.
The pieces are adjuſted in a fine balance: and thoſe which
prove too light are feparated from thofe too heavy; the firſt
to be melted again, and the fecond to be filed down. For it .
may be obſerved, that the mill through which the plates are
paffed can never be fo juft but there will be fome inequality,
whence will arife a difference in the blanks. And this inequality,
indeed, may be owing to the quality of the matter as well as of
the machine; fome parts being more porous than others.
When the blanks are adjusted they are carried to the blanch-
ing or whitening-houſe, i. e. the place where the gold blanks
have their colour given them, and the filver ones are whitened;
which is done by heating them in the furnace, and, when taken
out and cooled, boiling them fucceffively in two copper veffels,
with water, common falt, and tartar; and, after that, fcouring
them well with fand, and waſhing them with common water,
drying them over a wood fire, in a copper fieve, wherein they
are put when taken out of the boilers.
Formerly the planchets, as foon as blanched, were carried to
the prefs, to be ftruck, and receive their impreffions; but now
they are firft marked with letters or graining on the edges, to
prevent the clipping and paring of the fpecies, which is one of
the ways wherein the ancient money ufed to be damaged.
The machine uſed to mark the edges is very fimple, yet ingeni
ous; it conſiſts of two plates of ſteel, in form of rulers, about
the thickneſs of a line, on which the legend or edging is en-
graven, half on the one, and half on the other. One of thefe
plates is immoveable, being ſtrongly bound with ferews to a
copper plate; and that again to a ftrong board, or table: the
L 2
148
MACHINES.
other is moveable, and flides on the copper plate by means of a
handle, and a wheel, or pinion of iron, the teeth whereof catch
in a kind of other teeth, on the ſurface of the fliding plate.
Now, the planchet, being placed horizontally between theſe
two plates, is carried along by the motion of the moveable one;
fo as by that time it has made half a turn it is found marked
all round. See fig. 1. pl. XIV.
This machine is fo eafy, that a fingle man is able to mark
twenty thouſand planchets in a day. Savang pretends it was
invented by the fieur Caftagin, engineer to the French king,
and firſt uſed in 1685. But it is certain we had the art of let-
tering the edges in England long before that time; witneſs the
crowns and half-crowns of Oliver Cromwell ftruck in 1658,
which for beauty and perfection far exceed any French coins
we have ever ſeen.
Laſtly, the planchets, being thus edged, are to be ſtamped,
i. e. their impreffion is to be given them in a fort of mill, or
prefs, by the French called a balancier, invented towards the
latter end of the fixteenth century. See its figure in fig. 2.
pl. XIV.
Its chief parts are a beam, fcrew, arbor, &c. all contained in
the body of the machine, except the first, which is a long iron
bar, with a heavy ball of lead at each end, and rings, to which
are faſtened cords, which give it motion: this is placed hori-
zontally over the body of the machine. In the middle of the
beam is faſtened a fcrew, which, by turning the beam, ferves to
preſs the arbor underneath it; to the lower extremity of which
arbor, placed perpendicularly, is faſtened the dye, or matrice,
of the reverſe, or arm fide, in a kind of box, or caſe, wherein it
is retained by ſcrews: and under this is a box, or cafe, contain-
ing the dye of the image-fide, firmly faſtened to the lower part
of the engine, fig. 3.
Now when a planchet is to be ſtamped it is laid on the
image-matrice, upon which two men draw, each on his fide,
one of the ropes of the beam, and turn the fcrew faftened in
it; which by this motion lowers the arbor to which the dye of
the arms is faſtened: by which means the metal being in the
middle, at once receives an impreffion on each fide, from either
dye. As to the prefs formerly uſed, it has all the effential parts
of a balancier, except the beam, which is here, as it were, di-
vided, and only drawn one way.
2
The blanks having now all their marks and impreffions, both
on the edges and faces, become money; but they have not cur-
rency till they have been weighed and examined.
For the Coining of Medals the progreſs is the fame, in effect,
with that of money: the principal difference confifts in this
Beam Compaſſes
149
that money, having but a ſmall relievo, receives its impreffion
at a ſingle ſtroke of the engine; whereas, for medals, the
height of their relievo makes it neceffary that the ſtroke be
repeated ſeveral times: to this end the piece is taken out from
between the dyes, heated, and returned again; which proceſs,
in medallions, and large medals, is fometimes repeated fifteen
or twenty times, before the full impreffion be given; care being
taken, every time the planchet is removed, to take off the fuper-
fluous metal ſtretched beyond the circumference, with a file.
An improvement has been lately fuggefted in the coining-
prefs, by a Mr. Huigenan, we believe, who has introduced the
principle of the heart-wheel both in this contrivance and in his
univerfal lever. The method Mr. H. recommends may be
underſtood by referring to fig. 4. pl. XIV. CB is part of a table
or plane on which is fixed the box containing the dye F of the
image fide of the coin, and CA is a lever to which is attached
the dye E of the reverſe fide in a cafe retained by ſcrews; and
this is fo pofited, that by turning CA on the centre C the parts
E and F may be brought the one immediately above the other.
G is an elliptical or heart-wheel turning upon a fixed centre by
the handle or winch H, and, acting upon the friction wheel D,
gradually forces down the end A of the lever, and carries with it
the dye E, caufing it to prefs very hard upon the metal placed
on the lower dye F, at the time the extremity I of the elliptical
wheel is in contact with the upper part of the wheel D. Then
the motion of the winch proceeding, the fpring S raiſes up the
lever CA, and thus leaves room to remove the metal: place
another at F, and repeat the operation. The whole, it is obvi-
ous, may be carried on with confiderable expedition; but
whether the method is on the whole preferable to that before
deſcribed is what we do not here attempt to decide.
COMPASSES (BEAM), a kind of compaffes uſed to draw large
arcs, and to take large extents, &c. Theſe compaffes confift of
a ſtraight beam or bar, of 18 inches, 2 feet or more in length,
carrying two braſs curfors; one of theſe being fixed at one end,
the other fliding along the beam, with a fcrew to faſten it on
occafionally. To the curfors may be ſcrewed points of any
'kind, as of ſteel, braſs, pencils, &c. The fixed curfor has fome-
times an adjuſting or micrometer fcrew applied to it, for the
more nice obtaining of extents.
The beam is divided commonly into inches, tenths, and half
tenths: but Mr. Walton, an ingenious mechanic, in the proof
department of the Royal Arfenal, Woolwich, has improved
this inſtrument and much extended its utility, by applying a
nonius to its ſcale, which renders it fit to take diſtances to
hundredth parts of an inch. Part of a beam with the additions
of Mr. Walton are fhewn in fig. 1. pl. XVIII. where IK repreſents
}
150
MACHINES.
more than 4 inches in length of a beam, which is made of
ebony, the divifions being marked upon braſs laid into the ebony.
ABCD and EFGH are two brafs cafes which nearly fit the
beam, and may flide to and fro upon it: theſe braſs cafes carry
the curfors and points L and M, which are faſtened into fockets
by means of fcrews at N and O. The cafe ABCD has two
fcrews bc and a, both of which are turned by means of forked
turnfcrews: the firſt of theſe ſcrews, bc, ferves to move the braſs
cafe backwards and forwards on the beam, in order to adjuſt
the point L fo as to correſpond with the commencement of the
divifions on the beam; and when that is done the ſcrew a, by
preffing a ſpring, makes the whole faft to the beam. The other
brafs cafe EFGH carries the curfor and point M, as well as the
moveable nonius ei: this nonius is at the extremity of a piece.
ef g h ki, which is moved to and fro upon the cafe EFGH by
means of the ſcrew o p q s, which is turned by the milled head
rst: the ſhoulders at p and q prevent the fcrew from moving
either backward or forward with reſpect to the line FH, while
the threads of the fcrew between o and p, by taking upon
moveable piece efgb ki, cauſe the nonius to move along the
edge of the graduated ſcale of the beam: turning the head of
the ſcrew in the drection rst moves the nonius in the direc-
tion from K towards I on the beam; and turning that head in
the direction tsr advances the nonius according to the in-
creafing meaſure upon the ſcale from I towards K. The fcrew
d with its milled head P, by preffing upon a ſpring, will at any
time make the cafe EFGH faft to the beam, and thus prevent,
when neceffary, any change of diftance between L and M.
Fig. 2. is a tranfverfe fection of the braſs caſe EFGH: it ſerves
to fhew the form 1, 2, 3, 4, 5, of the beam, bevelled off to an
edge at 4; alſo the bevel of the nonius at e; the dovetail at
againſt which one fhoulder of the micrometer fcrew preffes; and
the piece fv, into which the three fcrews l, m, n (fig. 1.) enter.
Other parts of the conſtruction will be fufficiently obvious from
thefe figures.
the
q,
CONDENSER, a pneumatic engine or fyringe, by which an
extraordinary quantity of air may be crowded or puſhed into a
given fpace; fo that frequently ten times as much air as an equal
fpace would contain out of the engine may be thrown in by
means of it, and its egrefs prevented by valves properly diſpoſed.
The condenfer is made either of metal or of glafs, and either
in a cylindrical or globular form; and the air is forced into it
by an injecting fyringe. The receiver, or veffel containing the
condenfed air, fhould be made very ſtrong, to bear the force of
the air's elafticity thus increaſed: for which reafon it is com-
monly made of braſs. When glafs is uſed it will not fuftain ſo
Prony's Condenfer of Forces.
151
great a condenſation of air; but the experiment will, notwith-
ſtanding, be rendered more entertaining, as the effect of the
condenſed air upon any ſubject put within the receiver may be
viewed through the glaſs.
CONDENSER of Forces, a name given by M. Prony to a con-
trivance for obtaining the greateft poffible effect from a firſt
mover, the energy of which is ſubject to augmentation or dimi-
nution within certain limits; and in general to vary at pleaſure
the refiſtance to which the effort of the first mover forms an
equilibrium in any machine whatever, without changing any
part of their conftruction.
The general problem in mechanics, of which this condenfer
is intended as a practical folution, is enunciated by M. Prony
in theſe terms:
"Any machine being conftructed, to find, without making
any change in the conftruction, a means of tranfmitting to it
the action of the first mover, by fulfilling the following condi-
tions; viz.
cr
"1. That it may be poffible at pleaſure, and with great ſpeed
and facility, to vary the reſiſtance (againſt which the effort of
the first mover muft continually make an equilibrium) in limits
of any required extent.
"2. That the refiftance, being once regulated, fhall be
rigorously conftant until the moment when it is thought proper
to increaſe or diminiſh the fame.
66
3. That in the moſt ſudden variations of which the effort
of the first mover may be capable, the variation in velocity of
the machine ſhall never undergo a folution of continuity."
M. Prony applies his folution of this problem to the dynamic
effect of wind: it will be eafy to make the fame general when
the other firft movers are uſed.
The fection and plan of the machine are exhibited in plate
XIV. OO reprefents the vertical arbor to which windmill
fails are adapted; eeee is an affemblage of carpentry, of which
one of the radii, O e, bears a curved piece, bd, of iron or fteel:
vertical axes of rotation a a a, being placed round the axis OO,
alſo divide the circumference in which they are found into
equal parts.
•
2
Each of theſe axes carries a curve, a f, of iron, fteel, or copper;
fo fituated, that when the wind acts upon the fails the curve
bd preffes againſt one of the curves af, and cauſes the vertical
axis to which this laft curve is fixed to make a portion of a
revolution.
The curves b d and aƒ muſt be ſo diſpoſed, that when bd
ceaſes to preſs on one of the curves af, it fhall at the fame in-
152.
MACHINES.
ftant begin to act upon the following curve: the number of
axes which are provided with theſe curves muſt be determined
by the particular circumſtances of each caſe; and it is alſo
practicable to fubftitute, instead of bd, a portion of a toothed
wheel having its centre in the axis 00, and to place portions
of pinions inſtead of the curves a f; but the difpofitions repre-
fented in the figure are preferable.
Each of the axes aa aa (which are all fitted up alike,
though, for the fake of clearneſs, only one of them has its ap-
paratus repreſented in the drawing), carries upon it a drum or
pulley ttrr, on which is wound a cord that paffes over a pulley
p, and ferves to ſupport a weight Q by means of the lever FG,
upon which this weight may be flided and faſtened at different
diſtances from the point of motion G.
The fame axes a a paſs through the pinions q q, to which they
are not fixed; but theſe pinions carry clicks or ratchetts, which
bear againſt the teeth rr; ſo that, when the weight Q_tends to
rife, the ratchett gives way, and no other effect is produced on
the pinion qq, either by the motion of the axis or of the drum
ttrr, excepting that which cauſes the afcent of the weight q q.
But the inftant that the curve or tooth b d ceafes to bear againſt
one of the curves af, after having caufed the correfponding
weight Q to rife, that weight Q tends to redefcend, and then the
toothed wheel rr acts againſt the ratchett, fo that Q cannot
deſcend without turning the pinion qq along with the drum
The pinion qq takes in the wheel a b, from the motion of
which the uſeful effect of the machine immediately refults; fo
that the effect of the defcent of one of the weights Q is to
folicit the wheel AB to motion, or to continue the motion in con-
currence with all the other weights Q, which defcend at the
fame time. This wheel AB carries beneath it oblique or
bevelled teeth GD, which take in a like wheel CE, and cauſe the
buckets at S to riſe.
From the preceding deſcription it is feen that the machine,
being ſuppoſed to ſtart from a ſtate of repofe, the wind will at
firſt raiſe a number of weights Q, fufficient to put the machine
into motion, and will continue to raiſe new weights while thoſe
before raiſed are fallen; fo that the motion once impreſſed will
be continued.
Among the numerous advantages of this new mechaniſm we
may remark the following:
1. No violent fhock can take place in any part of the me-
chanifm.
2. The uſeful effect being proportioned to the number of
Crab for Artillery.
153
}
weights Q, which deſcend at the fame time, this effect will in-
creaſe in proportion as the wind becomes ftronger, and cauſes
the fails to turn with more velocity.
3. The weights Q being moveable along the levers FG, it
will always be very eafy to place them in fuch a manner as to
obtain that ratio of the effort of the first mover to the reſiſt-
ance which will produce the maximum of effect.
4. From this property it refults that advantage may be taken
of the weakest breezes of wind, and to obtain a certain product
in circumſtances under which all other windmills are in a ftate
of abfolute inactivity. This advantage is of great importance,
particularly with regard to agriculture: the windmills employed
for watering lands are fometimes inactive for feveral days, and
this inconvenience is more particularly felt in times of drought.
A machine capable of moving with the flighteſt breeze muſt
therefore offer the most valuable advantages.
CRAB or GIN, an engine ufed for mounting large guns on
their carriages, &c. It is compofed of three long and ftout legs,
meeting together at their tops; thefe legs are round poles of
about 12 or 13 feet long, whoſe diameters at the lower end are
about four inches, five juft below the roller, befides the cheeks
that are added to them in that place, and about 3 inches above.
Two of theſe poles can be fixed at a certain diſtance from
each other, by means of two iron bars placed horizontally, one
being about four feet long, the other about feven; and a roller is
made to run upon pivots turning on, or in, theſe two poles:
this roller is commonly 7 inches in diameter, and fix feet long.
A portion of 20 inches is left fquare at each end, and holes
made in each to receive the handſpikes by which the men turn
the roller: but the middle part is made cylindrical, to wind the
cable upon. The tranfverfe iron bars are fixed with one end
to one of the poles by means of a bolt, and with the other end
to the other pole with a bolt and key; fo as to be readily taken
out, in order that when the gin is to be removed from place to
place the poles may lie clofe together upon the carriage. There
are two iron bands and two iron bolts to faften each cheek (for the
pivots) to the poles, and iron plates round the poles where the
iron bars are fixed. The poles are hooped at each end; and
the upper ends have ftraps through which an iron bolt paffes:
this bolt keeps the upper ends together, as well as ferves to
fupport the iron to which the windlafs is hooked. The wind-
lafs contains two braſs pullies, about which the cable goes,
which is fixed to the dolphins of the gun or mortar with
another windlafs, containing two braſs pullies likewiſe. When
this machine is ufed the whole is laid flat on the ground, the
lower end of the fingle pole extending the contrary way, in
134
MACHINES.
order to faſten the upper windlafs after the cable has been
turned round both: after this the upper end is raiſed gradually
till the feet of the three poles (each of which has an iron prong)
ftand nearly at equal diſtances; in fuch a manner as the legs
of a theodolite or plain table, when ſet up for uſe in the practice
of furveying.
CRANE, a machine uſed in building, on wharfs, and in
warehouſes, for raifing and lowering huge ftones, ponderous
weights, packages, &c.
1. Cranes until of late years were commonly conſtructed as
follows: the principal member is a ftrong upright beam or
arbor, firmly fixed in the ground, and fuftained by eight arms,
coming from the extremities of four pieces of wood laid acrofs,
through the middle of which paffes the foot of the beam.
About the middle of the arbor the arms meet, and are mortifed
into it: its top ends in an iron pivot, on which is borne a tranf-
verfe piece, advancing out to a good diſtance, ſomething after
the manner of a crane's neck, whence the machine has its name.
This projecting piece is now more commonly called the jib or
gibbet. The middle and extremities of this are again fuftained
by arms from the middle of the arbor: and over it comes a rope
or cable, to one end of which the weight is fixed; the other is
wound about the ſpindle of a wheel, which when turned (com-
monly by means of men walking upon the infide of the rim of
the wheel) draws the rope, and that heaves up the weight;
which may afterwards be applied to any fide or quarter by the
mobility of the tranfverfe piece on the pivot. Thefe crahes
have ufually been made of two kinds: in the firft, called the rat-
tailed-crane, the whole machine with the load turns upon a ſtrong
axis: in the ſecond kind the gibbet alone moves on its axis.
But in either kind, if the machinery be put into motion by
men walking within the wheel, as has been till lately the nearly
univerfal practice in this country, the labourers employed are
expofed to extreme danger, and have frequently met with the
moft ſhocking and fatal accidents. It is not then to be won-
dered at, that ſkilful mechaniſts ſhould at length have deviſed
cranes that are not only more fafe, but more powerful in their
operations, than the common walking crane: a few of the beſt
of theſe will be defcribed in the prefert article.
2. The late Mr. Ferguſon invented a crane which has three
trundles, with different numbers of ftaves, that may be applied
to the cogs of a horizontal wheel with an upright axle; round
which is coiled the rope that draws up the weight. This
wheel has 96 cogs; the largeſt trundle 24 ftaves, the next 12,
and the ſmalleſt 6, fo that the largeft, revolves 4 times for one
revolution of the wheel; the next 8, and the fmalleft 16. Á
Cranes.
155
winch is occafionally fixed on the axis of either of theſe trundles
for turning it; and is applied to the one or the other according as
the weight to be raiſed is fmaller or larger. While this is draw-
ing up, the ratch-teeth of a wheel flip round below a catch
that falls into them, prevents the crane from turning backwards,
and detains the weight in any part of its aſcent, if the man who
works at the winch fhould accidentally quit his hold, or wifh
to rest himſelf before the weight is completely raiſed. Making
a due allowance for friction, a man may raiſe by fuch a crane
from three times to twelve times as much in weight as would
balance his effort at the winch; viz. from 90 to 360lbs. taking
the average labour.
Other ingenious contrivances by Mr. Ferguſon may be ſeen
in his Select Exerciſes; but as the book is in the hands of almoſt
every practical mechanic, we would rather refer to it than ex-
tract accounts of theſe inventions.
3. The crane prefented in plate VII. is a portable one, mount-
ed in a wooden frame and ftage, which is judged to be very
ufeful for loading and unloading carts with large heavy ſtones.
It is moveable to any part of a flone-yard or ground; the frame
is fufficiently wide for a cart to draw under the crane, and at
any time it may be taken to pieces. The frame AAAA is
made of wood, is about 9 or 10 feet high, and about 9 feet
fquare. The wheels BB are of iron, and are about 3 feet in
diameter; and the pinion D, that is fixed to the axis of the firſt
wheel B,, 8 inches in diameter: on the axis of the ſecond wheel
B the axis round which the rope coils is fixed. Now the
ftone being corded and hooked at the end of the rope, it is very
evident that the man at C will either raiſe or lower them as
may be neceffary, according as he turns the winch towards or
from him, and in a fafe and very eaſy manner. The advantage
in point of power being in proportion as the product of the
radii of the wheels to thoſe of the pinions.
4. Fig. 7. pl. XII. is a repreſentation of a crane-carriage
which Mr. Gottlieb conceives to be very uſeful in moving large
ftones in quarries, where carts and horfes cannot be conveniently
or at all managed. Its principle is evidently clear from a bare
view of the figure. It confifts only of two fets of crane-wheels
applied to the two ſets of wheels belonging to the carriage; fo.
that two men, one at each winch AA, turning the pinions and
wheels round, fhall act upon the carriage-wheels and move it
along. By their both turning forwards or backwards, the carri-
age goes accordingly; but if they turn contrary ways, the carri-
age will be turned round, or partly fo, as may be wanted. The
pinion B is 6 inches in diameter, which turns the wheel C of
}
15.6
MACHINES.
3 feet diameter, on the axis of which is fixed the pinion D of
foot diameter, which works into 2 wheels E, E, of 3 feet 6
inches diameter, that are fixed upon the carriage-wheels, and
give motion to the whole machine.
5. Mr. Abraham Andrews, of Higham Ferrers, in North-
amptonſhire, has invented a crane which weighs the body
fufpended at the time it is raifing: an improvement for which
the Society for the Encouragement of Arts, &c. granted him a
premium of 15 guineas. This crane is fhewn in fig. 3. pl. IX.
The jib of the crane ftands on a horizontal beam, moveable on
a centre at A: and the diſtance of the centre A, from the bear-
ing of the upright, being to the diſtance B, in proportion of 1
to 20, the weight placed at B determines that of the body fuf-
pended in the fame proportion. C is a ftub, or piece of wood,
which projects from the weight hanging at the end of the jib,
and ferves to prevent the beam from rifing to too great a height.
This jib fhould be placed in the fame vertical plane with the
part BA of the crane, at the time the weight is adjuſted; other-
wife it will occaſion a friction which may prevent the moveable
beam from playing freely. The other parts of the crane are ſo
obvious in their conftruction as not to require a more minute
defcription.
6. The fociety juſt mentioned have lately voted 40 guineas to
Mr. Robert Hall, jun. of Basford, near Nottingham, for his
ingenious invention of a method to expand a fet of bars parallel
to the axis of a crane, by which means the velocity of the rope
in raising weights may be increaſed or diminiſhed in proportion
to the load to be raiſed.
A defcription and engraving of this crane are given in the
twelfth volume of the Society's Tranfactions, from which we
have drawn up the following account of it:
The ends of the reel (fig. 1. and 5. plate III.) confiſt each of
two flat plates or circular pieces, fhewn feparately in fig. 2.
and 3. Thefe circular plates form the two ends of the reel, and
are held faft on the fpindle or axis by pins paffed through its
ends, of which one may be ſeen at a, fig. 2. and another in the
end fhewn in fig. 5. The outer circular plate (fig. 3.) of each
end of the reel has a fpiral groove cut in it, as fhewn at b; and
the inner circles have each eight mortices cut quite through
them, as fhewn at c, fig. 2. (feen partly alfo in fig. 1. and 5.)
The outer plates have alſo an iron tube, d, made faft to them by
means of a flange or collar, and the fcrews, ee, fig. 2.
When the parts are all joined (as fhewn in fig. 1.), the axis
paffes through the tube d, and thus the ends are connected.
In fixing the crofs bars, two of which are fhewn detached in
Cranes:
157
fig. 4., the parts g g ſlide in the mortices c of the inner circular
plates, and the fmall ends or tenons h h go fairly through the
inner and enter the ſpiral grooves of the outer plates.
The inner and outer circular plates are locked together by a
catch (i, fig. 1. 2. and 6.) the ſtationary part of which is made
faft to the inner plate (fee fig. 2.), while the catch itſelf, by
means of a ſpring, is kept in a notch on the edge of the outer
plate. When the diameter of the reel is to be enlarged or di-
miniſhed, it is effected by bringing the reel round to the pofition
fhewn in fig. 6., when a hook k is put into a hole 1, which keeps
the inner circular plate in that pofition till the adjuſtment is made
by lifting the catch from the notch of the outer end-plate far
enough to be kept difengaged by the hook k, before mentioned,
being thruft quite through the hole 1: the handle m being then
turned, the outer plate only is carried round, and the tenons of
fmall ends of the crofs bars (being prevented from being carried
round with it, by the mortices of the inner plates through which
they pafs being ſtationary) are obliged to change their diſtance
from the axis by the ſpiral groove fliding over them, while they
are able to move nearer or further from the axis by fliding in the
radial mortices of the inner end plate.
The handle m being turned till the reel is of the fize required,
the hook k is withdrawn or puſhed out, and the crane is then
ready for work.
It is neceffary to obſerve that the tenons ↳ ½ muſt be cut, ſo
that the outſide of all the bars next the rope fhall be at an equal
diſtance from the centre. If the tenon of the first bar that is
placed in the reel be cut like the tenons b 5, fig. 4. the laſt of
them muſt be cut the fame as the tenons n n, fig. 4.; and all
the other tenons, at the extremities of the feveral bars, muſt be
at proper diſtances between theſe extremes, as is fhewn by the
dots P in the mortices fig. 2.
The other parts of the crane may be fo eafily underſtood
from an infpection of the engraving, that any further defcrip-
tion is unneceffary. Phil. Mag. No. 71.
7. But the feveral cranes defcribed in this article as prefer-
able to the commön walking-crane, while they are free from
the dangers attending that machine, lofe at the fame time one
of its advantages; that is, they do not avail themſelves of that
addition to the moving power which the weight of the men
who are employed may furnish. Yet this advantage has been
long fince enfured by the mechaniſts on the continent, who caufe
the labourers to walk upon an inclined plane, turning upon an
axis, after the manner fhewn in the figure referred to under the
article Footmill, where we have deſcribed a contrivance of that
kind, well known in Germany nearly 150 years ago. The
•
158.
MACHINES.
fame principle has been lately brought into notice, probably
without knowing it had ever been adopted before, by Mr.
James Whyte, of Chevening, in Kent: his crane is exhibited in
fig. 3. and 4. pl. X. as it was defcribed in the Tranſactions of the
Society for the Encouragement of Arts.
A (fig. 3.) is a circular inclined plane, moving on a pivot
underneath it, and carrying round with it the axis Ē. A perſon
walking on this plane, and preffing againſt the lever B, throws
off the gripe D, by means of an iron rod C; and thus admits the
plane and its axis to move freely, and raiſe the weight G by the
coiling of the rope F round the axis E.
To fhew more clearly the conſtruction and action of the lever
and gripe, a plan of the circular inclined plane, with the lever
and gripe, is added (fee fig. 4.), where B repreſents the lever, D
the fpring or gripe. In this plan, when the lever B is in the
fituation in which it now appears, the fpring or gripe D preffes
againſt the periphery of the plane, as fhewn by the double line,
and the machine cannot move; but when the lever B is preffed
out to the dotted line H the gripe is alſo thrown off to the
dotted line I, and the whole machine left at liberty to move.
One end of a rope or cord, of a proper length, is fixed near the
end of the lever B, and the other end made faſt to one of the
uprights, ferving to prevent the lever moving too far when
preffed by the man.
The fuppofed properties of this crane, for which the premium
of 40 guineas was adjudged by the ſociety to the inventor, are
as follows:
·
1. It is fimple, confifting merely of a wheel and axle. 2. It
has comparatively little friction, as is obvious from the bare
inſpection of the figure. 3. It is durable, as is evident from
the two properties above-mentioned. 4. It is fafe; for it can-
not move but during the pleaſure of a man, and while he is.
actually preffing on the gripe-lever. 5. This crane admits of
an almoſt infinite variety of different powers, and this variation
is obtained without the leaft alteration of any part of the ma-
chine. If, in unloading a veffel, there fhould be found goods
of every weight, from a few hundreds to a ton and upwards,
the man that does the work will be able ſo to adapt his ſtrength
to each as to raiſe it in a ſpace of time proportionate to its
weight; he walking always with the fame velocity as nature
and his greateſt eaſe may teach him.
→
It is a great difadvantage in fome cranes, that they take as
long time to raiſe the ſmalleſt as the largeſt weight, unleſs the
man who works them turn or walk with ſuch velocity as muft
foon tire him. In other cranes, perhaps, two or three different
powers may be procured; to obtain which, fome pinion must
Cranes.
159
be ſhifted, or freſh handle applied or reforted to. In this crane,
on the contrary, if the labourer find his load fo heavy as to
permit him to aſcend the wheel without its turning, let him
only move a ſtep or two toward the circumference, and he will
be fully equal to the taſk. Again, if the load be fo light as
ſcarcely to refift the action of his feet, and thus to oblige him to
run through ſo much ſpace as to tire him beyond neceffity, let
him move laterally towards the centre, and he will foon feel
the place where his ftrength will fuffer the leaſt fatigue by
raifing the load in queſtion. One man's weight applied to the
extremity of the wheel would raiſe upwards of a ton; and it
need not be added, that a ſingle-ſheaved block would double
that power. Suffice it to fay, that the fize may be varied in
any required ratio; and that this wheel will give as great ad-
vantage at any point of its plane as a common walking-wheel
of equal diameter, as the inclination can be varied at pleaſure,
as far as expediency may require. It may be neceffary to ob-
ſerve, that what in the figure is the frame, and ſeems to form
a part of the crane, muſt be confidered as a part of the houſe
in which it is placed; fince it would be moftly unneceffary
fhould fuch cranes be erected in houfes already built. With
reſpect to the horizontal part, by walking on which the man
who attends the jib occafionally affifts in raifing the load, it is
not an eſſential part of this invention, where the crane is not
immediately contiguous to the jib, although, where it is, it
would be certainly very convenient and economical.
Notwithſtanding, however, the advantages which have been
here enumerated, Mr. Whyte's crane is fubject to this theo-
retical objection, that it derives leſs uſe than might be wiſhed
from the weight of the man or men: for a great part of that
weight (half of it, if the inclination be 30 degrees) lies directly
upon the plane, and has no tendency to produce motion. Be-
fides, when this crane is of fmall dimenfions, the effective
power of the men is very unequal, and the barrel too ſmall for
winding a thick rope: when large, the weight of the materials
added to that of the men put it out of fhape, and give it the
appearance of a large, unwieldy, moving floor. We know one
large crane of this conſtruction, which has an upright poſt near
the rim on each fide, to fupport it and keep it in ſhape; and, as
much as poffible to prevent friction, each poft had a vertical
wheel at its top. We were informed this crane was feldom
uſed, and that it was foon put out of order.. Nor, moreover, is
it every fituation that will allow the crane-rope to form a right
angle with the barrel on which it winds, and when this angle is
oblique the friction muſt be much increaſed. The friction
arifing from the wheels at top of the vertical crutches might,
160
MACHINES.
indeed, be got fhut of, by making the inclined wheel very
ftrong; but this would add greatly to the friction of the lower
gudgeon of the oblique fhaft, and confiderably enhance the ex-
pence of the machine.
8. There remains, then, another ſtage of improvement with
regard to the ſtructure of cranes, in which the weight of the
labourers fhall operate, without diminution, at the end of a
borizontal lever; and in which the impulfive force thus arifing
may be occafionally augmented by the action of the hands either
in puſhing or lifting. This ftep in the progreſs has been lately
effected by Mr. David Hardie, of the Eaft-India Company's
Bengal warehouſe. After a few preliminary obſervations, we
fhall point out the diſtinguiſhing particulars of this gentleman's
invention.
The capitan, the wheel and pinion, with a winch, and the
walking-wheel, are the cranes in common ufe at the prefent
time; though a flight view of the method of working theſe
machines might be fufficient to fhew that they are effentially
defective in regard to the grand object in procuring the force
of men, on which the quantity of work performed neceffarily
depends. The capftan and walking-wheel call for little or no
uſe of the arms; and the crane of the wheel and pinion derives
very little advantage from the legs, while the force of the men
acting upon the winch muft of neceflity be very fluctuating.
At the capftan, and wheel, and pinion, a confiderable force is
expended unproductively in giving action to the greater part of
the men's weight, which does not contribute to the moving
power of the machines; the power actually exerted feldom ex-
ceeding 20 lbs. at a moderate velocity. The merchants and
wharfingers would inſtantly diſcharge from their ſervice any
porter who would refufe to carry a load of more than 20 lbs.,
yet theſe very merchants and wharfingers are daily paying full
wages to cranemen for exerting a force which, when duly applied,
is greatly within the power of a boy of 10 or 12 years of. age.
And as to the common walking-wheel, the men who are fta-
tioned within it expend a great portion of their ſtrength in
moving themſelves forward; which proves unproductive, be-
cauſe the effective velocity is only according to the fum of the
heights attained, and the waſte of force through fuch unprofit-
able deviation from the vertical direction renders the men in-
capable of the due velocity of afcent: befides, the velocity of
deſcent, which ought to be proportional to a due velocity of
afcent, is materially impaired by fhortening of the effective
lever in the courfe of its depreffion, and a confequent diminu-
tion of mechanical power; and theſe obſtructions are frequently
aggravated, by placing men in the wheel to walk behind the
Cranes.
161
others. And when this lofs of labour by the often counter-
operation of a rear rank is avoided by applying an additional
wheel, the machine occupies much ſpace, becomes extremely
expenſive, and is attended with extraordinary friction. Al-
though nothing but neceflity can juſtify the hazarding of the
lives of men, yet the walking-wheel is attended with imminent
danger; and being a very defective engine, employed without
either neceffity or expediency, thoſe perſons who uſe them are
refponfible to humanity for the fhocking difafters they fre-
quently occafion. But the various evils juft enumerated, as
well as many others which attend the cranes now adverted to,
have been obviated in a very effectual manner by Mr. Hardie;
whoſe crane is at once fo fimple and efficient, as to render it no
eafy taſk to point out any faults which it has not avoided, or
any defects which it has not ſupplied. It is a walking-crane;
but the men walk on the outſide of the wheel, inſtead of infide
of the rim; and during the whole of their labour they are
expoſed to no kind of danger, and they can walk in an upright
poſture, well fuited to free refpiration. Five cranes of the kind
are at work at the Eaft-India warehouſes: and as the contriv
ance (for which Mr. Hardie has obtained a patent) muſt ulti-
mately prove a confiderable acquifition, we have examined the
conftruction and mode of operation of two of thefe machines
with particular attention, that we might be enabled to furniſh
the public with the following defcription.
The reader may turn to plate XI. where fig. 1. is an elevation
of the fide of the crane on which the men operate.
Fig. 2. An elevation of the end of the ſtage to affift the men
in ftepping on and off the wheel, as well as to fupport a feat
for them to rest upon, in the intervals between the operations.
The edge ƒ of this ſtage does not ftand more than 4 inches
from the points by which the edge of each ſtep paffes.
Fig. 3. An elevation of the end of the wheel.
Fig. 4. An elevation of the fide of the crane, oppofite to that
given in fig. 1. The fame letters of reference being put to the
correfponding parts in theſe figures.
AA is a wheel (on the principle of the wheel ufed in China
for men working at the chain-pump, for raifing water to the
higher grounds, employed in the culture of rice), on the outfidé
of which are placed 24 fteps for the men to tread upon, at a
fituation where the fteps are found at a height equal to that of
the axis, or where the plane of the ſteps become horizontal;
the diameter of the wheel being 6 feet, fteps included. The
crane reprefented in the figure is adapted for 4 men; though
they may easily be contrived for 5, 6, or 8. At one end is B,
the crane rope barrel, of a diameter fuited to the drafts of goods
commonly raiſed, and the number of men generally allowed,
VOL. II.
1
162
MACHINES.
with Ca brake-wheel, all fixed on the fame axis, and D a
brake attached to the framing of the crane, to prefs on the
brake-wheel, occafionally to ftop or retard the motion; being
conducted by a man at the loop-hole by means of E, a lever
of wood, loaded with a piece of lead or caft-iron at the ex-
tremity, to give it fufficient weight to ftop the motion of the
wheel; a rope faſtened to the end of this lever, and conveyed
over two pulleys, terminates in a handle for the loop-hole man,
with an iron ring at the lower part thereof to receive a pig,
fixed at the fide of the loop-hole for the purpoſe of keeping it
down, that the lever might difengage the brake from the brake-
wheel during the operation of raifing the goods. G, G, G, G, G,
are vertical handles, and H, H, H, H, H, horizontal handles for
the men to take hold of with both hands, when treading on the
fteps: fometimes both hands are applied to the vertical handles;
at others, one hand to a vertical, and the other to a horizontal
handle; and at others, both hands to the horizontal handles;
thus producing a variety in the action, and, when neceffary, a
confiderable augmentation to the force. I (fig. 1. and 3.) is a
pawl which drops in at every ſtep, to prevent the wheel and its
incumbent weight from overpowering the men at any time: it
has at its lower part a cord with a loop to pass over one of the
horizontal handles, near the extremity of which there is a notch
fufficiently deep to retain the loop when drawn into it, for the
purpoſe of raifing the pawl, to difengage it from the wheel
preparatory to the operation of lowering the goods or crane-
rope.
Now it is obvious, that by treading on the ſteps as they arrive
at the poſition t, t (figs. 1. 3.), juſt above the horizontal plane,
paffing through the axis, the men both aſcend and deſcend nearly
in the vertical direction: of confequence, the greateft poffible
velocity is produced without any unproductive labour; and the
men are enabled to maintain the action by means of a hold of
an upright handle on each hand; or occafionally to augment the
action, by pushing at theſe handles. Further, by taking hold of
the horizontal handles, each man can, by an act fimilar to that
of lifting, augment the force arifing from his weight through
all the degrees, from about 150 to 300 lbs. So that the fame
number of men can perform many operations of raifing greater
drafts than ufual; fuch as with the common walking-wheel
or moſt other crancs could not be accompliſhed without ad-
ditional men; and the pawl which drops in each, ftop provides
in the moſt effectual manner for the fafety of the men, even if
the crane had not been fo conftructed that their feet need never
be more than 12 inches diftant from the ftage Sƒ, and the di-
ſtance fs far too fmall to admit of falling through. Thus the
very judiciouſly chofen dimenfion of a 6-feet diameter unites
Hardie's Crane Regulator..
163
the advantages of a weight acting on a horizontal inſtead of
inclined lever with thofe accruing from the vertical and hori-
zontal handles; while it completely precludes the danger which
attends the common walking-wheel, and has by no means fo
much friction as neceffarily attends Mr. Whyte's crane.
Mr. Hardie has likewife contrived a truly advantageous
mode of operating without a gibbet, which he has carried into
effect with four of his cranes. He has placed the crane at the
top of the warehouſe, fo as to allow the crane-rope to drop
directly down from the barrel of the crane in front of the loop-
holes; and at the upper floors, where the fhortness of the rope
diminiſhes the fwing of the goods in or out of the loop-holes, he
has provided a fliding floor immediately under the floor of the
warehouſe, which one man draws out or in, by pulling a cord,
with the greateſt eaſe, to receive or deliver the goods by a truck
at the loop-hole. The part of the warehouſe floor which is im-'
mediately above the fliding floor confifts of a thin plate of caſt
iron, which allows the truck to run off the one on the other
without any obſtruction. Thus more than one man's labour in
five or fix is faved, by getting rid of the friction of the pulley
of a gibbet; and a ftill greater faving of labour is effected by
accelerating all the movements at the loop-holes.
9. The common method of lowering goods by the brake and
brake-wheel, even with the affiftance of a counter-weight, is
liable to injurious accidents to the men, as well as to the goods,
when they confift of periſhable articles, fuch as wine, fpirits,
glafs, &c. Sometimes, from the rapid motion of the crane,
parts of it fly off with violence, and kill or wound the perſons
near it at other times the brake-rope becomes entangled by
turning off the pulleys or otherwiſe, or the rope flips out of the
hand of the man who conducts it: in either of which caſes the
goods might defcend with all the accelerated velocity of a fall-
ing body, receiving damage, and killing or maiming the men,
horfes, &c. which happen to be under them. But theſe evils
are completely remedied by a lowering regulator of the following
defçription, invented by Mr. Hardie.
Pl. XI. fig. 5. A ſection of the regulator..
Fig. 6. An elevation of one end of the regulator. The fame
letters of reference being put to the correfponding parts in theſe
figures.
AA, a caft-iron box fixed to the floor B, divided into two
compartments, each 10 inches long, one of 4 inches. diameter,
and the other of 2 inches diameter: theſe are both filled with
oil, a liquid not fubject to any material change by froft; or
they may be filled with water in fummer and mild weather, and
fome fpirituous liquor (gin, for instance) in frofty weather. The
M 2.
'
#
164
MACHINES.
T
+
two cylinders communicate with each other by C, an aperture at
their top, and D, an aperture at their bottom; the fmaller com-
partment having a cock E, with its axle paffing through the ſide
of the iron box, guarded by a ſtuffing-box, and G a quadrant
with notches fixed at its end, to receive H the iron claw, which
keeps the cock in its proper fituation, and fhews the extent of
its apertures when opened. The larger compartment has a
pifton F, with its rod paffing through I, the top of the iron box
(guarded here alfo by a ftuffing-box), and paffing through a
guide: this rod is connected with a joint moved by a crank,
which is turned by a pinion P of about 6 teeth; and this pinion
is moved by a wheel, of a fize fuited to the diameter of the barrel
of the crane and the weight of the goods commonly lowered:
this latter wheel is fixed to the axle of the crane by a fimple
mode of connection, which admits of its being difengaged
during the operation of rifing; it is alfo provided with the
barrel rope and counter-weight, which are commonly uſed for
the purpoſe of winding up the flack crane rope on the barrel of
the crane, to be ready to repeat the operation of lowering.
If the cock E were quite ſhut, the oil or other liquid confined
between it and the pifton would prevent the piſton from mov-
ing, and of courſe hinder the goods hanging from the wheel,
&c. connected with P from defcending: but if the cock were
opened a very little the oil would pass flowly through it, and
would therefore allow the pifton F to move up and down
flowly, and the goods to defcend flowly alfo: and, in like
manner, a further opening of the cock will permit the load to
defcend with a greater velocity: thus the cock, by being more
or lefs opened, gives the precife velocity defired to the deſcent
of the goods, whatever their weight may be.
When a fmall pinion turned by a winch is applied to the
tooth-wheel, occafionally employed to turn the pinion of the
crank, one man with eafe raiſes the goods an inch or two, in
order to be fwung from the floor preparatory to lowering; the
natural defect of the winch as a raiſing inftrument being of no
confideration in fuch cafe, where the goods are raiſed merely to
clear the floor: fo that this crane and lowering apparatus
"poffeffes a much higher degree of perfection in lowering than
any of the other cranes. The means afforded of regulating it
to lower either ſmall or great weights with facility, expedition,
and fafety, and without depending, during the operation, on the
precarious attention and management of a man, render it, in
our opinion, far preferable to the hazardous and limited mode
of lowering goods by the brake: while, with refpect both to
afety and great faving of labour, it obvioully furpaffes the
modes of lowering by the capftan and the walking-wheel, which


Crane or Syphon.
166
require nearly the fame number of men to lower that they take
to raiſe any weight.
We have dwelt the longer upon the fubject of cranes, becauſe
it is manifeftly of the firft importance in a commercial nation:
fomething further, of too much utility to be entirely omitted,
may perhaps be found under the articles ENGINE to let down
weights, GIBBET, and LOADING and unloading of goods.
CRANE is alſo a popular name for a ſyphon employed in draw-
ing off liquors.
This crane or fyphon is nothing elſe than a bent tube, as
ABG (fig. 5. pl. X.). If the fhorter end AB be immerſed in a
veffel of water or other fluid C, then by applying the mouth to
the end G, and fucking till the liquor arrives there, it will con-
tinue to flow out at the end G, as long as that end is lower
than the furface of the fluid in the veffel C. If there be a
mouth-piece at E, then fucking at that mouth-piece (while the
end G is ftopt with a finger or otherwife) will make the fluid
flow when the obſtruction is taken away from G. When the
fluid has begun to flow, the hole at E muſt be ftopped up, or
the fluid will flow no longer than till the furface in the veffel
be as low as E.
The reaſon of the motion of the liquor in the fyphon is this:
the perpendicular height of the column BG being greater than
that of BA, the preffure at G is greater than at A; and the
preffure of the atmoſphere being the ſame at both orifices (fup-
pofing them of equal area), therefore the weight at G will
cauſe the fluid to flow out there, while the preffure of the at-
moſphere will force more liquor up the end A; and thus the
motion will continue fo long as there is any fluid in the veffel,
provided the end G is lower than the end A of the fyphon.
Hence it is manifeft that the height from the ſurface of the
fluid in the veffel to the top B of the fyphon muft not exceed
the altitude of a column of the fluid whofe weight is equal to
the preffure of the atmoſphere on the fame baſe.
The operation of fucking out the liquor at G, which is often
both difagreeable and troubleſome, may be prevented by having
an aperture at the top B, through which the fyphon may be
completely filled, and then that aperture clofed again. Or a
fmall fyphon may be inverted, and filled with the fluid, which
may be kept in by a finger applied at each end until it is placed
in the proper poſition for work, when the fingers may be re-
moved.
The fyphon will raiſe a ſtream of water through an exten,
five fpace in every fituation where a little defcent can be pro-
cured; but while the operation continues no water can be taken
r
166
MACHINES.
directly out of the ſtream above the loweſt part of the tube.
When, however, the two open ends of a fyphon are cloſed, a
quantity of water may be let out of the higheſt part, and its
place fupplied by introducing a like quantity which is of no
other ufe: all the avenues for the purpoſe being then cloſed,
and the ftream fuffered to flow through the tube, the uſeleſs
water will be difplaced, and a freſh quantity may be foon after
drawn off. This mode of exchange may be uſeful in furniſh-
ing a fupply for waſhing, and fome other purpoſes; but there
are feveral domeftic uſes for which the water drawn off will
not be thought fufficiently pure. A method of taking water
out of the ſyphon at any height within the limits of the elevation,
without retarding the ſtream or introducing another quantity,
has long been thought very defirable. Mr. William Clofe, of
Dalton, made a number of experiments and obſervations to
determine the practicability of the project; from which he at
length deduced the following arrangement for extracting a
quantity of water out of a fyphon at any elevation (within its
limits), and ſupplying its place with air.
う
​Into any part except the top fide of a vertical fyphon SY
´(fig. 5. pl. X.) infert two ſmall pipes, and let their apertures in
the infide of the tube be divided by a projecting piece about a
quarter of an inch thick; wherever the pipes are inſerted, the
piece muſt be placed in fuch a poſition that the current will
ftrike against one of its flat fides. The pipe which opens on that
fide of the obſtacle or dam ſtruck by the ſtream may be called
the water-pipe, and that on the other fide the air-pipe. Infert
their other ends into a veffel a w. The air-pipe oppofite to a
muſt riſe to near the top of this veffel, but the water-pipe w
need not ariſe above the place of its infertion. A cock, per-
fectly air-tight, muſt be fixed in each pipe between the veffel
and fyphon: the veffel a w muft have a tube t in its lower part,
for letting out water; and this tube muſt have a cock fixed in
it, or a valve covered with leather to cloſe its lower end. To
haften the delivery of the water in this veffel, the external air
may
be admitted, in fuch manner as is moſt convenient.
The communication between the veffel and fyphon being in-
tercepted by turning the cocks in the pipes a w, and the branches
of the fyphon clofed at their lower ends, the tube may be filled
with water through an aperture in the top. After this aperture
is clofed, and a ſtream of water let into the ciftern C for fupply-
ing the fyphon, the ends of the branches may be opened, and
a continued ſtream will flow through the tube.
When it is required to fill the veffel a w with water, exclude
the external air, and open the pipes between it and the fyphon,
Crane or Syphon.
167
'The veffel will foon be filled, and the water may be let out by
opening the tube t, after the ſmall pipes a wu are again clofed
by turning their cocks.
The water may be let out of the veffel without attendance, by
a quantity of water paffing through four veffels placed in the
following order one below another, and each provided with a
fyphon.
•
1. The higheſt, an immoveable veffel filled in a given time.
2. A defcending veffel, fufpended from a lever or a wheel, which
turns the cocks in the tubes oppofite a w in its axis. This vef-
fel muſt have a tube open at both ends, fixed in the middle of
its bottom. 3. A defcending veffel, to open the valve for letting
water out of the veffel a w. It muſt be fufpended upon the
valve by a cord or wire paffing through the tube, in the middle
of the fecond veffel. 4. The loweft, a veffel of the fame
width with the fecond. The brim of it must be connected to
the outfide circumference of the bottom of the ſecond, by wires
or chains.
In this arrangement the first veffel will empty itſelf into the
fecond, which will cloſe the cocks in the pipes oppofite a and
w, before air is admitted into the veffel a w. The third will
be filled from the ſecond, and the water in the veffel a w will
be let out again; the third will deliver its contents into the
fourth or loweft, which will keep the cocks in the ſmall pipes
oppofite a and w cloſe, until after the third veffel is empty, has
rifen up, and the external air can no longer enter the veſſel a w.
The fourth being then emptied by its fyphon, the pipes between
the veffel a w and fyphon SY will open.
The diameter of the fecond veffel fhould be fomething lefs
than either that above or below it. The fourth fhould be filled
before the ſecond is empty: the third will deſcend laſt, and rife
firft: the fecond and fourth will rife together, immediately after
the third. If the ſecond and fourth were to riſe before the third
the fyphon would directly receive a quantity of external air, and
its operations would ceafe. It will, therefore, require much
caution to manage the cocks and valves, if another veffel fimilar
to a w is to be filled while this laſt is emptied, and emptied
while it is filled.
The veffel a w ſhould not be large; and, in order to over-
come the buoyance of the extracted air, it is adviſable to make
the length of the deſcending branch of the fyphon exceed the
length of the afcending one as much as circumftances will ad-
mit, and to let the loweſt part of it be made of a conical
divergent form. The velocity of the ſtream will be thus en-
creaſed; the veffel a w will be ſooner filled with water; and the
depreffion of the two columns will be leſs liable to happen from
168
MACHINES.
very flight imperfections of workmanship. Nicholson's Journal,
4to, vol. IV. p. 55º.
Mr. Cloſe made many ſubſequent trials, to bring this appara-
tus to the greateſt perfection it would admit of: the reſult of
the whole may be ſeen in No. 45. of the New Series of Nichol
fon's Journal, where Mr. Clofe has given the deſcription and
effects of an apparatus for raiſing water by means of air con-
denſed in its deſcent through an inverted fyphon.
CYLINDERS for STEAM ENGINES, boring of, is an operation
uſually carried on at the foundery where they are caſt. Though
the moulder purſues the moſt correct method his art is capable
of, yet it is impoffible to be certain that when the mould has
received the metal from the furnace it fhall come out quite
straight; and if it ſhould come out crooked it muſt remain fo;
for the old method of boring will never make it otherwiſe in
that refpect. It is not like boring a piece of metal which is
quite ſolid, as in boring guns, &c. All the old boring can do
to a cylinder is to make it round and ſmooth, for there is no-
thing to conduct the boring bit in its progreſs through the piece
but the form given it by the moulder; and a piece bored after
this manner may look very well, yet if it is not ſtraight it is not
a cylinder: and an engine executed with fuch a veffel as that will
be good or ill in that refpect, as it approaches to or is further off
the degree of exactnefs conftituting it a cylinder.
The new method of boring (which, as is obſerved, article
STEAM ENGINE, was first practifed at Burham, a foundery be-
longing to Mr. Wilkinſon, iron-maſter) insures all the per-
fection the ſubject is capable of; and when the process is con-
ducted by an intelligent workman, if the cylinder should be caft
ever fo crooked, or ever fo thick on one fide more than another,
he can take out the redundancy on that fide, and but ſcarcely
touch the other. This will be eaſily admitted when it is un-
derstood that, whereas in the old method of boring the inftru-
ment which performs the part of cutting the metal is guided in
its progrefs by the already incorrect form of the piece itself; but
in the new method the cutting apparatus is conducted along a
thing, which in itself is a maſterpiece of workmanſhip, a per-
fect cylinder, and is what the workmen call the boring bar, and
is caft of the beft pigs that can be procured, and turned with
the utmoſt care and preciſion: confequently, whatever is con-
ducted along this bar will proceed in a right line; and as it is in-
tended that this fhall be the conductor of the cutter-block, being
furniſhed with proper cutters, it muſt cut the interior furface of
the piece quite ftraight, though it may have been ever fo crooked.
before.
Then this bar being turned very true, it is to have a groove of
T
Ellipfograph.
160
two cut oppofite to each other, in a line parallel to its axis; then
there is a focket of caſt iron of ſuch dimenſions as to fuit for cylin
ders of various diameters, and this focket is to be nicely bored and
ground on the bar; and then it muft have a fillet or two (ac-
cording to the groove or grooves in the bar) let in on the infide,
fo as to flide along the bar, but not to turn round upon it: the
external part must be made conical, with four or fix ftuds upon
the baſe of it to receive the cutter block. The next thing is to
give a progreffive motion to this focket and cutter block while
the bar is turning on its own axis; and that is done by fome
with a collar of metal fitted on the focket, and to that collar are
connected two racks, long enough to reach through the cylinder
and communicate with a pair of pinions, by which the focket is
drawn or puſhed along the boring bar by the means of two levers,
carrying a weight at each ſufficiently heavy to overcome all re-
fiftance in the operation.
Another method of giving a progreffive motion to the block
is to drill a hole through the whole length of the bar, to admit
a fingle rod, to be communicated to the focket by finking the
groove (for in this cafe there can be but one) entirely through
one fide of the bar, fo as to come into the hole that has juft
been drilled through the bar. Then a branch from the inter-
nal part of the focket muft be fitted into the groove with an eye
to receive the end of the rod, which is then to be furniſhed with a
key, or a nut and waſher, to keep it in its place while the bar and
focket is turning round, and a weight with a rope over a pulley
is applied to give motion to the focket along the bar. This is
the beſt way of applying this method to boring of ſmall cylin
ders, becauſe there is no incumbrance upon the focket; and if
the bar is fufficiently ftrong it will move with great ſteadineſs.
ELLIPSOGRAPH is the name given by the anonymous
author of a German publication, entitled "Beſchreibung eines
Ellipfograph, womit man wahre Ellipsen ohne Berechnung der
Brennpunkte fehr leicht befchreiben kann, &c. publiſhed at Gotha
in 1794, to a ſimple and univerfal inftrument for drawing ellipfes.
The inftrument has been long known to our mathematicians,
and has been deſcribed, though not in fach general terms as
it admits of, in Emerfon's Conics, Hutton's Mathematical
Dictionary, and other works; but as it has not yet been adopted
for practical purpoſes, though it is far preferable, in our opi
nion, to any inftrument for drawing ellipfes now in uſe, we
take this opportunity of recommending it to general notice.
The ellipfograph confifts of three flat and moderately thin
rulers of wood or brafs, two of which must be of equal lengths;
and it may be as well if the length of theſe two together be equal
to that of the third ruler. Let the two fhorter of these rulers be
{
170
MACHINES.
=
pierced with a number of holes at equal diſtances, the holes
being capable of receiving either a pin on which the rulers
may turn as upon a joint, or a pencil by which the curve may
be deſcribed: then by connecting thefe rulers either as in
fig. 5. or fig. 6. pl. XIV. an ellipſe may be readily deſcribed.
Thus, in fig. 5. hang one end of the ruler AB upon a pin in
the middle of the ruler KL, and take the point B fuch that AB
≈ BD, and AB +BI) femiconjugate + femitranſverſe of the
ellipſe, the ruler BD turning upon a pin in B as a joint: take
the point E fo that DE femiconjugate, and put a pencil into
the hole of that point: then, if the end D of the ruler BD be
flidden along the edge KL of the ruler which paffes through the
centre A, the pencil at E will defcribe a true ellipfe having the
propofed diameters. Again, taking the method repreſented in
fig. 6. upon the ruler AC, hang the ruler BG at B, fo that
AB+ BE = femitranfverfe, while AB = BD half the differ-
ence of the femitranfverfe and femiconjugate axes: then, while
a pin at D flides along the edge of the ruler KL the pencil at E
will defcribe the ellipfe required. The truth of this method of
conftruction is demonftrated in Emerfon's Conics, prop. 75.
ellipse.
This inftrument may, it is obvious, be eafily made either fo
as to conſtruct ſmall ellipfes, now commonly defcribed by
means of the elliptical compaſſes; or upon a larger ſcale, for
the purpoſe of defcribing elliptical centring for arches of bridges,
&c. In the latter cafe the ellipfograph may be made fufficiently
ftrong without being any way cumberſome in practice. In the
actual conftruction of the inftrument the ruler KL ſhould be
the thickeft, and the other two legs made to run upon friction
rollers, as in the conftruction of the pentagraph.
It may not be altogether uſeleſs juft to remark, that in both
methods of ufing the inftrument the point B will defcribe a
circular arc; and if the ruler DB had a part above B, equal tọ
DB, the upper extremity of that part would, during the motion
of the point D along KL, defcribe a right line. This follows
evidently from what was fhewn in art. 8. of the introductory part
of this volume.
ENGINE to let down heavy weights. The fimple method we
are now about to defcribe was invented by father Reffin, in
1714. Suppofé it were required to lower large ftones from the
top of a wall which is intended to be taken down: erect a frame,
or fet up a gin clofe by the fide of the wall, and let the pulley
P (fig. 4. pl. IV.) be firmly attached to this frame. Over this
pulley muſt paſs a cord, one end of which C has a hook to
which the ftone, &c. can readily be faftened; the other end D
carries a veffel, which may be filled with water from the re-
File-cutting Machine.
171
fervoir M, on the ground at the bottom of the wall. Then,
while one man is fixing the ftone to the hook at the top of
the wall, let another put water into the veffel D at the bottom
till it nearly equals the weight of the ftone: after, which, leaving
both to the free operation of gravity, or checking the motion
a little if neceffary, the ftone will gradually deſcend to the
ground, while the veffel D will be carried up to a funnel A,
into which the water may be poured, and thence conveyed by a
wooden or a leather pipe to the refervoir M. Then the veffel D
may be fuffered to defcend, and the hook C will be raiſed to be
fixed to another ftone: and thus the operation may be repeated
as often as is neceſſary.
The fame method may likewiſe be adopted in lowering facks
from a high granary, or packages from an upper warehouſe,
The velocity of the defcending weight may be fo regulated as
to have any proportion to that which gravity imparts to bodies
falling freely: thus, if W denote the weight to be lowered, V
that of the veffel of water, we ſhall have
I
W-V
W+v'
for the fraction
expreffing the ratio of the velocity to that freely imparted by
gravity when denoted by unity. Thus, if V=W, the weight
will fall through of 16½, or about 5 feet in the firft fecond;
if V=W, the weight will fall through of 16,2, or about 35
feet in the firft fecond: the friction of the pulley being in both
inſtances difregarded.
I
FILES, machine for cutting of. There have been various con-
trivances for this purpofe; but the beſt we are acquainted with
is deſcribed in the Tranfactions of the American Philofophical
Society, and is as follows: AAAA fig. 6. pl. X. is a bench
made of well-feafoned oak, the face of which is planed very
fmooth. BBBBB the feet of the bench, which fhould be fub-
ftantial. CCCC the carriage on which the files are laid, which
moves along the face of the bench AAAA parallel to its fides,
and carries the files gradually under the edge of the cutter or
chifel HH, while the teeth are cut: this carriage is made to
move by a contrivance fomewhat fimilar to that which carries
the log againſt the ſaw of a faw-mill, as will be more particu-
larly defcribed. DDD are three iron rods, inſerted into the
ends of the carriage CCCC, and paffing through holes in the
ftuds EEE, which are ſcrewed firmly against the ends of the
bench AAAA, for directing the courfe of the carriage CCCC,
parallel to the fides of the faid bench. FF two upright pillars,
mortifed firmly into the bench AAAA nearly equidiftant from
each end of it, near the edge, and directly oppofite to each
172
MACHINES.
#
and
other. G the lever or arm which carries the cutter HH (fixed
by the fciew I), and works on the centres of two ſcrews KK,
which are fixed into the two pillars FF in a direction right
across the bench AAAA. By tightening or loofening theſe
fcrews the arm which carries the chifel may be made to work
more or leſs ſteadily. L is the regulating fcrew, by means of
which the files may be made coarfer or finer; this ſcrew works
in a ftud M which is fcrewed firmly upon the top of the ftud F:
the lower end of the ſcrew L bears againſt the upper part of the
arm G, and limits the height to which it can rife. Ñ is a ſteel
fpring, one end of which is ſcrewed to the other pillar F,
the other end prees againſt the pillar O, which is fixed upon
the arm G; by its preffure it forces the faid arm upwards, until
it meets with the regulating fcrew L. P is an arm with a claw
at one end marked 6, the other end is fixed by a joint into the
end of the ítud or pillar O; and, by the motion of the arm G,
is made to move the ratch-wheel Q. This ratch-wheel is fixed
upon an axis, which carries a finall trundle-head or pinion R,
on the oppoſite end; this takes into a piece SS, which is in-
dented with teeth, and fcrewed firmly againſt one fide of the
carriage CCCC: by means of this piece motion is communicated
to the carriage. Tis a clamp for faftening one end of the file
ZZ in the place or bed on which it is to be cut. V is another
clamp or dog, at the oppofite end, which works by a joint W,
firmly fixed into the carriage CCCC. Y is a bridge, likewiſe
fcrewed into the carriage, through which the fcrew X paffes,
and preffes with its lower end againſt the upper fide of the
clamp V; under which clamp the other end of the file ZZ
is placed, and held firmly in its fituation while it is cutting,
by the preffure of the faid clamp V. 7777 is a bed of lead,
which is let into a cavity formed in the body of the carriage,
fomething broader and longer than the largeſt fized files; the
upper face of this bed of lead is formed variouſly, fo as to
fit the different kinds of files which may be required. At
the figures 22 are two catches which take into the teeth of
the ratch-wheel Q, to prevent a recoil of its motion. 33 is
a bridge to fupport one end 4 of the axis of the ratch-wheel Q.
5 a ftud to fupport the other end of the axis of that wheel..
When the file or files are laid in their place, the machine muft
be regulated to cut them of the due degree of fineneſs, by means
of the regulating fcrew L; which, by fcrewing further through
the arm M, will make the files finer, and; vice verfa, by un-
fcrewing it a little, will make them coarfer; for the arm G
will, by that means, have liberty to rife the higher, which will
occafion the arm P, with the claw, to move further along the
Fire-efcape.
178
periphery of the ratch-wheel, and confequently communicate a
more extenfive motion to the carriage CCCC, and make the files
coarfer.
When the machine is thus adjuſted, a blind man may cut a
file with more exactneſs than can be done in the ufual method
with the keeneft fight: for by ſtriking with a hammer on the
head of the cutter or chifel HH, all the movements are fet at
work; and, by repeating the ftroke with the hammer, the files
on one fide will at length be cut: then they muſt be turned, and
the operation repeated, for cutting the other fide. It is need-
lefs to enlarge much on the utility or extent of this machine;
for, on an examination, it will appear to perfons of but indif-
ferent mechanical ſkill, that it may be made to work by water
as readily as by hand, to cut coarſe or fine, large or ſmall, files,
or any number at a time; but it may be more particularly uſe-
ful for cutting very fine fmall files for watchmakers; as they
may be executed by this machine with the greateſt equality and
nicety imaginable. As to the materials and dimenfions of the
feveral parts of this machine, they are left to the judgment and
ſkill of the-artift who may have occafion to make one; only ob-
ferving that the whole ſhould be capable of bearing a good deal
of violence.
FIRE-ESCAPE, a machine for removing perfons from the up
per ſtories of houfes on fire. It confifts of a pole, a rope, and a
baſket. The pole is of fir, or a common fcaffold pole, of any
convenient length from 36 to 46 feet. The diameter at bottom,
or greateft end, about five inches; and at the top, or ſmalleſt
end, about three inches. At three feet from the top is a mortife
through the pole, and a pulley fixed to it of nearly the fame
diameter with the pole in that part. The rope is about three
quarters of an inch diameter, and twice the length of the pole,
with a ſpring hook at one end, to paſs through the ring in the
handle of the baſket when uſed: it is put through the mortife
over the pulley, and then drawn tight on each fide to near the
bottom of the pole, and made faft there till wanted. The baſket
fhould be of ftrong wicker-work, three feet and a half long, two
feet and a half wide, rounded off at the corners, and four feet
deep, rounding every way at the bottom. To the top of the
baſket is fixed a ftrong iron curve or handle, with an eye or ring
in the middle; and to one fide of the baſket, near the top, is fixed
a ſmall cord, or guide-rope, of about the length of the pole,
When the pole is raiſed, and fet againſt a houſe over the window
from which any perfons are to eſcape, the manner of ufing it is
fo plain and obvious, that it need not be defcribed. The moft
convenient diſtance from the houſe for the foot of the pole to
ftand, where practicable, is about 12 or 14 feet. If two ſtrong
1
174
MACHINES.
iron ftraps, about three feet long, riveted to a bár crofs, and
ſpreading about 14 inches at the foot, were fixed at the bottom
of the pole, this would prevent its turning round or flipping on
the
pavement: and if a ſtrong iron hoop, or ferrule, riveted (or
welded) to a femicircular piece of iron ſpreading about 12 inches,
and pointed at the ends, were fixed on at the top of the pole, it
would prevent its fliding againſt the wall.
When thefe two laft-mentioned irons are fixed on, they give
the pole all the ſteadineſs of a ladder; and becauſe it is not eafy,
except to perfons who have been uſed to it, to raiſe and fet upright
a pole of 40 feet or more in length, it will be convenient to have
two fmall poles or ſpars of about two inches diameter, fixed to
the fides of the great pole at about two or three feet above the
middle of it, by iron eyes riveted to two plates, fo as to turn every
way; the lower end of theſe ſpars to reach within a foot of the
bottom of the great pole, and to have ferules and ſhort ſpikes to
prevent fliding on the pavement, when ufed occafionally to fup-
port the great pole like a tripod. There should be two ſtrong afh
trundles let through the pole, one at four feet and one at five feet
from the bottom, to ftand out about eight inches on each fide,
and to ſerve as handles, or to twist the rope round in lowering
a very heavy weight. If a block and pulley were fixed at about
the middle of the rope, above the other pulley, and the other part
of the rope made to run double, it would diminiſh any weight in
the baſket nearly one-half, and be very useful in drawing any per-
fon up to the affiſtance of thoſe in the chambers, or for removing
any effects out of a chamber, which it might be dangerous to at-
tempt by the ſtairs.
It has been proved, by repeated trials, that fuch a pole as we
have been ſpeaking of can be raiſed from the ground, and two
or three perfons taken out of the upper windows of a houfé,
and fet down fafely in the ſtreet, in the ſpace of 35 feconds, or
a little more than half a minute. Sick and infirm perfons,
women, children, and many others, who cannot make ufe of a
ladder, may be fafely and eafily brought down from any of
the windows of a houfe on fire by this machine, and, by put-
ting a fhort pole, through the handles of the basket, may be
removed to any diftance without being taken out of the baſ
ket. The pole muſt always have the rope ready fixed to it, and
may be conveniently laid up upon two or three iron hooks un-
der any fhade or gateway, and the baſket fhould be kept at
the watch-houſe. When the pole is laid up, the two ſpars
fhould always be turned towards the head of it. The baſket
fhould be made of peeled rods, and the pole and fpars painted of
a light ftone-colour, to render it more viſible when uſed in the
night.
Fire-engine.
175
FIRE-ENGINE, the name now commonly given to a machine
by which water is thrown upon fires in order to extinguiſh them.
Various machines have been contrived for that purpofe at differ-
ent times; the moſt effential particulars in a few of which we
fhall here defcribe.
The ufual conftruction of the fire-engine, after the great im-
provements were made in it by Mr. R. Newfham, was nearly
that which is exhibited in fig. 2. pl. XV. where we have repre-
fented a vertical fection of the engine. The motion of the
water in this machine is effected by the preffure of the atmo-
fphere, the force of men acting upon the extremities H', H", of
a lever, and thence giving motion to the piſtons, and by the
elafticity of condenfed air, in the following manner :-When
the pifton Ris raiſed a vacuum would be made in the barrel
TU if the water did not follow it from the inferior canal EM
(through the valve H), which rifes through the tube EF im-
merfed in the water of a veſſel by the preffure of the atmoſphere
on its furface. The water of the barrel TU, by the fucceeding
depreffion of the pifton R, fhuts the valve H, and is forced,
through the ſuperior canal ON, to enter by the valve I into the
air-veffel a b c d; and the like being done alternately with re-
ſpect to the other barrel WX, and its pifton S, the air-veffel is,
by theſe means, continually filling with water, which greatly
compreffes the air above the furface of the water in that veffel,
and thereby proportionally augments its fpring; which at length
is ſo far increaſed as to re-act with great force on the furface YZ
of the fubjacent water, and compel it to aſcend through the ſmall
tube e f to the ftop-cock e g, where upon turning the cock the
water is fuffered to paſs through a pipe h fixed to a ball and
föcket; from the orifice of which it iffues in a continued ftream
with a great velocity, to a confiderable height or diſtance; and it
is ufually kept from diverging too foon in its progreſs by means
of a long feries of flexible leather pipes, properly joined to-
gether, and known among the fire men by the name of the
hofe.
Defaguliers remarks (vol. I. p. 257.) that Mr. Newham
contrived his engines in fuch a manner," that part of the men
who work them exert their force by treading, which is more
effectual than any other way that men can work at ſuch engines;
the whole weight of the body being fucceffively thrown, on "the
forcers of the pumps: and even part of a man's strength may be
added to the weight by means of horizontal pieces to which he
can apply his hands when he is treading: whereas, by applying
the hands to move levers or turn winches, the power muſt act
very unequally. This is the reaſon why with the fame number
of men he has generally thrown water further, higher, and in
39
176
MACHINES.
Į
greater quantities, with the fame fized engines, than other en-
gineers who have tried their engines against his." Notwithſtand-
ing the truth of this remark, we are not aware that the com-
bination of human weight and ſtrength here recommended has
been practifed in any ſubſequent fire-engines, or indeed in any
machines whatever, except the ingenious walking crane of Mr.
Hardie.
The greateſt artifice in the engine according to the con-
ftruction just defcribed is the contrivance to produce a continual
Stream, which is done by the compreffion and proportional elaſti-
city of air in the barrel a b c d, called the air-veffel. For the air,
being an elaſtic fluid, will be fufceptible of compreffion in any
degree by the water forced in through the valves at IK; and,
fince the force of the air's fpring will always be inverſely as the
fpace it poffeffes (art. 489. vol. I.), it follows that when the air-
veffel is half full of water the air will be compreffed into half
the ſpace it poffeffed at firſt, and therefore its fpring will be twice
as great as at firſt.
But this fpring at firft was equal to the preffure of the at-
moſphere on the ſame ſurface: for if it were not it could not
have ſuſtained or refifted the preffure of the atmoſphere which
ſtood over it, and conſequently could not have filled the veffel
before the water was driven in; which yet we find it did, and
maintained an equilibrium with the common air. The veffel
then being half filled with water, or the air compreffed into half
the firſt ſpace, its ſpring will in this cafe be equal to twice the
preffure of the atmofphere; and therefore when the ftopcock at
p is turned, the air within, preffing on the fubjacent water with
twice the force it meets with from the external air in the pipe ef
will cauſe the water to ſpout out of the engine to the height of
32 or 33 feet, if the friction is not too great.
423
When the air-veffel is full of water, the air takes up part;
whence its fpring will be three times as great as that of the
common air, and it will project the water with twice the com-
mon atmoſpheric preffure; confequently, it will rife to the
height of 62 or 64 feet. When the air-veffel is full of water
the air will be compreffed into its part, and fo will protrude
the water with three times the atmoſpheric preffure, and carry
it to the height of 96 or 99 feet. Hence it will be eaſy to ſtate
the law by which the ſpring of the air will act on the ſurface
of the water below it, as in the following table.
4
1
Fire-Engine.
177
Height of water
in air-bar.
Of the air
compressed.
Proportion of
air's elasticity.
Height of
the spout.
2
33
3.
66-
99
132
6
165
T
7
198
8
231
9
264
10
To
To
297
2- I
I
n
(n − 1) 33
n
•
Various alterations and improvements have been made from
time to time in the conftruction of Fire-engines. The con-
trivers of fome of theſe improvements, as Meffrs. Bramah,
Dickenſon, Simpkin, Rowntree, and Phillips, have fecured their
inventions from infringement by patents; the ſpecifications of
moſt of which may be ſeen in the Repertory of Arts and Manu-
factures. In the year 1785 the filver medal and twenty guineas
were conferred by the "Society for the Encouragement of Arts,"
&c. on Mr. Furft, as a reward for his contrivance to increaſe
the effect of engines in extinguiſhing fires; of which the follow-
ing is a fhort defcription: from a platform riſes an upright pole
or maft, of fuch height as may be judged neceffary; a gaft flides
upon it in an afcending direction, and along both is conveyed
the leather hofe from the engine. The branch or nofe-pipe of
the engine projects at the extremity of the gaft; towards which
an iron frame is fixed, whence two chains are fufpended; and
from thefe hang ropes, which ferve to give an horizontal di-
rection to the branch; while other ropes, that run through
proper pullies, and are thus conveyed down the maſt, ſerve
likewife to communicate a vertical motion to it. By theſe
means, the branch or nofe-pipe of the engine is conducted into
the window of any room where the fire more immediately
rages; and the effect of the water diſcharged is applied in the
moft efficacious manner to the extinguiſhing of the flames.
A very cheap and fimple fire-engine is that invented in Ame-
rica by Mr. Benjamin Dearborn, who communicated it to the
American Academy of Arts and Sciences, from whoſe Memoirs
for 1794 we extract the following particulars:
Fig. 4. pl. XV. AB and CD are the edges of two planks, con-
fined by four bolts; a b and c d are two cylindrical barrels, in
each of which a piston, with a valve, is faftened to the fpear e,
and is moved up and down alternately by the motion of the
arms EE. Beneath each barrel a hole is made through the
VOL. II.
178
MACHINES.
?
plank ÁB, which is covered with a valve. The arms EE are
fufpended on the common centre f: there are alſo arms parallel
to theſe on the oppofite fide: g g are the ends of handles which
are faſtened acroſs the ends of the arms. At h a bolt goes acrofs
from arm to arm, to which the piece i k is affixed, and on which
it plays; the lower end of this piece is faftened to the top of the
fpear e. Glf is a ſtandard for the purpoſe of ſupporting the
arms, to which there is a correfpondent one on the oppofite
fide; both are notched into the edges of the planks, where they
are fecured by a bolt, which paffes through them at 7, and has a
nut or fore-lock on the oppoſite fide. HI, HI, are ſquare braces,
anſwering the purpoſe of ducts, through which the water af-
cends from the barrels, paffing through the plank at m. KL,
KL, are irons in the form of a ftaple, in order to confine the
braces: the lower ends of theſe irons meet, and are fecured by
a bolt paffing through them, and MN n o, which is a piece that
goes up through a mortice in the centre of the planks. This
piece is ſquare from the lower end, till it reaches the top of the
braces; whence they become cylindrical to the top, the upper
end being perforated fufficiently low down, in order to com-
municate with the braces. OP is an iron ring that ſurrounds
the tube, and has two ſhanks which afcend through the head,
which ſcrews on the top at p q r s is a ferule nailed round
the tube.
Fig. 5. is the fame engine; the arms and ſtandards being
taken off, in order to delineate more clearly the mode of fecur-
ing the braces; an object which is completely effected by a
wedge driven into the mortice a: beneath the upper plank bis
a hole for admitting a paffage to the bolt,' which fecures the
ſtandards. In this figure a fide view of the head is given, with
the pipe in a perpendicular direction.
The machine is confined within a box, fet on wheels, as in
the common fire-engines. The whole is made of wood, ex-
cepting the ſpears of the pumps, and a few bolts, &c. The
advantages of this machine are, that it can be made in any
place where common pumps are manufactured; the interior
work will not exceed one-fourth of the price of thoſe which
are conſtructed on the uſual plan; and that they are incom-
parably more eafy to work than the common ones: circum-
ſtances which ſtrongly recommend the American fire-engine to
the attention of the public.
Since the conftruction of engines for the extinguiſhing of
fires has long been confidered of very great importance, it is
no wonder that many perfons have devoted much of their time
and talents to this fubject. Various treatifes have been written
upon it; the chief of which are mentioned below.

Writings on Fire-Extinguishers.
179
Beſchreibung eines wafferkrahns, welcher in groffen und
gefahrlichen feuerfbrünften ſehr nutz-lich zu gebrauchen, und
mit gar geringen unkoften angeſchafft werden kann; zugleich
in einem kupferftuck vorgeſtellt. 1665.
Deſcription d'une machine hydraulique, pour éteindre le feu
dans les incendies, tirée des regiſtres de L'Acad. Roy. des Sci.
de Paris.
1675-
Sur une nouvelle machine pour le feu, par M. de Reaumur.
Mém. de l'Acad. Roy. des Sci. &c. 1722.
Misflungene verfuche mit der Greyliſchen maſchine, von Thum-
mig. Auch. Brefl. Samml. 1721.
A new method of extinguiſhing fires by exploſion and ſuffo-
cation, by Mr. Godfrey. 1724.
Lettre de Londres, du 5 Juin, 1761, par M. Defchamps; fur
rine expérience publique touchant la nouvelle manière d'eteindre
le feu, inventée par M. Godfrey, faite par la Société formée
pour l'Encouragement des Manufactures et du Commerce en
Angleterre.
Mr. Ambros Godfrey's erfindung von gefchwinder auflöſchung
der feuerfbrünfte. Hannöveriſche Beytrage. v. J. 1761.
[The "Greyliſchen machines," mentioned above, were intro-
duced into this country by a Mr. Zachary Greyl: they were
made of wood, and contained only water; they were exhibited
before feveral of the nobility, but did not meet with encourage-
ment. A few years after, Dr. Godfrey produced certain veſſels
``which in every reſpect fucceeded. They are fuppoſed to have
been an improvement on Mr. Greyl's, were conſtructed with
wood, and filled with a chemical liquor, confifting of water, oil
of vitriol, and fal-ammoniac. When thrown into rooms and
other places that were purpoſely fet on fire, they burſt, and by
their exploſion completely extinguiſhed the flames: it is to be ob
ferved, that they were uſeleſs after the roof had fallen in. Thefe
contrivances, however, are evidently more calculated for fhips
than to be employed on land; as they would be of great fervice
for fuppreffing fires in veffels at ſea, and might be confidered as
neceffary a part of their cargo as naval ftores or ammunition.]
Nouvelle manière d'eteindre les incendies, avec pleufieurs
autres inventions utiles à la ville de Paris; par M. Moitrell d'Ele-
ment. 1725.
Jacob Leupold's beſchreibung und abbildung eines druckwerks
mit dem krummen zapfen und fchwungrad, welches als eine
feuerfpritze oder andere maſchine an unterſchiedenen orten
kann gebraucht werden. See his Theatri machinarum hydrauli-
carum. tom. II. cap. 5. 1725.
Defcription d'une machine ou pompe pour élever l'eau dans
les incendies, propofée par un armurier de Semur en Auxois. See
N 2
180
MACHINES.
Receuil mach. et invent. approuvées par l'Acad. Roy. Paris,
tom. II.
1735.
Architecture hydraulique, par Belidor, tome II. 1739.
A deſcription of the late Mr. Richard Newfham's engines to
put out accidental fires. See Defaguliers's Experimental philo-
fophy, vol. ii. 1744.
Joh. Gottfr. Dobe, fchloffers und fpritzeumachers in herzberg,
nachright von ſeiner neu erfundenen fpritze mit zwey auf-
guffröhen, aus welchen in gleicher quantität und entfernung,
jedoch in verfchiedenen direktionen, das waffer zu gleicher zeit
auſgeſpritzt warden kann. Leipz. Int. Bl. 1767.
Abhandlung und berechnung über die neubertſchen ſpritzen,
von Kampe, ſtadtbauherrn in Göttingen. 1769.
Nachricht von Feuerfpritzen von J. L. Riepenhauſen, me-
chanicus in Göttingen. 1770.
D. Wilh. Gottlieb Haffe praktiſche abhandlung zu verbefferung
der feuerfpritzen, welche auf die aufgeftellte preifsfrage von
Kurfürftl. Maynzifcher akademie nützlicher Wiffenfchaften
zu Erfurt den beyfall erhalten. Gotha, bey Karl. Wilhelm
Ettinger. 1778.
Lukas V'och's abhandlung von feuerfpritzen, &c. 1781.
Ueber den zweckmaffigen gebrauch der feuerfpritze und
anderer löſchmaſchinen. Zürch, b. Fuesfli. Tubing, gel. Anz.
1790.
Erfindung einer feuerfpritze, welche ganz ohne röhrwerk,
ohne kolben und ventile durch die kraft zweyer menſchen eine
überaus groffe menge waffer zu einer beträchtlichen höhe in die
luft treibt, durch den dritten mann nach allen gegenständen
gerechtet wird, und mit geringen koften nebft derfelben an-
wendung auf handfpritzen herzuftellen ift, von Karl Imanuel
Löscher. 1792.
Various fire-engines are deſcribed in the articles HYDRO-
STATICS and FIRE-engine, in the English Encyclopædia and the
Supplement to that work.
Entwurf die feuerfpritzen mittelft einer mechaniſchen vorrich-
tung vor dem einfrieren zu fichern, nebft einigen bemerkungen
über die löfchanftalten überhaupt, vorzüglich aber bey brand-
fällen im winter, bearbeitet von J. L. J. von Gerstenbergk.
Jena, in der akademifchen buckhandl, 1801. pp. 1 to 89.
This will not be altogether an improper place to ſpeak of the
means of extinguiſhing accidental fires in fhips, recommended
by Mr. Alexander Tilloch, the editor of the Philofophical Maga-
zine. Mr. Tilloch begins his paper on this fubject by ſome
account of the theory of combuftion; in which he takes occafion
to ſtate, that fire is more fupplied from the oxygen of the air
!
Fires in Ships, to extinguish.
181
than from the combuftible body; and that water may itſelf act
as an inciter to fire, inftead of extinguishing it, when expofed to
a fufficient temperature, in circumftances which fhall decompofe
it into its conftituent gafes, hydrogen, a combuſtible, and
oxygen the only fupporter of flame.
Mr. Tilloch ftates, alfo, that water acts as an extinguiſher,
merely by interpofing itſelf between the flame and the air, and
excluding the latter, thus acting "as a wall of feparation be-
tween the burning materials and the atmoſphere:" for this
reaſon he recommends mixing fand, or mould, or clay, with the
water employed to extinguiſh fire, to render its effect in this
refpect more powerful.
Mr. Tilloch ſtrongly ſtates the fuperior efficacy of cutting off
all communication between the burning bodies and the atmo-
ſphere, as the moſt certain means of ſtopping conflagration:
wherefore, when this takes place in a fhip, the hatches fhould
be cloſed, and all hands employed in ſtopping every crevice, by
which the air could pafs to the burning body, with oakum or
any other matter: by which means the fhip would become “
large extinguiſher," and the fire go out when it had conſumed
the oxygen of the confined air. By this method, if the fire
forced its way through the lower deck, it might be ſtopped in
the fecond deck, by clofing the ports, hatches, and all other
apertures belonging to it in every direction.
one
To haften the confumption of the oxygen of the confined air,
Mr. Tilloch recommends, before clofing the hatches, to light as
many other fires below, in pots, pans, and other veffels, as time
will permit; likewife to light up as many candles as poffible,
each of which confuming a gallon of air in a minute, will affift
in fooner rendering the enclofed air unfit for combuſtion.
Mr. Tilloch alfo propoſes, that a quantity of chalk or lime-
ftone fhould be ftowed on board, and an adequate proportion
of vitriolic acid; by means of which a quantity of fixed
air might be produced, which would alſo aſſiſt in extinguiſhing
the fire.
When the flames are ſtopped by theſe means, caution muſt be
uſed to carefully ventilate all the encloſed places by every poff-
ble means, before the men are fuffered to go down; otherwife
their inftant fuffocation muſt enfue.
When a fire takes place above deck, the uſe of water mixed
with fand or mould is recommended; and the ftrewing fand on
the decks, three inches thick, both to ftop and prevent fire in
that part, and to form a road by which the men can get at the
burning body, fo as to apply mops wet with the above mixture
to it, which Mr. Tilloch thinks would be more effectual than
182
MACHINES.
}
the efect of a fire-engine: in this operation the application of
the mop ſhould proceed from below upwards.
It is alſo adviſed to ſeparate the part of the fhip where fires
are moſt likely to originate from the reft, by air-tight partitions
(or bulk-heads), ſo that when a fire happened there it would
be only neceffary to cloſe and caulk up the entrance to this part
to put it out.
It is further recommended to cover all the upper works with
fheet-copper, to prevent their taking fire by any accident which
might happen on deck, and to encloſe the maſts in the fame
manner, having metallic chains added along the fhrouds, to
fecure them in cafe of the rigging being burned away.
Some of the particulars in this paper will appear fo chimerical
to a nautical man as to make him fet lefs value upon the reſt
than is due to them: but, as every thing which may tend to
fubdue fo dreadful an enemy as fire on board a thip deferves
being known and confidered, and as many of the fuggeftions in
this paper may undoubtedly be applied to moſt important
practical purpoſes, we thought it a duty to advert to it; and
would beg to refer to No. 82. of the Phil. Mag. for Mr. Tilloch's
obſervations at large.
FLAX-MILLS have been conftructed in great variety: but
one of the beſt we are acquainted with is deſcribed in Gray's
Experienced Millwright, in nearly the following terms.
Fig. 1. pl. XVI. is the plan. AA, the water-wheel. CC,
the ſhaft or axle upon which it is fixed. BB, a wheel faſtened
upon the fame fhaft, containing 102 teeth, to drive the pinion
D, having 25 teeth, which is fixed upon the middle bruifing-
roller: E, a pinion in which are 10 teeth, turned by the wheel
B, which is faſtened upon the under end of the perpendicular
ſhaft that carries the fcutchers. MM, the large frame that
fupports one end of the ſhaft C, and the perpendicular axle.
NN are frames in which the rollers turn that break or bruiſe
the rough flax. IA and L, the machine and handle to raiſe the
fluice when the water is to be let on the wheel AA to turn it
round. GG, doors in the fide-walls of the mill-houfe. IK,
windows to lighten the houſe. HH, ftairs leading up to the
loft.
Fig. 2. Elevation. AA, the water-wheel upon its fhaft CC,
on which ſhaft the wheel BB is alſo fixed: this latter wheel con-
taining 102 teeth, to turn the wheel E, having 25 teeth, which
is faſtened upon the middle bruifing-roller. FF is a vertical
fhaft, upon the lower end of which is fixed a pinion having 10
teeth, which is driven by the wheel B. There are two arms
that paſs through the ſhaft F; and upon theſe arms are faſtened,
Flax-mill.
183
with fcrewed iron bolts, the fcutchers that clear the refuſe off
the flax. DD, the frames which fupport one end of the axle
C, the vertical fhaft, and the breaking-rollers: L, a weight fuf-
pended by a rope, the other end of which is faftened to a
bearer, as is feen in fig. 3. SS a lever, the ſhort arm of which
is attached to the frame that the gudgeons of the upper roller
turn in; and by puſhing down the long arm, the upper roller is,
when neceffary, fo raiſed as to be clear of the middle one. NN,
the end-walls of the mill-houſe. RR, the couples or frame of the
roof. H, a door in the fide-wall. IK, windows.
Fig. 3. Section. AA, the great water-wheel fixed upon its
fhaft, and containing 40 aws or float-boards to receive the water
which communicates motion to the whole machinery. BB, a
wheel faſtened upon the fame axle, having, as before mentioned,
102 cogs, to drive the wheel C of 25 teeth which is fixed
upon the middle roller, No. 1. The thick part of this roller is
fluted, or rather has teeth all round its circumference. Theſe
teeth are of an angular form, being broad at their baſe, and
thinner towards their outward extremities, which are a little
rounded, to prevent them from cutting the flax as it paffes
through betwixt the rollers. The other two rollers Nos. 2. and
3. have teeth in them of the fame form and fize as thofe in the
middle roller, whofe teeth, by taking into thoſe of theſe two rollers,
turns them both round. The rough flax is made up into ſmall
parcels, which being introduced betwixt the middle and upper
rollers, paſs round the middle one; and this either having rollers
placed on its off fide, or being incloſed by a curved board that
turns the flax out betwixt the middle and under rollers, when it
is again put in betwixt the middle and upper one, round the fame
courſe, until it be fufficiently broken or ſoftened, and prepared for
the fcutching machine. The bearer in which the gudgeon of the
roller No. 1. turns is fixed in the frame at C; and the gudgeons
of the rollers Nos. 2. and 3. turn in fliders that move up or down
in grooves in the frames SS. The under roller is kept up to
the middle one by the weights DD, fufpended by two ropes
going over two ſheeves in the frames SS; their other ends being
faſtened to a tranſverſe bearer below the fliders in which the
gudgeons of the roller No. 3. turn. The weights DD muſt be.
confiderably heavier than the under roller and fliders, in order
that its teeth may be preffed in betwixt the teeth of No. 1. to
bruiſe the flax when paſſing between the rollers. The whole
weight of the roller No. 2. preffes on the flax which paffes
between it and No. 1. There is alſo a box fixed on the upper
edge of its two fliders to contain a parcel of ftones, or lumps of
any heavy metal, ſo that more or leſs weight can be added to
the roller, as is found neceffary. OO, is the large frame that
184
MACHINES.
ſupports one end of the ſhaft which carries the two wheels A, B,
and vertical axle FF; on the lower end of which is fixed the
pinion turned by the wheel B, and having 10 teeth. In the axle
F are arms upon which the fcutchers are faſtened with fcrewed
bolts, as feen at GG, fig. 2. Theſe fcutchers are incloſed in
the cylindrical box EE, having in its curved furface holes or
porches at which the handfuls of flax are held in, that they may
be cleaned by the revolving fcutchers. HH, the fall or courfe
of the water. TT, the fluice, machine, and handle, for raiſing
the fluice to let the water on the great wheel. The gudgeons
of the axles ſhould all turn in cods or buſhes of brafs. KK,
the fide-walls of the mill-houſe. GG, doors. LL, windows.
FLOUR-MILLS are put into motion in various ways: fome
times the firſt mover is wind, at others water, at others the force
of ſteam, at others the muſcular energy of animals. See Foot-
mill, Hand-mill, Wind-mill, &c.
The mechaniſm of the grinding part of moſt of theſe is
nearly the fame, and well underſtood; fo that it will not be
neceſſary to enter much into minutiæ, but merely to preſent a
general deſcription of a well-conftructed mill, with any firſt
mover; and fubjoin to this defcription fome remarks, rules,
and tables.
In plate XVII. we have given a fection of a double Flour-
mill, reduced from Gray's Experienced Millwright, with the
following account. AA, the water-wheel. BB, its fhaft or
axle. CC, a wheel fixed upon the fame fhaft, containing 90
teeth or cogs, to drive the pinion No. 1. having 23 teeth, which
is faftened upon the vertical ſhaft D. No. 2. a wheel fixed upon
the ſhaft D, containing 82 teeth, to turn the two pinions FF,
having 15 teeth, which are faſtened upon the iron axles or
fpindles that carry the two upper mill-ftones. EE, the beam
or fill that fupports the frame on which the under mill-ftones
are laid.
GG, the cafes or boxes that encloſe the upper mill-
ftones; they ſhould be about 2 inches diftant from the ftone all
round its circumference. TT, the bearers, called bridges, upon
which the under end of the iron ſpindles turn. Thefe fpindles
paſs upward through a hole in the middle of the nether mill-
ftones, in which is fixed a wooden bufh that their upper ends
turn in. The top part of the ſpindles, above each wooden
buſh, is made fquare, and goes into a fquare hole in an iron
croſs, which is admitted into grooves in the middle and under-
furface of the upper mill-ſtone. By this means that ſtone is
carried round along with the trundles FF, when turned by the
wheel No. 2. One end of the bridges TT is put into mortifes
in fixed bearers, and the other end into mortices in the bearers
that move at one end on iron bolts, their other ends hanging by
Flour-mill.
185
+
iron rods having fcrewed nuts, as UU; fo that when turned
forward or backward they raiſe or deprefs the upper mill-ftones,
according as the miller finds it neceffary. SS, the feeders, in
the under end of each of which is a fquare focket that goes
upon the fquare of the fpindles above the iron crofs or rind,
and having three or four branches that move the ſpout or fhoe,
and feed the wheat conſtantly from the hoppers into the hole
or eye of the upper mill-ftone, where it is introduced betwixt
the ftones; and by the circular motion of the upper ftone ac-
quires a centrifugal force; and proceeding gradually from the
eye of the mill-ftone towards the circumference, is at length
thrown out in flour or meal. RR, the fluice, machine, and
handle, to raiſe the fluice, and let the water on the wheel A to
drive it round. No. 3. is a wheel fixed upon the fhaft D,
containing 44 teeth, to turn the pinion No. 4. having 15 teeth,
which is faſtened upon the horizontal axle H. On this axle is
alfo fixed the barrel K, on which go the two leather belts that
turn the wire engine and bolting mill. L, an iron ſpindle, in
the under end of which is a fquare focket that takes in a fquare
on the top of the gudgeon of the vertical fhaft D. There is a
pinion M, of 9 teeth, fixed on the upper end of the ſpindle L,
to turn the wheel MM, having 48 teeth, which is faftened upon
the axle round which the rope ZZ rolls, to carry the facks of
flour up to the cooling benches. By pulling the cord OO a
little, the wheel MM and its axle are put into motion, in con-
ſequence of that wheel and its axle being moved horizontally,
until the teeth of the wheel are brought into contact with thoſe
of the pinion at the top of the ſpindle L: and, on the contrary, by
pulling the cord PP, the wheel M and its axle are moved in the
oppofite horizontal direction, till they are thrown out of geer
with the pinion, and the rotatory motion of that wheel ſtops.
But when the fack of flour is raiſed up to the lever Q, it puſhes
up that end of the lever, and of courſe the other end down;
by which means the pinion M is diſengaged, and thus that part
of the machine ftops of itſelf. NN are two large hoppers,
into which the clean wheat is put to be conveyed down to the
hoppers SS, placed on the frame immediately above the mill-
ftones. WW, the fide-wall of the mill-houſe. V, the couples
or frame of the roof. XX, windows to lighten the houſe,
Fig. 1. in the margin repreſents the furface of the under
grinding mill-ftone; the way of laying out the roads or channels;
the wooden buſh fixed into the hole in its middle, in which the
upper end of the iron fpindle turns round; and the cafe or
hoops that furround the upper one, which ought to be two
inches clear of the ſtone all round its circumference.
Fig. 2. the upper grinding mill-ftone, and iron crofs or rind
186
MACHINES.
in its middle; in the centre of which is a fquare hole that takes
in a ſquare on the fop of the iron fpindle, to carry round the
mill-ftone. When the working fides or faces of the mill-ftones
are laid uppermoft, the roads (or channels) muft lie in the fame
direction in both; fo that when the upper ftone is turned over,
and its furface laid upon the under one, then the channels may
croſs each other, which affifts in grinding and throwing out the
flour; the fharp edges of the two furrows then cutting againft
each other like fciffors. The roads are likewife laid out according
to the way the upper ftone revolves. In thoſe repreſented in
the figures the running mill-ftone is ſuppoſed to turn "fun-
way," or as in what is called a right-handed mill: but if the
ſtone revolves the other way the channels must be cut the re-
verfe of this, and then the mill is termed a left-handed one.
The elevation of this mill may be ſeen in Gray's Millwright,
pl. XXXI.
$
It will not be expected that we ſhould allot much space to
the theory of flour-mills, though it may not be adviſeable to
pafs it over entirely. We fhall therefore give two or three
theorems for a ſingle flour-mill of the common conſtruction,
which may be applied with facility, fo far as they are uſeful, to
double or triple mills.
Let the weight of the upper ftone when furrowed be=W,
the reſiſtance of the corn reduced to the diſtance of the centre
of gyration, or at of the radius of the upper ftone=R, then,
according to Belidor, R'-
W
23
W
35
while according to Fabre R
But when the upper ftone to work moft advantageously in
every reſpect goes round 60 times in a minute, we have
R =
60 2 W
60
2 W DW
N 35 450D 35 1314
This, however, would require an upper mill-ftone of about 7
feet diameter: for when the diameter of that ftone is D in feet,
and N the moſt advantageous number of rotations in 1 minute,
450
we have, from many obfervations, N= as introduced into
D
the preceding theorem; and this, when N = 60, gives D-74.
Let the whole friction when reduced to of the radius of
the upper ftone be repreſented by F, and the effective diſtance
of the force or power from the axe on which the ſtone revolves
=r, the number of teeth in the first or commanding wheel
M, and the number of ſtaves in the trundle =m, the number
of revolutions of the water-wheel in 1 minute
= n,
the power
Flour-mill.
187
which at the distance r from the axe of the water-wheel is necef-
ſary to retain the whole load in equilibrium=p; ſo ſhall we have
rp
M
m
whence, p =
or, becauſe
M
772
÷ D (R + F).
2MD
(R+ F)
3 m r
:
2ND
we have p =
(R+F).
3nr
Let the time in feconds in which the water-wheel revolves
be =t, the velocity with which any point in its circumference
moves =v, the height due to this velocity being =ḥ,π=
3'141593, and g = 16 feet, then is
ΤΣ
2π T
60
t=
and n =
600/8 h
Ngh
t
Tr
m
But it is alfo n =
N =
M
m 450
M D
therefore
450 m
DM
60/gh, and r =
πr
10 DM ✔gh
450 mm
An underſhot-wheel produces the greateſt uſeful effect, when
the height due to the velocity of the impinging water being H,
we have b=H, or v: V:: √//:::24 nearly: retaining
theſe as fufficiently exact for practice, the moſt advantageous
radius of the underfhot water-wheel, the water puſhing againft
fhovels or float-boards, is
୧
60 DM₁g H
0.019 DM₁g H
450 π Μ
or again g
OIOг DMV
m
m
where V is the velocity of the impinging water.
But in underfhot-mills the fall is feldom, if ever, more than
15 or 16 feet: in that cafe the moſt advantageous pofition of
the work is to have
·
M
m
122°27
DV
Further, let L = the number of pounds of meal which are
produced every hour, s = the ſpecific gravity of the upper mill-
ftone, that of water being unity, and B the folid content of the
ftone in cubic feet: the remaining letters having the fame ac-
ceptation as before: then
185
MACHINES.
for rye and wheat L = 0°021 D²s
s B
for old barley L = 0·06 D²s B
M
m r
pounds.
pounds.
mr
MU
Mr. Ferguſon has made fome practical obſervations on mills,
which, as they are not far from coincidence with the preceding
theorems, may be introduced here.
When the diameter of the upper ftone is about 6 feet, as is
generally the caſe, the lower is about an inch more: the upper
ftone then contains about 22 cubic feet, and weighs rather
more than 19000 pounds. A ftone of this kind ought never
to revolve more than 60 or 70 times in a minute; for a more
rapid motion would heat the meal. Nor muft the water-wheel
be too large, for in that cafe its angular motion will be too
flow; on the contrary, if the wheel be too fmall, it will be de-
ficient in moving power: 18 feet diameter is recommended as
a proper medium.
And Mr. Ferguſon, on the fuppofition that
the floats of the wheel ought to move with a third part of the
velocity of the water-a fuppofition, however, which is not
ftrictly confiftent either with theory or with Mr. Smeaton's
experiments (fee vol. I. arts. 473, 483, &c.)-gives the follow-
ing rules for conftructing the chief parts of the mill.
1. Meafure the perpendicular height of the fall of water in feet
above that part of the wheel on which the water begins to act,
and call that the height of the fall.
2. Multiply this conftant number 64-2882 (or rather 64)
by the height of the fall in feet, and extract the fquare root of
the product, which will be the velocity of the water at the bottom
of the fall, or the number of feet the water moves per fecond.
3. Divide the velocity of the water by 3; and the quotient
will be the velocity of the floats of the wheel in feet per fecond.
4. Divide the circumference of the wheel in feet, by the
velocity of its floats; and the quotient will be the number of
feconds in one turn or revolution of the great water-wheel, on
the axis of which is fixed the cog-wheel that turns the trundle.
5. Divide 60 by the number of feconds in one turn of the
water-wheel or cog-wheel; and the quotient will be the number
of turns of either of theſe wheels in a minute,
6. Divide 60 (the number of turns the millftone ought to
have in a minute) by the abovefaid number of turns; and the
quotient will be the number of turns the millstone ought to
have for one turn of the water or cog wheel. Then,
7. As the required number of turns of the millſtone in a
minute is to the number of turns of the cog-wheel in a minute,
ſo muſt the number of cogs in the wheel be to the number of
Flour-mill.
189
ſtaves or rounds in the trundle on the axis of the millftone, in
the neareſt whole number that can be found.
By theſe rules the following table is calculated; in which
the diameter of the water-wheel is fuppofed 18 feet, and con-
fequently its circumference 56:
The Mill-wright's Table.


Per-Velocity | Velocity | Number | Required? Nearest Number Num-
of turns of number of uum. of cogs of turns ber of
the wheel | turns of and staves
of the
turns of
in a mi- the mill- for that pur-millstone themill-
stone for pose. for one stone in
pendi-
of the
cular water in
height feet per
of the
wheel in
feet per
of the
second,
second.
fall of
water.
nute.

each turn
of the
wheel.
Stares.
Cogs.
turn of a min,
the wheel by these
by these cogs
cogs and and
stares. staves,
2
~ that
8.02
257
2.83
21'20
11*40
3.78
4.00
3
13.89 4.63
4.91
12'22
16:04
5:35
5.67
10.58
17.93
5.98
6.34
9.46
II
12
IS
14
15
16
17
18
19
6 78 9 0 1 2 ∞ 4 Yo No a
19.64
6.55
6.94
8.64
21*21
7:07
7:50
8.00
£5.00
127
105
98
95
85
78
72
22.63
7.56
8:02
7.48
776
679
200 in 500 ~
996
21.17
59.91
15.00
60.00
12.25
60.14
9
10.56
59.87
9
9'44
59.84
9
8.66
60.10
9
8.00
60.00
67
9
7'44
59.67
24.05
8.02
8.51
7:05
70 IO
7'00
59'57
ΙΟ 25*35
8.45
8.97
6·69
67
ΙΟ
6.70
60·09
2.6.59
8.86
9.40
6.38
64
10
6.40*
60.16
27.77
9.26
9.82
6.11
61 10
6.10
59'90
28.91
9.64
10.22
5.87
59 ΙΟ
5.80
60.18
30.00
10'00
10'60
5.66
56 10
5.60
59.36
31.05
10.35
10.99
5:46
55 ΙΟ
5'40
60.48
32.07
10.69
1134
5.29
53 10
5°30
60.10
33.06
II'02
II 70
5.13
SI ΤΟ
5'10
59.67
34.02
II.34
12'G2
4'99
50 10
5'00
60.10
34'95
11.65 12.37
4.85
49 ΙΟ
4.80
69.61
20
35.86 11.92
12.68
4.73
47. IO
4.70
59'59
Mr. Fenwick, the author of "Effays on Practical Mechanics,"
made a numerous fet of experiments on fome of the beſt mills
for grinding corn, in order to form a fet of tables illuſtrative of
the effect of a given quantity of water, in a given time, applied
on an overshot water wheel of a given fize. His obſervations,
tables, and examples, will form the remaining part of this article,
The quantity of water expended on the water-wheel was
meaſured with great exactnefs; the corn ufed was in a medium
ſtate of drinefs; the mills, in all their parts, were in a medium
working ftate; the millftones, making from 90 to 100 revolu-
tions per minute, were from 4 to 5 feet in diameter.
Σ
The refult of the experiments was, that the power requifite
to raiſe a weight of 300lbs. avoirdupois, with a yelocity of 190
feet per minute, would grind 1 boll of good rye in 1 hours
190
MACHINES.
but, for the fake of making the following tables hold in practice,
where imperfection of conſtruction exifts in ſome ſmall degree,
it is taken at 300lbs. raiſed with a velocity of 210 feet per
minute, (being 1-10th more); and for grinding 2, 3, 4, or 5
bolls of rye per hour requires a power equal to that which
could raife 300lbs. with the velocity of 350, 506, 677, or 865
feet per minute refpectively. The difference of the power re-
quifité to grind equal quantities of wheat from that for rye will
be very trifling.
The power required to raiſe a weight of 300lbs. avoirdupois,
with a velocity of 390 feet per minute, will prepare properly I
ton of old rope per week, for the purpoſe of making paper;
and for preparing, in like manner, 2 tons of the fame kind of
materials per week, requires a power able to raiſe 300 lbs.
with a velocity of 525 feet per minute, the mill working from 10
to 12 hours per day.
A SET OF TABLES, fhewing the quantity of water (ale meaſure)
requifite to grind different quantities of corn, from 1 to 5 bolls
(Winchester meaſure) per hour, applied on overshot waterwheels
from 10 to 32 feet diameter; alfo the fize of the cylinder of the
common fteam-engine to do the fame work.
The water-wheel, 10 feet di- The water-wheel, 12 feet di-
corn
ameter.
Bolls of Quantity of Diameter of
water requisite the cylinder
ground in ale gallons, of a steam-en-
per hour. per minute. gine to do the
corn
ameter.


Bolls of Quantity of | Diameter of
water requisite the cylinder
in ale gallons of a steam-en-
per minute. [gine to do the
ground
per hour.
same work,
in inches.
same work,
in inches.
I
786
12.5
I
655
플
​1056
14.6
11
873
12.5
14.6
2
1341
16.75
2
1091
16.75
2플
​1517
18.5
2호
​1343
18.5
3
1894
20'2
3
1576
20'2
3
2220
21.75
3/1/20
1840
21.75
2541
23.25
4
2117
23.25
41
2891
24.75
4를
​2408
24.75
3242
26.25
5
2700
26.25
The water-wheel, 11 ft. diam.
Bolls per Water, gallons Cylinder, in
hour.
per minute.
inches.
The water-wheel, 13 ft. diam.
Bolls per Water, gallons Cylinder, in
per minute.
inches.


hour.
2
Cn. p p. (A) G3 N 13, kad put,
I
705
12.5
I
it
945
14.6
1188
16.7,5
2월
​1454
18.5.
1723
20'2
3/
2014
21.75
2306
23.25
1122 cm 4
606
12.5
806
14.6
1009
16.75
22/2
1234
18.5
3
1458
20'2
31/
1705
21.75
1952
23.25
4€
2626
24.75
4/2
2223
24.75
2944
26.25
5.
2494
26.28
Flour-mill.
191
The waterwheel, 14 feet di- The water-wheel, 17 feet di-
"ameter.
Bolls of Quantity of
Diameter of
corn waterrequisite the cylinder
ground in ale gallons, of a steam-en-
per hour. per minute. gine to do the
same work,
in inches.
corn
ground
ameter,


Bo'ls of Quantity of Diameter of
water requisite the cylinder
in ale gallons, of a steam-en-
per hour, per minute. gine to do the
same work,
in inches.
I
564
I
12°5
458
12.5
MAN
1 /
Hier
740
14.6
1/
628
14.6
927
16,75
2
770
16.75
2/
1140
18.5
2/
943
18:5
3
5
HA
Mr erg ný og leg
1353
20'2
3
1117
20'2
fer
1583
21.75
3/
1300
21.75
1811
23.25
1482
23.25
2060
24.75
1695
24.75
2306
26.25
5
1906
26,25
The water-wheel, 15 feet di- The water-wheel, 18 feet di
ameter.
Rolls per Water, gallons Cylinder, in
ameter,


Bolls per Water, gallons] Cylinder, in
hour.
per minute,
inches.
hour.
per minute.
inches.
M
IN 2 M
535
12.5
I
I
2
21.
3
3/1/2
710
14.6
894
16.75
1090
18.5
2
1290
20.2
3
1503
21.75
4
1717
23.25
4/1/20
1967
·24.75
HİN
122 mm 4 +
440
12:51
11/
595
14.6
730
16.75
860
18.5
1054
20'2
3/1/20
1227
21.75
1400
23.25
4/2
1600
24'75
· 5
2211
26.25
5
+8co
26.25
!
:
The water-wheel, 16 feet di- The water-wheel, 19 feet di-
¡ameter.
Bolls per Water, gallons Cylinder, in
ameter,



Bolls perWater, gallons! Cylinder, in
hour.
per minute.
inches.
hour.
per minute.
inches.
I
491
1 /
650
£2.5
14.6
811
16.75
HHN
I
4II
550
12:5
14:6
2
690
16.75
993
18.5
2폴
​845
18.5
3.
1176
20.2
3
1000
20°2
31.
1380
21.75
3/1/
1165
21.75
4
1582
23.25
4
1330
23.25
1802
24.75
44
1517
24.75
2023
26.25
5
1707
26.25
192
MACHINES.
The water-wheel, 20 feet di-The water-wheel, 23 feet di-
Corn
ameter.
Bolls of Quantity of Diameter of
waterrequisite the cylinder
ground in ale gallons, of a steam-en-
per hour per minute. gine to do the
same work,
in inches.
ameter.



Bolls of Quantity of
corn
Diameter of
water requisite the cylinder
ground in ale gallons, of a steam-en-
per hour. per minute. gine to do the
same work,
in inches.
I
.392
12.5
530
14.6
2
675
16:75
2골
​808
18.5
3
945
20'2
HHN 2 ~
I
338
12:5
NM
454
14.6
2
570
16.75
2 1/2
HIN
707
18.5
3
824
20°2
31
ΙΙΙΟ
21.75
3
964
21.75
4
1270
23°25
4
1445
24.75
+4
I [24
23.25
1258
24.75
5
1623
26.25
1412
26.25
The water-wheel, 21 feet di- The water-wheel, 24 feet di-
ameter.
Bolls per Water, gallons Cylinder, in
hour.
ameter.


Bolls per Water, gallons Cylinder, in
hour. per minute.
per minute.
inches.
inches,
I
I
મા
Mex
HH22 cam the 1
370
12.5
I
327
12.5
500
14.6
11
436
14.6
635
16.75
2
545
16.75
2/1/2
767
18.5
21/
671
18.5
900
20.2
3
788
20'2
3/2/2
4
1060
21.75
34/
920
21.75
1212
23°25
4
1055
23.25
41
1379
24.73
41
1204
24.75
5
1547
26.25
5
1350
26.25
The water-wheel, 22 feet di- The water-wheel, 25 feet di-
ameter.
Bolls per Water, gallons Cylinder, in
ameter.


Bolls per Water, gallons, Cylinder, in
hour.
per minute.
inches.
bour.
per minute.
inches.
I
359
12.5
I
316
12.5
11
473
14.6
I L
418
14.6
2
594
16.75
2
520
16.75
23
722
18.5
21
635
18.5
3:
860
20*2
3
752
20'2
3/1/2
1007
21.75
31/2
876
21.75
4
1153
23°25
985
23°25
4½
HIN
1313
24.75
1150
24.75
ૐ
1472
26.25
5
1302
26.25
Flour-mill.
193

The water-wheel, 26 feet di-The water-wheel, 29 feet di-
corn
ameter.
Bolls of Quantity of Diameter of
water requisite the cylinder
ground in ale gallons, of a steam-en-
per hour per minute. gine to do the
same work,
in inches.
corn
ameter.
Bolls of Quantity of Diameter of
water requisite the cylinder
in ale gallons, of à steam én-
per minute. gine to do the
ground
per hour.
same work,
in inches.
I
2
2
3
5
MIN
HHN 2 en es et fi dey
303
12.5
I
1/
403
14.6
504
617
16.75
18.5
730
20*2
3
Hel
Mica
HHN 2 M
274
12.5
2
2
플
​363
455
14.6
16.75
557
18.5
660
20°2
31
852
21'75
3 1/
770
21.75
4
45
975
23.25
4
880
23.25
IIII
24*75
4/1/2
1005
24775
12:47
26.25
1130
26.25
The water-wheel, 27 feet di-The water-wheel, 30 feet di-
ameter.
Bolls per Water, gallons] Cylinder, in
ameter.
Bolls perfWater, gallons Cylinder, in
hour.
per minute.
inches.
hour.
per minute,
inches.
I
293
12.5
Ι
267
12.5
I
1 //
385
14.6
1/1/
355
14'6
2
482
16.75
2
447
16.75
2 //
593
18.5
2
545
18.5
3
703
20.2
3
645
20:2
3 1/2
82.2
21.75
3 -/-/
750
21.75
4
940
23.25
4
858
23°25
1070
24.75
4풀
​983
24.75
1200
26.25
5
1106
26.25
The water-wheel, 28 feet di-The water-wheel, 31 feet di-
ameter.
ameter.
Bolls per Water, gallons Cylinder, in
hour.
inches.
inches.
Bolls per Water, gallons Cylinder, in
hour. per minute.
inches.
WW N 2 --
I
282
플
​370
12.5
14.6
I
463
2/2
3
HIN
570
676
16.75
18.5
20.2
3
HIN
791
21.75
905
23.25
4골
​1030
24.75
5
1153.
26.25
HIN
HH22 c c 4 4 4
256
12'5
I플
​340
14.6
426
16.75
2/
520
18.5
620
20.2
717
21.75
827
23.25
4플
​940
2475
5
1058
26.25
VOL. II.
*
1
194
MACHINES.
The water-wheel, 32 feet diameter.

per hour.
Bolls of corn ground Quantity of water re- Diameter of the cylin-
quisite in ale gallons, der of a steami-engine
to do the same work,
per minute.
in inches.
I
245
I
325.
12.5
14.6
406
16.75
2₤
496
18.5
3
588
20°2
3 /1/10
690
21.75
4
791
23°25
4/
900
24.75
1012
26.25
5
To make the foregoing tables applicable to mills intended to
be turned by underſhot or breaft water-wheels: from Smeaton's
experiments it appears that the power required on an under-
fhot water-wheel, to produce an effect equal to that of an over-
fhot (to which the tables are applicable), is as 2'4 to 1; and
alſo the power required on a breaft water-wheel, which receives
the water on ſome point of its circumference, and afterwards
deſcends on the ladle boards, to produce an equal effect with an
overſhot water-wheel, is as 175 to 1.
A TABLE, fhewing the neceſſary fize of the cylinder of a common
Steam-engine to grind different quantities of corn, from 1 to 12 balls
(4 to 48 bufbels Wincheſter meaſure), per hour.
Bolls of corn ground, Diameter of the cylinder,

per hour.
I
11/
2
21/
3/2/2
in inches.
1223
14.6
16.75
18.5
20'2
21.75
4
23.25
44
24.75
5
26.25
27.25
28.1
6/1/
29
Ha
728
81
9
IO
10/1/
II
12
29.8
31'I
32
33.3
34.2
35°2
36
373
38
38.85
39'5
N.B. This table will be applicable to any improved steam-engine, as well as
that of the common kind, if the ratio of their efficacies is known.
-}
195
Fly.
Application of the tables.
EXAMPLE İ.—If a ftream of water, producing 808 gallons ale
meaſure per minute, can be applied on an overfhot water-wheel
20 feet diameter, what quantity of corn will it be able to grind
per hour?
Look in the tables under a 20 feet water-wheel, and oppo-
fite 808 gallons will be found 2 bolls of corn ground per
hour.
EXAMPLE II.—If a ftream of water, producing 808 gallons
ale meaſure per minute, can be applied to an underfhot water-
wheel 20 feet diameter, what quantity of corn can it grind per
hour?
It is found by the tables, that, if applied on an overshot
water-wheel 20 feet diameter, the ftream will grind 2½ bolls.
per hour; and, from page 194, the power required by the under-
hot to that of the over hot water-wheel, to produce an equal ef-
fect, is as 2.4 to 1; therefore, as 2'4: 1:25: 1'04 bolls of
corn ground per hour by means of the ſtream.
EXAMPLE III.-If a ſtream of water, producing 808 gal-
lons ale meaſure per minute, can be applied on a breaft water-
wheel 20 feet diameter, what quantity of corn can it grind per
hour?
It is found by the tables, that, if applied on an overſhot water
wheel of equal fize, 24 bolls of corn will be ground per hour;
and, from page 194, the power of a breaft water-wheel to that
of an overfhot water-wheel, to produce an equal effect, is as
175 to 1; therefore, as 1751 :: 25: 1'42 bolls of corn
ground per hour by the ſtream.
EXAMPLE IV. Of what diameter muft the cylinder of a
common ſteam-engine be made, to grind 10 bolls of corn per
hour?
By looking in the table, page 194, oppofite 10 bolls ground
per hour, the diameter of the fteam cylinder will be found to be
36 inches.
FLY, is a name given to a certain appendage to many ma-
chines, either as a regulator of their motions, or as a collector of
power. When uſed as a regulator, the fly is commonly a heavy
diſk or hoop balanced on its axis of motion, and at right angles
to it: though fometimes a regulating fly confifts of vanes or
wings, which as they are whirled round meet with confiderable
refiſtance from the air, and thus foon prevent any acceleration
in the motion: but this kind of regulator fhould rarely, if ever,
be introduced in a working machine, as it waftes much of the
moving force. When the fly is ufed as a collector of power, it
02
196
MACHINES.
↑
it is frequently feen in the form of heavy knobs at the oppofite
ends of a ſtraight bar; as in the coining-prefs. In arts. 18..23.
of the introductory part of this volume the reader will find feve-
ral remarks on the nature and operation of the different kinds of
flies uſed in machines.
FOOT-MILL, is a mill for grinding corn or any other fub-
ſtance, moved by the preffure of the feet of men or animals. In
fome foot-mills, a horſe or an ox is fixed to a ſtall upon a floor
above a vertical wheel; and a hole is made in the floor in the
place where the hind feet of the animal ſhould ſtand, thus ad-
mitting thofe feet to prefs upon the rim of a wheel, and cauſe
the wheel to turn upon its axle, and give motion to the whole
mill. But in this kind of machine the animal will be obliged
very unnaturally to move his hind feet while his fore feet will be
at reft: and further, the motive force being applied near the
vertex of the wheel will act but with little advantage; and the
work done will be comparatively trifling.
A much more judicious conftruction of a foot-mill is given
in G. A. Bockler's Theatrum Machinarum, publiſhed at Nu-
remburgh, in 1661. This mill is reprefented in fig. 1. pl. XV.
A is an inclined wheel, which is turned by the weight of a man,
and the impulfive force of his feet while he ſupports himſelf, or
occafionally puſhes with his hands at the horizontal bar H. The
face of this wheel has thin pieces of wood nailed upon it at
proper diftances, to keep the feet of the man from flipping
while he puſhes the wheel round; and the under fide has pro-
jecting teeth or waves which catch into the cogs of the trun-
dle B, and by that means turn the horizontal fhaft G with
its wheel C: this latter wheel turns the trundle D, the axle of
which carries the upper millſtone E. This kind of footmill
will anfwer extremely well to grind malt, &c. when no very
great power is required. The advantages and diſadvantages of the
inclined wheel have been ſtated under the article CRANE, when
deſcribing the contrivance of Mr. Whyte, which is the fame as
this of Bockler's in refpect to the wheel.
FORCER, TEMPORARY, for a pump, is a contrivance to pro-
duce a conſtant ftream. A very fimple forcer of this kind has
been devifed by Mr. R. Trevithick: it confiſts in fixing a barrel
with a folid pifton along the fide of the common pump, in ſuch
a manner, that the lower ſpace of the additional barrel may com-
municate with the ſpace between the two valves of the pump;
and, laftly, by connecting the rods fo that they may work to-
gether. This is fhewn in fig. 1. plate IX.; and the effect is, that
when the piſtons are raiſed, the ſpaces beneath, A and B, be-
come filled by the preffure of the atmoſphere, at the ſame time
that the upper column flows out at E. But again, when the
Gibbet of a Crane.
197
piſtons defcend, the valve C fhuts, and, confequently, the water
driven by the piſton in B muſt aſcend through A, and continue
to produce an equal diſcharge through E in the down ſtroke.
Nich. Journ. No. 7. N. S.
FOUNTAIN, HERO'S. See HYDRAULIC machines, No. 6.
GIBBET, or JIB, of a crane, the projecting beam, upon the
extremity of which is fixed a pulley for the rope to paſs over that
raiſes the weight: it is reprefented by DEF, in fig. 3. pl. IX.
Jibs of the ufual conftruction turn on two folid gudgeons. The
rope by which the goods are raiſed paffes over the upper
gudgeon, and is confined between two ſmall vertical rollers,
in order that it may conftantly lead fair with the pulley or fheave
at the extremity of the jib. According to this conftruction,
whenever the crane turns round its axis, the rope is bended fo
as to form an angle more or leſs acute, which cauſes a great in-
creaſe of friction, and produces a continual effort to bring the
arm of the jib into a parallel poſition to the inner part of the
rope. Theſe inconveniences may appear to be trifling on paper,
but in actual practice they are of no ſmall importance, for they
neceffarily imply a much greater exertion of power in raifing
goods, and the application of a conſtant force to keep the
jib in the pofition that may be requifite; while the partial
ftrefs which is exerted on only a few ftrands of the rope, when
bended into an acute angle, infallibly deſtroys it in a very ſhort
time.
The fimple conftruction propoſed by Mr. J. Bramah obviates
all theſe defects, and at the fame time poffeffes the very defirable-
property of permitting the jib of what is termed a campſhut or
landing crane wholly to revolve round its axis, and to land
goods at any point of the circle defcribed by the arm of the
jib.
It confifts in perforating the axis or pillar of the crane, and in
conducting the rope through this perforation by means of an ad-
ditional pulley fixed on the top of the arm of the jib. The rope
proceeds from the goods which are hoifted, through a pulley fixed
as uſual at the extremity of the jib; it then paffes over another
pulley fixed at the oppofite extremity of the jib, and is by this
pulley conducted through the perforated axis or pillar to a third
pulley; whence it is immediately directed to the crane by which
the weight is elevated.
It is almoſt unneceſſary to ſtate that the lower axis is ufually
fixed in an oil box, and that friction rollers are applied to the axis
wherever the circumstances may render it neceffary.
When great weights are to be raiſed, as large ftones from a
quarry, or pieces of ordnance from a fhip to a quay, the crane is
commonly a fixed one, and only the gibbet moveable, from
.198
MACHINES.
•
which the weight hangs. Here, in the common way of work-
ing a crane, the rope of which runs between two vertical rollers,
there is often much danger in turning the gibbet upon its axis.
A fmall rope, called a guide-rope, is faftened to the weight, or to
the upper part of the gibbet near its extremity, which a man
pulls to bring the weight over the place where it is to be
lowered. Now, in performing this, the main rope not con-
tinuing parallel to the arm of the gibbet, gives the weight a
tendency towards that fide to which it deviates, and that fome-
times fo fuddenly, that without care and much force applied,
the load will fwing with great violence, and do much mischief.
To prevent this, Mr. Ralph Allen of Bath, about the year 1728,
recommended the following method: Upon the ſhaft of the gib-
bet let there be fixed an iron wheel with ſeveral teeth or cogs, to
be carried round by a pinion fixed upon a horizontal axis, fuch
axis paffing through the wall or frame-work behind the ſhaft of
the gibbet, and having at its further extremity a vertical wheef
with handles projecting from the rim in the plane of the wheel,
A man ſtanding at this wheel is out of the reach of danger from
the load, and by applying a ſmall portion of his ftrength at
the handles of the wheel he can eaſily bring the gibbet and
its load to any pofition required, and retain it as long as necef-
fary in that pofition. A figure reprefenting this contrivance is
given in the Phil. Tranf. No. 411. and in Ferguſon's Select Lec-
tures.
GIMBALS, a contrivance by means of which barometers,
veffels of oil, mariner's compaffes, &c. may be fufpended fo as
to arrange their upper parts horizontally. The nature of this
contrivance will be at once underſtood by fhewing its applica-
tion to a mariner's compafs. It confifts of a hoop or ring
ſupported upon two pins diametrically oppofite each other, and
iffuing from the external furface of the ring in fuch a direction
that both lie in the fame diametrical line. When the hoop is
fufpended on theſe pins it is at liberty to turn freely about
the diameter of which they conſtitute the prolongation. The
notches or holes of fupport are difpofed horizontally. The
compaſs-box itſelf is placed in a fimilar ring with two project-
ing pivots; and theſe pivots are inferted in holes made in the
former ring at equal diftances from each of its pivots. If there-
fore the whole be left at liberty, the compafs-box may vibrate
upon the diametral line of the outer ring, as well as upon a
line formed by its own pivots, at right angles to that diametral
line. The confequence of this arrangement is, that the centre
of gravity of the compafs-box will difpofe itſelf immediately be-
neath the interfection of both lines on which it is at liberty to
movethat is to fay, if the weight of the box and its component
Glazier's Vice.--Gravimeter.
199
parts be properly difpofed, the compaſs will affume a poſition in
which the upper furface fhall be horizontal.
GIN. See CRAB.
I
GLAZIER'S VICE, is an inftrument for drawing window
lead. See fig. 3. pl. XII. PG, OH, are two axles running
in the frame KL, ML. C, D, two wheels of iron cafe-hard-
ened, 14inch broad, and of the thickneſs of a pane of glaſs';
thefe wheels are fixed to the axles, and run very near one an-
other, their diſtance not exceeding of an inch: acrofs their
edges feveral nicks are cut, the better to draw the lead through.
E, F, are two pinions each of twelve leaves, turning one another
and going upon the ends of the axles, which are ſquare, being
kept faft there by the nuts P, Q, which are fcrewed faſt with a
key.. A, B, are two cheeks of iron, cafe-hardened, and fixed on
each fide to the caſe with ſcrews; theſe are cut with an open-
ing where the two wheels meet, and ſet fo near to the wheels
as to leave a ſpace equal to the thickneſs of the lead; ſo that
between the wheels and the cheeks there is left a hole of the
form repreſented at N, which is the ſhape of the lead when cut
through. The frame KLML is held together by croſs bars paff-
ing through the fides, and ſcrewed on: and a cover is put over
the machine to exclude the duft. The whole is fcrewed down
faſt to a bench by ſcrew nails LL. When the vice is uſed, the
lead to be drawn is firft caft in moulds, into pieces a foot long,
with a gutter on each fide. One of thefe pieces is taken, and
an end of it ſharpened a little with a knife; then, being put into
the hole between the wheels, by turning the handle I the lead is
drawn through the vice, and receives the form defigned.
GRAVIMETER, the name given by M. Guyton to an in-
ftrument for meaſuring ſpecific gravities: he adopts this name
rather than either areometer or hydrometer, becauſe theſe latter
terms are grounded upon the ſuppofition that the liquid is always
the thing weighed; whereas, with regard to folids, the liquid is
the known term of compariſon to which the unknown weight is
referred.
Guyton's gravimeter is executed in glafs, and is of a cylin-
dric form, being that which requires the fmalleft quantity of
fluid, and is on that account preferable, except ſo far as it is
neceffary to deviate for the ſecurity of a vertical poſition. Like
Nicholſon's Hydrometer (art. 404. vol. I.) it carries two bafins;
one of them fuperior, at the extremity of a thin ftem, towards
the middle of which the fixed point of immerfion is marked.
The other, or lower bafin, terminates in a point; it contains
the ballaft, and is attached to the cylinder by two branches.
The moveable ſuſpenſion by means of a hook has the incon
1
200
MACHINES.
>
venience of ſhortening the lever which is to fecure the vertical
pofition.
The cylinder is 22 millimetres (0.71 inch) in diameter; and
21 centimetres (6.85 inches) in length. It carries in the upper
bafin an additional conftant weight of 5 grammes (115 grains).
Thefe dimenfions might be increaſed fo as render it capable of
receiving a much more confiderable weight; but this is unne-
ceffary. M. Guyton has added a piece which he calls the
plongeur, becauſe in fact it is placed in the lower baſin when
ufed, and is confequently entirely immerfed in the fluid. It is
a bulb of glaſs loaded with a fufficient quantity of mercury,
in order that its total weight may be equal to the conſtant ad-
ditional weight, added to the weight of the volume of water dif-
placed by this piece. It will be readily underſtood that the
weight being determined at the ſame temperature at which the
inftrument was originally adjuſted, it will fink to the fame
mark on the ftem, whether it be loaded with a conſtant ad-
ditional weight in the upper bafin, or whether the effect of
this weight be produced by the additional piece in the lower
difh. From this explanation there will be no difficulty in
feeing how this inftrument may be adapted to every caſe in
practice.
It may be uſed, 1. for folids. It differs not in this reſpect
from. Nicholſon's hydrometer. The only condition will be, as
in his inſtrument, that the abfolute weight of the body to
be examined fhall be rather lefs than the conftant additional
weight, which in this inftrument is 5 grammes, or 115 grains.
2. For liquids of leſs ſpecific gravity than water, the inftru-
ment, without the additional weight above mentioned, weighs
about 2 decagrammes (459 grains) in the dimenfions before laid
down. It would be eafy to limit its weight to the utmoſt ac-
curacy. We have therefore the range of one-fifth of buoyancy,
and conſequently the means of aſcertaining all the intermediate
denfities from water to the moſt highly rectified ſpirit of wine,
which is known to bear in this refpect the ratio of 8 to 10 with
regard to water.
3. When liquids of greater fpecific gravity than water are to
be tried, the conftant weight being applied below, by means
of the additional piece, which weighs about 6 grammes (138
grains), the inftrument can receive in the upper baſin more
than 4 times the ufual. additional weight, without lofing the
equilibrium of its vertical pofition. In this ftate it is capable
of fhewing the ſpecific gravity of the moſt concentrated acids.
4. It poffeffes another property common to Nicholſon's in-
Arument, namely, that it may be ufed as a balance to determine
Gravimeter.
201
the abfolute weight of fuch bodies as do not exceed its additional
load.
5. Laſtly, the purity of the water being known, it will indicate
the degrees of rarefaction and condenſation in proportion to its
own bulk.
This inftrument may be readily conſtructed by any workman
in glaſs. The additional piece for the lower bafin will require
ſome attention to make it perfectly agree with the conſtant
upper weight, as to the immerfion of the inftrument. But this
object may, by careful adjuſtment, be aſcertained with the ut-
moſt certainty and accuracy. The bulb of glafs is for this pur-
pofe drawn out to a fine point; a fufficient quantity of mercury
is then introduced to fink it, and the aperture cloſed with a little
piece of wax. The bulb being then placed in the lower balın
of the inſtrument, the upper baſin is to be loaded until the mark
on the ſtem becomes accurately coincident with the ſurface of
the water. The fum of the weights added above is preciſely
equal to that of the quantity of mercury neceffary to be added
to that in the glaſs bulb; which done, nothing more is needed
than to feal the point by fufion, taking care not to change its
bulk.
The whole is rendered portable by means of a cafe in which
all the delicate parts are fecured from preffure, and the heavier
parts ſupported in ſuch a manner as to refift the exceſs of motion
they are capable of acquiring by virtue of their maſs. This laft
circumftance is frequently overlooked by ſuch workmen as are
employed in the package of inftruments; whence it neceffarily
follows, that fome ftrain or fracture must be produced when mat-
ters of very unequal denſity are expoſed to receive a common im-
pulfe.
To find the ſpecific gravity of any folid by the gravimeter,
obferve this rule: "From the weight in the upper diſh, when
the inſtrument is properly immerfed in the unknown fluid, take
the weight which is placed with the body in the ſame ſcale at
the like adjuſtment. The remainder is the abſolute weight of
the folid. Multiply this by the ſpecific gravity of the fluid, and
referve the product. From the additional weight when the
body is placed in the lower bafin, take the weight when it was
placed in the upper. The remainder will be the loſs of weight
by immerfion. Divide the referved product by the lofs by im-
merſion, and the quotient will be the ſpecific gravity of the folid
with regard to diſtilled water at the ſtandard temperature and
preffure.
>>
To find the ſpecific gravity of a fluid proceed thus: “ To the
weight of the gravimeter add the weight required in the upper
bafin to fink it in the unknown fluid. Again, to the weight of
票
​202
MACHINES.
the gravimeter add the weight required in the fame manner to
fink it in diftilled water. Divide the firft fum by the latter,
and the quotient will be the ſpecific gravity of the fluid in
queftion.",
4
For figures of the gravimeter, fee Annales de Chimie, tome 21,
or Nicholfon's Journal, vol. I. 4to.
HANDMILLS, are commonly uſed for fome culinary pur-
pofes, as the grinding of coffee, pepper, and the like. Some-
times handmills of larger fize are ufed to grind malt, wheat,
&c. and in fuch cafes the hand is generally applied to a winch.
handle. But in Beckler's Theatrum Machinarum there is a de-
ſcription of a mill, in which the effort of a man is applied to a
lever moving to and fro horizontally, nearly as in the action of
rowing as this is a very advantageous method of applying hu-
man ftrength, the effort being greatly affifted by the heavinefs of
the man in leaning back, we fhall give a brief de feription of this
kind of mill, which is represented in fig. 4. pl. XII. The verti-
cal ſhaft EG carries a toothed wheel C, and a ſolid wheel F; the
latter being intended to operate as a regulating fly. Upon the
crank AB hangs one end of an iron bar I, the other end of
which hangs upon the lever HK; the motion being pretty free
at both ends of this bar I. One end of the lever HK hangs
upon the fixed hook K, about which as a centre of motion it
turns. Then, while a man, by pulling at the lever HK, moves
the extremity H from H to N, the bar I acting upon the crank
AB gives to the wheels C and F half a rotation; and the mo-
mentum they have acquired will carry them on, the man at the
lever fuffering it to turn back from N to H, while the other half
of the rotation of the wheels is completed. In like manner an-
other fufficient pull at the lever HK gives another rotation to the
wheel C, and fo on, at pleaſure. The wheel C turns by its
teeth the trundle D, the ſpindle of which carries the upper mill-
ftone, just as the fpindle D carries round the upper ftone in fig. 1.
pl. XV.
In this mill the nearer the end of the bar I upon the lever
HK is to the fixed hook K, the eaſier, cæteris paribus, will the
man work the mill. If the number of teeth in the wheel C be
6 times the number of cogs in the trundle D, then the la-
bourer by making 10 pulls at the lever H in a minute will give
60 revolutions to the upper mill-ftone in the fame ſpace of
time.
The Society of Arts have lately adjudged a filver medal to
Mr. Garnett Terry, of City Road, Finfbury-fquare, for his in-
vention of a mill to grind hard ſubſtances, by means of a wheel
turning upon a horizontal axis inſtead of a vertical one, as in the
common construction. Mr. Terry has conſtructed this mill on
1
Heart-wheel-Hydraulic Engines.
203
large fcale; there is alſo a model depoſited in the collection of
that fociety.
Plate VIII. fig. 4. A. The hopper or receptacle of the articles
which are intended to be ground.
B. A fpiral wire, in the form of a reverfed cone, to regulate
the delivery of them.
C. An inclined iron plate, hung upon a pin on its higher end;
the lower end refts on the grooved axis D, and agitates the
wire B.
D. The grooved axis, or grinding cylinder, which acts againſt
the channelled iron plate E.
F. A fcrew on the fide of the mill, by means of which the
iron plate E is brought nearer to or removed further from the
axis D, according as the article is wanted finer or coarſer.
G. The handle by which motion is given to the axis.
H. The tube from whence the articles, when ground, are re-
ceived.
*
** The front of the mill is taken off, in order to fhew its in-
terior conftruction.
HEART-WHEEL is the name given in England to a well
known method of converting a circuitous motion into an alter-
nating rectilinear one, which is common in cotton-mills. It is
an ellipfe turned either on an axle, or by means of a winch änd
handle on one of its foci, or its centre, on whoſe edge a move-
able point or circle preffes; the latter receives an alternating
motion from the circumference of the ellipfe, and preffes it in
its revolution to different diſtances from the centre of motion.
This method was contrived, we believe, by fir Samuel Morland,
about the year 1685. The practical difadvantages of this con-
trivance are the inequality of preffure and of moving force which
will be required at different parts of the rotation of the ellipfe,
and the conſequent wearing of fome parts of it much faſter than
others, which will render it frequently neceffary to have new
elliptical wheels. A late application of the heart-wheel has been
already mentioned, under the word COINING.
HOOKE'S JOINTS, or, as they are often called, univerfat
joints, have been defcribed in the introductory part of this vo-
lume.
HUNTER'S DOUBLE SCREW, was defcribed in art 161.
vol. I.
HYDRAULIC MACHINES, are ftructures contrived for the
purpoſe either of conveying water from one fituation to an-
other, particularly from a lower to a higher; or, by means of
the force or preffare of water, to perform fome mechanical
operation, as grinding, boring, fawing. The former kind of
1
204
MACHINES.
hydraulic engines will only be ſpoken of here; the latter being
defcribed under the various heads FLOUR-MILL, FLAX-MILL,
SAW-MILL, &c.
1. Of all the machines the ancients invented to raiſe water, it
appears that though Archimedes's fcrew (fee Archimedes's SCREW
in this volume) was the most curious, the tympanum, mentioned
by Vitruvius, elevated the greateſt quantity at once: a brief de-
fcription of this may fuffice, as preparatory to the account of a
machine made in imitation of it, but more ingenious and more
perfect.
The tympanum is a great hollow wheel, forming a kind of
barrel or drum (as its name imports), compoſed of feveral planks
joined together, well calked and pitched, and having a horizontal
axle on which it turns: the interior of this drum is divided
into 8 equal ſpaces by as many partitions placed in the direc-
tions of the radii; each ſpace or cell has an orifice of about half
a foot in the rim of the drum or wheel, fo fhaped as to facilitate
the admiffion of the water: moreover, there are 8 hollow chan-
nels running contiguous to each other and parallel to the axle of
the wheel, each correfponding to one of the 8 large cells; into
thefe channels the water paffes out of the cells juſt mentioned,
and, after running along the channels to a convenient diſtance,
it efcapes through orifices into a refervoir placed juſt under the
axle.
Thus the water is elevated through a vertical ſpace equal
to the radius of the hollow wheel. When the tympanum is
ufed to raiſe water from a running ftream, it is moved by means
of float boards which are impelled by the ftream: but when it
is employed to raiſe ſtagnant water, there is commonly a ſmaller
wheel on the fame fhaft, which is turned by men walking in it,
as in the old walking crane. The chief defect of this machine is
that it raiſes the water in the moſt diſadvantageous ſituation pof-
fible for the load being found always towards the extremity of
a radius of the wheel, the arm of the effective lever which an-
fwers to it increafes through the whole quadrant the water
deſcribes in paffing from the bottom of the wheel to the altitude
of its centre; ſo that the power muſt act in like manner as if it
were applied at a winch handle, and cannot, therefore, act uni-
formly.
2. To remedy this defect M. de la Faye devifed a machine
which may here be deſcribed, together with the proceſs of rea-
foning that led to it.
When we develope the circumference of a circle, a curve is
deſcribed (i. e. the involute) of which all the radii are fo many
tangents to the circle, and are likewife all refpectively perpen-
dicular to the ſeveral points of the curve deſcribed, which has for
Hydraulic Engines.
205
its greateſt radius a line equal to the periphery of the circle
evolved. The truth of which is fhewn by geometricians when
treating of the genefis of evolute and involute curves.
Hence, having an axle whofe circumference a little exceeds
the height which the water is propoſed to be elevated, let the cir-
cumference of the axle be evolved, and make a curved canal
whoſe curvature ſhall coincide throughout exactly with that of
the involute juſt formed: if the further extremity of this canal
be made to enter the water that is to be elevated, and the other
extremity abut upon the fhaft which is turned; then in the
courſe of the rotation the water will riſe in a vertical direction,
tangential to the fhaft, and perpendicular to the canal in what-
ever pofition it may be. Thus the action of the weight an-
fwering always to the extremity of a horizontal radius will be
as though it acted upon the invariable arm of a lever, and the
power which raiſes the weight will be always the fame and f
the radius of the wheel, of which this hollow canal fervès ás á
bent ſpoke, is equal to the height that the water is to be raiſed,
and confequently equal to the circumference of the axle or
fhaft, the power will be to the load of water reciprocally as the
radius of a circle to its circumference, or directly as 1 to 64
nearly.
In M. de la Faye's opinion, the machine ought to be compofed
of four of theſe canals: but it has often been conftructed with
8, as reprefented in fig. 1. pl. XIX. The wheel being turned
by the impulfion of the ſtream upon the float-boards, the orifices
F, E, D, C, &c. of the curvilinear canals, dip one after another
into the water which runs into them; and as the wheel revolves
the fluid rifes in the canals f, e, d, c, &c. and runs out in a ſtream
P from the holes at O; it is received into the trough Q, and
conveyed from thence by pipes.
By this conſtruction the weight to be raiſed offers always the
fame refiftance, and that the leaft poffible, while the power is
applied in the moſt advantageous manner the circumſtances will
admit of: theſe conditions both fulfilled at the fame time furniſh
the moſt deſirable perfection in a machine. Further, this ma-
chine raiſes the water by the ſhorteſt way, namely, the perpen-
dicular, or vertical; in this reſpect being preferable to Archi-
medes's fcrew, where the water is carried up an inclined path
and befides this, each curved channel in this wheel empties all
the water it receives in every revolution, while the fcrew of Ar-
chimedes delivers only a ſmall portion of the fluid it is charged
with, being often loaded with 20 times as much water as is
diſcharged in one rotation; and thus requiring an enormous
increaſe of labour when a large quantity is intended to be raiſed
by it.
+4
208
MACHINES.
The nature and advantages of this wheel evince very forcibly
how far the fpeculations of geometers are from being fo unfruit
ful in uſeful applications, as is often infinuated by practical
men.
3. The wheel juſt deſcribed would we think be the moſt per-
fect of any that could be employed for raiſing water, had it not
the diſadvantage attending the tympanum, which is, that it can
only raiſe water to the height of its femidiameter. As in many
cafes water is to be raiſed higher than the radius of any wheel
can well be made for practice, we ſhall next deſcribe a machine
called the Noria, common in Spain, which raiſes water nearly
through a diameter. This Noria confiſts of a vertical wheel of
20 feet diameter, on the circumference of which are fixed a
number of little boxes or fquare buckets, for the purpoſe of
raiſing the water out of the well, communicating with the canal
below, and to empty it in a reſervoir above, placed by the fide of
the wheel. The buckets have a lateral orifice, to receive and
to diſcharge the water. The axis of this wheel is embraced by
four fmall beams, croffing each other at right angles, tapering at
the extremities, and forming eight little arms. This wheel is
near the centre of the horſe-walk, contiguous to the vertical axis,
into the top of which the horſe-beam is fixed; but near the bot-
tom it is embraced by four little beams, forming eight arms
fimilar to thoſe above deſcribed, on the axis of the water-wheel.
As the mule which they ufe goes round, theſe horizontal arms,
fupplying the place of cogs, take hold, each in fucceffion, of thoſe
arms which are fixed on the axis of the water-wheel, and keep it
in rotation.
This machine, than which nothing can be cheaper, throws up
a great quantity of water; yet undoubtedly it has two defects:
the firft is, that part of the water runs out of the buckets and
falls back into the well after it has been raiſed nearly to the
level of the refervoir: the fecond is, that a confiderable propor-
tion of the water to be diſcharged is raifed higher than the re-
ſervoir, and falls into it only at the moment when the bucket is
at the highest point of the circle, and ready to defcend. Theſe
inconveniences are both remedied by the contrivance mentioned
in the next paragraph.
4. The Perfian wheel is a name given to a machine for raiſing
water, which may be turned by means of a ſtream AB acting upon
the wheel CDE according to the order of the letters; (fig. 1. pl.
XIX.) The buckets a, a, a, a, &c. inſtead of being firmly faftened,
are hung upon the wheel by ſtrong pins, b, b, b, b, &c. fixed in the
fide of the rim; which muſt be made as high as the water is in-
tended to be raiſed above the level of that part of the ſtream in
which the wheel is placed. As the wheel turns, the buckets on
Hydraulic Engines.
207
the right hand go down into the water, where they are filled,
and return up full on the left hand, till they come to the top at
K; where they ſtrike againſt the end n of the fixed trough M,
by which they are overfet, and fo empty the water into the
trough; from whence it is to be conveyed in pipes to any
place it is intended for: and as each bucket gets over the
trough, it falls into a perpendicular pofition again, and fo goes
down empty till it comes to the water at A, where it is filled
as before. On each bucket is a fpring r, which going over
the top or crown of the bar m (fixed to the trough M) raiſes the
bottom of the bucket above the level of its mouth, and fo cauſes
it to empty all its water into the trough.
To determine the due relation of the power and the weight fo
that this wheel may be capable of producing the greateſt effect,
the following may be taken as a good approximation. After
having fixed the diameter of the wheel, which must be fome-
thing greater than the altitude to which the water is to be
raifed; fix alfo upon an even number of buckets to be hung at
equal diſtances round the periphery of the wheel, and mark the
pofition of their centres of motion in ſuch a manner that they
will ſtand in correfponding pofitions in every quarter of the
circle conceive vertical lines drawn through the centre of
motion of each bucket in the rifing part of the wheel; they
will interfect the horizontal diameter of the wheel in points
at which if the buckets were hung they would furnish the
ſame reſiſtance to the moving force as they do when hanging
at their reſpective places on the rim of the wheel. Thus, fup
poſing there were 18 equidiftant buckets; then while & hung
on each fide a vertical diameter of the wheel there would be
8 on the other fide, and 2 would coincide with that diameter:
in this caſe the reſiſtance ariſing from all the full buckets would
be the fame as if one bucket hung on the prolongation of the
horizontal diameter at the diſtance of 2 fin. 20° +2 fin. 40° +
2 fin. 60° + 2 fin. 80°, theſe being the fines to the common
radius of the wheel.
To know the quantity of water that each bucket ſhould con-
tain, take of the abſolute force of the ſtream, that is, of the
weight of the priſm of water whoſe baſe is the ſurface of one of
the float-boards, and whofe height is that through which water
muft fall to acquire the velocity of the ſtream; fo have we the
power that should be in equilibrio with the weight of water in
the buckets of the rifing femicircle. Then fay, as the ſum of
the fines mentioned above is to radius, fo is the power juſt
found to a fourth term, the half of which will be the weight
of water that ought to be contained in one bucket. Laftly, as
the velocity of the wheel will be to that of the ſtream nearly

208
MACHINES.
as I to 23, the quantity of revolutions it makes in any deter-
minate time becomes known, and, of conſequence, the quantity
of water the wheel will raiſe in the fame time; fince we know
the capacity of each bucket, and the number of them emptied in
every revolution of the wheel.
5. Another mechanical contrivance for the purpoſe of railing
water is a chain-pump. This is now generally made from 12 to
24 feet in length; confifts of two collateral fquare barrels, and
an endleſs chain of piftons of the fame form fixed at proper
diſtances. The chain is moved round a coarſe kind of wheel-
work, fixed fometimes at one end, but often at both ends of the
machine. The teeth of the wheel-work are fo contrived as to
receive one half of the flat piſtons and let them fold in; and
they take hold of the links as they riſe. A whole row of the
piſtons (which go free of the fides of the barrel by about a
quarter of an inch) are always lifting when the pump is at
work; and, as this machine is generally worked briskly, the
piftons or pallets bring up a full bore of water in the pump.
Chain-pumps are wrought fometimes by men turning winches,
fometimes by horfes, and fometimes by the impulſe of a ſtream
of water: they are likewiſe ſo contrived that by the continual
folding in of the piſtons, ftones, dirt, or whatever comes in the
way, may be cleared off: they are therefore often uſed to drain
ponds, fewers, and remove foul water, when no other pump
could be employed.
Chain-pumps are not merely fixed in a vertical poſition, but
are often inclined; and in the latter cafe they are in a ſtate of
the greateſt perfection, or raiſe the moſt water, when the breadth
of the pallets is equal to their diſtance from each other, and the
plane is inclined under an angle of 24° 21'.
It is not unuſual for chain-pumps to be erected without a
barrel to receive the piftons, after the manner reprefented in
fig. 3. pl. XIX. The pallets are converted into ſquare boxes
5, s, &c. which are raiſed by means of hexagonal axles, each
fide of the hexagon being equal to the diſtance from box to box:
the boxes defcend with their mouths downwards, and forententhe
water.
Another contrivance for raifing water fimilar to the chain-
pump is an endleſs rope with ftuffed cufhions hung upon it,
which, by means of two wheels or drums, are cauſed to rife
in fucceffion in the fame barrel, and to carry water with them.
From the refemblance of this apparatus to a string of beads, it is
ufually called paternofter-work. But in this, as well as the chain-
pump, the magnitude of the friction is a formidable practical ob-
jection.
6. Jets and fountains are not now confidered as conducive to
Hydraulic Engines.
209
pictureſque beauty; nor can they be reckoned of much utility,
except perhaps in hot climates: we have not therefore defcribed
any in this work. But in the fountain of Hero of Syracuſe a
principle is introduced which has been found of great utility in
larger works; for the head of water is actually lower than the
orifice, but the preffure is communicated by the intervention of
a column of air: the conſtruction of this fountain is as follows.
It conſiſts of two veffels KLMN (fig. 5. pl. XIX.) and OPQR,
which are cloſe on all fides. A tube AB, having a funnel at
the top, paffes through the uppermoſt veffel without communi-
cating with it, being foldered into its top and bottom. It alſo
paffes through the top of the under veffel, where it is likewiſe
foldered, and reaches almoft to its bottom. This tube is open at
both ends. There is another open tube ST, which is foldered
into the top of the under veſſel and the bottom of the upper vef-
fel, and reaches almoſt to its top. Theſe two tubes ferve alſo to
fupport the upper veffel. A third tube GF is foldered into the
top of the upper veffel, and reaches almoſt to its bottom. This
tube is open at both ends, but the orifice G is very fmall. Now
ſuppoſe the uppermoft veffel filled with water to the height EN,
Ee being its furface a little below T. Stop the orifice G with
the finger, and pour in water at A. This will.defcend through
AB, and compreſs the air in OQRP into lefs room. Suppoſe
the water in the under veffel to have acquired the furface Cc,
the air which formerly occupied the whole of the ſpaces OPQR
and KL e E will now be contained in the ſpaces o P c C and.
KL e E; and its elafticity will be in equilibrio with the weight
of the column of water, whoſe baſe is the furface E e, and whofe
height is A c. As this preffure is exerted in every part of the
air, it will be exerted on the furface E e of the water of the
upper veffel; and if the pipe FG were continued upwards, the
water would be fupported in it to a height e H above E e, equal
to A c. Therefore, if the finger be now taken from off the
orifice G, the fluid will fpout up through it to the fame height
as-if it had fallen through a tube whofe altitude is e H. So long
as there is any water in the veffel KLNM there will be a dif-
charge through the orifice: therefore the play of the fountain
will continue whilst the water contained in the upper veffel,
having ſpouted out, falls down through the pipe AB: the height
of the water meaſured from the bafm VAW to the furface of
the water in the lower veffel OPQR is always equal to the
height meaſured from the top of the jet to the furface of the
water in the veffel KLMN. Now, fince the furface Ee is al-
ways falling, and the water in the lower veffel always rifing,
the height of the jet must continually decreafe, till it is fhorter
VOL. II.
·
P
/
210
MACHINES.
by the deph of KLMN, which is empty, added to the depth of
OPQR, which is always filling; and when the jet is fallen fo
low it immediately ceafes to play.
7. A machine defigned to raiſe water to a great height for
the irrigation of land, in fuch ſituations as have the advantage of
a ſmall fall, is deſcribed in Dr. Darwin's Phytologia: as it depends
on the principle of Hero's fountain, it may properly be inſerted
here.
Fig. 4. pl. XIX. a, b, is the ſtream of water.
b, c, c, repreſents the water-fall, fuppofed to be 10 feet.
d, e, are two leaden or iron veffels, containing a certain quan-
tity of water, which may be computed to be about 4 gallons
each.
f, g, h, i, k, l, are leaden veffels, each holding about two
quarts.
o, p, two cocks, each of which paffes through two pipes, open-
ing the one and clofing the other.
q, r, is a water-balance, that moves on its centres; and by
which the two cocks o and p are alternately turned.
t, u, and w, x, are two air-pipes of lead, both internally one
inch and a quarter in diameter.
Z
y, ≈ ; y, z ; y, z ; are water-pipes, each being one inch in
diameter.
-
The pipe b, e, c, is always full from the ftream a, b: the fmall
cifterns g, i, 1, and the large one d, are fuppofed to have been
previouſly filled with water. The fluid may then be admitted
by turning the cock o, through the pipe c, e, into the large
ciftern e. This water will prefs the air confined in the cifterne,
up the air-pipe w, x, and will force the fluid out of the cifterns
g, i,, into thoſe marked h, k, and C.-At the fame time, by
opening B, the water and condenſed air, which previouſly exiſted
in the large ciftern d, and in the ſmaller ones marked ƒ, h, k, will
be diſcharged at B.-After a fhort time, the water-balance,
q, r, s, will turn the cocks, and exclude the water, while it opens
the oppofite ones: the cisterns f, h, k, are emptied in their turns
by the condenfed air from the ciftern d, as the water progref-
fively enters the latter from the pipe b, c.
8. A very ingenious application of the fame principle has
been made in the celebrated Hungarian machine, at Chemnitz.
The beſt account we have been able to obtain of this is the fol-
*lowing.
In fig. 3. pl. XVIII. A reprefents the fource of water elevated
136 feet above the mouth of the pit. From this there runs
down a pipe D of four inches diameter, which enters the top of
a copper cylinder B, 84 feet high, 5 feet diameter, and 2 inches
Hydraulic Engines.
211
thick, and reaches to within 4 inches of the bottom: it has a
cock at I.*
This cylinder has a cock at Q, and a very large one at N.
From its top proceeds a pipe VEC two inches in diameter,
which goes 96 feet down the pit, and is inferted into the top of
another braſs cylinder C*, which is 64 feet high, 4 feet diameter,
and two inches thick: the latter containing about 83 cubic feet,
which is nearly one half of the capacity of the former, viz.
170 cubic feet. There is another pipe FO of 4 inches diame-
ter, which riſes from within 4 inches of the bottom of this
lower cylinder, is foldered into its top, and rifes to the trough
Z which carries off the water from the mouth of the pit. This
lower cylinder communicates at the bottom with the water
O, which collects in the drains of the mines. A large cock
P ferves to exclude or admit this water: another cock M at
the top of this cylinder communicates with the external air.
Now, fuppofe the cock I fhut, and all the reft open: the
upper cylinder will contain air, and the lower cylinder will be
filled with water, becauſe it is funk fo deep that its top is below
the ufual furface of the mine-waters. Shut the cocks Q, N,
M, P, and open the cock I. The water of the fource A muft
run in by the orifice J, and rife in the upper cylinder, com-
preffing the air above it and along the pipe VEC, and thus
acting on the furface of the water in the lower cylinder. It
will therefore cauſe it to rife gradually in the pipe OF, where it
will always be of fuch a height that its weight balances the
elafticity of the compreffed air. Suppofe no iffue given to the
air from the upper cylinder, it would be compreffed into one-
fifth of its bulk by the column of 136 feet high; for a column
of 34 feet nearly balances the ordinary elafticity of the air.
Therefore, when there is an iffie given to it through the pipe
VEC, it will drive the compreffed air along this pipe, and
it will expel water from the lower cylinder. When the upper
cylinder is full of water, there will be 34 cubic feet of water
expelled from the lower cylinder. If the pipe OP had been
more than 136 feet long, the water would have rifen 136 feet,
being then in equilibrio with the water in the feeding pipe D
by the intervention of the elaſtic air; but no more water would
have been expelled from the lower cylinder than what fills this
pipe. But the pipe being only 96 feet high, the water will be

* In the figure thefe veffels are in form of parallelopipeds, and there
are fome pipes and cocks which are not referred to in this defeription
but this happens, becauſe one diagram is made to ferve for both the
original machine, and Mr. Bofwell's improvements mentioned directly
after.
P 2
·

212
MACHINES.
thrown out at Z with a confiderable velocity. If it were not
for the great obftructions which water and air muſt meet with
in their paffage along pipes, it would iffue at Z with a velocity
of more than fifty feet per fecond. It iffues however much
more flowly, and at laft the upper cylinder is full of water, and
the water would enter the pipe VE and enter the lower cylin-
der, and, without diſplacing the air in it, would rife through the
difcharging pipe OP, and run off to wafte. To prevent this
there hangs in the pipe VE a cork ball or double cone, by a
brafs wire which is guided by holes in two crofs pieces in that
pipe. When the upper cylinder is filled with water, this córk
plugs up the orifice V, and no water is wasted; the influx at J
now ftops. But the lower cylinder contains compreffed air,
which would balance water in a difcharging pipe 136 feet high,
whereas OP is only 96. Therefore the water will continue to flow
at Z till the air has fo far expanded as to balance only 96 feet of
water, that is, till it occupies one-half of its ordinary bulk, that
is, one-fourth of the capacity of the upper cylinder, or 42 cubic
feet. Therefore 42 cubic feet will be expelled, and the efflux
at Z will ceafe; and the lower cylinder is about one-half full of
water. When the attending workman obferves this, he fhuts
the cock I. He might have done this before, had he known
when the orifice V was ftopped; but no lofs enfues from the
delay. At the fame time the attendant opens the cock N the
water iffues with great violence, being preffed by the condenfed
air from the lower cylinder. It therefore iffues with the fum
of its own weight and of this compreffion. Theſe gradually
decreaſe together, by the efflux of the water and the expanfion
of the air; but this efflux ftops before all the water has flowed
out; for there is 42 feet of the lower cylinder occupied by
air. This quantity of water remains, therefore, in the upper
cylinder nearly the workman knows this, becauſe the dif
charged water is received first of all into a veffel containing
three-fourths of the capacity of the upper cylinder. When-
ever this is filled, the attendant opens the cock P by a long
rod which goes down the fhaft; this allows the water of the
mine to fill the lower cylinder, and the air to get into the upper
cylinder, which permits the remaining water to run out of it.
Thus every thing is brought into its firft condition; and when
the attendant fees no more water come out at N, he fhuts the
cocks N and M, and opens the cock I, and the operation is re-
peated.
There is a very furprifing appearance in the working of this
engine. When the efflux at Z has stopped, if the cock Q be
opened, the water and air ruth out together with prodigious
violence, and the drops of water are changed into hail or lumps
Hydraulic Engines.
213
T
of ice. It is a fight uſually ſhown to ftrangers, who are defired
to hold their hats to receive the blafts of air: the ice comes out
with fuch violence as frequently to pierce the hat like a piftol
bullet. This rapid congelation is a remarkable inftance of the
general fact, that air by fuddenly expanding generates cold, its
capacity for heat being increaſed.
The above account of the procedure in working this engine
fhows that the efflux both at Z and N becomes very flow near
the end. It is found convenient therefore not to wait for the
complete diſcharges, but to turn the cocks when about 30 cubic
feet of water have been diſcharged at Z: more work is done
in this way. A gentleman of great accuracy and knowledge of
theſe ſubjects took the trouble of noticing particularly the per-
formance of the machine. He obferved that each ſtroke, as
it may be called, took up about three minutes and one-eighth ;
and that 32 cubic feet of water were diſcharged at Z, and 66
were expended at N. The expence therefore is 66 feet of water
falling 136 feet, and the performance is 32 raiſed 96, and they are
in the proportion of 66 x 136 to 32 x 96, or of 1 to 0,3422, or
nearly as 3 to 1. This is fuperior to the performance of the
moft perfect underſhot mill, even when all friction and irregu-
lar óbftructions are neglected; and is not much inferior to any
overſhot pump-mill that has yet been erected. When we re-
flect on the great obftructions which water meets with in its
paffage through long pipes, we may be affured that, by doubling
the fize of the feeder and difcharger, the performance of the
machine will be greatly improved; we do not hesitate to fay,
that it would be increaſed one-third: it is true that it will ex-
pend more water; but this will not be nearly in the fame pro-
portion, for moſt of the deficiency of the machine arifes from
the needlefs velocity of the firft efflux at Z. The diſcharging
pipe ought to be 110 feet high, and not give ſenſibly lefs water.
Then it must be confidered how inferior in original expence this
fimple machine must be to a mill of any kind which would raiſe
10 cubic feet 96 feet high in a minute, and how fmall the re-
pairs on it need be, when compared with a mill. And, laftly,
let it be noticed that fuch a machine can be uſed where no mill
whatever can be put in motion. A ſmall ſtream of water, which
would not move any kind of wheel, will here raiſe one-third of
its own quantity to the fame height; working as fast as it is fup-
plied,
For thefe reafons, we think that the Hungarian machine emi-
nently deferves the attention of mathematicians and engineers,
to bring it to its utmoft perfection, and into general ufe. There
are fituations where this kind of machine may be very ufeful.
Thus, where the tide rifes 17 feet, it may be uſed for compreff-
214
MACHINES.
}
+
ing air to ſeven-eighths of its bulk; and a pipe leading from a
very large veffel inverted in it may be uſed for raiſing the water
from a veffel of one-eighth of its capacity 17 feet high; or if
this veſſel has only one-tenth of the capacity of the large one fet
in the tide-way, two pipes may be led from it; one into the fmall
veffel, and the other into an equal veffel 16 feet higher, which
receives the water from the firft. Thus one-fixteenth of the
water may be raiſed 34 feet, and a ſmaller quantity to a ſtill
greater height; and this with a kind of power that can hardly
be applied any other way. Machines of this kind are deſcribed
by Schottus, Sturmius, Leupold, and other old writers; and they
fhould not be forgotten, becauſe opportunities may offer of
making them highly beneficial.
9. Mr. John Whitley Bofwell has deviſed an apparatus
which when attached to fuch a machine as that at Chemnitz
will enable it to work itſelf without attendance. The defcrip-
tion of this will be preſented to the reader in Mr. Bofwell's own
words.
Fig. 3. pl. XVIII. A is the refervoir, or upper level of water.
B, a chamber made of fufficient ftrength to bear the internal
preffure of a column of water the height of A above it, multiplied
by its own bafe.
C, a chamber of the ſame ſtrength as B, but of a ſmaller fize;
it is placed at the bottom of the pit from which the water is to
be raiſed, and under the level of the water.
Theſe chambers would be ftronger with the fame materials, if
of a globular or cylindrical form; but the fquare fhape is ufed
in the drawing merely for the facility of repreſenting the poſition
of the parts.
D, a pipe from the refervoir A which paffes through the top
of B, and ends near its bottom, to convey water from A to B.
E, a pipe from the top of B to the top of C, to convey air
from B to C.
F, a pipe from the bottom of C to the level of the ground at
the top of the pit, to carry off the water from the pit.
G, a pipe from the bottom of B to carry off the water from
H, a yeffel to contain the water uſed in working the cocks; it
is only placed on the top of B to fave the conftruction of a ſtand
on purpofe for it.
1, a cock, or moveable valve (worked by the lever there re-
prefented), in the large pipe D.
K, a ftop-cock in the fmall pipe which conveys water from D
to H. Its ufe is to make the engine work fafter or flower, by
letting water more or lefs quick into H; or to stop it altogether
from working when required.
ރ
Hydraulic Engines.
215
*
L, a moveable valve, or cock in the fmall pipe LK. The lever
which works it is connected by a strong wire with the lever
which works I, and is balanced by a weight at its oppofite ex-
tremity, fufficient to open both theſe cocks and ſhut N, when not
prevented by a counter weight.
N, a cock in the pipe G to open and ſhut it as wanted.
O, a felf-moving valve in the pipe F, which permits the water
to paſs upwards, but prevents its return.
P, a felf-moving valve at the bottom of C, which permits the
water to pafs into C, but prevents any from paffing out of it;
it is furniſhed with a grating, to prevent dirt getting in..
R, a veffel fufpended from the levers of I and L, capable of
containing a weight of water ſufficient to ſhut them.
S, a veffel fufpended from the lever of N: it muſt contain
water enough by its weight to open N: it is connected by a
chain to R, to keep it down as long as N is open.
T, a fyphon paffing from the bottom of H, near its. upper
edge, and down again to the mouth of R.
V, a ſelf-moving valve of a fufficient levity to rife, when the
water in B comes up to it, and cloſe the pipe E; into which no
water would elſe paſs from B. A ball-cock, fuch as uſed in
common water cifterns, would do here.
X, a ſyphon from the bottom of R rifing within an inch of its
top, and paffing down again to the mouth of S.
Y, a fmall pipe at the bottom of S: this may have a ſtop-
cock to regulate it, which, when stopped, will alfo ftop the
engine.
The mode of this engine's working is as follows: fuppofe
the veffels V, H, R, and S empty of water, and the cocks K
and Y open, and the veffel C full of water. The weight on
the lever of L will then open the cocks L and I, on which the
water from A will flow into B and H. As the water rifes in
B, it will force the air through E into C, which ſtrongly preff-
ing on the water in C, will force it up through the pipe F, till
the water in B rifes to the level of V and clofes it, at which
time H will be full of water (the quantity flowing in being fo
regulated by the cock K), and the water will flow from it
through the fyphon T into the veffel R, which as it fills fhuts
the cocks I and L, and prevents any more water coming into
B and H. When R is full, the water flows through its fyphon
X, which fills S, and by it opens N, which empties B of water,
and keeps N open as long as there is any water in H.
When H is empty, B will be fo too (being fo regulated by the
cock K), on which, in a moment or two, R and S will alſo be
empty; which will cauſe the cocks I and L to open, and all
216
MACHINES.
things will be again in the ſtate firſt fuppofed, for a repetition of
the operations defcribed.
+
*
To stop the engine, the cocks at K and Y fhould be ſhut,
while S is full of water. To fet it working, they ſhould be
open; and this is all the attendance it will require. As no one
but an engineer fhould attempt to conftruct fuch an
gine as this, it was uſeleſs to repreſent the manner of connect-
ing the pipes by flaches or otherwife; or the proper methods of
faſtening and clofing the parts, which are all well known to
fuch as have made this art their ſtudy. Nicholſon's Journal, 4to.
vol. I.
In No. 5. of the New Series of Nicholſon's Journal, Mr.
Bofwell has made fome further improvements in the application
of the Hungarian machine.
•
L
10. The Spiral pump is a very curious hydraulic engine, which
operates on nearly the fame principle as the Hungarian ma-
chine. The first engine of this kind, of which we have ſeen any
account, was invented and erected by H. Andreas Wirtz, a
tipplate-worker of Zurich, at a dye-houfe in Limmat, in the
vicinity of that city. It confifts of a hollow cylinder, like a
wery large grindstone, turning on a horizontal axis, and partly
plunged in a ciſtern of water. The axis is hollow at one end,
and communicates with a vertical pipe. This cylinder or drum
is formed into a fpiral canal, by a plate coiled up within it
like the main ſpring of a watch in its box; only the ſpires at a
distance from each other, ſo as to form a conduit for the water
of uniform width. This fpiral partition is well joined to the
two ends of the cylinder, and no water efcapes between them.
The outermost turn of the ſpiral begins to widen about ths of
a circumference from the end, and this gradual enlargement
continues nearly a femicircle, this part being called the horn:
it then widens fuddenly, forming a fcoop or fhovel. The
cylinder is fo fupported that this fhovel may, in the courſe of a
rotation, dip feveral inches into the water. As the cylinder
turns upon its axis,the fcoop dips and takes up a certain
quantity of water before it emerges again. This quantity is
fufficient to fill the horn; and this again is nearly equal in
capacity to the outermoft uniform ſpiral round.

L

After the fcoop is emerged, the water paffes along the ſpiral
by the motion of it round the axis, and drives the air before it
into the rifing pipe, where it efcapes. In the mean time, air
comes into the mouth of the ſcoop; and when the ſcoop again
dips into the water, it again takes in fome of that fluid. Thus
there becomes a part filled with water and apart filled with
air. Continuing this motion, a fecond round of water will be
to 941 i allt lie na. *¨
Hydraulic Engines.
217
received, and another of air. The water in any turn of the
fpiral will have its two ends on a level; and the air between
the fucceffive columns of water will be in its natural ſtate; for
fince the paffage into the rifing pipe or main is open, there is
nothing to force the water and air into any other pofition. But
Since the fpires gradually diminiſh in their length, it is plain
that the column of water will gradually occupy more and more
of the circumference of each. At laft it will occupy a complete
turn of fome fpire that is near the centre; and when fent
further in by the continuance of the motion, fome of it will
run back over the top of the fucceeding fpire. Thus it will
run over into the right-hand ſide of the third fpire; and confe
quently will push the water of this ſpire backwards, and raiſe
its other end, ſo that it will likewife run over backwards before
the next rotation be completed. At length this change of
difpofition will reach the outermoſt ſpire, and fome water will
run over into the horn and fcoop, and finally into the ciftern.
But as foon as water gets into the rifing pipe, and rifes a
little into it, it ſtops the efcape of the air when the next fcoop
of water is taken in. Hence there are then two columns of water
acting against each other by hydroftatic preffure, and the inter-
vening column of air: they muft compreſs the air between
them, and the water and air columns will now be unequal: this
will have a general tendency to keep the whole water back,
and cauſe it to be higher on the left or rifing fide of each ſpire
than on the right or defcending fide: the excefs of height being
juft fuch as produces the compreffion of the air between that
and the preceding column of water. This will go on increaſ
ing as the water mounts in the rifing pipe; for the air next to
the rifing pipe is compreffed at its inner end with the weight
of the whole column in the main: and it muſt be as much
compreffed at its outer end, which muſt be done by the water
column without it; and this column exerts this preffure partly
by reaſon that its outer end is higher than its inner end, and
partly by the tranfmiffion of the preffure on its outer end by
air, which is fimilarly compreffed from without. Thus it will
happen that each column of water being higher at its outer
than at its inner end, compreffes the air on the water column
beyond or within it, which tranfmits this preffure to the air
beyond it, adding to it the preffure arifing from its own want
of level at the ends. Confequently, the greatest compreffion,
viz. that of the air next the main, is produced by the fum of all
the tranfmitted preffures; and theſe are the fum of all the differ-
ences between the elevations of the inner ends of the water
_columns above their outer ends: and the height to which the
water will rife in the main will be juft equal to this fum.
218
MACHINES.
T
Suppoſe the left-hand fpaces of each fpire to be filled with
water, and the right-hand fpaces filled with air, as is fhewn, in
regard to one fpire, in fig. 3. pl. XVII. There is a certain
gradation of compreffion which will keep things in this pofition:
for the ſpaces manifeftly decreaſe in arithmetical progreffion;
and fo do the hydroftatic heights and preffures: if, therefore,
the air be denfe in the fame progreffion all will be in hydroſtatical
equilibrium. Now this may obvioufly be produced by the
mere motion of the machine; for fince the denſity and com-
preffion in each air column is fuppofed inverfely as the magni-
tude of the column, the quantity of air is the fame in all; there-
fore the column firft taken in will pafs gradually inwards, and
the increaſing compreffion will caufe it to occupy precifely the
whole right-hand of every fpire. The gradual diminution of
the water columns will be produced, during the motion, by the
water running over backwards at the top from ſpire to ſpire, and
ultimately coming out by the fcoop. Since the hydrostatic
height of each water column is now the greateſt poffible, viz.
the diameter of the fpire, it is evident that this difpofition of
the air and water will raife the water to the greateſt height.
This difpofition may be obtained thus; let CB be a vertical
radius of the wheel, C being the center, and B the highest point.
[the figure may eaſily be drawn]; upon CB, take CL to CB, as
the denfity of the external air to its denfity in the laſt column.
next the rifing pipe or main; that is, make CL to CB as 34 feet
(the height of the column of water which balances the preffure
of the atmoſphere), to the fum of 34 feet, and the height of the
rifing pipe: then divide BL into fuch a number of turns that
the fum of their equal diameters fhall be equal to the height of
the main; lastly, bring a pipe ftraight from L to the centre C.
Such is the conftruction of the fpiral pump, as originally in-
vented by Wirtz: it certainly indicates very confiderable me-
chanical knowledge and fagacity.
T
•
But when the main is very high this conſtruction will require
either an enormous, diameter, of the drum, or many turns of a
very narrow pipe. In fuch cafes it will be much better to make
the fpiral in the form of a corkscrew, than of this flat form like
a watch-fpring. The pipe which forms the fpiral may be
wrapped round the fruftrum of a cone, whofe greateft diameter
is to the leaft (which is next to the rifing pipe) in the proportion
juft affigned to CB and CL. By this conftruction the water
will fo ftand in every round as to have its upper and lower fur-
faces tangents to the top and bottom of the ſpiral, and the
water columns will occupy the whole afcending fide of the ma-
chine, while the air occupies the defcending fide. This form
is far preferable to the fat form; it will allow us to employ
Hydraulic Engines.
219
many turns of a large pipe, and therefore produce a great eleva-
tion of a large quantity of water.
The fame thing will be ſtill better accomplished by wrapping
the pipe on a cylinder, and making it gradually tapering to the
end, in fuch a manner that the contents of each ſpire may be the
fame as when it is wrapped round the cone. It will raiſe the
water to a greater height (though certainly with an increaſe of
the impelling power), by the fame number of fpires, becauſe
the vertical or preffing height of each column is greater.
In the preceding deſcription of this machine, that conftruc-
tion has been chofen which made its principle and manner of
working moft evident, namely, that which contained the fame
material quantity of air in each turn of the ſpiral, more and more
compreffed as it approaches to the rifing pipe. But this is not
the beſt conſtruction: for we fee that in order to raiſe water to
the height of a column of 34 feet, the air in the laſt ſpire is
compreffed into half its fpaće; and the quantity of water de-
livered into the main at each turn is but half what was received
into the firſt fpire, the reft flowing back from ſpire to ſpire, and
being difcharged at the ſpout.
But the conftruction may be fuch that the quantity of water
in each fpire may be the fame that was received into the firft;
by which means a greater quantity (double in the inſtance now
given) will be delivered into the main, and raiſed 'to the fame
altitude by very nearly the fame force. This may be done by
another proportion of the capacity of the fpires; either by a
change of their caliber, or of the diameters of the folid on
which they are folded. Suppoſe the bore to be uniform
throughout, the diameters muft fo vary that the conftant column
of water and the column of air, compreffed to the proper degree,
may occupy the whole circumference. Let A be the column
of water which balances the preffure, and H the height to
which the water is to be raifed. Let A be to A + H as I to
m.
Then it is plain that m will repreſent the denſity of the air
in the laft fpire, if its natural denfity be 1, becauſe it is preffed
by the column A+ H while the common air is preffed by A.
Let 1 reprefent the conftant water column, and confequently
it will be nearly equal to the air column in the firſt ſpire: then
the whole circumference of the laſt ſpire muſt be 1 +
I
m
in
order to hold the water 1, and to compreſs the air into the ſpace
I
or
772
A
A+H
The circumference of the firft fpire is 1 + 1 or 2:
and if D and d be the diameters of the firſt and laſt ſpires we
220
MACHINES.
m
have 2 : 1 + 1 :: D: d, or 2 m:m+1::D:d. If, therefore, a
pipe of uniform bore be wrapped round a conic fruftrum, of
which D and d are the end diameters, the fpirals will be very
nearly fuch as will answer the purpoſe. It will not be quite
exact, for the intermediate fpirals will be rather too large: the
conoidal fruftrum fhould in strictnefs be formed by the revolu-
tion of a logarithmic curve. With fuch a fpiral the full quantity
of water which was confined in the firſt ſpire will find room in
the laſt, and will be fent into the main at every rotation. This
is a very great advantage, eſpecially when the water is to be
much raifed. The faving of power by this change of con-
ftruction is always proportional to the greatest compreffion of
the air..
*
The chief difficulty in any of thefe forms is in determining
the form and pofition of the horn and the fcoop; yet on this
the performance of the machine greatly depends. The follow-
ing instructions will render this tolerably eafy. Let ABEO
(fig. 3. pl. XVII.) reprefent the firft or outermoft fpire, of
which the axis is C. Suppofe the machine immerged up to the
axis in the water whofe furface is VV': it has been ſeen that it
is moſt effective when the furfaces KB and On of the water
columns are diftant from each other the whole diameter
BO of the ſpire. Let therefore the pipe be first conceived of
equal caliber to the very mouth Ee, which we ſuppoſe to be
just about to dip into the water: the furface On is kept there
in oppofition to the preffure of the water column BAO by the
compreffed air contained in the quadrant OE, and in the qua-
drant which lies behind EB: and this compreffion is fupported
by the columns behind, between this fpire and the rifing pipe,
But the air in the outermoft quadrant ÉB is in its natural ſtate,
becauſe it as yet communicates with the external air. When,
however, the mouth Ee has come round to A, it will not have
the water ftanding in it in the fame manner, leaving the half
fpace BEO filled with compreffed air; for it took in and con-
fined only what filled the quadrant BE. It is obvious, there,
fore, that the quadrant BE muſt be ſo ſhaped as to take in and
confine a much greater quantity of air; fo that when it has come
to A, the ſpace BEO may contain air fufficiently denſe to ſup-
port the column AO. But this is not enough: for when the
wide mouth now at A a' rifes up to the top, the furface of the
water in it rifes alfo, becauſe the part AO oa' is more capaci-
ous than the part of uniform bore OE e o that fucceeds it, and
that cannot contain all the water which it previously held.
Since then the water in the ſpire rifes above A, it will prefs the
water back from On to fome other poſition m'n', “and the
ས
Hydraulic Engines.
221
**
preffing height of the water column will be diminished by this
rifing on the other fide of O... Hence it will appear that the
horn muft begin to widen, not from B, but from A, and
muft occupy the whole femicircle ABE, while its capacity
mult be to the capacity of the oppofite fide of uniform bore as
the fum of BO and the height of a column of water which
balances the atmoſphere to the height of that column for
then the air which filled it when of the common denſity will
fill the uniform fide BEO, when compreffed fo as to balance
the vertical column BO. But even this is not fufficient: for it
has not taken water enough. When it dipped into the ciftern
at E it carried air down with it, and the preffure of the water
in the cistern cauſed that fluid to rife into it a little way; and
fome water muſt have come over at B from the other fide,
which was drawing narrower. When, therefore, the horn is
in the pofition EOA it is not full of water: confequently,
when it comes into the fituation OAB it cannot be full, nor
çan it balance the air on the oppofite fide. Hence fome will
come out at O, and rife up through the water. The horn
muſt therefore extend at leaſt from O to B, or occupy half the
circumference; and it muft contain at leaft twice as much
water as would fill the fide BEO. Nay, if it be much larger,
there may be no difadvantage; becauſe the furplus of air which
it takes in at E will be difcharged as the end Ee of the horn
rifes from O to B, and it will leave the precife quantity that is
wanted. The overplus water will be difcharged as the horn
comes round to dip again into the ciſtern.
•
We muſt alſo fecure the proper quantity of water. When
the machine is fo much immerfed as to be up to its axis in
water, the capacity which thus fecures the proper quantity of
air will alſo take in the proper quantity of water. But it may
be erected ſo as that the ſpirals fhall not even reach the water:
and in this caſe it will anſwer the purpoſe if a ſcoop or fhovel
be joined to the horn, and fo formed as to take in at leaft as much
water as will fill the horn. This is all that is wanted in the
beginning of the motion along the fpiral, and more than is
neceffary when the water has advanced to the fucceeding fpire;
but the overplus is difcharged in the way juft mentioned. The
fcoop, it fhould be obſerved, must be very open on the fide next
the axis, that it may not confine the air as it enters the water;
for this would hinder it from receiving enough of that fluid.
As an example we fhall give the dimenfions of a machine
erected at Florence, whofe performance correfponded extremely
well with the theory. The fpiral is formed on a cylinder of 10
feet diameter, and the diameter of the pipe is 6 inches. The
$
:
222
•
MACHINES.
fmaller end of the horn is of the fame diameter; it occupies &
of the circumference, and is 7-8 inches wide at the outer end:
here it joins the fcoop, which lifts as much water as fills the
horn, which contains 4340 Swediſh cubic inches, each 1-577
Engliſh. The machine makes 6 revolutions in a minute, and
raifes 1354 pounds of water, or 22 cubic feet, 10 feet high in
a minute. Thus it raiſes more than ths of what the theory
would lead us to expect, and yet it is not perfect; for the fpiral
is throughout of equal caliber, and is formed on a cylinder
inſtead of a conoid.
In this machine the friction is fo inconfiderable that it need
not be mended: but the great excellency is, that whatever im-
perfections there may be in the arrangement of the air and
water columns, it only affects the elegance of the execution,
cauſing the water to make a few more turns in the ſpiral before
it can mount to the required height; but it waftes no power,
becauſe the power employed is always in proportion to the fum
of the vertical columns of water in the rifing fide of the ma-
chine, and the altitude to which the water is raiſed by it is in
the very fame proportion. The machine fhould be made to move
very flow, that the water be not always dragged up by the pipes,
which would cauſe more to run over from each column and di-
miniſh the preffure of the remainder. If the rifing pipe be made
wide, and thus room be made for the air to eſcape freely up-
wards through the water, it will rife to the height affigned; but
if the pipe be narrow, fo that the air cannot rife freely, it rifes
almoſt as flowly as the water; and by this circumſtance the water
mixed with, the air is raiſed to a much greater height, and this
with hardly any augmentation of the power. Thus it is that
the great performance of the Florentine machine (which is
almoft triple what a man can do with the beſt conſtructed
pump) is accounted for. Laftly, we may obferve that the
entrance into the rifing pipe fhould be no wider than the laſt
part of the fpiral; and it would be adviſeable to divide it into
four channels by a thin partition, and then to make the rifing
pipe very wide, and to put into it a number of flender rods,
which would divide it into feveral flender channels that would
ferve completely to entangle the air among the water: this pro-
cedure will greatly increase the heights to which the heterogene-
ous column may be carried.
We earnestly recommend the application and improvement
of this machine to practical engineers: the principles on which
its theory depends are confeffedly intricate; but when judici-
oufly conftructed it is very powerful and effective" in its opera-
tions: on which accounts we are forry that hitherto it has not,

Hydraulic Engines.
223
- as far as we recollect, been defcribed in more than two British
works, the Tranfactions of the Society of Arts, for 1776, and the
Encyclopædia Britannica.

!
11. Defaguliers deſcribes, in the fecond volume of his Ex-
perimental Philoſophy, a very fimple contrivance to raiſe water,
which is this: to one end of a rope is fixed a large bucket,
having a valve at its bottom, opening upwards; to the other
end is faſtened a ſquare frame, and the cord is made to pafs
over two pulleys, each of about 15 inches diameter (and fixed
in a horizontal plane), in fuch manner that as the bucket de-
fcends the frame afcends with equal velocity, and vice verfa.
The frame is made to run freely upon 4 vertical iron guide-
rods paffing through holes at its four corners: and when the
bucket is filling with water at the well, the frame ftands at the
horizontal plane to which the water is to be raiſed: when the
bucket is full a man ſteps upon the frame (his weight, together
with that of the frame, exceeding the weight of the veſſel and
its contained water); this gives an afcending motion to the
bucket, and cauſes the valve in its bottom to clofe. When the
bucket is raiſed to the proper height a hook fixed there catches
into a hafp at the fide of the bucket, turns it over, and cauſes it
to empty its water into a trough which conveys it where it is
required: at this time the man and the defcending frame have
arrived at a platform which prevents their further defcent,
where the man remains till he finds the bucket above is empty;
when he ſteps from the frame, and runs up a flight of ftairs to
the place from which he deſcended: the bucket in the mean
while, being ſomewhat heavier than the frame, defcends to the
water, and raiſes the frame to its original pofition. Thus the
work is continued, the man being at reſt during his deſcent, and
labouring in the aſcent.
Defaguliers employed in this kind of work a "tavern drawer,
who weighed 160 lbs. whom he defired to go up and down 40
fteps of 6 inches each (in all about 22 feet) at the fame rate he
would go up and down all day. He went up and down twice
in a minute: fo that allowing the bucket with a quarter of a
hogfhead in it to weigh 140 lbs. he is able to raiſe it up
through 22 feet twice in a minute: this Defaguliers eftimates
as equivalent to a whole hogshead raiſed 11 feet in a minute;
and rather exceeds what he has affigned as a maximum of
human exertion.
This machine is in many caſes not only the moſt fimple, but
the best that can be devifed; yet it is one that without due
precautions is likely to be a very bad one. The frame on
which the man ſteps must be brought up to its place again by
a preponderancy in the machine when unloaded: it fhould arrive
224
MACHINES.
•
preciſely at the fame time with the man; but it may arrive
fooner or later. If fooner, it is of no uſe, and waſtes power in
raiſing a counterpoife which is needlefsly heavy, or in fact lefs
water is elevated than the man is able to elevate; if later, there
is a lofs of time. Hence the perfection of this truly fimple ma-
chine requires the judicious combination of two maximums,
each of which varies in a ratio compounded of two other
ratios. It will not be difficult, however, to adjuſt the propor-
tions of the weight of the bucket and that of the frame: for if
B denote the weight of the bucket, F that of the frame, and
the force neceffary to overcome the friction and the inertia of
the pulleys, g denoting 32% feet, t the time occupied in walking
up the ſteps, and s the ſpace afcended or defcended, then muſt
B and F be fo adjuſted as to fatisfy the following equation, viz.
B-F
I
B+F+p • ½ 8 1º.
12. If there be a fpring affording but a fmall quantity of
water, or having but a fmall fall, it is poffible by the lofs of
fome of the water to raiſe the reft to ſupply a gentleman's feat,
or any place where it is wanted; but in a lefs quantity than
what runs wafte, if the place to which the water is to be raiſed
is higher than the ſpring or refervoir from which the water
falls. Schottus long ago contrived an engine for this purpoſe:
but the firſt who put fuch a thing in execution was Gironimo
Finugio, at Rome, in 1616; and the first in this country was
George Gerves, a carpenter, who, in the year 1725, erected an
engine called the Multiplying-wheel Bucket-engine, at the feat
of Sir John Cheſter, at Chichley, in Buckinghamſhire. This
engine was much approved by Sir Ifaac Newton, Dr. Deſaguliers,
and Mr. Beighton, and was certainly very ingenious. The
water from a fpring defcended in a large bucket hanging by a cord
from an axle, while a ſmaller quantity was raiſed from the fame
place by a cord hanging from a wheel on the fame axle: a fly
and other regulating apparatus were added, to make the en-
gine work itſelf, which it did for many years without being out
of order. As a whole, however, the contrivance is complex;
and we are not aware that any other engines of the fame kind
have been erected. A defcription, with a plate, may be ſeen in
Defaguliers's fecond volume.
Mr. H. Sarjeant, of Whitehaven, contrived a very cheap
engine for railing water, for which the Society for the En-
couragement of Arts awarded him a filver medal in the year
1801. A ſketch of this fimple invention is given in fig. 2.
pl. XIX.
This engine was erected at Irton-hall, which is ſituated on
an aſcent of 60 or 61 feet perpendicular height; at the foot of
1
Hydraulic Engines.
225
this elevation, about 140 yards diftant from the offices, there
runs a ſmall ſtream of water; and, in order to procure a con-
ſtant ſupply of that neceffary fluid, the object was to raiſe fuch
ftream to the houſe for culinary and domeftic ufes. With
this view, a dam was formed at a fhort diſtance above the
current, ſo as to caufe a fall of about four feet: the water was
then conducted through a wooden trough, into which a piece.
of leaden pipe, two inches in diameter, was inferted, and part
of which is delineated at A.
The ſtream of this pipe is directed in fuch a manner as to
run into the bucket B, when the latter is elevated; but, as
foon as it begins to defcend, the ſtream paffes over it, and flows
progreffively to fupply the wooden trough or well, at the foot
of which ftands the forcing-pump C, being three inches in
diameter.
D is an iron cylinder attached to the pump-rod, which
paſſes through it: fuch cylinder is filled with lead, and weighs
about 240 lbs. This power works the pump, and forces the
water to afcend to the houſe through a pipe one inch in di-
ameter, and which is 420 feet in length.
•
At E is fixed a cord, which, when the bucket approaches to
within four or five inches of its loweſt projection, extends, and
opens a valve in the bottom of the veſſel through which the
water is diſcharged.
An engine in a great degree fimilar to this was erected fome
years ago by the late James Spedding, efq. for a lead mine near
Kefwick, with the addition of a ſmaller bucket which emptied
itſelf into the larger near the beginning of its deſcent, without
which addition it was found that the beam only acquired a
libratory motion, without making a full and effective itroke.
To anſwer this purpofe in a more fimple way, Mr. Sarjeant
conſtructed the fmall engine in fuch manner as to finiſh its
ftroke (ſpeaking of the bucket end) when the beam comes into
an horizontal poſition, or a little below it. By this means the
lever is virtually lengthened in its deſcent in the proportion of
the radius to the cofine, of about thirty degrees, or as feven to
fix nearly, and confequently its power is increaſed in an equal
proportion.
It is evident, that the opening of the valve might have been
effected, perhaps better, by a projecting pin at the bottom; but
Mr. S. chofe to give an exact deſcription of the engine as it
ftands. It has now been fome years in ufe, and completely
anfwers the purpoſe intended.
The only artificers employed, except the plumber, were a
country blackſmith and carpenter; and the whole coft, excluſive
of the pump and pipes, did not amount to 5..
VOL. II.
1
226
MACHINES.
In a letter, dated Whitehaven, April 28, 1801, Mr. Sarjeant
obferves, that the pump requires about eighteen gallons of water
in the bucket to raiſe the counter-weight, and make a freſh
troke in the pump; but it makes three ftrokes in a minute,
and gives about a half-gallon into the ciftern at each ſtroke.
He adds, "I fpeak of what it did in the driest part of laſt
fummer; when it ſupplied a large family, together with work-
people, &c. with water for all purpoſes, in a fituation where
none was to be had before, except fome bad water from a com-
mon pump which has been fince removed. But the above
fupply being more than fufficient, the machine is occafionally
opped to prevent wear, which is done by merely cafting off
the ftring of the bucket valve."
*
13. Mr. Benjamin Dearborn, whofe fimple fire-engine has
already been mentioned, has contrived an hydraulic engine
which may be conveniently added to a common pump, and there-
by renders it uſeful in further elevating water, and particularly
in extinguiſhing fires: the following deſcription of his apparatus
is extracted from the Memoirs of the American Academy.
Plate XIX. fig. 7. A, B, C, D, repreſents a pump, the form
of which is fimilar to that of the pumps commonly employed on
ship-board.
E, the fpout.
F, a kopper.
D, d, a plank-cap, that is fitted to the pump, and provided
with leather on its lower furface; being fecured by the fcrews
4, b: in the centre is a hole, through which the fpear of the
pump paffes, and round which a leather collar is made, as re-
prefented at the letter c.
g, a nut for the ſcrew b.
f, a fquare piece of wood that is nailed acrofs one end of the
plank-cap, through both which the fcrew a is introduced: a
hole is made through fuch piece and the cap, that communicates
with the bore of the pump.
G, G, a wooden tube, which may be of any requifite length,
and confiſt of any number of joints: it is made fquare at the
lower extremity, and perforated for the reception of the cock;
the upper end being made with a nice fhoulder.
e, a wooden cock that opens or shuts the communication be-
tween the pump and the tube; being furniſhed on the oppofite
fide with a handle and with a lock, in caſe it ſhould be found
neceflary.
h, h, are two ferules, the object of which is to prevent the
tube from ſplitting.
H, H, braces, each of which ought to be croffed over an,
other, as nearly at right angles as poſſible..
Hydraulic Engines.
22T
i, i, are irons in form of a ftaple, which ſurround the tube,
and paſs through the braces; their ends being perforated with
holes for fore-locks.
.K, L, M, N, is a head made of five pieces of wood; k, l, m, n,
a fquare piece, in the lower part of which is a hole for the
reception of the extremity of the tube, and which piece reſts on
the ſhoulder o, p; to the lower end of this head is nailed a piece
of leather, with a hole in its centre, fimilar to that made in the
wood. Another piece of leather of the fame form is placed on
the top of the tube, and between both is a circle of thin plate
brafs; the two pieces of leather and the brafs being preffed
between the lower end of the head and the fhoulder of the
tube. Their edges are delineated at o, p.
K, N, and L, M, are the edges of two pieces of plank, of a
fimilar width with the head, to which they are cloſely nailed
each being provided with a tenon, that paffes through a mortice
in the end of the piece O, P: both tenons have holes for
fore-lock at q.
O, P, a piece of plank of the fame width as the fides; the
centre of which is perforated, in order that the tube may pafs
through; and in each end of which is a mortice for the res
ception of the tenons.

N, M, a cap.
r, r, are two pieces nailed to the fide of the tube; the lower
extremity of each is provided with a truck, with a view to
leffen the friction of the head in its horizontal revolution.
q, q, repreſent fore-locks, the deſign of which is to faſten
down the head, and prevent the water from eſcaping at the
joint o, p.
Q, R, is a wooden conductor; the extremity marked with
the letter Q being folid, while the oppofite end, R, is bored
with a ſmall auger.
s, a bolt that paffes through the conductor and head, and being
fecured on the back with a fore-lock or nut: this bolt is rounded
near the head, and fquare in the middle.
t, u, w, x, repreſents a piece of iron or brafs, defigned to
prevent the head of the bolt from wearing into the wood.
S, S, are ropes for the direction of the conductor.
Fig. 8. reprefents the head without fuch conductor.
a, b, c, d, is a thick braſs plate, the centre of which is perfor
ated, fo as to admit a paffage to impurities, that might other
wife obftruct the conductor: for which purpoſe a piece of
leather is nailed under it to the head. The fquare hole in the
centre is adapted to the fize of the bolt, which it prevents from
turning. The conductor has a hollow cut round the bolt on
the infide, of the fame fize as the circle of holes in the brafs:
2
228
MACHINES.
round fuch cavity is nailed, on the face of the conductor, a
piece of leather, that plays on the margin of the braſs-platě
when the conductor is in motion.
In the conclufion of his Memoir, Mr. Dearborn obſerves,
that he has raiſed a tube of 30 feet on his pump; and, though
the ſeverity of the feafon had prevented him from completing
it, ſo that one perſon only could work at the brake, yet he is
enabled to throw water on a contiguous building, the neareſt
part of which is 37 feet from the pump, and between 30 and
40 feet in height.
14. It will be expected that fome notice fhould be taken in
this place of two celebrated hydraulic engines, viz. the water-
works at London-bridge, and thofe at Marly. Of theſe, the
former has been fo often defcribed in well-known Engliſh
works, that a minute defcription appears quite unneceffary:
the latter will be briefly defcribed under the article Marly in
this volume. Other contrivances for raiſing water, ſuch as the
centrifugal machine, preffure engines, pumps, and Archimedes's
screw, are likewife treated under the reſpective words.
After all, it is not poffible within the limits to which the
fubject of hydraulic engines muft neceffarily be confined in
this work, to deſcribe a tenth part of thoſe which, by the in-
genuity of their conftruction, and their great utility, deſerve
the attention of thoſe who are likely to be engaged in the
erection of ſuch machines. To fupply the deficiency in fome
meaſure, a catalogue is here added of the moſt important and
valuable writings on theſe kinds of engines.
Defcriptio machine hydraulice curiofæ conftructa Joh.
Geor. Faudieri. Venet. 1607.
Nouvelle invention de lever l'eau plus haut que la fource,
avec quelque machines mouvantes par le moyen de l'eau, &c.
par Ifaac de Caus. 1657.
Jofephi Gregorii a Monte Sacr. Principia phyfico-mecha-
nica diverfarum machinarum feu inftrumentorum pneumatices
ac hydraulices. Venet. 1664.
Nouvelle machine hydraulique, par Francini. Journ. des
Sçav. 1669.
[An account of this machine is likewife given in the Archi-
tecture hydraulique of Belidor, tom. 2. and in the 2d vol. of
Defaguliers's Experimental philofophy: in both which perform-
ances many other hydraulic machines are defcribed.]
An undertaking for raifing water, by Sir Samuel Moreland.
Phil. Trans. 1674. No. 102.
An hydraulick engine, by
No. 128.
•
Phil. Trans. 1675.
A cheap pump, by Mr. Conyers. Phil. Trans. 1677. No.136.
Hydraulic Engines, Writings upon.
229
M. de Hautefeuille, Reflexions fur quelques machines à elever
les eaux, avec fa deſcription d'une nouvelle pompe, fans frotte-
ment et fans piſton, &c. 1682.
Elevation des eaux par toute forte des machines, reduite à la
mefure, au poids, à la balance, par le moyen d'un nouveau pifton
et corps de pompe, et d'un nouveau mouvement cyclo-elliptique,
et rejetant l'ufage de toute forte de manivelles ordinaires, par le
Chevalier Morland. 1685.
A new way of raiſing water, enigmatically propoſed, by Dr.
Papin. Phil. Trans. 1685. No. 173. The folutions by Dr.
Vincent and Mr. R. A. in No. 177.
M. du Torax, Nouvelles machines pour épuifer l'eau des
foundations, qui, quoi très fimples, font un effet fupprenant.
1695. Journ. des Sçav. 1695. p. 293.
An engine for railing water by the help of fire, by Mr. Tho.
Savery. Phil. Trans. 1699. No. 253.
D. Papin, Nouvelle manière pour lever l'eau par la force du
feu: à Caffel. 1707.
Memoire pour la conftruction d'une pompe qui fournit con-
tinuellement de l'eau dans le refervoir, par M. de la Hire,
Mem. Acad. Sci. Paris.
1716.
Deſcription d'une machine pour elever des eaux, par. M. de
la Paye, Mem. Acad. Sci. Paris. 1717.
Joh. Fac. Bruckmann's und Joh. Heinr. Weber's Elementar-
maſchine, oder univerfal-mittel bey allen waffer-hebungen.
Caffel.. 1720.
Jacob Leupold, Theatri machinarum hydraulicarum. 1724,
1725.
Joh. Frid. Weidleri Tractatus de machinis hydraulicis toto
terrarum orbe maximis Marlyenfi et Londinenfi, &c. 1727.
Vide A&. erudit. Lips. 1728.
A deſcription of the water-works at London-bridge, by H.
Beighton, F. R. S. Phil. Trans. 1731. No. 417.
An account of a new engine for raifing water, in which horſes
or other animals draw without any lofs of power (which has
never yet been practiſed); and how the ftrokes of the pifton
may be made of any length, to prevent the lofs of water by the
too frequent opening of valves, &c. by Walter Churchman.
Phil. Trans. 1734.
Sur l'effet d'une machine hydraulique propofée par M.
Segner, par M. Leon. Euler, Mem. Acad. Sci. Berlin. 1750.
Application de la machine hydraulique de M. Segner à toutes
fortes d'ouvrages, et de fes avantages fur les autres machines
hydrauliques, par M. Leon. Euler, Mem. Acad. Sci. Berlin.
1751.
[M. Segner's machine is no other than the fimple yet truly
1
230
MACHINES.
ingenious contrivance known by the name of Barker's mill,
which had been defcribed in the 2d volume of Defaguliers's
Philofophy, fome years before the German profeffor made any
pretenfions to the honour of the invention. The theory of it is
likewife treated by John Bernoulli at the end of his Hydraulics.]
Recherches fur une nouvelle manière d'elever de l'eau pro-
*pofée par M. de Mour, par M. L. Euler, Mem. Acad. Berlin.
17513
Difcuffion particulière de diverſes manières d'elever de l'eau
par le moyen des pompes, par M. L. Euler, Mem. Acad. Ber.
1752.
Maximes pour arranger le plus advantageufement les ma-
chines deſtinées à elever de l'eau par le moyen des pompes, par
M. L. Euler, Mem. Acad. Ber. 1752.
Reflexions fur les machines hydrauliques, par M. le Chevalier
D'Arcy, Mem. Acad. Sci. Paris. 1754
Memoire fur les pompes par M. le Chevalier de Borda, Mem.
Acad. Sci. Paris. 1768.
Dan. Bernoulli Expofitio theoretica fingularis machinæ hydrau-
licæ. Figuri helvetiorum, exftru&tæ. Nov. Com. Acad. Petrop.
17720
Abhandlungen von der wafferſchraube, von D). Scherffer,
Priefter. Wien. 1774.
Recherches fur les moyens d'exécuter fous l'eau toutes fortes
de travaux hydrauliques, fans employer aucun epuiſement, par
M. Coulumb. 1779:
Saemund Magnuffen Holm, Efterretning om ſkye pumpen.
Kiobenhavn. 1779.
Moyen d'augmenter la viteffe dans le mouvement de la vis
d'Archimede fur fon axe, tire des mémoires nanufcrits de M.
Pingeron, fur les arts utiles et agréables. Journ. d'Agric. Juin,
1780.
The theory of the fyphon, plainly and methodically illu̟-
ftrated. 1781. (Richardfon.)
Memoria fopra la nuova tromba funiculare umiliata, dal
Can. Carlo Caftelli. Milano. 1782.
Differtation de M. de Parcieux, fur le moyen d'elever l'eau
par la rotation d'une corde verticale fans fin. Amfterdam et
Paris. 1792.
Theorie der wirzifchen fpiral pumpe, erläutert von Heinr.
Nicander. Schwed. Abhandl. 1783.
Fac. Bernoulli, Effai fur une nouvelle machine hydraulique
propre à elever de l'eau, et qu'on peut nommer Machine Pitoti-
enne. Nov. A&t. Acad. Petrop. 1786.
K. Ch. Langsdorf's Berechnungen über die vortheilhæftere
benutzung angelegter_fammelteiche zur betreibung der maſ
chinen. Act. Acad. Elect. Mogunt. 1784, 1785.
Hygrometers.
231
Nicander's Theorie der ſpiral pumpe. 1789.
Nouvelle architecture hydraulique, par M. Prony.
1796.
$790,
A fhort account of the invention, theory, and practice of fire-
machinery; or introduction to the art of making machines
vulgarly called fteam-engines, in order to extract water from
mines, convey it to towns, and jets d'eaux in gardens; to procure
water-falls for fulling, hammering, ſtamping, rolling, and corn-
mills, by W. Blakey. 1793. (Egerton.)
To theſe may be added the Tranfactions of the Society of
Arts, the Repertory of Arts, Nicholſon's Philofophical Journal,
and Tilloch's Philofophical Magazine, in different places.
HYDROMETERS. See vol. I. arts. 401, 409.
HYGROMETER, or HYGROSCOPE, or NOTIOMETER, an in-
ftrument contrived to meaſure the humidity of the air.
'The inftruments hitherto invented for this purpoſe, have not
been attended with that accuracy which there was reaſon to
expect and to hope for. We have hygrometers, it is true, which
indicate that the air has been more or lefs moift; but they
have often this fault, that they indicate a greater degree of moiſt-
ure than really exifts in the atmoſphere: befides, they are not
comparable; that is to fay, it is not poffible by their means to
compare the moisture of one day, or of one place, with that of
another. It may not, however, be improper to defcribe a few
of the contrivances of this kind, if it be only that their utility
may be examined.
i. As fir wood is very ſuſceptible of participating in the dry-
neſs and moiſture of the atmoſphere, fome have conceived the
idea of applying this property to the conftruction of an hygrometer.
For this purpoſe, a ſmall, very thin fir board, is placed acroſs
between two vertical immoveable pillars, fo that the fibres ftand
in a horizontal direction; for it is in the lateral direction, or
that tranſverſal to its fibres, that fir and other kinds of wood
are extended by moisture. The upper edge of the board ought
to have a ſmall rack, fitted into a pinion, connected with a
wheel, and the latter with another wheel, having on its axis àn
index. It may be eaſily perceived, that by theſe means the leaft
motion communicated by the upper edge of the board to the
rack, by its rifing or falling, will be indicated in a very fenfible
manner by the index; confequently, if the motion of the index
be regulated in fuch a manner, that from extreme dryness to
extreme moiſture it may make a complete revolution, the di-
vifions of this circle will indicate how much the preſent ſtate
of the atmoſphere is diſtant from either of theſe extemes.
This invention is ingenious, but it is not fufficient. The
wood retains its moifture a long time after the air has loft that
232
MACHINES.
with which it was charged; befides, the board gradually be
comes lefs fenfible to the impreffions of the air, and therefore
produces little or no effect.
2. Suſpend a ſmall circular plate by a fine ſtring, or piece of
catgut, faftened to its centre of gravity, and let the other end
of the ftring be attached to a hook. According as the air is
more or lefs moift, you will fee the ſmall plate turn round in
one direction or in another.
The hygrometers commonly fold are conftructed on this
principle. They confift of a kind of box, the fore part of
which repreſents a building with two doors. On one fide of
the metal plate which turns round, ftands the figure of a man
with an umbrella, to defend him from the rain, and on the
other a woman with a fan. The appearance of the former of
theſe figures indicates damp, and that of the other dry, weather.
This pretended hygrometer can ſerve for no other purpoſe than
to amuſe children; for the philofopher muſt obſerve that, as
the variations of humidity are tranfmitted to this inftrument
only by degrees, it will indicate moiſture or drought when the
ftate of the atmoſphere is quite contrary.
3. Some have tried to conftruct an hygrometer, by making
faft a piece of catgut at one extremity, winding it backwards
and forwards over different pulleys, and fufpending from its
other extremity a ſmall weight, behind which is placed a gradu-
ated fcale. Others difpofe the extremity of the catgut in fuch
a manner, as to cauſe it to move an index round a graduated
plate, the different degrees of which indicate the dryneſs or
moiſture of the atmoſphere. This inftrument, however, is fub-
ject to the fame inconveniences as that before mentioned.
4. Put into one fcale of a balance any falt that attracts the
moiſture of the air, and into the other a weight, in exact equi-
librium with it. The fcale containing the falt will fink down
during damp weather, and thereby indicate that fuch is the
ftate of the atmoſphere. An index, to determine the different
degrees of drought or moiſture, may be eaſily adapted to it.
This inftrument however is worſe than any of the reft; for a
falt immerfed in moist air becomes charged with a great deal of
humidity, but lofes it very lowly when the air becomes dry:
fixed alkali of tartar even imbibes moiſture till it falls in deli-
quium, that is to fay, till it is reduced to a liquid or fluid ſtate.
5. Mufic may be employed to indicate the drynefs or moiſture
of the air. The found of a flute is higher during dry than during
moiſt weather, and the ftring of a violin exhibits the fame pheno-
menon; but neither of thefe can fhew the immediate ſtate of
the air in regard to drynefs or humidity.
6. M. De Luc's contrivance for an hygrometer is on this
Hygrometers.
233
principle. Finding that even ivory fwells with moiſture, and
contracts with drynefs, he made a ſmall and very thin hollow
cylinder of ivory, open only at the upper end, into which is
fitted the under or open end of a very fine long glafs tube, like
that of a thermometer. Into thefe is introduced fome quick-
filver, filling the ivory cylinder, and a fmall part of the length
up the glaſs tube. The confequence is this: when moisture
fwells the ivory cylinder, its bore or capacity grows larger, and
confequently the mercury finks in the fine glafs tube; and, vice
verfa, when the air is drier, the ivory contracts, and forces the
mercury higher up the tube of glafs." It is evident that an in-
ſtrument thus conftructed is in fact alfo a thermometer, and
muſt neceffarily be affected by the viciffitudes of heat and cold,
as well as by thofe of drynefs and moiſture; or that it muſt
act as a thermometer as well as an hygrometer. The contriv-
ances in the ftructure and mounting of this inftrument are
deſcribed in the Philos. Trans. vol. 63, art. 38; where it may
be ſeen how the above imperfection is corrected by fome fimple
and ingenious expedients, employed in the original conftruction
and fubfequent ufe of the inftrument; in confequence of which,
the variations in the temperature of the air, though they produce
their full effects on the inftrument as a thermometer, do not
interfere with or embarraſs its indications as an hygrometer.
7. In the Philof. Tranf. for 1791, M. De Luc has given a
fecond paper on hygrometry. This has been chiefly occafion-
ed by a Memoir of M. De Sauffure on the ſame ſubject, entitled
Effais fur l'Hygrometrie, in 4to, 1783. In this work M. De S.
deſcribes a new hygrometer of his conftruction, on the follow-
ing principle. It is a known fact that a hair will ſtretch when
it is moistened, and contract when dried: and M. De Sauffure
found, by repeated experiments, that the difference between the
greatest extenfion and contraction, when the hair is properly
prepared, and has a weight of about 3 grains fufpended by it,
is nearly one 40th of its whole length, or one inch in 40. This
circumftance fuggefted the idea of a new hygrometer. To ren-
der theſe ſmall variations of the length of the hair perceptible,
an apparatus was contrived, in which one of the extremities of
the hair is fixed, and the other, bearing the counterpoife above-
mentioned, furrounds the circumference of a cylinder, which
turns upon an axis to which a hand is adapted, marking upon a
dial in large divifions the almoſt infenfible motion of this axis.
About 12 inches high is recommended as the moſt convenient
and uſeful: and to render them portable, a contrivance is added,
by which the hand and the counterpoife can be occafionally.
fixed.
But M. De Luc, in his Idées fur la Meteorologie, vol. i.
234
MACHINES.
anno 1786, fhews that hairs, and all the other animal or veget-
able hygroſcopic ſubſtances, taken lengthwife, or in the direction
of their fibres, undergo contrary changes from different variations
of humidity; that when immerfed in water, they lengthen at
firft, and afterwards fhorten; that when they are near the great-
eft degree of humidity, if the moisture be increafed, they
fhorten themſelves; if it be diminished, they lengthen themſelves
first before they contract again. Theſe irregularities, which
render them incapable of being true meafures of humidity, he
fhews to be the neceffary confequence of their organic reticular
ftructure. De Sauffure takes his point of extreme moiſture
from the vapours of water under a glafs bell, keeping the fides
of the bell continually moiftened; and affirms, that the humidity
is there conftantly the fame in all temperatures; the vapours
even of boiling water having no other effect than thoſe of cold.
De Luc, on the contrary, fhews that the differences in humidity
under the bell are very great, though De Sauffure's hygrometer
was not capable of dicovering them; and that the real unde
compofed vapour of boiling water has the directly oppofite
effect to that of cold, the effect of extreme drynefs: and on
this point he mentions an intereſting fact, communicated to him
by Mr. Watt, viz. that wood cannot be employed in the ſteam-
engine for any of thoſe parts where the vapour of the boiling
water is confined, becauſe it dries fo as to crack as if expofed to
the fire.
To theſe charges of M. De Luc, a reply is made by M. De
Sauffure, in his Defence of the Hair Hygrometer, in 1788;
where he attributes the general difagreement between the two
inftruments to irregularities of M. De Luc's; and affigns fome
aberrations of his own hygrometer, which could not have pro-
ceeded from the above caufe, but to its having been out of
order, &c.
This has drawn from M. De Luc a fecond paper on hygro-
metry, publiſhed in the Philof. Tranf. for 1791, p. 1. and 389.
This author here refumes the four fundamental principles which
he had ſketched out in the former paper, viz. 1ft, That a fire is
a fure, and the only fure, means of obtaining extreme dryneſs.
2d. That water, in its liquid ftate, is a fure, and the only fure
means of determining the point of extreme moiſture. 3d. There
is no reafon, à priori, to expect from any hygroscopic fub-
flarice, that the meaſurable effects produced in it by moisture,
are proportional to the intenſities of that cauſe. But, 4th, per-
haps the comparative changes of the dimenfions of a fubftance,
and of the weight of the ſame or other ſubſtances, by the fame
variations of moisture, may lead to fome diſcovery in that re-
fpect. On theſe heads M. De Luc expatiates at.large in this
Fárk to raife Loads.
235
paper, fhewing the imperfections of M. De Sauffure's principles
of hygrometry, and particularly as to a hair, or any fuch ſubſtance
when extended lengthwife, being properly uſed as an hygrometer.
On the other hand, he fhews that the expanſion of fubftances
across the fibres, or grain, renders them, in that refpect, by far
the moſt proper for this purpoſe. He chooſes ſuch as can be
made very thin, as ivory or deal fhavings, but he prefers whale-
bone, as far the beſt.
The preceding general deſcription of the principal hygro-
meters will, we truft, be fufficient to fhew that great imper-
fection and uncertainty attends the uſe of any of them; and, at
the fame time, to justify us in not entering more into detail, re-
fpecting the conſtruction of theſe inftruments.
JACK, an inftrument in common uſe for raiſing heavy tim
ber, or very great weights of any kind; being a powerful com-
bination of teeth and pinions, and the whole incloſed in a
ftrong wooden ſtock or frame BC, and moved by a winch or
-handle HP; the outfide appearing as in fig. 5. pl. VIII. In
fig. 6. the wheel or rack work is fhewn, being the view of
the infide when the ſtock is removed. Though it is not
drawn in the juft proportions and dimenfions, for the rack
AB muſt be fuppofed at leaft four times as long in pro-
portion to the wheel Q, as the figure reprefents it; and the
teeth, which will be then four times more in number, to
have about 3 in the inch. Now if the handle HP be 7 inches
long, the circumference of this radius will bè 44 inches, which
is the diſtance or ſpace the power moves through in one re-
volution of the handle: but as the pinion of the handle has
but four leaves, and the wheel Q fuppofe 20 teeth,
or 5
times
the number, therefore to make one revolution of the wheel Q, it
requires 5 turns of the handle, in which caſe it paffes through
5 times 44 or 220 inches: but the wheel having a pinion R
of 3 leaves, theſe will raiſe the rack 3 teeth, or one inch, in
the fame fpace. Hence, then, the handle or power moving 220
times as fast as the weight, will raife or balance a weight of 220
times its own energy. And if this be the hand of a man who
can ſuſtain 50 pounds weight, he will, by help of this jack, be
able to raiſe, or ſuſtain, a weight or force of 11000 lb. or about
5 tons weight.
This machine is fometimes open behind from the bottom
almoſt up to the wheel Q, to let the lower claw, which in that
cafe is turned up as at B, draw up any weight. When the weight
is drawn or puſhed fufficiently high, it is kept from going back by
hanging the end of the hook S, fixed to a ſtaple, over the curved
part of the handle at b.
The Society of Arts rewarded a Mr. Mocock, of Southwark,



236
MACHINES.
with a premium of 20 guineas, for his contrivance to prevent a
jack' from taking a retrograde courſe whenever the weight by
any accidental circumftance overbalances the power. The im-
proved jack only differs from thofe in common ufe in this re-
ſpect, that it has a pail or clock, and ratchet, applied in fuch
manner as to ſtop the motion of the machine as foon as it begins
to run back again. As the difference in the mechanifm is very
trifling, the improvement may be eaſily applied to any common
jacks already made.
JACK is alfo the name of a well-known engine in the kitchen,
`ufed for turning a fpit. Here the weight is the power applied,
acting by a ſet of pulleys; the friction of the parts, and the
weight with which the fpit is charged, are the forces to be over-
come; and a ſteady uniform motion is maintained by means of
a fly.
The common worm-jack is reprefented at fig. 2. pl. XII.
ABC is the barrel round which the cord QR is wound: KL
the main wheel, commonly containing 60 teeth. N the worm
wheel of about 30 teeth, cut obliquely. LM the pinion, of
about 15. O the worm or endleſs fcrew, confifting of two
fpiral threads, making an angle of 60 or 70 degrees with its
axis. X the ftud, and Z the loop of the worm fpindle. Pa
heavy wheel, or fly, connected with the fpindle of the endleſs
fcrew to make the motion uniform. DG the ftruck wheel
fixed to the axis FD. S, S, S, are holes in the frame, by which
it may be nailed to a board, and thence to any wall, the end D
being permitted to pafs through it. HI the handle going upon
the axis ET, to wind up the weight when it has run down. R
is a box of fixed pulleys, and V a correfponding one of moveable
pulleys carrying the weight. The axis ET is fixed in the barrel
AC, which axis being hollow, both it and the barrel turn round
upon the axis FD, which is fixed to the wheel KL, when it turns
in the order BTA; but cannot turn the contrary way, by reafon
of a catch nailed to the end AB, which lays hold of the crofs-bars
in the wheel LK.
The weight by means of the cord QR, in confequence of its
defcent, carries about the barrel AB, which by the action of
the catch carries the wheel KL, and this moves the pinion LM
and wheel N, the latter moving the worm O and the fly P.
Alfo the wheel LM carries the axis FD with the wheel DG,
which carries the cord or chain that goes about the wheel or
pulley at the head of the fpit. But when the handle H gives
motion to the axis in a contrary order to that given by the
weight, the catch is depreffed; fo that although the barrel BC
moves and winds the cord upon it, the wheel DG continues at
reft. The time which the jack will continue in motion de-
Kneading-mill.
237
7
pends upon the number of pulleys at R and V: and as theſe
increaſe or decreaſe, ſo muft the weight which communicates
the motion, in order to perform the fame work in the ſame
time.
SMOKE-JACK is an engine uſed for the fame purpoſe as
the common jack; and is fo called from its being moved by
means of the ſmoke, or rarefied air, aſcending the chimney, and
ftriking againſt the fails of the horizontal wheel AB (plate XII.
fig. 1.), which being inclined to the horizon, is moved about the
axis of the wheel, together with the pinion C, which carries
the wheels D and E; and E carries the chain F, which turns
the fpit. The wheel AB fhould be placed in the narrow part
of the chimney, where the motion of the ſmoke is ſwifteft, and
where alſo the greateſt part of it muſt ſtrike upon the fails.-
The force of this machine depends upon the draught of the
chimney, and the ſtrength of the fire.
Smoke-jacks are fometimes moved by means of ſpiral flyers
coiling about a vertical axle; and at other times by a vertical
wheel with fails like the float-boards of a mill: but the aboye is
the more customary conftruction.
JOINT, UNIVERSAL. See the introductory part of this vo-
lume.
KNEADING-MILL, is a contrivance by which large quan-
tities of flour may be mixed and incorporated into dough.
In many places bakers follow the diſguſting practice of knead-
ing the dough with their bare feet: and in others the buſineſs is
effected by a wooden implement, being a lever; which, faftened
at one end by a moveable hinge, is worked up and down ſo as
to preſs and knead the dough. But the machine we are about
to defcribe is far preferable, as it will knead the dough very
completely, with a great faving of time and labour. It is ufed
at the public baking-houſes of Genoa, and was firſt deſcribed in
the Atti della Societa Patriotica di Milano, vol. II.
A, in fig. 4. pl. XVIII. is a frame of wood which ſupports
the axis of the machine: a wall 14 palms high from the ground
may be made ufe of inſtead of this frame. B a wall, three
palms and a half thick, through which the aforefaid axis paffes.
C another wall fimilar to the former, and facing it, at the
diſtance of 21 palms. D, the axis, thirty palms in length, and
one palm and one-third in thickneſs. E the great wheel, fixed
to the faid axis, between the frame and the wall; its diameter
is 28 palms; and its breadth, which is capable of holding two
men occafionally, is five palms. F, are ſteps, by treading on
which the men turn the wheel very fmartly; they are two
palms diftant from each other, and one third of a palm in
height. G, a ſmall wheel with cogs, fixed almoft at the further
238
MACHINES.
3
I
Σ
extremity of the axis: its diameter is 12 palms. H a beam of
wood which extends from one wall to the other; being 21
palms in length, and one and a third in thickneſs. A fimilar
beam, not ſeen in the figure, is on the oppofite fide of the axis.
I, a tranſverſe piece of wood, placed near the wall C; it is fixed
into the two beams, and ferves to fupport the further extremity
of the axis: its length is 14 palms, and its thickneſs one and a
third: there is likewife a tranfverfe piece (which cannot be ſeen.
in the figure) 14 palms long, and half a palm thick, płaced cloſe
to the wall B. K is a ſtrong curved piece of oak, fixed tranf
verfely in the fidebeams H, to receive the axis of the trundle:
its length is 14 palms, and its thickneſs 14. L is a trun-
dle of 5 palms in diameter, and 1 in height, which is moved.
by the cogged-wheel G. M is an axis proceeding from the
trundle L, and continued through the croſs N to the bottom of
the tub P; its centre is made of iron, partly fquare and partly
round, and it turns in a focket of brafs. The first part of this
axis between the trundle L and the crofs N is of fquare iron,
furrounded by 2 pieces of wood, held together by iron hoops,
which may be removed at pleaſure to examine the iron within :
its length is 3 palms, its diameter about 1 palm. The fecond part
of the axis which is within the tube, is made like the firft part: its
height is 14 palm, its diameter 1. The wooden fheath of this
part of the axis is fixed to the bottom of the tub, by means of
three fcrews with their nuts. This axis is diftant one-third of
a palm from the neareft triangular beater of the crofs. N the
croſs, formed of two bars of wood unequally divided, ſo that the
four arms of the crofs are of different lengths: one of the two
pieces of wood of which the croſs is made, is 6 palms in length,
the other 5 their thickneſs is of a palm, and their breadth
1 palm. Ö, four pieces of wood, called beaters, of a triangular
fhape, fixed vertically into the extremities of, and underneath,
the arms of the fore-mentioned crofs: they are 12 palm in
length, and half a palm in thickneſs; and beat or knead the
dough in the tub at unequal diſtances from the centre.
P is a
ftout wooden tub, about a quarter of a palm thick, well
hooped with iron: its diameter is 6 palms, its height 14 in the
clear.
7
Fig. 5. is a box or trough of wood, 4 palms long, and 3 wide,
in which the leaven is formed (in about an hour) in a ſtove, and
in which it is afterwards carried to the tub P.
Fig. 6. exhibits a view of the trundle, crofs, &c. with a fection
of the tub.
Fig.7. is a bird's-eye view of the croſs and tub, with the upper
ends of the triangular beaters.
This tub, P, will contain 18 rubbi (about 19 bushels) of flour,
Lathe. Lens-grinder.
239
2
which is carried to it in barrels: the leaven is then carried to it
in the box or trough, fig. 5. and when the whole is tempered
with a proper quantity of warm water, the men work in the
wheel till the dough is properly and completely kneaded. ; In
general a quarter of an hour is fufficient to make very good
dough; but an experienced baker who fuperintends, determines
that the operation fhall be continued a few minutes more or lefs,
according to circumſtances.
The meafures in the preceding defcription are given in Ge-
noeſe palms, each of which is very nearly equal to 9.85 of our
inches. The machinery may be varied in its conftruction ac-
cording to circumftances, and the energy of the first mover
much better applied than by men walking in a common wheel.
LATHE, a very uſeful engine for the turning of wood, ivory,
metals, and other materials. The invention of the lathe is very
ancient: Diodorus Siculus fays, the first who ufed it was a
grandſon of Dædalus, named Talus. Pliny afcribes it to Theo-
dōre of Samos; and mentions one Thericles, who rendered him-
felf very famous by his dexterity în managing the lathe. With
this inftrument the ancients turned all kinds of vafes, many
whereof they enriched with figures and ornaments in baffo re-
lievo. Thus Virgil: " Lenta quibus torno facili fuperaddita vitis."
The Greek and Latin authors make frequent mention of the
lathe; and Cicero calls the workmen who uſed it vafcularii. It
was a proverb among the ancients, to fay a thing was formed in
the lathe, to exprefs its delicacy and juſtneſs.
The common lathe is compofed of two wooden cheeks or
fides, parallel to the horizon, having a groove or opening be-
tween: perpendicular to theſe are two other pieces called pup-
pets, made to ſlide between the cheeks, and to be fixed down at
any point at pleaſure. Thefe have two points, between which
the piece to be turned is ſuſtained: the piece is turned round
backwards and forwards by means of a ſtring put round it, and
faſtened above to the end of a pliable pole, and underneath to a
tredle or board moved with the foot. There is alfo a reft which
bears up the tool, and keeps it fteady. But the moſt ingenious.
lathes now conſtructed are different from the above: we ſhall
defcribe them under the article TURNING.
LENS GRINDING MACHINES, have been invented of many
different kinds; but, fince it has been admitted that, on the
whole, ſpherical lenfes are the moſt practically uſeful, the con-
ftruction of lens-grinders has become comparatively fimple. One
of the beſt we have ſeen was invented by Mr. Sam. Jenkins,
and deſcribed in No. 459. vol. xli. of the Phil. Tranfac. It is
contrived to turn a ſphere at one and the fame time on two axes,
cutting each other at right angles, and will produce the fegment
240
MACHINES:
4
of a true ſphere merely by turning round the wheels, without
any care or ſkill of the workmen. A (fig. 1. pl. XX.) is a globe
covered with cement, in which are fixed the pieces of glafs to
be ground: this globe is faftened to the axis, and turns with the
wheel B. C is the brafs cup which poliſhes the glaſs: this is
faſtened to the axis, and turns with the wheel D. The motion
of the cup C, therefore, is at right angles to the motion of the
globe A; whence it follows, demonftrably, that the pieces of
glafs ground by this double motion, muſt be formed into the
fegments of ſpheres.
THE LEVER, treated as one of the mechanical powers, fell
under our notice in book I. ch. iii. vol. I. where the theory of
the various kinds of levers, whether ſtraight or bent, was laid
down. Our prefent object is to defcribe a combination of the
lever with the axis in peritrochio, by means of which the re-
ciprocating motion of the lever is made uſeful in giving a con-
tinued rectilinear motion to a heavy body, without changing the
fituation of the fulcrum of the lever. This contrivance is de-
ſcribed by Belidor (Archit. Hydraul. tom. I.) under the name
of le levier de la Garouffe, and is generally called in England the
univerſal lever. FGH (fig. 2. pl. XX.) is a ſtraight lever, whoſe
centre of motion is G: on its extremity F, hang two bars FD,
FE, the former of which has a hook to catch into the teeth of
the wheel ACD, and the latter has its end flightly bent, ſo as to
flide over the outer parts of thoſe teeth. The axle A has a
cord wound about it, to the lower end of which is attached
the weight W. Now fuppofe the end H of the lever raiſed
from H by I, while the other end defcends from F to B; the
bar FE will then pufh the point E of the wheel from E to C,
while the hook D flides over an equal ſpace on the other fide of
the wheel. After this, on the end H. of the lever being brought
down again by I to H, the end F afcends through BF, and the
hook Draifes up the left hand fide of the wheel through a ſpace
equal to EC. Thus the reciprocating motion of the lever is
made to communicate a continued rotatory motion to the wheel,
and confequently to raiſe the weight W fufpended from its axle
by the cord. Here the advantage gained, neglecting friction
and the ſtiffneſs of the cord, will be in the ratio compounded of
the ratio of HG to GF, and the ratio of the radius of the wheel
to that of the axle. Thus if HG were 10 times GF, and the
radius of the wheel 10 times that of the axle, the power would
then be to the weight raiſed nearly as 1 to 100.
This machine has been advantageously applied in drawing
heavy loads along a plane nearly horizontal: in that cafe, the
cord has been carried from A in nearly an horizontal direction,
paffed round a pulley p, attached to the load w or its carriage,
Loading-machine.
241
and its end fixed to a poft as at a, or perhaps to the frame of
the wheel and axle. The pulley, it is obvious. almoſt doubles
the advantage of the power; and fince the force to be over-
come when once the fyftem is put in motion is not equiva-
lent to the whole load w, but merely to the friction, and the
rigidity of the rope, a very great weight may be moved in this
manner by a comparatively ſmall power. If the lever have an-
other arm to the left of G (as it appears in the figure) equal to GH,
a man may then work at each end, either by preffing upon it or
by pulling downwards with a cord; and thus the labourers will
alternately relieve each other. Sometimes a heart-wheel has
been combined with this univerſal lever: but it is not, we think,
a combination to be recommended in practice.
If the centre of motion G were vertically above the centre of
the wheel, and if another bar and hook fimilar and equal in
length to FD hung from the point f,f G being equal to GF;
thefe two hooks would then catch alternately into the teeth on
the rifing fide of the wheel, and thus produce the continual ro-
tatory motion: but this conftruction has a practical diſadvan-
tage; for when both bars work on the fame fide of the wheel,
they will be in great danger of catching together and impeding
each other's motions.
Univerfal levers have long been introduced into faw-mills, for
the purpoſe of drawing along the logs to be fawn. See SAW-
MILL, alfo PIPE-BORER.
LINT-MILL. See FLAX-MILL.
*
LOADING AND UNLOADING MACHINE, an invention of Mr.
G. Davis, of Windſor, for the purpoſe of removing ponderous
fubftances to or from waggons, &c. with fafety and convenience.
This portable machine is repreſented in fig. 6. pl. XV. where A
is the winch turning the bar B, on which are two endleſs ſcrews,
or worms, CC, that work in the toothed wheels DD. Theſe
wheels are fixed to the barrels EE, round which the ropes FF
coil, wind up, or let out the fame occafionally: the ropes pafs
over the pulleys GG; are brought round; and their ends, being
furniſhed with hooks for that purpoſe, are hitched into ſtaples
fixed to the front of the cart, or other carriage. Within theſe
ropes, the load H is placed on a common ftep-ladder I, that
forms an inclined plane, up which, by turning the winch, the
ropes are wound upon the barrels; and thus the load is raifed
into the carriage.
KK, the frame, intended to fhew the part of the cart, or
other carriage, on which the machine is to be occafionally
placed.
The whole of the barrels and cogged wheels are contained in
an iron box L; the fides of which are repreſented in the plate, as
VOL. II.
R
1
249
MACHINES.
t
taken off, in order that the arrangement of the different parts
may be better conceived.
The pulleys on the ſtage (GG) may, in moſt caſes, be affixed
to the machine itself; which is adapted to every direction, and
will fuit carriages of every conftruction.
The model correfponding to the preſent engraving is made on
the ſcale of about four inches to a foot; and the inventor ftates,
that it will raiſe upwards of five cwt.-He is therefore confident,
that his machine, when conftructed of its intended fize, will be
capable of loading a ton weight by one man only; and that, even
upon this enlarged plan, it does not exceed 112lb. in weight.
The Society of Arts in 1797 awarded 40 guineas to Mr. Davis,
for this uſeful invention.
LOCK, a well-known inſtrument uſed for faſtening doors,
chefts, &c. generally opened by a key. The lock is reckoned
the maſter-piece in fmithery; a great deal of art and delicacy
being required in contriving and varying the wards, ſprings,
bolts, &c. and adjuſting them to the places where they are to be
ufed, and to the feveral occafions of uſing them. From the
various ſtructure of locks, accommodated to their different in-
tentions, they acquire various names. Thofe placed on outer
doors are called stock locks; thofe on chamber-doors, ſpring-locks;
thoſe on trunks, trunk-locks, padlocks, &c. Of theſe the ſpring-
lock is the most confiderable, both for its frequency and the
curioſity of its ſtructure. Its principal parts are, the main-plate,
the cover-plate, and the pin-hole: to the main-plate belong the
key-hole, top-hook, croſs-wards, bolt-toe or bolt-knab, drawback-
fpring tumbler, pin of the tumbler, and the ſtaples; to the cover-
plate belong the pin, main-ward, croſs-ward, ſtep-ward or dape
ward; to the pin-hole belong the hook-ward, main croſs-ward,
ſhank, the pot or bread, bow-ward, and bit.
The principle on which all locks depend is the application of
a lever to an interior bolt, by means of a communication from
without; fo that, by means of the latter, the lever acts upon
the bolt, and moves it in ſuch a manner as to fecure the lid or
door from being opened by any pull or push from without. The
fecurity of locks in general therefore depends on the number of
impediments we can interpoſe betwixt the lever (the key) and
the bolt which fecures the door; and theſe impediments are well
known by the name of wards, the number and intricacy of
which alone are ſuppoſed to diſtinguiſh a good lock from a bad
If thefe wards, however, do not in an effectual manner
preclude the accefs of all other inftruments befides the proper
key, it is ftill poffible for a mechanic of equal ſkill with the lock-
maker to open it without the key, and thus to elude the labour
one.
of the other.
Mangle.
243
The excellence of locks confifts in the fecurity they afford;
and as numberlefs ſchemes are continually brought forward by
defigning men, to elude every contrivance of the moſt inge-
nious mechanics, the invention of a durable lock, ſo conſtructed
as to render it impoffible for any perfon to open it without its
proper key, has ever been an object of confiderable import-
ance.
In the year 1784 the Society for the Encouragement of Arts,
&c. conferred their filver medal on Mr. Taylor, of Petworth,
for his improvement on the latch or fpring-bolts of common
locks. This is effected by fimply reverfing the tumbler, ſo that
its curved fide acts againſt two ſtubs fixed on the tail of the latch,
and thruſts back the latter with eafe; whether the knob be
turned to the right or to the left, when the lock is opened. Mr.
Taylor has alfo, behind the tail of the latch, fixed a guide con-
taining a groove, in which runs a ſmall friction-wheel, that ferves
to keep the latch in its direct fituation, and at the ſame time to
diminith its friction: the arms of his tumbler are fomewhat
contracted, in order that the latch or fpring-bolt may move with
greater facility. By this conftruction, the parts of the tumbler
and latch, which are in contact, move in a line, fo that they pafs
over the greateſt ſpace, under the ſmalleſt angle; and the lock it
felf may be conftantly uſed for feveral years, without requiring
the application of oil.
Various patents have been obtained for the conftruction of
locks, fo as to prevent the poffibility of picking them: the prin-
cipal of theſe is Mr. Bramah's, regiſtered in 1784; and Mr.
Spears's, in 1795: but as the account of thofe inventions
would be unintelligible without the aid of ſeveral engravings,
the curious reader will confult the 5th and 8th vols. of the
Repertory of Arts and Manufactures, where they are minutely fpe-
cified.
MANGLE, a valuable domeftic machine, employed for the
purpoſe of ſmoothing fuch linen as cannot be conveniently
ironed.
Various patents have been granted for improvements in this
machinery; but, as they are not expired, and too complicated to
be underflood without very tedious details, we have annexed the
figures in pl. XII. reprefenting an improved mangle contrived
by Mr. Jee, of Rotherham; to whom the Society for the En-
couragement of Arts, &c. in 1798, voted their filver medal, for
the ingenuity diſplayed on that occafion.
The following is a defcription of Mr. Jee's improved mangle:
A (fig. 5.) points out the great wheel, which, in machines
of a full fize, is 15 inches in diameter. B, the arbor, on which
R 2
244
MACHINES.
the nut, C, is fixed. D, the handle of the winch. E, the crank,
21 inches in length. F, the rod of the crank. GG, reprefents
the hollow ftuds, by which the ends of the bed are lifted up.
HH, the levers. IIII. the four pulleys fixed on the moveable bed
K. LL, the ends of the rollers.
Fig. 6. repreſents a front view of one of the hollow ftuds.
G, to fhew its form, when ſtanding at the end of the bed;
and into which the levers enter alternately, as often as it becomes
neceffary to elevate the bed, in order to put in, or take out, the
rollers.
Mr. Jee's mangle is ſo conſtructed, that the handle requires
to be turned one way only, in confequence of which the ma-
chine moves with greater facility, and with incomparably leſs
injury to the linen, than by varying the turnings, and in a man-
ner cutting the different folds. Befides, it poffeffes the great
advantage, that a woman and one boy are fufficient to work it,
and can perform as much labour in the fame period of time
as three or four perſons with mangles of the common con-
ſtruction.
The machine at MARLY, being ſo much celebrated, on ac-
count of its magnificence and the multiplicity of its parts, we
fhall here give ſome account of it, with a few remarks upon its
conſtruction.
•
This machine, which was erected by one Rannequin, of the
country of Liege, and began to work in 1682, is fituated be-
tween Marly and the village de la Chaussée: in that place the
river is barred up, partly by the machine and partly by a dam
which keeps up the water; but that the navigation may not
be interrupted, two leagues above Marly a canal has been cut.
for the paffage of boats and barges: there has alſo been erected
(about 30 fathoms from the machine) a contrivance called an
ice-breaker, to prevent floating pieces of ice or timber which
come down the ſtream from damaging the machine; and the
better to fecure the penftocks and the channels in which the
wheels move, there is a grate of timber to stop whatever may
come through the ice-breaker.
The water is raiſed to its deftined height by means of
14 wheels which ſerve to work the pumps, by three different
ftages: first, from the river to a refervoir, at the elevation.
of 160 English feet above the level of the Seine; then to a
fecond refervoir, 346 feet higher; and from the latter to the
ſummit of a tower rather more than 533 feet above the river.
The breadth of the machine comprehends 14 gets, or water-
courſes, ſhut by fluices or penſtocks, which are raiſed and de-
preffed by racks; and in each of theſe gets is placed a wheel :
;
Engine at Marly.
245
theſe wheels are difpofed on three lines; in the firft, on the fide
which points up the ſtream there are ſeven, fix in the ſecond, and
only one in the third.
The ends of the axle of each wheel go beyond their bear-
ing pieces, and are bent into a crank, which makes a lever of
two feet; and it is to be obſerved, that the crank which is to-
wards the mountain fucks and lifts up the water of the river, to
drive it into the firſt ciſtern, and the other crank gives motion to
the balances.
Six of the wheels on the first line give motion by one of their
cranks to an engine of eight pumps, without reckoning the
feeder: theſe engines are compounded of a regulator, at each
end of which hangs a fquare piece of wood, that carries and
directs four piſtons; the regulator is put in motion by two beams
or leaders, one of which lying along anfwers to the crank of the
wheel and a vertical regulator, and the other hanging down is
united to the fame regulator and to the balance.
Of the fix wheels we have mentioned, there are five which
by their other crank give motion to the pumps that work in
the ciſtern of the firft lift, by means of horizontal levers and
chains that communicate the motion. The fixth wheel, which
is the firſt towards the dam, moves a long chain that works
the pumps of one of the wells of the upper ciftern, which is
called the ciſtern of the great chevalets. Each of the cranks of
the ſeventh wheel of the first line moves a chain which goes to
the first ciftern.
The fix wheels of the fecond line move, by each of their
cranks, a chain that goes to the upper ciftern, which (reckoning
the chain that comes from the fixth wheel of the firſt line) makes
13 chains. Theſe chains go over one of the ciſterns of the firſt
lift; and five of them at the fame time give motion to the piſtons
of thirty pumps, whilft the other chains go on ftraight to the
upper ciſtern.
Laftly, the wheel which is on the third line, by each of its
cranks, works an engine of eight fucking and lifting pumps, and
of itſelf fupplies one conduit pipe.
The feven chains of the wheels of the firft line in going along
work alfo eight fucking pumps placed a little below the ciftern
of the first lift, becauſe in that place there are the waters of a
confiderable ſpring brought thither by an aqueduct; and theſe
fame chains take up that water the fecond time to force it by
49 pumps into the upper refervoir, through two conduit pipes
of eight inches, and three others of fix inches diameter. The
thirty pumps of the cistern of the firſt lift drive their water alfo
through two pipes of eight inches diameter, which carry it inta
the upper ciftern.
246
MACHINES.
The water raifed at the two cifterns in the way up the hill
diſcharges itſelf into a great refervoir, and thence, by two conduit
pipes of a foot diameter each, it runs into refervoirs of commu-
nication to be diſtributed into the feveral wells or little cifterns
of the upper ciftern, whence it is raiſed by 82 pumps, through
6 conduit pipes of 8 inches diameter, up into the tower which
anfwers to the aqueduct.
The eight great chains that go ftraight to the upper ciſtern,
without moving any engines by the way, work 16 pumps behind
the upper ciftern, to bring back into the refervoir of the faid
ciftern the water which is loft out of the fix pipes that go to the
tower.
The eight engines which fuck and lift the water from the
river contain 64 pumps: the two cifterns in the way up the hill
together contain 79 pumps, and the upper cifterns 82, to which
adding the fucking pumps called feeders, and the 8 others which
are below the midway ciftern, and befides the 16 pumps which
we mentioned as placed behind the upper ciftern, the machine
has in all 253 pumps.
The bafin of the tower which receives the water raiſed from
the river, and fupplies the aqueduct, is 610 fathoms diftant
from the river. The water having run along an aqueduct of
36 arches is feparated into different conduits which lead it
to Marly, and formerly conveyed it alſo to Veṛfailles and
Trianon.
Such is the mechaniſm of the machine of Marly. Its mean
produce is from 30000 to 40000 gallons of water per hour.
We fay mean produce, becauſe, under certain favourable circum-
ftances, it raifes more than 60000 gallons per hour. But during
inundations, or when the Seine is frozen, when the water is very
low, or when any repairs are making, the machine ftops in great
meaſure, if not entirely.
The annual expence of the machine, including the ſalaries of
thofe who fuperintend it, and the "wages of the workmen em-
ployed, together with repairs, neceffary articles, &c. may amount
to about 3300/. fterling, or gl. per day: which makes about
I farthing for 90 gallons. Or, taking into the account the in-
tereft of 33300cl. the original expence of erection, 90 gallons
will coft three halfpence, which is at the rate of a farthing for
15 gallons*.
* This is very far from the price which the king of Denmark thought
he might ſet on this water; for that prince, when he vifited Marly in
1769, being aftoniſhed at the immenfe magnitude of the machine, the
multiplicity of its movements, and the number of workmen it employed,
conjectured that the water probably coſt as much as wine.
1
Hydraulic Engine at Marly.
247
Whoever has an opportunity of examining this machine, or
perufes attentively the minute account of it given by Belidor in
his fecond volume, will be convinced that Rannequin was an in-
genious practical machanic, but no mathematician or philofo-
pher. In feveral poſitions the moving forces act unneceflarily
obliquely, which occafions a great lofs of power, and renders
the machine lefs effectual. About 2 of the whole moving
power of fome of the water-wheels are employed in giving a re-
ciprocating motion to a fet of rods and chains, which extend
from the wheels to the ciftern nearly three-fourths of a mile
diſtant, where they work a fet of pumps. By fuch injudicious
conſtruction, this engine is no lefs a monument of ignorance
than of magnificence.
It is probable Rannequin thought his moving force would not
be fufficient to raiſe the water to the height of 533 feet, at once;
but this is not agreeble to theory: for a proper calculation
would fhew that the force of one crank is more than fufficient
to raiſe a cylinder of water of that altitude, and above 8 inches
in diameter. To effect this with fafety, however, the conftruc-
tion of the machine must be varied in feveral refpects. But
even according to the preſent conftruction, the water might be
raiſed in one jet to the ſecond refervoir. This is manifeft from
two experiments, one made in 1738, and the other in 1775. In
the firft M. Camus endeavoured to make the water rife in one
jet to the tower: his attempt was not attended with fuccefs; but
he made the water rife to the foot of the tower, which is con-
fiderably higher than the fecond refervoir. During this experi-
ment the machine was prodigiouſly ſtrained, and it was found
neceffary to fecure fome parts of it with chains. The object
of the fecond trial, made in 1775, was to raiſe the water only
to the fecond well. It indeed afcended thither at different times,
and in abundance: but the pipes were exceedingly ftrained at
the bottom, fo that feveral of them burſt; and it was neceffary
to fufpend and recommence the experiment feveral times. This
however arofe from the age of the tubes and their want of
ftrength, a fault which might easily have been remedied. Hence,
it refults from this trial, that the chains which proceed from the
river to the firſt well might be fuppreffed, together with the firſt
well itſelf and this perhaps is all that is to be expected without
a complete change in the machinery.
MILL, properly denotes a machine for grinding, or pulverifing
fubftances, as corn, &c. ; but, in a more general fignification, is
now applied to many machines whofe action arifes in great mea-
fure from a circular motion. Of theſe there are various kinds
deſcribed in different parts of this volume, as Bark-mill, Barker's

:
248
MACHINES.
mill, Flax-mill, Flour-mill, Foot-mill, Hand-mill, Kneading-mill,
Oil-mill, Paper-mill, Saw-mill, Tide-mill, Water-mill, &c
As a well-conftructed, yet cheap, family-mill cannot but be
highly uſeful in many parts of the country, we fhall here pre-
fent a deſcription of the Family-mill and Bolter of Mr. T.
Ruftall, of Purbrook-heath, near Portſmouth, who received
a premium of 40 guineas from the Society of Arts for his in-
vention*.
•
In pl. XX. fig. 4. A, is the handle of the mill; B, one of
the mill-ftones, which is about 30 inches in diameter. and
5 inches in thickneſs, moving with its axis C: D, is the other
mill-ſtone, which, when in ufe, is ftationary; but which may
be placed near to, or at a diſtance from, the moveable ftone B,
by means of three fcrews paffing through the wooden block E,
that ſupports one end of the axis C; after it has been put
through a hole or perforation in the bed ftone.
The grain
likewife paffes through this perforation from the hopper F,
into the mill. F, reprefents the hopper, which is agitated by
two iron pins on the axis C, that alternately raiſe the veffel con-
taining the grain, which again finks by its own weight. In
confequence of this motion the corn is conveyed through a
ſpout that paffes from fuch hopper into the centre of the mill
behind, and through the bedſtone D. G, a paddle, regulating
the quantity of corn to be delivered to the mill; and, by raiſing
or lowering which, a larger or ſmaller proportion of grain may
be furniſhed: H, the receptacle for the flour, into which it
falls from the mill-ftones, when ground: I, repreſents one of
the two wooden fupporters on which the bedſtone, D, refts.
Theſe are ſcrewed to the block E, and likewife mortifed into
the lower frame-work of the mill at K, which is connected by
means of the pins or wedges L, L, L, that admit the whole mill
to be eaſily taken to pieces: M, a fly-wheel, placed at the furtheſt
extremity of the axis C, and on which another handle may be
occafionally fixed; N, a fmall rail, ferving to keep the hopper
in its place; the furtheft part of fuch hopper refting on a ſmall
pin, which admits of fufficient motion for that veffel, to fhake
forward the corn: O, a fpur-rail, for ftrengthening the frame-
work of the mill; P, the front upright, that is mortifed into the
frame-work, and ſerves as a reft for the end of the iron axis C,
which is next to the handle. On each extremity of fuch axis
there is a fhoulder, which keeps it fteady in its place. Laftly,
there is a cloth-hood fixed to a broad wooden hoop, which is
* Mr. Ruſtall engages to furniſh the whole apparatus, and deliver it
free of carriage, in London, for the moderate price of twenty guineas.
1
· Family-mill.
249
}
placed over the ftones while working, to prevent the finer parti-
cles of flour from eſcaping.
Fig. 5. repreſents the bolter, with its front removed, in order
to diſplay its interior ſtructure; the machine being 3 feet 10
inches in length, 19 inches in breadth, and 18 inches in depth,
A, is a moveable partition, fliding about four feet backwards or
forwards, from the centre of the box, upon two wooden ribs,
which are fixed to the back and front of the box, and one of
which is delineated at the letter B, C, the lid of the bolter, re-
preſented open; D, a ſlider, which is moveable in a groove made
in the lid, by means of two handles on the back of fuch lid; E,
a forked iron, fixed in the flider D, and which, when the lid is
fhut, takes hold of the edge of the fieve F, and moves it back-
wards and forwards on the wooden ribs B, according to the agi-
tation of the flider; G, reprefents a fixed partition in the lower
centre of the box, which it divides into two parts, in order to
ſeparate the fine from the coarſe flour; from this partition the
ſlider A moves each way about four inches, and thus affords
room for working the fieve: H, a board that is parallel to the
bottom of the bolter, and forms part of the flider A; this board
ferves to prevent any of the fifted matter from falling into the
other partition: I, repreſents two of the back feet, which ſupport
the bolter.
Fig. 6. of the plate above mentioned is a view of the top, or
upper part, of the lid of the bolter; K, the flider that moves the
length wife of the bolter; L, L the handles by which the flider is
worked; M, a fcrew, ferving to hold the fork, which imparts
motion to the fieve.
Fig. 7. repreſents the forked iron, E, feparately from the
lid.
►
Both the mill and bolter may be conſtructed at a moderate
expence, and they occupy only a ſmall ſpace of ground. The
former may even be worked in a public kitchen, or within a
room in a farm-houſe, without occafioning any great incum-
brance.
The particular excellence of the mill confifts in this circum-
ftance, that, from the vertical pofition of its ftones, it may be
put in action without the intervention of cogs or wheels. It may
be employed in the grinding of malt, the bruising of oats for
horſes, and for making flour, or for all theſe purpoſes: it may
likewiſe be eaſily altered, fo as to grind either of thoſe articles to
a greater or lefs degree of fineness.
Another advantage peculiar to Mr. Ruftall's contrivance is,
that one man is fufficient to work it; though, if two perfons,
namely, a man and a boy, be employed, they will be able to
I
230
MACHINES.
1
produce, in the courfe of two hours, a quantity of flour faf-
ficient to ferve a family, confifting of fix or eight perfons,
for a whole week:-repeated fatisfactory trials have proved,
that this milk grinds the corn completely, and at the rate of
one bufhel of wheat within the hour. Befides, the induftri-
ous farmer will thus be enabled to make comparative experi-
ments on the quality of his grain, and may furnish himself,
at a trifling expence, with flour from his own wheat, with-
out apprehending any adulteration; or without being expofed
to the impofitions, or caprice, of fraudulent and avaricious
millers.
Lastly, though Mr. R.'s bolter be more particularly calculated
for hfting flour, it may alfo be applied to various other ufeful
purpofes, and efpecially with a view to obviate the inconveniences
neceffarily attendant on the levigation of noxious fubftances, and
to prevent the waste of their finer particles.
The fubject of mill-work has engaged the attention of many
authors in different countries: the following is a catalogue of the
chief writings, both theoretical and defcriptive.
Kinftliche abrifs, allerhand waffer wind- rofs- und hand-
muhlen, &c. von Jacob. de Strada à Rofberg. 1617:
Georg Chriftoph Luerner Machina toreutica nova; oder, bef-
chreibung der neu erfundenen Drehmühlen.
1661.
Theatrum machinarum novum; das iſt, neu vermehrter
Schauplatz der mechanifchen Künfte, handelt von allerhand
waffer- wind- rofs- gewicht- und hand- muhlen. Von Geo. And.
Bocklern. 1661.
Contenta difcurfus mechanici, concernentis defcriptionem
optimæ formæ velorum horizontalium pro ufu molarum, nec
non fundamentum inclinatorum velorum in navibus, habita
coram Societate Regia, a R. H. tranflata ex collectionibus philo-
fophicis M. Dec. num. 3. pà. 61. 1681.
Differtatio hiftorica de molis, quam præfide Job. Phil. Treuer
defend. Fo. Tob. Mühlberger Ratifbonens. Jenae. 1695.
Martin Marten's Wilkundige befchouwinge der wind-of
wadermoolens, vergeleken met die van den heer Jobann Lulofs.
Amfterdam. 1700.
{
Vollſtändige mühlen-baukunft, von Leonhard Chriftoph. Sturm.
1718.
Jacob Leupold's Theatrum machinarum. 1724, 1725.
Remarques fur les aubes ou pallettes des moulins, et autres
machines mues par le courant des rivières. Par M. Pitat
mem. Acad. Roy. Paris.
Joh. van. Zyl theatrum
gemeen moolen-bock, &c.
1729.
machinarum univerfale of groot al-
Amfterdam. · 1734.
Writings relative to Mill-work.
251
fo. Caral. Totens Differ. de machinis molaribus optime con-
ftruendis. Lugd. Batav. 1734.
Kurze, aber deutliche anweiſung zur conftruction der wind-
und waffer-muhlen, von Gottfr. Kinderling. 1735.
Defaguliers's experimental philofophy. ~ 1735, 1744.
Architecture hydraulique, par M Belidor. 1737, 1753.
Part of a letter from Mr. W. Anderſon, F. R. S. to Mr.
Baker, F. R. S. containing a defcription of a water-wheel for
mills invented by Mr. Philip Williams. Phil Tranſ. vol. 44,
1746.
Leonh. Euleri, De conftructione aptiffima molarum alatarum
difp. Nov. Com. Acad. Petrop. tom. 4. 1752.
Mémoire dans lequel on démontre que l'eau d'une chûte
deftinée à faire mouvoir quelque machine, moulin ou autre,
peut toujours produire beaucoup plus d'effét en agiffant, par
fon poids qu'en agiffant par fon choc, et que les roues à pots
qui tournent lentement produifent plus d'effet que celles qui
tournent vite, relativement aux chûtes et aux dépenfes, Par M.
de Parcieux, Acad. Roy. Paris. 1754.
Jo. Alberti Euleri Enodatio queftionis: quo modo vis aquæ
aliufve fluidi cum maximo lucro ad molas circumagendas, aliave
opera perficienda impendi poffit, præmio à focietate Regia. Sci.
Gotting. 1754-
Recherches plus exactes fur l'effet des moulins à vent, par
M. Euler. Hift. Acad. Roy. Berlin. 1756.
An experimental enquiry concerning the natural powers of
wind and water to turn mills and other machines depending on
a circular motion. By Mr. 7. Smeaton, F. R. S. Phil. Tranf.
1759.
[Abstracts of this and Mr. Smeaton's other papers on water
and wind mills have been given in book iv. of our firſt volume,
and the Introduction to this. They were collected and pub-
lifhed by Taylor, Holborn, in 1794.]
Mémoire dans lequel on prouve que les aubes des roues mûes
par les courans des grandes rivières feroient beaucoup plus
d'effet fi elles étoient inclinées aux rayons, qu'elles ne font étant
appliquées contre les rayons mêmes, comme elles le font aux
moulins pendans et aux moulins fur bateaux qui font fur les
rivières de Seine, de Marne, de Loire, &c. Par M. de Parcieux,
mem. Acad. Roy. Paris. 1759-
Joh. Albert Euler's Abhandlung von der bewegung ebener
flächen, wenn fie vom winde getrieben werden. 1765.
Schauplatz des mechaniſchen mühlenbaues, darinnen von
verfchiedenen hand- trett- rofs- gewicht- waffer- und wind-
mühlen gehandelt wird, durch Johann Georg Scopp I. C. iter
Theil. 1766.
252
MACHINES.
Theatrum machinarum molarium, oder ſchauplatz der mü-
ħlenbaukunſt. als der neunte theil von des fel hru Jac. Leupolds
theatro machinarum, von Joh. Mathias Beyern. 1767, 1788,
1802.
A memoir concerning the most advantageous construction
of water-wheels, &c. by Mr. Mallet of Geneva. Phil. Trans.
1767.
Mémoire fur les roues hydrauliques, par M. le Chevalier de
Borda, mem. Acad. Roy. Paris. 1767.
Kurzer unterricht, allerley arten von wind- und waffer- mühlen
auf die vortheilhafteſte weiſe zu erbauen, nebst einigen gedanken
über die verbefferung des räderwerks an den mühlen, von Joh.
König. 1767.
G. G. Bifchoff's Beyträge zur mathefis der muhlen. 1767.
Sur la pofition des ailes des moulins à vent. D'Alembert.
Opufc. mathema. tom. 5. 1768.
Determination générale de l'effet des roues mûes par le choc
de l'eau, par M. l'abbé Boſſut, mem. Acad. Roy. Paris. 1769.
Andreas Kaovenhöfer, Deutliche abhandlung von den rädern
der waffermühlen, und von dem einrandigen werke der ſchnei-
demühlen. 1770.
Manuel du meûnier et du charpentier des moulins, redige par
Edm. Bequillet. 1775-
Rémarques fur les moulins à vent, par M. Lambert.
Rémarques fur les moulins et autres machines, où l'eau
tombe en deffus de la roue, par M, Lambert,
Experiences et rémarques fur les moulins que l'eau meut par
en bas dans une direction horizontale, par M. Lambert.
Rémarques fur les moulins et autres machines dont les roues
prennant l'eau à une certaine hauteur, par M. Lambert.
[The laft four articles are inferted in Mem. Acad. Roy,
Berlin. 1775-1
Of the degrees and quantities of winds requifite to move the
heavier kinds of wind-machines, by John Stedmann, M. D. Phil.
Trans. 1777.
Ausführliche erklärung der vorſchläge für die längere dauer
der muhlenwerke, nebít ähnlichen gegenstanden, in ein geſpräch
verfaffet, von Johann Chriftian Fullmann, Mühlenmeiſter. 1780.
Obfervations théoriques et experimentales fur l'effet des
moulins à vent, et fur la figure de leurs ailes, par M. Coulumb,
mem. Acad. Roy. Paris. 1781.
Tratado de los granos y modo de molerlos con economia, dẹ
la confervacion de aftos y de las harinas; efcr. en Fr. par M.
Beguillet, y extract, y trad. al Caft. con algun notas y un ſupplem,
por Ph. Marefcaulchi. Madrid. 1786.
Suite de l'architecture hydraulique, par M. Fabrre, 1786.
Concave Muller.
253
Mémoires fur les moyens de perfectionner les moulins, et la
mouture économique, par C. Bucquet. 1786.
Manuel ou vocabulaire des moulins à pot. A Amſt. 1786.
Die nothigſten kenntniffe zur anlegung, beurtheilung und
berechnung der waffermühlen, und zwar der mahl- oehl- und
säge- mühlen, sür anfänger und liebhaber der mühlenbaukunft,
von Joh. Chrift. Huth. 1787.
An effay proving iron far fuperior to ftone of any kind for
breaking and grinding of corn, &c. by W. Walton. 1788.
Mühlenpraktik, oder unterricht in dem mahlen der brod-
früchte, für polizeybeamte, gaverkſleute und hauſwirthe, von
L. Ph. Hahn. 1790.
The young millwright and miller's guide, by Oliver Evans.
Philadelphia. 1790.
Manuel du meûnier et du conftructeur des moulins à eau et
à grains, par C. Bucquet. 1791.
Praktiſche anweifung zum mühlenbau, von Lr. Claufen.
1792.
Beſchreibung zweir maſchinen zur reinigung des korns, von
Lr. Claufen. 1792.
Inftructions fur l'ufage des moulins à bras, inventés et per-
fectionnés par les Citoyens Durand père et fils, mécaniciens.
1793-
Theoretiſch-praktiſche abhandlung über die befferung der
muhlräder von dem verfaffer der zweckmäffigen luftreiniger,
&c. 1795.
A treatise on mills, in four parts, by John Banks. 1795.
Handbuch der maſchinenlehre, fur praktiker und akademiſche
lehrer, von Karl Chriftian Langsdorf. 1797, 1799.
On the power of machines: including Barker's-mill, Weft-
garth's engine, Cooper's-mill, horizontal water-wheel, &c. by
John Banks. 103.
The experienced millwright, by Andrew Gray, millwright.
1804.
The tranfactions of the Society of Arts and Manufactures;
feveral of the volumes of which contain improvements in mill-
work. See alſo the Repertory of Arts, in ſeveral places.
MULLERS for grinding colours, according to the common
conſtruction, are too well known and too fimple to need a par-
ticular deſcription here. But Mr. James Rawlinfon, of Derby,
has invented a concave muller, for which the Society of Arts
preſented him a filver medal and ten guineas, on account of its
ingenuity. He has uſed his machine for feveral years, and has
found it much more effectual and expeditious in reducing the
colour to extreme fineness than the uſual method, and much
254
MACHINES.
鸞
​lefs injurious to the health of the workman, who frequently has
done as much with it in three hours as he could in twelve with
the muller and ſlab.
The machine conſiſts of a flat cylinder of black marble, fix-
teen inches and a half diameter, and four and a half thickneſs,
with an axle traverfing its centre (thus fomewhat refembling a
common cutler's grindstone). It is fufpended on a fimilar frame,
in a vertical poſition, and turned round in the ſame manner by
a winch: a concave piece of marble is provided, of the fame
breadth as the circular ftone, forming a fegment of the fame cir-
cle one third of the circumference in extent: this, which may
be confidered as the muller, is fitted into a piece of folid wood
of fimilar ſhape, one end of which is fecured 'lcofely by a hinge
or otherwife to the frame; the other end, rifing over the circular
ftone and ſupported by it, is further preffed down on it by a long
fpring bent over from the oppofite extremity of the ſtand, and
regulated as to its preffure by a fcrew, whofe end turns againſt
the concave muller: a flight frame of iron in front, moveable
on a hinge, by which it is fecured to the frame, fupports a fera-
per, for taking off the colour, formed of a piece of watch-fpring,
which is turned back out of the way when not in uſe. Mr. R.
thinks the circular grindstones might be made much larger than
that he uſed, to advantage, and that one of two feet diameter
would not occafion too much labour to one man to turn it: he
computes that in his machine there are ſeventy ſquare inches of
furface of the concave muller in conftant work on the paint,
while in the common muller not more than ſixteen fquare inches
are uſually in contact with the flab. The machine will be found
equally ferviceable for the colours ground in water as for thoſe
prepared with oil, according to Mr. R., who highly recommends
its ufe to all colourmen.
Mr. R. adviſes, in making up the colours in bladders, to in-
fert a bit of quill or reed in the neck of the bladder, which will
thus bind better in tying; and, admitting of a fecure ftopper,
will be more cleanly and leſs wafteful than the uſual method of
ftopping with a nail, and keep the colour more fafe from the
air. Retrofpect, &c. No. 1.
NORIA. See HYDRAULIC-machines, No. 3.
OIL-MILL, a mill for expreffing the oils from fruits, or
grains, &c. As theſe kingdoms do not produce the olive, it
would be needlefs to defcribe the mills which are employed in
the fouthern parts of Europe. We fhall content ourſelves, there-
fore, with a defcription of a Dutch oil-mill, employed for grind-
ing and preffing lint-feed, rape-feed, and other oleaginous grains.
Further, to accommodate our defcription ftill more to our local
Oil-mill.
255
circumſtances, we fhall employ water as the firft mover; thus
avoiding the enormous expence and complication of a windmill.
In plate XXI. fig. A,
1. Is the elevation of a wheel, over or under-fhot, as the fitua
tion may require.
2. The bell-metal focket, fupported by mafonry, for receiving
the outer gudgeon of the water-wheel,
*3. The water-courſe.
Fig. B.
1. A ſpur-wheel upon the fame axis, having 52 teeth.
2. The trundle that is driven by No. 1. and has 78 ftaves,
3. The wallower, or axis for raiſing the peſtles. It is furniſh-
ed round its circumference with wipers for lifting the peftles, fo
that each may fall twice during one turn of the water-wheel,
that is, three wipers for each peſtle.
4. A frame of timber, carrying a concave half-cylinder of
bell-metal, in which the wallower (cafed in that part with iron
plates) reſts and turns round.
5. Mafonry fupporting the inner gudgeon of the water-wheel
and the above-mentioned frame.
6. Gudgeon of the wallower, which bears againſt a bell-
metal ſtep fixed in the wall. This double fupport of the wallower
is found to be neceffary in all mills which drive a number of
heavy ſtampers.
Fig. C, is the elevation of the peſtle and prefs-frame, theiṛ
furniture, the mortars, and the prefs-peftles.
1. The fix peſtles.
2. Crofs pieces between the two rails of the frame, forming,
with thefe rails, guides for the perpendicular motion of the
peſtles.
3. The two rails. The back one is not feen. They are check-
ed and bolted into the ſtandards No. 12.
4. The tails of the lifts, correfponding to the wipers upon the
wallower. See the article WIPER.
5. Another rail in front, for carrying the detents which hold
up the peſtles when not acting. It is marked 14 in fig. M.
6. A beam a little way behind the peftles. To this are
fixed the pulleys for the ropes which lift and ſtop the peſtles.
It is reprefented by 16 in fig. M.
7. The faid pulleys with their ropes.
8. The driver, which ſtrikes the wedge that preffes the oil.
9. The diſcharger, a ftamper which ſtrikes upon the inverted
wedge, and loofens the prefs.
10. The lower rail with its crofs pieces, forming the lower
guides of the peftles.
11. A ſmall cog-wheel upon the wallower, for turning the
256
MACHINES.
fpatula, which ſtirs about the oil-feed in the chauffer-pant. fe
has 28 teeth, and is marked No. 6. in fig. M.
12. The four ſtandards, mortifed below into the block,
above into the joiſts and beams of the building.
and
13.
The fix mortars hollowed out of the block itſelf, and in
fhape pretty much like a kitchen pot.
14. The feet of the peftles, rounded into cylinders, and fhod
with a great lump of iron.
15. A board behind the peſtles, ſtanding on its edge, but in-
clining a little backwards. There is fuch another in front, but
not repreſented here. Thefe form a fort of trough, which pre-
vents the feed from being fcattered about by the fall of the
peftles, and loft.
16. The firſt preſs-box (alſo hollowed out of the block), in
which the grain is fqueezed, after it has come for the first time
from below the mill-ftones.
M
17. The fecond prefs-box, at the other end of the block, for
fqueezing the grain after it has paffed a fecond time under the
peftles.
18. Frame of timber for fupporting the other end of the
wallower, in the fame manner as at No. 4. fig. B.
19. Small cog-wheel on the end of the wallower, for giving
motion to the mill-ftones. It has 28 teeth.
20. Gudgeon of the wallower, bearing on a bell-metal ſocket
fixed in the wall.
21. Veffels for receiving the oil from the prefs-boxes.
Fig. D. Elevation and mechaniſm of the mill-ftones.
1. Upright ſhaft, carrying the great cog-wheel above, and the
runner mill-ftones below in their frame.
2. Cog-wheel of 76 cogs, driven by No. 19. of fig. C.
3. The frame of the runners.
4. The innermoft runner, or the one neareſt the ſhaft.
5. Outermoft ditto, being further from the ſhaft.
6. The inner rake, which collects the grain under the outer
runner
runner.
7. The outer-rake, which collects the grain under the inner
In this manner the grain is always turned over and
over, and cruſhed in every direction. The inner rake lays the
grain in a flope, of which fig. O is a ſection; the runner flattens it,
and the fecond rake lifts it again, as is marked in fig. P; fo
that every fide of a grain is prefented to the mill-ftone, and the
reft of the legger or nether mill-ftone is fo fwept by them, that
not a fingle grain is left on any part of it. The outer rake is
alſo furniſhed with a rag of cloth, which rubs againſt the border
or hoop that furrounds the nether mill-ſtone, fo as to drag out
the few grains which might otherwife remain in the corner.
•
Oil-mil.
257
8. The ends of the iron axle which paffes through the up-
right ſhaft, and through the two runners. Thus they have two
motions: Imo, A rotation round their own axis; 2do, That
by which they are carried round upon the nether mill-ftone on
which they roll. The holes in theſe mill-ftones are made a
little wide; and the holes in the ears of the frame, which carry
the ends of the iron axis, are made oval up and down. This
great freedom of motion is neceffary for the runner mill-ſtones,
becauſe frequently more or lefs of the grain is below them at a
time, and they muft therefore be at liberty to get over it without
ftraining, and perhaps breaking, the fhaft.
9. The ears of the frame which lead the two extremities of
the iron axis. They are mortifed into the under fide of the
bars of the fquare frame, that is carried round with the ſhaft.
10. The border or hoop which furrounds the nether milk-
ftone.
11. and 12. The nether mill-ſtone, and maſonry which fup-
ports it.
Fig. K. Plan of the runner mill-ftones, and the frame which
carries them round.
I, I. Are the two mill-ftones.
3, 3, 3, 3. The outfide pieces of the frame.
4, 4, 4,4. The croſs-bars of the frame which embrace the
upright fhaft 5, and give motion to the whole.
6, 6. The iron axis upon which the runners turn.
7. The outer rake.
8. The inner ditto.
Fig. L. Repreſents the nether mill-ftone feen from above.
1. The wooden gutter, which furrounds the nether mill-ftone
2. The border or hoop, about fix inches high, all round, tó
prevent any feed from being ſcattered.
3. An opening or trap-door in the gutter, which can be
opened or fhut at pleaſure. When open, it allows the bruifed
grain collected in and fhoved along the gutter by the rakes to
paſs through into troughs placed below to receive it.
4. Portion of the circle defcribed by the outer runner.
5. Portion of the circle defcribed by the inner one. By
thefe we fee that the two ftones have different routes round the
axis, and bruiſe more ſeed.,
6. The outer rake.
7. The inner ditto.
8. The ſweep, making part of the inner rake, occafionally let
down for fweeping off all the feed when it has been fufficiently
bruifed. The preffure and action of theſe rakes is adjusted by
means of wooden fprings, which cannot be eaſily and diſtinctly
reprefented by any figure. The oblique pofition of the rakes
VOL. II.
$
1
"
+
258
MACHINES.
7
(the outer point going foremoſt) cauſes them to fhove the grain
inwards or toward the centre, and at the ſame time to turn it
over, fomewhat in the fame manner as the mould-board of a
plough fhoves the earth to the right hand, and partly turns it
over. Some mills have but one fweeper; and, indeed, there is
great variety in the form and conftruction of this part of the
inachinery.
Fig. M. Profile of the peftle frame.
1. Section of the horizontal ſhaft.
2. Three wipers for lifting the peſtles. See WIPer.
3. Little wheel of 28 teeth, for giving motion to the ſpatula.
4. Another wheel, which is driven by it, having 20 teeth.
5. Horizontal axle of ditto.
6. Another wheel on the fame axle, having 13 teeth.
7. A wheel upon the upper end of the ſpindle, having 12
teeth.
8. Two guides, in which the fpindle turns freely, and ſo that
it can be ſhifted higher and lower.
9. A lever, moveable round the piece No. 14. and having a
hole in it at 9, through which the fpindle paffes, turning freely.
The fpindle has in this place a ſhoulder, which refts on the
border of the hole 9; fo that by the motion of this lever the
fpindle may be difengaged from the wheel-work at pleaſure.
This motion is given to it by means of the lever 10, 10, move-
able round its middle. The workman employed at the chauffer
pulls at the rope 10, 11, and thus difengages the ſpindle and
Spatula.
11. A peſtle feen fidewife.
12. The lift of ditto.
13. The upper rails, marked No. 3. in fig. C.
14. The rail, marked No. 5. in fig. C. To this are fixed
the detents, which ſerve to ſtop and hold up the peſtles.
15. A detent, which is moved by the rope at its outer end.
16. A bracket behind the peftles, having a pulley, through
which paffes the rope going to the detent 15.
17. The faid pulley.
18. The rope at the workman's hand, paffing through the
pulley 17, and fixed to the end of the detent 15.
This detent naturally hangs perpendicular by its own weight.
When the workman wants to ftop à peftle, he pulls at the rope
18, during the rife of the peftle. When this is at its greateſt
height, the detent is horizontal, and prevents the peſtle from
falling by means of a pin projecting from the fide of the peſtle,
which refts upon the detent, the detent itſelf being held in that
pofition by hitching the loop of the rope upon a pin at the work-
man's hand.
Oil-mill.
*
19. The two lower rails, marked No. 10. fig. C.
20. Great wooden, and ſometimes ſtone, block, in which the
mortars are formed, marked No. 21. in fig. €.
21. Veffel placed below the prefs-boxes for receiving the oil.
22. Chauffer, or little furnace, for warming the bruiſed grain.
23. Backet in the front of the chauffer, tapering downwards,
and opening below in a narrow flit. The hair bags, in which
the grain is to be preffed after it has been warmed in the chauffer,
are filled by placing them in this backet. The grain is lifted
out of the chauffer with a ladle, and put into theſe bags; and a
good quantity of oil runs from it through the flit at the bottom
into a veffel fet to receive it.
24. The ſpatula attached to the lower end of the ſpindle, and
turning round among the grain in the chauffer-pan; thus
preventing it from ſticking to the bottom or fides, and getting
too much heat.
The first part of the proceſs at an oil-mill is bruifing the feed
under the runner ftones*. That this may be more expeditiously
done, one of the runners is fet about 3ds of its own thickneſs
nearer the ſhaft than the other. Thus they have different
treads; and the grain, which is a little heaped towards the centre,
is thus bruiſed by both. The inner rake gathers it up under
the outer ſtone into a ridge, of which the ſection is repreſented in
plate XXI. fig. O. The ftone paffes over it and flattens it. It is
gathered up again into a ridge, of the form of fig. P, under the
inner ftone, by the outer rake, which confifts of two parts.
The outer part preffes clofe on the wooden border which fur-
rounds the nether ſtone, and ſhoves the feed obliquely inwards,
while the inner part of this rake gathers up what had ſpread
toward the centre. The other rake has a joint near the middle
of its length, by which the outer half of it can be raiſed from
the nether ftone, while the inner half continues preffing on it,
and thus fcrapes off the moift pafte. When the feed is fuffici-
ently bruiſed, the miller lets down the outer end of the rake,
This immediately gathers the whole paſte, and ſhoves it obliquely
outwards to the wooden rim, where it is at laſt brought to a part
that is left unboarded, and it falls through into troughs placed
to receive it. Thefe troughs have holes in the bottom, through
which the oil drips all the time of the operation. This part of
the oil is directed into a particular ciftern, being confidered as the


* We are told, that in a mill at Reichenhoffen, in Alface, a confider-
able improvement has been made by paffing the feed between two fmall
iron rollers, before it is put under the mill-ftones. A great deal of work
is faid to be ſaved by this preliminary operation, and finer oil produced:
which we think very probable. The amping and preffing go on as in
other mills.
$ 2
200
MACHINES.
pureft of the whole; having been obtained, without preffure, by
the mere breaking of the hull of the feed.
In ſome mills this operation is expedited, and a much greater
quantity of this beft oil is obtained, by having the bed of
mafonry which fupports the legger formed into a little furnace,
and gently heated. But the utmoft care is neceffary to prevent
the heat from becoming confiderable. This, enabling the oil to
diffolve more of the fermentable fubftance of the feed, expofes
the oil to the riſk of growing foon yery rancid; and, in general,
it is thought a hazardous practice, and the oil does not bring fo
'high a price.
When the paſte comes from under the ftones it is put into
the hair bags, and ſubjected to the first preffing. The oil thus
obtained is alſo eſteemed as of the firft quality, fcarcely inferior
to the former, and is kept apart: (the great oil ciftern being
divided into ſeveral portions by partitions).
The oil cakes of this preffing are taken out of the bags,
broken to pieces, and put into the mortars for the firſt ſtamping.
Here the pafte is again broken down, and the parenchyma of
the feed reduced to a fine meal. Thus free egrefs is allowed to
the oil from every vehicle in which it is contained. But it is
now rendered much more clammy, by the forcible mixture of
the mucilage, and even of the finer parts of the meal. When
fufficiently pounded, the workman ftops the peſtle of a mortar,
when at the top of its lift, and carries the contents of the
mortar to the first chauffer pan, where it is heated to about the
temperature of melting bees-wax (this, we are told, is the teft),
and all the while ftirred about by the fpatula. From thence it
is again put into hair bags, in the manner already defcribed;
and the oil which drips from it during this operation is con-
fidered as the beft of the fecond quality, and in fome mills is
kept apart. The paſte is now ſubjected to the fecond preffing,
and the oil is that of the fecond quality.
All this 'operation of pounding and heating is performed by
one workman, who has conftant employment by taking the four
mortars in fucceffion. The putting into the bags and conduct-
ing of the preffing gives equal employment to another work-
man.'
#
In the mills of Picardy, Alface, and moſt of Flanders, the
operation ends here; and the produce from the chauffer is in-
creafed, by putting a ſpoonful or two of water into the pan
among the paste.
But the Dutch take more pains. They add no water to the
paste of this their firft ftamping. They fay that this greatly
lowers the quality of the oil. The cakes which refult from this
preffing, and are there fold as food for cattle, are ſtill fat and
Oil-mill.
261
foftiſh. The Dutch break them down, and fubject them to
the peſtles for the ſecond ſtamping. Thefe reduce them to an
impalpable paſte, ftiff like clay. It is lifted out, and put into
the ſecond chauffer pan; a few fpoonfuls of water are added,
and the whole kept for fome time as hot as boiling water, and
carefully ſtirred all the while. From thence it is lifted into
the hair bags of the laſt prefs, fubjected to the preſs; and a
quantity of oil, of the loweſt quality, is obtained, fufficient for
giving a fatisfactory profit to the miller. The cake is now
perfectly dry, and hard, like a piece of board, and is fold to the
farmers. Nay, there are ſmall mills in Holland which have no
other employment than extracting oil from the cakes which they
purchaſe from the French and Brabanters; a clear indication of
the fuperiority of the Dutch practice.
The nicety with which that induſtrious people conduct all
their buſineſs is remarkable in this manufacture.
In their oil cistern, the parenchymous part, which unavoid-
ably gets through, in ſome degree, in every operation, gradually
fublides; and the liquor, in any divifion of the ciftern, comes to
confift of ftrata of different degrees of purity. The pumps
which lift it out of each divifion are in pairs; one takes it up
from the very bottom, and the other only from half depth. The
laft only is barrelled up for the market, and the other goes into a
deep and narrow ciftern, where the dreg again fubfides, and
more pure oil of that quality is obtained. By fuch careful and
judicious practices, the Dutch not only fupply themſelves with
this important article, but annually fend confiderable quantities
even into thoſe provinces of France and Flanders where they
bought the feed from which it was extracted. When we re-
flect on the high price of labour in Holland, on the want of
timber for machinery, on the expence of building in that
country, and on the enormous expence of wind-mill machinery,
both in the firft erection and the fubfequent wear and tear, it
muſt be evident, that oil-mills erected in England on water falls,
and after the Dutch manner, cannot fail of being a great national
advantage. The chatellanie or feigneurie of Lille alone makes
annually between 30,000 and 40,000 barrels, each containing
about 26 gallons.
What is here delivered is only a ſketch. Every perfon ac
quainted with machinery will underſtand the general move-
ments and operations. But the intelligent mechanie well knows,
that operations of this kind have many minute circumftances
which cannot be deſcribed, and which, nevertheleſs, may have
a great influence on the whole. The rakes in the bruifing-mill
have an office to perform which reſembles that of the hand, di-
262
MACHINES.
rected by a careful eye and unceafing attention. Words cannot
communicate a clear notion of this; and a mill, conſtructed
from the beſt drawings, by the moſt ſkilful workman, may ga-
ther the feed fo ill, that the half of it ſhall not be bruiſed after
many rounds of the machinery. This produces a fcanty re-
turn of the fineſt oil; and the mill gets a bad character. The
proprietor loſes his money, is difcouraged, and gives up the
work. There is no fecurity but by procuring a Dutch mill-
wright, and paying him with the liberality of Britons. Such
unhoped-for tafks have been performed of late years by ma
chinery; and mechanical knowledge and invention are now fo
generally diffuſed, that it is highly probable that we ſhould ſoon
excel our teachers in this branch. But this very diffuſion of
knowledge, by encouraging fpeculation among the artists,
makes it a ftill greater riſk to erect a Dutch oil-mill with-
out having a Dutchman, acquainted with its moſt improved
prefent form, to conduct the work.—Supp. Encyclo. Britan.
¿
Boring of ORDNANCE. Till within a few years, iron
ordnance were caft with a cylindrical cavity, nearly of the di-
menſions of the caliber of the piece, which was afterwards en-
larged to the proper caliber by means of feel cutters fixed into
the dog-head of a boring bar-iron. Three equidiftant ſide-cutters
were requifite to preſerve the caliber ftraight and cylindrical
and a fingle cutter was uſed at the end of the bar to fmooth the
breech of the piece. In boring ordnance caft hollow, the piece
was fixed upon a carriage that could be moved backwards and
forwards in a direct line with the centre of a water-wheel; in
this centre was fixed the boring-bar, of a fufficient length to
reach up to the breech of the piece, or more properly to the
further end of the caliber. The carriage with the piece being
drawn backwards from the centre of the water-wheel to intro-
duce the boring and finiſhing bars and cutters, it is then preffed
forwards upon this bar by means of levers, weights, &c. and
the water-wheel being fet a going, the bar and fullers are turned
round, and clean out and ſmooth the caliber to its proper di-
menfions.
Experience at laft pointed out many inconveniences arifing
from the method of cafting guns hollow, and widening the cali-
bers by thefe boring bars. For the body of iron of the hollow
gun, being, at cafting, in contact with the core that made the
caliber within-fide, and with the mould without-fide, began to
confolidate towards theſe fides in the firft place fooner than in
the intermediate ſpace, where of courſe the contraction of the
iron takes place; by which means, all guns caft hollow became
more or lefs fpongy where they ought to have been moſt com-
Borers for Ordnance.
263
A
pact; and numberleſs cavities alſo were created round the cores,
from ftagnated air generated in them, which were too deep to be
cut out by the boring.
To remedy thefe defects, iron ordnance as well as braſs is now
univerfally caft folid, by which means the column of metal is
greatly enlarged, and the grain more compreffed; and the con-
traction becomes in the heart of the column, and conſequently is
cut out by the perforation for the caliber.
Guns are bored out of the folid reverſely from the hollow
method. The piece A (pl. XXI.) is placed upon two ſtandards
BB, by means of two journeys, turned round by a water-wheel;
the breech D being introduced into the central line of the wheel,
with the muzzle towards the fliding carriage E, which is preffed
forwards by a ratch F, and weights in the fame way as the gun-
carriage was in hollow-boring. Upon this fliding carriage is
fixed, truly horizontal and central to the gun, the drill-bar G,
to the end of which is fixed a carp's tongue drill or cutter H.
which, being preffed forward upon the piece whilft it is turning
round, perforates the bore, which is afterwards finiſhed with bars
and cutters as the hollow guns were.
The machinery for boring of ordnance is fometimes put in mo-
tion by a fteam-engine: and in this way, from 18 to 24 great guns
have been boring at the fame time; the borer in each piece being
brought up to its proper place in the gun, by a lever and weights.
In this method of bringing up the borer the preffure may always
be made equable, and the motion of the borer regular; but the
difadvantage is, that without due attention the borer may work
up too far towards the breach, and the piece be ſpoiled. In the
Royal Arſenal at Woolwich, only one piece is bored at a time
in the fame mill: the gun to be bored lies with its axis parallel
to the horizon, and in that poſition is turned round its axis by
means of wheel-work, moved by one or more horſes. The
borer is laid, as above deſcribed, in the direction of the axiş
of the gun, and is incapable of motion in any direction ex-
cept that of its length; and in this direction it is conſtantly
moved by means of a fmall rack-wheel, kept in proper mo-
tion by two men, who thus make the point of the borer fo
to bear againſt the part of the gun that is boring, as to pierce
and cut it. The outfide of the gun is ſmoothed at the fame
time by men with inftruments fit for the purpoſe, whilft it
turns round, ſo that the bare may be exactly in the centre of the
metal.
In this way the boring is performed with great nicety, the
guns fcarcely ever failing in the examination. But in thefe mills
the horſes work to great diſadvantage, the diametersof the walks
'
264
MACHINES.
in which they move being far too fmall. See the introductory
part of this volume, art. 76.
PARALLEL MOTION, is a term ufed among practical me-
chanics to denote the rectilinear motion of a piston rod, &c. in
the direction of its length: and contrivances by which fuch al-
ternate rectilinear motions are converted into rotatory ones, and
vice verfa, in pumps, fteam-engines, faw-mills, &c. are ufually
called contrivances for parallel motions.
In motions of this kind it is generally thought a defirable thing
to give the piston rod, the faw, or the like, a uniform velocity
through the whole of its progrefs; then to bring it at once to reft,
again to give it inftantaneously a finite velocity in the oppofite
direction, and ſo on. But this feems impoffible in nature; all
changes of motion which we obferve are gradual, becauſe all im-
pelling bodies have fome elafticity or foftnefs by which they
yield to compreffion; and, in the way in which piſtons are
commonly moved, viz. by cranks, or fomething analogous to
them, the motion is very fenfibly gradual. Hence, it may be ob-
ferved that most attempts to correct thefe inequalities in motion
are miſplaced; and if they could be accomplished would greatly
injure the pump or other machine. One of the best methods of
producing this effect is to make the piſton-rod confift of two
parallel bars, having teeth in the fides which front each other.
Let a toothed wheel be placed between them, having only the
half of its circumference furniſhed with teeth. It is evident,
without any further defcription, that if this wheel be turned
uniformly round its axis, the piſton-rod will be moved uniformly
up and down without intermiflion. This has often been put
in practice, and the piſton-rod made to work between grooved
rollers; but the machine always went by jolts, and feldom
lafted a few days. Unfkilled mechanifts.attributed this to de-
fect in the execution: but the fault is effential, and lies in the
principle. The machine could not perform one ftroke if the
first mover did not flacken a little, or the different parts of the
machine did not yield by bending, or by compreffion; and no
ftrength of materials could withstand the violence of the trains
at every reciprocation of the motion. This is chiefly experi-
enced in great works which are put in motion by a water-wheel,
or fome other equal power exerted on the mafs of matter of
which the machine confifts. The water-wheel being of great
weight moves with confiderable fteadineſs or uniformity; and
when an additional refiftance is oppoſed to it by the beginning
of a new ſtroke of the pifton, its great quantity of motion is but
little affected by this addition, and it proceeds very little retarded;
and the machine muſt-either yield a little by bending and com
Parallel Motions.
265
preffion, or go to pieces, which is the common event. Cranks
are free from this inconvenience, becauſe they accelerate the
piſton gradually, and bring it gradually to reft, while the water-
wheel moves round with almoft perfect uniformity. The only
inconvenience (and it may be confiderable) attending this flow
motion of a piſton at the beginning of its ftroke is, that the valves
de not ſhut with rapidity, fo that fome water gets back through
them. But when they are properly formed and loaded, this is but
trifling.
It would feem, then, that thofe contrivances in which the
pifton-red communicates the rotatory motion by means of a
crank, or fomething fimilar in its effect, are moſt fit to be
adopted in practice; and that the attempts of mechaniſts in
this point of view may in all probability be properly reſtrained
to the methods of keeping the pifton-rod, &c. from deviating
to any fide, during its alternate motion. Two or three of the
beft methods of performing this, with which we are acquainted,
are the following.
1. Let a fixed circular ring whofe diameter is equal to the
Stroke of the pifton have teeth all round the interior part of its
circumference; and let a fmaller wheel whofe diameter is only
half that of the ring have equal teeth on the exterior part of its
rim, to play into the teeth of the ring: let the axis of the wheel
to which the rotatory motion is to be communicated pafs through
the centre of the larger ring; and let a moveable bar join the
centre of this ring to that of the ſmaller wheel. Then, if the
upper extremity of the pifton-rod be attached to a pin fixed on
the rim of the inner wheel, at the place where the two wheels
are in contact in their loweſt point, and the rod be put into
motion, it will cauſe the ſmall wheel to revolve upon the inner
part of the fixed ring, and by this means give the propoſed
rotatory motion to the axis paffing through the centre of the
ring. At the fame time the extremity of the pifton-rod will
be confined to move in the vertical diameter of the ring: be-
cauſe it is made to defcribe an epicycloid of that kind which is
formed by a circle rolling along the infide of another circle
of double diameter; in which cafe, it is well known, the
epicycloid becomes a diameter of the larger circle, and the
fmaller circle makes two complete revolutions while it is mov-
ing from any one point of the larger circle to the fame point
again.
罩
​This contrivance was devifed, we believe, by Mr. White, an
Anglo-American. It is almoft unneceffary to obferve that the
converfe is equally applicable in the conve fion of a rotatory
into a parallel mction.
2. Another method is reprefented in figure 10. pl. XXIII.
286
MACHINES.
where the piston rod is kept from deviation. A is the cylinder,
B the pifton, C the pifton-rod, D the crank, and E the connect-
ing rod of the crank and piſton-rod. When the piſton is at
e, the crank is at a; when the pifton is at B, the crank is either at
g or b; and when the piſton is at g, the crank is atƒ: ſo that
when the motion of the crank is uniform that of the piſton is
variable. The rod H equal in length to the crank D moves
about the centre F, and is joined to one end of the rod I, to
the other end of which is connected the ſocket L that receives
the top end of the pifton-rod. A certain point m is taken at
pleaſure in the rod I, to carry a ſhort axle for the rods K, which
are broken in the figure to fhew the focket L. To find the
centre of motion of the rods K, move the end L of the rod I
up and down in the vertical line Cfa, and mark three pofitions
#, m, r, of the point m on that rod: defcribe a circle to pafs
through thofe three points; its radius will be equal to the length
of the rods K, and its centre will be the point where thofe rods
muft be fixed to a bolt or axle in the framing. This contrivance
cauſes the top of the pifton-rod to move from P by L to O, and
back again by L top; and the dotted lines ſhew the poſition of
the feveral rods at the extremities of the motion.
In fig. 11. pl. XXIII. we have given a horizontal ſection, to
fhew the connection of H, I, K, &c. pointing out in what way
I grafps L, and E both. The inequality of the pifton's motion
will be reduced by making the connecting rod E as long as cir-
cumftances will permit.
If the rod I were extended to the left of the point p, the
fame kind of apparatus would become a lever with a moveable
fulcrum, by means of which a weight might be raiſed in a verti-
cal line from P to O; or a pump pifton-rod worked without de-
viation.
3. A third method is exhibited in fig. 8. pl. XXIII. where
there are three rods A, B, and C, befides the connecting rod D.
The rods A and C are of equal lengths, and the connecting rod
is attached to the middle point of the rod B. The guides A, and
C, are fixed at their ends E, and F, by bolts to the framing.
Thus the point B, to which is fixed the top of the pifton-rod, is
made to move in the right line b B b'; and the dotted lines fhew
the poſitions of the rods at the extremities of the ſtroke. Fig.7.
thews in what way the pifton-rod P and connecting rod D might
be joined to the guides B and C.
This method and the preceding were deviſed by Mr. Wil-
liam Dryden a mechanic whofe ingenuity needs not our en
comium.
4. Another method is fhewn in fig. 12. pl. XXIII. A and B
are two bolts in the framing at equal diſtances on oppoſite ſides
Pendulums
+
of the vertical line in which the pifton is to move. AC, BD,
two bars of equal length, each equal to about half the diſtance
AB. CL, DL, two other equal bars, rather more than double
the length of the former, moving freely on joints at C and D.
At L is a focket, as in fig. 10. to receive the top of the piſton-
rod, and to which the bars CL, DL, and the connecting rod E,
are attached. By this contrivance it is obvious, that as the rods
BC, BD, turn upon the centres A, B, in contrary directions,
the pifton-rod will be made to move in the right line PM
without deviation; NM being the length of the ſtroke. The
relative lengths of the bars AC, CL, may be varied at plea
fure: but thoſe we have mentioned will be found as well as any
in practice.
5. A pifton-rod may alſo be kept from deviating to either,
fide, while it gives motion to a crank, and vice verfa, thus:
place a croſs-bar at a diſtance from the end of the cylinder rather
greater than the ftroke of the pifton, and make the pifton-rod
play in a hole made in this croſs-bar; let an axle be fixed to a
proper point of the pifton-rod between the end of the cylinder
and the croſs-bar, and from this axle let two equal connecting
rods paſs to the crank, one on each fide the croſs-bar: by this
fimple contrivance the alternating and circular motions may be
communicated to the different parts of the machine with great
facility.
PARCIEUX'S AREOMETER. See Vol. I. art. 401, 400.
PATERNOSTER-WORK. See HYDRAULIC Engines, No. 5-
PENDULUM, in mechanics, any heavy body, fo fufpended as
that it may fwing backwards and forwards, about fome fixed
point, by the force of gravity.
Thefe alternate afcents and defcents of the pendulum are
called its ofcillations, or vibrations; each complete ofcillation
being the defcent from the higheſt point on one fide down to
the loweſt point of the arch, and fo on up to the higheſt point
on the other fide. The point round which the pendulum moves,
or vibrates, is called its centre of motion, or point of ſuſpenſion,
and a right line drawn through the centre of motion, parallel to
the horizon, and perpendicular to the plane in which the pen-
dulum moves, is called the axis of ofcillation. There is alſo a
certain point within every pendulum, into which, if all the mat-
ter that compoſes the pendulum were collected, or condenſed as
into a point, the times in which the vibrations would be per-
formed would not be altered by fuch condenſation; and this
point is called centre of ofcillation. The length of the pendu-
Tum is always eſtimated by the diftince of this point below the
centre of motion; being ufually near the bottom of the pendu-
Jum; but in a cylinder, or any other uniform priſm or rod, it is
268
MACHINES.
at the diſtance of one-third from the bottom, or two-thirds be-
low the centre of motion.
+
The length of a pendulum, fo meaſured to its centre of ofcil-
lation that it will perform each vibration in a ſecond of time,
thence called the fecond's pendulum, has, in the latitude of Lon-
don, been generally taken at 39 or 39 inches; but by fome
very ingenious and accurate experiments, the late celebrated Mr.
George Graham found the true length to be 39,12%, inches, or
39 inches very nearly.·´
The length of the pendulum vibrating ſeconds at Paris was
found by Varin, Des Hays, De Glos, and Godin, to be 440ģlines;
by Picard 440 lines; and by Mairan 44037 lines.
In our first volume (book II. ch. ii.), where the theory of
pendulums was laid down, we remarked that the length of the
fecond pendulum was different in different parts of the earth.
It would not be eafy to exhibit a completely accurate theorem
for the length of the pendulum at all places on the earth's fur-
face: but the beſt and moſt fimple with which we are ac-
quainted was firſt given by Mr. Krafft in the New Peterſburgh
Memoirs, vol. vii. It is this: if x be the length of a pendulum
that fwings feconds in any given latitude l, and in a tem-
perature of 10 degrees of Reaumur's thermometer, then will
the length of that pendulum, for that latitude, be thus expreffed,
viz.
x=(439·178+2*321 × fin.) lines of a French foot.
And this expreffion agrees very nearly, not only with all the ex-
periments made on the pendulum in Ruffia, but alſo with thoſe
of Mr. Graham, and thofe of Mr. Lyons in 79° 50' north latitude,
where he found its length to be 241.38 lines.
Since metals expand by heat and contract by cold, pendulums,
which are conftituted chiefly of metal, muſt be ſubject to varia-
tions in confequence of fuch expanfion and contraction; and
various are the contrivances which have been deviſed to correct
the errors in the eſtimates of time which have been thus pro-
duced: a few of theſe will here be deſcribed.
The vulgar method of remedying the inconvenience, arifing
from the extenfion and contraction of the rods of common pen-
dulums is by applying the bob, or fmall ball, with a fcrew,
at the lower end; by which means the pendulum is at any
time made longer or fhorter, as the ball is fcrewed downwards
or upwards; and thus the time of its vibration is kept continually
the fame.
The gridiron PENDULUM was the invention of Mr. John Har-
rifon, a very ingenious artist, and celebrated for his invention of
the watch for finding the difference of longitude at fea, about
Pendulums.
269
the year 1725; and of feveral other time-keepers and watches
fince that time: for all which he received the parliamentary re-
ward of between 20 and 30 thouſand pounds. It confifts of
5 rods of ſteel, and 4 of brafs, placed in an alternate order;
the middle rod being of ſteel, by which the pendulum ball is
fufpended: theſe rods of brafs and fteel, thus placed in an
alternate order, and ſo connected with each other at their ends,
that while the expanſion of the fteel rods has a tendency to
lengthen the pendulum, the expanſion of the braſs rods, acting
upwards, tends to fhorten it. And thus, when the lengths of
the braſs and ſteel rods are duly proportioned, their expanſions
and contractions will exactly balance and correct each other,
and fo preferve the pendulum invariably of the ſame length.
The fimplicity of this ingenious contrivance is much in its fa-
vour; and the difficulty of adjuſtment ſeems the only objection
to it.
Mr. Harriſon, in his first machine for meaſuring time at fea,
applied this combination of wires of brafs and fteel, to pre-
vent any alterations by heat or cold; and in the machines
or clocks he has made for this purpofe, a like method of
guarding againſt the irregularities arifing from this cauſe is
ufed.
The principal objections to this mode of compenfation are,
ft. The difficulty of exactly adjuſting the lengths of the rods.
2dly. Of proportioning their thickneſs, fo that they fhall all
begin to expand or contract at the fame inftant. 3dly. The
connecting bars of a pendulum thus conftructed are apt to
move by tarts. 4thly. This kind of pendulum is more ex-
pofed to the air's refiftance than a fimple pendulum.
Another excellent contrivance for the fame purpoſe is de-
fcribed by M. Thiout, a French author on clock-making. It
was uſed in the north of England by an ingenious artiſt about
40 years ago. This invention is as follows: a bar of the fame
metal with the rod of the pendulum, and of the fame dimen-
fions, is placed againſt the back part of the clock-cafe: from
the top of this a part projects, to which the upper part of the
pendulum is connected by two fine pliable chains or filken
ſtrings, which juſt below paſs between two plates of brafs,
whofe lower edges will always terminate the length of the pen-
dulum at the upper end. Thefe plates are fupported on a pe-
deſtal fixed to the back of the cafe. The bar refts upon an
immoveable baſe at the lower part of the cafe, and is inferted
into a groove; by which means it is always retained in the
fame pofition. From this conftruction, it is evident that the
extenfion or contraction of this bar, and of the rod of the
pendulum, will be equal, and in contrary directions. For, fup-
270
MACHINES.
pofe the rod of the pendulum to be expanded any given quan
tity by heat; then, as the lower end of the bar refts upon a
fixed point, the bar will be expanded upwards, and raiſe the
upper end of the pendulum juft as much as its length was in-
ereafed; and hence its length below the plates will be the fame
as before.
In Voigt's Magazin fuer den neveſten Zuſtande de Na-
turkunde, vol. iv. are deſcribed the gridiron pendulums of Mr.
Benzenberg, which are compofed of lead and iron. Mr. B. was in-
duced to employ lead on account of its great dilatability, which is
to iron as 2:57 to 1, fo that 16'5 inches of lead compenfate 13
of iron; and he chofe iron in preference to ſteel, becauſe eafier
to work. The compenfation was made by a fingle rod in the
centre, 15 inches long, French meaſure, and half an inch thick.
It was fimply pinned into gorges in the cross-piece of cop-
per; but the other parts of the gridiron were rivetted in the
nfual way.
The iron rods were made of the beſt thick iron
wire.
The materials of this pendulum are cheap, and it may be made
in a couple of days. As the preffure takes place in a vertical di-
rection, there is no danger, according to Mr. B., of rods of theſe
dimenfions bending.
To correct the compenfation, the central rod of lead muſt be
left fo long that we may be fure the compenfation is in exceſs.
The quantity of error may then be found by the freezing appara-
tus, and how much it is requifite to cut from the rod may be
calculated with the greateſt exactneſs.
The mercurial PENDULUM was the invention of the ingenious
Mr. Graham, in confequence of feveral experiments relating to
the materials of which pendulums might be formed, in 1715.
Its rod is made of braſs, and branched towards its lower end,
fo as to embrace a cylindric glafs veffel 13 or 14 inches long,
and about 2 inches diameter; which being filled about 12
inches deep with mercury, forms the weight or ball of the
pendulum. If upon trial the expanfion of the rod be found
too great for that of the mercury, more mercury muſt be
poured into the veffel: if the expanfion of the mercury ex-
ceeds that of the rod, fo as to occafion the clock to go faſt
with heat, fome mercury muſt be taken out of the veffel, ſo as
to fhorten the column. And thus may the expanfion and con-
traction of the quickfilver in the glafs be made exactly to ba-
lance the expanſion and contraction of the pendulum rod, fo as
to preſerve the diſtance of the centre of ofcillation from the point
of ſuſpenſion invariably the fame.
Mr. Graham made a clock of this fort, and compared it with
one of the beft of the common fort, for three years together; when
Pendulums.
271
he found the errors of his but about one-eighth part of thofe of
the latter. Philof. Tranf. numb. 392.
The only defect we have ever heard aſcribed to this pendulum,
is that the expanſion of the mercury commences fooner than that
of the rod: but, after all, there are many ftrong proofs of its
practical excellence.
The lever PENDULUM. From all that appears concerning this
conſtruction of a pendulum, we are inclined to believe that the
idea of making the difference of the expanſion of different.
metals operate by means of a lever originated with Mr.
Graham, who in the year 1737 conftructed a pendulum,
having its rod compofed of one bar of fteel between two of
brafs, which acted upon the fhort end of a lever, to the other
end of which the ball or weight of the pendulum was fuf-
pended.
This pendulum however was, upon trial, found to move by
jerks; and therefore laid afide by the inventor, to make way fo
the mercurial pendulum, juſt mentioned.
J
Mr. Short informs us in the Philof. Tranſ. vol. 47, art. 88,
that a Mr. Frotheringham, a quaker in Lincolnſhire, caufed a
pendulum of this kind to be made: it confifted of two bars, one
of brafs, and the other of fteel, faftened together by fcrews,
with levers to raiſe or let down the bulb; above which theſe
levers were placed. M. Caffini too, in the Hiftory of the
Royal Academy of Sciences at Paris, for 1741, deſcribes two
forts of pendulums for clocks, compounded of bars of brafs and
fteel; and in which he applies a lever to raiſe or let down the bulb
of the pendulum, by the expanſion or contraction of the bar of
brafs.
Mr. John Ellicott alſo, in the year 1738, conftructed a pendu-
lum on the fame principle, but differing from Mr. Graham's in
many particulars. The rod of Mr. Ellicott's pendulum was com-
poſed of two bars only; the one of brafs and the other of ſteel.
It had two levers, each ſuſtaining its half of the ball or weight;
with a ſpring under the lower part of the ball to relieve the le-
vers from a confiderable part of its weight, and ſo to render their
motion more ſmooth and eaſy. The one lever in Mr. Graham's
conftruction was above the ball: whereas both the levers in Mr.
Ellicott's were within the ball; and each lever had an adjuſting
ſcrew, to lengthen or ſhorten the lever, fo as to render the adjuſt-
ment the more perfect. See the Philof.Tranf. vol. 47, p. 479;
where Mr. Ellicott's methods of conftruction are defcribed, and
illuftrated by figures.
Notwithſtanding the great ingenuity diſplayed by theſe emi-
nent artiſts on this conftruction, it muſt further be obferved, in
the hiſtory of improvements of this nature, that Mr. Cum-
}
272
MACHINES.
ming, another eminent artift, has given, in his Effays on the
Principles of Clock and Watch-work, Lond. 1766, an ample
defcription, with plates, of a conſtruction of a pendulum with
levers, in which it ſeems he has united the properties of Mr.
Graham's and Mr. Ellicott's, without being liable to any of the
defects of either. The rod of this pendulum is compofed of
one flat bar of brafs, and two of fteel: he ufes three levers
within the ball of the pendulum; and, among many other in-
genious contrivances, for the more accurate adjuſting of this
pendulum to mean time, it is provided with a fmall ball and
crew below the principal ball or weight, one entire revolution
of which on its ſcrew will only alter the rate of the clock's going
one fecond per day; and its circumference is divided into 30,
one of which divifions will therefore alter its rate of going one
fecond in a month.
Mr. Edward Troughton has lately invented a tubular pendu-
lum, which acts on the principle of the gridiron pendulum: in
this conſtruction the apparent rod is a tube of brafs reaching
from the bob nearly to the top; this contains another tube and
five wires in its belly, fo difpofed as to produce altogether (like
the nine-bar gridiron of Harriſon) three expanfions of ſteel
downwards, and two of brafs upwards; whofe lengths being
inverſely proportioned to their dilatation, when properly com-
bined, deſtroy the whole effect that either metal would have
fingly. The fmall viſible part of the rod near the top is a braſs
tube, whofe ufe is to cover the upper end of the middle wire,
which is fingle, and otherwife unfupported. Drawings of this
pendulum may be ſeen in Nicholſon's Journal, No. 36. N. S..
After all, fo long as the vibration of pendulums is performed
in a medium of varying denfity we muſt not look for an accu-
rate time-piece for aſcertaining the longitude, &c.; unleſs a
felf-corrrecting mercurial pendulum could be contrived, adapted
to counteract the fmalleft variations effected by the ambient
air. The errors of a time-piece are but half corrected by the
fabrication of pendulums adapted to obviate the expanfion of
metals by increaſe of temperature, if the works themſelves ſtill
remain conftructed of fuch expanfible materials. A correct
time-piece, therefore, will be that of which not only the works
and pendulum are conftructed of the leaft expanfible materials,
but the pendulum itſelf fhall vibrate in a medium of unalterable
denfity; a defideratum only to be obtained by cauſing the vibra-
tions to be performed in vacuo, or by a felf-correcting pendu-
Jum, as above alluded to. Mr. 'G. J. Wright, of Kennington,
who has fome obfervations on this fubject in Tilloch's Philo-
fophical Magazine, No. 57. fays the beft fubftance to compofe
the works of a correct time-keeper is ivory, or the horn of the
Penstock
273
T
narwhal or fea-unicorn (which is almost entirely compofed of
enamel); eſpecially if any means were known of increafing their
hardneſs ſo as to vie with the metals.
The moſt general remedy againſt the chief inconveniences of
pendulums, is to make them long, to vibrate in ſmall´ares, and
to have the bobs as ponderous as is confiftent with the ſtructure
of the machine. In thoſe caſes where it is wiſhed to increaſe
the time of vibration without increafing the length of the pen-
lum, recourſe muſt be had to the angular pendulum, the theory
of which has been given in art. 311, vol. I.
PENSTOCK is a fluice or floodgate, ferving to retain or
let go at pleaſure the water of a mill-pond. The following is
a defcription of a pentrough and ſtock for equalifing the water
falling on water-wheels, by George Quayle, efq.
To inſure a regular ſupply of water on the wheel, and to ob
viate the inconveniences arifing from the uſual mode of deliver-
ing it from the bottom of the pentrough, this method is deviſed
of regulating the quantity delivered by a float, and taking the
whole of the water from the ſurface.
Section of the pentrough. (Plate XVI. fig. 4.) A, the en-
trance of the water. B, the float, having a circular aperture in
the centre; in which is fufpended C, a cylinder, running down
in the cafe E below the bottom of the pentrough. This is
made water tight at the bottom of the pentrough at F, by a
leather collar placed between two plates, and ſcrewed down to
the bottom.
The cylinder is fecured to the float fo as to follow its rife and
fall; and the water is admitted into it through the opening in
its fides, and there, paffing through the box or cafe E, rifes and
iffues at G on the wheel. By this means, a uniform quantity of
water is obtained at G; which quantity can be increaſed or dimi-
niſhed by the affiftance of a ſmall rack and pinion attached to the
cylinder, which will raife or deprefs the cylinder above or under
the water line of the float; and, by raifing it up to the top, it
ſtops the water entirely, and anfwers the purpoſe of the common
fhuttle. This pinion is turned by the handle H, fimilar to a
winch-handle; and is fecured from running down by a ratchet-
wheel at the oppofite end of the pinion axis.
K and L are two upright rods to preferve the perpendicular
rife and finking of the float, running through the float, and fe-
cured at the top by brackets from the fides.
M, a board let down acroſs the pentrough nearly] to_the
bottom, to prevent the horizontal impulfe of the water from
diſturbing the float.'
Fig. 5. A tranfverfe fection, fhewing the mode of fixing the
rack and pinion, and their fupports, on the float. The rack is
VOL.II.
T
1

274
MACHINES.
inſerted into a piece of metal running acroſs the cylinder near
the top. That the water may paſs more freely when nearly ex-
hauſted, the bottom of the cylinder is not a plane, but is cut
away fo as to leave two feet, as at C, fig. 4. The float is alſo
kept from lying on the pentrough bottom by four ſmall feet;
fo that the water gets under it regularly from the firft.
Fig. 6. An enlarged view of the cylinder, fhewing the rack
and ratchet-wheel, with the click, and one of the openings on
the fide of the cylinder: the winch or handle being on the op-
pofite fide, and the pinion, by which the rack is raiſed, incloſed
in a box between them. Tranfactions of the Society of Arts,
vol. XI. A. D. 1793.
PERSIAN-WHEEL. See HYDRAULIC Engines. No. 4.
PILE-ENGINE, a machine by which piles are driven into
the earth for the foundations of piers and other ftructures.
In pile-engines the contrivance confifts in drawing up a great
weight, called a ram or hammer, to a moderate height, and then
letting it fall freely with a confiderable momentum upon the
head of the pile. In the moft fimple pile engines the ram is
drawn up by men pulling at a cord running over a fixed pulley,
and fuffering the cord to flip from their hands when the weight
is fufficiently elevated. Among more complex engines, the beſt
we have ſeen are thoſe invented by Mr. Vauloue and by Mr.
S. Bunce.
A is a
Deſcription of Vauloue's pile-engine. (See pl. XXII.)
great upright fhaft or axle, on which are the great wheel B
and the drum C, turned by horfes joined to the bars S, S.
The wheel B turns the trundle X, on the top of whoſe axis is
the fly O, which ferves to regulate the motion, as well as to act
againſt the horſes, and to keep them from falling when the
heavy ram Q is diſcharged to drive the pile P down into the
mud in the bottom of the river. The drum C is loofe upon
the ſhaft A, but is locked to the wheel B by the bolt Y. On
this drum the great rope HH is wound; one end of the rope
being fixed to the drum, and the other to the follower G, to
which it is conveyed the pulleys I and K. In the follower
G is contained the tongs F, that take hold of the ram Q by
the ſtaple R for drawing it up. D is a ſpiral or fuſee fixed to
the drum, on which is wound the fmall rope T that goes over
the pulley U, under the pulley V, and is faſtened to the top of
the frame at 7. To the pulley-block V is hung the counter-
poiſe W, which hinders the follower G from accelerating as it
goes down to take hold of the ram; for, as the follower tends
to acquire velocity in its defcent, the line T winds downwards
upon the fufee on a larger and larger radius, by which means the
counterpoife W acts ftronger and ftronger against it; and fq al-
Pile Engine.
275
→
lows it to come down with only a moderate and uniform ve-
locity. The bolt Y locks the drum to the great wheel, being
puſhed upward by the ſmall lever 2, which goes through a mor-
tife in the fhaft A, turns upon a pin in the bar 3, fixed to the great
wheel B, and has a weight 4, which always tends to push up
the bolt Y through the wheel into the drum. L is the great
lever turning on the axis m, and reſting upon the forcing bar 5,5,
which goes through a hollow in the fhaft A, and bears up the
little lever 2.
By the horſes going round, the great rope H is wound about
the drum C, and the ram Q is drawn up by the tongs F in the
follower G, until the tongs come between the inclined planes
E; which, by fhutting the tongs at the top, opens it at the
foot, and diſcharges the ram, which falls down between the
guides b b upon the pile P, and drives it by a few ſtrokes as far
into the mud as it will go; after which, the top part is fawed
off cloſe to the mud by an engine for that purpoſe. Immediately
after the ram is diſcharged, the piece 6 upon the follower G
takes hold of the ropes a a, which raiſe the end of the lever L,
and cauſe its end N to defcend and prefs down the forcing bar
5 upon the little lever 2, which, by pulling down the bolt Y,
unlocks the drum C from the great wheel B; and then the fol-
lower being at liberty comes down by its own weight to the
ram; and the lower ends of the tongs flip over the ſtaple R, and
the weight of their heads cauſes them to fall outward and ſhut
upon it. Then the weight 4 puſhes up the bolt Y into the drum,
which locks it to the great wheel, and fo the ram is drawn up as
before.
As the follower comes down, it cauſes the drum to turn back-
ward, and unwinds the rope from it, whilft the horſes, great
wheel, trundle, and fly, go on with an uninterrupted motion;
and as the drum is turning backward, the counterpoife W is
drawn up, and its rope T wound upon the fpiral fuſee D.
There are ſeveral holes in the under fide of the drum,
and the bolt Y always takes the firſt of them that it finds, when
the drum ftops by the falling of the follower upon the ram;
until which ſtoppage the bolt, has not time to flip into any of the
holes.
The peculiar advantages of this engine are, that the weight
called the ram, or hammer, may be raiſed with the leaft force;
that, when it is raiſed to a proper height, it readily difengages
itfelf and falls with the utmoſt freedom; that the forceps or
tongs are lowered down fpeedily, and inftantly of themfelves
again lay hold of the ram and lift it up.
This engine was placed upon a barge on the water, and fo was

T 2
י
276
MACHINES.

eafily conveyed to any place defired. The ram was a ton weight;
and the guides bb, by which it was let fall, were 30 feet high.
Defcription of Bunce's Pile-engine.
Fig. 1 and 2. plate XXII. repreſent a fide and front ſection
of the machine. The chief parts are, A, fig. 1. which are two
endleſs ropes or chains, connected by crofs pieces of iron, B
(fig. 2.), correſponding with two crofs grooves cut diametrically
oppofite in the wheel C (fig. 1.), into which they are received;
and by which means the rope or chain A is carried round.
FHK is a fide-view of a ſtrong wooden frame moveable on the
áxis H. D is a wheel, over which the chain paffes and turns
within at the top of the frame. It moves occafionally from F
to G upon the centre H, and is kept in the pofition F by the
weight I fixed to the end K. In fig. 3. L is the iron ram,
which is connected with the croſs pieces by the hook M. N
is a cylindrical piece of wood fufpended at the hook at O,
which, by fliding freely up the bar that connects the hook to
the ram, always bring the hook upright upon the chain when
at the bottom of the machine, in the pofition of GP. See
fig. 1..
When the man at S turns the uſual crane-work, the ram being
connected to the chain and paſſing between the guides, is drawn
up in a perpendicular direction; and when it is near the top of
the machine, the projecting bar Q of the hook ſtrikes againſt
a croſs piece of wood at R (fig. 1.), and confequently dif-
charges the ram; while the weight I of the moveable frame in-
ftantly draws the upper wheel into the poſition fhewn at F, and
keeps the chain free of the ram in its defcent. The hook, while
defcending, is prevented from catching the chain by the wooden
piece N for that piece being ſpecifically lighter than the iron
weight below, and moving with a lefs degree of velocity, cannot
come into contact with the iron till it is at the bottom and the
ram ftops. It then falls, and again connects the hook with the
chain, which draws up the ram as before.
In this machine, as well as Vauloue's, the motion of the firſt
wheel is uninterrupted, fo that very little time is loft in the
operation with a flight alteration it might be made to work
with horfes. It has the advantage over Vauloue's engine in
point of fimplicity; it may be originally conftructed at lefs
expence, and is not fo liable to be deranged. Both, how-
ever, are ingenious performances, and part of their conftruc-
tion might be advantageoufly introduced into other machines.
PIPES, for conveying of water, for pumps, water-engines,
&c. are ufually of lead, iron, earth, or wood: the latter are
uſually made of oak or elder. Thoſe of iron are caſt in forges;

Pipe-borer.
: 277

their uſual length is about two feet and a half: feveral of theſe
are commonly faſtened together by means of four ſcrews at each
end, with leather or old hat between them, to ftop the water.
Thoſe of earth are made by the potters; theſe are fitted into one
another, one end being always made wider than the other. To
join them the clofer and prevent their breaking, they are co-
vered with tow and pitch: their length is uſually about that of
the iron pipes. The wooden pipes are trees bored with large
iron augers of different fizes, beginning with a lefs, and then
proceeding with a larger fucceffively; the firft being pointed,
the reſt being formed like ſpoons, increaſing; in diameter from
one to fix inches or more: the pipes are fitted into the extremi-
ties of each other (as repreſented in pl. XXII. fig. 1.), and are
fold by the foot.
Wooden pipes are bored either by a borer advancing hori-
zontally while the wood to be pierced is turned round, in ſome
ſuch manner as in boring of ordnance; or, by cauſing the tim-
ber to be gradually advanced, while the borer turns round: the
latter method is the moſt common. The apparatus moſt fre-
quently adopted, when the first mover is a ftream of water, is
that invented by M. Morel, and defcribed by Belidor (Archi-
tecture Hydraulique, tom. I.). This machinery is repreſented
at pl. XXII. fig. 1. where the vertical wheel A is put into mo-
tion by water defcending upon it through a trough or floping
canal: upon the horizontal axle of this wheel is a cog-wheel B,
which gives motion to the lanterns C, D, the common axis
of theſe lanterns being in a vertical pofition. The lantern D
turns at the ſame time two cog-wheels E and F: the first, E,
which is vertical, turns the auger that bores the wood; and the
ſecond, F, which is horizontal, has attached to it by a pin which
is at a ſmall diſtance from its centrè, a lever or arm H, with a
hook at its end, taking into the indentations of one of the
wheels of the carriage that carries the wood to be bored. An-
other lever, I, hanging upon the former, is prevented from
falling by a ſpring, and pushes by its extremity againſt the
notches in the lower end of the fame wheel. Thus, as the
cog-wheel turns round, the carriage-wheel is first pulled for-
ward by the hook and lever H, and then pushed backward as
far by the arm I; by this means cauſing a pinion upon the axle
of the carriage-wheel to advance the rackwork above it, to-
gether with the timber to be bored: fo that the timber is ad-
vanced by a flight reciprocating motion of the carriage. The
auger, being generally fome feet in length, plays in holes in two
pieces L, L, which retain it in its horizontal pofition; and thus
it forms a cylindrical cavity in the wood, as required.
-
273
MACHINES.
+
PLANET WHEELS are wheels by whoſe mutual connection
a variable angular motion, fuch as that of the radius vector of
a planet in its orbit, may be exhibited. The common con-
trivance now in ufe for this purpoſe was invented, we think,
by Defaguliers: it confifts of two elliptical wheels connected
either by teeth running into each other, or by a band; theſe
wheels revolve on their foci, and while the driving ellipfes move
uniformly, the radius vector of the other has the required
motion.
A much older, and at the fame time far better, method than
that of Defagulier's, is deſcribed in the first volume of the
Recueil des Machines et Inventions approuvées par l'Acad. Roy.
des Sci. 1699: it was the invention of M. Joli de Dijon. The
following account of this method is tranflated from the work
just mentioned.
If it be defired to move a wheel of 24 teeth by a pinion of
6, in ſuch a manner that in ſome parts of its revolution it ſhall
move as ſwiftly as if it had but 12 teeth, and in other parts as
flowly as if it had 48 teeth, the method of accompliſhing this is
as follows:
i. Deſcribe the rectangle LMNO (fig. 1. pl. XXIII.) having
its fide NO equal to the radii of the great wheel and the pinion
taken together, and its breadth LN equal to their thickneſs;
which laſt muſt be greater the more confiderable the inequality
of the propofed movement. Let NO be ſo divided in Q, that
QO may be to QN as 6 to 48, that is to fay, reciprocally as the
velocity of the pinion to the greateſt velocity of the wheel. Alfo
divide LM in P in the proportion of 6 to 12, or reciprocally as
the velocity of the pinion to the leaft velocity of the wheel.
Then join PQ, and draw as many lines SR parallel to LM, as
there are intended to be teeth in the great wheels; upon which
write the degrees of velocity they exprefs, which are in the in-
verſe ratio of their lengths.
2. Let two truncated cones be formed in the lathe; one équal
to that which would be formed by the revolution of the trape-
zoid LPQN about LN as an axis; and the other equal to what
would be formed by the revolution of the trapezoid POMO
about the axis MO. On the largeſt of theſe two cones let the
circles generated by the revolution of the points P, T, Q, be
marked and diſtinguiſhed by the fame numeral figures as the
correfponding parallels of the rectangle LO. Upon the two
baſes of the conic fruftrum defcribe radial lines, which ſhall
make angles at the centre (fig. 3.) in the fame proportion to
each other as the intended velocities of the wheel, as expreffed
in fig. 2. and let teeth be cut in the curve ſurface of the cone
Preffes
279
correfponding with theſe lines: after this, look on the circles
that exprefs the different velocities, and have been traced on
the fame ſurface, to find what part of each tooth ought to
remain oppofite its correfponding radius, and cut or file the
reft away.
Thus will the teeth lie in an oblique or ellip-
tical curve on the conical ſurface, as is exhibited in the figure
by a darker ſhade. The pinion muſt be made of a regular conic
ſhape, as is fhewn at MÕ in fig. 3.
By this contrivance the largeft or wideft teeth will always
meet the largeſt part of the pinion, and the narroweft will cor-
refpond with the ſmalleſt part: on which account, though the
motion of the pinion be uniform, the wheel will be carried un-
equably, according to the affigned law.
In a fimilar manner may planet-wheels be defcribed to exhibit
any other propoſed variation.
PRESS, a machine of wood, or iron, ferving to fqueeze any
body very cloſe.
Preffes ufually confift of fix pieces: two flat fmooth planks,
between which the things to be preffed are laid; two fcrews or
worms faſtened to the lower plank, and paffing through two
holes in the upper; and two nuts in form of an S, that ferve
to drive the upper plank, which is moveable, againſt the lower,
which is fixed.
- PRESSES fed for expreffing Liquors are in moft refpects the
fame with the common preffes, only the under plank is perfo-
rated with a great number of holes for the juice to run through.
Others have only one fcrew, or arbor, paffing through the mid-
dle of the moveable plank, which defcends into a kind of ſquare
box full of holes, through which the juices flow as the arbor ís
turned.
· PRESS uſed by Joiners to keep cloſe the pannels, &c. of wain-
ſcot, confifts of two fcrews, and two pieces of wood, four or
five inches fquare, and two or three feet long, whereof the holes
at two ends ferve for nuts to the ſcrews.
Founders' PRESS, is a ſtrong ſquare frame, confiſting of four
pieces of wood firmly joined together with tenons, &c. It is
of various fizes: two of them are required to each mould at
the two extremes whereof they are placed; fo as that, by
driving wooden wedges between the mould and fides of the
prefs, the two parts of the mould for the metal may be preffed
clofe together.
PRESS, binders' cutting-, is a machine ufed equally by book-
binders, ftationers, and pafteboard-makers; confifting of two
large pieces of wood in form of cheeks, connected by two
ftrong wooden fcrews; which, being turned by an iron bar,
draw together, or ſet aſunder, the cheeks, as much as is necef-
280
MACHINES.
fary for the putting in the books or paper to be cut. The
cheeks are placed lengthwife on a wooden ſtand; in form of
a cheft, into which the cuttings fall. Afide of the cheeks are
two pieces of wood of the fame length with the ſcrews, ſerving
to direct the cheeks, and prevent their opening unequally.
Upon the cheeks the plough moves, to which the cutting-knife
is faftened by a fcrew; which has its key, to difmount it, on
occafion, to be ſharpened.
The plough confifts of feveral parts; among the rest, a
wooden ſcrew or worm, which, catching within the nuts of the
two feet that ſuſtain it on the cheeks, brings the knife to the
book or paper which is faſtened in the prefs between two boards.
This fcrew, which is pretty long, hastwo directories, which re-
ſemble thoſe of the fcrews of the prefs. To make the plough
flide ſquare and even on the cheeks ſo that the knife may make
an equal paring, that foot. of the plough where the knife is not
fixed, flides in a kind of groove, faftened along one of the cheeks.
Laftly, the knife is a piece of ſteel, fix or feven inches long, flat,
thin, and ſharp, terminating at one end in a point, like that of a
ſword, and, at the other, in a ſquare form, which ferves to faften
it to the plough.


:
As the long knives ufed by us in the cutting of books or
papers are apt to jump in the cutting thick books, the Dutch are
faid to ufe circular knives with an edge all round; which not
only cut more ſteadily, but last longer without grinding.
Various other preffes are uſed in different arts and manu-
factures; but it does not feem neceffary to give particular de-
fcriptions of any others, except the prefs ufed in printing of
books, and the rolling prefs uſed in copper-plate printing.
The common PRINTING-prefs reprefented in plate XXIII. is a
curious and rather complex machine. The body confifts of
two ftrong cheeks, a, a, ftanding perpendicularly, and joined
together by four crofs-pieces; the cap b, and the head c, which is
moveable, being partly fuftained by two iron pins or long fcrew-
bolts that paſs the cap; the till or shelf dd, by which the
ſpindle and its apparatus are kept in their proper pofition; and
the winter e, which bears the carriage, and fuftains the effort of the
prefs beneath. The ſpindle ƒ is an upright piece of iron pointed
with ſteel, having a male fcrew, which goes into the female one
in the head about four inches. Through the eye g of this
fpindle is faſtened the bar k, by which the preffman makes the
impreffion. The fpindle paffes through a hole in the middle of
the till; and its point works into a braſs pan or nut, ſupplied
with oil, which is fixed to an iron plate let into the top of the
platen. The body of the fpindle is fuftained in the centre of
an open frame of poliſhed iron, 1, 4, 2, 2, 3, 3,. fixed to it in

Printing-prefs.
281
fuch a manner as, without obſtructing its free play, to keep it in
a ſteady direction; and at the fame time to ſerve for fufpending
the platen. This frame confifts of two parts; the upper called
the garter, 1; 1; the under called the crane, 2, 2. `Theſe are
connected together by two fhort legs or bolts, 3, 3; which
being fixed below in the two ends of the crane, pafs upward
through two holes in the till, and are received at top into two
eyes at the ends of the garter, where they are fecured by fcrews.
The carriage is placed a foot below the platen, having its
fore-part fupported by a prop called the fore-ftay, while the other
refts on the winter. On this carriage, which fuftains the plank,
are nailed two long iron bars or ribs; and on the plank are
nailed ſhort pieces of iron or fteel called cramp-irons, equally
tempered with the ribs, and which flide upon them when the
plank is turned in or out. Under the carriage is fixed a long
piece of iron called the pit, with a double wheel in the middle,
round which leather girts are faſtened, nailed to each end of
the plank: and to the outfide of the ſpit is fixed a rounce m, or
handle, to turn round the wheel Upon the plank is a fquare
frame or coffin, in which is incloſed a poliſhed ſtone on which
the form n is laid; at the end of the coffin are three frames,
viz. the two tympans and frifket: the tympans o are ſquare, and
made of three flips of very thin wood, and at the top a piece of
iron ſtill thinner; that called the outer tympan is faſtened with
hinges to the coffin: they are both covered with parchment;
and between the two are placed blankets, which are neceſ-
fary to take off the impreffion of the letters upon the paper.
The friſket p is a ſquare frame of thin iron, faſtened with hinges
to the tympan: it is covered with paper cut in the neceffary
places, that the fheet, which is put between the friſket and the
great or outward tympan, may receive the ink, and that nothing
may hurt the margins. To regulate the margins, a fheet of
paper is faſtened upon this tympan, which is called the tympan
fheet; and on each fide is fixed an iron point, which makes two
holes in the fheet, which is to be placed on the fame points
when the impreffion is to be made on the other fide. In pre-
paring the prefs for working, the parchment which covers the
outer tympan is wetted till it is very foft, in order to render the
impreffion more equable; the blankets are then put in, and
fecured from flipping by the inner tympan: then, while one
preffman is beating the letter with the balls covered with ink
taken from the ink-block, the other perfon places a fheet of
white paper on the tympan fheet; turns down the friſket upon
it, to keep the paper clean and prevent its flipping; then, bring-
ing the tympans upon the form, and turning the rounce, he
brings the form with the ftone, &c. weighing about 300 lbs.
•
·
282
MACHINES.
weight, under the platen; pulls with the bar, by which means
the platen preffes the blankets and paper cloſe upon the letter,
whereby half the form is printed; then eafing the bar, he draws
the form ftill forward; gives a fecond pull, and letting go the
bar, turns back the form, takes up the tympans and frisket,
takes out the printed ſheet, and lays on a freſh one; and this is
repeated till he has taken off the impreffion upon the full num-
ber of fheets the edition is to confift of. One fide of the ſheet
being thus printed, the form for the other is laid upon the preſs,
and worked off in the fame manner.
The Rolling-PRESS ufed in copper-plate printing, is repreſented
in fig. 3. pl. XV. This machine, like the common prefs, may be
divided into two parts, the body and carriage, analogous to thoſe
in the other.
The body confifts of two cheeks PP of different dimenſions,
ordinarily about four feet and a half high, a foot thick, and two
and a half apart, joined at top and bottom by crofs pieces. The
cheeks are placed perpendicularly on a wooden ftand or foot,
LM, horizontally placed, and fuftaining the whole prefs. From
the foot likewife rife four other perpendicular pieces, c, c, c, c,
joined by other crofs or horizontal ones d, d, d, which may be
confidered as the carriage of the preſs, as ſerving to ſuſtain a
fmooth, even plank, HIK, about four feet and a half long, two
feet and a half broad, and an inch and a half thick; upon which
the engraven plate is to be placed. Into the cheeks go two
wooden cylinders of rollers DE, FG, about fix inches in diame-
ter, borne up at each end by the cheeks, whoſe ends, which are
leffened to about two inches diameter, and called trunnions, turn
in the cheeks between two pieces of wood, in form of half-
moons, lined with poliſhed iron, to facilitate the motion. The
fpace in the half-moons, left vacant by the trunnion, is filled
with paper, pafteboard, &c. that they may be raiſed and lowered
at difcretion; fo as only to leave the space between them necef-
fary for the paffage of the plank charged with the plate, paper,
and blankets. Laftly, to one of the trunnions of the upper roller
is faſtened a crofs, confifting of two levers AB, or pieces of
wood, traverſing each other. The arms of this croſs ſerve in
lieu of the handle of the common prefs; giving a motion to
the upper roller, and that to the under one; by which means
the plank is protruded, or paffed between them.
The practice of printing from copper-plates is nearly as fol-
lows. The workmen take a fmall quantity of the ink, on a
rubber made of linen rags, ſtrongly bound about each other, and
with this fmear the whole face of the plate as it lies on a grate
over a charcoal fire. The plate being fufficiently inked, they
firſt wipe it over with a foul rag, then with the palm of their left

Preſſure Engine.
283
hand, and then with that of the right; and to dry the band and
forward the wiping, they rub it from time to time in whiting.
The addrefs of the workmen confifts in wiping the plate per-
fectly clean, without taking the ink out of the engraving. The
plate thus prepared is laid on the plank of the prefs; over the
plate is laid the paper, firft well moistened, to receive the im-
preffion; and over the paper two or three folds of flannel.
Things being thus difpofed, the arms of the croſs are pulled, and
by that means the plate with its furniture is paſſed through
between the rollers, which pinching very strongly, yet equally,
preffes the moiſtened paper into the ftrokes of the engraving,
whence it licks out the ink, and receives the required im-
preffion.
PRESSURE ENGINES for raifing water by the preffure and
deſcent of a column inclofed in a pipe, have been lately erected
in different parts of this country. The principle now adverted
to was adopted in fome machinery executed in France about
1731 (fee Belidor de Arch. Hydraul. lib. iv. ch. 1.), and was
likewife adopted in Cornwall about forty years ago. But the
preffure engine of which we are about to give a particular de-
fcription, is the invention of Mr. R. Trevithack, who probably
was not aware that any thing at all fimilar had been attempted
before. This engine, a fection of which, on a ſcale of a quarter
of an inch to a foot, is fhewn in pl. XXIII. was erected about
fix years ago at the Druid Copper Mine, in the parish of Illogan,
near Truro. AB repreſents a pipe fix inches in diameter,
through which water defcends from the head to the place of its
delivery to run off by an adit at S, through a fall of 34 fathom
in the whole; that is to fay, in a cloſe pipe down the flope of a
hill 200 fathoms long, with 26 fathoms fall; then perpen-
dicularly fix fathoms, till it arrives at B, and thence through the
engine from B to S two fathoms. At the turn B the water
enters into a chamber C, the lower part of which terminates in
two brafs cylinders four inches in diameter; in which two
plugs or piſtons of lead, D and E, are capable of moving up and
down by their piſton rods, which paſs through a cloſe packing
above, and are attached to the extremities of a chain leading
over and properly attached to the wheel Q, ſo that it cannot
flip.
-
1
•
The leaden piecés D and E are caft in their places, and have
no packing whatever. They move very eafily; and if at any
time they should become loofe, they may be ſpread out by a
few blows with a proper inftrument, without taking them out of
their place. On the fides of the two braſs cylinders, in which
D and E move, there are fquare holes communicating towards
F and G, which is an horizontal trunk or fquare pipe, four inches
284
MACHINES.
wide and three inches deep. All the other pipes G, G, and R,
are fix inches in diameter, except the principal cylinder wherein
the piſton H moves; and this cylinder is ten inches in diameter,
and admits a nine-foot ftroke, though it is here delineated as if
the ſtroke were only three-foot."
The piſton-rod works through a ſtuffing-box above, and is at-
tached to MN, which is the pit-rod, or a perpendicular piece
divided into two, fo as to allow its alternate motion up and
down and leave a fpace between, without touching the fixed
apparatus or great cylinder. The pit-rod is prolonged down
into the mine, where it is employed to work the pumps, or if
the engine were applied to mill-work, or any other uſe, this
rod would form the communication of the firft mover.
KL is a tumbler or tumbling-bob, capable of being moved
on the gudgeons V, from its prefent pofition to another, in
which the weight L fhall hang over with the fame inclination
on the oppofite fide of the perpendicular, and confequently
the end K will then be as much elevated as it is now depreffed.
The pipe RS has its lower end immerſed in a ciſtern, by which
means it delivers its water without the poffibility of the external
air introducing itſelf; fo that it conftitutes a torricellian column
or water barometer, and renders the whole column from A to S
effectual: as we fhall fee in our view of the operation.
The operation. Let us fuppofe the lower bar KV of the
tumbler to be horizontal, and the rod PO fo fituated, as that
the plugs or leaden piſtons D and E fhall lie oppofite to each
other, and ſtop the water-ways G and F. In this ſtate of the
engine, though each of theſe piſtons is preffed by a force equi-
valent to more than a thouſand pounds, they will remain motion-
lefs, becauſe theſe actions being contrary to each other, they are
conftantly in equilibrio. The great piſton H being here fhewn
as at the bottom of its cylinder, the tumbler is to be thrown by
hand into the pofition here delineated. Its action upon OP
and confequently upon the wheel Q, draws up the plug D,
and depreffes E, fo that the water-way G becomes open from
AB, and that of F to the pipe R: the water confequently de-
fcends from A to C; thence to G G G, until it acts beneath
the pifton H. This preffure raiſes the pifton, and if there be
any water above the pifton, it cauſes it to rife and paſs through
Finto R. During the rife of the piſton (which carries the pit-
rod MN along with it), a fliding block of wood I, fixed to this
rod, is brought into contact with the tail K of the tumbler, and
raiſes it to the horizontal poſition, beyond which it overfets by
the acquired motion of the weight L.

+
The mere riſe of the piſton, if there were no additional mo-
tion in the tumbler, would only bring the two plugs D and E
Preſſure Engine.
285
to the pofition of reft, namely to cloſe G and F, and then the
engine would ftop; but the fall of the tumbler carries the plug
D downwards quite clear of the hole F, and the other plug E
upwards, quite clear of the hole G. Theſe motions require no
confumption of power, becauſe the plugs are in equilibrio, as
was juft obferved.
In this new fituation the column AB no longer communi-
cates with G, but acts through F upon the upper part of the
pifton H, and depreffes it; while the contents of the great
cylinder beneath that pifton are driven out through G G G,
and paſs through the opening at E into R. It may be ob-
ferved, that the column which acts againſt the piſton is affifted
by the preffure of the atmoſphere, rendered active by the co-
lumn of water hanging in R, to which that affifting preſſure is
equivalent, as has already been noticed.
When the piſton has defcended through a certain length, the
flide or block at T, upon the pit-rod, applies againſt the tail K
of the tumbler, which it depreffes, and again overfets; producing.
once more the pofition of the plugs DE, here delineated, and
the conſequent afcent of the great piſton H, as before deſcribed.
The afcent produces its former effect on the tumbler and plugs;
and in this manner it is evident that the alternations will
go on
without limit: or until the manager fhall think fit to place the
tumbler and plugs DE in the pofitions of reft; namely, ſo as to
ftop the paffages F and G.
The length of the ſtroke may be varied by altering the pofi-
tions of the pieces T and I, which will fhorten the ſtroke the
nearer they are together; as in that caſe they will fooner alter-
nate upon the tail K.
As the fudden ſtoppage of the defcent of the column AB, at
the inſtant when the two plugs were both in the water-way,
might jar and ſhake the apparatus, thofe plugs are made half
an inch ſhorter than the depth of the fide holes; fo that in that
cafe the water can efcape directly through both the fmall cylin-
ders to R. This gives a moment of time for the generation of
the contrary motion in the piſton and the water in G G G,
and greatly deadens the concuffion which might elſe be pro-
duced.
Some former attempts to make preffure engines upon the
principle of the fteam-engine have failed; becauſe water, not
being elaſtic, could not be made to carry the pifton onwards a
little, lo as completely to fhut one ſet of valves and open an-
other. In the prefent judicious conftruction, the tumbler per-
forms the office of the expanfive force of fteam at the end of
the ſtroke.


28.6
MACHINES.
Mr. Bofwell fuggefts, as a confiderable improvement, that
the action of this engine fhould be made elaſtic by the addition
of an air-chamber, on the fame principle as that uſed in fire-
engines; this, he thinks, might be beft effected by making the
pifton hollow, with a fmall orifice in the bottom, and of a larger
fize, to ferve for this purpoſe, as the fpring of the air would
then act both on the upward and downward preffure of the
water. Nich. Four. N. S. vols. i. ii.
PULLEY, one of the fimple machines, or, as they are com-
monly called, mechanical powers: its theory is laid down in arts.
148-151, 267, &c. of our first volume. The prefent article is in-
troduced for the purpoſe of mentioning fome ingenious practical
combinations of pulleys, in addition to thofe exhibited in pl. VI.
vol. i.
The ufual methods of arranging pulleys in their blocks may
be reduced to two. The first confifts in placing them one by
the fide of another upon the fame pin: the other, in placing
them directly under one another upon feparate pins. Each of
thefe methods however is liable to inconvenience; and Mr.
Smeaton, to avoid the impediments to which theſe combinations
are fubject, propofes to combine theſe two methods in one.
•
A very confiderable improvement in the conftruction of
pulleys has been made by Mr. James White, who obtained a
patent for his invention, of which he gives the following de-
fcription. Fig. 6. pl. XIX. fhews the machine, confifting of
two pulleys, Q and R, one fixed and the other moveable. Each
of thefe has fix concentric grooves capable of having a line put
round them, and thus acting like as many different pulleys,
having diameters equal to thofe of the grooves. Suppofing
then each of the grooves to be a diftinct pulley, and that all
their diameters were equal, it is evident that if the weight 144
were to be raiſed by pulling at S till the pulleys touch each
other, the firſt pulley muſt receive the length of line as many
times as there are parts of the line hanging between it and the
lower pulley. In the prefent cafe there are 12 lines b, d, f, &c.
hanging between the two pulleys, formed by its revolution about
the fix upper and lower grooves. Hence, as much line muſt paſs
over the uppermoft pulley as is equal to twelve times the di-
ftance of the two. But, from an infpection of the figure, it is
plain that the fecond pulley cannot receive the full quantity of
line by as much as is equal to the diſtance betwixt it and the
firft. In like manner, the third pulley receives leſs than the
first by as much as is the diſtance between the firſt and third;
and fo on to the laft, which receives only one-twelfth of the
whole. For this receives its fhare of line from a fixed point
Pulleys.
287
in the upper frame, which gives it nothing; while all the others
in the fame frame receive the line partly by turning to meet its
and partly by the line coming to meet them. e bleno.
Suppofing now theſe pulleys to be equal in fize, and to move
freely as the line determines them, it appears evident, from the
nature of the ſyſtem, that the number of their revolutions, and,
confequently their velocities, muſt be in proportion to the num-
ber of fufpending parts that are between the fixed point above.
mentioned and each pulley refpectively. Thus the outermoft
pulley would go twelve times round in the time that the pulley
under which the part n of the line, if equal to it, would revolve
only once; and the intermediate times and velocities would be.
a ſeries of arithmetical proportionals, of which, if the firft num-
ber were 1, the laſt would always be equal to the whole number
of terms. Since then the revolutions of equal and diſtinct
pulleys are meaſured by their velocities, and that it is poffible
to find any proportion of velocity on a fingle body running on
a centre, viz. by finding proportionate diftances from that
centre; it follows, that if the diameters of certain grooves in
the ſame ſubſtance be exactly adapted to the above feries (the
line itſelf being ſuppoſed inelaſtic, and of no magnitude), the
neceffity of ufing feveral pulleys in each frame will be obviated,
and with that fome of the inconveniences to which the uſe of
the pulley is liable.
In the figure referred to, the coils of rope by which the
weight is fupported, are repreſented by the lines a, b, c, &c.:
a is the line of traction, commonly called the fall, which paffes
over and under the proper grooves, until it is faſtened to the
upper frame juſt above n. In practice, however, the grooves
are not arithmetical proportionals, nor can they be fo; for the
diameter of the rope employed muft in all cafes be deducted
from each term; without which the ſmaller grooves, to which
the faid diameter bears a larger proportion than to the larger
ones, will tend to riſe and fall fafter than they, and thus intro-
duce worſe defects than thoſe which they were intended to
obviate,

}
The principal advantage of this kind of pulley is, that it de-
ſtroys lateral friction, and that kind of ſhaking motion which is
fo inconvenient in the common pulley. And left (fays Mr.
White) this circumftance fhould give the idea of weakneſs, I
would obferve, that to have pins for the pulleys to run on, is
not the only nor perhaps the beft method; but that I fometimes.
ufe centres fixed to the pulleys, and revolving on a very ſhort
bearing in the fide of the frame, by which ſtrength is increaſed,
and friction very much diminiſhed; for to the laſt moment the
motion of the pulley is perfectly circular: and this very circum-
288
MACHINES.
ftance is the caufe of its not wearing out in the centre as foon
as it would, affifted by the ever-increafing irregularities of a
gullied bearing. Thefe pulleys, when well executed, apply to
jacks and other machines of that nature with peculiar advant-
age, both as to the time of going and their own durability; and
it is poffible to produce a fyftem of pulleys of this kind of fix or
eight parts only, and adapted to the pocket, which, by means
of a ſkain of ſewing filk, or a clue of common thread, will raiſe
upwards of a hundred weight.
The friction of the pulley is now reduced to nothing, as it
were, by Mr. Garnett's ingenious patent friction-rollers, which
produce a great faving of labour and expence, as well as in the
wear of the machine, both when applied to pulleys and to the
axles of wheel-carriages. His general principle is this; between
the axle and nave, or centre pin and box, a hollow ſpace is left,
to be filled up by folid equal rollers nearly touching each other.
Thefe are furniſhed with axles inferted into a circular ring at
each end, by which their relative diſtances are preferved; and
they are kept parallel by means of wires faftened to the rings
between the rollers, and which are rivetted to them.
PUMP, an hydraulic machine for raifing water by the preffure
of the atmoſphere.
The moſt important and certain part of the theory of pumps
has been laid down in arts. 524-538, of our firſt volume: and
the conftruction of two or three kinds has been already de-
fcribed in this volume under the articles CENTRIFUGAL machine,
FIRE-engine, FORCER, and HYDRAULIC engines. A few other
ufeful, yet not complex, pumps, will be defcribed in the prefent
article: and fome account will be added of the moſt ingenious
piftons and valves.
1. A modification of the fucking-pump which has been much
recommended, is exhibited in plate XXV. fig. 17. Here the
fuction-pipe CO comes up through a ciftern KMNL deeper or
longer than the intended ftroke of the piſton, and has a valve
C at top. The piſton, or what acts in lieu of it, is a tube
AHGB, open at both ends, and of a diameter fomewhat larger
than that of the fuction-pipe. The interval between them is
filled up at HG by a ring or belt of ſoft leather, which is faſt-
ened to the outer tube, and moves up and down with it, fliding
along the ſmoothly polifhed furface of the fuction-pipe with
very little friction. There is a valve I on the top of this pifton,
opening upwards. Water is poured into the outer ciftern.
The outer cylinder or pifton being drawn up from the bot-
tom, there is a great rarefaction of the air which was between
them, and the atmoſphere preffes the water up through the
fuction-pipe to a certain height; for the valve I keeps thut by

Pumps.
289
the preffure of the atmoſphere and its own weight. Puſhing
down the piston cauſes the air, which had expanded from the
fuction-pipe into the pifton, to eſcape through the valve: I;
drawing it up a fecond time allows the atmoſphere to prefs
more water into the fuction-pipe, to fill it, and alſo part of the
piſton. When this is pushed down again, the water which
had come through the valve C is now forced out through the
valve I into the ciftern KMNL, and now the whole is full of
water. When, therefore, the pifton is drawn up, the water.
follows, and fills it, if not. 33 feet above the water in the cistern;
and when it is pufhed down again, the water which filled the
pifton is all thrown out into the ciftern; and after this it de-
livers its full contents of water every ftroke. The water in the
ciſtern KMNL effectually prevents the entrance of any air be-
tween the two pipes; ſo that a very moderate compreffion of the
belt of ſoft leather at the mouth of the piſton cylinder is fuffici-
ent to make all perfectly tight.
It might be made differently. The ring of leather might be
faſtened round the top of the inner cylinder at DE, and flide on
the infide of the pifton cylinder: but the firft form is moft
eafily executed. Muſchenbroeck has given a figure of this
pump in his large fyftem of natural philofophy, and fpeaks
very highly of its performance. But we do not fee any advan-
tage which it poffeffes over the common fucking-pump. He
indeed fays that it is without friction, and makes no mention of
the ring of leather between the two cylinders. Such a pump
will raife water extremely well to a ſmall height, and it ſeems
to have been a model only which he had examined: but if the
fuction-pipe be long, it will by no means do without the leather;
for on drawing up the pifton, the water of the upper ciftern will
rife between the pipes, and fill the piſton, and none will come
up through the fuction-pipe.
In
We may take this opportunity of obferving, that the many
ingenious contrivances of pumps without friction are of little
importance in great works; becauſe the friction which is com-
pletely fufficient to prevent all eſcape of water in a well-con-
ftructed pump is but a very trifling part of the whole force.
the great pumps which are uſed in mines, and are worked by a
fteam-engine, it is very ufual to make the piftons and valves
without any leather whatever. The working barrel is bored
truly cylindrical, and the piſton is made of metal of a fize that
will juſt paſs along it without ſticking. When this is drawn
up with the velocity competent to a properly loaded machine,
the quantity of water which eſcapes round the piſton is infigni-
ficant. The pifton is made without leathers, not to avoid fric-
tion, which is alfo infignificant in fuch works; but to avoid the
VOL. II.
U
290
MACHINES.
neceffity of frequently drawing it up for repairs through ſuch a
length of pipes.
If a pump abfolutely without friction is wanted, the fol-
lowing feems preferable for fimplicity and performance to any
we have ſeen, when made uſe of in proper fituations. Let NÓ
(fig. 18.) be the furface of the water in the pit, and K the place
of delivery. The pit muſt be as deep in water as from K te
NO. ABCD is a wooden trunk, round or fquare, open at
both ends, and having a valve P at the bottom. The top of
this trunk muſt be on a level with K, and has a ſmall ciftern
EADF. It alſo communicates laterally with a rifing pipe
GHK, furniſhed with a valve at H opening upwards. LM is
a beam of timber fo fitted to the trunk as to fill it without
ſticking, and is of at leaſt equal length. It hangs by a chain
from a working beam, and is loaded on the top with weights
exceeding that of the column of water which it difplaces.
Now ſuppoſe this beam allowed to deſcend from the poſition in
which it is drawn in the figure; the water muſt riſe all around
it, in the crevice which is between it and the trunk, and alſo
in the rifing pipe; becauſe the valve P fhuts, and H opens; fo
that when the plunger has got to the bottom, the water will
ſtand at the level of K. When the plunger is again drawn up
to the top by the action of the moving power, the water finks
again in the trunk, but not in the rifing pipe, becauſe it is
ſtopped by the valve H. Then allowing the plunger to deſcend
again, the water muſt again riſe in the trunk to the level of K,
and it muſt now flow out at K; and the quantity diſcharged
will be equal to the part of the beam below the furface of the
pit-water, deducting the quantity which fills the ſmall ſpace
between the beam and the trunk. This quantity may be re-
duced almoſt to nothing; for if the inſide of the trunk and the
outfide of the beam be made tapering, the beam may be let
down till they exactly fit; and as this may be done in ſquare
work, a good workman can make it exceedingly accurate. But
in this cafe, the lower half of the beam and trunk muſt not
taper; and this part of the trunk muſt be of fufficient width
round the beam to allow free paffage into the rifing pipe. Or,
which is better, the rifing pipe muſt branch off from the bottom
of the trunk. A diſcharge may be made from the ciſtern EADF,
ſo that as little water as poffible may defcend along the trunk
when the pifton is raiſed.
One great excellence of this pump is, that it is perfectly free
from all the deficiencies which in common pumps refult from
want of being air-tight. Another is, that the quantity of wa-
ter raiſed is precifely equal to the power expended; for any
want of accuracy in the work, while it occafions a diminution
Pumps.
291
鳖
​of the quantity of water diſcharged, makes an equal diminution
in the weight which is abfolutely neceffary for pufhing down the
plunger. We have ſeen a machine confifting of two fuch pumps
fufpended from the arms of a long beam, the upper fide of which
was formed into a walk with a rail on each fide. A man ſtood on
one end till it got to the bottom, and then walked gently up to
the other end, the inclination being about twenty-five degrees
at firſt, but gradually diminiſhed as he went along, and changed
the load of the beam. By this means he made the other end
go to the bottom, and ſo on alternately, with the eaſieſt of all
exertions, and what we are moft fitted for by our ſtructure.
With this machine, a very feeble old man, weighing 110
pounds, raiſed 7 cubic feet of water 11 feet high in a minute,
and continued working 8 or 10 hours every day. A ftout young
man, weighing nearly 135 pounds, raiſed 8 to the fame
height; and when he carried 30 pounds, conveniently flung
about him, he raiſed 94 feet of this height, working 10 hours
a-day without fatiguing himſelf. This exceeds Defagulier's
maximum of a hogfhead of water 10 feet high in a minute, in
the proportion of 9 to 7 nearly. It is limited to very moderate
heights; but in fuch fituations it is very effectual. Belidor ap-
plies a nearly fimilar contrivance to the working of double
pumps in general.
3. The moft ingenious contrivance of a pump without
friction is that of Mr. Hafkins, defcribed in Phil. Tranf. No.
370, and called by him the QUICKSILVER PUMP. Its conftruc-
tion and mode of operation are pretty complicated; but the
following preliminary obſervations will, we hope, render it
abundantly plain.
Let there (fig. 19.) be a cylindrical iron pipe, about fix feet
long, open at top, alſo another cylinder, connected with it at
bottom, and of ſmaller diameter. It may either be ſolid, or, if
hollow, it muſt be cloſe at top. Let a third iron cylinder, of an
intermediate diameter, be made to move up and down between
the other two without touching either, but with as little interval
as poffible. This middle cylinder communicates, by means of the
pipe AB, with the upright pipe FE, having valves C and D
(both opening upwards) adjoining to the pipe of communication.
Suppofe the outer cylinder fufpended by chains from the end of
a working beam, and let mercury be poured into the interval
between the three cylinders till it fills the ſpace to about three-
fourths of their height. Alfo fuppofe that the lower end of
the pipe FE is immerfed into a ciſtern of water, and that the
valve D is leſs than 33 feet above the furface of this water.
Now ſuppoſe a perforation made fomewhere in the pipe AB,
and a communication made with an air-pump. When the

U 2
1
292
MACHINES.
air-pump is worked, the air contained in CE, in AB, and in
the ſpace between the inner and middle cylinders, is rarefied,
and is abſtracted by the air-pump; for the valve D imme-
diately fhuts. The preffure of the atmoſphere will cauſe the
water to rife in the pipe CE, and will cauſe the mercury to riſe
between the inner and middle cylinders, and fink between the
outer and middle cylinders. Let us fuppofe mercury 12 times.
heavier than water: then for every foot that the water riſes in
EC, the level between the outfide and infide mercury will vary an
inch; and if we fuppofe DE to be 30 feet, then if we can rarefy
the air fo as to raiſe the water to D, the outfide mercury will be
depreffed to q, r, and the inſide mercury will have risen to s, t,
sq and tr being about 30 inches. In this ftate of things,
the water will run over by the pipe BA, and every thing will
remain nearly in this pofition. The columns of water and
mercury balance each other, and balance the preffure of the
atmoſphere.
While things are in this ſtate of equilibrium, if we allow
the cylinders to defcend a little, the water will rife in the pipe
FE, which we may now confider as a fuction-pipe; for by this
motion the capacity of the whole is enlarged, and therefore the
preffure of the atmoſphere will ſtill keep it full, and the fitua-
tion of the mercury will again be fuch that all ſhall be in equi-
librio. It will be a little lower in the infide fpace and higher
in the outfide.
Taking this view of things, we fee clearly how the water is
fupported by the atmoſphere at a very confiderable height.
The apparatus is analogous to a ſyphon which has one leg
filled with water and the other with mercury. But it was not
néceffary to employ an air-pump to fill it. Suppofe it again
empty, and all the valves fhut by their own weight. Let the
cylinders deſcend a little. The capacity of the ſpaces below
the valve D is enlarged, and therefore the included air is rare-
fied, and ſome of the air in the pipe CE muſt diffuſe itſelf into
the ſpace quitted by the inner cylinder. Therefore the atmo-
ſphere will preſs ſome water up the pipe FE, and fome mercury
into the inner ſpace between the cylinders. When the cylinders
are raiſed again, the air which came from the pipe CE would
return into it again, but is prevented by the valve C.—Raiſing
the cylinders to their former height would compreſs this air;
it therefore lifts the valve D, and efcapes. Another depreffion
of the cylinders will have a fimilar effect. The water will rife
higher in FC, and the mercury in the inner ſpace; and then,
after repeated ſtrokes the water will pafs the valve C, and fill
the whole apparatus, as the air-pump had cauſed it to do before.
The pofition of the cylinders, when things are in this ſituation,
Pumps.
293
is reprefented in fig. 20. the outer and inner cylinder in their
loweſt poſition having defcended about 30 inches. The mer-
cury in the outer ſpace ſtands at q, r, a little above the middle
of the cylinders, and the mercury in the inner ſpace is near the
topts of the inner cylinder. Now let the cylinders be drawn
up. The water above the mercury cannot get back again
through the valve C, which fhuts by its own weight. We
therefore attempt to compreſs it; but the mercury yields, and
defcends in the inner ſpace, and riſes in the outer till both are
quickly on a level, about the height vv. If we continue
to raise the cylinders, the compreffion forces out more mercury,
and it now ftands lower in the inner than in the outer fpace.
But that there may be fomething to balance this inequality of
the mercurial columns, the water goes through the valve D, and
the equilibrium is reftored when the height of the water in the
pipe ED above the furface of the internal mercury is 12 times
the difference of the mercurial columns (on the former fup-
pofition of ſpecific gravity). If the quantity of water be ſuch
as to rife two feet in the pipe ED, the mercury in the outer
ſpace will be two inches higher than that in the inner ſpace.
Another depreffion of the cylinders will again enlarge the ſpace
within the apparatus, the mercury will take the poſition of
fig. 19. and more water will come in.. Raifing the cylinders
will fend this water four feet up the pipe ED, and the mercury
will be four inches higher in the inner than in the outer space.
Repeating this operation, the water will be raiſed ſtill higher
in DE; and this will go on till the mercury in the outer ſpace
reaches the top of the cylinder; and this is the limit of the
performance. The dimenfions with which we fet out will
enable the machine to raiſe the water about 30 feet in the pipe,
ED; which, added to the 30 feet of CF, makes the whole height
above the pit-water 60 feet. By making the cylinders longer,
we increaſe the height of FD. This machine muſt be worked
with great attention, and but flowly; for at the beginning of
the forcing ſtroke the mercury very rapidly finks in the inner
ſpace and rifes in the outer, and will dash out and be loft. To
prevent this as much as possible, the outer cylinder terminates
in a fort of cup or diſh, and the inner cylinder ſhould be tapered
at the top.
The machine is exceedingly ingenious and refined; and there
is no doubt but that its performance will exceed that of any
other pump which raiſes the water to the fame height, becauſe
friction is completely avoided, and there can be no want of
tightneſs of the pifton. But this is all its advantage; and from
what has been obſerved, it is but trifling. The expence would
be enormous; for with whatever care the cylinders are made,
294
MACHINES.
the interval between the inner and outer cylinders muſt contain
a very great quantity of mercury. The middle cylinder muſt
be made of iron plate, and muſt be without a feam, for the
mercury would diffolve every folder. For fuch reafons, it has
never come into general ufe. But it would have been unpar-
donable to have omitted the deſcription of an invention which
is fo original and ingenious; and there are ſome occafions where
it may be of great ufe, as in nice experiments for illuſtrating
the theory of hydraulics, it would give the fineſt piftons for
meaſuring the preffures of water, in pipes, &c.
The following pump, without friction, may be conſtructed
in a variety of ways by any common carpenter, without the
affiftance of the pump-maker, or plumber, and will be very
effective for raiſing a great quantity of water to fmall heights,
as in draining marſhes, marle pits, quarries, &c. or even for the
fervice of a houſe.
4. ABCD (pl. XXV. fig. 21.) is a fquare trunk of carpenter's
work open at both ends, and having a little ciftern and fpout
at top. Near the bottom there is a partition made of board,
perforated with a hole E, and covered with a clack. ƒƒƒƒ
repreſent a long cylindrical bag made of leather or of double
canvas, with a fold of thin leather, ſuch as ſheepſkin, between
the canvas bags. This is firmly nailed to the board E with ſoft
leather between. The upper end of this bag is fixed on a round
board having a hole and valve F. This board may be turned
in the lathe with a groove round its edge, and the bag faſtened
to it by a cord bound tight round it. The fork of the pifton-
rod FG is firmly fixed into this board; the bag is kept diftended
by a number of wooden hoops or rings of ftrong wire ƒfƒ,ff,
ff, &c. put into it at a few inches diſtance from each other. It
will be proper to connect theſe hoops before putting them in,
by three or four cords from top to bottom, which will keep
them at their proper diftances. Thus will the bag have the
form of a barber's bellows powder-puff. The diſtance between
the hoops ſhould be about twice the breadth of the rim of the
wooden ring to which the upper valve and piſton-rod are fixed.
Now let this trunk be immerſed in the water. It is evident
that if the bag be ſtretched from the compreffed form which its
own weight will give it by drawing up the piſton-rod, its
capacity will be enlarged, the valve F will be ſhut by its own
weight, the air in the bag will be rarefied, and the atmoſphere
will prefs the water into the bag. When the rod is thruſt down
again, this water will come out by the valve F, and fill part of
the trunk. A repetition of the operation will have a fimilar
effect; the trunk will be filled, and the water will at last be
diſcharged by the ſpout.
Pumps.
295
Here is a pump without friction, and perfectly tight. For
the leather between the folds of canvas renders the bag imper-
vious both to air and water. And the canvas has very con-
fiderable ſtrength. We know from experience that a bag of
fix inches diameter, made of fail-cloth No. 3. with a fheep-
fkin between, will bear a column of 15 feet of water, and ſtand
fix hours work per day for a month without failure, and that
the pump is confiderably ſuperior in effect to a common pump
of the fame dimenſions. We must only obſerve, that the
length of the bag muſt be three times the intended length of
the ſtroke; ſo that when the piſton-rod is in its higheſt poſition,
the angles or ridges of the bag may be pretty acute. If the bag
be more ſtretched than this, the force which must be exerted by
the labourer becomes much greater than the weight of the
column of water which he is raifing. If the pump be laid
aflope, which is very uſual in thefe occafional and hafty draw-
ings, it is neceffary to make a guide for the piſton-rod within
the trunk, that the bag may play up and down without rubbing
on the fides, which would quickly wear it out.
The experienced reader will fee that this pump is very like
that of Goffet and De la Deuille, defcribed by Belidor, vol. ii.
p. 120, and moft writers on hydraulics. It would be ſtill more
like it, if the bag were on the under fide of the partition E, and
a valve placed further down the trunk. But we think that our
form is greatly preferable in point of ftrength. When in the
other fituation, the column of water lifted by the piston tends to
burſt the bag, and this with a great force, as the intelligent
reader well knows. But in the form recommended here, the
bag is compreſſed, and the ſtrain on each part may be made much
lefs than that which tends to burſt a bag of fix inches diameter.
The nearer the rings are placed to each other the ſmaller will
the ſtrain be.
The fame bag-piſton may be employed for a forcing-pump,
by placing it below the partition, and inverting the valve; and
it will then be equally ftrong, becauſe the refiftance in this cafe
too will act by compreffion.
5. An ingenious variation in the conftruction of the fucking-
pump, is that with two pifton-rods in the fame barrel, invented
by Mr. Walter Taylor, of Southampton. A vertical ſection of
this pump is given in fig. 1. pl. XXIV. The pifton-rods have
racks at their upper parts working on the oppofite fides of a
pinion, and kept to their proper pofitions by friction-rollers.
The valves uſed in this pump are of three kinds, as fhewn at a,
b, and c. The former is a fpheric fegment which flides up and
down on the piſton-rod, and is brought down by its own weight:
the ſecond, b, is called the pendulum-valve: and the third, c, is
296
MACHINES.
£
a globe which is raiſed by the rifing water, and falls again by its
own weight. Each of thefe valves will difengage itſelf from
chips, fand, gravel, &c. brought up by the water. In this kind
of pump the pistons may either be put in motion by a handle in
the uſual way, or a rope may pafs round the wheel de in a
proper groove, the two ends of which, after croffing at the lower
part of the wheel, may be pulled by one man or more on each
fide. A pump of this kind, with a feven-inch bore, heaves a ton
twenty-four feet high in a minute, with ten men, five only
working at a time on each fide.
6. Another improvement of the common pump has been
made by Mr. Todd of Hull. This invention in fome particulars
bears a refemblance to the ordinary one, but he has contrived
to double its powers by the following means:
Having prepared the pifton-cylinder, which may be twelve
feet high, he cuts from the bottom thereof about three feet;
at the end of the great cylinder he places an atmoſpheric-valve,
and to the top of the fmall cylinder a ferving-valve. In the
bottom of the ſmall cylinder, which contains the ferving-valve,
is inferted an oblong elliptical curved tube, of equal calibre
with the principal cylinder, and the other end is again inferted
in the top of the great cylinder. This tube is divided in the
fame manner as the first cylinder, with atmoſpheric and ferving
valves, exactly parallel with the valves of the firſt cylinder.
The pump, thus having double valves, produces double effects,
which effects may be ftill further increafed by extending the
dimenſions.
The cylinder is fcrewed, for fervice on a male tube-ſcrew,
which projects from the fide of a refervoir or water ciftern, and
is worked by hand.
The piſton-plunger is worked by a toothed fegment-wheel,
fimilar to the principle of the one uſed in working the chain-
pumps of fhips belonging to the royal navy; and the wheel
receives its motion from a hand-winch, which is confiderably
accelerated by a fly-wheel of variable dimenfions, at the oppofite
end.
This pump, in addition to its increafed powers, poffeffes
another very great and prominent advantage. By fcrewing to
it the long leather tube and fire-pipe of the common engine, it
is in a few minutes converted into an effective fire-engine.
Hence, whoever poffeffes one may be faid to have a convenient
domeftic apparatus againſt fire. Three men can work it; one
to turn the winch, another to direct the fire-pipe, and a third to
ſupply the water.
7. Double, triple, or quadruple pumps, admit of great variety
in their conſtruction, to fuit different purpoſes. The beſt col-
}.
Pumps.
297
lection of theſe with which we are acquainted, is to be found
in Leupold's Theatrum Machinarum Hydraulicarum: fome in
this collection are very fingular and ingenious, and have par-
ticular advantages to fuit local circumſtances, and give them a
preference. The late Mr. Benjamin Martin invented a curious
and powerful pump with two piftons, the friction of which was
exceedingly fmall. An admirable engraving of this pump, by
Lowry, is given in vol. 20. of Tilloch's Philofophical Magazine.
The triple pump, a fketch of which may be feen in fig. 9. pl.
XXIV. is taken from Bockler's Theatrum Machinarum; the
nature of the machinery by which this pump is worked, will be
fufficiently obvious to any perſon after an inſpection of the figure:
the horizontal wheel C, and its fhaft A, are turned by the
capftan bars B, this wheel drives the pinion D, on the axle of
which is the equalizing fly E, and the crank F: the rotatory
motion of the crank alternately raiſes and depreffes the bar G,
with the lever H turning on a roller and pivots, and thus works
the pump I: at the fame time the connecting rods K move in
like manner the lever M, and work the pump O; and the rods
K move the lever N, and work the pump P. If the levers H,
M, N, are not ſo contrived that the extremities of each fhall
move through equal ſpaces, the bores of I, O, and P, muſt be
made in the inverſe ratio of thoſe ſpaces, otherwiſe one or other
of the refervoirs may be drawn dry; a defect that ſhould be
carefully guarded against.
8. Our attention may now be directed to ſome of the differ-
ent forms which may be given to the pistons and valves of a
pump.
霉
​*. The great defideratum in a piſton is, that while it be as tight
as poffible, it ſhould have as little friction as is conſiſtent with
this indifpenfable quality. The common form, when carefully
executed, poffeffes theſe properties in an eminent degree. This
piſton is a fort of truncated cone, generally made of wood not
apt to ſplit, ſuch as elm or beech. The fmall end of it is cut
off at the fides, ſo as to form a fort of arch, by which it is
faſtened to the iron rod or fpear. The two ends of the conical
part may be hooped with braſs. This cone has its larger end
furrounded with a ring or band of ſtrong leather faſtened with
nails, or by a copper hoop, which is driven on it at the fmaller
end. The further this band reaches beyond the baſe of the
cone, the better; and the whole must be of uniform thickneſs
all round, fo as to fuffer equal compreffion between the cone
and working barrel. The feam or joint of the two ends of this
band muſt be made very clofe; but not fewed or ftitched to-
gether, as that would occafion bumps or inequalities, which
would fpoil its tightnefs; and no harm can refult from the want
293
MACHINES.
of it, becauſe the two edges will be fqueezed clofe together by
the compreffion in the barrel. Nor is it by any means necef-
fary that this compreffion be great: this is a very detrimental
error of the pump-makers. It occafions enormous friction, and
deftroys the very purpoſe which they have in view, viz. render-
ing the piston air-tight; for it cauſes the leather to wear through
very foon at the edge of the cone, and it alſo wears the working
barrel. This very foon becomes wide in that
foon becomes wide in that part which is con-
tinually paffed over by the piſton, while the mouth remains of
its original diameter, and it becomes impoffible to thrust in a
pifton which ſhall completely fill the worn part. Now, a very
moderate preffure is fufficient for rendering the pump perfectly
tight, and a piece of glove leather would be fufficient for
this purpofe, if loofe or detached from the folid cone; for
fuppofe fuch a loofe and flexible, but impervious, band of
leather put round the pifton, and put into the barrel; and let it
even be fuppofed that the cone does not compreſs it in the
fmalleſt degree to its internal furface. Pour a little water
carefully into the infide of this fort of cup or difh; it will cauſe
it to fwell out a little, and apply itſelf cloſe to the barrel all
round, and even adjuſt itſelf to all its inequalities. Let us
ſuppoſe it to touch the barrel in a ring of an inch broad all
round. We can eaſily compute the force with which it is prefs-
ed. It is half the weight of a ring of water an inch deep and
an inch broad. This is a trifle, and the friction occafioned by
it not worth regarding; yet this trifling preffure is fufficient to
make the paffage perfectly impervious, even by the moſt enor-
mous preffure of a high column of incumbent water: for let
this preffure be ever fo great, the preffure by which the leather
adheres to the barrel always exceeds it, becauſe the incumbent
fluid has no preponderating power by which it can force its way
between them, and it muſt infinuate itſelf preciſely fo far, that
its preffure on the infide of the leather ſhall ſtill´exceed, and
only exceed, the preffure by which it endeavours to infinuate it-
felf; and thus the pifton becomes perfectly tight with the
ſmalleſt poſſible friction. This reafoning is perhaps too refined
for the uninftructed artift, and probably will not perfuade him.
To fuch we would recommend an examinátion of the piſtons
and valves contrived and executed by that artiſt, whoſe ſkill far
furpaffes our higheſt conceptions, the all-wife Creator of this
world. The valves which ſhut up the paffages of the veins,
and this in places where an extravafation would be followed by
inftant death, are cups of thin membrane, which adhere to the
fides of the channel about half way round, and are detached
in the rest of their circumference. When the blood comes in
the oppofite direction, it puſhes the membrane afide, and has a
Pump-piftons.
299
1
paffage perfectly free. But a ftagnation of motion allows the
tone of the (perhaps) mufcular membrane, to reſtore it to its
natural fhape, and the leaft motion in the oppofite direction
cauſes it inſtantly to clap cloſe to the fides of the vein, and then
no preffure whatever can force a paffage. We fhall recur to
this again when deſcribing the various contrivances of valves,
&c. What we have faid is enough for fupporting our direc-
tions for constructing a tight pifton. But we recommend
thick and ſtrong leather, while our prefent reaſoning feems to
render thin leather preferable. If the leather be thin, and the
folid pifton in any part does not prefs it gently to the barrel,
there will be in this part an unbalanced preffure of the incum-
bent column of water, which would inftantly burſt even a ſtrong
leather bag; but when the folid pifton, covered with leather,
exactly fills the barrel, and is even preffed a little to it, there
is no fuch riſk; and now that part of the leather band which
reaches beyond the folid pifton performs its office in the com-
pleteft manner. We do not heſitate, therefore, to recommend
this form of a piſton, which is the moſt common and fimple
of all, as preferable, when well executed, to many of thoſe
more artificial, and frequently very ingenious, conſtructions,
which we have met with in the works of the firſt engineers.
Belidor, an author of the firft reputation, has given the de-
ſcription of a piſton which he highly extols, and is undoubtedly
a very good one, conftructed from principle, and extremely well
compofed.
9. It confifts of a hollow cylinder of metal (XXV. fig. 22.)
pierced with a number of holes, and having at top a flanch, whoſe
diameter is nearly equal to that of the working barrel of the
pump. This flanch has a groove round it. There is another
flanch below, by which this hollow cylinder is faſtened with
bolts to the lower end of the piſton, repreſented in fig. 23.
This confifts of a plate with a grooved edge fimilar to AB, and
an intermediate plate which forms the feat of the valve. The
compofition of this part is better underſtood by inſpecting the
figure than by any defcription. The pifton-rod HL is fixed to
the upper plate by bolts through its different branches at G, G.
This metal body is then covered with a cylindrical bag of leather,
faſtened on it by cords bound round it, filling up the grooves in
the upper and lower plates. The operation of the piſton is as
follows.
A little water is poured into the pump, which gets paſt the
fides of the piſton, and lodges below in the fixed valve. The
pifton being pushed down dips into this water, and it gets into it
by the valve. But as the piſton in defcending compreffes the
air below it, this compreffed air alfo gets into the infide of the
300
MACHINES.
piſton, ſwells out the bag which ſurrounds it, and compreffes it
to the fides of the working-barrel. When the pifton is drawn
up again, it muſt remain tight, becauſe the valve will fhut and
keep in the air in its moſt compreffed ſtate; therefore the piſton
muft perform well during the fuction. It muſt act equally well
when pushed down again, and acting as a forcer; for, however
great the reſiſtance may be, it will affect the air within the
piſton to the ſame degree, and keep the leather cloſe applied to
the barrel. There can be no doubt therefore of the pifton's per-
forming both its offices completely; but we imagine that the
adhesion to the barrel will be greater than is neceffary: it will
extend over the whole furface of the pifton, and be equally great
in every part of its furface; and we fufpect that the friction will
therefore be very great. We have very high authority for ſup-
pofing that the adheſion of a piſton of the common form, care-
fully made, will be fuch as will make it perfectly tight; and it
is evident that the adheſion of Belidor's pifton will be much
greater, and it will be productive of worfe confequences. If
the leather bag be worn through in any one place, the air efcapes,
and the piſton ceaſes to be compreffed altogether; whereas in
the common piſton there will very little harm reſult from the
leather being worn through in one place, eſpecially if it project
a good way beyond the baſe of the cone. We ftill think the
common piſton preferable.
10. Belidor defcribes another forcing piſton, which he had
executed with fuccefs, and prefers to the common wooden forcer.
It confifts of a metal cylinder or cone, having a broad flanch
united to it at one end, and a ſimilar flanch which is ſcrewed on
the other end. Between theſe two plates are a number of rings
of leather ftrongly compreffed by the two flanches, and then
turned in a lathe like a block of wood, till the whole fits tight,
when dry, into the barrel. It will fwell, fays he, and ſoften with
the water, and withſtand the greateſt preffures. We cannot
help thinking this but an indifferent pifton. When it wears,
there is nothing to ſqueeze it to the barrel. It may indeed be
taken out and another ring or two of leather put in, or the
flanches may be more ftrongly fcrewed together: but all this
may be done with any kind of piſton; and this has therefore no
peculiar merit.
11. The following will, we prefume, appear greatly prefer-
able. ABCD (fig. 24.), is the folid wooden or metal block of
the pifton; EF is a metal plate, which is turned hollow or difh-
like below, fo as to receive within it the folid block. The
pifton-rod goes through the whole, and has a ſhoulder above.
the plate EF, and a nut H below. Four fcrew-bolts alfo go
through the whole, having their heads funk into the block, and
Pump-piſtons.
301
i
nuts above. The packing, or ſtuffing, as it is termed by the
workmen, is reprefented at NO. This is made as folid as poffi-
ble, and generally conſiſts of foft hempen twine well foaked in
a mixture of oil, tallow, and rofin. The plate EF is gently
ſcrewed down, and the whole is then put into the barrel, fitting
it as tight as may be thought proper. When it wears loofe, it
may be tightened at any time by fcrewing down the nuts which
cauſe the edges of the difh to fqueeze out the packing, and
compreſs it againſt the barrel to any degree.
The greateſt difficulty in the conſtruction of a piſton is to
give a fufficient paffage through it for the water, and yet allow
a firm ſupport for the valve, and fixture for the piſton-rod.
It occafions a confiderable expence of the moving power to force
a piſton with a narrow perforation through the water lodged in
the working barrel. When we are raiſing water to a ſmall height,
fuch as 10 or 20 feet, the power fo expended amounts to a fourth
part of the whole, if the water-way in the piston is leſs than
one-half of the ſection of the barrel, and the velocity of the
pifton two feet per fecond, which is very moderate. There
can be no doubt, therefore, that metal piſtons are preferable,
becauſe their greater ftrength allows much wider apertures.
12. The following piſton, deſcribed and recommended by
Belidor, feems as perfect in theſe reſpects as the nature of
things will allow. We fhall therefore defcribe it in the author's
own words, as a model which may be adopted with confidence
in the greateſt works.
"The body of the piſton is a truncated metal cone CCXX
(fig. 25.), having a ſmall fillet at the greater end. Fig. 26.
ſhows the profile, and fig. 27, the plan of its upper baſe; where
appears a crofs bar DD, pierced with an oblong mortife E for
receiving the tail of the pifton-rod. A band of thick and
uniform leather AA (fig. 26. and 28.) is put round this cone,
and fecured by a brafs hoop BB firmly driven on its fmaller
end, where it is previouſly made thinner to give room for the
hoop.
"This pifton is covered with a leather valve, fortified with
metal plates GG (fig. 29.). Theſe plates are wider than the
hole of the pifton, fo as to reſt on its rim. There are ſimilar
plates below the leather of a ſmaller fize, that they may go into
the hollow of the piſton; and the leather is firmly held between
the metal plates by fcrews H, H, which go through all. This
is reprefented by the dotted circle IK. Thus the preffure of
the incumbent column of water is fupported by the plates GG,
whofe circular edges reft on the brim of the water-way, and
thus ftraight edges reft on the croſs-bar DD of fig. 26. and 27.
This valve is laid on the top of the conical box in ſuch a man,
302
MACHINES.
ner that its middle FF refts on the croſs-bar. To bind all to-
gether, the end of the piſton-rod is formed like a croſs, and the
arms MN (fig. 30.) are made to reft on the diameter FF of
the valve, the tail EP going through the hole E in the middle
of the leather, and through the mortife E of the croſs-bar of
the box; as well as through another bar QR (fig. 28. and 29.)
which is notched into the lower brim of the box. A key V
is then driven into the hole T in the pifton-rod; and this
wedges all faft. The bar QR is made ftrong; and its extre-
mities project a little, fo as to fupport the braſs hoop BB which
binds the leather band to the pifton-box."
This piſton has every advantage of ſtrength, tightneſs, and
large water-way. The form of the valve (which has given it
the name of the butterfly-valve) is extremely favourable to the
paffage of the water; and as it has but half the motion of
a complete circular valve, lefs water goes back while it is
fhutting.
13. The following pifton is alſo ingenious, and has a good
deal of merit. OPPO (pl. XXIV. fig. 5.) is the box of the
piſton, having a perforation Q, covered above with a flat valve
K, which reſts in a metal plate that forms the top of the box.
- ABCBA is a ftirrup of iron to which the box is fixed by fcrews
a, a, a, a, whofe heads are funk in the wood. This ftirrup is
perforated at C, to receive the end of the piſton-rod, and a nut
H is fcrewed on below to keep it faft. DEFED is another
ftirrup, whoſe lower part at DD forms a hoop like the fole of
a ftirrup, which embraces a ſmall part of the top of the wooden
box. The lower end of the pifton-rod is fcrewed; and before
it is put into the holes of the two ftirrups (through which holes
it flides freely) a broad nut G is fcrewed on it. It is then put
into the holes, and the nut H firmly fcrewed up. The packing
RR is then wound about the pifton as tight as poffible till it
completely fills the working-barrel of the pump. When long
uſe las rendered it in any degree looſe, it may be tightened again
by fcrewing down the nut G. This caufes the ring DĎ to
compreſs the packing between it and the projecting fhoulder
of the box at PP; and thus caufes it to fwell out, and apply
itfelf cloſely to the barrel. Prony, in his Architecture Hydrau-
lique, afcribes this invention to M. Bettancourt.
14. We fhall add only another form of a perforated piſton;
which being on a principle different from all the preceding, will
fuggeſt many others; each of which will have its peculiar ad-
vantages. OO in fig. 3. pl. XXIV. reprefents the box of this
piſton, fitted to the working-barrel in any of the preceding ways
as may be thought beft. AB is a crofs-bar of four arms, which
is fixed to the top of the box. CF is the pifton-rod going
Pump-valves.
303
L
through a hole in the middle of AB, and reaching a little way
beyond the bottom of the box. It has a fhoulder D, which
prevents its going too far through. On the lower end there is
a thick metal plate, turned conical on its upper fide, ſo as to fit
a conical feat PP in the bottom of the pifton-box.
When the piſton-rod is pushed down, the friction on the
barrel prevents the box from immediately yielding. The rod
therefore flips through the hole of the croſs-bars AB. The
plate E, therefore, detaches itſelf from the box. When the
ſhoulder D preffes on the bar AB, the box muft yield, and be
puſhed down the barrels, and the water gets up through the
perforation. When the piſton-rod is drawn up again, the box
does not move till the plate E lodges in the feat PP, and thus
ſhuts the water-way; and then the piſton lifts the water which
is above it, and acts as the piſton of a fucking-pump.
This is a very ſimple and effective conftruction, and makes a
very tight valve. It has been much recommended by engineers
of the firſt reputation, and is frequently uſed; and, from its
fimplicity, and the great folidity of which it is capable, it ſeems
very fit for great works. But it is evident that the water-way
is limited to leſs than one-half of the area of the working-
barrel. For if the perforation of the piſton be one-half of the
area, the diameter of the plate or ball EF muſt be greater;
and therefore leſs than half the area will be left for the paffage
of the water by its fides.
15. We come now to confider briefly the forms which may
be given to the valves of an hydraulic engine.
The requifites of a valve are, that it fhall be tight, of fufficient
ſtrength to refift the great preffures to which it is expoſed, that
it afford a fufficient paffage for the water, and that it do not
allow much to go back while it is fhutting.
The butterfly-valve reprefented in figures 29, &c. is free
from moſt of the inconveniences, and feems the moſt perfect
of the clack valves. Some engineers make their great valves
of a pyramidal form, confifting of four clacks, whofe hinges are
in the circumference of the water-way, and which meet with
their points in the middle, and are ſupported by four ribs which
riſe up from the fides, and unite in the middle. This is an ex-
cellent form, affording the moft fpacious water-way, and ſhut-
ting very readily. It feems to be the beſt poffible for a piſton.
The rod of the pifton is branched out on four fides, and the
branches go through the piſton-box, and are faſtened below with
ſcrews. Theſe branches form the fupport for the four clacks.
We have ſeen a valve of this form in a pump of fix feet diameter,
which difcharged 20 hogfheads of water every ftroke, and made
12 ſtrokes in a minute, raiſing the water above 22 feet.
304
MACHINES.
16. There is another form of valve, called the button or tail
valve. It confifts of a plate of metal AB (fig. 4. pl. XXIV.)
turned conical, fo as exactly to fit the conical cavity a b of its
box. A tail CD projects from the under fide, which paffes
through a croſs-bar EF in the bottom of the box, and has a
little knob at the end, to hinder the valve from rifing too high.
This valve, when nicely made, is unexceptionable. It has
great ſtrength, and is therefore proper for all fevere ſtrains, and
it may be made perfectly tight by grinding. Accordingly it is
ufed in all cafes where this is of indifpenfable confequence. It
is moſt durable, and the only kind that will do for paffages
where ſteam or hot water is to go through. Its only imper-
fection is a ſmall water-way; which, from what has been ſaid,
cannot exceed, nor indeed equal, one-half of the area of the
pipe.
If we endeavour to enlarge the water-way, by giving the
cone very little taper, the valve frequently ſticks fo faft in the
feat that no force can detach them.-And this fometimes hap-
pens during the working of the machine; and the jolts and
blows given to the machine in taking it to pieces, in order to
diſcover what has been the reaſon that it has diſcharged no
water, frequently detaches the valve, and we find it quite looſe,
and cannot tell what has deranged the pump. When this is
guarded against, and the diminution of the water-way is not of
very great confequence, this is the beſt form of a valve.
•
17. Analogous to this is the fimpleft of all valves. It is
nothing more than a ſphere of metal, to which is fitted a ſeat
with a ſmall portion of a ſpherical cavity. Nothing can be
more effectual than this valve; it always falls into its proper
place, and in every pofition fits it exactly. Its only imper-
fection is the great diminution of the water-way. If the di-
ameter of the ſphere do not confiderably exceed that of the
hole, the touching parts have very little taper, and it is very apt
to ſtick faft. It oppofès much lefs refiftance to the paffage of
the water than the flat under-furface of the button-valve. The
ſpherical valve muſt not be made too light, otherwiſe it will be
hurried up by the water, and much may go back while it is
returning to its place.
Belidor deſcribes with great minutenefs (vol. ii. p. 221, &c.)
a valve which unites every requifite. But it is of fuch nice
and delicate conſtruction, and its defects are fo great when this
exactneſs is not attained, or is impaired by ufe, that we think
it hazardous to introduce it into a machine in a fituation where
an intelligent and accurate artiſt is not at hand. For this rea-
fon we have omitted the defcription, which cannot be given in
few words, nor without many figures; and defire our curious
Pumps.
305
readers to confult that author, or peruſe Dr. Defaguliers's tranſ-
lation of this paffage. Its principle is preciſely the ſame with
the following rude contrivance.
18. Suppoſe ABCD (fig. 2. pl. XXIV.) to be a ſquare
wooden trunk. EF is a piece of oak board, exactly fitted to
the trunk in an oblique pofition, and ſupported by an iron pin
which goes through it at I, one-third of its length from its
lower extremity E. The two ends of this board are bevelled,
fo as to apply exactly to the fides of the trunk. . It is evident,
that if a ftream of water come in the direction BA, its preſſure
on the part IF of this board will be greater than that upon EI.
It will therefore force it up and rufh through, making it ftand
almoſt parallel to the fides of the trunk. To prevent its rifing
fo far, a pin muſt be put in its way. When this current of
water changes its direction, the preffure on the upper fide of
the board being again greateft on the portion IF, it is forced
back again to its former fituation; and its two extremities reft-
ing on the oppofite fides of the trunk, the paffage is completely
ftopped. This board therefore performs the office of a valve;
and this valve is the moſt perfect that can be, becauſe it offers
the freeft paffage to the water, and it allows very little to get
back while it is fhutting; for the part IE brings up half as
much water as IF allows to go down. It may be made ex-
tremely tight, by fixing two thin fillets H and G to the fides of
the trunk, and covering thoſe parts of the board with leather
which apply to them; and in this ſtate it perfectly reſembles
Belidor's fine valve.
19. This conftruction of the valve fuggefts, by the way,
a form of an occafional pump, which may be quickly fet up by
any common carpenter, and will be very effectual in fmail
heights. Let a b c d e (fig. 2.) be a fquare box made to flide
along this wooden trunk without ſhake, having two of its fides
projecting upwards, terminating like the gable ends of a houſe.
A piece of wood e is mortifed into theſe two fides, and to this
the piſton-rod is fixed. This box being furniſhed with a valve
fimilar to the one below, will perform the office of a pifton.
If this pump be immerſed ſo deep in the water that the piſton
fhall alfo be under water, we fcruple not to ſay that its per-
formance will be equal to any. The pifton may be made
abundantly tight, by covering its outfide neatly with foft lea-
ther. And as no pipe can be bored with greater accuracy than
a very ordinary workman can make a fquare trunk, we think
this pump will not be very deficient even for a confiderable
fuction.
Thus much will, we hope, fuffice for the defcriptive part of
theſe uſeful machines: as to the theory of the motion of water in
VOL. II.
X
1
306
MACHINES.
pumps, at the fame time that it is extremely intricate, it prefents
but few reſults that are of any practical utility. The curious
student may be referred to the Mafchinenlehre of Langfdorf, the
Hydrodynamique of Boffut, the Hydraulique of Buat, the Architec-
ture Hydraulique of Prony, and the article Pump in the Encyclo-
pædia Britannica. The laſt two pieces have furniſhed us with
the moſt valuable parts of the prefent article. Some remarks on
the variable motion of the pifton-rod may be feen under the title
PARALLEL motion in this volume.
PYROMETER, a machine contrived to meaſure the ex-
panſion of metals, and other bodies, occafioned by heat.
Mufchenbroeck was the original inventor of the Pyrometer:
the nature and conſtruction of his inftrument may be underſtood
from the following account. If we fuppofe a ſmall bar of metal,
12 or 15 inches in length, made faft at one of its extremities, it
is obvious that if it be dilated by heat it will become lengthened,
and its other extremity will be pushed forwards. If this ex-
tremity then be fixed to the end of a lever, the other end of
which is furniſhed with a pinion adapted to a wheel, and if
this wheel move a ſecond pinion, the latter a third, and ſo on,
it will be evident that by multiplying wheels and pinions in
this manner, the laſt will have a very fenfible motion; ſo that
the moveable extremity of the ſmall bar cannot pafs over the
hundredth or thouſandth part of a line, without a point of the
circumference of the laft wheel paffing over ſeveral inches. If
this circumference then have teeth fitted into a pinion, to
which an index is attached, this index will make feveral revo-
lutions, when the dilatation of the bar amounts only to a quantity
altogether infenfible. The portions of this revolution may be
meaſured on a dial-plate, divided into equal parts; and by
means of the ratio which the wheels bear to the pinions, the
abfolute quantity which a certain degree of heat may have ex-
panded the fmall bar can be afcertained: or, converfely, by
the dilatation of the ſmall bar the degree of heat which has
been applied to it may be determined.
Such is the conftruction of Mufchenbroeck's pyrometer. It
is neceffary to obferve that a fmall cup is adapted to the ma-
chine, in order to receive the liquid or fufed matters, fubjected
to experiment, and in which the bar to be tried is immerfed.
When it is required to meaſure, by this inftrument, a con-
fiderable degree of heat, fuch as that of boiling oil or fufed
metal, fill the cup with the matter to be tried, and immerſe the
bar of iron into it. The dilatation of the bar, indicated by the
index, will point out the degree of heat it has affumed, and
which muſt neceffarily be equal to that of the matter into which
it is immerſed.
Pyrometer.
307
This machine evidently ſerves to determine the ratio of the
dilatation of metals, &c.: for by fubftituting in the room of the
pyrometric bar other metallic bars of the fame length, and then
expofing them to an equal degree of heat, the ratios of their
dilatation will be fhewn by the motion of the index.
Mufchenbroeck has given a table of the expanſion of the dif-
ferent metals, in the fame degree of heat. Having prepared
cylindric rods of iron, fteel, copper, braſs, tin, and lead, he ex-
poſed them firſt to a pyrometer with one flame in the middle
then with two flames; and fucceffively to one with three, four,
and five flames. But previous to this trial, he took care to cool
them equally, by expoſing them fome time upon the ſame ſtone,
when it began to freeze, and Fahrenheit's thermometer was at
thirty-two degrees. The effects of theſe experiments are di-
geſted in the following table, where the degrees of expanſion
are marked in parts equal to the part of an inch.
Expanſion of
By one flame
I

Iron Steel Copper Brafs Tin Lead
80 85 89 110 153 155
By two flames placed
clofe together
117 123
115
220
274
By two flames 2
inches diftant
109 94
92 141 219 263
By three flames placed
clofe together
142 168
193 275
By four flames placed
211270 270 361
230310 310 377
clofe together
By five flames
It is to be obſerved of tin, that it will eafily melt, when
heated by two flames placed together. Lead commonly melts
with three flames, placed together, eſpecially if they burn long.
From theſe experiments, fo far as they are correct, it ap
pears, at firft view, that iron is the leaſt rarefied of any of theſe
metals, whether it be heated by one or more flames; and there-
fore is moft proper for making machines or inftruments which
we would have free from any alterations by heat or cold, as the
rods of pendulums, for clocks, &c. So likewife the meaſures of
yards or feet ſhould, if of metal, be made of iron, that their length
may be as nearly as poffible the fame, fummer and winter. The
X 2
308
MACHINES.
'
expanſion of lead and tin, by only one flame, is nearly the fame;
that is, almoſt double of the expanſion of iron. It is likewife
obfervable, that the flames placed together caufe a greater
rarefaction than when they have a fenfible interval between
them; iron, in the former cafe, being expanded 117 degrees,
and only 109 in the latter; the reafon of which difference is
obvious. By comparing the expanſions of the ſame metal, pro-
duced by one, two, three, or more flames, it appears, that two
flames do not caufe double the expanſion of one; nor three
flames three times that expanfion, but always lefs; and theſe
expanſions differ fo much the more from the ratio of the num-
ber of flames, as there are more flames acting at the fame time.
It is alſo obſervable, that metals are not expanded equally, at the
time of their melting, but fome more, fome lefs. Thus tin
began to run, when rarefied 219 degrees; whereas braſs was
expanded 377 degrees, and yet was far from melting.
By the help of this inftrument Mr. Ellicott found, upon a
medium, that the expanſions of bars of different metals, as
nearly of the ſame dimenfions as poffible, by the fame degree of
heat, were as follow;
Gold, Silver, Brafs, Copper, Iron, Steel,
89
60 56
103
95
Lead,
149
73
The great difference between the expanſions of iron and
brafs has been applied with good fuccefs to remedy the irre-
gularities in pendulums arifing from heat. Phil. Tranſ. vol.
xlvii. p. 485. See PENDULUM.
Mr. Graham uſed to meaſure the minute alterations, in
length, of metal bars, by advancing the point of a micrometer-
fcrew, till it fenfibly ſtopped against the end of the bar to be
meaſured. This fcrew, being fmall and very lightly hung, was
capable of agreement within the three or four-thouſandth part
of an inch. On this general principle Mr. Smeaton contrived
his pyrometer, in which the meaſures are determined by the
contact of a piece of metal with the point of a micrometer-
fcrew.
The following table fhews how much a foot in length of each
metal grows longer by an increaſe of heat, correfponding to
180° of Fahrenheit's thermometer, or to the difference between
freezing and boiling water, expreffed in fuch parts of which the
unit is equal to the 10,000 part of an inch.
1. White glaſs barometer tube,
2. Martial regulus of antimony,
3. Bliſtered steel,
4. Hard fteel,
1
1
100
130
138
147
Pyrometer.
309
5. Iron,
6. Biſmuth,
7. Coppered hammered
8. Copper eight parts, with tin one,
9. Caft brafs,
10. Brafs fixteen parts, with tin one,
11. Brafs wire,
12. Speculum metal,
1
151
167
204
218
1
225
229
232
232
13. Spelter folder, viz. braſs two parts, zinc one,
247
14. Fine pewter,
274
15. Grain tin,
298
16. Soft folder, viz. lead two, tin one,
301
323
18. Lead,
344
353
373
17. Zinc eight parts, with tin one, a little hammered,
19. Zinc or fpelter,
20. Zinc hammered half an inch per foot,
M. de Luc, in confequence of a hint fuggefted to him by
the late Mr. Ramfden, invented a pyrometer, the bafis of
which is a rectangular piece of deal board two feet and a half
long, 15 inches broad, and one inch and a half thick; and to
this all the other parts are fixed. This is mounted in the man-
ner of a table, with four deal legs, each a-foot long and an inch
and a half ſquare, well fitted near its four angles, and kept to-
gether at the other ends by four firm crofs pieces. This fmall
table is fufpended by a hook to a ftand; the board being in a
vertical fituation in the direction of its grain, and bearing its
legs forward in fuch a manner as that the croſs-pieces which join
them may form a frame, placed vertically facing the obſerver.
This frame fuftains a microſcope, which is firmly fixed in
another frame that moves in the former by means of grooves,
but with a very confiderable degree of tightneſs; the friction of
which may be increaſed by the preffure of four fcrews. The
inner ſliding frame, which is likewiſe of deal, keeps the tube of
the microſcope in a horizontal pofition, and in great part with-
out the frame, infomuch that the end which carries the lens is
but little within the ſpace between the frame and the board.
This microſcope is conſtructed in ſuch a manner as that the
object obſerved may be an inch diſtant from the lens; and it
has a wire which is fituated in the focus of the glaffes, in which
the objects appeared reverſed. At the top of the apparatus there
is a piece of deal, an inch and a half thick and two inches broad,
laid in a horizonal direction from the board to the top of the
frame. To this piece the rods of the different ſubſtances, whoſe
expanſion by heat is to be meaſured, are fufpended: one end of
it flides into a focket, which is cut in the thickneſs of the board;
and the other end, which reſts upon the frame, meets there with
310
MACHINES.
a ſcrew which makes the piece move backward and forward,
to bring the objects to the focus of the microſcope. There is
a cork very strongly driven through a hole bored vertically
through this piece; and in another vertical hole made through
the cork, the rods are fixed at the top; fo that they hang only,
and their dilatation is not counteracted by any preffure. In
order to heat the rods, a cylindrical bottle of thin glaſs, about
21 inches high, and four inches in diameter, is placed in the
infide of the machine, upon a ſtand independent of the rest of
the apparatus. In this bottle the rods are fufpended at a little
leſs than an inch diſtance from one of the infides, in order to
have them near the microſcope. Into it is poured water of
different degrees of heat, which muſt be ſtirred about, by moving
upwards and downwards, at one of the fides of the bottle, a
little piece of wood, faftened horizontally at the end of a ſtick:
in this water is hung a thermometer, the ball of which reaches
to the middle of the height of the rods. During theſe opera-
tions the water rifes to the cork, which thus determines the
length of the heated part; the bottle is covered, to prevent the
water from cooling too rapidly at the furface; and a thin caſe
of braſs prevents the vapour from fixing upon the piece of deal
to which the rods are fixed.
The late Mr. Ferguſon alfo invented two pyrometers, deſcrip-
tions and figures of which are given in his Lectures.
Mr. Wedgwood, the ingenious manufacturer of the fineſt
earthenware from baſaltic maffes, or terra cotta, has contrived a
curious pyrometer: he employs fmall cubes of dry clay; be-
cauſe that ſpecies of earth has the remarkable property of con-
tracting in its bulk, when ſubmitted to the fire, and not again
expanding on fuddenly expofing it to the cold air. In order to
afcertain the precife degree of heat in an oven, he puts one of
his clay-cubes into it; and, after having acquired the tempera-
ture of the place, he immediately plunges it into cold water,
Now, the fize of the cube (that was exactly adjuſted to half an
inch ſquare) is meaſured between two brafs rules, the fides of
which are ſomewhat obliquely difpofed, fo as to form an inclin-
ing groove, into which the cube may be flidden. In proportion
as the bulk of the latter has been contracted by heat, it paffes
down deeper between the ſcales, on which the various degrees
of temperature have been previously marked. Thus, when the
divifion of the ſcale commences from the point of red heat
viſible in day-light, and the whole range be divided into 240
equal parts, it will be found that Swediſh copper melts at 28;
gold at 32; iron at from 130 to 150 degrees: above this point,
the cubes could not be heated. But if one of theſe clay fquares
be put into an oven where other materials, fuch as bread,
Ramfden's Dividing Machine.
311
earthen-ware, &c. are to be baked, they may be uſefully em-
ployed, for regulating the neceffary degree of heat.
M. Fourmy has lately given, in the Journal des Mines, a
paper "On the Thermometers of baked Earths, termed Py-
rometers;" in which he fhews that the effect of fhrinking,
upon which Wedgwood's pyrometer is founded, does not re-
fult folely and invariably from the caufe to which it-is af-
cribed; that it is not neceffarily proportionate to it; that, what-
ever may be the graduation and the continuity of temperature
applied to an aluminous mixt, its fhrinking is not only not
neceffarily graduated, or neceffarily continuous, but it alfo does
not always neceffarily take place; and therefore that a pyrome-
ter founded upon fuch fhrinking does not afford fo conſtant and
accurate a meaſure for the highest degrees of heat, as the dila-
tation of mercury or of alcohol does for the lower. A tranf
lation of M. Fourmy's obfervations is inferted in the Repertory
of Arts, &c. No. 38. N. S.
RAMSDEN's MACHINE for dividing MATHEMATICAL IN-
STRUMENTS is an uſeful invention, by which theſe divifions can
be performed with exceedingly great accuracy, fuch as would
formerly have been deemed incredible. On difcovering the
method of conftructing this machine, its inventor, Mr. Jeffe
Ramſden, received 615/. from the commiffioners of longitude;
engaging himſelf to inftruct a certain number of perfons, not
exceeding ten, in the method of making and uſing this ma-
chine from the 28th October 1775, to 28th October 1777:
alſo binding himſelf to divide all octants and fextants by the
fame engine, at the rate of three fhillings for each octant,
and fix fhillings for each brafs fextant, with Nonius's divifions
to half-minutes, for as long time as the commiffioners fhould
think proper to let the engine remain in his poffeffion. Of
this fum of 6151. paid to Mr. Ramſden, 300% were given him
as a reward for the improvement made by him in diſcover-
ing the engine, and the remaining 3157. for his giving up the
property of it to the commiffioners. The following deſcription
of the engine is that given upon oath by Mr. Ramfden him-
felf.
"This engine confifts of a large wheel of bell-metal, fup-
ported on a mahogany ftand, having three legs, which are
ftrongly connected together by braces, fo as to make it perfectly
fteady. On each leg of the ſtand is placed a conical friction-
pulley, whereon the dividing wheel refts: to prevent the wheel
from fliding off the friction-pulleys, the bell-metal centre under
it turns in a focket on the top of the ſtand.
"The circumference of the wheel is ratched or cut (by a
method which will be defcribed hereafter) into 2160 teeth, in
?
312
MACHINES.
which an endleſs ſcrew acts. Six revolutions of the ſcrew will
move the wheel a ſpace equal to one degree.
"Now a circle of braſs being fixed on the fcrew arbor, having
its circumference divided into 60 parts, each divifion will confe-
quently anſwer to a motion of the wheel of 10 ſeconds, fix of
them will be equal to a minute, &c.
"Several different arbors of tempered ſteel are truly ground
into the ſocket in the centre of the wheel. The upper parts of
the arbors that ſtand upon the plane are turned of various fizes,
to fuit the centres of different pieces of work to be divided.
"When any inftrument is to be divided, the centre of it is
very exactly fitted on one of theſe arbors; and the inftrument is
fixed down to the plane of the dividing wheel, by means of
fcrews, which fit into holes made in the radii of the wheel for
that purpoſe.
"The inftrument being thus fitted on the plane of the
wheel, the frame which carries the dividing point is connected
at one end by finger fcrews with the frame which carries the
endleſs ſcrew; while the other end embraces that part of the
fteel arbor which ſtands above the inftrument to be divided,
by an angular notch in a piece of hardened ſteel: by this means
both ends of the frame are kept perfectly ſteady, and free from
any ſhake.
"The frame carrying the dividing-point or tracer is made
to flide on the frame which carries the endleſs ſcrew to any
diſtance from the centre of the wheel as the radius of the inftru-
ment to be divided may require, and may be there faſtened by
tightening two clumps; and the dividing-point or tracer being
connected with the clumps by the double-jointed frame, admits
a free and eaſy motion towards or from the centre for cutting the
divifions, without any lateral fhake,
"From what has been faid, it appears that an inftrument
thus fitted on the dividing-wheel may be moved to any angle by
the fcrew and divided circle on its arbor, and that this angle may
be marked on the limb of the inftrument with the greateft exact-
nefs by the dividing-point or tracer, which can only move in a
direct line tending to the centre, and is altogether freed from thoſe
inconveniences that attend cutting by means of a ftraight edge.
This method of drawing lines will alfo prevent any error that
might ariſe from an expanſion or contraction of the metal dur-
ing the time of dividing.
"The fcrew frame is fixed on the top of a conical pillar,
which turns freely round its axis, and alfo moves freely to-
wards or from the centre of the wheel, ſo that the ſcrew-frame
may be entirely guided by the frame which connects it with the
centre; by this means any eccentricity of the wheel and the
w
Ramfden's Dividing Machine.
313
arbor would not produce any error in the dividing; and by a
particular contrivance (which will be deſcribed hereafter), the
fcrew when preffed againſt the teeth of the wheel always moves
parallel to itfelf; fo that a line joining the centre of the arbor
and the tracer continued will always make equal angles with the
fcrew.
"Fig. 1. in Pl. XXVI. repreſents a perſpective view of the
engine.
"Fig. 2. in Pl. XXVII. is a plan of which fig. 3. repre-
fents a fection on the line II A,
"The large wheel A is 45 inches in diameter, and has ten
radii, each being ſupported by edge-bars, as reprefented in fig. 3.
Theſe bars and radii are connected by the circular ring B, 24
inches in diameter and 3 deep; and, for greater ftrength, the
whole is caft in one piece in bell-metal.
"As the whole weight of the wheel A refts on its ring B,
the edge bars are deepeſt where they join it; and from thence
their depth diminiſhes, both towards the centre and circum-
ference, as reprefented in fig. 3.
worked very even and
The ring C, of fine
circumference of the
"The furface of the wheel A was
flat, and its circumference turned true.
brafs, was fitted very exactly on the
wheel; and was faftened thereon with fcrews, which, after
being ſcrewed as tight as poffible, were well rivetted. The
face of a large chuck being turned very true and flat in the lathe,
the flattened furface A (fig. 3.) of the wheel was faſtened againſt
it with hold-fafts; and the two furfaces and circumference of
the ring C, a hole through the centre and the plane part round
[b] it, and the lower edge of the ring B, were turned at the ſame
time.
"D is a piece of hard bell-metal, having the hole, which
receives the ſteel arbor [d], made very ftraight and true. This
bell-metal was turned very true on an arbor; and the face,
which refts on a wheel at [b], was turned very flat, ſo that
the ſteel arbor [d] might ſtand perpendicular to the plane of the
wheel: this bell-metal was faſtened to the wheel by fix fteel
fcrews [1].
"Abraſs focket Z is faftened on the centre of the mahogany
ſtand, and receives the lower part of the bell-metal piece D,
being made to touch the bell-metal in a narrow part near the
mouth, to prevent any obliquity of the wheel from bending the
arbor: good fitting is by no means neceffary here; fince any
ſhake in this focket will produce no bad effect, as will appear
hereafter when we defcribe the cutting-frame.
"The wheel was then put on its ftand, the lower edge of the
ring B (fig 1, 2, and 3.) reſting on the circumference of three
314
MACHINES.
1
conical friction-pulleys W, to facilitate its motion round its
centre. The axis of one of theſe pulleys is in a line joining
the centre of the wheel and the middle of the endleſs ſcrew,
and the other two placed ſo as to be at equal diſtances from each
other.
"(Fig. 1.) is a block of wood ftrongly faſtened to one of
the legs of the ftand; the piece [g] is fcrewed to the upper fide
of the block, and has half-holes, in which the tranfverfe axis
[h] (fig. 4.) turns: the half-holes are kept together by the
fcrews [i].
"The lower extremity of the conical pillar P (fig. 1. & 4.)
terminates in a cylindrical ſteel pin [k], (fig. 4.) which paffes
through and turns in the tranſverſe axis [b], and is confined by
a cheek and fcrew.
"To the upper end of the conical pillar is faſtened the frame
G, (fig. 4.) in which the endleſs ſcrew turns: the pivots of the
ſcrew are formed in the manner of two fruftums of cones joined
by a cylinder, as reprefented at X (fig. 5). Thefe pivots are
confined between half-poles, which prefs only on the conical
parts, and do not touch the cylindric parts: the half-holes are
kept together by fcrews [a] which may be tightened at any time,
to prevent the fcrew from fhaking in the frame.
"On the fcrew-arbor is a ſmall wheel of brafs K (fig. 1, 2,
4, 5.), having its outſide edge divided into 60 parts, and num-
bered at every 6th divifion with 1, 2, &c. to 10. The motion
of this wheel is ſhown by the index [y] (fig. 4 & 5.) on the
fcrew-frame G.
"H (fig. 1.) repreſents a part of the ftand, having a parallel
flit in the direction towards the centre of the wheel, large
enough to receive the upper part of the conical braſs pillar P,
which carries the fcrew and its frame and as the refiftance,
when the wheel is moved by the endleſs-fcrew, is againſt the
fide of the flit H which is towards the left hand, that fide of the
flit is faced with brafs, and the pillar is preffed againft it by a
fteel ſpring on the oppofite fide: by this means the pillar is
ſtrongly ſupported laterally, and yet the fcrew may be eafily
preffed from or againſt the circumference of the wheel, and the
pillar will turn freely on its axis to take any direction given it
by the frame L.
"At each corner of the piece I (fig. 4.) are ſcrews [n] of
tempered ſteel, having poliſhed conical points: two of them
turn in conical holes in the ſcrew-frame near [o], and the points
of the other two fcrews turn in the holes in the piece Q; the
fcrews [p] are of fteel, which being tightened, prevent the
conical pointed fcrews from unturning when the frame is
moved.
Ramfden's Dividing Machine.
315
"L (fig. 1, 2, 6.) is a braſs frame, which ſerves to connect
the endleſs-ſcrew, its frame, &c. with the centre of the wheel:
each arm of this frame is terminated by a ſteel ſcrew, that may
be paſſed through any of the holes [q] in the piece Q_(fig. 4.),
as the thickneſs of work to be divided on the wheel may require,
and are faſtened by the finger-nuts [r] (fig. 1. & 2.)
"At the other end of this frame is a flat piece of tempered
fteel [b] (fig. 6.), wherein is an angular notch: when the endleſs-
fcrew is preffed againſt the teeth of the circumference of the
wheel, which may be done by turning the finger-ſcrew S
(fig. 1 & 2.) to preſs againſt the ſpring [t], this notch embraces
and preſſes againſt the ſteel arbor [d]. This end of the frame
may be raiſed or depreffed by moving the prifmatic flide [u]
(fig. 2.), which may be fixed at any height by the four ſteel-
fcrews [v] (fig. 1, 2, 6.).
"The bottom of this flide has a notch [k] (fig. 1. & 6.),
whoſe plane is parallel to the endleſs-fcrew; and by the point
of the arbor [d] (fig. 3.) refting in this notch, this end of the
frame is prevented from tilting. The fcrew S (fig. 1, 2.) is pre-
vented from unturning, by tightening the finger-nut [w].
"The teeth on the circumference of the wheel were cut by
the following method:
"Having confidered what number of teeth on the circum-
ference would be moft convenient, which in this engine is 2160,
or 360 multiplied by 6, I made two fcrews of the fame dimen-
fions, of tempered ſteel, in the manner hereafter deſcribed, the
interval between the threads being fuch as I knew by calculation
would come within the limits of what might be turned off the
circumference of the wheel; one of theſe ſcrews, which was in-
tended for ratching or cutting the teeth, was notched acroſs the
threads, ſo that the ſcrew, when preffed againſt the edge of the
wheel and turned round, cut in the manner of a faw. Then
having a ſegment of a circle a little greater than 60 degrees,
of about the fame radius with the wheel, and the circumfer-
ence made true, from a very fine centre, I deſcribed an arch
near the edge, and fet off the cord of 60 degrees on this arch.
This fegment was put in the place of the wheel, the edge of it
was ratched, and the number of revolutions and parts of the
ſcrew contained between the interval of the 60 degrees were
counted. The radius was corrected in the proportion of 360
revolutions, which ought to have been in 60 degrees, to the
number actually found; and the radius, fo corrected, was
taken in a pair of beam-compaffes: while the wheel was on
the lath, one foot of the compaffes was put in the centre, and
with the other a circle was deſcribed on the ring; then half the
depth of the threads of the fcrew being taken in dividers, was ſet
7
316
MACHINES.
from this circle outwards, and another circle was deſcribed
cutting this point; a hollow was then turned on the edge of the
wheel of the fame curvature as that of the ſcrew at the bottom
of the threads: the bottom of this hollow was turned to the
fame radius or diſtance from the centre of the wheel, as the
outward of the two circles before mentioned.
“The wheel was now taken off the lathe; and the bell-metal
piece D (fig. 3.) was fcrewed on as before directed, which after
this ought not to be removed.
ΤΟ
"From a very exact centre a circle was deſcribed on the
ring C (fig. 1, 2, 3.), about of an inch within where the
bottom of the teeth would come. This circle was divided with
the greateſt exactneſs I was capable of, firſt into five parts, and
each of theſe into three. Theſe parts were then bifected four
times (that is to fay), fuppofing the whole circumference of
the wheel to contain 2160 teeth, this being divided into five
parts, each would contain 432 teeth; which being divided into
three parts, each of them would contain 144; and this ſpace
bifected four times would give 72, 36, 18, and 9: therefore
each of the laft divifions would contain nine teeth. But, as I
was apprehenſive fome error might arife from quinquefection
and trifection, in order to examine the accuracy of the diviſions,
I deſcribed another circle on the ring C (fig. 7.) inch within
the former, and divided it by continual bifections, as 2160, 1080,
540, 270, 135, 67, and 33; and as the fixed wire (to be de-
fcribed preſently) croffed both the circles, I could examine
their agreement at every 135 revolutions; (after ratching, could
examine it at every 334): but, not finding any fenfible difference
between the two fets of divifions, I, for ratching, made choice
of the former; and, as the coincidence of the fixed wire with
an interſection could be more exactly determined than with a
dot or divifion, I therefore made ufe of interfections in both
circles before defcribed.
I
ΤΟ
"The arms of the frame L (fig. 7.) were connected by a
thin piece of braſs of 2 of an inch broad, having a hole in the
middle of of an inch in diameter; acroſs this hole a filver
wire was fixed exactly in a line to the centre of the wheel: the
coincidence of this wire with the interfections was examined
by a lens inch focus, fixed in a tube which was attached to
one of the arms L*. Now a handle or winch being fixed on
the end of the fcrew, the divifion marked 10 on the circle K
was ſet to its index, and, by means of a clamp and adjuſting-
ſcrew for that purpoſe, the interſection marked 1 on the circle
The interfections are marked for the fake of illuſtration, though
properly invifible, they lying under the brafs plate.
Ramfden's Dividing Machine.
317
:
C was fet exactly to coincide with the fixed wire; the fcrew
was then carefully preffed againſt the circumference of the
wheel, by turning the finger-fcrew S; then, removing the
clamp, I turned the fcrew by its handle 9 revolutions, till the
interfection marked 240 came nearly to the wire; then, un-
turning the finger-fcrew S, I releafed the fcrew from the wheel,
and turned the wheel back till the interfection marked 2 exactly
coincided with the wire; and, by means of the clamp before
mentioned, the divifion 10 on the circle being fet to its index,
the ſcrew was preffed againſt the edge of the wheel by the
finger-fcrew S; the clamps were removed, and the ſcrew turned
nine revolutions till the interfection marked I nearly coincided
with the fixed wire; the ſcrew was releaſed from the wheel by
unturning the finger-fcrew S as before; the wheel was turned
back till the interfection 3 coincided with the fixed wire; the
divifion 10 on the circle being fet to its index, the fcrew was
preffed againſt the wheel as before, and the ſcrew was turned
9 revolutions, till the interfection 2 nearly coincided with the
fixed wire, and the ſcrew was releaſed; and I proceeded in this
manner till the teeth were marked round the whole circum-
ference of the wheel. This was repeated three times round, to
make the impreffion of the fcrew deeper. I then ratched the
wheel round continually in the fame direction without ever
difengaging the ſcrew; and, in ratching the wheel about 300
times round, the teeth were finiſhed.
I
"Now it is evident, if the circumference of the wheel was
even one tooth or ten minutes greater than the ſcrew would
require, this error would in the first inftance be reduced to
240 part of a revolution, or two feconds and a half; and theſe
errors or inequalities of the teeth were equally diſtributed round
the wheel at the diſtance of nine teeth from each other. Now,
as the ſcrew in ratching had còntinually hold of ſeveral teeth
at the fame time, and theſe conftantly changing, the above-
mentioned inequalities foon corrected themſelves, and the teeth
were reduced to a perfect equality. The piece of braſs which
carries the wire was now taken away, and the cutting-ſcrew was
alſo removed, and a plain one (hereafter defcribed) put in its
place: on one end of the ſcrew is a ſmall braſs circle, having its
edge divided into 60 equal parts, and numbered at every fixth
divifion, as before mentioned. On the other end of the ſcrew
is a ratchet-wheel C, having 60 teeth, covered by the hollowed
circle [d] (fig. 5.), which carries two clicks that catch upon thẻ
oppofite fides of the ratchet when the fcrew is to be moved
forwards. The cylinder S turns on a ftrong fteel arbor F,
which paffes through and is firmly fcrewed to the piece Y: this
piece, for greater firmnefs, is attached to the fcrew-frame G
318
MACHINES.
(fig. 4.) by the braces [v]: a ſpiral groove or thread is cut onì
the outſide of the cylinder S, which ferves both for holding the
ſtring, and alſo giving motion to the lever J on its centre by
means of a ſteel tooth [n], that works between the threads of
the fpiral. To the lever is attached a ſtrong ſteel pin [m], on
which a braſs ſocket [r] turns: this focket paffes through a flit
in the piece [p], and may be tightened in any part of the flit by
the finger-nut [f]: this piece ferves to regulate the number of
revolutions of the ſcrew for each tread of the treadle R.
"T (fig. 1.) is a brafs box containing a ſpiral ſpring; a
ftrong gut is faftened and turned three or four times round the
circumference of this box; the gut then paffes feveral times
round the cylinder S, and from thence down to the treadle R
(fig. 1.). Now, when the treadle is preffed down, the ſtring
pulls the cylinder S round its axis, and the clicks catching hold
of the teeth on the ratchet carry the ſcrew round with it, till,
by the tooth [n] working in the fpiral groove, the lever J
(fig. 4.) is brought near the wheel [d], and the cylinder
ftopped by the ſcrew-head [x] ftriking on the top of the lever
J; at the fame time the fpring is wound up by the other end of
the gut paffing round the box T (fig. 1.). Now, when the foot
is taken off the treadle, the fpring unbending itſelf pulls back
the cylinder, the clicks leaving the ratchet and ſcrew at reft till
the piece [t] ſtrikes on the end of the piece [p] (fig. 1.): the
number of revolutions of the ſcrew at each tread is limited by
the number of revolutions the cylinder is allowed to turn back.
before the ſtop ſtrikes on the piece [p].
"When the endleſs-ſcrew was moved round its axis with a
confiderable velocity, it would continue that motion a little after
the cylinder S (fig. 1. and 4.) was ftopped: to prevent this, the
angular lever was made; that when the lever J comes near to
ftop the fcrew [x], it, by a fmall chamfer, preffes down the
piece x of the angular lever; this brings the other end of the
fame lever forwards, and ftops the endleſs-ſcrew by the fteel
pin u ftriking upon the top of it: the foot of the lever is raifed
again by a ſmall ſpring preffing on the brace [v].
ทุ
"D, two clamps, connected by the piece a, flide one on each
arm of the frame L (fig. 1, 2, 6.), and may be fixed at pleaſure
by the four finger-ſcrews, which preſs againſt ſteel ſprings to
avoid ſpoiling the arms: the piece [q] is made to turn without
fhake between two conical pointed fcrews [f], which are pre-
vented from unturning by tightening the finger-nuts N.
"The piece M (fig. 6.) is made to turn on the piece [q],
by the conical pointed ſcrews [f] refting in the hollow centres
[e].
"As there is frequent occafion to cut divifions on inclined
Ramfden's Dividing Machine.
319
planes, for that purpoſe the piece y, in which the tracer is fixed,
has a conical axis at each end, which turn in half holes: when
the tracer is ſet to any inclination, it may be fixed there by
tightening the ſteel ſcrews ß.
"Deſcription of the Engine by which the Endleſs-ſcrew of the Divid-
ing-engine was cut.
"Fig. 9. reprefents this engine of its full dimenfions ſeen
from one fide.
<<
Fig. 8. the upper fide of the fame as feen from above.
"A repreſents a triangular bar of steel, to which the tri-
angular holes in the pieces B and C are accurately fitted, and
may be fixed on any part of the bar by the ſcrews D.
"E is a piece of ſteel whereon the fcrew is intended to be
cut; which, after being hardened and tempered, has its pivots
turned in the form of two fruftums of cones, as reprefented in
the drawings of the dividing-engine (fig. 5.). Theſe pivots were
exacly fitted to the half-holes F and T, which were kept
together by the fcrews Z.
"H repreſents a ſcrew of untempered fteel, having a pivot I,
which turns in the hole K. At the other end of the fcrew is a
hollow centre, which receives the hardened conical point of the
fteel pin M. When this point is fufficiently preffed againſt the
fcrew, to prevent its fhaking, the fteel pin may be fixed by
tightening the ſcrews Y.
"N is a cylindric nut, moveable on the ſcrew H; which,
to prevent any ſhake, may be tightened by the fcrews O. This
nut is connected with the faddle-piece P by means of the inter-
mediate univerſal joint W, through which the arbor of the
ſcrew H paffes. A front view of this piece, with a fection
acroſs the ſcrew-arbor, is reprefented at X. This joint is con-
nected with the nut by means of two fteel flips S, which turn
on pins between the cheeks T on the nut N. The other ends
of theſe flips S turn in like manner on pins (a). One axis of
this joint turns in a hole in the cock (b), which is fixed to the
faddle-piece; and the other turns in a hole (d), made for that
purpoſe in the fame piece on which the cock (b) is fixed. By
this means, when the fcrew is turned round, the faddle-piece
will flide uniformly along the triangular bar A.
·
"K is a ſmall triangular bar of well-tempered fteel, which
ſlides in a groove of the fame form on the faddle-piece P. The
point of this bar or cutter is formed to the ſhape of the thread
intended to be cut on the endlefs-fcrew. When the cutter is
ſet to take proper hold of the intended fcrew, it may be fixed
!
320
MACHINES.
f
by tightening the fcrews (e), which prefs the two pieces of
brafs G upon it.
"Having meaſured the circumference of the dividing-wheel,
I found it would require a ſcrew about one thread in a hundred
coarfer than the guide-fcrew H. The wheels on the guide-
fcrew arbor H, and that on the fteel E, on which the fcrew was
to be cut, were proportioned to each other to produce that
effect, by giving the wheel L 198 teeth, and the wheel Q_200.
Theſe wheels communicated with each other by means of the
intermediate wheel R, which alſo ſerved to give the threads on
the two ſcrews the fame direction.
"The faddle-piece P is confined on the bar A by means of
the pieces (g), and may be made to flide with a proper degree
of tightneſs by the ſcrews (n).”
REVERSING OF MOTIONS, contrivances for. We do not
here mean to ſpeak of alternating or reciprocating motions after
intervals of ſhort continuance; thofe being already treated of
in the introductory part of this volume, alfo under the title.
PARALLEL motions, befides that they occur incidentally in the
ſeparate deſcriptions of ſeveral machines. We fhall now
mention fome methods of reverfing motions after much longer
intervals; as in the cafe of drawing up buckets from wells or
mines, where no change of direction may be required for ſeveral
minutes; or in different kinds of mill-work, where the direction
may not be changed for fome hours.
Contrivances to effect fuch reverfion of motion are very
numerous; but almoſt all of them may be reduced to two
general methods: for the required change is generally produced
either by making two equal pinions on one and the fame axis
take alternately into the teeth of thoſe parts of a larger wheel
which are nearly diametrically oppofite; or, by means of an
additional wheel which may, as the practical mechanics term
it, be thrown in and out of gear alternately.
In many engines for drawing buckets out of mines that are
moved by horſes, the motion is frequently reverſed by turning
round the animal, and caufing him to retrace his fteps and
draw the contrary way: but this is found very injurious to the
horfe, a circumftance which has frequently led to the adoption.
of other methods. In Emerfon's Mechanics a fimple con-
trivance is deſcribed, confifting merely of a horizontal face-
wheel upon the fame vertical ſhaft as the horſepole is attached
to, and two equal pinions upon the fame axle as carries the
drum or barrel on which the rope winds. The axle which
carries the drum and pinions is fixed horizontally a little above
a diameter of the face-wheel; and firft one and then the other
Reverfing of Motions.
321
of the pinions is made to be driven by that wheel; thus, mani-
feftly, reverfing the motion as required. There are two
methods of attaching theſe pinions to the axle, and making
them to be acted upon by the face-wheel: in one of them, the
pinions are faſtened upon the axle at a diſtance from each other
exceeding the diameter of the face-wheel only 3 or 4 inches;
then, the axle being moved horizontally through this ſmall
diſtance brings firft one and then the other pinion into contact
with the wheel at oppofite extremities of a diameter, and thus
changes the direction of the motion; but this method is at-
tended with the diſadvantage of having often to move a heavy
weight with the horizontal axle, befides that there is much
danger of breaking the teeth of the pinions and wheel when
they first come to embrace each other. In the ſecond method,
the lanterns or pinions both turn conftantly with the face-
wheel, but they play freely upon their common axle, except
they are ſtopped by a pin which fixes them; the application of
fuch pin to firft the one and then the other of the lanterns pro-
duces the alternating motion, as propofed.
M. Prony has two contrivances for reverfing the motion in
horſe-whims, without changing that of the animal: in both of
which, however, the general principle is the fame as that
adopted by Mr. Emerfon. In the firſt a horizontal wheel,
toothed at its face, lay juſt above two vertical pinions, fixed on
the oppofite extremities of an axis of the length of its diameter.
This wheel was fo contrived as to incline a little from its hori.
zontal pofition to either fide at pleaſure; fo that on the one
inclination its teeth locked with thoſe of one pinion, and
receded from the other; and on the other pofition, its operation
on the pinions was reverfed: by which the axis of the pinions
turned round first in one direction, and afterwards in the
contrary.
M. Prony, finding this method fubject to fome inconveni-
ences, contrived the following, which he eſteems much fuperior
to it.
An horizontal wheel, toothed at its face, and attached
to a perpendicular arbor (which gives it motion), turns two
pinions, moveable on the fame axis, which it meets at the
oppofite fides of its circumference: thefe pinions are not
attached to the axis, but turn round freely upon it: the inter-
mediate part of the axis is fquare, and has, adjoining to each
pinion, boxes which flide back and forwards on it, each of
which fupport a faced wheel, with ftrong ferrated teeth; the
ferration being in a different direction on the oppoſite wheels:
the boxes are connected by two iron bars, fo as to change their
places by one movement; to the pinions there are alſo ferrated
faced wheels attached, fo as to lock on thoſe oppoſite to them
VOL. II.
Y
322
MACHINES.
on the fliding boxes. From this conftruction it follows, that
when the boxes are flidden to one extremity of the axis, the
pinion at that fide will be connected with the axle, and com-
municate its motion to it in one direction; and when the boxes
are moved to the other extremity, then the first pinion will be
difengaged, and the fecond be locked to the axle, and cauſe it
to turn round in a direction the reverſe of that in which it
moved before. There is a lever on another axle, whofe office
is to move the before-mentioned boxes backwards and forwards:
an arm projects from the axis, which moves between two pieces,
proceeding from the frame connected with the boxes: the lever
rifes upwards, and has a weight at its top, by which it preffes
Itrongly in either direction, when it paffes the perpendicular
polition; forming thus the contrivance vulgarly called a tumbling-
bob, which is uſed in various engines for a fimilar purpoſe.
Upon the fame axle on which the pinions move is faſtened a
drum-wheel, round which paffes the chain or cord to which the
buckets are attached; another chain or cord is placed below the
buckets, from the bottom of one to that of the other, to form an
equilibrium between the whole of the appendage of one bucket
and that of the other in all poſitions. A bar is fo placed, that,
on one of the buckets rifing to a certain height, it catches the
bar, forces it upwards, and thereby throws over the tumbling-
bob connected with its other extremity: this reverſes the
movement of the buckets; and, on the other bucket rifing, it
operates in the fame way on another lever, which throws the
bob to the other fide, and caufes the first bucket to rife again.
M. Prony has annexed a contrivance to this engine by which
the horfe that puts it in motion is difengaged when any
accident happens, which would tend to ftop the movement of
the wheels: for this purpoſe the traces pafs under two pulleys in
the ends of the yoke; and their extremities, which have loops
wrought in them, are thereby attached to two pins in a roller,
round which a cord is wound two or three turns, and paffes
from thence through rings in the lever, which caufes the arbor
to revolve, and over a pulley on the arbor to a weight which
hangs befide it. When the draught exceeds this weight, it is
evident the roller will be drawn round by the traces, and that
they will flip off the pins, and be difengaged during the firſt
revolution.
The method of reverfing motion by caufing pinions to be
operated upon by the oppofite parts of a face-wheel, has been
long known and practifed by mill-wrights; and they have
various contrivances for performing the alternation, as by levers,
fcrews, tumbling-bobs, &c. One of theſe will be illuſtrated
by a figure, when we come to the article TIDE-mill.
Rotatory Apparatus.
325
As to the fecond general method, it has perhaps an ap-
pearance of greater fimplicity; though, when reduced to practice,
it is commonly found more expenfive than the former. Suppoſe
that while the horizontal wheel A (fig. 2. pl. XXVIII.) con
tinues to turn always one way, it is required to have the hoti
zontal wheel B turn, fometimes in one direction, and fometimes
in another by means of an additional wheel C, equal in
diameter and number of teeth (fuppofing the velocities in both
directions to be equal), this may be accompliſhed, thus: Let the
two wheels B and C have the lower pivots of their axles refting
in boxes or cafes that may be moved up and down by means of
fcrews; and, while the wheels A and B are nearly of equal
thickneſs, let the wheel C be fomewhat more than double the
thickness of either : when the motion of the wheel B is to be in a
contrary direction to that of A, let the wheel C be lowered fo
much that its teeth play neither into thofe of A nor B, while the
teeth of A take into thofe of B and drive it round: when, on the
contrary, B is to be moved in the fame direction as A, let the
wheel B be lowered till its teeth do not come into contact with
thoſe of A, and let C be raiſed until the upper parts of its teeth
take between thofe of the wheel A, while the lower parts of
other teeth play into the teeth B; fo fhall the rotation of Bhave
the direction required. If the motion of the wheel A were
ſometimes in one direction and ſometimes in another, the
motion of B might all along be preferved in one direction, by
the occafional application of C as an intermediate wheel.
REGULATOR of defcending motions. See Hardie's CRANE
ROTATORY MOTION, when produced by a reciprocating
motion, requires fome contrivance to render it uniform, or
nearly fo. The ufual method of equalizing is by attaching a
fly-wheel to fome part of the machinery: but Mr. Arthur
Woolf has invented an apparatus to be fubftituted for the fly
in fteam-engines, which poffeffes the advantage of equalizing
the motion, with the property of being flopped and fet to work
at any part of the ftroke.
Plate XXIII. fig. 4. A reprefents part of the engine-beam;
B the connecting-rod; C the crank-arm; D a cog-wheel,
working into another cog-wheel E, of half the fize; Fa crank-
arm on the fhaft of the ſmall wheel; G a cylinder cloſed at
bottom, in which a folid or unperforated pifton moves, leaving
a vacuum beneath. This acts fimply inſtead of a weight on
the crank F, by the conftant preffure of the atmoſphere; and
the diameter of the pifton must be fuch as nearly to equal one-
third of the power of the engine.
In fig. 5. the outer circle is the line defcribed by the crank;
the circumference of the inner circle is equal to twice the

X 2
$24
MACHINES.
;
1
diameter of the outer, and the fquare has the fame circum-
ference: this laft exhibits the inequality ftill remaining, which
by this method is reduced to about one fifth; but by the
affiftance of a ſmall fly on the fecond motion, the effect will
become nearly the fame as that of a rotative engine, with the
advantages here mentioned.
The fame motion may be applied to a pump, but in this caſe
the two cranks muſt be horizontal at the fame time. Nich.
Jour. No. 23. N. S.
SAWMILLS, conftructed for the purpoſe of fawing either
timber or ſtone, are moved by animals, by water, by wind, or
by fteam. They may be diftinguiſhed into two kinds: thoſe in
which the motion of the faws is reciprocating, and thoſe in
which the faws have a rotatory motion. In either cafe the
reſearches of theorists have not yet turned to any account:
inſtead, therefore, of giving any uncertain theory here, we fhall
proceed to the defcriptive part, and refer thoſe who wiſh to fee
fome curious inveſtigations on this fubject to a Memoir on the
Action of Saws, by Euler, in Mem. Acad. Roy. Berlin, 1756.
Reciprocating fawmills for cutting timber and moved by
water, do not exhibit much variety in their conftruction. The
fawmill repreſented in pl. XXVIII. is taken from Gray's
Experienced Millwright; but it only differs in a few triding
particulars from fome which are defcribed in Belidor's Archi-
tecture Hydraulique, and in Gallon's Collection of Machines
approved by the French academy.
1. The plate juft referred to fhews the elevation of the mill.
A A the fhaft or axle, upon which is fixed the wheel BB (of
17 or 18 feet diameter), containing 40 buckets to receive the
water which impels it round. CC a wheel fixed upon the fame
Thaft containing 96 teeth, to drive the pinion No. 2. having
22 teeth, which is faftened upon an iron axle or ſpindle, having
a coupling box on each end that turns the cranks, as DD,
round: one end of the pole E is put on the crank, and its other
end moves on a joint or iron bolt at F, in the lower end of the
frame GG. The crank DD being turned round in the pole E,
moves the frames GG up and down, and theſe having faws in
them, by this motion cut the wood. The pinion, No. 2. may
work 2, 3, or more cranks, and thus move as many frames of
faws. No. 3, an iron wheel having angular teeth, which one
end of the iron K takes hold of, while its other end rolls on a
bolt in the lever HH. One end of this lever moves on a bolt
at I, the other end may lie in a notch in the frame GG ſo as to
be puthed up and down by it. Thus the catch K pulls the
wheel round, while the catch L falls into the teeth and prevents
`it from going backwards. (See Univerſal LEVER.) Upon the
*
Sawmills.
.32,5
axle of No. 3. is alfo fixed the pinion No. 4. taking into the
teeth in the under edge of the iron bar, that is faftened upon
the frame TT, on which the wood to be cut is laid by this
mean the frame TT is moved on its rollers SS, along the fixed
frame UU; and of courſe the wood faſtened upon it is brought
forward to the faws as they are moved up and down by reafon
of the turning round of the crank DD. VV, the machine and
handle to raiſe the fluice when the water is to be let upon the
wheel B B to give it motion. By pulling the rope at the longer
arm of the lever M, the pinion No. 2. is put into the hold or
grip of the wheel CC, which drives it; and by pulling the
rope R, this pinion is cleared from the wheel. No. 5. a pinion
containing 24 teeth, driven by the wheel CC, and having upon
its axle a ſheave, on which is the rope PP, paffing to the heave
No. 6. to turn it round; and upon its axle is fixed the pinion
No. 7. acting on the teeth in an iron bar upon the frame TT,
to roll that frame backwards when empty. By pulling the rope
at the longer arm of the lever N, the pinion No. 5. is put into
the hold of the wheel CC; and by pulling the rope O it is
taken off the hold. No. 8. a wheel fixed upon the axle No.
having upon its periphery angular teeth, into which the catch
No. 10. takes; and being moved by the lever attached to the
upper part of the frame G, it puſhes the wheel No. 8. round
and the catch No. 11. falls into the teeth of the wheel, to pre-
vent it from going backwards while the rope rolls in. its axle,
and drags the logs or pieces of wood in at the door Y, to be laid
upon the moveable frames TT, and carried forward to the faws
to be cut. The catches No. 10. II. are eafily thrown out of
play when they are not wanted. The gudgeons in the fhafts,
rounds of the cranks, fpindles, and pivots, fhould all turn round
in cods or buſhes of brafs. Z, a door in one end of the mill-
houſe at which the wood is conveyed out when cut.
WW
walls of the mill-houfe. QQ, the couples or framing of the roof.
XXX, &c. windows to admit light to the houſe.
A plan of this mill is given in pl. 43. of Mr. Gray's book.
2. Sawmills for cutting blocks of ſtone are generally, though
not always, moved horizontally: the horizontal alternate motion
may be communicated to one or more faws, by means of a.
rotatory motion, either by the ufe of cranks, &c. or in fome fuch
way as the following. Let the horizontal wheel ABDC
(fig. 3. pl. XX.) drive the pinion OpN, this latter carrying a
vertical pin P, at the diſtance of about of the diameter from
the centre.
This pinion and pin are reprefented feparately in
No. 2. of fig. 3. Let the frame WSTV, carrying four faws,
marked 1, 2, 3, 4, have wheels V,T,W,W, each running in a
groove or rut, whofe direction is parallel to the propofed

*
326
1
MACHINES.
2.
direction of the faws: and let a tranfverfe gropve PR, whofe
length is double the distance of the pin P from the centre of the
pinion, be cut in the faw frame to receive that pin. Then, as
the great wheel revolves, it drives the pinion, and carries round
the pin P: and this pin, being compelled to flide in the ſtraight
groove PR, while by the rotation of the pinion on which it is
fixed its diſtance from the great wheel is conſtantly varying, it
cauſes the whole faw frame to approach to and recede from the
great wheel alternately, while the grooves in which the wheels
run confine the frame ſo as to move in the direction Tt, Vv.
Other blocks of ſtone may be fawn at the fame time by the
motion of the great wheel, if other pinions and frames running
off in the directions of the refpective radii EB, EA, EC, be
worked by the teeth at the quadrantal points B, A, and C.
And the contrary efforts of theſe four frames and pinions will
tend to foften down the jolts, and equalize the whole motion.
The fame contrivance, of a pin fixed at a fuitable diſtance
from the centre of a wheel, and fliding in a groove, may ſerve
to convert a reciprocating into a rotatory motion: but it will
not be preferable to the common converfion by means of a crank.
3. When faws are uſed to cut blocks of ftone into pieces
having cylindrical furfaces, a ſmall addition is made to the
apparatus. See figs. 8, 9. pl. XX. The faw, instead of being
allowed to fall in a vertical groove as it cuts the block, is
attached to a lever or beam FG, fufficiently ſtrong; this lever
has ſeveral holes pierced through it, and fo has the vertical
piece ED, which is likewife moveable towards either fide of
the frame in grooves in the top and bottom pieces AL, DM.
Thus, the length KG of the radius can be varied at pleaſure, to
fuit the curvature of NO; and as the faw is moved to and fro
by proper machinery, in the direction CB, BC, it works lower
and lower into the block, while, being confined by the beam FG,
it cuts the cylindrical portion from the block P, as required.
When a completely cylindrical pillar is to be cut out of one
block of ftone, the firſt thing will be to aſcertain in the block
the poſition of the axis of the cylinder; then lay the block fo
that fuch axis fhall be parallel to the horizon, and let a cylin-
drical hole of from one to two inches diameter be bored
entirely through it. Let an iron bar, whofe diameter is rather
lefs than that of this tube, be put through it, having juft room
to flide freely to and fro as occafion may require. Each end of
this bar fhould terminate in a fcrew, on which a nut and frame
may be faftened: the nut frame ſhould carry three flat pieces of
wood or iron, each having a flit running along its middle nearly
from one end to the other, and a fcrew and handle muſt be
adapted to each flit: by thefe means the frame-work at each


Circular Sawvs.
48270
;
end of the bar may readily be ſo adjuſted as to form equal
ifofceles or equilateral triangles; the iron bar will connect two
correfponding angles of theſe triangles, the faw to be uſed two
other correfponding angles, and another bar of iron or of wood
the two remaining angles, to give fufficient ftrength to the whole
frame. This conftruction, it is obvious, will enable the work-
men to place the faw at any propofed diſtance from the hole
drilled through the middle of the block; and then, by giving the
alternating motion to the faw frame, the cylinder may at length
be cut from the block, as required. This method was firſt
pointed out in the Collection of Machines approved by the Paris
academy.
9.121.
If it were propofed to faw a conic fruftum from fuckca
block, then let two frames of wood or iron be fixed to thofe
parallel ends of the block which are intended to coincide with
the baſes of the fruftum, circular grooves being previously eat
in theſe frames to correfpond with the circumferences of the
two ends of the propoſed fruftum; the faw being worked in
thefe grooves will manifeftly cut the conic furface from the
block. This, we believe, is the contrivance of fir George
Wright.

W
The beſt method of drilling the hole through the middle of
the propofed cylinder feems to be this on a carriage running
upon four low wheels let two vertical pieces (each having sa
hole juft large enough to admit the borer to play freely) be
fixed two or three feet afunder, and ſo contrived that the pieces
and holes to receive the borer may, by fcrews, &c. be raiſed or
lowered at pleaſure, while the borer is prevented from fliding
to and fro by fhoulders upon its bar, which are larger than the
holes in the vertical pieces, and which, as the borer revolves,
preſs againſt thofe pieces: let a part of the boring bar between
the two vertical pieces be fquare, and a grooved wheel withe a
fquare hole of a fuitable fize be placed upon this part of the
bar; then the rotatory motion may be given to the bar by an
endleſs band which fhall paſs over this grooved wheel and a
wheel of a much larger diameter in the fame plane, the latter
wheel being turned by a winch handle in the uſual way. As
the boring proceeds, the carriage with the borer may be brought
nearer and nearer the block, by levers and weights, in the
fame manner as is deſcribed under the article boring of ORD-
NANCE.
:
Shin
4. Circular faws, acting not by a reciprocating, but by a
rotatory, motion, have been long known in Holland, where they
are uſed for cutting wood ufed in veneering. They were intro-
duced into this country, we believe, by general Bentham, and
are now uſed in the dock yard at Portfmouth, and in a few
晶
​328
MACHINES.
1
f
other places: but they are not, as yet, fo generally adopted as
might be wifhed, confidering how well they are calculated to
abridge labour, and to accomplish with expedition and accuracy
what is very tedious and irkſome to perform in the uſual way.
Circular faws may be made to turn either in horizontal, vertical,
or inclined, planes; and the timber to be cut may be laid upon
a' plane inclined in any direction; fo that it may be fawn by
lines making any angle whatever, or at any propoſed diſtance
from each other. When the faw is fixed at a certain angle,
and at a certain diſtance from the edge of the frame, all the
pieces will be cut of the fame fize, without marking upon them
by a chalked line, merely by cauſing them to be moved along
and keeping one fide in contact with the fide of the frame; for
then, as they are brought one by one to touch the faw revolving
on its axle, and are preffed upon it, they are foon cut through.
·
Mr. Smart, of Ordnance Wharf, Weftminster-bridge, has
¨ ſeveral circular faws, all worked by a horſe in a moderate fized
walk: one of thefe, intended for cutting and boring tenons uſed
in this gentleman's hollow mafts, is reprefented in fig. 2.
pl. XXVI. -NOPOR is a hollow frame, under which is part
of the wheel-work of the horſe-mill.-A, B, D, C, E, F, are
pulleys, over which pafs ftraps or endleſs bands, the parts of
which out of fight run upon the rim of a large vertical wheel:
by means of this fimple apparatus, the faws S, S', are made to
revolve upon their axles with an equal velocity, the fame band
paffing round the pulleys D, C, upon thoſe axles; and the
rotatory motion is given to the borer G by the band paffing over
the pulley A. The board I is inclined to the horizon in an
angle of about 30 degrees; the plane of the faw S' is parallel to
that of the board I, and about 4 of an inch diſtant from it, while
the plane of the faw S is vertical, and its loweſt point at the
fame diftance from the board I. Each piece of wood K out of
which the tenon is to be cut is 4 inches long, an inch and a
"quarter broad, and of an inch thick. One end of fuch piece
is laid fo as to flide along the ledge at the lower part of the
board I; and as it is pushed on, by means of the handle H, it is
firft cut by the faw S', and immediately after by the faw S:
after this the other end is put loweft, and the piece is again cut
by both faws: then the tenon is applied to the borer G, and
as foon as a hole is pierced through it, it is dropped into the
box beneath. By this procefs, at leaſt 30 tenons may be com-
pleted in a minute, with greater accuracy than a man could
make one in a quarter of an hour, with a common hand-ſaw and
gimblet. The like kind of contrivance may, by flight alterations,
be fitted for many other purpoſes, particularly all fuch as may
require the fpeedy fawing of a great number of pieces into
1
Scapements-
1 829
exactly the fame fize and fhape. A very great advantage
· attending this fort of machinery is, that, when once the pofition
of the faws and frame is adjuſted, a common labourer may per-
form the buſineſs juſt as well as the beſt workman.
;
SCAPEMENT, from the French word echappement, a tèrm
ufed among clock and watch-makers, to denote the general con-
trivance by which the preffure of the wheels, which move
always in one direction, and the reciprocating motion of the
pendulum or balance, are accommodated the one to the other.
When a tooth of a wheel has given the balance or pendulum a
motion in one direction, it must quit it, that it may get an
impulfion in the oppofite direction; and it is this efcaping of the
tooth of the wheel from the balance or pendulum, or of the
latter from the former, whichever we pleaſe to call it, that has
given rife to the general term.
*
*
•
i
From the nature of a pendulum, it follows, that it need only
to be removed from the vertical, and then let go, in order to
- vibrate and meaſure time. Hence it might feem that nothing
is wanted but a machinery fo connected with the pendulum as
to keep a regifter, as it were, of the vibration. It could not be
difficult to contrive a method of doing this; but more is wanted:
the air must be difplaced by the pendulum. This requires
fome force, and must therefore employ fome part of the
momentum of the pendulum. The pivot on which it wings
occafions friction the thread, or thin piece of metal by which
it is hung, in order to avoid this friction, occafions fome ex-
penditure of force by its want of perfect flexibility or tafticity.
Thefe, and other caufes, make the vibrations grow more and
more narrow by degrees, till at laſt the pendulum is brought to
reft. We muft, of courfe, have a contrivance in the wheelwork
which will reſtore to the pendulum the ſmall portion of force
which it lofes in every vibration. The action of the wheels
therefore may be called a maintaining power, becauſe it keeps up
the vibrations. But this may affect the regularity of vibration.
If it be fuppofed that the action of gravity renders all the vi-
brations ifochronous, we muſt grant that the additional impulſion
by the wheels will deftroy that ifochroniſm, unleſs it be fo
applied that the fum total of this impulfion and the force of
gravity may vary fo with the fituation of the pendulum as ſtill
to give a feries of forces, or a law of variation, perfectly fimilar
to that of gravity. This cannot be effected, unleſs we know
both the law which regulates the action of gravity, producing
ifochroniſm of vibration, and the intenſity of the force to be de-
rived from the wheels in every fituation of the pendulum.
Thus it appears that confiderable ſcientific ſkill as well as
mechanical ingenuity may be diſplayed in the conftruction of
1
330
MACHINES.
fcapements; and the judicious confideration of them becomes
of great importance to the artift: yet, notwithstanding this, no
material improvement was made in them from the first appli-
cation of the pendulum to clocks till the days of Mr. George
Graham; nothing more was attempted before his time than to
apply the impulfe of the fwing-wheel, in ſuch manner as was
attended with the leaft friction, and would give the greateſt
motion to the pendulum. Dr. Halley difcovered, by fome
experiments made at the Royal Obfervatory at Greenwich,
that by adding more weight to the pendulum, it was made to
vibrate larger arcs, and the clock went fafter; by diminiſhing
the weight of the pendulum, the vibrations became fſhorter, and
the clock went flower: the refult of thefe experiments being
diametrically oppofite to what ought to be expected from the
theory of the pendulum, probably firſt rouſed the attention of
Mr. Graham, who was not only fkilful in practice, but had
much mathematical knowledge, and was well qualified to
examine the fubject fcientifically: he foon made fuch further
trials as convinced him, that this feeming paradox was occă-
fioned by the retrograde motion, which was given to the ſwing-
wheel by every conftruction of fcapement that was at that time
in ufe; and his great fagacity foon produced a remedy for this
defect, by conftructing a fcapement which prevented all recoil
of the wheels, and reftored to the clock pendulum, wholly in
theory, and nearly in practice, all its natural properties in its
detached fimple ftate. This fcapement, with a few others of the
molt approved conftruction, will now be briefly deſcribed.

I
J.

1. The fcapement which has been in ufe for clocks and
watches ever fince their first appearance in Europe is extremely
fimple, and its mode of operation is too obvious to need much
explanation. In fig. 1. pl. XXIX. XY repreſents a horizontal
axis, to which the pendulum P is attached by a flender rod, or
otherwife. This axis has two leaves C and D attached, one
near each end, and not in the fame plane, but ſo that when the
pendulum hangs perpendicularly, and at reft, the piece C in-
clines a few degrees to the right hand, and D as much to the
left. They commonly make an angle of from 70 to 90 de-
grees: they are called by the name of pallets. AFB repreſents
a wheel turning round on a perpendicular axis EO, in the order
of the letters AFEB. The teeth of this wheel are cut into the
form of the teeth of a faw, leaning forward, in the direction of
the motion of the rim. As they fomewhat refemble the points
of an old-faſhioned royal diadem, this wheel has got the name
of the crown-wheel. In watches it is often called the balance-
wheel. The number of the teeth is generally odd; fo that when
one of them B is preffing on a pallet D, the oppofite pallet C is
Recoiling Scapements.
331
整​村
​in the ſpace between two teeth A and I. The figure repreſents
the pendulum at the extremity of its excurfion to the right hand,
the tooth A having juſt eſcaped from the pallet C, and the tooth
B having juft dropped on the pallet D. It is plain, that as the
pendulum now moves over to the left, in the arch PG, the
tooth B continues to prefs on the pallet D, and thus accelerates
the pendulum, both during its defcent along the arch PH, and
its afcent along the arch HG. It is no lefs evident, that when
the pallet D, by turning round the axis XY, raiſes its point
above the plane of the wheel, the tooth B eſcapes from it, and I
drops on the pallet C, which is now nearly perpendicular. I
preffes C to the right, and accelerates the motion of the pen-
dulum along the arch GP. Nothing can be more obvious than
this action of the wheel in maintaining the vibrations of the
pendulum. We can eaſily perceive, alſo, that when the pen-
dulum is hanging perpendicularly in the line XH, the tooth
B, by preffing on the pallet D, will force the pendulum a little
way to the left of the perpendicular, and will force it ſo much
the further as the pendulum is lighter; and, if it be fufficiently
light, it will be forced fo far from the perpendicular that the
tooth B will efcape, and then I will catch on C, and force the
pendulum back to P, where the whole operation will be re-
peated. The fame effect will be produced in a more remarkable
degree, if the rod of the pendulum be continued through the
axis XY, and a ball Q put on the other end to balance P. And,
indeed, this is the contrivance which was firft applied to clocks
all over Europe, before the application of the pendulum. They
were balance clocks. The force of the wheel was of a certain
magnitude, and therefore able, during its action on a pallet, to
communicate a certain quantity of motion and velocity to the
balls of the balance. When the tooth B efcapes from the pal-
let D, the balls are then moving with a certain velocity and
momentum. In this condition, the balance is checked by the
tooth I catching on the pallet C. But it is not inftantly top-
ped. It continues its motion a little to the left, and the pallet
C forces the tooth I a little backward. But it cannot force it fo
far as to eſcape over the top of the tooth I, becauſe all the mo-
mentum of the balance was generated by the force of the tooth
B; and the tooth I is equally powerful. Befides, when I catches
on C, and C continues its motion to the left, its lower point
applies to the face of the tooth I, which now acts on the ba-
lance by a long and powerful lever, and foon ftops its further
motion in that direction; and now, continuing to prefs on C, it
urges the balance in the oppofite direction. Thus we fee that
in a fcapement of this kind the motion of the wheel muſt be
very hobbling and unequal, making a great ftep forward, and


$
+
1
KOLISH
Cop
110)
•
332
MACHINES.
•
a ſhort ſtep backward, at every beat. This has occafioned the
contrivance to get the name of the recoiling fcapement, or the
Scapement of recoil.
In this fcapement the vibrations are quicker than if the ba-
lance or pendulum vibrated freely: for the recoil fhortens the
afcending part of the vibration, by contracting the extent of the
arc, and the re-action of the wheel accelerates the defcending
part of the vibration. In this ſcapement, too, if the maintain-
ing power be increaſed, the vibrations will be performed in
larger arcs, but in leſs time: becauſe the greater preſſure of
the crown-wheel on the pallet will cauſe the balance to vibrate
through larger arches; and the time will be lefs increaſed on
this account than it will be diminiſhed by the acceleration that
preffure gives to the balance and the diminution of the time of
recoil.
2. The preceding ſcapement not being well adapted to fuch
vibrations as are performed through arcs of a few degrees only,
another conftruction has been made which has been in conſtant
ufe for about a century in clocks, with a long pendulum beating
feconds. In fig. 2. AB reprefents a vertical wheel called the
fwing-wheel, having thirty teeth. CD repreſents a pair of pal-
lets connected together, and moveable in conjunction with the
pendulum on the centre or axis F. One tooth of the wheel,
as fhewn in the figure, refts on the inclined furface of the inner
part of the pallet C; on which its difpofition to flide tends to
throw the point of the pallet further from the centre of the
wheel, and confequently affifts the vibration in that direction.
While the pallet C moves outwards and the wheel advances, the
point of the pallet D of courſe approaches towards the centre
in the opening between the two neareſt teeth; and when the
acting tooth of the wheel flips off, or eſcapes from the pallet
C, another tooth on the oppofite fide immediately falls on the
exterior inclined face of D, and by a fimilar operation tends to
puſh that pallet from the centre. The returning vibration is
thus affifted by the wheel, while the pallet C moves towards
the centre, and receives the fucceeding tooth of the wheel, after
the eſcape from the point of D. Thus may the alternation be
conceived to go on without limit.
In this fcapement, as well as the former, the vibrating part
is conftantly under the influence of the maintaining power, ex-
cept during the interval of the drop, or actual efcape of the
wheel from one pallet to the other. One principal recommenda-
tion of this fcapement ſeems to have been the facility with which
it affords an index for feconds in the face of the clock. Though
the pendulum, according to this conftruction, is conftantly
connected with the maintaining power in a clock, yet the va-
Dead-beat Scapements.
233
riations of that power have not the fame mischievous effect as in
a watch, becauſe the momentum of the pendulum, compared
with the impulfe of the maintaining power, is prodigioufly
greater in the former of theſe inſtruments. A very confiderable
change in the maintaining power of a clock with a long pen-
dulum will only caufe a variation of a few feconds in the daily
rate.
3. Mr. Graham's ſcapement, already ſpoken of, was a confi-
dérable improvement upon that juft defcribed. He took off
part of the flope furtheft from the points of the pallets; and in-
ftead of that part he formed a circular or cylindrical face, having
its axis in the centre of motion. Pallets of this kind are fhewn
at the lower part of fig. 2. at E and G, having H for their centre
or axis. A tooth of the wheel is feen refting upon the circular
inner furface of the pallet G, which therefore is not affected by
the wheel, excepting fo far as its motion, arifing from any other
cauſe, may be affected by the friction of the tooth; and this re-
fiſtance is exceedingly minute, not amounting to one-eighth of
the preffure on the arch. Nay, we think it appears from the
experiments of Coulomb, that, in the cafe of fuch minute
preffures on a furface covered with oil, there is no fenfible re-
tardation analogous to that produced by friction, and that what
retardation we obferve arifes entirely from the clamminefs of the
oil. If the vibration of the pendulum be fuppofed to carry G
outwards, the flope furface will be brought to the point of the
tooth, which will ſlide along it, and urge the pallet outwards
during this ſliding action. When the tooth has fallen from the
point of this pallet, an oppofite tooth will be received on the
circular furface of E, and will not affect the variation, excepting
when the ſlope ſurface of E is carried out fo as to fuffer the
tooth to ſlide along it. This contrivance is known by the name,
of the dead beat, the dead fcapement; becauſe the feconds index
ftands ſtill after each drop, whereas the index of a clock with a
recoiling ſcapement is always in motion, hobbling backward and
forward.
In this fcapement, an increaſe of the maintaining power ren
ders the vibrations larger and flower: becauſe the greater
preffure of the tooth on the edge of the pallet throws it round
through a greater arch; and its increaſed preffure on both fur-
faces of the pallet retards its motion.
4. The effect of the fcapement which has been called ho
rizontal, becauſe the laft wheel in watches of this conftruction.
has its plane parallel to the rest of the fyftem, is fimilar to that
of the dead-beat fcapement of Graham. In fig. 5, the ho-
rizontal wheel is feen with twélye teeth, upon each of which is
fixed a ſmall wedge fupported above the plane of the wheel, as
334
MACHINES.
may be feen at the letters A and B. On the verge of the ba
lance there is fixed part of a hollow cylinder of ſteel or other
hard material, the imaginary axis of which paffes through the
pivots of the verge. Čreprefents this cylindrical piece, into
which the verge D may be ſuppoſed to have fallen. While the
vibration cauſes the cylindrical piece to revolve in the direction
which carries its anterior edge towards the axis of the wheel,
the point of the wedge will merely rub the internal ſurface, and
no otherwife affect the vibration of the balance than by retarding
its motion. But when the return of the vibration clears the cylin-
der of the point of the wedge D, the wheel will advance, and the
flope furface of the wedge acting againſt the edge of the cylinder
will affift the vibration of the balance. When the edge of the
cylinder arrives at the outer point of the wedge D, its pofterior
edge muft arrive at the pofition denoted by the dotted lines of
continuation; immediately after which the wedge or tooth E
will arrive at the poſition é, and reft on the outer ſurface of the
cylinder, where it will produce no other effect than that of re-
tardation from friction, as was remarked with regard to the
wedge D, until the courſe of the vibration fhall bring the po-
fterior edge of the cylinder clear of the point of the wedge. In
this.laft fituation, the wedge will act on the edge of the cylin-
der, and aſſiſt the vibration, as in the former cafe, until that
edge fhall arrive at the outer or pofterior point of the wedge;
immediately after which the leading point will fall on the
inner furface of the cylinder in the firſt poſition, as was fhewn
in the wedge D.
1
Horizontal watches were greatly eſteemed during the laſt
thirty years, until lately, when they gave place to thoſe con-
ſtructions which are known by the name of detached or free
fcapements. In the common fcapement, fig. 1, an increaſe of
the maintaining power increaſes the recoil, and accelerates the
vibrations: but with the horizontal ſcapement there is no re-
coil; and an increaſe of the maintaining power, though it may
enlarge the arc of vibration, will not neceffarily diminish or
alter the time. It is accordingly found, that the experiment of
altering the maintaining power by the application of the key
does not alter the rate in the fame perceptible manner as in
common watches.
5. Fig. 6, reprefents the free fcapement of our beſt portable
time-pieces. Fig. 4, exhibits the fcapement on a large fcale.
On the verge of the balance is fixed a circular piece of ſapphire,
or of hard fteel, EL, out of which a fectoral piece is cut. HG is
a ftraight ſpring fixed near its extremity H, and having at the
-other extremity a pin G, againſt which one of the teeth of the
wheel D reſts when the train is at reft.. This fpring has a flight
1
Detached Scapements.
335
tendency towards the centre of the wheel, but is prevented by the
ftop K from throwing the pin further inwards than juſt to receive
the point of the tooth. I is a very flender ſpring fixed at the end
I, and preffing very flightly against the pin G, in a direction tend
ing to throw it from the wheel D, but which on account of the
greater power of HG it cannot effect. It may be obferved that
the fpring I proceeds a little beyond the pin G-F is a lever pro-
ceeding from the verge of the balance directly oppofité the end
of the fpring I, and long enough to ſtrike it in its vibration.
The action is as follows:-From the preffure of the main fpring
the wheel (fig. 4.) is urged from D towards F, but is prevented
from moving by the pin G. Let the balance be made to vi
brate, and the lever F will move through the arc Ff, ftrike the
inner extremity of the fpring I, and diſplace the pin G. At
this inftant the face E, which may be called the pallet, will
have arrived at the pofition e, againſt which the tooth of the
wheel will fall, and communicate its impulfe through about
15° or 16° of the vibration. But F quits the fpring I fooner
than the wheel quits the pallet E, and confequently the pin G
will have returned to its firft ftation before the wheel can have
advanced a whole tooth, and the ſpring or detent HG will re-
ceive the wheel as before, immediately after its eſcape from the
pallet. The returning vibration of the balance will be made
with the piece EL perfectly at liberty between two teeth of the
wheel, as in the ſketch, and the back ftroke of the lever F
againſt the tender fpring I will have no effect whatever on the
pin G; this fpring being like the back ſpring of the jacks of the
harpfichord, active in one direction only. The third vibration of
the balance will unlock the detent as before; the impulſe will
again be given, and the whole proceſs will be repeated: and in
this manner, the balance, though it may vibrate through the
greatest part of the entire circle, will be entirely free of the
works, except during the very ſmall time of the drop of the
wheel.
It is hardly neceffary to make any remark on this fcapement.
It requires little or no oil; and when all the parts, particularly
the pendulum fpring, are duly adjusted, it is found that a very
great variation in the first mover will remarkably alter the arc of
vibration without affecting the rate. The piece EL might have
confifted of a ſingle pallet or arm, inſtead of a portion of a circle
or cylinder; but fuch a piece would have been rather lefs conve
nient to make in fapphire, or ruby, as in the beſt time-piecès,
and would alfo have been lefs uſeful. For if by any accident or
'fhock the pin G ſhould be difplaced for an inſtant, the wheel
D will not ran down, becauſe it will be caught upon the eir-
cular furface of EL. It is indeed very easy to obfervé, that the

336
MACHINES.
piece EL would operate without the detent, though with much
friction during the time of repofe. The tooth of the wheel
would in that cafe reft upon its circular face.
*
6. In the two laft fcapements we have ſeen the variable effects
of the maintaining power almost entirely removed, as far as can
be practically difcerned. Fig. 7, exhibits the fcapement of
Mudge; in which the balance is perfectly detached from the
train of wheels, except during the extremely fhort interval of
ftriking out the parts which ferve the purpofe of detents.
ONEBQ is the circumference of the balance, vibrating by the
action of a ſpiral fpring as ufual on its axis CA DH paffing
through the centre C: the axis is bent into a crank, AXYD,
to make room for the other work. LM, ZW, are two rods
fixed to the crank at the points L and Z, parallel to XY.
cdefrs are fixed parts of the machine. TR is an axis con-
centric with that of the balance, and carrying an arm Go nearly
at right angles to it, and a ſmall auxiliary fpring u, which is
wound up
whenever the arm Go is moved in the direction o h.
p is a curved pallet fixed to the axis TR, which receives the
tooth of the balance wheel near the axis. The tooth, proceed-
ing along the curved furface, by the force of the main fpring
turns the axis and its arm Go, and winds up the ſpring z A
fmall projection at the extremity of the curved furface of the
pallet p prevents the further progrefs of the tooth, when the arm
G has been turned through an arc oh, of about 27°; and con-
fequently the fpring u has been wound up through the fame angle
or arc, o Gh 27°. FS is another. axis exactly fimilar to
TR. It carries its arm Io, and fpring v, and the tooth of the
balance-wheel Im winds up the fpring v, by acting on the pal-
let q, and is detained by a projection, after having carried it
through an angle of 27°, exactly as in the former cafe. The
arcs paffed through by the arms Go and Io, and marked in
the figure, are alfo denoted by the fame letters on the rim of
the balance.
The effect of this fcapement may be thus explained: let the ba
lance be in the quiefcent ftate, the main ſpring being unwound,
and the branch or crank in the pofition repreſented in the figure.
If the quiefcent points of the auxiliary fprings coincide with that
of the balance-fpring, the arm Go will juft touch the rod LM, and
in like manner the arm Io will just touch the rod WZ; the two
arms Go and I in this pofition are parallel to the line CO. This
pofition of the balance and auxiliary fprings remains as long as
the main ſpring of the machine continues unwound; but when-
ever the action of the main fpring fets the balance-wheel in
motion, a tooth thereof meeting with one or other of the pallets
or q, will wind up one of the auxiliary ſprings: fuppofe it
Mudge's Scapements.
337
:
po
Thould be the ſpring u. The arm Go being carried into the
fition Gb, by the force of the balance-wheel acting on the pal-
let p, remains in that poſition as long as the tooth of the ba
lance-wheel continues locked by the projection at the extremity
of the pallet; and the balance itſelf not being at all affected
by the motion of the arm Go, nor by the winding up of the
fpring u, remains in its quiefcent pofition: confequently no vi-
bration can take place, except by the affiftance of fome external
force to fet the balance in motion. Suppoſe an impulfe to be
given fufficient to carry it through the femi-arc OB, which is
about 135° in Mr. Mudge's conftruction.

-
The balance, during this motion, carries with it the crank
AXYD, and the affixed rods LM, ZW. When the balance
has deſcribed an angle of about 27° the angle o Ch, or o Gh,
the rod LM meets with the arm GH, and by turning the axis
TR, and the pallet p in the direction of the arc o b, releaſes the
tooth of the balance-wheel from the projection at the extremity
of the pallet p: the balance-wheel immediately revolves, and
the lower tooth meeting with the pallet q, winds up the auxi-
liary ſpring, and carries the arm Io with a circular motion
through the angle. Ik, about 27°, in which poſition the arm'
Io remains as long as the tooth of the balance-wheel is locked
by the pallet q. While the fpring vis winding up through the
arc ok, the balance defçribes the remaining part of the femi-arc
b B, and during this motion the rod LM carries round the arm
Gh, caufing it to defcribe an angle h CB, or h·GB, which is
meaſured by the arc bB 108°. When the balance has ar-
rived at the extremity of the femi-arc OB 135°, the auxiliary
fpring u will have been wound up through the fame angle of
130°, that is to fay, 27°, by the force of the main-fpring acting
on the pallet p, and 108° by the balance itſelf, carrying along
with it the arm Go, or Gb, while it defcribes the arc h B. The
balance therefore returns through the arc-BO, by the joint action
of the balance fpring and the auxiliary fpring u; the accelera-
tion of both ſprings ceafing the inftant the balance arrives at the
quiefcent point o. When the balance has proceeded in its vi-
bration about 27 beyond the point O, to the pofition Ck, the
rod. ZW meets with the arm Ik, and by carrying it forward re-
leaſes, the tooth of the balance-wheel from the pallet q. The
balance-wheel accordingly revolves, and the upper tooth meeting
with the pallet.pwinds up the auxiliary ſpring u as before.
The balance with the crank proceeding to deſcribe the remain-
ing femi are kE, winds up the fpring v through the further
angle CE108, and returns through the femi-arc E6, by
the joint action of the balance-ſpring and the auxiliary ſpring


VOL. H.
Z
}
:

338
MACHINES.
v, both of which ceafe to accelerate the balance the inftant it
has arrived at O.
It may be remarked, in this curious ſcapement, that the mo-
tion of the balance in its femi-vibration from the point of qui-
eſcence is oppoſed through an arc of no more than 108, but is
accelerated in its return through the whole arc of 135˚, and
that the difference is what maintains the vibrations; and more-
over, that the force from the wheel being exerted to wind up
each auxiliary ſpring during the time it is totally difengaged
from the balance, this laſt organ cannot be effected by its irre-
gularities, except fo, far as they may render it more difficult
to difengage the rim of the pallet from the tooth. The balance
defcribes an arc of about 8° during this difengagement.
Count Bruhl, in his pamphlet " On the Inveſtigation of
Aftronomical Circles," after defcribing Mudge's fcapement,
proceeds thus: " By what has been faid, it is evident, that
whatever inequality there may be in the power derived from
the main ſpring (provided the latter be fufficient to wind up
thofe little pallet-fprings), it can never interfere with the regu-
larity of the balance's motion, but at the inſtant of unlocking
the pallets, which is ſo inſtantaneous an operation, and the re-
fiſtance ſo exceedingly ſmall, that it cannot poffibly amount to
any
fenfible error.
error. The removal of this great obſtacle was cer-
tainly never fo effectually done by any other contrivance, and
deferves the higheſt commendation, as a probable means to per-
fect a portable machine that will meaſure time correctly. But
this is not the only, nor indeed the principal, advantage which
this time-keeper will poffefs over any other; for, as it is im-
poffible to reduce friction to ſo ſmall a quantity as not to affect
the motion of a balance, the conſequence of which is, that it
deſcribes fometimes greater and fometimes fmaller arcs, it be
came neceflary to think of ſome method by which the balance
might be brought to deſcribe thoſe different arcs in the fame
time. If a balance could be made to vibrate without fric-
tion or refiftance from the medium in which it moves, the
mere expanding and contracting of the pendulum-ſpring would
probably produce the fo much wiſhed for effect, as its force is
ſuppoſed to be proportional to the arcs deſcribed; but as there
is no machine void of friction, and as from that cauſe, the ve-
locity of every balance decreaſes more rapidly than the ſpaces
gone through decreafe, this inequality could only be removed
by a force acting on the balance, which affuming different ra-
tios in its different ftages, could counterbalance that inequality.
This very material and important remedy, Mr. Mudge has
effected by the conſtruction of his fcapement; for his pallet-
*
Mudge's Scapements.
339
fprings having a force capable of being increaſed almoſt at plea-
fure, at the commencement of every vibration, the proportion
in their different degrees of tenfion may be altered till it an-
fwers the intended purpofe. This fhews how effectually Mr.
Mudge's fcapement removes the two greateſt difficulties that
have hitherto baffled the attempts of every other artiſt, namely,
the inequalities of the power derived from the main fpring, and
the irregularities ariſing from friction, and the variable refift-
ance of the medium in which the balance moves."
7. Fig. 8, is the ſketch of an adaptation of Mudge's fcape-
ment to a clock. LM is a part of the periphery of the wheel.
GA, GB, are two arms ſeparately moveable on the fame axis,
and terminating in the pallets A, B. Theſe pallets have in-
clined faces, with a claw or detent at the lower part of each.
GO, IO, are tails proceeding from each pallet-piece refpec.
tively, and the dark ſpot at N reprefents a pin proceeding from
the pendulum rod, and capable of moving either of the tails ac-
cording to the courſe of the vibration. The dotted circles u
and v reprefent weights which are ſtuck upon two pins, and
may be changed for others, greater or ſmaller, until the moſt
fuitable quantity is found. Suppofe the wheel to be urged
from L towards MM, and the pendulum made to vibrate by ex-
ternal impulfe. The pin N proceeding towards L will ftrike
the tail GO, raiſe the pallet A, and fet the wheel at liberty:
which fliding along the inner ſurface of the pallet B, will raifè
it, and ftop againſt the claw at its lower end. IO will confe-
quently be carried into the pofition IP; and the pallet A in its
return will be oppofite a vacancy, which will permit the tail
GO to follow the pin N as far as the perpendicular fituation.
The pendulum will therefore be affifted by the weight u through
a longer arc in its defcent, than it was impeded by it in its
afcent. In the oppofite femi-vibration toward M, the pen
dulum will proceed unoppofed by v, while it paffes through
the angle OIP, when it will raiſe B, and permit the wheel to
elevate the pallet A. In the motion on this fide of the perpen
dicular, it is alſo clear that the deſcent will be more affifted
than the afcent was impeded. Whence it follows, that the
clock will continue to go: and no variation of the force of the
wheel LM, which raifes the pallets in the abfence of the pen
dulum, will affect the vibration, except fo far as it may afford a
variable refiftance at the detent or claw.
8. Mr. Mudge has alfo given another detached ſcapement,
which he recommends for pocket-watches, and executed en-
tirely to his fatisfaction in one made for the queen. A dead-
beat pendulum fcapement is interpofed between the wheels
and the balance. The crutch EDF (fig. 3.) has a third arm





Z 2
340
MACHINES.

SUF
•
DG ftanding outwards from the meeting of the other two, and
of twice their length. This arm terminates in a fork AGB.
The verge V has a pallet C, which, when all is at reft, would
ftand between the points A, B, of the fork. But the wheel, by
its action on the pallet E, forces the fork into the pofition Bg b
the point A of the fork being now where B. was before, juft
touching the cylindrical furface of the verge. The fcapement
of the crutch EDF is not accurately a dead-beat, fcapement, but
has a very fmall recoil beyond the angle of impulfion. By this
circumſtance the branch A (now at B) is made to prefs moft
gently on the cylinder, and keeps the wheel locked, while the
balance is going round in the direction BHA. The point A gets a
motion from A to B by means of a notch in the cylinder, which
turns round at the fame time by the action of the branch AG
on the pallet C; but A does not touch the cylinder during this,
motion, the notch leaving free room for its paffage. When the
balance returns from its excurfion, the pallet Cftrikes on the
branch A (ſtill at B), and unlocks the wheel. This now acting
of the crutch-pallet F, caufes the branch.b of the fork to follow,
the pallet C, and give it a ftrong impulfe in the direction in
which it is then moving, caufing the balance to make a femi-
vibration in the direction AHB. The fork is now in the fi-
tuation A ga, fimilar to B gb, and the wheel is again locked on
the crutch-pallet E.

.
The intelligent reader will admit this to be a very ſteady and
effective fcapement. The lockage of the wheel is procured in a
very ingenious manner; and the friction on the cylinder, ne-
ceffafy for effecting this, may be made as fmall as we pleafe,
notwithſtanding a very ſtrong action of the wheel: for the
preffure of the fork on the cylinder depends entirely on the de-
gree of recoil that is formed on the pallets E and F, Preure
of the cylinder is not indifpenfably neceffary, and the crutch-
fcapement might be a real dead-beat. But a fmall recoil, by
keeping the fork în contact with the cylinder, gives the moft:
perfect fteadinefs to the motion. The ingenious inventor, a
man' of approved integrity and judgment, declares that her ma-
jetty's Watch was the belt pocket-watch he had ever feen. We
are not difpofed to question its excellency.
9. Another fcapement, in which a confiderable degree of in-..
genuity is
is united with comparative fimplicity is that of Mr. De
Lafons. The inventor's defcription, and fome of his obferva-
tions, as prefented to the Society of Arts, are as follows:

967
Although the giving an equal impulſe to the balance has
been already moft ingeniouſly done by Mr. Mudge and Mr.
Haley (from whofe great merit I would not wifh to detract),
yet the extreme difficulty and expence attending the firſt, and
་
De Lafon's Scapement.
341

the very compound locking of the ſecond, render them far from
completing the defired object.
"The perfections and advantages arifing from my improve-
ments on the remontoire detached fcapement for chronometers,
which gives a perfectly equal impulfe to the balance, and not
only entirely removes whatever irregularities arife from the dif
ferent ſtates of fluidity in the oil, from the train of wheels, or
from the main fpring, but does it in a fimpler way than any
with which I am acquainted. I truft it will not be thought
improper in me to anfwer fome objections made at the examina
tions before the committee, as I am fully perfuaded the more
mathematically and critically the improvements are inveſtigated,
the more perfect they will prove to be.
"It was firft obferved, that my method did not ſo com-
pletely detach the train of wheels from the balance as another
ſcapement then referred to. I beg leave to remark, that the
train of wheels in mine is prevented from preffing againſt the
locking, by the whole power of the remontoire-fpring; fo that
the balance has only to remove the fmall remaining preffure,
which does away that objection, and alfo that of the difadvan-
tage of detents, as this locking may be compared to a light ba-
Fance turning on fine pivots, without a pendulum-fpring; and
has only the advantage of banking, fafe at two turns of the ba-
lance, and of being firmer, and lefs liable to be out of repair
than any locking where fpring-work is uſed, but likewife of
unlocking with much lefs power. It was then obferved, it
required more power to make it go than ufual. Permit me
to fay, it requires no more power than any other remontoire-
fcapement, as the power is applied in the moft mechanical
manner poffible.—And, laftly, it was faid, that ſet or re-
quired the balance to vibrate an unuſually large arch before
the piece would go. This depends on the accuracy of the
execution, the proportionate diameter and weight, of the ba
lance, the ftrength of the remontoire-fpring, and the length
of the pallets. If thefe circumftances are well attended to, it
will fet but little more than the most generally detached fcape-

ments.”
A, fhews the fcape-wheel, pl. XXIX.
B, the lever-pallet, on an arbor with fine pivots, having at the
lower end
C, the remontoire or ſpiral ſpring fixed with a collar and ſtud,
as pendulum-fprings are.
D, the pallet of the verge, having a roller turning in ſmall
pivots for the lever-pallet to act againſt.
E, Pallets to difcharge the locking, with a roller between, as
in fig. 10.

$42
MACHINES.
1
J
G
F, the arm of the locking-pallet continued at the other end to
make it poife, having ftuds and fcrews to adjuft and bank
quantity of motion.
the
a and b, the locking-pallets, being portions of circles, faſtened
on an arbor turning on fine pivots.
G, the triple fork, at the end of the arm of the locking
pallets.
The centre of the lever-pallet in the draft, is in a right line be-
tween the centre of the fcape-wheel and the centre of the verge,
though in the model it is not: but may be made fo or not, as beſt
fuits the calliper, &c.
the
"The fcape-wheel A, with the tooth 1, is acting on the
lever-pallet B, and has wound up the fpring C: the verge-
pallet D (turning the way reprefented by the arrow)
ment it comes within the reach of the lever pallet, the dif
charging pallet E, taking hold of one prong of the fork, removes
the arm F, and relieves the tooth 3 from the convex part of the
lock a. The wheel goes forward a little, juft fufficient to për-
mit the lever-pallet to pafs, while the other end gives the im-
pulſe to the balance: the tooth 4 of the wheel is then locked on
the concave fide of the lock b, and the lever-pallet is ſtopped
againſt the tooth 5, as in fig. 11. So far the operation of giving
the impulfe, in order again to wind the remontoire-fpring (the
other pallet at E, in the return, removing the arm F the con-
trary direction), relieves the tooth 3 from the lock b. The
wheel again goes forward, almoft the whole fpace, from tooth
to tooth, winds the ſpiral ſpring again, and comes into the fitua-
tion of fig. I, and thus the whole performance is completed.
The end of the lower pallet B refting on the point of the tooth
1, prevents the wheel exerting its full force on the lock a, as
in fig. 1. The fame effect is produced by the pallet lying on
the tooth 5, by preventing the wheel from preffing on b; and
thus the locking becomes the tighteft poffible. This fcape-
ment may be much fimplified by putting a ſpring with a pallet
made in it, as in fig. 12. inftead of the lever-pallet, and fpiral-
fpring. The operation will be in other reſpects exactly the
fame, avoiding the friction of the pivots of the lever-pallet.
This method I prefer for a piece to be in a ftate of reft, as a
clock; but the difadvantage, from the weight of the fpring in
different pofitions, is obvious. The locking may be on any two
teeth of the wheel, as may be found moft convenient."



“
Many other ingenious fcapements have been contrived by
Harrifon, Hindley, Ellicot, Lepaute, Le Roy, Berthoud, Ar-
nold, Whiethurſt, Earnshaw, Nicholfon, &c. But defcriptions
of them would extend this article to much too great a length.
What is here collected will, we truſt, furniſh fome infight into
Archimedes's Screw.
343

the nature of a few of the most approved fcapements; and
thoſe who need further information will do well to confult fome
of the beſt treatiſes mentioned in the general catalogue given
under the word CLOCKWORK.
ARCHIMEDES'S SCREW, or the Waterfnail, is a machine for
raiſing water, which confifts either of a pipe wound ſpirally
round a cylinder, or of one or more fpiral excavations formed
by means of fpiral projections from an internal cylinder, covered
by an external coating, fo as to be watertight. This fcrew is
one of the moſt ancient, and at the fame time ingenious, ma-
chines we know, being truly worthy of the name it bears, fup-
pofing Archimedes to be the real inventor. Though Timple in
its general manner of operation, its theory is attended with fome
difficulties which could only be conquered by the modern
analyſis: it was firft ftated correctly, as far as we have been able
to afcertain, by M. Pitot, in the Mémoires de l'Academie Royale
des Sciences, and afterwards more elaborately by Euler in Nov.
Comment. Petropol. tom. 5. Later attempts by Langsdorf in his
Handbuch der Maſchinenlehre, and fome other authors, are not to
be relied on. That the nature of this curious machine may be
the better underſtood, we ſhall firſt ſtate generally it's manner of
operation; and then prefent a more particular view of the cal-
culus neceffary to fhew the work it will really perform, and the
force required as a firſt mover.





}
1. If we conceive that a flexible tube is rolled regularly about
a cylinder from one end to another; this tube or canal will be
a fcrew or ſpiral, of which we ſuppoſe the intervals of the fpires
or threads to be equal. The cylinder being placed with its
axis in a vertical pofition, if we put in at the upper end of the
ſpiral tube a ſmall ball of heavy matter, which may move freely,
it is certain that it will follow all the turnings of the fcrew from
the top to the bottom of the cylinder, defcending always as it
would have done had it fallen in a right line along the axis of
the cylinder, only it would occupy more time in running through
the fpiral. If the cylinder were placed with its axis horizon-
tally, and we again put the ball into one opening of the canal, it
will defcend, following the direction of the firft demi-fpire;
but when it arrives at the loweſt point in this portion of the
tube it will stop. It must be remarked that, though its heavi-
nefs has no other tendency than to make it defcend in the demi-
fpire, the oblique pofition of the tube, with refpect to the
horizon, is the cauſe that the ball, by always defcending, is
always advancing from the extremity of the cylinder whence it
commenced its motion, to the other extremity. It is impoffible
that the ball can ever advance more towards the further, or as
we fhall call it, the fecond extremity of the cylinder, if the

344
MACHINES.
هم
cylinder placed horizontally remains always immoveable: but
if, when the ball is arrived at the bottom of the first demi-ſpire,
we caufe the cylinder to turn on its axis without changing the
pofition of that axis, and in fuch manner that the lowest point
of the demi-fpire on which the ball preffes becomes elevated,
then the ball falls neceffarily from this point upon that which
fucceeds, and which becomes loweft; and fince this fecond
point is more advanced towards the fecond extremity of the
cylinder than the former was, therefore by this new defcent the
ball will be advanced towards that extremity, and fo on through-
out, in fuch a manner that it will at length arrive at the fecond
extremity by always defcending, the cylinder having its rotatory
motion continued. Moreover, the ball, by conftantly following
its tendency to defcend, has advanced through a right line equal
to the axis of the cylinder, and this diſtance is horizontal be-
caufe, the fides of the cylinder were placed horizontally. But
if the cylinder had been placed oblique to the horizon, and we
fuppofe it to be turned on its axis always in the fame direction,
it is eafy to fee that if the first quarter of a fpire actually de-
fcends, the ball will move from the lower end of the fpiral tube,
and be carried folely by gravity to the lowest point of the firft
demi-fpire, where, as in the preceding cafe, it will be abandoned
by this point as it is elevated, by the rotation, and thrown by its
heavinefs upon that which has taken its place: whence, as this
fucceeding point is further advanced towards the fecond ex-
tremity of the cylinder, than that which the ball occupied juft
before, and confequently more elevated; therefore the ball
while following its tendency to deſcend by its heavineſs, will be
always more and more elevated by virtue of the rotation of the
cylinder. Thus it will, after a certain number of turns, be ad-
vanced from one extremity of the tube to the other, or through
the whole length of the cylinder; but it will only be raiſed
through the vertical height determined by the obliquity of the
pofition of the cylinder.
Inftead of the ball let us now confider water as entering by the
lower extremity of the ſpiral canal, when immerſed in a reſervoir:
this water defcends at firft in the canal folely by its gravity;
but the cylinder being turned, the water moves on in the canal
to occupy the loweſt place; and thus by the continual rotation
is made to advance further and further in the ſpiral, till at
length it is raiſed to the upper extremity of the canal where it
is expelled. There is, however, an effential difference between
the water and the ball: for the water, by reaſon of its fluidity,
after having defcended by its heavinefs to the lowest point of
the demi-fpire, riſes up on the contrary fide to the original
level; on which account more than half one of the ſpires may foon


Achimedes's Screw.
345
be filled with the fluid. This is an important particular, which,
though it need not be regarded in a popular illuſtration, muſt be
attended to in the more particular exhibition of the theory to
which we now proceed.
2. The moſt fimple nethod of tracing a fcrew or a helix
upon a cylinder is well known to be this: take the height or
length of a cylinder for ne leg of a right-angled triangle, and
make the other leg equa to as many times the circumference
of the baſe of the cylinde, as the ſcrew is to make convolutions
about the cylinder itſelf, then if this triangle be enveloped
about the ſurface of the folid, the two legs being made, the
one to lie parallel to the ais of the cylinder, the other to fold
apon the circumfererice of its bafe, the hypothenufe will form
the contour of the fcrew Suppofe therefore here, that upon
the cylinder ABCD (fig.6. pl. XXIV.) we have rolled the
right-angled triangle BDE, and that its hypothenufe DE traces
upon the cylinder the contour of the helix or the fpires BF,
GH, &c. Then if a tubebe formed according to the direction
of this ſpiral, and a fmall all put into it, if the cylinder were
place upright, the ball would roll to the bottom with the fame
veli city and the fame force, as it would have defcended upon
the plane DE, if BĘ were orizontal and BD vertical. But if
the cylinder be inclined until it makes with the vertical CL an
angle ACL equal to the angle BED, or the angle which the
threads of the fcrew make conftantly with the bafe of the
cylinder, in that cafe DE will be parallel to the horizon; and
whether the ſpires be few or many, they will all be parallel to
the horizon: fo' that there being nothing to occafion the ball F.
to move toward either G'er H, it will remain immoveable, fup-
pofing the cylinder to be it reft: but if the cylinder be turned
on its axis in one directiot, the ball (abftracting from friction)
will move the contrary way, in conformity with the first law of

motion.
P
3. The inclination ACL BED which we have juft affign-
ed, is the leaft we can give, ſo that the ball fhall not defcend of
itself: but if we'augment this inclination, or, make the angle
LAC ſmaller, then by turning the cylinder in the direction
CMD, the ball will always lave a defcent on the fide towards-
H, and will mount, fo to fpák, by defcending. The reaſon is
very fimple: the plane which carries it makes it rife more in confe-
quence of the rotatory motion, than it defcends by virtue of the force of
gravity.
4. There are feveral methods of determining the ratio of the
weight of the ball P to the force F, neceffary to make it rife by
turning the ſcrew: The following is perhaps the moft fimple {
the force or power is to the weight elevated, as the vertical

* 346
MACHINES --
fpace paffed over by the weight, is to the ſpace paffed through by
the power in moving it. Here the vertical ſpace is CL, and if
the moving force act at the circumference of the cylinder, the
Space paffed over by that force will be equal to as many times
the circumference of the cylinder's bae, as there are convolu-
tions of the helix: thus we fhall haveBE: CL : : P : F.
Example. Let the diameter AB of he cylinder be 14 inches,
the vertical altitude CL 12 feet a 144 inches, and 12 the
convolutions of the fpiral, the cylinder being fo placed that the
angle LAC is lefs than BED; the wight to be raiſed being a
48 lb. ball. Then the circumferene of the cylinder will be
nearly 44 inches, and the 12 turns equal to 12 × 44 528
= BÉ. Hence we have 528: 144 :: P: F::48:133
lbs. the
meafure of the requifite force at the furface of the cylinder.
If the moving force deferibe a circle whofe diameter is 3 times
that of the cylinder, or act at a wincl, whoſe diſtance from the
axis of motion is 21 inches, that force will then be reduced to
of 13 or 44 lbs. which is lefs that of the weight of the
ball. The friction upon the pivots, &c. is not here confidered.

I
To
Thus it appears that Archimedes's fcrew may be uſed for
other purpoſes than raifing of water. It might be adapted with
advantage in raifing cannon balls from a fhip to a wharf: and
with the addition of a bevel-wheel or two and their pinions,
might be worked either by men or horfes.
5. The helix folded about a cylinder is a curve fimilar in all
its parts; that is, all the demi-fpires, as AIC, CR, RS, are
fimilar and equal; it is alſo the ſame of the thirds, the fourths,
&c. of the fpires, and generally of all he equal portions of the
curve. But when the cylinder is incined, if we refer all the
points of a demi-fpire, fuch as AIC,by perpendiculars, to the
horizontal fection of the cylinder (vhich fection is elliptical,
though repreſented in fig. 7. pl. XXIV. by a right line AD to
prevent confufion in the diagram), we fhall find that this demi-
fpire has, with regard to the horizontal plane AD, a higheſt
point E, a loweſt point E, and a man point I. In order to
become acquainted with the effect of the fcrew in raiſing water,
it is important to determine theſe three points.
6. The mean point I is a point of inflection very eaſy to
determine. To this end put the diameter AB 2 r, the half-
circumference AMB = c, the abſéſſa AP = x, the indeter-
minate arc AMs, the ordinate ME of the ſpiral
= y; and
the height BC of a demi-ſpire = b. Hence, fince we may con-
fider the demi-fpire AIC as having been formed by the hypo-
thenuſe of a right-angled triangle, one leg of which is equal to
the half-circumference AMB, and the other equal to the line
BC, we have this proportion, AMB: BC: AMME, or c´: B


C
Archimedes's Screw.
SIT
sy; whence, s= , the fluxion of which is s
But by the nature of the circles = √(27-2²)
TI
*/ {2rx — x²)
сў
TJ
; fo that
cy. Therefore, following the ufual method
for points of inflexion, by taking the ſecond fluxions and fup-
pofing conſtant, we have
h r x x² — h r² x²
= ÿ = o, which
y
c₁(2rx-x²)
gives x = r, and indicates that the point of inflexion I is in the
middle of the demi-fpire AIC.
7. To find the higheft and loweſt points E, E', in addition to
the characters before uſed, put BD = a, and ADf: we
እያ
have from the foregoing article y, and the fimilar triangles
.C
ABD, APF, give AB: BD :: AP: PF, or 2 r:a::x:
PF. Therefore EF PE - PF =
ks
T
27; for fince we
confider PM as perpendicular to PE, it follows that ME and
hs
PE will be equal, and confequently PE = . The fimilar tri-
angles ABD, EFG, give AD : AB :: EF: EG, or, ƒ:2 ri:
= EG. This value of EG ought to
hs
a x 2 hrs
27
cƒ
a a
be a maximum; its fluxion, therefore, that is,
!
2 hrs
a x
cf
ƒ
But from the nature of the circle we have s
Subftituting for sin the preceding equation this value of it,
and reducing, we foon find x = r ±
a c
a² c² - 4 b² Ÿ².
Of these two values of x, the lower determines the value AP
*
書
​correſponding to the higheſt point E; the upper fhews the
value AP' correfponding to the loweſt point E'.
8. Through the higheſt point E having drawn the horizontal
plane EO, this plane will cut the demi-ſpire COS in the point O
fig. 8. pl. XXIV.), thus determining the arc ECO which carries
water, or as it is fometimes called the hydrophorous arc; for all
the points of this arc being below the points E, O, and theſe

C.
348
MACHINES.
two points being in the level of the furface, the water will be in
equilibrio in that arc. To find the magnitude, and of confe
quence the quantity of water carried by an hydrophorous arc,
the diameter of the tube which forms the fcrew being given, it is
evident that we have only now to determine the point O or
extremity of the arc ECO, the other extremity having been
found by the preceding article. In order to this, denote AB,
BD, by the fame letters as before; the variable abfciffa BQ by z,
and its are BN by: the line EF (found as in art. 7.), or its
equal OR put = e. Then the fimilar triangles ABD, AQR,
give AB BDAQ:QR, or 2 r:a::2r-z:
#
1
therefore QO
bic th⋅s
2 ar-
2 T
a 223
2 ar
2 T
az
=QR:
+ e. Now, by the property of the
frew, we have AMB: BC:: AMBN: NO, or ch::c+s:
= NO. But QO and NO being two lines perpen-
dicular to the baſe of the cylinder, and both of them terminat-
ing in the plane of the ellipfe, or of the cylindric fection EO, it
follows that QQ = NO; that is, from what has gone before,
C
zar—az
2ri.
hcths
+
+e= or²² + hs+b-a-e = o. As the re-
C
2.
27
folution of this equation depends upon the rectification of the
arcs, we can only fubftitute the value of s in terms of z, by an
infinite feries formed of z and its powers; where the refulting
equation becoming more and more complex and embarraffing,
as a greater number of terms of the ſeries is taken, we ſhould,
by purſuing it, be involved in a very long and tireſome opera-
tion: to avoid this we ſhall have recourſe to the following table
caculated by M. Pitot.
This table contains values of the arcs BN = s, correfponding
to thoſe of BQ➡z, given in parts of the diameter AB ± 213
divided in 200 parts. This granted, having found by the pre-
ceding article the value of e, we reduce b-a-e to one number
only, which let be reprefented by #: then have we
aiz
2 r
+
hs
C
Laftly, we take in the table different values of z and of the
correfponding arc, till we have difcovered that which renders
.ช
-h's
+ equal to the number », or nearly ſo.
To find the length of the hydrophorous arc ECO, having de
termined the arcs AM and BÑ, it is proper to obferve that, by
the formation of the fcrew (art. 2.), the length of one of the
demi-ſpires AEC is equal to the hypothenufe of a right-angled
Archimedes's Screw.
349*
triangle, of which. AMB=c, and BC= b are the legs: thus
bare
the demi-fpire AEC ce+bb. If now we put m for the
known arc MBN, we may take this analogy, viz. AMB AEC
:: MBN : ECO, or c : √ e² + b²³ : : m : "Ve² + b² ECO,
and thus obtain the value of the arc which carries the water, or
of the hydrophorous arc fought.
Table of arcs correſponding to parts of radius
divided into 100 equal parts.

Part of Ares in parts Arcs in deg.
Parts of Arcs in parts Arcs in deg.
Radius.
of radius.
and-niin.
radius..
of ra dius
and min.
I;
14:14:
8° 6'
18:
60.88
34 $4
2
20°
II 28
19
62.62
35.54
3
24.54
14 4
20
64'31
30 52°
4
28:35
1615
21
65.94
37 48
31*72
18 11
2 22
67*57°
38 44-
6
34.77
19 56
*23
69.17
39.39
37*59
2133
24
70°74
40 33.
40 24
23 4
25
72 73
41 25
9
* 42*71:
24 29
26
73.73.
42 16
10.
45'06:
25 50.
27
75*2x
43 7
II.
47.30
27 7.
28
76.66
43 57
P. 12 L
49 45
2821:
29
78.16%
44 46
:
1.3
5452.
2932
30
79°52
45*35.
14.
53°52
3041
31
80'90
46 22
15..
55'44
3547
32
82.25
47 9
16:
*
57.30
32.51
33.
83.62
47 56
17 1. 59:16:
33 55
9. Example of the calculation of an hydrophorous arc. For an
example of this kind of calculation for the length of the hydro-
phorus arc ECO, let us take the diameter AB 2 r of 200 -
parts, the height BC= 80 of the fame parts, BD =a=100
parts; then the femi-circumference AMB will be nearly 314
of thofe parts. Subftituting theſe values in the expreffion x =
√ a²c² - 4 b²² (art. 7.), there refults AP = 1345
of the fame parts: and by means of the table. juft given, the:
arc AMs, is found 53:3. Subftituting thefe values of x
and s in the equation
ks.
a x
=e, we find the value, e, of
EF or RO=6·86;·
350.
MACHINES.
¿
To have at the fame time the value of BQz, and of the
arc BN which we now calls; theſe values of a, b, c, 2 r and e
a % h s
muſt be ſubſtituted in the equation
2 T
to have z +
805
157
+
= a−b+e, ſo as
= 53°72. By means of the preceding table it
is foon found that BQ = z = 21, and BN = s = 66, very
nearly.
=
Then to find the arc MBN, which we have called m, we
have the whole arc AMBN = 314 + 66 = 380, from which de-
ducting the arc AM 53.3, there remains MBN m=326′7.
The length of the demi-fpire AEC =✔c² + b² = 324.03 :
and finally √²+b² = 337′13 the length of the hydrophor-
ous,arc ECO.
m
G
10. The diameter of the cylinder of the fcrew being given with
that of the tube which forms the fpiral, and the given length of the
fcrew, to find the quantity of water carried by the hydrophorous ares,
and the height to which the water is elevated, the inclination of the
fpiral being as before.
Let the diameter AB of the ſcrew be I foot, that of the fpiral
tube in which the water is raiſed 3 inches, and the length of the
fcrew 30 feet. This granted, to have the length in feet and
inches of an hydrophorous arc, fay, as the 200 parts of the
diameter of the table: I foot or 12 inches :: 337 13 before
found: 20:2278 inches, the real length of the hydrophorous arc.
Every fuch arc then carries a cylinder of water 3 inches di-
ameter and 20 2278 inches long. Let us next enquire how
many fuch arcs there will be in the whole length of the fcrew,
or 30 feet. It is evident, in the first place, that every turn or
convolution of the helix on the arbor of the fcrew carries one-
hydrophorous are: to find, therefore, the number of turns, it
must be obſerved that the height BC of one of the demi-fpires
is in our example 80 parts, or the height AS of an entire fpire
160 parts; the diameter AB of the bafe, which is r foot, being
200 of thofe parts: hence 200: 12:160:96 inches, the height
of one fpire. Dividing the inches in 30 feet by 9:6, the quotṛ-
ent gives more than 37 for the number of fpires; confequently
there will be 37 hydrophorous arcs. The quantity of water in
all thefe hydrophorous arcs is equal to the quantity in a cylinder
the diameter of whoſe baſe is 3 inches, and height=20°2278***
37748 4286 inches, or nearly 62 feet. Such a cylinder of
water is eafily found to weigh 191313 lbs. avoirdupois.
We have now to determine the vertical height to which the
Archimedes' Scretu.
351
!
fcrew we have taken pr an example will elevate the water: and
this may be accomplihed very eafily; for, the triangles ADB,
BYZ, being fimilar, we have AD: AB:: BY: YZ=26.833 feet.
Finally, under this lead, to find the angle which the arbor or
axle of this fcrew makes with the horizon, fay, as BD: BA::
rad.: tan. ADB = tal. YBZ the angle fought: thus the angle
YBZ is found 63°26'.
11. Computation of the force requifite to turn the fcrew.-In the
example we have talen, the weight of the water contained in
the 37 hydrophorous arcs being 191313 lbs. to find the force
neceffary to be applied at the circumference of the cylinder, we
muft fay, according to the rule in art. 4. as 37 times the cir-
cumference of the cylinder's bafe (= 1395 714 inches) is to
the vertical height through which the water is elevated (= 26f.
10i. = 322 inches), o is the weight of water (=191-313 lbs.)
to the weight 44'14 lbs. equivalent to the force which must be
applied to the circumference of the fcrew to keep it in motion
when once it has begun to turn. But if this force or power,
inſtead of being applied at the circumference of the fcrew, acts
by a handle and winch at the diſtance of 10 inches from the
axis of the cylinder, the requifite force will only be 1% or 3 of
the former; it will, therefore, be 26:48 lbs.
•
+
12. Computation of the quantity of water which the fcrew will
raife in a given time. To find the quantity of water raifed by
the fcrew propofed as our example, we muſt know the velocity
with which the affigned force carries round the handle. Sup-
pofe, for inftance, the handle, and confequently the ſcrew,
makes one rotation in 5 feconds, it is very manifeft the ſcrew
will then expel the quantity of water contained in 1 hydro-
phorous arc in 5 feconds; and in 37 times 5 feconds, that is 185
feconds or 35, it will raiſe a quantity weighing 191.313 lbs.
To find the quantity raiſed in an hour, fay, as 185: 3000
(feconds in an hour):: 191313: 3719 lbs. nearly. Or, if the
quantity be calculated in ale gallons, it will be found equal to
364 62. If the velocity with which the handle is moved be
tripled, which it may be, without rendering the work too
fatiguing, the quantity raiſed will be tripled, and nearly 1094
gallons will be raiſed 26 feet 10 inches, in an hour. This
coincides very nearly with Defaguliers's eſtimate of the water
which a man can raiſe by almoſt any hydraulic engine.
1
#5
气
​13. Having dwelt thus long upon the theory of Archimedes's
fcrew, but little remains to complete our obfervations. It is
obvious from what has been remarked, that this fcrew can never
raiſe water when the angle which the central line of the ſpiral
makes with the baſe of the cylinder is larger than the angle
included between the bafe of the cylinder and the horizon; that
152
MACHINES.
+

is, it is always neceflary that BAZ fhoull be equal to, if not
greater than, BED (fig. 6. pl. XXIV). In practice, indeed, it
is advifeable that CAL be between 40° anc60°, and BAZ – BED
between 10 and 20°. The mean of boh thefe is moft to be
recommended.
Sometimes Archimedes's fcrew, infteal of being worked by
men at a winch, is turned by means of flat-boards fixed about
the circumference of its lower end, upon which a ſtream of
water acts: if the water have a moderae fall,, it will have
fufficient efficacy to turn two fcrews, ont above another; the
top of the lower fcrew and the bottom of the upper fcrew may
act, the one upon the other, by means of a wheel upon each.
with an equal number of teeth taking into each other: in this,
cafe the upper fcrew will turn in a contrary direction from the
other, and confequently the fpiral tube nuft be wound about
the cylinder in an oppofite direction. A folid wheel, or a light
wheel with a heavy rim, turning upon the middle of the fcrew.
as an axis, will operate like a fly, and ir fome cafes be very
uſeful.
In the preceding inveſtigations no notice has been taken of
the effects of the air included in the ſpiral: yet if the fpiral had
been folded upon a cone inſtead of a cylinder, or if it had been
formed of a flexible tube of varying diameter, theſe effects
would have been important: fome of them are confidered in our
account of the ſpiral pump. See Hydraulic Machines, No. 10.
a
Z
SHOEMAKERS' IMPLEMENT, to enable them to work in a
funding pofture. This inftrument has been lately contrived by
Mr. Thomas Holden of Fettleworth, Suffex, and its inventor
has been rewarded with fifteen guineas by the Society of Arts..
It reſembles a ſtand, fuch as is ufed for reading-deſks at the
top of which is a ſmall block of wood, excarated fo as to
proper bed for the laft, and the moulds or nftruments uſed in
making boots, which are kept firm upon it, by a ftirrup or
endlefs ftrap. The hollow block is joined into another piece
(which connects it to the ftand), fo as to admit of a vertical
motion, and it is retained, at any angle, in this motion, by a
circular eatch, with notches formed in its fide, to faften it on
an iron catch projecting from the lower piece. This lower
piece is thaped into a fmall cylinder beneath, which entering
into a hole formed for it in the top of the pillar of the ftand,
permits the hollow block to be moved round about, without
ftirring the ftand; fo that, by the combination of theſe two
motions, it may be placed in any pofition. Behind the hollow
block, and on a level with it, an horizontal piece of board is
fupported by a fmall pillar, rifing from one of the feet of the..
ftand, and fecured firmly by a brace to the ftand itfelf; this board

Steam Engines.
353-
fupports the tools and implements wanted,ready at hand for
the workman's uſe.
The defign of this invention is to obviate the neceffity of
ufing that very unwholeſome poſture in which fhoemakers are
accuſtomed to work; which compreffes the lungs and bowels in
fuch a manner, as to occafion.confumption, inflammation of
the bowels, and a variety of other frightful complaints.
The efficacy of the alteration of pofture permitted by this
inftrument, which enables the workman to ftand at his work, is
very well proved in the caſe of the inventor of it; who has
produced a medical certificate, that he was, for many years, fo
afflicted with bowel complaints and piles, that he was under the
neceffity of leaving off his trade entirely, if he could not contrive
to work flanding; and that, fince he has made uſe of this
implement, his complaints are entirely removed, and he is fo
improved in fleſh and countenance, that he “looks not like the
fame man ;" and, for fome years, has had no occafion for
medicine. He has made many hundred pair of fhoes on this
ftand, and recommends alfo its uſe, as "the quickeſt way of
clofing all the thread work.”
This implement might be made ftill more fimple, by leaving
out the part uſed to give the hollow block a circular motion,
which does not appear always neceffary, from the facility which
the workman has, when ſtanding at it, to place himſelf inſtantly
at any fide of the work he pleaſes; it would, as appears to us,
be full as little, if not lefs, trouble to him to let the inftrument
remain unmoved, and turn himſelf round inſtead of it, as to
ftand ſtill while he turned it about: though a ſmall quantity of
light confined to one direction may in fome cafes render the
increaſed apparatus neceffary.
A wooden vice of a proper height, fixed to a ſtake, and
fecured even by a wedge, if a fcrew fhould be deemed ex-
penfive, would alſo hold a laft in any pofition required for the
workman.
Theſe additional obfervations are given, becauſe any con-
trivance which will enable fhoemakers to work in poſtures lefs
injurious to their health muſt be confidered as important and
valuable and whatever may fuggeft to the workman cheap
inftruments for this purpofe, eafily conftructed, and pleaſant in
the practice, cannot but be beneficial to the public.
SIPHON. See CRANE.
i
SPIRAL-PUMP, at Zurich. See HYDRAULIC Engines. No. 10.
STEAM-ENGINE, an engine originally contrived for raifing
water by means of the expanfive force of the fteam or vapour
produced from water or other liquids in a ſtate of ebullition.
This has been often called the Fire-engine, becauſe of the fire
voi ir.
A A
354
MACHINES.
uſed in boiling the liquid; but the latter term has, of late, been
properly confined to machines for extinguifhing fires. The
fteam-engine is juftly deemed one of the moſt curious, im-
portant, and ferviceable mechanical inventions, not only of
modern, but of any, times; particularly when it is conſidered
with regard to fome of its late improvements, which render it
applicable to all kinds of mill-work, to planing, fawing, boring,
and rolling machines, and indeed to almost every purpoſe that
requires a powerful firſt-mover, whofe energy may be modified
at the pleaſure of the mechanift.
The principles and manner of operation of the ſteam-engines
of Savery, Newcomen and Cawley, and of Watt, may be under-
food from the following brief explanations and remarks, which
are meant as preparatory to the more detailed accounts of
feveral engines with which we have been favoured.
1. Let there be a fucking pipe with a valve opening upwards
at the top, communicating with a clofe veffel of water, not more
than thirty-three feet above the level of the refervoir, and the
team of boiling water be thrown on the furface of the water in
the veffel, it will force it to a height as much greater than
thirty-three feet as the elaftic force of the fteam is greater than
that of air; and if the fteam be condenfed by the injection of
cold water, and a vacuum thus formed, the veffel will be filled
from the reſervoir by the preffure of the atmoſphere; and the
fteam being admitted as before, this water will alſo be forced
up; and fo on fucceffively.
1
Such is the principle of the firſt ſteam-engine, ſaid by the
English to be invented by the marquis of Worcester; while the
French afcribe it to Papin: though we believe the fact is that
Brancas, an Italian, applied the force of ſteam ejected from a
large œlopile as an impelling power for a ftamping-engine fo
early as 1629. The hint fo obfcurely exhibited in the marquis
of Worcester's Century of Inventions was carried into effect by
captain Savery.
2. If the team be admitted into the bottom of a hollow
cylinder, to which a folid piſton is adapted, the piſton will be
forced upwards by the difference between the elaftic forces of
fteam and common air; and the fteam being then condenfed,
the piston will defcend by the preffure of the atmoſphere, and
fo on fucceffively. This is the principle of the fteam-engine.
first contrived by Meffieurs Newcomen and Cawley, of Dartmouth.
This is fometimes called the atmoſpherical engine, and is com-
monly a forcing-pump, having its rod fixed to one end of a
lever, which is worked by the weight of the atmoſphere upon a
pifton at the other end, a temporary vacuum being made below
it by fuddenly condenſing the ſteam, that had been admitted
Steam-Engines.
355
into the cylinder in which this piſton works, by a jet of cold
water thrown into it. A partial vacuum being thus made, the
weight of the atmoſphere preffes down the piſton, and raiſes the
other end of the ftraight lever, together with the water, from the
well. Then immediately a hole is uncovered in the bottom of
the cylinder, by which a freſh quantity of hot ſteam ruſhes in
from a boiler of water below it, which proving a counterbalance
for the atmoſphere above the pifton, the weight of the pump-
rods, at the other end of the lever, carries that end down, and
raiſes the pifton of the fteam-cylinder. The fteam hole is then
immediately fhut, and a cock opened for injecting the cold
water into the cylinder of ſteam, which condenſes it to water
again, and thus making a vacuum below the piſton, the atmo-
fphere again preffes it down and raifes the pump-rods, as before;
and fo on continually.
3. The great features of improvement made by Mr. Watt
upon the engine of Newcomen and Cawley are, as Mr.
Nicholſon remarks, firft, that the elaſticity of the ſteam itſelf is
uſed as the active power in this engine; and fecondly, that
befides various other judicious arrangements for the economy
of heat, he condenſes the ſteam, not in the cylinder, but in a
ſeparate veffel.
In the cylinder or fyringe, concerning which we have ſpoken,
in mentioning the engine of Newcomen, let us fuppofe the
upper part to be clofed, and the pifton-rod to flide air-tight
through a collar of leathers. In this fituation, it is evident that
the piſton might be depreffed by throwing the fteam upon its
upper furface, through an aperture at the fuperior end of the
cylinder. But if we fuppofe the external air to have acceſs to
the lower furface of the piſton, we fhall find that ſteam no
ftronger in its elafticity than to equal the weight of the atmo-
ſphere would not move the pifton at all; and confequently that
this new engine would require much denfer fteam, and con-
fume much more fuel than the old engine. The remedy for
this evil is to maintain a conftant vacuum beneath the piſton.
If fuch a vacuum were originally produced by fteam, it is
certain that its permanency could not be depended on, unleſs
the engine contained a provifion for conftantly keeping it up.
Mr. Watt's contrivance in his fimpleft engine is as follows: The
fteam is conveyed from the boiler to the upper part of the
cylinder through a pipe, which alfo communicates occafionally
with the lower part, and beyond that ſpace with a veffel im-
merſed in a trough of water; in which veffel the condenſation
is performed by an injected ftream of cold water. This water
is drawn off, not by an eduction-pipe but by a pump, of which
A A 2
356
MACHINES.
the ſtroke is fufficiently capacious to leave room for the elaſtic
fluid, feparated during the injection, to follow and be carried
out with the injection water. Suppoſe now the piſton to be at
its greateſt elevation, and the communication from the boiler to
the upper as well as to the lower parts of the cylinder to be
opened. The ſteam will then paſs into the whole internal part
of the engine, and will drive the air downwards into the con-
denfer, and thence through the valves of the air-pump. In this
fituation, if the communication from the boiler to the lower part
of the cylinder be ftopped, and an injection be made into the
condenfer, a vacuum will be produced in that veffel, and the
fteam contained in the lower part of the cylinder and com-
munication pipe will expand itſelf with wonderful rapidity
towards the condenſer, ſo that in a period of time too minute to
be appreciated the whole of the fteam beneath the pifton will
be practically condenfed. The fteam which continues to act
above the piston will immediately depreſs it into the vacuum
beneath; at the fame time that by connection with the external
apparatus the piſton of the air-pump alfo defcends in its barrel.
When the ſtroke is nearly completed downwards, the requifite
part of the apparatus fhuts the communication with the boiler,
opens that between the upper and lower parts of the cylinder
and condensing veffel, and turns the injection-cock. At this
very.inftant the pifton lofes its tendency to defcend, becauſe the
fteam preffes equally on both furfaces, and continues its equality
of preffure while the condenſation is performed. It therefore
rifes; the injection is stopped; and the air-pump making its
ſtroke, fuffers the injection water and a confiderable part of the
elaftic fluid to paſs through its lower valve. The vacuum is
thus kept up through the whole internal capacity of the engine.
As foon as the pifton has reached the upper part of the
cylinder, the communication to the under part of the cylinder is
ftopped, and that with the boiler opened, as before; the confe-
quence of which is, that the piston again defcends; and in this
manner the alternations repeatedly take place.
The principal augmentation of power in this engine, com-
pared with that of Newcomen, arifes from the cylinder not
being cooled by the injection water, from its being practicable
to ufe fteam, which is more powerful than the preffure of the
atmoſphere, and from the employing of this team both to
elevate and to deprefs the pifton. In general, theſe engines are
worked by fteam, which would ſupport a column of four or five
inches of mercury befides the preffure of the atmoſphere, and
ſometimes more, for Mr. Nicholſon fays, he has fometimes
feen the gage as high as eight inches. Mr. Watt has made
Steam-Engines.
357
ſeveral fucceffive modifications and additions to the engine juft
defcribed, ſome of which will be further ſpoken of in the courſe
of this article.
4. It has been cuſtomary, when treating of fteam-engines,
to preſent ſeveral theorems for the computation of their power
and effects. But as all which has hitherto been advanced on
theſe points feems to us very vague and unfatisfactory, we ſhall
not delude the ftudent with an appearance of mathematical
accuracy, when it is fo far from being attained. It is obvious
enough that the abfolute power of a ſteam-engine is in the
compound ratio of the area of the pifton, the preffure upon
each inch of it, the length of the ftroke, and the number of
ftrokes in any affigned time: but the preffure upon any portion
of the piston can only be afcertained by experiment and ob-
fervation, and that with difficulty, becaufe of our uncertain
methods of eſtimating friction and other ſpecies of refistance;
while judicious obfervations would with much leſs labour
determine the work actually performed, either when the ſteam-
engine works pumps, or gives motion to any kind of mills.
The quantity of water raiſed by pumps in a given time may
foon be eſtimated; and when the alternating motion of the
fteam-piſton is converted into a rotatory one, the real effect the
engine is capable of producing may be aſcertained by obſerving
the velocity with which a given weight is raiſed when fufpended
from the axle to which the rotation is firſt given.
The ufual method of eſtimating the effects of engines by
what are called "horfe powers" muft inevitably be very
fallacious, unleſs all engineers could agree as to the quantity of
work which they would arbitrarily affign to one horſe, and in
that cafe the term would manifeftly be nugatory. It may alſo
be obferved, that in determining the comparative value of
different fteam-engines, it is not fufficient to compare the
quantities of work each will perform in equal times; for the
expence of erection, the probability of repairs being more or
leſs frequent on account of the complexnefs or fimplicity of
conſtruction, and the quantities of fuel confumed by each, muſt
likewife be taken into the account.
Thefe particulars might eafily be enlarged upon : but it will
probably be more beneficial to the reader if we now ſuſpend
our own remarks, in order to preſent them with the communi-
cations with which we have been favoured: thefe are, one from
Mr. J. C. Hornblower, engineer, containing a ſketch of the later
hiftory, with deſcriptions of the principal engines; another from
Mr. 7. Farey, jun. of Crown-ftreet, Weltminfter (a young
gentleman of remarkable mechanical attainments), being an
358.
MACHINES.
J
account of an engine erected in 1802 by Meffrs. Murray and
Wood, of Leeds.
I. It is remarkable that we have nothing handed to us on this
fubject that is worthy of our reception, notwithſtanding the
number of our Cyclopedias and Encyclopedias, unleſs it be what
is publiſhed in the Minor's Friend by Mr. Thomas Savery, and
afterwards in Harris's Lexicon Technicum; and thefe, but efpe-
cially the former, with all the frankneſs and faithfulneſs of
undiſguiſed fact, have put to the bluſh thoſe pompous conceits
and abfurdities that have either wilfully or ignorantly been
trumped up to allure the undiſcerning multitude, or to prattle
the praiſe of the ingenious inventors.
It will be unneceffary to go over the ground already beaten ſo
bare by Defaguliers and his followers, though there are ſome
things which do deferve notice. The first thing is as to the
degree of credit that is to be attached to the doctor's account of
what paffed in the fucceffive improvements of what was then,
and for a long while after, called the fire-engine. No doubt
there were many accidental diſcoveries in the improvement of
this as well as other pieces of machinery; and it cannot be a
reflection on the underſtanding of any man when we are told
that it is in this way that many, if not moſt, of our acquifitions
in chemiſtry and experimental philoſophy are brought to light;
forcing themſelves, as it were, upon us, challenging our judg-
ment and humbling our pride. But to proceed. The doctor has
met with an unhappy inftance of this fort when he tells us
that the way of leathering the pifton was found out by accident,
which he relates thus: "Having ſcrewed a large broad piece of
leather to the pifton, which turned up the fides of the cylinder
two or three inches, in working it wore through and cut that
piece from the other, which falling flat on the pifton wrought
with its edge to the cylinder, and, having been in a long time, was
worn very narrow: which being taken out, they had the happy
difcovery whereby they found that a bridle rein, or even a foft
thick piece of rope or match going round, would make the piſton
air and water tight." We need not fay any thing to the
practical engineer about leathering a team-pifton, nor is it ne
ceffary to comment on the doctor's acquaintance with ſteam
and leather in contact. The next thing is the refult of an
experiment made by Mr. Beighton to determine the bulk of
ſuch ſteam uſually applied to working a fire-engine, in com-
pariſon with the bulk of water which produces it, which he
Steam-Engines.
359
makes out to be as 13338 to 1; and our bookmakers, in their
expanding regard to the interefts of the rifing generation, have
quoted this experiment one edition after another, till it is
doubtful whether it will be poffible to undeceive them. Nay,
the editor of the Encyclopedia Britannica has improved upon
this eſtimate, and calls it 14000 to 1.
191
16
But let us ſee what it is according to the data we can collect
from Mr. Beighton's ſtatement. Griff cylinder held 113
gallons, wrought 16 ftrokes per minute, and took 5 pints of
water to ſupply ſteam for that number of ſtrokes, each pint
containing 38.2 inches. Now 38.2 x 5 = 191 inches in 5
pints; 12, the number of inches required to make ſteam
for 1 ftroke. Then 113× 282=the inches contained in the
cylinder=31866, and this divided by 12 gives 26551, the number
of times the water is rarefied, or as 2655 to 1. But this being an
atmoſpherical engine expoſed to all the defects which we have
been fo anxious to improve, muſt have given a very different re-
fult: this being even more than what may be obſerved in fome of
the moſt improved engines of the prefent time. In fhort, little
dependence muſt be placed on the relation of experiments at fo
remote a period, or even on the experiments themſelves, being
in general very looſely conducted. But it ſeems rather fingular
that at the firſt dawn of the fteam-engine its principles and
mode of operation ſhould be related with ſo much more accuracy
than what fucceeded it, or even at any period of improvement is
to be found any where in print, at leaſt in this country.
However, we may ceaſe our recurrence to thefe former times,
which, though they afforded examples of indefatigable zeal and
ardour in the purſuit of a prime object, yet we perceive little
ſketch of thought, little difplay of genius, and a fond conclufion
that when one of their favourite defiderata had been accom-
pliſhed, there remained nothing more of much conſequence
even to wish for. Friction and inertia were become the moſt
important objects to be done away; except that fome different
modes of condenſation had been tried, but with little effect.
The principal of them were to keep the jet from applying itſelf
to the fides of the cylinder: for this purpoſe a plate of iron was
placed horizontally over the aperture of the injection-pipe, fo
as to prevent the water from ftriking the bottom of the pifton,
and being thereby diſperſed over the lower part of the cylinder:
but it was found that it would not produce fo prompt a con-
denfation as the general mode. Another mode was tried alfo,
which was to form the nether fide of the pifton into a ſort of
inverted cup, nearly the whole area of the pifton, and the jet
was thrown up into it. This produced a remarkable change
660
MACHINES.
in the temperature of the cylinder, and preferved all the
advantages of the former mode of injection: but no ſucceſs was
obtained in point of power, for the vacuum was as incomplete
as before; occafioned by the fides of the cylinder being con-
ſtantly layed by the water on the pifton, and the temperature of
the cylinder being raiſed ſo much above what it was before. In
the common method of injection there was an inſtantaneous
generation of vapour from the fides of the cylinder, which could
not fail to vitiate the vacuum; added to that, the water in the
pifton wherever it was a tight one (which was feldom the cafe)
grew hot, and the vapour carried off a deal of heat; and no
attempts were made to prevent theſe unexpected effects. Many
projects were fuggefted for the improvement of boilers, fome
of which fucceeded, and are ſtill in ufe: but the great obſtacle
was referved to be overcome by. Mr. Watt.
It is neceffary. here to obferve, that hitherto the mode of
boring cylinders was the moft vile that can be imagined. The
way ufually was, at fome of our first founderies, to put the
cylinder on a carriage, infert the cutter block, fet the mill a
going, hang a cloth at the open end to keep in the duft,
and let it bore away, which it would be doing on a large
cylinder for three weeks, or a month: and if it was tolerably
fmooth, it was faid to be well done. But this was not all: in
thoſe engines which were dependent on the water drawn from
the mine for the condenſation of the fteam, the fides of the
cylinder were corroded in a few months in fuch a manner that
no kind of packing could keep the piſton tight; and as theſe
inconveniences increaſed like a fpreading ulcer, it became
neceffary to ram the packing fo hard, as in many cafes to
fuftain the whole preffure of the atmoſphere without making one
ftroke: all the while a cock of at leaft a round inch water-way
from a cistern 12 feet high was neceffary to fupply the leaking
of the piston. This was not the cafe in collieries, or any-where
befide thoſe mines the water of which contained the vitriolic
acid; but fo great was that at fome mines, that wherever the
water fell on the working gear, or any other part conftructed of
iron, it had the appearance of being fabricated from copper
intirely.
·
It was in this ſtate of things that Mr. Watt brought forth his
improvement, when he engaged to grant licences to uſe his
engines for the confideration of receiving one third part of the
profits arifing from the abatement of coal uſually confumed in
the miferable ſtate of the old engines; and the favings turned
out to be very advantageous, but more to him than to the pro-
prietors for there opened other channels of expenditure on the
new engines which were not taken into the account, and which
Steam-Engines.
361
5
1
овам
were never heard of in the account of the old ones. Firſt, in
the expence of erection, which was generally cent per cent
above the coſt of the old engines; and fecondly, the monthly
expence for maintainance; for as there was a neceffary degree
of accuracy to be obſerved in getting up the various apparatus
belonging to them, ſo it was neceſſary that this accuracy ſhould
be preſerved: this made a difference in the pay of thoſe perfons
who had the care of the engines. To this was added a con-
fiderable conſumption of oil and tallow over and above what
was common to the old way of working; fo that it has been
more than mere conjecture that had they the advantages of the
improvements in boring cylinders and in fitting up the other
acting parts of the engine on the atmoſpherical principle, they
would have been benefited nearly as much as they were by the
new improvement. Here too we muſt be allowed to obſerve,
that much of the merit aſcribed to the fertile mind of Mr. Watt
really originated with Mr. John Wilkinfon, who was always
foremoſt in the improvement of any thing which related to the
iron foundery. It was there the true method of boring cylinders
originated, and they were executed in a manner which has not
fince admitted of improvement; and whatever may be affirmed
of the eminence of Mr. Watt as an engineer, it is ftill in the
minds of fome yet in exiſtence that the firft engines which were
erected, particularly the Bloomfield engine, and the engine at
Bedworth, exhibited but miſerable fpecimens of his mechanical
abilities. This declaration is confirmed by his own confeffion
in his application to the parliament for an extenfion of the term
of his patent, where he ſays, on account of the many diffi-
culties which always arife in the execution of fuch large and
complex machines, and of the long time requifite to make the
neceffary trials, he could not complete his intention until 1774,"
though he had his patent in January, 1769; nor muſt it be
forgotten, that fome fterling acknowledgments are due to Mr.
Watt's coadjutors, of which he availed himſelf in a region of
rare talents*.
r
Nevertheleſs, let it be remarked that Mr. Watt took up the
fubject of improvement with a large and important object in
view; it was not only to renovate the principle, but to affimilate
this moft grand affemblage of philofophical and mechanical ſkill
to thoſe machines which, on a fmaller fcale, had hitherto
engroffed the talents of our moſt ingenious artificers, and been
the admiration of other nations wherever they came ; nor do we
* Thefe obfervations had not come into view, if it had not been for
the partial, yea fulfome, compliments paid to this gentleman by the
writer of the article fteam-engine in the Encyclopedia Britannica.
362
MACHINES.
mean to withhold the acknowledgment, that through his means
it now ranks foremost among the productions of the philofo-
phical or mechanical world.
In this ſhort hiftory, however, we must not omit to notice
a circumſtance known but to few. About the time that Mr.
Watt was engaged in bringing forward the improvement of the
engine, it occurred to Mr. Gainsborough, the paftor of a dif-
fenting congregation at Henly-upon-Thames, and brother to
the painter of that name, that it would be a great improvement
to condenſe the ſteam in a veffel diftinct from the cylinder,
where the vacuum was formed: and he undertook a fet of
experiments to apply the principle he had eſtabliſhed; which he
did by placing a ſmall veffel by the fide of the cylinder, which
was to receive juft fo much ſteam from the boiler as would
diſcharge the air and condenfing water in the fame manner as
was the practice from the cylinder itſelf in the Newcomenian
method; that is, by the fnifting valve and finking pipe. In this
manner he uſed no more ſteam than was juſt neceffary for that
particular purpoſe, which, at the inſtant of diſcharging, was
entirely uncommunicated with the main cylinder; fo that the
cylinder was kept conftantly as hot as the ſteam could make it.
Whether he clothed the cylinder as Mr. Watt does is un-
certain but his model fucceeded fo well as to induce fome of
the Cornifh adventurers to fend their engineer to examine it;
and the report was fo favourable as induced an intention of
adopting it. This, however, was foon after Mr. Watt had his
act of parliament paffed for the extenfion of his term; and he
had about the fame time made propoſals to the Cornifh gentle-
men to fend his engine into that country. This neceffarily
brought on a competition, in which Mr. Watt fucceeded; but it
was afferted by Mr. Gainsborough, that the mode of condenſing
out of the cylinder was communicated to Mr. Watt by the
officious folly of an acquaintance, who was fully informed of
what Mr. Gainsborough had in hand. This circumftance, as
here related, receives fome confirmation by a declaration of Mr.
Gainsborough the painter to Mr. S. More, late fecretary to the
Society for the Encouragement of the Arts, who gave the writer
of this article the information; and it is well known that Mr.
Gainsborough oppoſed the petition to the houſe of commons
through the intereft of general Conway.
Perhaps it may not be unacceptable to mention, that before
this period an attempt was made to drain the deep mines in.
Cornwall by a new application of Savery's engine, for which
patent had been obtained by Mr. William Blakey, who pro-
poſed to employ the expanfive force of fteam, with an inter-
medium of air between it and the water; this air was to ferve
Blakey's Steam-Engines.
363
as a means of preventing the condenfation of the fteam, by
keeping it from coming in contact with the water.
Great con-
tention aroſe among fome of thoſe who counted themſelves
men of ſcience as to the practicability of fuch a project: fome
giving it as their opinion, that if the principle were to be ad-
mitted it would be very difficult to apply it in mines, where it
would require ten atmoſpheres at leaft: while others, with
exalted pretenfions, declared it poffible to conduct its influence
to the centre of the earth. But an accident terminated the event
as to this engine in Cornwall, by one of the ſteam-veffels burft-
ing through the force of the ſteam, though much under the de-
gree of power required for the end propofed to the Cornifh
gentlemen. This being the first date of the application of
trong fteam to raiſing water, and, by an eaſy tranſition, to do
any thing elſe, we fhall give a ſketch of the boiler and fire-
place of this engine, copied from the author's ſmall tract on the
fubject, publiſhed in French at the Hague, in 1776; (ſee fig. 9.
pl. XXIII.) by which it will be feen, that the method of ge-
nerating ſteam lately publiſhed in the Philofophical Magazine
has been made ufe of nearly thirty years ago, and has nearly as
long fince received its final condemnation: but fuch is the de
generacy of man, that while the Academy of Sciences at Paris,
and the delegates of the ftates-general in Holland, were plum-
ing the author with the gaudieft expreffions of their approbation,
not one inſtance can be found where he received the encourage-
ment he was led to expect.
But ftill this engine is no other than Savery's engine, fur-
niſhed with apparatus intended to open and thut the ufual
communications by cocks and valves. The fame may be faid
of Papin's and Defaguliers's engines; they were all nothing elſe
than Savery's, without the advantage which Blakey had con-
nected to it; and had nothing but a mere nick-name to conceal
their legitimacy.
As to the application of the expanfive power of the ſteam to
the purpoſe fet forth by Mr. Blakey, or indeed we may ſay by
Mr.Savery, it was by no means an impoffible thing; but the diffi-
culty would not be here to obtain veffels capable of refifting the
action of ten atmoſpheres, but how to preſerve them in a ſtate
of fecurity, the decay of veffels placed in circumſtances like
thefe, which cannot be acceffible to the inſpection of the moſt
diligent attendant, and the conftant anticipation of probable evil
circumſtances, muſt render life painful to endure. But there is
another cafe which ought to be noticed, viz. the difficulty of
preſerving the ſteam in the degree of temperature by which it
was generated; for it is well known that it is condenfible to a
very great degree by the common temperature indicated by the
364
MACHINES.
thermometer; and this extent of expanfibility is not to be ob-
tained without the acceffion of a fuperadded quantity of heat.
Then, unless the veffels in which the fteam is to operate are
kept up to that temperature, the extra expanſion is annihilated.
We have heard of patents being paffed for this mode of uſing
fteam; but we never heard that we were to be forbid to uſe ſteam
of any particular intenſity, efpecially where cafes quite unexpected
have compelled engineers to the prompt uſe of it as a neceffary
expedient; and we ſhould imagine that, after reading Mr.
Watt's fpecification of 1769, no perſon would attempt a mono-
poly of the uſe of ſteam at any intenſity whatever.
It ſhould be obſerved, that in treating on the principle and
operation of the atmoſpherical engine thoſe who have taken up
the fubject have done it in a very loofe and imperfect manner,
fo far as relates to the power and effect; accounting for the
lofs of the former and want of the latter from falfe premiſes:
but we ſhall adjuſt that matter in a review of what has been
publifhed in the Encyclopedia Britannica, of the improvement
of the fteam-engine by Mr. Watt. This article Teems to have
been written for a different purpofe than merely to inform the
public of the gradations and accidents by which Mr. Watt ac-
compliſhed his projected improvement; and either the writer
muft have been misinformed, or he had greatly mifunderflood
the fubject.
It has been an egregious error among thoſe who have taken
upon them to difcriminate the defects of Newcomen's engine, by
expreffing the effect for the power, faying, that the application
of the principle to the purpoſe of pumping, &c. will not admit
of more than feven or at moft feven and one-half pounds per
inch in the area of the pifton: but this is evidently a looſe un-
guarded expreffion; for it is well known, that by attending to
the various lifts of pumps in the engine-fhaft of a coal or a
copper mine, taking into the account the altitudes and the dia-
meters, the friction of the buckets, and the water on the fides
of the pumps, the opening of ftrong double-leathered valves,
together with the ftones and gravel that enter at the foot of the
pump, the inertia of the pump-rods, the chains, the maflive
lever placed between the cylinder and the pumps, all operating
against this feven and one-half pound, if it were only fo, muft
have produced a very different effect to what has been done:
The fact is, that with all thefe impediments, added to the fric-
tion of the pifton in a very bad cylinder, the columns of water
only have been equal to feven and one-half pounds per fquare
inch on the pifton. This could not have been accompliſhed by
fuch a vacuum as afforded only a preffure of ſeven and one-half
pounds per square inch on the pifton.
Atmoſpherical Steam-Engines.
365
This has alſo been the outcry againſt the various attempts to
improve boilers and fire-places; and the queſtion ufually was,
on the report of fuch a new boiler being fet, " How many
pounds do you get to the inch ?" Surely it cannot but excite
admiration, that the queſtion feldom or ever came to, " What
can you do with a chaldron of coals ?"
Another fubject of complaint has been the neceffity of a
counter-weight to return the piſton for another ftroke: this has
been very ſeriouſly diſcuffed by many who have had opportu-
nities of feeing an engine in their fummer's tour; and very in-
genious formula have been invented to enable the practical en-
gineer to come at the maximum of effect in engines particu-
larly circumſtanced in this refpect: and we are congratulated
on the annihilation of the injurious effects attendant on this
matter in the old engines by the improvements of Mr. Watt.
We are by no means difpofed to detract one atom from the
advantages refulting to the community through the perfection.
of Mr. Watt's engine: but we fee it made ufe of for invidious
purpoſes; not to elevate Mr. Watt above his inherent merit,
but to fubordinate every other profeſſional man in the ſcale of
compariſon, to reprefs the energies of his cotemporaries, and
give a deadly blow to competition.
The operation of the counter-weight in the atmoſpherical
engine is not affected in the manner this writer has fet forth:
it may be fo, indeed, in an engine conftructed on purpoſe for
amuſement or experiment; but we have to do only with en-
gines prepared to fome important execution, many particulars of
which muft fubmit to exifting circumſtances.
If we underſtand the precife meaning of the writer of this
article in the Encyclopedia Britannica, it is, that in atmoſphe-
rical engines the weight on the outer end of the lever is em-
ployed to overcome part of the preffure of the atmoſphere at the
return of the ſtroke of the engine: that is not the cafe, and we
muft first of all confider what is the defign of the engineer in
giving or allowing a preponderance to that end of the lever. It
is fimply that the buckets may deſcend, and the piſton may rife
without any further combination of apparatus employed for
that purpoſe. Now let us obferve its operation in an engine
juſt erected; in which cafe the mathematician and the unlet-
tered artift ftand on the fame level in eftimating the quantum
of outſide ballaſt for the engine, with the water already up to
the top of the pumps, or in other words to the level of the
adit. But the fteam being admitted into the cylinder, the ope-
rator fhuts the fteam-cock, and without any injection the en-
gine makes a firſt ftroke, though very quietly: perhaps he then
gives ſteam again to the cylinder, and according as he feels the
366
MACHINES.
pifton's tendency to rife, he ſuits his judgment to the degree of
opening in the cock: if it rifes too slow, he puts old iron
or ftones
upon the
pump end of the lever; and if it riſes too
quick, he places theſe weights on the inner end. Here then are
three important circumftances to be attended to in this regula-
tion: first, that the pump-buckets fhall defcend, but without
fuch force as fhall endanger the breaking of the pump-rods;
fecondly, that this deſcent ſhall nevertheleſs be as quick as pof-
fible; but, thirdly, that it fhall not impede the diſcharging
functions of the engine: and here are three caſes before which
the vulgar ſtoker may turn up his nofe at the acuteſt mathema-
tician in the world; cafes to which the higher powers of the
human mind muft bend in filent fubjection to mere mechanical
inftin&t.
It is the first object (when an engine is erected on a mine),
to get out the water with the leaft delay poffible; and at this
time the engine goes ding dong, night and day: but as the water
gets down, this counter-weight must be adjuſted, if the rods
were hung on for more than one lift of pumps: the principal
thing within the engine indicating the neceffity of this adjuſt-
ment is the discharging of the engine, getting rid of the air and
condenfing water; and unleſs theſe are performed punctually
the engine foon ceafes to work. Now, neither the air nor the
water can be diſcharged inftantaneoufly, but require a certain
time in proportion to the quantity of each and the degree of
ftrength in the fteam; and therefore the pifton muſt not rife fo
quick as to prevent the fteam's action on the air and condenſing
water, which it will do when the engine is thus employed, and
the fteam is low; for if the piſton afcends faſter than the boiler
ſupplies there can be no diſcharge, and after a ſtroke or two the
engine will ſtop.
Now, then, let us fee how far this counter-weight has to do
with "overcoming the unbalanced part of the preffure of the
atmoſphere." It is granted on all hands, that working ſteam
muſt more than balance the preffure of the atmoſphere; and
where this is not the cafe (except in very lightly burdened en-
gines) the engine will ftop, as juft now obſerved; yet not by
want of any thing to balance the atmoſpheric preffure on the
pifton, but for want of fleam ftrong enough to diſcharge by:
for let the counter-weight be ever fo fmall (and in engines hea-
vily loaded we are obliged to let the pump-end preponderate
but flowly), unleſs the engine is a very bad one, a moderate
ſupply of fteam will reſtore the equilibrium: nay even no fteam
at all, if a ſpigot is taken out of the flanch piece at the fnifting
clack, to let in the air.
But without any reflection on the application of ſteam on
!
Atmospherical Steam-Engines.
367
the piſton, which we are given to underſtand is one ground of
fuperiority over the atmoſpherial engine, there is an advantage
in the atmoſpherial engine in this point of view which Mr.
Watt's fingle engines cannot admit.
It is well known, that when a mine is going down, and the
engine-ſhaft is conftituted to receive all the water from different
parts of the mine, that the gait of the engine must depend on
the uniform influx of the water, and the engine must be fo
nicely regulated to this quantity of water as that it muſt fup it up
at every ftroke. Now, if this fupping is violent, the air which
enters at the conclufion of the ftroke will, at the return of the
buckets, blow a deal of the water out of the pumps, which will
fall to the bottom, and become ſo incommodious as to prevent
the miners from working; and on the other hand, if the ſtrokes
of the engine are not quick enough the water will gain on
the men, and they muſt give over working.
Now the old engine man can retard or accelerate the ſtrokes
of the engine, merely by the regulation of the fire; for, if the
engine ſhould return too quick he lets down the damper, and
if it is too flow he raiſes the damper: by theſe means, he can
vary the action of the fteam on the nether fide of the pifton
from 0 to 2 pounds on the inch over the preffure of the atmo-
ſphere, which in a fixty-inch cylinder will be from 0 to 7200
pounds this cannot be done in the new engine; for the piſton
rifes in one uniform medium. Thus is this counter-weight re-
lieved from the charge of hinderance to the engine, and proves
to be of importance rather than impediment; particularly when
it may be depended on that it may be fo adjuſted as to admit
the elafticity of ſteam to have a great ſhare in the power of the
engine: for let the counter-weight be fo adjufted as to leave
all in equilibrium; then it is manifeft, if the engine will work
at all, it muſt be by the elaſtic force of the ſteam acting on the
under fide of the pifton: and to compenfate that quantity of
fteam we have the fuperabundant weight on the pifton-end of
the lever to act in concert with the preffure of the atmoſphere;
which in the cafe ftated above, in a cylinder of 60 inches dia-
meter, may be ſo much as 7200 pounds.
Concerning the ftate of the vacuum in the old engines we
'know but little; but it muſt be confiderably more than has been
ſuggeſted: for an engine carrying a load of 7 pounds on the
ſquare inch of the pifton, together with the friction and inertia,
eſpecially in large engines, can hardly be leſs than 14 pounds on
the inch.
The writer of this article, about thirty years ago, tried the va-
cuum of ſeveral engines in the county of Cornwall; and one which
was reckoned the leaft brought the gauge to 23, and fometimes
368
MACHINES.
24. If we take the extreme, it will be 11.6 pounds on the
fquare inch but that is not enough to work an engine with
that load, taking in the other confiderations; and we have no
heſitation in ſaying, that where engines have raiſed a column of
water equal to 7½ pounds on the inch of the pifton it muſt have
little inertia and friction, or it muſt be laid to the account of
the aforefaid impulfe of the fteam in elevating the piston.
This was one way which Mr. Gainsborough propofed to
increaſe the power of an engine then erected in the county of
Cornwall, in a mine which ſtood in need of fome prompt af-
fistance: but the timid had the majority; and Mr. Gainsborough
having it not to boast that he had erected feveral large engines
as fpecimens of his invention, could not come forward with
the fame confidence and fuccefs as Mr. Watt. But had Mr.
Gainsborough fucceeded to have a fair experiment with a good
cylinder, and have accepted a reaſonable premium, Mr. Watt's
engines would not have obtained the degree of celebrity they fo
foon acquired in that county.
Since the application of the fteam-engine to the purpoſes of
giving motion to mill-work, it has been a defideratum to main-
tain an uniform force or action on the crank, in order to have
the fame effect on the fly.
When the engine was firft applied for the purpoſes of rota-
tion, it had not then the advantage it has at preſent of the
double ſtroke; and the mode of equalifing (as near as could be
in thoſe circumftances) the working and returning ftrokes was
by making the rod which connected the engine and the mill to-
gether (and ftill called the connecting rod) equal to half the
power of the engine, being of caft-iron; and when the weight
was not in the rod, it was laid on the lever at that end: but
this could not well apply by the old engine, except in cafes
where the work was nearly the fame throughout the day; for
as the diſcharging muſt be performed at every ſtroke, it would
require a quantum of fteam proportionate thereto, and that in-
variably; fo that in breweries, and thoſe works which demanded
attention to varying refiftance, this could not apply; for when
they had ftruck off the grinding, for inftance, if fomething did
not operate to retard the effect of the counter-weight, the en-
gine would increaſe in its gait beyond all bounds, fo as to
work itſelf to pieces: and as the only remedy was to check
the quantity of fteam at the returning ftroke, fo the dif
charge must be interrupted, and the engine muſt ſtop. But
Mr. Watt's fingle engine accommodated this circumftance,
from the mode of diſcharging being conftant, and not poffible
to be effected by the work applied to it, be it uniform or var
riable: hence to leffen the momentum of the rod it was only
Steam-Engines,
369
to check the entrance of the ſteam, by any contrivance that
would prevent the plenum valve from opening to its greateſt
limit.
One mode of giving a uniform action on the crank was at-
tempted in an engine erected about nine years fince at the
brewery of Meffrs. Meux and Co., where the power was at a
conftant diſtance from the centre of the lever, while the other
end, which was connected to the crank by the connecting-rod,
varied nearly its whole length.
This engine had two cylinders in alternate action on a band-
wheel by means of two chains. The wheel which carried the
connecting-rod was fixed on the fame fhaft with the band-
wheel, and had a pin near its periphery on which the con-
necting-rod was attached. This pin traverſed about 120° of the
whole circle, and may be denominated the end of the lever,
which, in its action upward and downward, accedèd and re-
ceded to and from the centre of motion; and had it traverſed
through the remainder of the femicircle it would then have
preffed on the crank, proportionate to the fines of every angle
it makes in its revolution. But confidering the infinite preffure
on this pin in the crank-wheel, it would have demanded a de-
gree of ftrength at that part, which would have been prepo-
fterous compared with the reſt of the work. See the ſketch of
this contrivance at fig. 13. pl. XXX.
This engine has its merits and its, defects: it is fubject to a
deal of friction, by having double cylinders, and their append-
ages; and unleſs the communication between the cylinders is
clothed with the beſt materials for that purpoſe, a great lofs of
heat muſt enſue. From the unfiniſhed ſtate in which the en-
gineer left it, and. the prejudices of the proprietor, and the
people he employs about it, we can hardly imagine that it can
have derived much advantage; but the work uſually laid on it
was, the grinding with four pairs of ftones, the liquor-pump,
houſewater-pump, ftanding-pump, beer-pump, wort-pump,
maſhing-machine, befide fack-tackle, all at once, and a very
extenfive communication by vertical and horizontal fhafts, in
which alone the effect was equal to thirty-eight horfes, accord-
ing to Boulton and Watt's eſtimate. Its form was ſuch as to ad-
mit an appearance of novelty and elegance; and might have been
fo modified as to abridge much of the principal defect, had it
not been for the glorious uncertainty of the law.
If it had not been for the negligent manner of delineating and
explaining the principles of Mr. Watt's engine in the Encyclo-
pedia Britannica, we needed not have gone any further into
the matter than merely to particularife fome circumftances
which chance or defign is ſeemingly always calling forth at this


VOL. II.
B B
370
MACHINES. ·
*
2
period of philofophical inquiry: but let any judicious mechani
look at the plate containing. Mr. Watt's engine in that Ency-
clopedia, and then let him ride from Berwick-upon-Tweed to
the Land's-end, and fee if he can find ſuch an one, or if he can
hear tell of fuch an one being erected any-where.
If we are right in our conjectures, this fly at the pifton-end
of the lever, together with many other fanciful and ridiculous
projects, were inftituted to equalise the action of the fteam
in its expanfive force on the pifton, according to the disco-
very noticed by Mr. Watt's hiftoriographer at No. 70, article
Steam-engine: all which may be found in the Rolls chapely
where Mr. Watt's ſecond ſpecification on ſteam-engines is fafely
depofited. But if this drawing is given as a fpecimen of the in-
genuity of the inventor, it muſt have been intended according
to the inverſe ratio of things.
A
We ſhall therefore prefent our readers with a genuine appli-
cation of the principle of Mr. Watt's engine, as far as is pof-
fible in a work of this extent. But the whole volume would not
have afforded ſpace fufficient to develope and exemplify many
particulars which muft pafs unnoticed here; not on account of
their infignificance, for the fmalleft parts are to the whole as
the hand or the foot to the body: but it will be neceffary to ob-
ferve here, that within theſe five-and-twenty years we have a
fpecies of ſteam-engine invented, which until then was not
known; and that is the fteam-engine applied to produce a ro-
tative motion from a reciprocating one, whereas the other is
applied principally to pumping water from mines, &c.; and
each will require a diftinct confideration. The engines ufually
erected for drawing water have been what are termed Jingle en-
gines; though there are not wanting inftances enough where
the double engines have been applied to that purpoſe; fome of
which we have feen fo unwieldy and complicated, that it ſeemed
to us like the fport of genius having nothing elſe to do. It is
true it was in a latitude where money bears no compariſon with
the calls of the moment, and where beauty and fimplicity have
no charms. But while we touch as lightly as poſſible on many
other particulars, we muſt cenfure exceedingly that enormous
affemblage of materials which, even in a state of reft, tend pow-
erfully to cruſh each other; but when put into motion by fuch
a powerful agent, the relaxation of which depends on the con-
nection of a wooden pin perhaps, or a ſtrap of leather, we deem
it not inconfiftent with the province of an engineer to affign a
limitable magnitude to machinery of this fort, without being fa-
tisfied of the practicability of the accompliſhment: it is a daring
outrage of art upon nature, for the former may have the knack
of piling together, nature has not the like: facility in preferving

Watt's Steam-Engines.
371
texture, componency, divifibility, &c. efpecially under pref-
ſure and agitation, like what is to be obſerved in a double en-
gine of a fixty-fix inch cylinder*; yet it is recorded in the En-
cyclopedia Britannica, that the engine at the Albion Mills,
though the largeſt in the kingdom, had its movements ſo judi-
ciouſly contrived and fo nicely executed, that not the leaſt noiſe
was heard, nor the flighteft tremor felt in the building !!!
·
In giving a clear explanation of the principle of this machine,
it will be neceffary to deviate from the precife difpofition of the
parts as they are ufually put together: but in fig. 1. pl. XXX.
this deviation is very little, and repreſents a ſingle engine. A the
cylinder in which the piston moves, B the fteam-pipe, D the
condenfer, E the difcharging-pump, F a bottom common to the
pump and condenſer, in which is an occafional communication
by a hanging valve at F: g is a valve to be lifted by the engine
at every ſtroke, for the purpoſe of condenfing the fteam; b is
a valve placed outſide the ciftern (of which xxxx is a ſection
on purpoſe to ſhew the contents), but communicates only with
the condenfer by a pipe paffing through the fide of the cistern,
and is inferted at the fide of the condenfer; i is a valve to be
lifted by the engine, and opens a communication between the
cylinder and the condenſer; k is a valve to be lifted by the en-
gine, and opens a communication between the lower part of
the cylinder and the fteam-pipe; and is alſo a valve of the ſame
kind, opening a paffage from the boiler to all parts of the
engine.
*
The pifton-rod, which is here broken off at m, is çonnected
by a chain to the lever or beam, which is fupported on a wall
of good maſonry, with proper pivot-blocks for ſupport to the
gudgeons; and as this kind of engine is ufually employed for
pumping water, another fet of chains at the other end of the
beam is appropriated to connect to the pump-rods.
Then to ſet the engine to work, the firſt thing is to lift the
three valves i, k, and I (for which there are apparatus too mi-
nute to lay down on this ſcale); theſe being opened, the ſteam
occupies every cavity and crevice of the engine, and in a little
while difplaces all the air in the cylinder, condenfer, &c. which
is diſcharged at the valve h: this valve is always covered with
water in a ſmall ciftern attached to the fide of the large ope;
for it is hardly in the power of art to fit it to that degree of ac-
* It is better in many reſpects to have two moderate fized engines ·
than one of theſe unwieldy things, but particularly for management and
durability. It is with regret we recollect an error of this kind by one of
the first engineers this country ever faw, where he erected one of thoſe
machines, the lever of which was fo large as would require a cylinder
equal to the power of near 40 horſes to give it motion.


BB 2
372
MACHINES.
1
curacy as to enfure its tightneſs: but here the air is diſcharged
at firſt ſetting the engine to work; and this valve is called the
blowing valve. When the cylinder and other veffels are properly
heated and the air diſcharged, which is well known by a very
fmart crackling noiſe at that valve, like a violent decrepitation
of falt in a fire *: theſe valves k and i are to be fhut; and after
waiting a few feconds, gently open the valve i: and if the en-
gine does not move, the injection-valve g muſt be opened a
little+; and if the engine does not move, then the operation of
blowing muſt be performed again, though but for a few ſeconds,
and the engine in general will go off fmartly ‡.
In treating on this ſubject, it is neceffary to obſerve, that if
we were to attempt a thorough information to the various
claffes of readers into whofe hands this may come, it muſt
have been taken up on a ſcale of greater magnitude than what
is conſiſtent with the plan of this publication: we muſt there-
fore ſuppoſe our readers are not entirely ignorant of the general
outline of this invention; to fuch readers only will thefe expla-
nations be of any importance.
In all engines on this principle, it is neceffary that the parts
appropriated to condenſation of the ſteam fhould be kept as cold
as poffible, and that thoſe parts intended for the operation or
paffage of the ſteam be kept as hot as poffible: hence the dif-
charging-pump § and condenſer are placed in a ciſtern of cold
water kept conftantly full, and a little running away; and if
the injection-valve is placed low in this ciftern, it will take
the water in the coldeft ftate. See the injection-cock in fig. 2.
As the condenſer is immerſed in water to be kept cold, fo
the cylinder fhould if poffible be immerfed in fteam to be kept
kot: for which purpoſe Mr. Watt formerly fed a cafing round
the cylinder, and at the top and bottom; and this would have
* This noife is occafioned by the air being all gone, and the water pro-
ducing a fudden and rapid condenfation of the team.
+ The valve i being opened, there is a paffage made from the cylinder
to the condenfer; but on account of long blowing, the fides of the con-
denfer become hot, and the water in the ciftern hot likewife: fo that the
condenſation muſt needs be very flow, even at the firſt injection of the
water into the condenfer.:
We believe, that until Mr. Watt went into Cornwall, this blowing
valve had never been applied to any of his engines, it being the ufual
method to pump out the air by a temporary brake attached to the dif
charging-pump; and that this valve was first applied by Mr. Horn-
blower at an engine on a mine called Ting Tong; which engine he put
up for the proprietors of the work, not for Meffrs. Boulton and Watt.
§ We chooſe to call it thus from the nature of its office. It diſcharges
all whatever comes into the engine, but eſpecially the water and the
air 5 and it is no more an air-pump than it is a water-pump, exclufively;
in fact, it is both、-`
Watt's Steam-Engines.
373
been attended with very beneficial effects if it did not enlarge
the ſteam ſurface, and expofe it to a more rapid condenſation
when it ought to be preferved; for to have the vacuum as per-
fect as poffible, it is neceffary that the cylinder be kept up to
ſuch a temperature as to prevent the leaft' condenſation on the
internal ſurface either above or below the pifton: becauſe, if
the fides of the cylinder were to be wet, as in the common at-
moſpherical engine, the vacuum would be vitiated, as it is there
occafioned by this wetnefs or moiſture gradually forming to
fteam, which the outfide cafing prevents, being filled with ſteam
from the boiler. But if it were poffible to cover this outward
cafe with any fort of fübftance which would entirely prevent the
tranfmiffion of heat for that cafing, it would. fuperfede the uſe
of the caſing altogether, and would apply with more advantage
to the cylinder itſelf. But we do not know of any fubſtance
which will not admit this tranfmiflion more or lefs. They who
wiſh for information on this fubject may find it in count Rum-
ford's Effays.
But the first circumftance of importance to the proportion and
difpofition of the ſeveral parts, is the folidity of the veffels and the
pérfection of the joints. Copper tubes are apt to be unfound at
the feams, and other parts which are required to be bent out
of a right line; and iron caftings, which require any parti-
cular fort of ſtay in the moulding to keep the core from the out-
fide, as thefe ftays are made moftly of wrought iron, they con-
tract more in cooling than the caft-iron does about them, even
fo as to become loofe fometimes; in fuch cafes, it is unutter-
ably perplexing to find out the places or cauſe of this defec-
tion; the joints are fufpected for the most part, but even remaking
them fometimes proves no amendment; and this muſt be the
cauſe in general why one engine from the fame patterns is better
or worſe than others. And we have reaſon to fear that this
matter of complaint is on the increafe; for felf-intereft has fo
powerful a preponderancy, eſpecially in the metropolis, that we
fhall deſpair of having theſe objects regarded as they were for-
merly; ſemblance being for the greateſt part the order of the day.
Mr. Watt has adopted a gauge (very improperly called a ba-
rometer), to indicate the degree of vacuum in his engines; and
we deem it of important confequence to the well-going of the
engine, the profit of the proprietor, and the credit of the en-
gineer: yet in many engines in London we fee this important
inſtrument either out of repair, or wholly laid afide. The form
is given at fig. 3. They have been made of glaſs; but if the
quickfilver is not very pure, the alloy with which the venders of
this article adulterate it is by conſtant action brought to the
furface, and that and the vapour together make the tube fo foul
a
374
MACHINES.
+
that no precifion can be obtained. Iron therefore is the beft
material: both parts of the tube ſhould be correctly of one dias
meter, or elſe the refult will be erroneous. This tube muſt
communicate with the condenſer by a ſmall copper pipe, and
a ftop-cock be placed between the gauge and condenfer.
The index in this inftrument is a light deal rod, which is put
into the ſhorter tube; and quickfilver being poured into it
within three inches of the end, the rod is put into the tube, and
it floats on the quickfilver. It is almoſt needleſs to remark, that
the graduations on this inftrument muſt be inverted with regard
to thofe of a ſingle tube.
Perhaps it ſhould have been noticed before, that the rod of
the diſcharging pump is connected with the lever at ſome point
determinable by the length of the ftroke; and in this figure it
rifes with the pifton, and brings up the air and water with it,
both of which are difcharged at the branch p, in which is a
hanging valve opening outward.
It is intimated in the large account of Mr. Watt's engine,
that this is the moſt preferable mode of working this pump,
viz. at the inner end of the lever; but we do not fee why: as
far as our judgment would lead us, we ſhould prefer the outer
end, where the conftruction will admit of it; and we think we
have ſeen ſome engines fo conftructed that have made a better
vacuum than when it is connected infide: depending, as we
think, on an impulſe given to the remaining air of the laſt ſtroke
at the inftant the bucket begins to rife; for na fooner is the
valve i opened than the ſteam rufhes towards the condenfer, and
giving a momentary tendency to a plenum, does give a puſh to
the air through the hanging valve between the pump and the
condenfer; and hence we are warranted to conclude, that more
air enters the pump by this means than if it be left to its own
expanſion.
We muſt obſerve how this pump affects the power of the
engine. By fome obfervations of thofe who have confidered
the fubject, we ſhould be led to conclude, that it is an addition
to the load of the engine: but if we attend to its conftruction,
having a valve to keep off the preffure of the atmoſphere, it is
certain it can have but little weight until the bucket is near the
higheſt limits of the ſtroke; and taking the ſum of the reſiſtance
from the commencement of the ftroke to its termination, it will
be found to be very little in compariſon with the power of the
cylinder. But if the weight of the atmoſphere was conftantly
on, it could make no other difference in a well-conftructed en-
gine than what arifes from the friction.
From fome authentic reports on the fuccefs which attended
Mr. Watt's labours in applying the principle of this engine, it
Watt's Steam-Engines.
375
#
appears he did not imagine it would require fo large a portion of
the content of his cylinder to be transferred to his pump as he
afterwards found neceffary *. And on this account, one experi-
ment among many others, which is related in the Encyclopedia
Britannica, we must be permitted to enter our proteſt againſt : it
is this, viz. fection 57," a globular veffel communicated by
means of a long pipe to a cylinder of four inches diameter and
thirty inches long: the globe was immerſed in water: the pipe
had a ſtop-cock: the cylinder was filled with ftrong fteam: the
cock was turned (nay ſcarcely turned), when the fides of his
cylinder were crushed together like an empty bladder.”
Not to notice the ſtriking figure of the crufhing, let us take
a view of the experiment: a veffel of the form of a ſphere was
connected to the cylinder by a pipe of an inch diameter; this
veffel was immerfed in the water unexhausted, we may fairly
fuppofe the cylinder, containing 390 cylindrical inches, was
filled with ſtrong fteam; the cock was hardly turned when a
complete vacuum took place in the cylinder.-Now the credi-
bility which the relation of this experiment demands muſt de-
pend on fome particulars unrelated by the reporter: for if we
admit that this globe and a part of the pipe alfo contained the
air of the atmoſphere, what could there be, befides mere magic,
to induce the ſteam to leave the cylinder in fuch a hurry? No :
we have ſeen the experiment tried again and again; and the
naked truth is-it cannot be.
We will advert to another experiment or two of this kind.
Encyclopædia Britannica, Steam-Engine, fection 10. "Expe-
riments have been made on ſteam-veffels, fix feet in diameter
and ſeven feet high and it has been found that about four
ounces of water as warm as the human blood will produce a
complete condenfation in lefs than a fecond." "In another
experiment with the fame veffel, no cold water was allowed to
get into it; but it was made to communicate by a long pipe
four inches diameter with another veffel. The condenfation
was fo rapid, that it could not be meaſured." Upon thefe expe-
riments a deal of hypothetical reafoning fucceeds, all which is
evaporated in the Supplement to the above work. See STEAM-
ENGINE.
Now here is a fact related, which afterwards is acknowledged
to be no fact at all. We fhould not have thought ſo much
about it, if it had not been related fo circumftantially. So, in
the experiment made with fuch fcrupulous care as the ex-
panfion of boiling water in a veffel holding 12600 grains of

In the best engines we have feen, or hear of, this proportion is not
lefs than one-eighth of the content of the cylinder for a single engine
376
MACHINES.
1
fteam, which weighed not more than one grain; making the
expanſion to a certainty 10000 to 1: and here, in the Supplement
aforefaid, it comes to 1800 to-1. Now the question is, Which
of them is true?
But, to proceed:-The moſt novel circumftance in the opera-
tion of this engine is, that when the fteam has been permitted
to act on the piſton to the limits of the ſtroke, it has permiffion
to enter the cylinder a ſecond time beneath the pifton; and fo
the pifton rifes in a medium of ſteam more or leſs rare as it
happens: nor is that point of any fignificance, even if it were
all to be condenſed in its paffage from the upper to the nether
fide of the piſton; and it is a beautiful accompaniment of the
prime object of the improvement. To make this part of the
evaporation as perfect as poffible, the valve k ſhould be placed
at the top of the pipe B, juft under the valve 7; otherwiſe that
pipe full of steam is wafted every ſtroke.
But it generally happens in engines erected for pumping
water, that they are calculated to go deeper than the preſent
bottom of the mine; and therefore, if all the fteam which
enters the cylinder for one ftroke was to be condenſed, the en-
gine would act with its whole power, and the effect would be
to deſtroy itſelf: on which account, in engines thus circum-
ſtanced, the injection is to be ftopped long before the termina-
tion of the ſtroke, which leaves a refiduum of fteam at the bot-
tom of the cylinder, that proves an effectual banking to the pi-
ſton; even fo far as to fupport it while the chains to which it is
appended are become quite flack by the momentum given to the
lever during the action of the ſteam on the piſton. We believe
it was this circumſtance that indicated to Mr. Watt the advan-
tage of ſhutting off the fteam from the boiler foon after the
commencement of the ſtroke; which is done in the following
manner.
The valve 1, the office of which is to open or ſhut the com-
munication between the cylinder and the boiler, is ſo parti-
cularly connected with the working gear, that by altering the
place of a pin it is fhut fooner or later, as occafion requires;
and when the pifton has proceeded half way down, if this
valve is fhut at that inftant, the piflon is carried through the
remainder of the ſtroke, partly by the momentum it has already
acquired, and partly by the remaining expanſion of the ſteam,
which, notwithſtanding its growing rarer and rarer, is fufficient
with its momentum to complete the ſtroke.
We have obſerved, that' in order to give action to the engine
at its firſt onſet, and indeed at every fucceeding ftroke, the valve
i is to be lifted. Thialve is kept down by a weight equal to
the preſſure of the atmoſphere, added to the elaſticity of the
Steam-Engines.
37H
}
"
fteam above that preffure; there being a vacuum beneath it,
and the action of the ſteam upon it. Hence, in large engines
it requires a great force to lift it up, in fome engines equal to
ICOO or 1200 lbs. and it muſt be lifted in an inſtant, if poffible.
The ufual method of doing this was by an apparatus being a
part of the working gear, conſtructed after the following man-
ner. Let c, fig. 4. be the centre of the ſection of a ſtrong bar
of iron about two inches fquare: on one of the angles of this
bar a piece of iron, in the form repreſented at b, is welded on;
and on the next fide but one there is an arm fixed in the form
d. This bar, which is ufually about three feet long, or little
more, is made to work between two poſts, and is called a Y
ſhaft, and the pofts are called Y pofts, conformably to the old
plan of working gear. This Y fhaft, with its arm d, is brought
to the pofition fhewn in the figure to be ready for opening the
valve, when a ſmall pin in the plug p lifts a detent x, that is
made to preſerve the whole in its proper poſition, and a balance-
weight w brings this arm or branch into the action of turning
up againſt the ſpanner or lever h attached to the valve v, and
working on the fpindle or centre g: by this means here is a very
powerful force at the firſt inſtant applied to the very end of the
lever b, which is continually diminiſhing as the valve riſes; for
the preffure on the valve and the very end of the lever is, or
ought to be, exactly the fame in every pofition of the crooked
C
arm.
Still it was a heavy load on the hand to manage this part of
the working gear; and in converfation on the fubject, it was
fuggefted to Mr. Watt to make theſe large valves of two valves,
that is, by making a ſmaller-fized valve in the middle of the
large one, and then, after the ſmaller one was lifted a little, the
whole would rife together-and it was adopted: but it being
difficult to keep in order fo as to be tight, we believe it was
laid afide.
We cannot help taking notice of another illiberal infinuation
of the writer of this article in the Encyclopædia Britannica :
when in ſetting forth a contrivance to render the opening of this
valve as eafy as was poffible, and which was abfolutely invented
at an engine at Radſtock near Bath, he ſays, "it has been
ſervilely copied from Mr. Watt," as if it could not be copied
from any one befides; and if copied, it muſt be copied fervilely:
now although hundreds are ſaid to have copied from Mr. Watt,
it might rather perhaps have been faid Mr. Watt copied from
hundreds *. But it does not appear that the writer underſtood
}
* We do not directly implicate Mr. Watt as being the illiberal coad-
jutor in this indiſcriminate ſcandal and defamation: but it would not
378
MACHINES.
the modus operandi of this wonderful project, by the figure he
has given of it, or by what he advanced in the text, both of
which are alike falfe. He fays, "though the valve has not
moved the hundredth part of an inch, the preffure is over.'
It would be wasting time, and an affront to the underſtanding
of our intelligent readers, to go about formally to prove the re-
verfe of this affertion; but as he has fo awkwardly reprefented
it, we will explain it at fig. 6.
Let A be the valve, BB a lever attached for the purpoſe of
raiſing it; CC is a rod with a joint in it at i; D is an arm
ftretching horizontally, with a weight W hung to it. This arm
D and the part of the pointed rod C have motion round the
centre : fo that when the weight W is at liberty to fall, it
carries the arm D round the common centre downwards, and
raiſes C round the fame centre upwards in the direction of the
dotted arch, at which the whole apparatus affumes a new po-
fition according to the dotted lines. From this ſketch, the prin-
ciple by which this valve is opened may be eaſily comprehended:
but it must be added, that this valve is not opened by the
plug (here and throughout in the Encyclopedia Britannica
called the plug-frame), but by the action of a weight which is
raifed by the plúg*.
"
It is neceffary to the good performance of an engine, that
this valve be opened as fuddenly as poffible, that the fteam may
have its releaſe quite inftantaneoufly, if it could be done; for
until the valve is opened the engine has not its full power.
Hence the reaſon why in the beft engines univerfally a weight
or fpring is applied to open it, and all the plug does is to return
the weight to its former elevation.
But a much better method than this, or any of them, has been
fuggefted by a delicate thought of Mr. Jof. Hornblower, of Chare-
water near Truro, and confifts in conſtructing the valve on an
entirely new principle: we fhall give a repreſentation of this valve
in fig. 7. AAAA, is the box containing the valve, BB is a valve
inverted, and fixed firmly to the bottom of the focket S; this
focket ferves as a guide to that part of the valve that is to be
lifted by a fhort cylindrical rod, as is very common.
have difhonoured him if he had, in the fupplement to this farrago of
falfehood and abfurdity, demanded a recantation of whatever may have
been previouſly inferted either through prejudice or miſinformation; and
we would never have interfered with the difgufting panegyric that per-
vades the whole ſubject.
* The plug is that vertical piece of timber which is alternately rifing
and falling by the motion of the engine; and by the pin's being fet inta
particular holes, the ftroke of the engine is adjufted to a very great
nicety.. .A.
#
Watt's Steam-Engines.
879
The part which is to be lifted is DD EE: which lifting is per-
formed by any of the ufual methods attached to the eye F,
which is a part of the croſs-bar EE in the figure below, which
is a plan of the upper ſurface of the valve and upper feat; for
it muſt be obſerved that it has two feats, and that the principal
paffage for the ſteam is at the lower feat; for the fteam in its
paffage goes down through the body of the valve: indeed it has
always access to the lower ſeating, the body of the valve being
entirely open, except what is taken up by the croſs-bar EE; fo
that in this fenfe we lift the thickneſs of the metal only of
which the body of the valve is conftructed. To help our ideas
of the operation of this valve, we must conceive the upper
ſpace in the box to be always full of ftram, and confequently
the inner part OO of the valve (which, for better underſtanding
it, is fhewn by a fection along the croſs-bar); then the lower
fpace of the box will be a vacuum, when upon lifting the
valve (which is a cylinder open at both ends) the fteam will
paſs through it, and into the lower ſpace at the inverted lid BB.
In this figure the cylinder part is raiſed a little, to fhew how it
feparates from the lower lid BB.
We have prefumed on this mode of applying the principle,
not knowing the precife manner in which the inventor has
thought moſt proper to do it, but we have no doubt of its
being a very welcome improvement in thoſe large engines in the
county where he refides.
Adverting to the other parts of the engine, fig. 1. On the
top of the cylinder n is a box to contain fomething foft, yet
pretty cloſe, but not leather, to embrace the piſton-rod m in its
motion up and down; and this is uſually a fort of plaited rope
of white yarn, nicely laid in and rammed down gently, occupying
about a third of its depth: then upon that is placed a fort of
tripod, having a flat ring of braſs for its upper, and another for
its lower, part; and thoſe rings are in breadth equal to the ſpace
between the pifton-rod and the fide of the box; that being put
on over the end of the pifton-rod, another quantity of this
rope is to be put upon it, and gently rammed as before: then
there is a hollow fpace between theſe two packings, and that
ſpace is to be fupplied with ftrong fteam from the boiler. Thus
is the packing about the pifton-rod kept in fuch a ſtate as to pre-
vent the air from entering the cylinder when at any time there
may be a partial vacuum above the piston.
This then is a deſcription of Mr. Watt's improvement as to
what he originally had in view, and as to what prefented itſelf
in perfecting his primary notions of the conftruction; and in
addition to what is paft, we have only to recapitulate, the
references belonging to the figure 1. A reprefents the cylinder
*
1
380
MACHINES.
with its piſton ſuppoſed to be within it; B a pipe occafionally
communicating with the upper and lower fide of the pifton.
E the difcharging pump with its bucket within; y its dif
charging nozzle with a hanging valve opening outwards; (
part of the bucket-rod to be connected with the great lever;
D the receiver or condenfer, having communication with the
cylinder by the valve i; F the place of a hanging-valve placed
between the pump and receiver opening towards the pump;
g the injection-valve; b the blowing-valve, the outer part of it
being immerſed in water in a ſmall ciftern; x x x x a ſection of
the condenfing-ciftern, to fhew the lower parts of the engine;
k a valve for opening a communication between the upper and
nether fides of the pifton; b is a box and valve, for receiving
and giving the ſteam from the boiler; n the box containing the
packing for the piſton-rod ;.and m part of the piſton-rod broken
off for want of room.
Such was the moſt perfect ſtate of Mr. Watt's engine until
circumstances demanded what was impoffible, at leaſt what
ought not to be. It was found that fome of the mines in
Cornwall, already at a great depth, wanted to go ftill deeper;
but, alas! no fingle engine, unleſs it were a monſter, could be
large enough: but "Mr. Watt's genius, always fertile in re-
fources," found out the means of making two engines in one,
and the double-ftroke engine came forth in two-fold cumbrous
majefty to what had ere been ſeen before. It would take more
room than is allotted to this department to develope the enor-
mous limbs and features of this creature as fet up at fome of
the mines in Cornwall: which, even on a more manageable ſcale,
applies but very difcompofedly to drawing, or, as we ought to
fay, thruſting, water from ſuch a depth.
But it is here in London and its vicinity that he has applied
the principle to a purpofe that enobles both him and it, and
where we conceive it to have reached its acme both in deſign
and execution.
We have reprefented this mode of working at fig. 2. where
we muſt deviate largely from the practical application, in order
to give a comprehenfive explanation. A is the cylinder, as in
the fingle engine; B is a pipe appropriated to deliver the ſteam
from the boiler through the branch L; from thence it enters the
cylinder alternately by the valves v, w, both opening towards
the ſteam fide. The pipe C has alfo two valves, one at the
upper end of the pipe in the box t, and one which we muſt
defignate at the joint r, both opening toward the cylinder.
The condenser D has a blowing-valve, like the former figure in
the fingle engine; but the injection is made by a cock G, which
has a pipe reaching near the bottom of the cistern; and when
Hornblower's Steam-Engines.
381
the engine is at work this cock is always open, and the injection
always running in, becauſe the ſteam is conftantly coming from
the cylinder either above or below the piſton, and its operation
is as follows:
When the air is blown out of the engine, and the pifton
happens to be in its upper fituation, the valve v on the fteam
fide is lifted, and the valve r on the exhauſting fide is opened:
the exhauſting-valve r takes the ſteam from below the piſton,
while the ſteam by the valve v enters on the upper furface, and
a ftroke is made; and at the inſtant the piſton comes to its
place at the bottom of the cylinder, theſe valves are both ſhut,
and the valves w and t are opened, and the upward ſtroke com-
mences, and fo on alternately.
Ի
It muſt be obſerved here that, whereas the pifton in the fingle
engine is pendant on the lever by the chains lying in the arch
of the inner end, this must be connected by a mode that ſhall
render the rod rigid in its action upward; for which purpoſe
there is a ſyſtem of tranſverſe joints which compel the rod to a
motion, parallel to itſelf, exhibiting at once a moft ingenious
and pleaſant piece of machinery. At the other end of the beam
or lever is a rod which connects the motion of the engine to a
fly; and Mr. Watt has chofen to do this by a very ingenious
application of one wheel fixed on the axis of the fly, and another
fixed on the rod that is connected to the lever, by which means
the fly makes one entire revolution, while the engine makes but
one ſtroke; and thus the fly makes as many revolutions as the
engine does ſtrokes: but we are inclined to give the preference
to a fimple crank with a fly of fuch weight as fhall have the
defired momentum with lefs velocity, fimplicity being ever a
defideratum in the conftruction of machinery.
It is related in the Encyclopædia Britannica that a Mr. Fitz-
gerald took out a patent for communicating a rotative motion
from the ſteam-engine, and it may be fo: but the firſt notice
we ever had of a patent being obtained for that invention was
about the year 1778, when a young man at Briſtol, Mr. Matthew
Wafbrough, obtained letters patent for that purpoſe, and did
apply it to his own works for turning lathes, &c. and alſo one
at Southampton at Mr. Taylor's works, befides two or three for
grinding corn. However, this was previoufly to Mr. Watt's
patent for that purpoſe; and, little as it was thought of at that
period, it is now become of mighty confequence to the kingdom
at large.
We are glad to have an opportunity of preſenting the public
with an improvement on the fingle engine of Mr. Watt by
Meffrs, Hornblower, a patent for which was taken out by M
Jonathan Hornblower of Penryn, in the year 1781. We will
$82
MACHINES.
give a fhort account of this engine, not only that our readers
may ſee what attempts have been made to carry on the progreſs
of improvement, but that they may have an opportunity of
comparing it with the account given of it in the Encyclopedia
Britannica; as various opinions are ftill entertained on the merit
of that invention.
The intention of this improvement was to obtain a greater
power by a complicated force of the fteam than was fuppofed
could be done by its action in a fimple way; and, as it ne-
ceffarily involves a novelty of conftruction, we will give a re-
prefentation of the whole at fig. 8. where A and B are two
cylinders of different capacities; and in this figure A is double
the capacity of B: both of the cylinders are furniſhed with a
pifton with their connection with the lever, as in the figure.
The boiler is fuppofed to be placed on one fide, having a pipe
communicating it with the engine at G, and by occafional
communication through the branches by means of the four cocks
dr valves, the ſteam is fent through the engine in the following
manner: but here alfo we must deviate from the precife con-
ftruction to give a clear, an unequivocal idea of what paffes in
thefe two cylinders: therefore let A B fig. 9. be two cylinders,
and let A be double the capacity of B, and let them be fet one
on the other each having a piſton, and both piſtons fixed on the
fame rod, and this rod to a lever having a weight at the other
end; then if we ſuppoſe the upper piſton to be 1 inch diameter,
the lower one will be the fquare root of 2 =
= the fquare root of 2 = 1'414 + of any
determinate length, which we will fay here 10 inches: and that
we may not have our conceptions warped by complex notions,
we will employ the preffure of the atmofphere in this experi-
ment, instead of fteam; and we will, for the fake of round
numbers, allow 12 lb. on every circular inch wherever the
whole preffure is employed.
The first thing, then, that is to be done is to let the lower
pifton come very nearly in contact with the upper end of its
own cylinder; that is, coming exceedingly near to a a, as in the
figure: then both theſe piftons working with very great niceneſs,
being well oiled, let the atmoſpheric air enter between the two
piftons at the cock x, while there is a perfect vacuum in the
larger cylinder under its pifton. If the whole of this little
engine is at liberty, it will begin to make a ſtroke with 23 lbs.
hanging on the outer end of the lever; becauſe there is 12 lbs.
on the upper pifton, and 12 lbs. on the exceſs of area on the
lower pifton. Then certainly it will balance a weight of 24 lbs.
on the outer end of the lever; but next put a weight of 23 lbs.
inſtead of 24, and we fhall fee that it will begin to make a
troke a little way downward: but it will foon ftop, becauſe the

Hornblower's Steam-Engines.
383
atmoſpheric air between the two piſtons begins to be attenuated,
and therefore its preffure on the lower pifton will diminish; and
this will be the cafe, gradually diminiſhing until it comes to the
bottom, where its preffure will be but half of what it was at
the beginning; that is, 6 lbs. But let us now take notice of
what has been going on with the ſmall pifton; and that is, that
while the lower pifton has been defcending with a decreasing
preffure this piſton has had the whole preffure of the atmo-
1phere upon it all the time; fo that whereas it did equilibriate
with 24 lbs. on the rod, it now ceafes with the whole preffure
on the ſmaller piſton, and one half of the original preſſure on
the excess of the larger pifton above the fall one, or one
fourth of the preffure of the whole lower pifton,, making in the
whole 18 lbs. at the termination of the ftroke; and taking the
fum of the preffures it will amount to 21.
Now let us ſee what is the true ſtate of the cafe with refpect
to Mr. Watt's application of the fteam in what is called his
expanſive engine, according to the reprefentation in fig. 1. Let
A, fig. 10. reprefent the pifton of a cylinder equal to the capacity
of the largeſt of the before mentioned 1414 + diameter, and
10 inches long, with its rod pendant to the lever as before:
making uſe of air of the fame denfity, for its effects must be
the fame, 12 lbs. on the circular inch. Then, fuppofing an
entire vacuum in the cylinder, let the pifton be brought as near
the top of the cylinder as poffible: being nicely oiled as before;
let the air have acceſs to the upper fide of the pifton, and it will
ſupport a weight of 24 lbs. as before. Let this piſton defcend
half way down the cylinder, being fupplied with air, and it ftill
fupports 24 lbs. Now let the air-cock be fhut, and no more air
fuffered to enter; and take off the 24 lb. weight and hang on a
12 lb. and they will be in equilibrium at the termination of the
ftroke.
Here then we may compare the different refults; for different
they are, and will be, notwithſtanding the high authority to the
contrary. If we obtain the accumulated preffure by taking a
mean of the extremes, we fhall find Mr. Watt's application to
be 24+24+12 =20, leaving 12 lbs. at the termination of the
3

ftroke. Application of the principle in the preſent inſtance
by taking the mean of the extremes, will be →⇒21, having
2 beaving
2419
18 at the termination of the ſtroke; which, in point of advantage
in favour of the double cylinder, is as 3 2, a point of no ſmal
magnitude in the practical application of this principle, and
which feems to have been overlooked by all thofe who have
taken up the ſubject. Even the learned profeffor himſelf has not
SSTINY
384
MACHINES.
taken into the account this diftinguishing peculiarity, as he has
only brought out the accumulated preffure of both in a com
parative view. Indeed the method he has adopted to investi!!
gate this problem does not account for the ultimate expenditure
of fleam.
•
But we are warranted to preſent this to our readers in this
popular and experimental manner by a very ſcrupulous attention
to an engine erected in the vicinity of Bath fome years ſince
on this very principle, and under very diſadvantageous circum-
ftances. The engine had its two cylinders 19 and 24, with
#trokes on each fuitable to the occafion, that is 6 feet and 8 feet
refpectively. The condenfing apparatus a very bad one,
through a fervile fear of infringement on a patent which in-
fringed on every body; by which the greateſt degree of vacuum
obtained was no more than 27 inches. The engine wrought
4 lifts of pumps to the depth of 576 feet, 4500 lbs. 14 ftrokes
in a minute, 6 feet each, with a cylinder 6 feet long, and
19 inches diameter, with a deal of inertia and friction in the
rods and buckets; fome of the latter of which were not more
than 34 inches diameter: and this it did under all theſe diſad-
vantages, with 70 lbs. of coal, light coal, per hour; which would
have required a 24-inch cylinder of Mr. Watt's fingle engine
making a 6-foot ſtroke, with all the ſteam he could apply.
*
Two remarkable circumstances prefented to fhew the ad- ·
vantage of this application of the principle. The one was, that,
in defiance of all order and regularity, the man who tended the
engine, and pretended to underſtand it better than his mafter,
would clandeftinely detach the ſmaller cylinder from the other,
and work only with the large one: but whenever detected, an
idle excufe only intervened between it and the reſtoration of
things; and whereas the boiler (which was proverbially ex-
cellent) would ſcarcely by hard firing raife fteam enough to
keep the engine going: but no fooner was the fmall cylinder
rod hung to the lever than the engine refumed its wonted
activity, and the ſteam would blow up the fafety valve; and the
boiler without great attention would boil over, nearly to
emptying.
The next circumſtance is, that when the detent which kept
the exhaufting-valve fhut happened to mifs ftays, as we may
call it the pifton would be balked, as it were, not being per-
mitted to rife the whole of the returning ftroke; when it would,
as by an inſtructive nature, come down' again and again until
the detent performed its office-a practical' argument for the
power of the engine at the termination of a ſtroke; but we
believe nobody faw, this effect with jealous eye but Mr.
Watt, and hence the production of Mr. Watt's fecond patent
Hornblower's Steam-Engines.
385
}
Here, then, was an engine working with the effect of 16 lbs.
on the fquare inch of the pifton; for all the fteam that was
employed in producing this effect, was no more than what
fupplied the ſmaller cylinder. The various diſputes and con-
tentions about the fuperiority of Mr. Watt's engines comparing
the effects with this engine, fubfifted only on account of the
difficulty of making a fair comparative experiment which, unleſs
they could be done with engines on the fame circumſtances,
could not be done at all, and on account of the nature of
drawing the water in different mines, no circumſtances could
be found to juſtify this compariſon.
We are told in the Supplement to the Encyclopedia Britannica,
that the form of the engine mentioned in the 766th page of the
body of that work was put in practice about the year 1775, and
that this is mentioned," becauſe we have been told Mr. Horn-
blower puts in a prior claim to the invention ;" and then adds,
"We do not think that Mr. Hornblower erected any of his engines
before 1782; and as Mr. Hornblower was, we believe, working
with Boulton and Watt before that time, we think it fully more
than probable that he has in this refpect profited by the in-
ſtruction of fuch intelligent employers." We forbear to
defcant on the mechanical intelligence of the employers, at that
period; but we are authoriſed to ſtate this as an unjuſtifiable libel
on Mr. Hornblower. In the firſt place, Mr. Hornblower never
worked with Boulton and Watt; and fuppofing Mr. Hornblower
never put up any of his engines until 1782, are we to infer
from thence that the principle was not thought on, nor any
experiments inftituted to afcertain the beft mode of applying
that principle? We have likewiſe to ſtate that Mr. Hornblower
took up the fubject of his engine early in the year 1776, if not
before, and continued it until he made a large working model
whoſe cylinders were 11 and 14 inches diameter, and that a
drawing of this engine was fent to the editor of the Encyclo-
pedia Britannica, with a proper defcription and references
accompanying it; that Dr. Gleig returned the drawing to Mr.
Hornblower with a very polite letter of acknowledgment for the
favour done to his work, adding, that it would appear with Dr.
Robifon's marks of peculiar approbation, who was to under-
take the writing on that article, &c. &c. and that when theſe
marks of high approbation were publiſhed, it was to ſet forth
how ingeniouſly Mr. Hornblower had contrived the framing of
the lever, his valves, and ftuffing-box, but that the engine was in
no refpect preferable to Mr. Watt's with a fingle cylinder, but
in ſome accounts very much inferior! That Mr. Hornblower
addreffed a letter of furpriſe and refentment to Dr. Robiſon at
ſuch an indirect inftance of behaviour, which probably brought
VOL. II.
CC
386
MACHINES..

the prejudices of the candid philofopher into view whenever he
had accafion to refer to Mr. Hornblower's name. We have to
Date further, that we do not believe that Mr. Watt's use of the
expanſion-valve had ever been put in practice until lazig after
Mr. Hornblower projected his defign of the double engine.
However, we are certain that this engine brought forth Mr.
Watt's fecond patent for the moſt arrant fyftem of abſurdities
that ever came into view in the mechanical world, to avail
himfelf of the means of continuing the preffure on his piston
with as much effect as he faw inherent in the principle on which
Mr. Hornblower's engine was conftructed; but we have never
ſeen one inſtance in which any of the prepofterous methods
fanctioned by the patent referred to were put in practice.
We are now to take notice of another engine of Mr. Horn-
blower's, for which letters patent have been lately granted,
having a rotary motion within itſelf by the immediate action of
fteam on 4 revolving pistons. We confefs our inability to do
juftice to this moft fimple fteam-engine we ever faw, fo novel
in its conftruction, yet fimple in its operation. The pistons just
mentioned are four vanes like thoſe of a ſmoke-jack, though
not of thin iron, but of fome confiderable thicknefs, fufficient to
form a groove to hold fome ftuffing for the purpoſe of being
tight in their action. They are mounted on an arbor, which
has a hollow nave in the middle. Into this nave the tails of
the vanes are inferted, and each oppofite vane is affected alike
by having a feady connection with each others: for inſtance, if
we ſhould alter the angle of one of the vanes with the arbor,
the oppoſite one will be altered too, and they are not fet in the
fame plane, but at right angles to the plane of each other; fo
that, if we (in retaining the notion of the vanes of a fſmoke-jack)
conceive theſe vanes to be held in a vertical poſition as the fails
of a windmill, when one vane is flatly oppofed to the wind, the
oppofite vane will prefent its edge to the wind, and this they are
conftantly doing in their rotation on their common arbor, fo
at the team acts againſt the vane on its face in propelling it
and this it does for about of a circle or 90 degrees
where it is defined to act; and as foon as it has
gone through the quarter of the circle, it inftantly turns its
edge to the ſteam, while at the fame inftant another vane has
entered the working part of the box, and the rotation proceeds
without interruption..


a
t

It muſt be obferved, that though the engine has the power of
prefenting the edge of the vanes to the team in returning to
its place of active force, that yet there must be fame power loft
according to the re-action on the thickness of the edge, and this
lofs of power is greatest only in ſmall engines; but in a ſyſtem
Hornblower's Steam-Engines.
3987

}
*
+
•
of vanes extending 5 or 6 feet, moving at the rate of 30 revolu-
tions in a minute, there must be a great accumulation of force';
and that this accumulation is in favour of the principle of the
engine, where the velocity of the power may be of any deter-
minate ratio to the velocity of the weight, according to the
exifting circumftances. It muft alfo be understood that this
engine is to be furniſhed with condenfer and diſcharging-pump,
according to the new mode of condenſation eſtabliſhed by Mr.
Watt; but Mr. Hornblower has (as we think) an improved
method of difcharging, whereby he takes all the air from the
condenſer in a most perfect manner. This apparatus is to be
connected to one end of the arbor which carries the vanes or
piſtons, while the other end is connected with the work.
Fig. 1. is the plan of horizontal fection of the engine
where AA is the exterior box or cafing; BC two of the vanes;
C prefenting its whole furface of one, and B. fhewing the edge
of the other; pppp forms an entire partition; fo that all the
communication between the upper and nether parts of the box
are at BC; D is the nave through which the vanes are con-
nected, and OO is the arbor. Fig. 12. fhews a vertical fection
through the fame line; C and B fhew the fame vanês in the
fame pofition as before. The nave in the middle is open to
thew how the two vanes are connected. Another two being
connected in the ſame manner, will have liberty to turn a
quarter round without obftruction by the crooked part of the
communicating axis; this is the fteam-pipe, and the exhauſting-
pipe may be placed any-where above the partition*.

1...
The author, at the fame time that he entertains the greateſt refpect
for the practical talents of the ingenious contributor of this defcriptive
hiftory, and of the inventor of the ſteam-wheel juft deſcribed, ftill thinks.
it right to ſtate his apprehenfions that it may not be found in practice to
poffefs all the advantages which at firſt view one would be inclined to
afcribe to it. Is there not fome ground to fear that in this contrivance,
befides the force loft by the action of the ſteam upon the edges of the
vanes, there will be a confiderable lofs arifing from the greater friction
attending its opèrations than thoſe of a common fteam-engine? In this
fteam-wheel there will be a great quantity of rough ſurface (that of the
ftuffing) expofed to frequent contact, and confequent refiftance to the
moving from the fixed parts. Befides, as the ftuffed parts are here of
great extent with regard to the magnitude of the machinery, and exhibit
rapid variations of ſhape, they may, when brought into conſtant work,
be found difficult to keep in order. Whether the diſadvantages which
may ariſe from thefe caufes, may be as great as thofe that are known to
attend the other engines, and particularly whether they will be equi-
valent to the force abforbed by giving a new impulfe to the whole mafs
of matter fubject to the reciprocating motion at every change thhe
direction, can only be fatisfactorily afcertained by fübjecting both engines
to comparative work in as nearly the fame circumftances as the difference
in conſtruction will admit. But if by further attention to this ingenious



CC 2
J
388
MACHINES.
It would be employing time to very little purpofe te enu-
merate the various projects which are fet up to rival Mr. Watt's
engine; and if we had not ſeen that the moſt palpable abfur-
dities are not without patronage, not in engineering only, but
in concerns of greater or lefs importance, we ſhould not be
able to account for the preference fhewn to fome of as im
meritorious productions as have peſtered the world at any age:
but the misfortune in our country is, that we all are great
mechanics and ſage politicians, and while one engine is con-
demned on account of its complex conſtruction, however ef
fential, others are celebrated for their fimplicity, however
abfurd.
We muſt however redeem from this charge an engine in-
vented by Mr. Edmund Cartwright, which has as much merit
as can poffibly be attributed to a gentleman engaged in the
purfuit of mechanical ftudies for his own amufement. Mr.
Cartwright has two very important defiderata in view, a tight
pifton and a vacuous condenfer; that is to fay, a condenfer
from which the atmoſpheric air is excluded: to accomplish
which it is made of as thin copper as it will admit, expoſing a
large furface to the water, then the ſteam internally comes in
contact with the metal of the fame temperature, and hence the
condenfation. We wish it were poffible to put this grand
defign into a decided effect: but from fome particulars we have
obferved in the doctrine of condenfation, no method yet ex-
plored will obtain fo rapid a condenfation as actual contact
with the water: we do not account for this by any chemical
affinity, but by the expoſure of ſurface; for the experiment has
been tried to our fatisfaction, that when the jet was not in a
difperfive ftate, the condenfation was tardy and inactive; and if
it were poffible to difperfe the jet into a miſt, we ſhould obtain
the moft prompt condenfation poffible.
P
1
But. ftill we do not conceive an inftantaneous condenfation is
abfolutely neceflary; for if it is performed during the time of
the required ftroke, that is all which is wanted. We cannot fay
whether Mr. Cartwright has fucceeded ultimately to this point
or not.
We remember to have feen preparations for an apparatus for
this mode of condenfing fome years fince, by an affemblage of
taper pipes, of about a quarter of an inch diameter, expofing a
furface of between 90 and 100 feet to a 20-inch cylinder; but
1.
contrivance, Mr. Hornblower fhould be able to work his fteam-wheel in
a manner free from any material draw-back upon the advantage arifing
from its conftant rotatory motion in one direction, it would then un-
doubtedly be fuperior to any fteam-engine, of which we have ever heard,
or that has probably been yet invented.
1
Cartwright's Steam-Engines.
389
an acendent from a rude hand prevented its application for that
time, and we do not think it was ever refumed.
•
}
The packing of Mr. Cartwright's pifton is compofed of a
feries of fegments of brafs, the arches of which conform exactly
to the circumference of the cylinder; theſe are to be laid on the
verge of the pifton fo as to make one entire difk, then another
and another ftratum fuper ftratum until the defigned thickneſs
is acquired: then to keep thefe fegments in conſtant tendency
to the place of action, there are a fet of ſprings very nicely con
trived to act on the concave edge, which, no doubt, will keep
them to their work; but the difficulty is how to preferve the fit
at the junctures: it is impoffible for the fegment of a fmall
circle to become the fegment of a larger circle*. But we do
not ſuppoſe Mr. Cartwright to have intended this metallië
packing to compenfate the irregular figure of the fteam-veſſel,
for it is impoffible; befide, Mr. Cartwright's notions of accuracy
would never ſuffer him to admit a ſteam-veffel to his engine
which was not a perfect cylinder; in which caſe theſe fegments
may have but little wear, though, if they were of metal in any
degree ſofter than the cylinder, the duft which will find its way
there, would wear away the cylinder fo as to be fenfibly detri
mental: added, that this packing could never apply to a double
engine. It, however, ferves as a very elegant fpecimen of the
inventor's inclination to accurate working.

A
Since the above was written, we have ſeen an engine of Mr.
Cartwright's at a tan-yard near Horfley-Down, which gives great
fatisfaction to the proprietor. The pifton, by the account of
the tender of the engine, has not even been looked at for many
months, nor has he any indications that it will be neceffary for
many more. This account receives ſtrong confirmation by the
appearance of the quantity of condenſed fteam which is dif-
charged from the engine every ſtroke, which, as it is not
effected in the common way (by injection), can be very exactly
eſtimated. Its conftruction is very fimple, and it performs its
operations very ſmoothly and effectually†.
Admitting that theſe ſegments wear away on the outer arches, the
inner arches muſt recede from the centre, and therefore will be one con
tinued deduction from the entire circle.
✦ Mr. Cartwright's contrivance for preferving the parallel motion of
the piſton-rod, at the fame time that it communicates the rotatory motion
to the fly, is very ingenious, and is therefore fhewn in plate XXXV. fig. 3.
where P is the top of the pifton-rod, upon which is fcrewed a tranfverfe
bar B: to the ends of this bar, at equal diſtances from the top of the
pifton-rod, are attached the two equal connecting rods H, H, which as the
pifton rifes and falls turn the cranks and the two equal wheels W, W;
theſe two equal wheels work into each other, and one of them drives
the pinion C upon the ſame axis as the fly-wheel O; thus communicat
ing the rotatory motion to the other parts of the machinery. AUTHORI
A
A
390
MACHINES.
To conclude this fubject: Mr. Watt's engine, as it now.
ftands, is the work of fix-and-thirty years, and we may hold it
as complete in its kind as it poffibly can be. It has exerciſed
all the ingenuity of the inventor, befide frequent acceffions
from the ingenuity of other men: various pretensions and
conceits no doubt will abound to rival its excellency, and time
only, the arbiter in human affairs, will determine their fate,
We would rather fee a laudable competition prevail to ſimplify
its parts, without affecting the principle, either by reducing
their number, or by difpenfing with their coftly finiſh, or per-
haps both, that it may come within the compaſs of the middle
ranks as well as of the more opulent: and the man who fets the
example will deferve well of his country.
Wie
II. A communication from Mr. Farey, junior.
+
+
Pl. XXXI. fig. 1. reprefents a STEAM-ENGINE, erected in
1802, by Meffrs. Murray and Wood of Leeds, for Francis.
Brewin, efq. at his tan-yard in Willow Walk, Bermondſey;
and fig. 2. reprefents fome parts thereof on a larger ſcale: AA
is the fhaft for conveying the power of the engine to work a
bark-mill and feveral pumps. The fteam from the boiler en-
ters through the pipe B into the affemblage of pipes, technically
termed nofsels, or valve-boxes, reprefented feparately in fig. 2,
which contain the valves for diftributing the fteam at proper
intervals into the cylinder CC, and letting the fame off again
to the condenfer M. The cylinder CC, which is cafed with
wood to keep in the heat, has a folid pifton moving in it,
whoſe poliſhed pifton-rod D paffes through a ſtuffing-box; the
upright motion of this rod is converted into a rotary one by the
following contrivance: the circular rim E, three feet diameter,
with feventy-two teeth on the infide, is firmly fixed and fuf-,
pended from the floor, by two caft-iron pillars FF and braces
LL; the ſmall wheel G, of eighteen inches diameter and
thirty-fix teeth, is made to revolve within-fide of the rim, fo
as always to touch the teeth by a pin (the end of which is re-
prefented in the centre of the wheel G), firmly fixed on the
wheel H, parallel to its axis AA, with which it always moves;
and nine inches from its centre, on the circumference of the
wheel G, is a bolt I, fcrewed on perpendicular to its plane, in
fuch a place, that when the wheel G is at the bottom of the
rim E, the bolt is on the loweft tooth; and when the fmall
wheel is at the top of the rim, it is on the higheft: to this bolt
the pifton-rod D and the air-pump-rod K are attached, and the
tops of thefe rods, by moving up and down in right lines, paffing.
Murray and Wood's Steam-Engine.
391 -
through the axis of the wheel H, will communicate a fotatory
motion to that wheel, and all on the fame fhaft. (See the article
PARALLEL Motion).
The wheel a, on the axis AA of the fly-wheel NN, commu-
nicates its motion by the wheels fhewn in fig. 2, to the wheel
which wheels are fo contrived, that one revolution of the
fly will produce one of the wheel b, on wheſe axis are two ec-
centric wheels cand d, which alternately raife the rods e and f
for opening the valves contained in the fhort cylinders or valve-
boxes gg and bb: each of theſe boxes has three divifion's; thể
upper divifion of the upper box contains a valve 1, called the
upper fleam-valve; its ufe is to admit fteam from the boiler
through the pipe B, into the middle divifion which communi-
cates with the cylinder; in this box is a valve 2 (which is moved
by a rod paffing through the rod of the other valve †), called the
upper condenfing-valve (or exhausting-valve); it is for opening a
paffage from the top of the cylinder to the condenfer by the
pipe q. In the fame manner, the upper valve 3 of the lower
box is called the tower fteam-valve, and is for admitting team
into the lower part of the cylinder by means of the pipe r; the
valve 4 is for connecting the bottom of the cylinder with the
condenfer, and is therefore called the lower condenfing-valve.
The rod ƒ connects at its top with the upper condenſing-valve (2),
and the lower Ream-valve (3) at its bottom; it will therefore,
when it is lifted up by the eccentric wheel d, open thofe valves,
and by catifing a vacuum above, and a preffure of feam be-
neath, the pifton, force it upwards, and move the machinery
alfo the rod é, connecting with the upper feam-valve 1 at its
top, and the lower condenfing-valve 4 at its bottom, being lifted
up by the eccentric wheel c, will caufe the piſton to deſcend;
but this will not be the cafe, uffles one rod is permitted to de-
ſcend by its own weight, as the other is lifted, otherwife the
fteam will leave free paffage from the boiler to the condenfer
which operation is called blowing through.


+
The condenfer M is a cylindric veffel, into which is admitted
a fmall jet of cold water, by the cock, called the injection-
cock: the bottom of the condenfer communicates by a fhort
pipe O (which pipe contains a valve fhutting towards the con-
denfer), with the air-pump P, four inches diameter and three
feet ftroke; the pifton of the arr-pump has a valve in it, and is
moved by the rod K, as before defcribed; the air-pump's office
is to extract the water of the condenſed fteam, injection, &c.
from the condenfer, and keep the vacuum perfect. The air-
pump and condenfer must be in a well or ciftern of cold water.
To work this engine, the fteam must be made of fufficient
elafticity to ruth forcibly out of the boiler when permitted;

.
392
….. MACHINES.
draw the handles n and o:apart from each other, which ading
as levers againſt the ſtubs on the rods e.and fy will raife.them
up in a ſmall degree, and open all the valves at once; and the
fteam by blowing through, will expel the water, air, &c. which
may have filled the cylinder and condenfer, at a valve fhutting
outwards in the condenſer for that purpoſe...When it is thought
that the air, &c. is all driven out, one or other of the handles
must be dropped (according to the pofition of the wheel G);
the injection cock is then opened by its handle p, which fud-
denly cooling the ſteam, reduces it to the bulk it formerly pof-
feffed in the boiler, and forms a vacuum in the condenser, the
Steam from the cylinder which ruſhes in to reſtore the equili-
brium is condenfed as it goes, and almoſt inſtantaneouſly a
nearly perfect vacuum is formed on one fide of the piſton; and
the fteam from the boiler preffing on the other, deftroys the
equilibrium on it, and puts the engine in motion. When the
pifton is at the top of its stroke by the arrangement of the
wheels in fig. 2, the eccentric wheel & will lift the rod e (at the
time the rod fis permitted to defcend by its weight), and cauſe
the pifton to defcend; and when at the bottom the rod ƒ will be
lifted, and e will fall, which forces it upwards again.
To ftop the engine, nothing is neceffary but to lift up both
the handles and shut the injection-cock (which ſhould always
be hut when the engine is not at work), to prevent the con-
denfer from filling with water; and as foon as the mornentum
of the fly-wheel is ſpent, the motion of the engine will ceaſe;
it might alſo be ſtopped by only cutting off the injection, which
would, after a confiderable number of ſtrokes, render the va-
cuum fo imperfect as to deſtroy its
deſtroy its power.
The cylinder of this engine is twelve inches diameter, and
has a three-feet ftroke; its power is computed at four horſes,
it makes about fifteen ftrokes per minute, and burns about nine
bushels of coals in fourteen hours, being the uſual period of
working.
III. M. Bettancourt, whofe curious and valuable experiments.
on the expanfive force of fteam are mentioned in the introduc-
tory part of this volume, was employed by the court of Spain to
make a collection of refearches and of models for the perfection
of hydraulics: when in England he took occafion (according to
M. Prony) to vifit the fteam-engines (machines à feu) of
Meffrs. Boulton and Watt. He faw, in part, the exterior con-
ftruction and operation of thoſe machines; but the interior me-
chamim was to concealed, that M. Bettancourt could only


Bettantourt's Steam-Engine.
8893
му
gnefs at the nature of the construction. He obferved that the
chains were fuppreffed, which are ufually put at the extremi-
ties of the great beam; and feparating walls, &c. prevented
him from examining all even of the exterior parts, fo as
thoroughly to underſtand their correfpondence and complete
effect: he concluded, notwithſtanding, from his obfervations,
that the pifton of the cylinder was urged with the fame effort,
both in its deſcent and its afcent; and this, in fact, was diſco-
vering the double effect which conftitutes effentially the chief
improvement made in theſe machines by Meffrs, Boulton and
Watt.
:
·
M. Bettancourt foon after devifed fome fteam-engines of
double effect; one of which being very fimple and ingenious,
may here be defcribed, at leaſt all which is peculiar to it. See
fig. 3. pl. XXXI. The fteam coming in the ordinary way from
the boiler, which is omitted to render the defign more fimple,
paffes through the tube b, and introduces itſelf by the aperture
into the ſpace of which the circle ee reprefents the profile or
vertical ſection. This chamber ee' has, befides the orifice v,
two others, the one placed by the fide of the canal d, to com-
municate by means of that canal with the fuperior part B of the
cylinder BB'; the other placed below at v', and communicates
by means of the tube or canal v'd' with the inferior part B of
the cylinder, of which the pifton is reprefented in X. The
ſpace, or circular chamber e" e", communicates in a fimilar man-
ner with the upper and lower parts of the cylinder, by means
of the tubed, and the canal d. Moreover, this chamber
ee" communicates by means of the orifice" with the cham-
berff, where the valve j is found adapted to the aperture
through which iffues the water of injection deftined to condenfe
the vapour: this valve is always open, except when we would
ftop the machine; but it may approach the orifice more or leſs,
according to the velocity which we would give to the piston.
The outlets v and "" are, in like manner, always open.
1
v
•
The orifices v', v", and thofe which eftablish the communica-
tion with the cylinder by means of the canals d and d', are
cloſed alternately by the valves gb, or g'b' of a particular kind.
Fig. 3. no. 2. reprefents the profile of either of thefe valves. The
part g h curved into the arc of a circle of the fame radius as that
of the vertical fections eé, é" e", and turning upon an axis placed
at the centre o, may in its revolution clofe any aperture what-
ever placed upon the circumference of thofe fections.""
This being understood, fuppofe things in the ftate repre-
fented in fig. 3. no. 1. and the vacuum eſtabliſhed in the
part
of the cylinder above the pifton. The ſteam entering by the
orifice, finds the canal d cloſed, paffes through the tube

394
MACHINES.
>
vd, but cannot introduce itſelf into the chamber e"" bez
caufe of the valve g'b'; it therefore enters wholly into the
lower part B' of the cylinder. Hence it acts upon the piston X,
with all the energy of which it is capable: the piſton pufhes"
the great beam by means of the pifton-rod XK, and the oppo
fite part of that beam acts with a like effort upon the rod or
bar deſtined to give the rotatory motion to the fly. The pifton
X having thus arrived at the highest point of its courſe, the
valve g' h makes a part of a rotation, ſo as to cloſe the orifice "
and open the canal d'; in the ſame time the valve gʼn makes part
of a revolution likewife, to cloſe the aperture v' and open the
canal d. The aqueous gas continuing to enter at v, which is
conftantly open, finds the orifice v clofed, penetrates into the
canal d, and not having any paffage through the orifice v", goes
entirely into the upper part of the cylinder: during this time,
the ſteam which was in B' is expelled through d', penetrates into
v", which is always open, and becomes condenſed about the
valvej. By thefe means the fteam which enters B, acting with
all its energy upon the piſton X, makes it defcend, and pro
duces, by defcending, equal effects to thofe it caufed when
afcending. The piſton, then, having arrived at the loweſt
point of its courfe, the valve gh which clofed the orifice v',
and the valve gb', which clofed the orifice v", return both to
their primitive fituation; and fo on throughout.
V
The extent of the ftroke of the piſton muſt manifeftly be fuch-
that the apertures of the canals at d, and d', placed in the fide
of the cylinder, are never stopped by the piston.
It is almoſt needlefs to fay, that the interior mechanifm re-
lative to the valves gh, g'h', may be moved by various con-
trivances, each depending upon the alternating motion of the
pifton: fo that no other agents will be required diftinct from
the machinery, than what are wanted for keeping up the fire.
IV. Before we entirely quit the ſubject of ſteam-engines, we
fhall preſent the reader with fome account of the late improve-
ments in their conftruction, &c. by Mr. Arthur Woolf.
Mr. Woolf founds his improvements on a very important
diſcovery which he has made refpecting the expanfibility of
fteam when increaſed in temperature beyond the boiling point,
or 212° of Fahrenheit's thermometer. It has been known for,
ſome time-and for this diſcovery the world is indebted to Mr.
Watt, the principal improver of the ſteam-engine—that ſteam:
acting with the expanfive force of four pounds the fquare inch
againſt a ſafety-valve expoſed to the atmosphere, is capable of
་
Woolf's ´Steam-Engines.
395
expanding itſelf to four times the volume it then occupies,
and ſtill to be equal to the preffure of the atmoſphere. Mr.
Woolf has difcovered that, in like manner, fteam of the
force of five pounds the fquare inch can expand itſelf to five
times its volume; that maffes or quantities of fteam of the
like expanfive force of fix, feven, eight, nine, or ten pounds
the fquare inch, can expand to fix, feven, eight, nine, or ten
times their volumes, and ftill be refpectively equal to the at-
moſphere, or capable of producing a fufficient action againſt
the pifton of a ſteam-engine to cauſe the fame to rife in the old
engine (with a counterpoife) of Newcomen, or to be carried
into the vacuous part of the cylinder in the improved engines
firft brought into effect by Meffrs. Boulton and Watt; that
this ratio is progreffive, and nearly if not entirely uniform, ſo
that fteam of the expanfive force of twenty, thirty, forty, or
fifty pounds the ſquare inch of a common fafety-valve will ex-
pand itſelf to twenty, thirty, forty, or fifty times its volume;
and that, generally, as to all the intermediate or higher degrees
of elaftic force, the number of times which fteam of any tem-
perature and force can expand itſelf is nearly the fame as the
number of pounds it is able to fuftain on a ſquare inch expofed
to the common atmoſpheric preffure; provided always that the
ſpace, place, or veffel, in which it is allowed to expand itfelf, be
of the fame temperature as that of the team before it be allowed
room to expand.
Refpecting the different degrees of temperature required to
bring ſteam to, and maintain it at, different expanfive forces
above the weight of the atmoſphere, Mr. Woolf has found, by
actual experiment, fetting out from the boiling point of water,
or 212°, at which degree ſteam of water is only equal to the
preffure of the atmoſphere, that in order to give it an increaſed
elaftic force equal to five pounds the ſquare inch, the tempera-
ture muſt be raiſed to about 2274°, when it will have acquired'
a power to expand itſelf to five times its volume, ſtill be equal
in preffure to the atmoſphere, and capable of being applied as
fuch in the working of fteam-engines, according to his inven-
tion; and with regard to various other preffures, temperatures,
and expanfive forces of fteam, the fame are shown in the fol-
lowing table:

}
596
MACHINES.

and
Table of the relative preffure per square inch, temperature.
expanfibility of fream at degrees of heat above the boiling point of
water, beginning with the temperature of fteam of an elastic
force equal to five pounds per square inch, and extending to fleam
able to fuftain forty pounds on the fquare inch.
(

Pounds per
square Inch.
Degrees
of heat.
Expan-
fibility.
Steam of
57
82272 7
I
57
an elaftic
force pre-
dominat-
ing over
the pref-
Hare of
6
230/1/
6
times its
and at
78
requires
232
theſe re-
7
volume,
to be
235
8
9
maintain-
237/1/2
237를
​ſpective
and con-
degrees of
9
tinue
ΙΟ
ed by a
239
2
heat,
10
equal in
15
250/1/
the atmo-
tempera-
fteam can
15
elasticity
20
2591
20
to the
fphere
ture equal
25
to about
267
expand
I itſelf to
25
preffure
upon a
30
273 about
30
of the at
fafety-
35
278
35 moſphere
valve.
140!
(282 J
L40]
So in like manner, by fmall additions of temperature, an ex-
panfive power may be given to fteam to enable it to expand to
fifty, fixty, feventy, eighty, ninety, one hundred, two hun-
dred, three hundred, or more times its volume, without any li-
mitation but what is impofed by the frangible nature of every
material of which boilers and the other parts of ſteam-engines
have been or can be made; and prudence dictates that the ex-
panfive force fhould never be carried to the utmoſt the materials
can bear, but rather be kept confiderably within that limit.
Having thus briefly explained the nature of Mr. Woolf's dif-
covery, we ſhall proceed to give a defcription of his improve-
ments grounded upon them; and for which he has obtained
the ufual fecurity of a patent. Mr. Woolf in his fpecifica-
tion ftates, that in defcribing his invention he has found it ne-
ceflary to mention the entire fteam-engine and its parts, to
which, as an invention well known, he neither can nor does
affert any exclufive claim: he obferves, however, that from the
nature of his aforefaid diſcovery, and its application, there can
be no difficulty in diftinguifhing his faid improvements from
the improved engine (of Mr. Watt) as to its other common and
well-known parts, and then gives the following account of an
engine embracing his new improvements.
"If the engine be conftructed originally with the intention
of adopting my faid improvement, it ought to have two ſteam-
Woolf's Steam-Engines.
397
veffels of different dimenfions, according to the temperature or
the expanſive force determined to be communicated to the
ſteam made uſe of in working the engine; for the fmaller fteam-
veffel or cylinder must be a meaſure for the larger. For ex-
ample, if team of forty pounds the fquare inch is fixed on,
then the ſmaller fteam-veffel fhould be at leaſt one-fortieth part
the contents of the larger one; each ſteam-veffel ſhould be fur-
niſhed with a piſton, and the ſmaller cylinder fhould have a
communication both at its top and bottom (top and bottom be-
ing here employed merely as relative terms, for the cylinders
may be worked in a horizontal or any other required pofition,
as well as vertical), the fmall cylinder, I fay, ſhould have a
communication both at its top and bottom with the boiler which
fupplies the ſteam; which communications, by means of cocks
or valves of any conftruction adapted to the uſe, are to be al-
ternately opened and fhut during the working of the engine.
The top of the ſmall cylinder fhould have a communication
with the bottom of the larger cylinder, and the bottom of the
fmaller one with the top of the larger, with proper means to
open and fhut theſe alternately by cocks, valves, or any other
well-known contrivance. And both the top and bottom of the
larger cylinder or fteam-veffel fhould, while the engine is at
work, communicate alternately with a condenfing veffel, into
which a jet of water is admitted to haften the condenſation, or
the condenfing veffel may be cooled by any other means cal-
culated to produce that effect. Things being thus arranged,
when the engine is at work, fteam of high temperature is ad-
mitted from the boiler to act by its elaſtic force on one fide of
the ſmaller piſton, while the ſteam which had laft moved it has
a communication with the larger fteam-veffel or cylinder, where
it follows the larger pifton now moving towards that end of its
cylinder which is open to the condenfing veffel. Let both pi-
ftons end their ftroke at one time, and let us now ſuppoſe
them both at the top of their refpective cylinders, ready to de-
fcend; then the fteam of forty pounds the fquare inch entering
above the ſmaller pifton will carry it downwards, while the
fteam below it, inftead of being allowed to efcape into the at-
moſphere or applied to any other purpoſe, will paſs into the
larger cylinder above its pifton, which will take its downward
ftroke at the fame time that the pifton of the finall cylinder is
doing the ſmall thing; and while this goes on, the fteam which
laft filled the larger cylinder, in the upward ftroke of the engine,
will be paffing into the condenfer to be condenfed during the
downward ftroke. When the piftons in the fmaller and larger
cylinder have thus been made to defcend to the bottom of their
refpective cylinders, then the fteam from the boiler is to be
ſhut off from the top and admitted to the bottom of the ſmaller
$98
MACHINES.
cylinder, and the communication between the bottom of the
fmaller and the top of the larger cylinder is alfo to be cut
off, and the communication, to be opened between the top of
the fmaller and the bottom of the larger cylinder; the fteam,
which in the downward ftroke of the engine filled the larger cy-
finder, being now open to the condenfer, and the communica-
tion between the bottom of the larger cylinder and the condenfer
fhut off; and fo on alternately, admitting the ſteam to the dif-
ferent fides of the ſmaller pifton, while the ſteam laſt admitted
Into the ſmaller cylinder paffes alternately to the different fides
of the larger pifton in the larger cylinder, the top and bottom
of which are made to communicate alternately with the con-
denfer.
"In an engine working with the improvements which have
been juft defcribed, while the fteam is admitted to one fide of
the pifton in the fmaller cylinder, the fteam on the other fide
has room made for its admiffion into the larger cylinder, on one
fide of its pifton, by the condenſation taking place on the other
fide of the large pifton which is open to the condenfer; and
that wafte of fteam which takes place in engines worked only
by the expanfive force of ſteam, from fteam paffing the pifton,
is prevented; for all fteam that páffes the piſton in the ſmaller
cylinder is received into the larger.
"In fuch an engine, where it may be more convenient for
any particular purpoſe, the arrangement may be altered, and
the top of the fmaller made to communicate with the top of the
larger, and the bottom of the fmaller with the bottom of the
larger cylinder; in which cafe the only difference will be, that
when the piston in the fmaller cylinder defcends, that in the
larger will afcend; and while the other defcends, the former will
afcend; which for fome particular purpoſes may be more conve-
nient than the arrangement before defcribed."
Mr. Woolf, in his fpecification, deſcribes various other mo-
difications of his invention; and points out means for applying
his improvements, before ftated, to the working of fteam-
engines already conftructed, and in ufe; that is, to the working
of engines with one fteam-veffel only, without taking advantage
of the expanfive force of the fteam on a pifton in another cy-
finder. Suffice it to fay, that proper means being employed to
keep the fteam-veffel or working cylinder at the required tem-
perature, the fteam is admitted into it in quantities proportioned
to its expanfive power: for example, if the fteam be of a force
equal to forty pounds the fquare inch, the throatle-valve is fo ad-
jufted as to admit into the working cylinder a quantity of ſteam
equal to only one-fortieth part of its capacity, which ſteam ex-
pands as it enters, fo as to fill completely the whole cylinder.
In this firft improvement of Mr. Woolf, though the faving
Woolf's Steam-Engines.
329
of fuel might be carried to a confiderable length, and, with an
engine erected by Meffrs. Murray and Cay of Leeds, has
actually been proved to be more than one-half of the whole
quantity employed in a well-constructed double engine of the
fame power, it was ftill neceffarily limited by the ſtrength of
materials; for in the employment of high fteam, there muft
always be ſome danger of an explofion. Mr. Woolf, however,
by a happy thought, has completely obviated every danger of
this kind, and can now take the full advantage of the expanfive
principle without the leaft danger whatever. This he effects
by throwing into common fteam the additional temperature
neceffary for its high expanſion, after the fteam is admitted into
the working cylinder, which is heated by means adequate to the
end intended to be obtained; and the advantage which he thus
gains, he effectually fecures by a moft ingenious improvement in
the pifton. It may be safily conceived that fteam of fuch high
rarity as Mr. Woolf employs, could not be made fully effective
with the pifton in common ufe; for in proportion to its rarity, fo
maft be the facility with which a portion of it would eſcape,
and paſs by the fide of the pifton to the vacuous part of the
Cylinder: but Mr. Woolf's contrivance, which confifts in em-
ploying upon the pifton a column of mercury or other metals
in a ſtate of fufion of an altitude equal to the preffure of the
fteam, feems perfectly adapted to prevent the lofs of even the
fmalleft portion of the fteam.
Befides thefe improvements on the common fteam-engine,
he has alſo found means to apply the fame principles to the old
engine, known by the name of Savary's, in fuch a way as to
fender the fame a powerful and economical engine for a great
variety of purpoſes.
Such is the outline of Mr. Woolf's new improvements on
this moſt uſeful engine: but, for the general information of
practical engineers, we fhall here fubjoin a more technical
deſcription in Mr. Woolf's own words, extracted from his
fpecification of his fecond patent.
"I have found out and invented a contrivance, by which
the temperature of the fteam-veffel or working-cylinder of a
fteam-engine, or of the fteam-veffels or cylinders where more
than one are uſed, may be raiſed to any required temperature,
without admitting fteam from the boiler into any furrounding
receptacle, whether known by the name of a ſteam-cafe, or by
'any other denomination. That is to fay, inſtead of admitting
fleam of a high temperature into fuch receptacle or fteam-cafe,
which is always attended with a risk of exploſion proportioned
to the elafticity of the fteam employed, I put into the faid fur-
rounding receptacle, or cafe, oil or the fat of animals, or wax
or other fubftances capable of being melted by a lower tempera-

400
MACHINES.
:
ture than the heat intended to be employed, and of bearing that
heat without being converted into vapour: or I put into the faid
cafe or cafes mercury or mixtures of metals, as of tin, biſmuth,
and lead, capable of being kept in a ſtate of fufion in a lower
temperature than that intended to be employed in working the
Ateam-engine and I fo form the furrounding cafe or cafes as to
make it or them admit the aforefaid oil, or other ſubſtance em-
ployed, to come into contact not only with the fides of the
team veffel or veffels, or working cylinder or cylinders, but
alſo with the bottom and top of the fame, fo that the whole
may be as much as poffible maintained at one uniform tempe-
rature; and this temperature I keep up by a fire immediately
under or round the caſe or cafes that contain the aforefaid oil
or other ſubſtance, or by connecting the ſaid cafe or caſes with
a feparate veffel or veffels, kept at a proper temperature, filled
with the oil or other fubftance made ufe of as aforefaid. In
fome circumſtances, or whenever the fame may be convenient
or deſirable, I employ the fluid-metals, or mixtures of metals,
in the part of the cafe or veffel expofed to the greateſt actión
of the fire, and in the parts leſs expoſed to the action of the
fire I put oil, or other ſubſtances capable of bearing the requifite
heat without being converted into vapour.
"By this arrangement, and method of applying the fur-
rounding heat, I not only obviate the neceffity of employing
fteam of a great expanſive force round the fteam veffel or
veffels, or the working cylinder or cylinders, as already men-
tioned, to maintain them at the temperature required, but F
am enabled to obtain from ſteam of a comparatively low tem-
perature, or even from 'water itſelf, admitted into the fteam
veffel or veffels, all the effects that can be obtained from ſteam
of a high temperature, without any of the riſk with which the
production of the latter is accompanied, not only to the boiler
and other parts of the machinery, but even to the lives of the
workmen for fuch low fteam, or even water (but in every cafe
fteam is preferable), being admitted into a ſteam veffel or vef-
fels, or working cylinder or cylinders, kept at the requifite
higher temperature by the forementioned means, will there be
expanded in any ratio required, and produce an effect in the
working of the engine, which cannot otherwiſe be obtained but
at a greater expence of fuel, or with the risk of an explofion. By
this means I can make uſe of ſteam expanded in any required
ratio, or of any given temperature, without the neceffity of ever
having the fteam of any greater elaſticity than equal to the pref
fure of the common atmoſphere.

;
"Another improvement which I make ufe of in ſteam-en-
gines confifts in a method of preventing, as much as poffible,
the paffage of any of the ſteam from that ſide of the piſton
Woolf's Steam-Engines.
401
+
which is acted upon by the faid fteam to the other fide which is
open to the condenfer; and this I effect in thofe fteam engines
known by the name of double-engines, by employing upon or
above the pifton mercury or fluid metal or metals in an altitude
equal to the preffure of the fteam. The efficacy of this arrange
ment will appear obvious, from attending to what must take
place in working fuch a piston. When the pifton is aſcending,
that is, when the ſteam is admitted below the piiton, the ſpace
on its other fide being open to the condenfer, the fteam endea-
vouring to paſs up by the fide of the pifton is met and effectually
prevented by the column of metal equal or fuperior to it in
preffure, and during the down-ftroke. no fteam can poffibly
paſs without first forcing all the metal through. In working
what is called a fingle engine, a, lefs confiderable altitude of
metal is required, becauſe the fteam always acts on the upper?
fide of the pifton. For fingle-engines, oil or wax, or fat of
animals, or fimilar fubftances, in fufficient quantity, will an-.
fwer the purpoſe, if another improvement, which conftitutes
part of my faid invention, be applied to the engine, namely, to
take care that in either the double or fingle engine fo to be
worked, the outlet that conveys the fteam to the condenſer
fhall be fo pofited, and of ſuch a fize, that the ſteam may paſs
without forcing before it or carrying with it any of the metal or
other fubftance employed that may have paffed by the pifton;
taking care at the fame time to provide another exit for the
metal or other ſubſtance collected at the bottom of the Ateam-
veffel or working-cylinder to convey the fame into a refervoir
kept at a proper heat, whence it is to be conveyed to the upper
fide of the pifton by a ſmall pump worked by the engine or by
any
other contrivance. In order that the fluid metal or metals
ufed with the pifton may not be oxidated, I always keep fome
oil or other fluid fubftance on its furface to prevent its coming
in contact with the atmoſphere; and to prevent the neceffity of
employing a large quantity of fluid metal, I generally make my
pifton of the depth of the column required, but of a diameter a
little less than the fteam-veffel or working-cylinder, excepting
where the packing or other fitting is neceffary to be applied; fo
that, in fact, the column of fluid metal forms only a thin body
round the pifton. In fome cafes I make a hollow metallic
piſton, and apply an altitude of fluid metal in the infide of the
fame to prefs its outfide into contact with the ſteam-veſſel or
working-cylinder.
*
"It may be neceffary, however, to ſtate, that in applying my
improved method of keeping the ſteam-veffels of ſteam-engines
at any required temperature to the engine known by the name
of Savary's in any of its improved forms, in which a ſeparate
VOL. II.
DD
7

402
MACHINES.
par-
condenfer has been introduced, I fometimes employ oil, or
any other ſubſtance lighter than water, and capable of being
kept fluid in the temperature employed, without being con-
verted into vapour, in the upper part of the tube or pipe at-
tached to the ſteam-veffel; by which means fteam of
any tem-
perature may be uſed without being expoſed to the riſk of
tial condenſation by the admiſſion of any colder body into the
ſteam-veffel; for the oil, or other ſubſtance employed for this
purpoſe, foon acquires the requifite temperature; and to pre-
vent unneceffary eſcape of heat, I conftruct of, or line with,
an imperfect conductor of heat, that part of the tube or pipe
attached to the ſteam-veffel which may not be heated exteriorly.
And further (as is already the practice in fome engines, and
therefore not exclufively claimed by me), I cauſe the water
raiſed by the engine to paſs off through another aſcending tube
than the one attached to the fteam-veffel, but connected with
it at ſome part lower than the oil or other fubftance employed
in it is ever ſuffered to defcend to the working of the engine.
The improvement which I have juſt mentioned, of introducing
oil into the pipe attached to the fteam-veffel of fuch engines,
may alſo be introduced without applying heat externally to the
fteam-veffel; but in this cafe, part of the effect which would
otherwife be gained is loſt.”
From the foregoing details, there feems to be a reaſonable
ground to hope that a great defideratum, a real faving of fuel,
will be effected by Mr. Woolf's improvements, founded on his
difcovery of the ratio in which fteam of any high temperature
can expand itſelf. It is certainly a new and curious fact, that
team may, by mere additions of temperature, be increaſed in
volume in the way he ftates, and ftill be equal in force to the
common atmoſphere. The advantage which he gains, or, in
other words, the faving which he effects in the quantity of
fuel, depends entirely on the correctneſs of this fact; for, ac-
cording to the ideas hitherto entertained, ſteam of the ftrength
of about thirty pounds the inch, above the common atmoſphere,.
ought only to effect the work of two atmoſpheres more than
fteam of 212°; but according to Mr. Woolf, by proper ma-
nagement, it may be made to produce the work of thirty at-
moſpheres!
:
By what we have juſt ſtated, we would not be underſtood to
call in queſtion the accuracy of Mr. Woolf's experiments; for
he has had ſo much practical experience in his capacity of en-
gineer to one of the largeſt concerns in London (Meffrs.
Meux's brewhouse), that it would be difficult to believe he
could be miſtaken on a point of fo much importance. His in-
vention will foon be put to the teft of experience; a large en-
.
•
Woolf's Steam-Engines.
403
gine being now erecting under his direction at Meffṛs. Meux's,
Beſides others in different manufactories. Should they answer
the expectations that have been formed of them, Mr. Woolf's
diſcovery will form a new and fingular epoch in the hiſtory of
an engine, which had previously been brought to a ftate of fuch
high perfection as almoft to exclude the hope of any further
improvement.
Mr. Woolf has alſo invented fome boilers for ſteam-engines,
different from the ufual conſtruction; in which, befides employ-
ing fafety-valves, he has introduced a valve of a new construc-
tion to regulate the quantity and power of the fteam paffing
from the boiler. In theſe the fteam-box is joined to the neck
or outlet for the fteam by flanges. The top or cover of the
ſteam-box, which is well fecured in its place, has a hole through
it for the rod of the valve, fo contrived as to anſwer the pur-
poſe of a ſtuffing-box to make the rod work up and down ſteam-
tight, the ſtuffing being kept in its place by the uſual means, well
known to engineers. By means of a pin or nail, and two yer-
tical pieces, the pifton-rod is made faſt to a cover joined to the
hollow cylinder. The cover fits ſteam-tight into a collar, which
is made faft on the flange before mentioned. The cylinder is
open at the bottom, having a free communication with the main
cylinder, and has three vertical flits. The fum of the ſurface
of all theſe flits or openings is equal to the area of the opening
of the collar in which the cylinder works. When the fteam
acquires a fufficient degree of elaſtic force to raiſe the valve
(that is, the hollow cylinder with its cover and rod), and what-
ever weight it may be loaded with, then the openings, getting
above the ſteam-tight collar, allow the fteam to pafs into the
fteam-box. The quantity of ſteam that paffes is proportioned
to the elaſtic force it has acquired, and the weight with which
the valve is loaded; and the riſe of the openings above the col-
lar will be in the fame proportion. This valve may be loaded
in any of the ufual methods; but Mr. Woolf prefers one in
which the upper part of the rod is joined by means of a chain
to a quadrant of a circle with an arm projecting from it, which
carries a weight that may be moved near to or further from the
centre of the quadrant, according as the preffure of the valve is
wiſhed to be increaſed or diminiſhed. As the valve rifes, the
weight moves upward, giving an increaſed refiftance to the fur-
ther rifing of the valve, proportioned to the greater horizontal
diſtance from the centre of the quadrant, which the weight at-
tains by its rife in the faid arch, that diftance being meaſured
in the horizontal line by a perpendicular from the faid line pafs-
ing through the centre of the weight. Thus the rod joining
the quadrant and the great weight, may be made to ſerve at the
DD 2
404
MACHINES.
fame time as an index to the perſon who attends the hire, no-
thing more being neceffary for this purpoſe than to graduate
the arch deſcribed by the end of the rod. In the fide of the
fteam-box there is an opening to allow the fteam to paſs from
it by a pipe or tube to the fteam-engine, or to any fecondary
boiler, or for the purpoſe of conveying and applying it to any.
other veffel or ufe to which fteam is applicable. A figure of
this ſteam-valve may be feen in Tilloch's Philofophical Maga-
zine, No. 66.
As to Mr. W.'s propoſed improvements in boilers, they con-
fiſt, first, of two or more cylindrical veffels properly connected
together, and ſo difpofed as to conftitute a ftrong and fit recep-
tacle for water, or any other fluid intended to be converted into
ſteam, whether at the ufual heats or at temperatures and under
preffure's uncommonly high; and alfo to prefent an extenfive
portion of convex furface to the current of flame, or heated air
or vapour from a fire: fecondly, of other cylindrical receptacles
placed above thefe cylinders, and properly connected with them,
for the purpoſe of containing water and fteam, and for the re-
ception, tranfmiffion, and uſeful application of the fleam ge-
nerated from the heated water or other fluid: and, thirdly,
of a furnace ſo adapted to the cylindrical parts juſt mentioned,
as to cauſe the greater part of the furface of all and each of
them, or as much of the faid furface as may be convenient or
deſirable, to receive the direct action of the fire, or heated air
and vapour.
:
The principal of theſe improvements, if they be really fuch,
occurred to Mr. Blakey long ago, as was obferved by Mr. Horn-
blower. Blakey's boiler and furnace are reprefented in fig. 9.
pl. XXIII. Mr. Woolf's may be ſeen in No. 65 of the Phi-
loſophical Magazine.
*
From the whole of the preceding accounts the reader will,
we hope, be able to obtain more correct and uſeful informa-
tion relative to the nature and manner of operation of the prin-
cipal ſteam-engines than can be obtained from any Treatife of
Mechanics yet publifhed in this country. Yet, as the ſubject
is of great importance, and furniſhes variety fufficient to fill a
volume of itſelf, we beg to refer thoſe who wiſh to learn the
conſtruction-of other kinds of theſe uſeful machines, to the
different volumes of Nicholson's Journal, Tillock's Magazine, the
Repertory of Arts and Manufactures, and the Architecture Hy-
draulique of Prony. -
•
J
We fhall conclude with a fint refpecting the economical
Steel-yard.
405
fupply of fteam-engines. In many manufactories and public
works the fteam may be generated by the waste heat arifing
from ſome effential branch of the concern; and thus great part
of the daily expence of the machine may be faved. Mr. Blakey,
who paid confiderable attention to this point, fays, in his Mif-
cellaneous Works, "The moſt complete engine I made was in
1783 at Namur, for a rolling mill; it raiſed 7500 pounds of
water every condenſation, which fell on wheels of 15
and 16
fect diameter; the wafte heat for heating the metal was fufficient,
to make more fteam than was wanted to work the engine." Again,
"I have brought my engines to work fugar-mills with no other
power than that of the wafte heat coming from the fire for boil-
ing ſugar; by which means all the charge of cattle and of water-
mills for fugar works will be faved." And, once more, there is
"a capital amendment made by General Conway, and which
defrays the whole expence of fuel. This is done by means of the
flame or heat that comes from coaking ovens, which heat
creates all the ſteam neceffary to work the engine. By theſe
means all iron foundries heated with coke can work their engines
clear of all expence of fire."
·
STEEL-Ý ARD, an inftrument uſed for weighing of goods,
&c.; the theory of which was conciſely ſtated in art. 138 of our
firſt volume, and fucceeded by a few remarks on its conve-
niences and inconveniences. In addition to what was there
obferved we may now ftate, that ſteel-yards, in the common
purpoſes of commerce, have two advantages over balances.
1. That their axis of fufpenfion is not loaded with any other
weight than that of the merchandiſe, the conftant weight of
the apparatus itſelf excepted; while the axis of the balance,
befides the weight of the inftrument, fuftains a weight double
to that of the merchandiſe. 2. The uſe of the balance requires
a confiderable affortment of weights, which caufes a propor-
tional increaſe in the price of the apparatus, independently of
the chances of error which it multiplies, and of the time em-
ployed in producing an equilibrium, Thefe motives induced
C. Paul, inſpector of weights at Geneva, to employ his thoughts
on the means of fo far improving ſteel-yards, that, either in
delicate operations of the arts, or in thofe of the fame kind
which are often fo neceffary in the practice of the phyfical
ſciences, theſe inſtruments might be ſubſtituted with advantage
for common balances. In order that we may better explain in
what the improvements of thefe fteel-yards confift, it will be
proper to point out what were the faults of the common ones,
1. There were none of them, in which the points of fuf-
penfion were exactly in the prolongation of the line of the
divifions of the beam; a circumftance which neceffarily changed

406
MACHINES.
the relation between the arms of the lever, the power, and the
reſiſtance, according as the direction of the beam was changed
from a horizontal pofition. We have ſeen ſteel-yards, in which
a degree only of difference in the inclination of the beam pro-
duced the difference of more than a pound in the reſult.
2. When the fhell, the beam, and weight, are made at
hazard, a perſon who poffeffes a ſteel-yard cannot know when
the inſtrument is deranged; and even an artiſt cannot repair it,
but by repeated trials, and with a great lofs of time.
3. The conftruction of the common ſteel-yards, which have
a fmall and a large fide, renders it neceffary to invert them
frequently: a laborious operation when theſe inſtruments are
heavy, and which expoſes the axes to the danger of damage by
the effect of the ſhocks which that turning occafions.
As thefe double fides renders it neceffary to have a beam
very ftraight, in order that it may be lefs faulty, it readily bends,
which is a new fource of error; and, the face which bears the
numbers being narrow in proportion, it is difficult to form on it
numbers fufficiently vifible. Theſe inconveniences are all
avoided by the conſtruction of C. Paul, which preſents, befides,
ſeveral other advantages not poffeffed by the old ſteel-yards.
1. The centres of the movement of ſuſpenſion, or the two
conftant centres, are placed on the exact line of the divifions of
the beam; an elevation almoſt imperceptible in the axis of the
beam, deſtined to compenfate for the very flight flexion of the
bar, 'alone excepted.
2. The apparatus, by the construction of the beam, is
balanced below its centre of motion; fo that when no weight
is fufpended, the beam naturally remains horizontal, and re-
fumes that pofition when removed from it, as alſo when the
fteel-yard is loaded and the weight is at the divifion, which
ought to fhew how much the merchandiſe weighs. The
horizontal ſituation in this ſteel-yard, as well as in the others,
is known by means of the tongue, which riſes vertically above
the axis of fufpenfion.
3. It may be difcovered that the ſteel-yard is deranged, if,
when not loaded, the beam does not remain horizontal.
4. The advantage of a great and a fmall fide (which in the
others augments the extent of their power of weighing) is
ſupplied by a very fimple procefs, which accompliſhes the fame
end with fome additional advantages. This procefs is to em-
ploy, on the fame divifion, different weights. The numbers of
the divifions on the bar, point out the degree of heaviness
expreffed by the correfponding weights. For example, when
the large weight of the large fteel-yard weighs eighteen pounds,
each divifion it paffes over on the bar is equivalent to a pound;
Steel-yard of C. Paul.
407
the mall weight, weighing eighteen times lefs than the large
one; will reprefent, on each of theſe divifions, the eighteenth
part of a pound or ounce; and the oppofite face of the bar is
marked by pounds at each eighteenth divifion. In this con-
ftruction, therefore, we have the advantage of being able, by
employing both weights at once, to aſcertain, for example,
almoſt within an ounce, the weight of 500 pounds of mer-
chandiſe. It will be fufficient to add what is indicated by the
ſmall weight in ounces, to that of the large one in pounds, after
an equilibrium has been obtained by the pofition of the two
weights, viz. the large one placed at the next pound below its
real weight, and the ſmall one at the divifion which determines
the number of ounces to be added.
5. As the beam is graduated only on one fide, it may have
the form of a thin bar, which renders it much leſs fufceptible
of being bent by the action of the weight, and affords room for
making the figures more visible on both the faces.
6. In theſe fteel-yards the difpofition of the axes is not only
fuch that the beam repreſents a mathematical lever without
weight; but in the principle of its divifion, the interval between
every two divifions is a determined and aliquot part of the
diſtance between the two fixed points of fufpenfion; and each
of the two weights employed has for its abfolute weight the
unity of the weight it reprefents, multiplied by the number of
the divifions contained in the interval between the two`conſtant
centres of motion. Thus, fuppofing the arms of the ſteel-yard
divided in ſuch a manner that ten divifions are exactly contained
in the diſtance between the two conftant centres of motion, a
weight to exprefs the pounds on each divifion of the beam muft
really weigh ten pounds; that to point out the ounces on the
fame divifions, muſt weigh ten ounces, &c. So that the fame
fteel-yard may be adapted to any fyftem of meaſures whatever,
and in particular to the decimal fyftem, by varying the abſolute
heavineſs of the weights, and their relation with each other.
The application of this principle will be feen hereafter in the
defcription of the fteel-yard, to which C. Paul, with great pro-
priety, has given the name of univerſal feel-yard.
}
But to trace out, in a few words, the advantages of the
ſteel-yards conſtructed by C. Paul for commercial purpoſes, we
thall only obferve, 1. That the buyer and feller are certain of
the correctneſs of the inftrument, if the beam remains hori-
zontal when it is unloaded and in its ufual pofition. 2. That
theſe ſteel-yards have one ſuſpenſion leſs than the old ones, and
are ſo much more fimple. 3. That by theſe means we obtain,
with the greateſt facility, by employing two weights, the exact
weight of merchandiſe, with all the approximation that can be
408
MACHINES,
deſired, and even with a greater precifion than that given by
common balances. There are few of theſe which, when loaded
with 500 pounds at each end, give decided indications of an
ounce variation; and the fteel-yards of C. Paul poffefs that
advantage, and coſt one-half leſs than balances of equal do-
minion. 4. In the laft place we may verify, every moment, the
juſtneſs of the weights, by the tranfpofition which their ratio
to each other will permit; for example, by obſerving whether,
when the weight of one pound is brought back one divifion,
and the weight of one ounce carried forwards eighteen diviſions,
the equilibrium ſtill remains.
If, instead of ascertaining the weight of the merchandiſe in
pounds, you wiſhed to find it according to the new ſyſtem in
decagrammes, hectogrammes, and kilogrammes, it will be fuffi-
cient to ſubſtitute, for the ordinary weights, an aſſortment of
three weights bearing the above names. Theſe three weights
are the decuple one of the other; and the abfolute weight of
that called kilogramme, is to the abfolute weight of that called
pound, in the exact ratio of theſe two quantities. It may be
here feen, that, by adapting to the fteel-yard a fyftem of three
weights, we may arrive at the fecond decimal, or the centiemes
of the unity of the weights employed, and even without adding
or changing any thing in the divifion of the beam.
It is on this fimple and advantageous principle that C. Paul
has conſtructed his univerſal ſteel-yard. It ferves for weighing
in the uſual manner, and according to any ſyſtem of weights, all
ponderable bodies to the precifion of half a grain in the weight
of hundred ounces; that is to fay, of a ten-thouſandth part.
It is employed, befides, for aſcertaining the ſpecific gravity of
folids, of liquids, and even of the air itſelf, by proceffes ex-
tremely fimple, and which do not require many ſub-divifions in
the weights.
+
The beam of this fteel-yard when unloaded reſts in equilibrio
in a horizontal pofition. The fhears are fufpended by a ſcrew
to a croſs horizontal bar of wood fupported by two vertical
pillars, which rest on the two extremities of a ſmall wooden
box furniſhed with three drawers, and which ferves as the
ſtand of the apparatus. This beam is divided into 200 equal
parts, beginning at its centre of motion. The divifion is
differently marked on the two faces: on the anterior face the
numbers follow each other from 10 to 200, proceeding towards
the extremity; and on the other face, the numbers are marked
in the oppofite direction. We shall foon explain the uſe of this
difference in the order of numeration.
·
A ſmall vertical frame hangs from the croſs-bar nearly at the
further extremity of the fleel-yard, and is deſtined to prevent the
Steel-yard of C. Paul.
409
ofcillation of the beam; it is placed at the proper height by
means of the nut and ſcrew by which it is fufpended. Above
the beam is a fmall croſs-bar of brafs, fufpended by its two
extremities from the croſs-bar of wood. Different weights are
hooked to it, each having marked on it its particular value.
And, in the laft place, a fmall mercurial thermometer having
the two moft ufual divifions, viz. Fahrenheit's and Reaumur's
and deſtined to point out the temperature of the air and the
water during the experiments. The axis of ſuſpenſion of the
fteel-yard refts upon two beds of very hard well-poliſhed ſteel.
The cafe is the fame, but in a reverfed fituation, with the axis
which ſupports the hook, that ferves for fufpending different
parts of the apparatus, according to the purpoſe to `which it is
to be applied.
When you wish to employ it as a common ſteel-yard, yoù
fufpend from it a hrafs fhell, which is an exact counterbalance
for the weight of the beam when unloaded. The latter then
affumes of itſelf a horizontal fituation. You then fearch for
the equilibrium of the ſubſtance put into this fhell, by placing
at the proper place, on the beam, the weight and its fractions
correfponding with the fyftem of weights adopted; and when
you have found the equilibrium, you obferve the weight in-
dicated by the divifions on which each of the weights employed
is found, exactly in the fame manner as is done in regard to
the common ſteel-yard.
There is alfo, as part of the apparatus, a glafs fhell fufpended
occaſionally in a jar filled to a certain height with water. This
ſhell is intended for experiments relative to the fpecific gravity
of folids. It is in equilibrium, if, when immerfed into water
at 20° of Reaumur, as far as the junction of the three filver
wires by which it is fupported, it exactly balances the weight
of the beam unloaded.
When you wish then to try the fpecific gravity of a folid,
you firft weigh it in air; but by putting it into the braſs fhell,
and then fubftituting the glafs one, you weigh it in water. It
is well known that the difference of theſe weights, employed
as a divifor of the total weight in air, gives for quotient the
fpecific gravity. Care must be taken, as in all experiments of
the kind, that no bubble of air adheres to that part of the
apparatus immerſed in the water, or to the fubftance, the
weight of which is required, and which is immerſed alſo.
There is likewife a folid glass ball deftined for the purpoſe of
afcertaining the ſpecific gravity of liquids, in the following
manner :-This piece is furniſhed with a hook of fine gold, that
it may be immerſed without inconvenience in acids. When it
is fuſpended to the hook of the ſteel-yard, and in the air, it is in
410
MACHINES.
•
equilibrium with the beam loaded at its extremity (either at the
divifion marked O (nothing) on the back fide of the beam) with
weights entitled ſpecific, and of fpecific hooked on at the
other.
.
This ball, immerſed in diſtilled water at 12° of Reaumur as
far as the end of the straight metal wire which fufpends it, is
ftill in equilibrium with theſe two weights placed in the fol
lowing manner, viz. the large one at the divifion in the middle
of the beam marked water on the backſide of the beam, and the
fmall one at the divifion O, that is to fay, the extremity.
When the apparatus is thus prepared, you fill a jar with the
liquid, the specific gravity of which you wish to afcertain;
fufpend the glaſs ball to the hook of the fteel-yard, and immerfe
it into the liquid till it rifes exactly above the ring from which
the ball hangs, obferving the temperature, and difengaging
carefully all the air-bubbles that may adhere to the ball; then
remove the ſmall, weight to the diviſion O at the end of the
beam, and convey the large one as far as that divifion, preceding
that where the weight of the ball would raiſe the beam; and
afterwards move the fmall weight as far as the divifion where
the equilibrium will be restored, the beam being horizontal.
Mark the diviſion at which the large weight is found, and add
two cyphers; to this number add the indication immediately
refulting from the poſition of the ſmall weight, and the fum of
theſe two numbers gives the ſpecific gravity of the liquid, or its
ratio with the weight of diftilled water, to a ten-thousandth part.
The larger balloon is uſed in trying the weight of any given
kind of gas compared with that of atmoſpheric air, in the
following manner-The weight entitled air-tare is arranged in
fuch a manner that when placed in a notch, at the further
extremity of the beam beyond the divisions, it forms an equili
brium with the balloon exhauſted by the air-pump and fufpended
from the hook of the fteel-yard. If the fteel-yard is not then
in equilibrium, it is an indication that the inſtrument is deranged,
or that the vacuum is not perfect. The air, the relative weight
of which in regard to atmoſpheric air you wiſh to afcertain, is
to be introduced into the balloon, and the weight marked air
is to be moved along the beam. The divifion at which it
ftands when an equilibrium is produced will indicate, in
hundredth parts of the weight of the volume of atmoſpheric air
that could be contained in the balloon, the weight of the gas
actually incloſed in it. This indication is read about the
middle. of the anterior part of the beam, where the words atmo
fpheric air are marked.
Not ſatisfied with having procured to philofophers, and thoſe
fond of accurate experiments, an inſtrument extremely con-
Steel-yards to afcertain Animal Strength.
411
venient for the cloſet, and of very extenfive ufe, C. Paul has
endeavoured to render this apparatus 'portable, and has con
Aructed various pocket fteel-yards, with which the niceft ex-
periments may be made, and the quality of gold coin be afcer-
tained by the trial of its fpecific gravity. They are conſtructed
exactly on the fame principles as the Roman ſmall ſteel-yard,
but are neceffarily lefs extenfive in their uſe. They cannot be
employed, for example, in determining the ſpecific gravity of
an aëriform fluid, and do not extend beyond 100 deniers of
weight; but as they poffefs all the advantages of a balance,
beſides thofe peculiar to themſelves, they are extremely con-
venient for philofophers who are obliged to travel.
A figure of this ſteel-yard and apparatus may be ſeen in
Tilloch's Philof. Magazine, vol. iii.
STEELYARDS to afcertain animal ftrength, may feadily be
attached to almoſt any kind of machinery in which animals are
the firſt movers: and it is much to be wifhed that experiments
were frequently made with them, in order that our knowledge
on this point might be increaſed.
A
The following contrivance falling under this head, has been
lately propoſed for determining the power of horfes drawing in
mills. Let AB (fig. 10. pl. XXXII.) be the vertical fhaft to
which the horizontal horfe- poles AC, AD, are attached. Let
one horſe work the machine by drawing at the ear E; but
inſtead of the tranſverſe ſplinter-bar, to which the harneſs is
fixed, being fimply hung upon the hook b, let a good fpring
fteel-yard be interpofed between that crofs-bar and the hook,
the graduations of which fhall, when the machinery is put into
motion, indicate the reſiſtance (in lbs.) overcome by the animal,
including the weight of the maſs moved, the friction, &c.
Near the extremity of the oppofite horſe-pole AD, let there be
fixed a ſtrong and correct common fteel-yard, whofe divifions
ſhall fhew the various weights from 40 or 50 to 200 lbs. and
whoſe centre of motion ſhall be at the point fon the fixed ſtand.
Let the cord c, which is faſtened to the ſhorter arm of this ſteel-
yard, pafs (with as little friction as poffible) over the pulley p,
and thus, being turned into the horizontal direction, or rather
inclining a little upwards, let it be fixed to the croſs-bar of the
harneſs of a ſecond horfe, equal in point of ſtrength to the
former. Then, if the two horfes thus attached to the ears E
and F be made to pafs over the walk in the fame direction,
following each other conftantly at the diftance of a femi-cir
cumference; while that which draws at the ear E overcome's
the whole preffure and refiftance oppofed by the work, the other
which draws at F by the cord over the pulley p, will raife the
*
412
MACHINES.
weight w of the ſteel-yard; which, therefore, by being moved
to and fro upon the arm fi, may be brought to exhibit an exact
counterpoiſe, or meaſure of the exertion and power of the horſe.
And in order to enfure the greatest degree of accuracy in this re-
ſpect, the motion of the two animals and the pofition of the
weight w, fhould be fo adjuſted, that the fame weight ſhould be
fhewn by the graduations both of the fpring and of the lever
fteel-yard. The fhaking of the machinery will in fome meaſure
difturb the effect: but an ingenious manager of the experiments
will find means of checking this: and as to the centrifugal
force to which the weight w is expofed, it will never be of ma-
terial confequence in any of the flow motions which will be
produced by this kind of work.
Each experiment fhould occupy the place of a fair day's work
for the horſes; for the conclufions deduced from fhorter and
irregular efforts are always erroneous in excefs, and fhould be
guarded againft. The rate at which the animals move may
readily be afcertained from the known circumference of the
walk, and the number of rounds they are obſerved to make in
ten or fifteen minutes.
A flight modification will adapt this contrivance to the deter-
mination of the power of men puſhing at the bars of a capſtan:
to this end it will only be neceffary to have a fufficiently ftrong
frame in form of a T, one end of which may be faftened to
a nooſe in the cord paffing round the pulley p, while a man
puſhes at the ⚫anfverfe bar of the frame, with the fame energy
as he would employ at the capftan bar.
By means of fuch fteel-yards properly applied to waggons,
&c. upon tolerably fmooth roads, and two horfes marching
abreaft (one drawing the load, the other raifing the weight), ex-
periments might be inſtituted to afcertain the magnitude of the
efforts of horfes when drawing in rectilinear paths.
In Defaguliers's Experimental Philofophy, vol. 1. fome fteel-
yards are deſcribed, by which the ftrength of men may be aſcer-
tained when ſtanding ſtill, and pulling or pufhing upwards or
downwards: we had, at firſt, propoſed to defcribe them in this
place; but as all theſe contrivances are nearly on the fame prin-
ciple, and may eaſily be adapted to any particular purpofe, we
omit the minute delcriptions and drawings to make room for
other fubjects.
STREAM-MEASURERS, are inftruments by which the velo-
city of currents of water in rivers, mill-ponds, &c. may be de-
termined.
In the introductory part of this volume, we ſpoke of the
common and grofs methods of aſcertaining the velocity of run-
#
Stream-Meaſurers.
413
ning water in canals, &c. But as more ſcientific and accurate
methods have been deviſed, it ſeems proper to infert the beſt
of them with which we are acquainted, in this place.
1. M. Pitot invented a ſtream meaſurer of a ſimple conſtruc-
tion, by means of which the velocity of any part of a ſtream
may readily be found. This inftrument is compofed of two
long tubes of glaſs open at both ends; one of theſe tubes is cy-
lindrical throughout; the other has one of its extremities bent
into nearly a right angle, and gradually enlarges like a funnel,
or the mouth of a trumpet: theſe tubes are both fixed in grooves
in a triangular prifm of wood; fo that their lower extremities
are both on the fame level, ftanding thus one by the fide of
the other, and tolerably well preferved from accidents. The
frame in which theſe tubes ftand is graduated, cloſe by the fide
of them, into divifions of inches and lines.
$
To ufe this inftrument, plunge it perpendicularly into the
water, in ſuch manner that the opening of the funnel at the
bottom of one of the tubes fhall be completely oppoſed to the
direction of the current, and the water paſs freely through the
funnel up into the tube. Then obferve to what height the
water rifes in each tube, and note the difference of altitudes;
for this difference will be the height due to the velocity of the
ſtream. It is manifeft, that the water in the cylindrical tube
will be raiſed to the fame height as the furface of the ftream,
by the hydroſtatic preffure: while the water entering from the
current by the funnel into the other tube, will be compelled to
rife above that furface by a ſpace at which it will be fuftained
by the impulfe of the moving fluid: that is, the momentum of
the ſtream will be in equilibrio with the column of water ſuf-
tained in one tube above the furface of that in the other. In
eftimating the velocity by means of this inftrument, we muſt
have recourſe to the theory in art. 439. &c. vol. I. as corrected
by the experiments in art. 460. Thus, if b, the height of
the column fuftained by the ſtream, or the difference of heights
in the two tubes, be in feet, we fhall have v 65√b, nearly,
the velocity, per ſecond, of the ſtream; if b be in inches, then
v = 22:47 v. b, nearly.
=
It will be eafy to put the funnel into the moſt rapid part of
the ftream, if it be moved about to different places until the dif-
ference of altitude in the two tubes becomes the greatest. In
ſome caſes it will happen, that the immerſion of the inftrument
will produce a little eddy in the water, and thus difturb the
accuracy of the obfervation; but keeping the inftrument im-
merſed only a few feconds will correct this. The wind would
alfo affect the accuracy of the experiments.; it is, therefore, ad-
viſable to make them when there is little or no wind. By means
414
MÁCHINES.
•
of this inftrument a great number of curious and uſeful obs
fervations may eaſily be made: the velocity of water at various
depths in a canal or river may be found with tolerable accuracy,
and a mean of the whole drawn, or they may be applied to the
correcting of the theory of waters running down gentle flopes.
The obſervations may likewiſe be applied to aſcertain whether
the augmentations of the velocities are in proportion to the in-
creaſe of water paffing along the fame canal, or what other rela-
tion fubfiſts between them, &c.
Where great accuracy is not required, the tube, with the fun-
nel at bottom, will alone be fufficient; as the furface of the
water will be indicated with tolerable precifion, by that part of
the prifmatic frame for the tube which has been moiſtened by
the immerſion.
M. Pitot likewife propoſed that a fimilar înftrument ſhould
be uſed inſtead of a log to determine the rate at which a ſhip
fails. For this purpofe, place in the middle of the veffel, or as
near as can be at the centre of its ofcillations two tubes of
metal of three or four lines in diameter, one of them being
ftraight, the other bent at bottom, and enlarged into a conical
funnel; the bottoms of both are to dip into the water of the
fea in which the veffel fails, and there will be no evil to appre-
hend from orifices fo minute: into theſe metallic tubes are
cloſely fitted two others of a convenient height for the obferva-
tions. The water will rife in the firſt of theſe tubes up to its
level on the outſide of the ſhip; and in the fecond up to a certain
height, which will indicate, as above, the velocity of the veffel:
for the funnel being turned towards the prow of the ſhip, it will,
in confequence of the motion, be affected in like manner, as if
it were plunged into the ſtream of a running water; and thus
the velocity of the veffel is found by the fame theorem as that
of the current. This method has lately been re-propofed in this
country, without any acknowledgments to M. Pitot. We do
not, however, recommend its adoption aboard a fhip; for, not-
withſtanding its theoretical ingenuity, it is liable to many fources
of error in the practice, and would not, it is probable, furniſh
more accurate meaſures of a fhip's way than thofe deduced
from the log.
2. Another good and fimple method of meaſuring the velo-
city of water in a canal, river, &c. is that deſcribed by the Abbé
Mann, in his Treatife on Rivers, Philofophical Tranfactions,
vol. 69. It is this:-Take a cylindrical piece of dry light wood,
and of a length fomething leſs than the depth of the water in
the river; about one end of it let there be fufpended as many
fmall weights as may keep the cylinder in a vertical or upright
pofition, with its head juft above water. To the centre of this
Surface-planing Machinery.
415
end fix a ſmall ſtraight rod, preciſely in the direction of the
cylinder's axis: to the end that, when the inftrument is fuf-
pended in the water, the deviations of the rod from a perpen-
dicularity to the ſurface of it, may indicate which end of the
cylinder goes foremost, by which may be difcovered the dif-
ferent velocities of the water at different depths; for when the
rod inclines forward, according to the direction of the current,
it is a proof that the furface of the water has the greateſt velo-
city; but when it reclines backward, it fhews that the ſwifteſt
current is at the bottom; and when it remains perpendi-
eular, it is a ſign that the velocities at the top and bottom are
equal.
This inftrument, being placed in the current of a river or
canal, receives all the percuffions of the water throughout the
whole depth, and will have an equal velocity with that of the
whole current from the ſurface to the bottom at the place where
it is put in, and by that means may be found, both with exact-
nefs and eaſe, the mean velocity of that part of the river for any
determinate diſtance and time.
But to obtain the mean velocity of the whole fection of the
river, the inftrument must be put fucceffively both in the
middle and towards the fides, becauſe the velocities at thoſe
places are often very different from each other. Having by
this means found the ſeveral velocities, from the fpaces rum
over in certain times, the arithmetical mean proportional of all
theſe trials, which is found by dividing the common fum of
them all by the number of the trials, will be the mean velocity
of the river or canal. And if this 'medium velocity be multiplied
by the area of the tranſverſe ſection of the waters at any place,
the product will be the quantity running through that place in a
fecond of time.
If it be required to find the velocity of the current only at the
furface, or at the middle, or at the bottom, a ſphere of wood
loaded, or a common bottle corked with a little water in it, of
fuch a weight as will remain fufpended in equilibrium with the
water at the furface or depth which we want to meaſure, will
be better for the purpofe than the cylinder, becauſe it is only
affected by the water of that fole part of the current where it
remains fufpended.
༈
Both the cylinder and the globe may be eafily guided into
that part which we want to meaſure by means of two threads
or fmall cords, which two perfons, one on each fide of the
canal or river, muſt hold and direct; taking care at the ſame
time neither to retard nor accelerate the motion of the inftru-
ment.
SURFACE-PLANING Machinery. In October, 1802, a patent
}
416
MACHINES.
was taken out by Mr. Jofeph Bramah for machinery for the
purpoſe of producing ſtraight, ſmooth, parallel furfaces, and
curvilinear furfaces, on wood, and other materials requiring ac-
curacy, in a manner much more expeditious and perfect than
can be performed by the ufe of axes, faws, planes, and other
cutting inftruments, uſed by hand. As many particulars in the
fpecification of this patent are highly curious, and cannot fail
to be very beneficial, we ſhall extract the greater part of it from
the Repertory of Arts and Manufactures, vol. ii. N. S.
"The principal parts of my invention are as follows; that is
to fay, to fhorten and reduce manual labour, and the confequent
expences which attend it, by producing the effects ſtated in my
patent by the uſe of machinery, which may be worked by ani-
mal, elementary, or manual force; and which faid effects are
to produce ſtraight, true, fmooth, and parallel furfaces, in the
preparation of all the component parts of work confifting of
wood, ivory, horn, ftone, metals, or any other fort of mate-
rials, or compofition ufually prepared, and render it (them)
true and fit for ufe, by means of edge-tools of every deſcrip-
tion. I do not reft the merits of this my faid invention on any
novelty in the general principle of the machinery I employ, be-
caufe the public benefit I propofe will rather depend on new
effects, produced by a new application of principles already
known, and machinery already in ufe for other purpoſes, in
various branches of Britiſh manufacture. This machinery,
and the new manner of ufing it, with fome improvements in
the conftruction, together with fundry tools and appendages
never in uſe before, are particularly defcribed and explained
hereunder.
"I mean to uſe and apply for the purpoſes above ſtated,
every kind of edge-tool, or cutter, already known, either in
their preſent ſhape, or with fuch variations and improvements
as the variety of operations I may encounter may feverally call
for. But the tools, inftead of being applied by hand, as ufual,
I fix, as judgment may direct, on frames drove (driven) by
machinery: fome of which frames I move in a rotary, direction
round an upright ſhaft; and others having their ſhaft lying in
a horizontal pofition, like a common lathe for turning wood,
&c. In other inftances I fix thefe tools, cutters, &c. on frames
which flide in ftationed grooves, or otherwife, and like the
former calculated for connexion with, and to be driven by, ma-
chinery, all of which are hereafter further explained and paṛti-
cularifed.
"The principal points on which the merits of the invention
reft are the following. First, I caufe the materials meant to be
wrought true and perfect, as above defcribed, to flide into con-
Surface-planing Machinery.
417
tact with the tool, inftead of the tool being carried by the hand
over the work, in the uſual way.
"Secondly, I make the tool, of whatfoever cutting kind it be,
to, traverſe acroſs the work in a fquare or oblique direction;
except in ſome caſes, where it may be neceflary to fix the tool
or cutter in an immoveable ſtation, and cauſe the work to fall
in contact with it by a motion, confining it ſo to do, ſimilar to
the operations performed on a drawing-bench.
Thirdly, in fome caſes I uſe, inſtead of common ſaws, axes,
planes, chifels, and other fuch inftruments, ufually applied by
hand; cutters, knives, fhaves, planes, and the like, variouſly, as
the nature of the work may render neceffary; ſome in form of
bent knives, fpoke-fhaves, or deep-cutting gouges, fimilar to
thoſe uſed by turners for cutting off the rougheft part. I alſo
apply planes of various fhapes and conftruction, as the work
may require, to follow the former in fucceffion, under the fame
operation; and which latter I call furnishers.
"Fourthly, theſe cutters, knives, &c. I fix on frames of wood,
or metal, properly contrived for their reception, and from
which they may be eafily detached for the purpoſe of ſharpen-
ing, and the like-thefe I call cutter-frames. Theſe cutter-
frames I move in cafes like thoſe on which the faws are fixed
in a fawing-mill, and fometimes to reciprocate in a horizontal
direction, confined and ftationed, by grooves or otherwiſe, as
may be found beft, calculated to anſwer the feveral works in-
tended. In other inftances, and which I apprehend will gene-
rally have the preference, I fix cutter-frames on a rotary upright
fhaft, turning on a ftep, and carrying the frame round in a direc
tion fimilar to the upper mill-ftone; and ſometimes I caufe the
frames to turn on a horizontal fhaft, juſt reſembling the man-
drel of a common turning-lathe, or thofe machines uſed for
cutting logwood, &c. for the dyers' ufes. When thefe frames
are mounted in any of the foregoing directions for cutting,
planes, &c. are fixed fo as to fall fucceffionally (fucceffively)
in contact with the wood or other materials to be cut, fo that
the cutter or tool calculated to take the rough and hilly part
operates the firſt, and thofe that follow muft be fo regulated as
to reduce the material down to the line intended for the fur-
face. Thefe cutter-frames muft alfo have the property of being
regulated by a ſcrew or otherwiſe, ſo as to approach nearer the
work, or recede at pleaſure, in order that a deeper or ſhallower cut
may be taken at difcretion, or that the machine may repeat its
action without raiſing or depreffing the materials on which they
act. The manner of thus regulating the cutter-frames, when
on an upright ſhaft, is particularly defcribed below., Thefe cut-
ter-frames may be made of any magnitude and dimenſions the
VOL. II.
E E
418
MACHINES,SM
work requires, only obferving to make the diameter of thoſe
on the rotary plane fo as to exceed twice the width of the ma
terials to be cut, as the faid materials muſt ſlide ſo as to paſs the
fhaft on which the cutter-frame revolves, when on the upright
principle.
Fifthly, when I uſe upright ſhafts, for the purpoſe of carry-
ing the cutter-frame as above deſcribed, I do not mean that the
lower end or point of fuch fhafts fhall come in contact with,
or reſt on, the bottom of the ftep or box in which they ſtand;
neither do I mean that fuch faid fhafts fhall reft or turn on any
ftationed unalterable point at reft, but the pivot or lower point
of the shaft ſhall actually reft and turn on a fluid body, fuch as
oil, or any other fluid proper for that purpoſe, a conſiderable
portion of which is always to be kept between the lower point
of the fhaft and the bottom of the ſtep in which it works. The
faid fhafts may be either raifed or depreffed at pleaſure to any
required altitude, by means of a greater or lefs quantity of the
faid fluid being confined as aforefaid between the end of the
fhaft and the bottom of the ftep. This device* I deem of great
confequence in the fabrication of all kinds of machinery, where
mally and heavy loaded upright fhafts are ufed; and I perform
it in the following manner; that is to fay: The lower part of the
fhaft muſt be turned perfectly fmooth and cylindrical, to a
height fomething above the greateft diftance or length the ſhaft
will ever be required to be raiſed or depreffed when in ufe.
This part of the Thaft I immerſe or drop into a hollow cylinder,
which fits its circumference near enough to allow freedom of
inotion, but fufficiently fitted to prevent thake. This cylinder I
call the ſtep-cylinder, and (which) muſt be of a length nearly
équal to that of the cylindrical part of the ſhaft above mentioned,
fo that when the point of the fhaft refts on the bottom of the ey
linder, the parallel or cylindrical part may be ſomething above
the top or upper end of the ftep-cylinder. In the upper end of
this flep-cylinder I make a fluffing-box, by means of a double
cupped leather, or other materials, furrounding the cylindrical
part of the ſhaft, in ſuch a way as will cauſe the junction, when
the ſhaft is paffed through it, to remain water-tight under any
preffure that may be felt from the efforts of the fluid retained
as before mentioned, to make its efcape upwards through this
part, (which) I have called the ftuffing-box, when the fhaft,
with all its load, is paffed through it, and immerfed in the cy-
linder below. When this is done, the injecting-pipe of a ſmall
foreing-pump, fimilar to thofe I ufe in my patent prefs, muft
form a junction with the ftep-cylinder in fome part below the
P
* See Count de Thiville's ſpecification, published in the fourteenth volume
of the firſt ſeries of the Repertory, or the Engliſh Encyclopædia, art. WATER-
WORKS, for the developement of a fimilar invention.
Surface-planing Machinery.
419
ftuffing-box; then the pump being worked, the oil, or other
fluid injected by it, will, by preffing in all directions, caufe the
ſhaft to be raiſed from its reft, on the bottom of the cylinder,
and to be flided up through the ſtuffing-box just the fame as
the piston of my patent prefs; and by this means the fhaft, with
all its incumbrance, and whatever may be its weight, may be
raiſed to any given point at pleaſure, and at the fame time it
will be left refting on the fluid under it, whatever the quantity
or thickneſs of ſuch fluid may be between its point and the bot-
tom of the ſtep-cylinder. By this means the fhaft, with all
its incumbent load, as aforeſaid, ſhould it even amount to hun-
dreds or thouſands of tons, can be eaſily raiſed and depreſſed to
any required point at pleaſure, by the alternate injunction (in-
jestion) or difcharge of the fluid uſed, exactly the fame as per-
formed by my patent prefs as aforefaid; and at the ſame time
all friction will be avoided, except that of the ftuffing-box,
which will be comparatively trifling to that which would refult
from the refting of ſuch a ſhaft on the bottom of the ſtep, in
the ufual way. Thus will be gained the properties above ftat-
ed; and in addition thereto, I think it may be inferred, that,
provided the ſtuffing-box is kept perfectly fluid tight, fuch
a fhaft, thus buoyed up by and turning in a proper fluid, may
continue working for years, or perhaps hundreds of years, with-
out a freſh ſupply of oil, or whatever other fluid fubftance is
found the moſt proper to apply.
"
Sixthly, the material that is to be cut and made true must
be firmly fixed on a platform, or frame, made to flide with
perfect truth, either on wheels or in grooves, &c. fimilar to
thoſe frames in a faw-mill on which the timber is carried to the
faws. Thefe frames must be moved in a steady progreflive
manner, as the cutter-frame turns round either by the fame
power which moves the latter, or otherwife, as may be found
to anſwer beſt in practice. This motion alfo muſt be under
the power of a regulator; fo that the motion of the fliding-
frame may be properly adjusted according to the nature of
the work. The motion of the cutter-frames muſt alſo be under
the_control of a regulator; fo that the velocity of the tool in
paffing over the work may be made quicker or flower, as ſuch
work may refpectively require, to cauſe the cutter to act pro-
perly, and to the beſt advantage.
►
46.
Seventhly, I regulate the motions of both theſe parts of the
apparatus, as aforementioned, by means of a new invention,
which I call a univerfal regulator of velocity, and which is
compoſed as follows; viz. I take any number of cog-wheels,
of different diameters, with teeth, that will exactly fit each
other through the whole, fuppofe ten, or any other number,
but for example fay ten, the fmalleft of which shall not exceed
E E 2
420
MACHINES.
1
'
one inch in diameter, and the largeſt ſuppoſe ten inches in di-
ameter, and all the reft to mount by regular gradations in their
diameters from one to ten. I fix theſe ten wheels faft and im-
moveable, on an axis perfectly true, ſo as to form a cone of
wheels. I then take ten other wheels, exactly the fame in all
reſpects as the former, and fix them on another axis, alſo per-
fectly true, and the wheels in conical gradation alfo; but theſe
latter wheels I do not fix faft on their axis, like the former, but
leave them all looſe fo as to turn upon the ſaid axis, contrary
to the former which are fixed. All theſe latter wheels I have
the power of locking by a pin, or otherwiſe, ſo that I can at
diſcretion lock or fet faft any fingle wheel at pleaſure. I then
place the two axises (axes) parallel to each other, with the
wheels which form the two cones, as above deſcribed, in re-
verſe poſition, ſo that the large wheel at the one end of the
cone may lock its teeth into the ſmalleſt one in the cone oppo-
fite, and likewife vice verfa. Then ſuppoſe the axis on which
the wheels are permanently fixed to be turned about, all the
wheels on the other axis will be carried round with an equal
velocity with the former, but their axis will not move. Then
lock the largest wheel on the looſe axis, and by turning about
the faſt (fastened) axis as before, it muſt make ten revolutions,
while the oppofite performs but one: then by unlocking the
Jarget wheel and locking the ſmalleſt one at the contrary end
of the cone in its ftead, and turning as before, the faft (faften-
ed) axis will then turn the oppofite ten times while itfelf only
revolves once. Thus the axes, or ſhafts, of theſe cones, or
conical combination of wheels, may turn each other recipro-
cally, as one to ten, and as ten to one; which collectively pro-
duces a change in velocity under a uniform action of the pri
mum mobile, as ten to a hundred: for when the fmall wheel
on the looſe axis is locked, and the faft one makes ten revolu-
tions, the former will make one hundred. And by adding to
the number of thoſe wheels and extending the cones which
may be done ad infinitum, velocity may be likewife infinitely
varied by this fimple contrivance-A may turn B with a ſpeed
equal to thouſands or millions of times its own motion; and
by changing a pin and locking a different wheel, as above de-
fcribed, B will turn A in the fame proportion, and their power
will (be) transferred to each, in proportion as their velocities,
reciprocally. Here is then a univerfal regulator at once for
both power and velocity.. In fome inftances I produce a like
effect by the fame neceſſary number of wheels, made to corre-
fpond in conical order, but inftead of being all conftantly
mounted on the axises (axes) or fhafts, as bove defcribed,
they will reciprocally (be) changed from one axis to the other
in Gingle pairs, match according to the speed or power wanted,
Surface-planing Machinery.
just as in the former inflance. This method will have in all
reſpects the fame effect, but not fo convenient as when the
wheels are all fixed, &c.
"
"Eighthly, when ſpherical furfaces are to be produced perfect-
ly true, and parallel to (equidiftant from their centres in all
directions, I uſe a tool, or cutter, of a proper shape, according
to the nature of the materials to be cut. This tool must be
fixed on a cutter-frame, faftened to the rest of any common
lathe, fo as to preſent its point exactly to a line drawn through
the centre of the mandrel of the lathe horizontally, and the
faid frame on which the cutter is fixed muſt have the capacity
of drawing out, at pleaſure, to any required diſtance, to accom.
modate the diameter of the fphere to be cut or turned true.
This cutter-frame muſt be likewife made to turn upon a centre
or pin, very firm, and ſteadily fixed on the reſt above mens
tioned, ſo as to enable the cutter to be turned by its frame
round a centre exactly perpendicular to the centre of the lathe
or line, before mentioned, by which the altitude of the tools
point is to be regulated; when this is done, and the wood or
other materials fixed on the lathe in the ufual way, the cutter
frame muſt be drawn nearer, or farther diſtant from the cent
tre on which it turns, to acommodate the diameter, just the
fame as the common reft. If the materials be rough, and re-
quire to be reduced to a ſpherical form by gradations, the work
may be repeatedly gone over by the cutter, before it reaches
the diameter propofed.. By this fimple apparatus the difficul
ty of turning perfect fpheres is overcome; as it must be obvi
ous to any perſon of the moſt ordinary capacity in mechanics,
that while the work is turning in the lathe in a vertical direc
tion,,and the tool or cutter is by the hand, or otherwiſe, turn-
ed, at the ſame time, in a perfectly horizontal direction, round
a centre, oppofite to the actual centre of the fphere, the point of
the tool or cutter, muft, of neceffity, generate or turn a per
fect ſphere, true in all directions, without the ſmalleſt attention
or aſſiſtance-from the uſe of the inftrument. I mention here
the application of the cutter-frame to a common lathe, conceiv?
ing it will, by fuch an explanation, be more familiarly under-
flood without a drawing; but, by this method, fpheres of any
practical magnitude may be cut with perfect eafe and certainty.
7
"
•
A
Ninthly, when concave furfaces are to be produced perfect-
ly true, ſmooth, and parallel to (equidiftant from) their re-
ſpective ſpherical centres, the work is fixed on a machine the
fame in all refpecs as the common turning lathe, as in the
inftance last referred to: I then fix a tool or cutter on ¹á
centre, exactly in a line, both perpendicular to, and on a level
with the exact centre of the fhaft or mandrel on which the
422
MACHINES.
1
work revolves: and which cutter or tool projects to the re-
quired radial diſtance with its point, fo that when the work
goes round by the revolution of the lathe, the tool or cutter at
the fame time revolving round its centre, a ſpherical concave
will be generated and produced by the fluction* of its point,
as in the inftance of the convex ſphere.
60
Tenthly, I convert folid wood, or other materials, into a
thin concave fhell, fimilar to a diſh, I cut them alternately out
of each other, beginning at the fmalleft, by means of another
tool or cutter, likewife moving on a ſtationed centre, as before,
exactly on a level with, and perpendicularly true with the cen.
tre of the mandrel or ſhaft of the machine on which the work
is fixed. This tool, or cutter, is made at its exterior point, or
cutting end, of fuch a ſhape as beſt ſuits the nature of the work;
and its thank, or ſtem, is bent to the exact circle the concave is
meant to be; it is then fixed on an arm or frame calculated to
receive others of different circles, according to the work; in
fact the fame frame may be ufed which is above deſcribed to
hold the tool for cutting ſpheres, either of the concave or con-
vex kind. The tool muſt be fixed on this frame or arm, as
above mentioned, at fuch a radial diſtance from the centre on
which the frame or arm turns, fo as to form a quadrant with one
leg, turning on its centre, and the tool forming the periphery
with its cutting point projecting to the line of the deficient leg.
Before this tool begins its action, a common reft muft be
applied close to the face of the work, in order to fupport the
tool when it begins its cut; and on which reft the tool will
Alide till its point proceeds under the control of the centre on
which its frame is fixed, until it reaches the horizontal line of
the lathe's centre, when the part cut off, or the inner diſh, will
fall from the flock, and leave the reft for the operation of an-
other tool, of a larger circle. Thus the operation may be re-
peated till the whole lump is converted according to the in-
tentions of the owner.
SYPHON, with Mr. Clofe's new application of it to con-
vey water above the level of the refervoir. See CRANE.
TEETH OF WHEELS, and LEAVES of pinions, require great
care and judgment in their formation, that they may neither
clog the machinery with unneceffary friction, nor act fo irre-
gularly as to produce any inequalities in the motion, and a
confequent wearing away of one part before another is much
affected by the work.
Several eminent mathematicians upon the continent, and
a few in England and Scotland, have directed their inveftiga.
* Compared with the record,
Teeth of Wheels.
423
tions towards a fubject ſo eſſential to the perfection of machi-
nery: yet, although Roemer, Varignon, De la Hire, Camus*
Euler,* Kaeftner, and Robiſon, have turned their thoughts to
this object, and have ftruck out fome rules of ready applica-
tion in practice, it is to be regretted that thefe rules have been
little followed by practical mechanics, most of whom have in
this caſe been more inclined to follow in their conftructions
the rules of Imifon and others, though completely deftitute of
mechanic principle.
As the conftruction of teeth of a proper form is exceedingly
eafy, we beg to recommend it earneſtly to practical men, and
as we merely touched upon the ſubject in our first vol. (art. 147,)
it may not be amifs to enter a little into detail here, availing
ourfelves, for the most part, of the judicious remarks juſt pub-
lithed by Mr. Brewfer.
-
It has been long known to mathematicians, and need not
here be demonftrated, that one wheel will not drive another
with uniform velocity, unleſs the teeth of one or of both
wheels have their faces formed into a curve, generated after
the manner of an epicycloid, comprehending, under curves of
this kind, thofe which are formed by evolving the circumfer
ences of circles. But in order to insure a uniformity of
preffure and velocity in the action of one wheel upon another,
it is not abfolutely neceffary that the teeth either of one or both
wheels be exactly epicycloids, in the ſenſe to which geometers
commonly reftrift that term. If the teeth of one of them be
either circular or triangular, with plain fides, or like a triangle
with its fides.converging to the centre of the wheel, or, in fhort,
of any other form, this uniformity of force and motion will
be attained, provided that the teeth of the other wheel have a
figure which is compounded of that of an epicycloid, and the
figure of the teeth of the firft wheel. De la Hire has fhewn,
in a variety of cafes, how to find this compound curve: and w
have lately examined a mill in which fome teeth have been
thus conftru&ted with great fkill and fuccefs. But as it is often
difficult to defcribe this compound curve, and fometimes impof-
ſible to diſcover its nature, we ſhall endeavour to felect fuch a
form for the teeth as may be easily deſcribed by the practical me-
chanic, while it enfures a uniformity of preffure and velocity.
In order to avoid circumlocution and obfcurity, we ſhall call,
* Camus's popular differtation on this fubject may be found in the fecond
vol. of his Courſe of Mathematics, the edition of 1767; the edition of 1751
does not contain it. Euler's paper is inferted in Nov. Comment. Petropol.
tom. 5. 1754, 1755. It will be interefting to mathematicians, as it exhibits
frong traces of his maſterly hand: but it is too abftrufe to be recommended
to the practical mechanic.

1424
MACHINES.
as is cuſtomary with practical men, the ſmall wheel (which is
fuppofed always to be driven by a greater one) the pinion, and
its teeth, the leaves of the pinion. The line which joins the
centres of the wheel and pinion may be called the line of cen-
tres. Now there are three different ways in which the teeth of
one wheel may act upon the teeth of another; and each of
thefe modes of action requires a different form for the teeth..
I. When the teeth of the wheel begin to act upon the leaves of
the pinion juft as they arrive at the fine of centres; and,
* when their mutual action is carried on after they have palled
this line.
II. When the teeth of the wheel begin to act upon the leaves
of the pinion, before they arrive at the line of centres, and
conduct them either to this line, or a very little beyond it."
III. When the teeth of the wheel begin to act upon the leaves
of the pinion, before they arrive at the line of the centres,
and continue to act after they have paffed this line.
+
•
I. The firſt of theſe modes of action is recommended by Ca-
mus and De la Hire, the latter of whom has inveftigated the
form of the teeth folely for this particular cafe. When this
mode of action is adopted, the acting faces of the leaves of the
pinion fhould be parts of an interior epicycloid generated by a
circle of any diameter rolling upon the concave fuperficies of
the pinion, and the acting faces of the teeth of the wheel ſhould
be portions of an exterior epicycloid formed by the fame gene
rating circle rolling upon the convex fuperficies of the wheel.
A
Now it is demonftrable (fee the article CYCLOID, Supp.
English Encyclo.) and has before been mentioned in our ar-
ticle PARALLEL motions, that when one circle rolls within
another, whoſe diameter is double that of the rolling circle, the
line generated by any point of the latter will be a traight line,
tending to the centre of the larger circle. If the generating
circle, therefore, mentioned above, ſhould be taken with its dia-
meter equal to the radius of the pinion, and be made to roll
upon the concave fuperficies of the pinion, it will generate a
ftraight line tending to the pinion's centre, which will be the
form of the acting faces of its leaves; and the teeth of the
wheel will, in this cafe, be exterior epicycloids, formed by a
generating circle, whoſe diameter is equal to the radius of the
pinion, rolling upon the convex fuperficies of the wheel. This
form of the teeth, viz. when the acting faces of the pinion's
leaves are right lines tending to its centre, is exhibited in fig.
14. pl. XXXII. and is perhaps the most advantageous, as it re-
quires lefs trouble, and may be executed with greater accuracy
than if the epicycloidal form had been employed; it is juſtly re-
Teeth of Wheels.
425
commended both by De la Hire and Camus as particularly ad-
vantageous in clock and watch work.
The attentive reader will perceive that, in order to prevent
the teeth of the wheel from acting upon the leaves of the pini-
on, before they reach the line of centres, and that one tooth of
the wheel may not quit the leaf of the pinion till the fucceed-
ing tooth begins to act upon the fucceeding leaf, there muſt be
a certain proportion between the number of leaves in the pi-
nion and the number of teeth in the wheel, or between the ra❤
dius of the pinion and the radius of the wheel, when the di-
itance of the leaves is given.. But in machinery the number of
leaves and teeth are always known from the velocity which is
required at the working point of the machine: it becomes a
matter, therefore, of great importance, to determine with accu-
racy the relative radii of the wheel and pinion.
For this purpoſe let A, fig. 14. be the pinion, having the act-
ing faces of its leaves ftraight lines tending to the centre, and
B (not fhewn in the figure) the centre of the wheel; AB will
be the diſtance of their centres. Then, as the tooth C is ſuppoſ
ed not to act upon the leaf A m'till it arrives at the line AB, it
ought not to quit A m till the following tooth F has reached
the line AB. But fince the tooth always acts in the direction
of a line drawn perpendicular to the face of the leaf A m from
the point of contact, the line CH, drawn at right angles to the
face of the leaf A m, will determine the extremity of the tooth
CD, or the last part of it, which fhould act upon the leaf Am,
and will alſo mark out CD for the depth of the tooth. Now,
in order to find AH, HB, and CD, put a for the number of
teeth in the wheel, b for the number of leaves in the pinion,
for the diſtance of the pivots A and B, and let.x repreſent the
radius of the wheel, and y that of the pinion. Then, fince the
circumference of the wheel is to the circumference of the pi-
nion as the number of teeth in the one to the number of leaves
in the other, and as the circumferences of circles are propar-
tional to their radii, we fhall have a: b :: x: y, or by compofi,
tion a+bb::c:y (c being equal to x+y), and confequently the
radius of the pinion, viz. y=then, by inverting the firſt
analogy, we have b:a::y:x, and conſequently the radius of the
ay
*
cb
3
wheel, viz. x= ;y being now a known number,
t
Now, in the triangle AHC, right-angled at C, the fide AH
is known and likewife all the angles (HAC being equal to
360
); the fide AC, therefore, can be eaſily found by plane trigo,
nometry. Then, in the oblique-angled triangle ACB, the an-
#26
MACHINES.
gle CAB, equal to HAC, is known, as well as the two fides
AB, AC, which contain it; the third fide, therefore, viz. CB,
may be determined; from which DB, equal to HB, already
found, being ſubtracted, there remains CD for the depth of the
teeth. When the action is carried on after the line of centres,
it often happens that the teeth will not work in the hollows of
the leaves. In order to prevent this, the angle CBH muſt alı
ways be greater than half the angle HBP. The angle HBP is
equal to 360 degrees, divided by the number of teeth in the
wheel, and CBH is eaſily found.
·Inſtead of pinions our mill-wrights frequently ſubſtitute lan
terns or trundles, confifting of round flaves fixed by both ends
nearly at the circumferences of two equal circular pieces of
board; and theſe may often be adopted with great propriety,
provided the teeth of the wheel have a proper form affigned to
them. As the form recommended by feveral writers, and even
by Belidor, is by no means accurate, we ſhall here call the 1
read-
er's attention to the conſtruction pointed out by Mr Brewſter,
which turniſhes a ready method of greatly diminiſhing the frica
tion arifing from the mutual action of the teeth.
Let A, pl. XXXII. fig. 13. be the centre of the pinion or
fmall wheel TCH, whofe teeth are circular like ICR, having
their centres in the circle PDE. Upon B, the centre of the
large wheel, at the distances BC, BD, deſcribe the circles FCK,
GDO; and with PDE, as a generating circle, form the exte
rior epicycloid DNM, by rolling it upon the convex fuper
ficies of the circle GDO. The epicycloid DNM thus formed
would have been the proper form for the teeth of the large
wheel GDO, had the circular teeth of the ſmall wheel been
infinitely ſmall; but as their diameter must be confiderable, the
teeth of the wheel ſhould have another form.. In order to de-
termine their proper figure, divide the epicycloid DNM into a
number of equal parts, 1, 2, 3, 4, &c. as fhewn in the figure, and
let-thefe divifions be as fmall as poffible. Then, upon the
points 1, 2, 3, &c. as centres, with the distance DC equal to the
radius of the circular tooth, deſcribe portions of circles fimilar
to thoſe in the figure; and the curve OPT, which touches
theſe circles, and is parallel to the epicycloid DNM, will be
the proper form for the teeth of the large wheel.
In order that the teeth may not act upon each other till they
reach the line of centres AB, the curve OP ſhould not touch
the circular tooth ICR till the point O has arrived at D. The
tooth OP, therefore, will commence its action upon the cir.
cular tooth at the point I, where it is cut by the circle DRE.
On this account, the part ICR of the cylindrical pin being fu-

Teeth of Wheels.
427
perfluous, may be cut off, and the teeth of the fmall wheel will
be fegments of circles fimilar to the fhaded parts of the figure..
If the teeth of wheels and the leaves of pinions be formed
according to the directions already given, they will act upon
each other, not only with uniform force, but alſo without fric
tion. The one tooth rolls upon the other, and neither flides
nor rubs to ſuch a degree as to retard the wheels, or wear their
teeth. But as it is impoffible in practice to give that perfect cur
vature to the acting faces of the teeth which theory requires, a
certain quantity of friction will remain after every precaution
has been taken in the formation of the communicating parts.
This friction may be removed, or at leaſt greatly diminiſhed, in
the following manner.
If, inftead of fixing the circular teeth, as in fig. 13, to the
wheel DRE, they are made to move upon axles or fpindles
fixed in the circumference of the wheel, all the friction will be
taken away except that which arifes from the motion of the
cylindrical tooth upon its axis. The advantages which attend
this mode of conftruction are many and obvious. The cylin
drical teeth may be formed by a turning-lathe with the great-
eft accuracy; the curve required for the teeth of the large
wheel is eaſily traced; the preffure and motion of the wheels
will be uniform; and the teeth are not ſubject to wear, becauſe
whatever friction remains is almoft wholly removed by the res
volution of the cylindrical ſpokes about their axes. The reader
will alfo obferve, that this improvement may be moft eafily
introduced when the ſmall wheel has the form of a trundle or
lantern; and that it may be adopted in cafes where lanterns
could not be conveniently uſed. It however can only be
adopted where the machinery is large. For fmall works, the
teeth of the pinion or ſmall wheel fhould be rectilineal, and
thoſe of the large wheel epicycloidal.
II. Having hitherto ſuppoſed, that the mutual action of the
teeth does not commence till they arrive at the line of centres,
let us now attend a little to the form which muſt be given them
when the whole of the action is carried on before they reach
the line of centres, or when it is completed a very little below
this line. This mode of action is not fo advantageous as that
which we have been confidering, and ſhould, if poſſible, always
be avoided. It is evident that the tooth of the wheel acts upon
the leaf of the pinion before they arrive at the line of centres,
that it quits the leaf when they reach this line, and that the
tooth works deeper and deeper between the leaves of the pia
nion the mearer it comes to the line of centres. From this laft
circumftance a confiderable quantity of friction arifes, becauffe
the tooth does not, as before, roll upon the leaf, but flides upon
428
MACHINES.
it; and from the fame cauſe the pinion foon becomes foul, as
the dust which lies upon the acting faces of the leaves is puſh-
ed into the hollows between them. One advantage, however,
attends this mode of action, for it allows us to make the teeth
of the large wheel rectilineal, and thus renders the labour of
the mechanic lefs, and the accuraey of his work greater, than
if they had been of a curvilineal forin. If the teeth therefore
of the wheel are made rectilineal, having their ſurfaces directed
to the wheel's centre, the acting faces of the leaves muſt be
epicycloids formed by a generating circle, whofe diameter is
equal to the fum of the radius of the wheel, added to the depth
of one of its teeth, rolling upon the circumference of the pinion.
But if the teeth of the wheel and the leaves of the pinion are
made curvilineal, the acting faces of the teeth of the wheel muſt
be portions of an interior epicy cloid formed by any generating
circle rolling within the concave. fuperficies of the large circle,
and the acting faces of the pinion's leaves muſt be portions of
an exterior epicycloid produced by rolling the fame generating
cncle upon
the convex circumference of the pinion.
When the teeth of the large wheel are cylindrical ſpindles
either fixed or moveable upon their axes, an exterior epicycloid
mufl be formed like DNM in fig. 13. pl. XXXII, by a gene-
rating circle whofe radius is AC, rolling upon the convex cir.
cumference FCK, AC being in this cafe the diameter of the
wheel, and FCK the circumference of the pinion. By means
of this epicycloid a curve OPT muſt be formed as before de-
fcribed, which will be the proper curvature for the acting faces
of the leaves of the pinion, when the teeth of the wheel are cy-
lindrical. The relative diameter of the wheel and pinion, when
the number of teeth in each is known, may be found by the
fame theorems which were given for the firft mode of action,
with this difference only, that in this cafe the radius of the
wheel is reckoned from its centre to the extremity of its teeth,
and the radius of the pinion from its centre to the bottom of its
leaves.
H. The third way in which one wheel may drive another,
is when the action is partly carried on before the acting teeth
arrive at the line of centies, and partly after they have paſſed
this line.
This mode of action, which is reprefented in fig. 5, plate
XXXI, is a combination of the two firft modes, and confequent-
by partakes of the advantages and disadvantages of each. It is
evident from the figure that the portion e h of the tooth acts
upon the part b c of the leaf till they reach the line of centres
AB (B the centre of the wheel is here alfo omitted in the
figure), and that the part e d of the tooth acts upon the portion
Teeth of Wheels..
429
ba of the leaf after they have paffed this line. It follows,
therefore, that the acting parts eh and b c muſt be formed ac
cording to the directions given for the firft mode of action, and
that the remaining parts ed, ba, muſt have that curvature
which the fecond mode of action requires; conſequently eh
fhould be part of an interior epicycloid formed by any generat.
ing circle rolling on the concave circumference. m n of the
wheel, and the correſponding part bc of the leaf fhould be
part of an exterior epicycloid formed by the fame generating
circle rolling upon b EO, the convex circumference of the
P
nion: the remaining part c d of the tooth fhould be a portion
of an exterior epicycloid, engendered by any generating circle
rolling upon e L, the concave fuperficies of the wheel; and
the correſponding part b a of the leaf fhould be part of an in-
terior epicycloid defcribed by the fame generating circle, rolling
along the concave fide b EO of the pinion. As it would
be extremely troubleſome, however, to give this double curva
ture to the acting faces of the teeth, it will be proper to uſe a
generating circle, whoſe diameter is equal to the radius of the
wheel BC, for defcribing the interior epicycloid e hand the
exterior one bc, and a generating circle, whofe diameter is
equal to AC, the radius of the pinion, for deſcribing the inte
rior epicycloid ha, and the exterior one ed. In this cafe the
two interior epicycloids eh, ba, will be ftraight lines tending
to the centres B and A*, and the labour of the mechanic will
by this means be greatly abridged.
•
In order to find the relative diameters of the wheel and pinion,
when the number of teeth in the one and the number of leaves
in the other are given, and when the diſtance of their centres is
alſo given, and the ratio of ES to CS, let a be the number of
teeth in the wheel, b the number of leaves in the pinion, c the
diſtance of the pivots A, B, and let m be to n as ES to CS,
then the arch. ES, or the angle SAE, will be equal to b
and LD, or the angle LBD, will be equal to
360°
a
360°
But at
'ES: CS::m:n; conſequently LD: LC::m:n, and LCLD xn
360°
m.
but LD is equal to therefore by fubftitution we have LC
360 xn
·am·
a
Now, in the triangle APB, AB is known, and also PB,
which is the cofine of the angle ABD, PC being perpendi
cular to DB, AP therefore may be found by plain trigo
* Traité des Epicycloids, par M. De La Hire. Prop. V.1
130
MACHINES.
nometry. The point P marks out the parts of the tooth
D and the leaf SP where they commence their action; and
the point I marks out the parts where their mutual action
ccafes*; AP therefore is the proper radius of the pinion,
and BI the proper radius of the wheel, the parts of the
tooth L without the point I, and of the leaf SP without the
point P being fuperfluous. Now, to find BI, we have ES:
CS::m:n, confequently CS= ; but ES was formerly
ES xn
m
360
therefore, CS=
360 X#
Now the
b
·b m
360
b
>
and CS, or the
fhewn to be equal to
arch ES, or angle EAS, being equal to
their difference EC, or the
angle CAȘ, being equal to
360 x n
b m
360.
b
>
360 X n
-> or =
bm
angle EAC, will be equal to
360° x (m—n)
b m
The angle EAC being thus found, the triangle EAB, or IAB,
which is nearly equal to it, is known, becauſe AB is given, and
likewife Al, which is equal to the cofine of the angle IAB,
AC being radius, and AIC being a right angle; conſequently
IB the radius of the wheel may be found by trigonometry. It
was formerly fhewn that AC, the radius of what is called the
primitive pinion, was equal to
a+b₁ and that BC, the radius of
the primitive wheel, was equal to ACX. If then we fub-
cb
b
a
tra&t: AC or AS from AP, we ſhall have the quantity SP,
which must be added to the radius of the primitive pinion, and
if we take the difference of BC (or BL) and DE, the quantity,
LE will be found, which must be added to the radius of the
primitive wheel. We have all along fuppofed that the wheel
drives the pinion, and have given the proper form of the teeth
upon this fuppofition. But when the pinion drives the wheel,
the form which was given to the teeth of the wheel, in the first
caſe, muſt in this be given to the leaves of the pinion; and the
hape which was formerly given to the leaves of the pinion
muſt now be transferred to the teeth of the wheel.
•
Another form for the teeth of wheels, different from any
which we have mentioned, has been often recommended. Á
perfect uniformity of action may be fecured, by making the
acting faces of the teeth involutes of the wheel's circumfer
ence. Thus, in pl. XXXV, fig. i. let AB be a portion of the
* The letter L marks the interſection of the line BL with the arch e m,
and the letter E the interfection of the arch b O with the upper ſurface of
the leaf. The letters D and S correfpond with L and E reſpectively, and
P with I.
-
Teeth of Wheels.
481
bea
wheel on which the tooth is to be fixed, and let A
thread wrapped round its circumference, having a loop-hole at
its extremity a. In this loop-hole fix the pin a, and with i
defcribe the curve or involute, abcdek, by unwrapping the
thread gradually from the circumference A pm.
This curve
will be the proper form for the teeth of a wheel whoſe diame
ter is AB. As this form admits of feveral teeth to be afting
at the fame time (twice the number that can be admitted in M.
De la Hire's method), the preffure is divided among feveral
teeth, and the quantity upon any one of them is fo diminished
that thofe dints and impreffions which they unavoidably make
upon each other are partly prevented.
This form however, which we have before mentioned (vol. I.
art. 147.), is only a modification of the general principle; as an
involute may be reckoned, and indeed is called, by De la Hire,
the laft of the exterior epicycloids.
The involute a b c d, &c. may alfo be produced by an epi
cycloidal motion; for, fince the circumference of a generating
circle, whoſe centre is infinitely diſtant, must be a ftraight line,
we may form the involute a b c, by making a ſtraight rules roll
upon the circumference of the circle to be evolved. In fig. 1.
let on be a ftraight ruler at whofe extremity is fixed the pin nj
and let the point of the pin be placed upon the point m of the
circle, then by rolling the ftraight ruler upon the circular bafe,
fo that the point in which it touches the circle may move grai
dually from m towards B, the curve m n will be generated ex
actly fimilar to the involute a b c, &c.
As nothing can be of greater importance to the practical me
chanic, than to have a method of drawing epicycloids with fas
pility and accuracy; we give the following from Mr. Brewer
as an ample mechanical method. Take a piece of plain wood
GH, fig. 2, pl. XXXV, and fix upon it another piece of wood E,
having its circumference mb of the fame curvature as the eir-
cular baſe upon which the generating circle AB is to roll.
When the generating circle is large, the fhaded fegment B will
be fufficient: in any part of the circumference of this fegment
fix a fharp-pointed nail a, floping in fuch a manner that the
diſtance of its point from the centre of the circle may be e
actly equal to its radius; and faften, to the board: GH a piece
of thin braſs, or copper, or tin plate a b, diftinguiſhed by the
dotted lines. Place the fegment B in fuch a pofition that the
point of the nail a may be upon the point b, and roll the feg-
ment towards G, fo that the nail a may rife gradually, and the
point of contact between the two circular, fegments may advance
towards m; the curve a b deſcribed upon the braſs plate will be
án accurate exterior epicycloid. Remove, with a file, the part

ex
A CEW
1
432
MACHINES.
of the brafs on the left hand of the epicycloid, and the remain.
ng concave arch or gage a b will be a pattern tooth, by means
of which all the reft may be easily formed. When an interior
epicycloid is wanted, the concave fide of its circular bafe mult
be ufed. The cycloid, which is ufeful in forming the teeth of
rack-work, is generated precifely in the fame manner, with this
difference only, that the baſe on which the generating circle
rolls muſt be a ſtraight line.
0
Although, in general, it is neceffary to give the proper curve
ature only to one fide of the teeth, yet it may be proper to
form both. fides with equal care, that the wheels may be able
to move in a retrograde direction. This is particularly necef,
fary when a reciprocating power is employed. In the cafe of
a mill moving by the force of a fingle-ſtroke fteam-engine, the
direction of the preffure on the communicating parts of the
machinery is changed twice every firoke. During the work-
ing ftroke, the teeth of the wheels which convey the motion
from the beam to the machinery are acting with one fide of
their teeth; but during the returning ftroke the wheels act with
the other fide of their teeth.
In order that the teeth may not embarraſs one another before
their action commences, and that one tooth may begin to act
upon its correfponding leaf of the pinion, before the preced-
ing tooth has ceafed to act upon the preceding leaf, the height,
breadth, and diftance of the teeth must be properly proportion,
ed. For this purpoſe the pitch line or circumference of the
wheel which is repreſented in pl. .XXXI. fig. 5. by the dotted
arches mult he divided into as many equal fpaces as the num-
ber of teeth which the wheel is to carry. Divide each of theſe
ſpaces into 16. equal parts; allow 7 of theſe for the greateſt
breadth of the tooth, and 9 for the diftance between each. If
the wheel drives a trundle, each ſpace, fhould be divided into
7.equal parts, and 3 of theſe allotted for the thickneſs of the
tooth, and 3 for the diameter of the cylindrical ftave of the
trundle. If each of the fpaces already mentioned, or if the
diſtance between the centres of each tooth, be divided into 3
equal parts, the height of the teeth must be equal to 2 of theſe.
Thefe diftances and heights, however, vary according to the
mode of action which is employed. See Wolfi Opera Ma
themat. tom. i. pa. 696.. Belidor, Arch. Hydraulique, tom.i.
chap. 2. Camus Courfe, tom. ii. and Brewfter's Ferguson,vol. ii.
Such are fome of the methods fuggefted by theory for the
formation of the teeth of wheels; but it is feldom indeed that
any of them are made ufe of by practical mechanics. Among
them. feveral methods are practifed, almoft every, celebrated
mill-wright or engineer having his favourite conftruction; of
J
Teeth of Wheel's.
433.
thefe we ſhall only defcribe one in this place; and that, being
tolerably eaſy in application, allowing much ftrength to the
teeth, while it is pretty free from friction in compariſon with
many practical methods, may fometimes, perhaps, be fafely
adopted. Let A and B (fig. 11. pl. XXXV.) be two fpur-wheels
of different diameters, of which the cogs are intended to work
into each other half the pitch. The dotted circular arcs GH,
EF, touching each other between s and d, are the centre or
pitch lines, from which the teeth are formed. If the teeth
of both wheels are iron, as is generally the cafe in the first mo-
tions of works, thoſe teeth are then made nearly both of a fize
at the pitch line: but if the teeth of one be wood and the other,
iron, then the iron ones are made to have a good deal lefs pitch
than the wooden ones; for then they are found to wear better.
In the figure both are fuppofed of iron. Suppoſe the wheels
to move from G towards H, and from E towards F, and that
the fides of the teeth at b, c, and d, e, are in contact. From b
as a centre with a radius equal to bp, defcribe the arcs p d, I m;
from das a centre with the fame radius the arcs ki, fg, c k.
Thus the fame opening of the compaffes, and a centre chofen
where the wheels are in contact on the pitch line, will mark
the contour of the upper part of a tooth of one wheel, and the
lower part of a correfponding tooth of the other wheel: and by
taking feveral centres on the two pitch lines, the various teeth
may be formed. To prevent the cogs from bottoming, as the
workmen call 'it, let the lower part re of one tooth be made
rather longer than the upper part pd of the other which is to
play into it. The way in which cogs thus conftructed will
work into one another may be understood by confidering the
motion of two of them, n and o for example: when they firſt
they
come into contact, they will appear as at the curve xó Pi;
when they arrive at Q the fame fides will appear as in the dotted
lines there repreſented; and when the fame arrive at RS, they
are in contact on their middle points.
८.
,لا
and
In bevel work (ſee fig. 7, pl. III.) when this method of
forming the teeth is adopted, the radii hy, gy, of the wheels
muft not be taken as thofe of the fpur-wheel; but drawing a.
line through y perpendicular to xy, till it meets x g, and x h,
produced, the fegments of that line intercepted between
the produced lines xg, xh, muſt be uſed as the radii of the
fpur-wheels, and the other part of the conftruction will be as
above. The line through y drawn perpendicular to xy, is
called by mill-wrights fquare of the bevel. For more on the
fubject of bevel geer, confult the introductory part of this
volume. And for Mr. Maudlay's contrivance for cutting
teeth of wheels, fee the article TURNING.
VOL. II.
FF
! . .
I
484
MACHINES.
TELEGRAPH (derived from ryλs and yeapw), is the name
very properly given to an inftrument, by means of which in-
formation may be almoſt inftantaneously conveyed to a confi-
derable diſtance.
The telegraph, though it has been generally known and uſed
by the moderns only for a few years, is by no means a modern
invention. There is reaſon to believe that amongst the Greeks
there was ſome ſort of telegraph in ufe. The burning of Troy
was certainly known in Greece very ſoon after it happened, and
before any perſon had returned from thence. Now that was al-
together fo tedious a piece of buſineſs, that conjecture never
could have ſupplied the place of information. A Greek play
begins with a ſcene, in which a watchman defcends from the
top of a tower in Greece, and gives the information that Troy
was taken. "I have been looking out theſe ten years (fays he)
to ſee when that would happen, and this night it is done." Of
the antiquity of a mode of conveying intelligence quickly to a
great diſtance this is certainly a proof.
The Chineſe, when they fend couriers on the great canal,
or when any great man travels there, make fignals by fire
from one day's journey to another, to have every thing pre-
pared; and moſt of the barbarous nations uſed formerly to
give the alarm of war by fires lighted on the hills or rifing
grounds.
Polybius calls the different inftruments uſed by the ancients
for communicating information Tugosial, pyrfia, becauſe the
fignals were always made by means of fire. At firft they commu-
nicated information of events merely by torches; but this me-
thod was of little uſe, becauſe it was neceffary before-hand to
fix the meaning of every particular fignal. Now as events are
exceedingly various, it was impoffible to exprefs the greater
number of them by any premeditated contrivance.
It was
eafy, for inſtance, to exprefs by fignals that a fleet had arrived
at fuch a place, becauſe this had been foreſeen, and fignals
accordingly had been agreed upon to denote it, but an un-
expected revolt, a murder, and fuch accidents, as happen
but too often, and require an immediate remedy, could not be
communicated by fuch fignals; becauſe to foreſee them was
impoffible.
A new method was invented by Cleoxenus (others fay by
Democritus), and very much improved by Polybius, as he him-
ſelf informs us. He defcribes this method as follows: Take the
letters of the (Greek) alphabet, and divide them into five parts,
each of which will confist of five letters, except the laſt divi-
fion, which will have only four. Let theſe be fixed on a
board in five columns. The man who is to give the fignals is
then to begin by holding up two torches, which he is to keep
1
Telegraphs.
435
aloft till the other party has alfo fhewn two. This is only to
ſhew that both fides are ready. Theſe firft torche are then
withdrawn. Both parties are provided with boards, on which
the letters are difpofed as formerly deſcribed. The perfon
then who gives the fignal is to hold up torches on the left to
point out to the other party from what column he fhall take the
letters as they are pointed out to him. If it is to be from the
firft column, he holds up one torch; if from the fecond, two;
and ſo on for the others. He is then to hold up torches on the
right, to denote the particular letter of the column that is to be
taken. All this muft have been agreed on before-hand.
The
man who gives the fignals muſt have an inftrument (diolgay),
confifting of two tubes, and fo placed as that, by looking
through one of them, he can fee only the right fide, and
through the other only the left, of him who is to anſwer. The
board muſt be fet up near this inftrument; and the ſtation on
the right and left muſt be ſurrounded with a wall (rapareρxxxı),
ten feet broad, and about the height of a man, that the torches
raifed above it may give a clear and strong light, and that when
taken down they may be completely concealed. Let us now
ſuppoſe that this information is to be communicated—A number
of the auxiliaries, about a hundred, have gone over to the enemy.
In the first place, words must be chofen that will convey the
information in the feweft letters poffible; as, A hundred Cretans
have deferted, Κρείες εκατον αφ' ημών ηυτομόλησαν. Having written
down this fentence, it is conveyed in this manner..
The firft
letter is a K, which is in the fecond column; two torches are
therefore to be raiſed on the left hand to inform the perfon who
receives the fignals to look into that particular column. Then
five torches are to be held up on the right, to mark the letter k,
which is the left in the column. Then four torches are to be
held up on the left to point out the g (r), which is in the fourth
column, and two on the right to show that it is the fecond letter
of that column. The other letters are pointed out in the fame
manner. Such was the pyra or telegraph recommended by
Polybius.
+
But neither this nor any other method mentioned by the an-
cients feems ever to have been brought into general ufe: nor
does it appear that the moderns had thought of fuch a machine
as a telegraph till the year 1663, when the marquis of Wor-
cefter, in his Century of Inventions, affirmed that he had dif-
covered “a method by which, at a window, as far as eye can
difcover black from white, a man may hold difcourfe with his
correfpondent, without noiſe made or notice taken; being ac-
cording to occafion given, or means afforded, ex re nata, and
no need of provision beforehand; though much better if fore-

FF 2
436
MACHINES.
f
ſeen, and courſe taken by mutual confent of parties." This could
be done only by means of a telegraph, which in the next fen-
tence is declared to have been rendered fo perfect, that by means
of it the correfpondence could be carried on " by night as well
as by day, though as dark as pitch is black."
Dr. Hooke, whofe genius as a mechanical inventor was per-
haps never furpaffed, delivered a "Difcourfe to the Royal
Society, May 21, 1684, fhewing a way how to communicate
one's mind at great diftances." In this diſcourſe, he afferted the
poffibility of conveying intelligence from one place to another
at the diſtance of 30, 40, 100, 120, &c. miles, " in as fhort
a time almoft as a man can write what he would have fent." He
takes to his aid the then recent invention of the teleſcope, and
explains the method by which characters expoſed at one ſtation
may be rendered plain and diftinguiſhable at the others. He di-
rects," First, for the ſtations; if they be far diftant, it will
be neceffary that they ſhould be high, and lie expoſed to the
fky; that there be no higher hill, or part of the earth beyond
them, that may hinder the diftinctneſs of the characters that
are to appear dark, the ſky beyond them appearing white: by
which means alſo the thick and vaporous air near the ground
will be paffed over and avoided." "Next, the height of the fta-
tions is advantageous, upon the account of the refractions or
infections of the air."Next, in choofing of theſe ſtations,
care muſt be taken, as near as may be, that there be no hill that
interpoſes between them, that is almoſt high enough to touch
the vifible ray; becauſe in fuch cafes the refraction of the air
of that hill will be very apt to diſturb the clear appearance of
the object.” “The next thing to be confidered is, what tele-
fcopes will be neceffary for fuch ftations." "One of theſe te-
lefcopes muft be fixed at each extreme ftation, and two of them
in each intermediate; fo that a man for each glaſs, fitting and
looking through them, may plainly diſcover what is done in the
next adjoining ftation, and with his pen write down on paper,
the characters there expofed in their due order; ſo that there
ought to be two perfons at each extreme ftation, and three at
each intermediate; fo that, at the fame time, intelligence may
be conveyed forwards and backwards." "Next, there must be
certain times agreed on, when the correfpondents are to ex-
pect; or elfe there mult, be fet at the top of the pole, in the
morning, the hour appointed by either of the correfpondents
for acting that day: if the hour be appointed, pendulum clecks
may adjust the moment of expectation and obferving." "Next,
there must be a convenient apparatus of characters, whereby
to communicate any thing with great eaſe, diſtinctneſs, and fe
crecy. And thoſe muſt be either day characters or night cha-
Telegraphs.
437
racters The day characters "may all be made of three flit.
deals" the night characters" may be made, with links, or
other lights, difpofed in a certain order." The doctor invented
24 fimple characters, each conftituted of right lines, for the
letters of the alphabet; and feveral fingle characters, made up
of femicircles, for whole fentences. He recommended that
three very long mafts or poles fhould be placed vertically, and
joined at top by one ſtrong horizontal beam; that a large fcreen
ſhould be placed at one of the upper corners of this frame, be-
hind which all the deal-board characters fhould hang, and by the
help of proper cords fhould quickly be drawn forwards to be
expoſed, and then drawn back again behind the ſcreen.
"By
thefe means," fays the doctor, "all things may be made fo
convenient that the fame character may be feen at Paris, within
a minute after it hath been expofed at London, and the like in
proportion for greater diftances; and that the characters may
be expofed fo quick after one another, that a compofer fhall not.
much exceed the expofer in fwiftnefs." Among the ufes of
this contrivance, the inventor ſpecifies thefe: "The firft is for.
cities or towns befieged; and the fecond for fhips upon the
fea; in both which cafes it may be practifed with great cer-
tainty, fecurity, and expedition." The whole of Dr. Hooke's
paper was publiſhed in Derham's collection of his Experiments
and Obfervations; from which it appears, that he had brought
the telegraph to a ſtate of far greater maturity and perfection
than M. Amontons, who attempted the fame thing about the
year 1702; and indeed to a ſtate little inferior to feveral which
have been propoſed during the last twenty years.
It was not, however, till the French revolution that the tele-
graph was applied to uſeful purpoſes. Whether M. Chappé,
who is faid to have invented the telegraph firft ufed by the
French about the end of 1793, knew any thing of Hooke's or
of Amonton's invention, it is impoffible to fay; but his tele-
graph was constructed on principles nearly fimilar. The man-
ner of uſing this telegraph was as follows: at the first ftation,
which was on the roof of the palace of the Louvre at Paris, M.
Chappe, the inventor, received in writing, from the committee
of public welfare, the words to be fent to Life, near which
the French army at that time was. An upright poſt was erected
on the Louvre, at the top of which were two tranverfe arms,
moveable in all directions by a fingle piece of mechaniſm, and
with inconceivable rapidity. He invented a number of pofitions
for theſe arms, which ſtood as figns for the letters of the al-
phabet; and thefe, for the greater celerity and fimplicity, he
reduced in number as much as poffible. The grammarian will
eaſily conceive that fixteen figns may amply fupply all the
•
438
MACHINES.
letters of the alphabet, fince fome letters may be omitted, not
only without detriment, but with advantage. Theſe ſigns, as
they were arbitrary, could be changed every week; fo that the
fign of B for one day might be the fign of M the next; and it
was only neceffary that the perfons at the extremities fhould
know the key. The intermediate operators were only inftructed
generally in theſe fixteen fignals; which were fo diftinct, fo
marked, fo different the one from the other, that they were
eafily remembered. The conftruction of the machine was fuch,
that each fignal was uniformly given in preciſely the fame man-
ner at all times: it did not depend on the operator's manual
ſkill; and the pofition of the arm could never, for any one
fignal, be a degree higher or a degree lower, its movement being
regulated mechanically..
M. Chappe having received at the Louvre the fentence to be
conveyed, gave a known fignal to the ſecond ſtation, which was
Mont Martre, to prepare. At each ſtation there was a watch-
tower, where teleſcopes were fixed, and the perfon on watch
gave the fignal of preparation which he had received, and this
communicated fucceffively through all the line, which brought
them all into a ftate of readineſs. The perfon at Mont Martre
then received, letter by letter, the fentence from the Louvre,
which he repeated with his own machine; and this was again
repeated from the next height, with inconceivable rapidity, to
the final ſtation at Liſle.
The firſt deſcription of the telegraph was brought from Paris
to Frankfort on the Maine by a former member of the parlia
ment of Bourdeaux, who had feen that which was erected on the
mountain of Belville. As given by Dr. Hutton from fome of the
English papers, it is as follows. AA is a beam or maſt of wood
placed upright on a rifing ground (fig. 1. pl. XXXIII.), which
is about fifteen or fixteen feet high. BB is a beam or balance
moving upon the centre AA. This balance-beam may be placed
vertically or horizontally, or any how inclined, by means of
ftrong cords, which are fixed to the wheel D, on the edge of
which is a double groove to receive the two cords. This ba-
lance is about eleven or twelve feet long, and nine inches broad,
having at the ends two pieces of wood CC, which likewife turn
upon angles by means of four other cords that paſs through the
axis of the main balance, otherwiſe the balance would derange
the cords; the pieces C are each about three feet long, and may
be placed either to the right or left, ftraight or fquare, with
the balance-beam. By means of theſe three the combination of
movement is very extenfive, remarkably fimple, and eafy to
perform. Below is a fmall wooden gouge or hut, in which
a perfon is employed to obferve the movements of the ma-
2
・・・ Telegraphs.
-439
chine. In the mountain neareſt to this, another perfon is to
repeat theſe movements, and a third to write them down. The
time taken up for each movement is twenty feconds; of which
the motion alone is four feconds, the other 16 the machine is
ftationary. Two working models of this inftrument were exe-
cuted at Frankfort, and fent by Mr. W. Playfair to the duke of
York and hence the plan and alphabet of the machine came
to England.
the
Various experiments were in confequence tried upon tele-
graphs in this country; and one was foon after fet up by go-
vernment in a chain of ſtations from the admiralty-office to the
fea-coaft. It confifts of fix octagon boards, each of which is
poiſed upon an axis in a frame, in fuch a manner that it can be
either placed vertically, fo as to appear with its full ſize to
obferver at the neareſt ſtation, as in fig. 2. or it becomes invi-
fible to him by being placed horizontally, as in fig. 3. fo that
the narrow edge alone is expofed, which narrow edge is from
a diſtance invifible. Fig. 2. is a reprefentation of this telegraph,
with the parts all fhut, and the machine ready to work T, in
the officer's cabin, is the teleſcope pointed to the next ſtation.
Fig. 3. is a repreſentation of the machine not at work, and with
the ports all open. The opening of the firft port (fig. 2.) ex-
preffes a, the fecond b, the third c, the fourthed, the fifth e, and ·
the fixth f, &c.
Six boards make 36 changes, by the moft plain and fimple
mode of working; and they will make many more if more were
neceffary: but as the real fuperiority of the telegraph over all
other modes of making ſignals confifts in its making letters, we
do not think that more changes than the letters of the alphabet,
and the ten arithmetical cyphers, are neceffary; but, on the con-
trary, that thoſe who work the telegraphs fhould avoid com-
municating by words or figns agreed upon to exprefs fentences;
for that is the fure method never to become expert at fending
unexpected intelligence accurately..

、
Several other telegraphs have been propofed to remedy the
defects to which the inſtrument is ſtill liable. The dial-plate of
a clock would make an excellent telegraph, as it might exhibit
144 figns fo as to be vifible at a great diftance. A telegraph on
this principle, with only fix divifions inftead of twelve, would
be fimple and cheap, and might be raiſed 20 or 30 feet high
above the building without any difficulty: it might be fupported
on one poft, and therefore turn round, and the contraft of co-
lours would always be the ſame.
A very ingenious improvement of the telegraph has been
propofed in the Gentleman's Magazine. It confifts of a femi-
di nolraq
377
J
and son tea an
m
en
440
MACHINES.
circle, to be properly elevated, and fixed perpendicularly on a
Atrong ftand. The radius 12 feet; the femicircle confequently
ſomewhat more than 36. This is to be divided into 24 parts.
Each of theſe will therefore compriſe a ſpace of 18 inches, and
an arch of 7° 30' on the circumference. Thefe 24 divifions to
be occupied by as many circular apertures of fix inches dia-
meter; which will leave a clear ſpace of fix inches on each fide
between the apertures. Thefe apertures, beginning from the
left, to denote the letters of the alphabet, omitting K, J con-
fonant, V, X, and Q. as ufelefs for this purpoſe. There are
then 21 letters. The four other ſpaces are referved for fignals.
The inftrument to have an index moveable by a windlafs on the
centre of the femicircle, and having two tops, according as it
is to be uſed in the day or night; one, a circular top of lac-
quered iron or copper, of equal diameter with the apertures
(and which confequently will eclipſe any of them againſt which
it refts); the other, a fpear or arrow-fhaped top, black, and
highly polished, which in ftanding before any of the apertures
in the day-time, will be diftinctly vifible. In the night, the
apertures to be reduced by a diaphragm fitting cloſe to each, fo
as to leave an aperture of not more than two inches diameter,
The diaphragm to be of well-poliſhed tin; the inner rim lac-
quered black half an inch. All the apertures to be illuminated,
when the inſtrument is uſed in the night-time, by ſmall lamps;
to which, if neceffary, according to circumstances, convex
lenfes may be added, fitted into each diaphragm, by which the
light may be powerfully concentrated and increafed. Over each
aperture one of the five prifmatic colours leaft likely to be mif-
taken (the remaining two being lefs diftinguishable, and not
wanted, are beft omitted) to be painted; and, in their natural
order, on a width of eighteen inches and a depth of four, red,
orange, yellow, green, blue; or, ftill to heighten the contraft,
and render immediately fucceffive apertures more diftinguish-
able, red, green, orange, blue, yellow. The whole inner circle
beneath and between the apertures to be painted black.
When the inſtrument is to be uſed, the index to be fet to the
fignal apertures on the right. All the apertures to be covered
or dark when it begins to be ufed, except that which is to give.
the fignal. A fignal gun to be fired to apprife the obferver. If
the index is ſet to the first aperture, it will denote that words
are to be expreffed; if to the fecond, that figures; if to the
third, that the figures ceafe; and that the intelligence is carried
on in words. When figures are to be expreffed,. the alternate
apertures from the left are taken in their order, to denote from
1 to 10 mclufively; the fecond from the right denotes 100; the
Telegraphs.
441
fifth rooo. This order, and theſe intervals, are taken to pre
vent any confufion in fo peculiarly important an article of the
intelligence to be conveyed.
Perhaps, however, none of the telegraphs hitherto offered to
the public exceeds the following, either in fimplicity, cheap
nefs, or facility in working; and it might, perhaps, with a few
trifling additions, be made exceedingly diftinct. It is thus de-
ſcribed in the Repertory of Arts and Manufactures: for a noc-
turnal telegraph, let there be four large patent reflectors, lying
on the fame plane, parallel to the horizon, placed on the top of
an obfervatory. Let each of theſe reflectors be capable, by
means of two winches, either of elevation or depreflion to a
certain degree. By elevating or depreffing one or two of the re-
flectors, eighteen very diftinct arrangements may be produced,
as the following ſcheme will explain,

3194

A
B
O
000
O
8
DE
F
O
O
IK
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M
N
Na
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000
O
P
R
S
00
T
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SURS
groddsib oda
med 2orld baisup

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both ornings
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00
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$10
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For the fake of example, the above arrangements are made
to anſwer to the most neceflary letters of the alphabet; But al
terations may be made at will, and a greater number of changes
produced, without any addition to the reflectors. In the first
obfervatory there need only be a ſet of ſingle reflectors, but
in the others each reflector fhould be double, fo as to face
both the preceding and fubfequent obfervatory and each obs
fervatory fhould be furnished with two teleſcopes. The proper
diameter of the reflectors, and their diftarice from each other,
will be aſcertained by experience; and it muſt be obſerved, that


*
442
MACHINES.
each reflector, after every arrangement, must be restored to its
place.
To convert this machine into a diurnal telegraph, nothing
more is neceffary than to infert, in the place of the reflectors,
gilt balls, or any other confpicuous bodies.
Since theſe inventions were made public, telegraphs have
been brought to fo great a degree of perfection, that they now
convey information fpeedily and diftinctly, and are fo much
fimplified, that they can be conſtructed and maintained at little
expence. The advantages too which reſult from their uſe are
almoſt inconceivable. Not to ſpeak of the ſpeed with which in-
formation is communicated and orders given in time of war, by
means of them, the whole kingdom could be prepared in an in-
ftant to oppoſe an invading enemy. A telegraph might be alſo
ufed by commercial men to convey a commiffion cheaper and
ſpeedier than an exprefs can travel. An eſtabliſhment of tele-
graphs might be made like that of the poſt; and inſtead of being
an expence, it would produce a revenue. Something of this
Lind has lately been fet up to facilitate the intercourfe between
Norwich and Yarmouth.
THERMOMETER, an inftrument for meaſuring the de-
gree of heat or cold in any body. The thermometer was in-
vented about the beginning of the 15th century; but, like many
other uſeful inventions, it has been found impoffible to afcer-
tain to whom the honour of it belongs.
The firſt form of this inftrument for meaſuring the degrees
of heat and cold was the air-thermometer. It is a well-known
fact that air expands with heat fo as to occupy more ſpace
than it does when cold, and that it is condenfed by cold fo
as to occupy leſs ſpace than when warmed, and that this expan
fion and condenfation is greater or lefs according to the de-
gree
of heat or cold applied. The principle then on which
the air-thermometer was conftructed is very fimple. The air
was confined in a tube by means of fome coloured liquor; the
liquor rofe or fell'according as the air became expanded or con-
denfed.***
→
This inftrument was extremely defective: for the air in the
tube was not only affected by the heat and cold of the atmo-
there, but alfo by its weight.
The air being found improper for meaſuring with accuracy
the variations of heat and cold according to the form of the
thermometer which was firft adopted, another fluid was pro-
pofed about the middle of the 17th century by the Florentine
academy. This fluid was fpirit of wine, or alcohol, as it is
now generally named. The alcohol being coloured, was in-
clofed in a very fine cylindrical glaſs tube previouſly exhaufted
Thermometers.
443
3
of its air, having a hollow ball at the lower end, and hermeti-
cally fealed at the other end. The ball and tube are filled with
rectified fpirit of wine to a convenient height, when the wea-
ther is of a mean temperature, which may be done by inverting
the tube into a veffel of ſtagnant coloured fpirit, under a re-
ceiver of the air-pump, or in any other way. When the ther-
mometer is properly filled, the upper end is heated red-hot by a
lamp, and then hermetically ſealed, leaving the included air of
about of its natural denſity, to prevent the air which is in the
ſpirit from dividing it in its expanfion. To the tube is applied
a ſcale, divided from the middle into 100 equal parts, upwards
and downwards.
4-3

As ſpirit of wine is capable of a very confiderable degree of
rarefaction and condenfation by heat and cold, when the heat
of the atmoſphere increaſes the ſpirit dilates, and conſequently
rifes in the tube; and when the heat decreaſes the fpirit de-
fcends, and the degree or quantity of the motion is ſhown by a
fcale.
The fpirit of wine thermometer was not fubject to fome of
the inconveniences which attended the air-thermometer. In
particular, it was not affected by variations in the weight of
the atmoſphere: accordingly it foon came into general ufe
among philofophers. It was, at an early period, introduced
into Britain by Mr. Boyle. To this inftrument, as then uſed,
there are, however, many objections. The liquor was of dif
ferent degrees of ftrength; and therefore different tubes filled
with it, when expofed to the fame degree of heat, would not
correfpond. There was alfo another defect; the fcale which
was adjuſted to the thermometer did not commence at any fixed.
point. The higheſt term was adjuſted to the great fun
fun-fhine.
heats of Florence, which are too variable and undetermined;
and frequently the workman formed the ſcale according to his
own fancy. While the thermometer laboured under fuch dif-
advantages it could not be of general uſe.

-
91
To obtain fome fixed unalterable point by which a deter
mined fcale might be difcovered, to which all thermometers
might be accurately adjuſted, was the ſubject which next drew
the attention of philofophers. Mr. Boyle, who feems at an
early period to have ſtudied this fubject with much anxiety, pro-
pofed the freezing of the effential oil of annifeeds as a conve-
nient point for graduating thermometers; but this opinion he
foon laid afide. Dr. Halley next propofed that thermometers
fhould be graduated in a deep pit under ground, where the
temperature both in winter and fummer is pretty uniform; and
that the point to which the fpirit of wine fhould rife in fuch a
fubterraneous, place fhould be the point from which the Icale


BRITY S01
MOSDAO
EM DOO
444
MACHINES.
***
fhould commence. But this propofal was evidently attended
with fuch inconveniences that it was foon abandoned. He
made experiments on the boiling point of water, of mercury,
and of spirit of wine; and he ſeems rather to give a preference
to the fpirit of wine. He objected to the freezing of water as
a fixed point, becauſe he thought that it admitted confiderable
latitude.
It ſeems to have been reſerved to the genius of Newton to
determine this important point, on which the accuracy and va-
Jue of the thermometer depends. He chofe, as fixed, thofe
points at which water freezes and boils; the very points which
the experiments of fucceeding philofophers have determined to.
be the moſt fixed and convenient. Senfible of the diſadvan-
tages of fpirit of wine, he tried another liquor which was ho-
mogeneous enough, capable of a confiderable rarefaction, about-
15 times greater than ſpirit of wine. This was linfeed oil. It
has not been obferved to freeze even in very great colds, and it
bears a heat about four times that of water before it boils. With
thefe advantages it was made ufe of by Newton, who diſcovered
by it the comparative degree of heat for boiling water, melting
wax, boiling fpirit of wine, and melting tin; beyond which it
does not appear that this thermometer was applied. The mc-.
thod he uſed for adjuſting the ſcale of this oil-thermometer was
as follows: fuppofing the bulb, when immerged in thawing
fnow, to contain 10,000 parts, he found the oil expand by the
heat of the human body fo as to take up th more ſpace, or
10,256 fuch parts; and by the heat of water boiling ftrongly
10,725, and by the heat of melting tin 11,516. So that reckon-
ing the freezing point as a common limit between heat and
cold, he began his fcale there, marking it o, and the heat of the
human body he made 12°; and confequently, the degrees of
heat being proportional to the degrees of rarefaction, or
256:725:12:34, this number 34 will exprefs the heat of
boiling water; and by the fame rule, 72 that of melting tin.
This thermometer was conftructed in 1701.
To the application of oil as a meafure of heat and cold there
are infuperable objections. It is fo vifcid, that it adheres too
ftrongly to the fides of the tube. On this account it afcends and
defcends too lowly in cafe of a fudden heat or cold. In a fud-
den cold, fo great a proportion remains adhering to the fides of
the tube after the reft has fubfided, that the furface appears
lower than the correſponding temperature of the air requires.
An oil thermometer is therefore not a proper meaſure of heat
and cold.
D
All the thermometers hitherto propoſed were liable to many
inconveniences, and could not be confidered as exact ſtandards
Thermometers:
A
443
for pointing out the various degrees of temperature. This led
Reaumur to attempt a new one, an account of which was
publiſhed in the year 1730, in the Memoirs of the Academy of
Sciences. This thermometer was made with fpirit of wine.
He took a large ball and tube, the dimenfions and capacities of
which were known: he then graduated the tube, ſo that the
ſpace from one divifion to another might contain 1000th part
of the liquor; the liquor containing 1000 parts when it ſtood
at the freezing point. He adjufted the thermometer to the
freezing point by an artificial congelation of water: then put-
ting the ball of his thermometer and part of the tube into boil-
ing water, he obferved whether it rofe 80 divifions: if it ex-
ceeded thefe, he changed his liquor, and by adding water, low-
ered it, till upon trial it ſhould juſt riſe 80 divifions; or if the
liquor, being too low, fell short of 80 divifions, he raised it by
adding rectified fpirit to it. The liquor thus prepared fuited his
purpofe, and ferved for making a thermometer of any fize,
whofe fcale would agree with his ſtandard.
تھے
This thermometer was far from being perfect. As the bulbs
were three or four inches in diameter, the furrounding 'ice
would be melted before its temperature could be propagated to
the whole ſpirits in the bulb, and confequently the freezing
point would be marked higher than it ſhould be. Dr. Martine
accordingly found, that inftead of coinciding with the za
degree of Fahrenheit, it correfponded with the 34th, or a point
a little above it. Reaumur committed a miſtake alſo refpecting
the boiling point; for he thought that the fpirit of wine,
whether weak or ftrong, when immerged in boiling water,
received the fame degree of heat with the boiling water. Båt
it is well known that highly-rectified fpirit of wine casinot be
heated much beyond the 175th degree of Fahrenheit, while
boiling water raiſes the quickfilver 37 degrees higher. There
is another thermometer that goes by the name of Reaumur's,
which fhall be afterwards deſcribed.
+
At length a different fluid was propofed, by which thermo
meters could be made free from moſt of the defects hitherto
mentioned. This fluid was mercury, and feems firft to have
occurred to Dr. Halley in the laft century; but was not adopted
by him, on account of its having a ſmaller degree of expanfibility
than the other fluids. ufed at that time. Boerhaave fays that
the mercurial thermometer was first conftructed by Olaus
Roemer; but the honour of this invention is generally given to o
Fahrenheit of Amfterdam, who prefented an account of it to
blog but
the Royal Society of London in 1724.
Mercury is far fuperior to alcohol and oil, and is much more
manageable than air, . As far as the experiments! already
}
1
446
MACHINES.
**
made can determine, it is of all the fluids hitherto employed in
the conftruction of thermometers that which meaſures moft
exactly equal differences of heat by equal differences of its bulk:
its dilatations are in fact very nearly proportional to the
augmentations of heat applied to it. 2. Of all liquids it is the
moft eafily freed from air. 3. It is fitted to meaſure high degrees
of heat and cold. It fuftains a heat of 600° of Fahrenheit's
fcale, and does not congeal till it falls 39 or 40 degrees below o.
4. It is the moſt fenfible of any fluid to heat and cold, even air
not excepted. Count Rumford found that mercury was heated
from the freezing to the boiling point in 58 feconds, while
water took two minutes 13 feconds, and common air 10 minutes
and 17 feconds. 5. Mercury is a homogeneous fluid, and every
portion of it is equally dilated or contracted by equal variations
of heat. Any one thermometer made of pure mercury is, cæteris
paribus, poffeffed of the fame properties with every other ther-
mometer made of pure mercury. Its power of expanſion is
indeed about fix times less than that of ſpirit of wine, but it is
great enough to anſwer moft of the purpoſes for which a ther-
mometer is wanted.
The fixed points which are now univerfally chofen for ad-
jufting thermometers to a ſcale, and to one another, are the
boiling and freezing water points. The boiling water point, it
is well known, is not an invariable point, but varies fome degrees
according to the weight and temperature of the atmoſphere.
In an exhauſted receiver, water will boil with a heat of 98° or
100°; whereas in Papin's digefter it will acquire a heat of 412°.
Hence it appears that water will boil at a lower point, according
to its height in the atmoſphere, or to the weight of the column
of air which preffes upon it. In order to enfure uniformity
therefore in the conftruction of thermometers, it is now agreed
that the bulb of the tube be plunged in the water when it boils
violently, the barometer ftanding at 30 English inches (which
is its mean height round London), and the temperature of the
atmoſphere 55°. A thermometer made in this way, with its
boiling point at 212°, is called by Dr. Horley Bird's Fahrenheit,
becauſe Mr. Bird was the firſt perſon who attended to the ſtate
of the barometer in conftructing thermometers.
As artifts may be often obliged to adjuſt thermometers under
very different preffures of the atmoſphere, philofophers have
been at pains to diſcover a general rule which might be applied
on all occafions. M. de Luc, in his Recherches fur les Mod. de
l' Atmoſphere, has given, from a ſeries of experiments, an equation
for the allowance on account of this difference, in Paris meaſure,
which has been verified by Sir George Schuckburgh; alſo Dr.
Horſley, Dr. Mafkelyne, and Sir George Schuckburgh, have

Thermometers:
447
27
adapted the equation and rules to Engliſh meafures, and have
reduced the allowances into tables for the ufe of the artift. Dr.
Horfley's rule, deduced from De Luc's, is this:
99
8990000 log. z-92·864=h.
2−92.804=k.
where denotes the height of a thermometer plunged in boiling
water, above the point of melting ice, in degrees of Bird's
Fahrenheit, `and z the height of the barometer in 10ths of an
inch. From this rule he has computed the following table for
finding the heights to which a good Bird's Fahrenheit will rife
when plunged in boiling water, in all ſtates of the barometer,
from 27 to 31 English inches; which will ferve, among other
ufes, to direct inftrument-makers in making a true allowance
for the effect of the variation of the barometer, if they fhould
be obliged to finiſh a thermometer at a time when the barometer
is above or below 30 inches; though it is beft to fix the boiling
point when the barometer is at that height.
Equation of the Boiling Point.

+
Barometer.
Equation.
Difference.
310
+ 1'57
·0.78
30.5
+ 0.79.
0.79
30°0
0.00
0·80
29'5
9.80
0.82
29'0
1.62
0.83
28.5
2.45
0.85€
28.0
3:31
0'86
27.5
4.16
0·88
27.0
5'04
The numbers in the firft column of this table exprefs heights
of the quickfilver in the barometer in Engliſh inches and
decimal parts: the fecond column fhows the equation to be
applied, according to the fign prefixed, to 212° of Bird's
Fahrenheit, to find the true boiling point for every ſuch ſtate of
the barometer. The boiling point for all intermediate ftates of
the barometer may be had with fufficient accuracy, by taking
proportional parts, by means of the third column of differences
of the equation. See Phil. Tranf. lxiv. art. 30. alfo Dr.
Mafkelyne's Paper, vol. lxiv, art. 20.
Sir George Schuckburgh alſo has given the following general
table for the uſe of artiſts in conftructing the thermometer, both
according to his own obfervations and thofe of M. de Luc.


تھے
J
4
448
MACHINES.
#

Height of the Correct. of the
Correct.accord.
Difference.
Difference.
Barometer. boiling point.
to M. de Luc.
•
26'0
7'09
6.83
'91
26′5
6.18
5'93
'91
فاوا
•89
27.0
5.27
5°04
•88
*90
27'5
4'37
- 4°16
•89
.87
280
· 3'48
3°31
⚫89
.86
28.5
2.59
2.45
.87
.83
1.62
29'0
1.72
·87
•82
29'5
0.85
0.80
.85
'80
30'0
0'00
0'00
30.5
+0·85
•85
*79
.84
+0.79
·78
31.0
+ 1.69
+1.57
The Royal Society, fully appriſed of the importance of
adjuſting the fixed points of thermometers, appointed a com-
mittee of ſeven gentlemen to confider of the beft method for
this purpoſe; and their report is publiſhed in the Phil. Tranf.
vol. Ixvii. part ii. art. 37.
They obferved, that though the boiling point be placed fo
much higher on fome of the thermometers now made than on
others, yet this does not produce any confiderable error in the
obfervations of the weather, at leaft in this climate; for an
error of 14° in the pofition of the boiling point will make an
error only of half a degree in the pofition of 92°, and of not
more than a quarter of a degree in the point of 62°. It is only
in nice experiments, or in trying the heat of hot liquors, that
this error in the boiling point can be of much importance.
In adjuſting the freezing as well as the boiling point, the
quickfilver in the tube ought to be kept of the fame heat as that
in the ball. When the freezing point is placed at a con-
fiderable diſtance from the ball, the pounded ice ſhould be piled
to ſuch a height above the ball, that the error which can ariſe
from the quickſilver in the remaining part of the tube, not being
heated equally with that in the ball, ſhall be very ſmall, or the
obferved point must be corrected on that account according to
the following table:
Y
Thermometers: £
44.0

Heat of the Air. Correction.
42°
*00087
52
'00174
62
*00261
72
•00348
82
•00435.
The correction in this table is expreffed in 1000th parts of the
diſtance between the freezing point and the furface of the ice:
e. g. if the freezing point ftands feven inches above the furface
of the ice, and the heat of the room is 62, the point of 32° fhould
be placed 7x00261, or '018 of an inch lower than the ob-
ferved point. A diagonal fcale will facilitate this correction.
The committee obferve, that in trying the heat of liquors,
care fhould be taken that the quickfilver in the tube of the
thermometer be heated to the fame degree as that in the ball;
or if this cannot be done conveniently, the obſerved heat ſhould
be, corrected on that account; for the manner of doing which,
and a table calculated for this purpoſe, we muſt refer to their.
excellent report in the Phil. Tranf. vol. lxvii. part ii. art. 37
With regard to the choice of tubes, they ought to be exactly
cylindrical. But though the diameter fhould vary a little, it is
eafy to manage that matter in the manner propofed by the
Abbé Nollet, by making a ſmall portion of the quickfilver, e. g.
as much as fills up an inch or half an inch, flide backward and
forward in the tube; and thus to find the proportions of all its
inequalities, and from thence to adjuſt the divifions to a ſcale of
the most perfect equality. The capillary tubes are preferable
to others, becauſe they require fmaller bulbs, and they are alſo
more fenfible, and lefs brittle. The moſt convenient fize for
common experiments has the internal diameter about the 40th
or 50th of an inch, about 9 inches long, and made of thin glaſs,
that the rife and fall of the mercury may be better feen.
*
It is commonly obferved of thermometers, that upon equal
augmentations and diminutions of heat they feldom vary
equally, though they are filled with the fame liquor. To
account for this circumſtance it ſhould be recollected that the
variation of a thermometer is directly as the capacity of the
ball, and inverſely as the baſe of the ftem. Thus, if there be
two mercurial thermometers, for example, and we call the
capacites of the balls C and c, and the bafes of the ſtems B
and b, the variations will be as C to c directly, and as B to bin-
verſely, or as ğ to 5. Confequently the variations will not be
to.
VOL. II.
C
G G
J
430
MACHINES.
+
equal in thoſe thermometers unless and this cannot be
:
=
B
the caſe unleſs C: c :: B: b; therefore, to render the variations
in the two thermometers equal, the capacities of their balls
muſt be to each other as the baſes of their cylindrical ſtems.
The next thing to be confidered, is of what number of
degrees or divifions the fcale ought to confift, and from what
point it ought to commence. As the number of the divifions
of the ſcale is an arbitrary matter, the fcales which have been.
employed differ much from one another in this circumftance.
Fahrenheit has made 180 degrees between the freezing and
boiling water point. Amonton's made 73, and Sir Ifaac Newton
only 34. There is, however, one general maxim, which ought
to be obferved: That fuch an arithmetical number should be chofen
as can eafily be divided and fubdivided, and that the number of
divifions should be fo great that there shall feldom be occafion for
fractions. The number 80 chofen by Reaumur anfwers ex-
tremely well in this refpect, becauſe it can be divided by feveral
figures without leaving a remainder; but it is too fmall a
number: the confequence of which is, that the degrees are
placed at too great a distance from one another, and fractions
muft therefore be often employed. We think, therefore, that
160 would have been a more convenient number. Fahrenheit's
number 180 is large enough; but when divided its quotient foon
becomes an odd number.
As to the point at which the fcale ought to commence,.
various opinions have been entertained. If we knew the be-
ginning or loweſt degree of heat, all philofophers would agree
that the lowest point of the thermometer ought to be fixed
there; but we know neither the loweft nor the highest degrees.
of heat; we obferve only the intermediate parts. All that we
can do, then, is to begin it at fome invariable point, to which
thermometers made in different places may eafily be adjuſted.
If poffible, too, it ought to be a point at which a natural well-
known body receives fome remarkable change from the effects
of heat or cold. Fahrenheit began his fcale at the point at
which fnow and falt congeal. Kirwan propofes the freezing
point of mercury. Sir Ifaac Newton, Hales, and Reaumur,
adopted the freezing point of water. The objection to Fahren-
heit's lowest point is, that it commences at an artificial cold
never known in nature, and to which we cannot refer our
feelings, for it is what few can ever experience. There would
be feveral great advantages gained, we allow, by adopting the
freezing point of mercury. It is the lowest degree of cold to
which mercury can be applied as a meafure; and it would
render unneceſſary the uſe of the figns plus and minus, and the

Thermometers.
431
extenfion of the ſcale below o.
But we object to it, that it is
hot a point well known; for few, comparatively ſpeaking, who
ufe thermometers; can have an opportunity of feeing mercury
congealed. As to the other advantage to be gained by adopting
the freezing point of mercury, namely; the abolition of negative
numbers, we do not think it would counterbalance the advantage
to be enjoyed by afing a well-known point. Befides, it may
be aſked, Is there not a propriety in ufing negative numbers to
exprefs the degree of cold, which is a negative thing? Heat and
cold we can only judge of by our feelings: the point then at
which the fcale fhould commence, ought to be a point which
can form to us a ſtandard of heat and cold; a point familiar to
us from being one of the moſt remarkable that occurs in nature,
and therefore a point to which we can with moſt clearneſs and
precifion refer in our minds on all occafions. This is the
Freezing point of water choſen by Sir Ifaac Newton, which of
all the general changes produced in nature by cold is the moſt
remarkable. It is therefore the moft convenient point for the
thermometers to be uſed in the temperate and frigid zones, or
we may fay over the globe, for even in the hotteſt countries of
the torrid zone many of the mountains are perpetually covered
with fnow.
Having now explained the principles of the thermometer as
fully as appears neceffary in order to make it properly under-
ftood, we will here fubjoin an account of thoſe thermometers
which are at preſent in moſt general uſe. Theſe are Fahren-
heit's, De l'Ifle's, Reaumur's, and Celfius's. Fahrenheit's is
ufed in Britain, De l'Ifle's in Ruffia, Reaumur's in France, and
Celfius's in Sweden. They are all mercurial thermometers,
Fahrenheit's thermometer confifts of a flender cylindrical
tube and a ſmall longitudinal bulb. To the fide of the tube is
annexed a ſcale which Fahrenheit divided into 600 parts,
beginning with that of the ſevere cold which he had obferved in
Iceland in 1709, or that produced by furrounding the bulb of
the thermometer with a mixture of fnow or beaten ice and fal
ammoniac or ſea falt. This he apprehended to be the greateſt
degree of cold, and accordingly he marked it, as the beginning
of his fcale, with o; the point at which mercury begins to boil,
he conceived to fhew the greateſt degree of heat, and this he
made the limit of his ſcale. The diſtance between theſe two
points he divided into 600 equal parts or degrees; and by trials,
he found that the mercury ftood at 32 of thefe divifions, when
water juſt begins to freeze, or fnow or ice juft begins to thaw;
it was therefore called the degree of the freezing point. When
the tube was immerfed in boiling water, the mercury rofe to
212, which therefore is the boiling point, and is juft 180 degrees

GG 2
Y
452
MACHINES.
#
above the former or freezing point. But the prefent method of
måking the fcale of theſe thermometers, which is the fort in
most common uſe, is firſt to immerge the bulb of the thermo-
meter in ice or fnow juſt beginning to thaw, and mark the place
where the mercury ftands with a 32; then immerge it in boiling
water, and again mark the place where the mercury ftands in
the tube, with the num. 212, exceeding the former by 180;
dividing therefore the intermediate ſpace into 180 equal parts,
will give the fcale of the thermometer; which may afterwards
be continued upwards and downwards at pleaſure.
Other thermometers of a fimilar conftruction have been
accommodated to common uſe, having but a portion of the
above ſcale. They have been made of a ſmall ſize and portable
form, and adapted with appendages to particular purpoſes; and
the tube with its annexed ſcale has often been encloſed in
another thicker glaſs tube, alſo hermetically fealed, to preferve
the thermometer from injury. And all theſe are called Fahren-
heit's thermometers.
In 1733, M. De l'Iſle of Peterſburgh constructed a mercurial
thermometer on the principles of Reaumur's ſpirit thermometer.
In his thermometer, the whole bulk of quickfilver, when im-
merged in boiling water, is conceived to be divided into 100,000
parts; and from this one fixed point the various degrees of heat,
either above or below it, are marked in theſe parts on the tube
or ſcale, by the various expanſion or contraction of the quick-
filver, in all imaginable varieties of heat.-Dr. Martine appre-
hends it would have been better if De l'Iſle had made the integer.
100,000 parts, or fixed point, at freezing water, and from thence
computed the dilatations or condenfations of the quickfilver in
thofe parts; as all the common obfervations of the weather, &c.
would have been expreffed by numbers increafing as the heat
increaſed, inftead of decreafing, or counting the contrary way..
However, in practice it will not be very eafy to determine
exactly all the divifions from the alteration of the bulk of the
contained fluid. And befides, as glafs itſelf is dilated by heat,
though in a lefs proportion than quickfilver, it is only the excefs
of the dilatation of the contained fluid above that of the glaſs
that is obferved; and therefore if different kinds of glafs be
differently affected by a given degree of heat, this will make a
ſeeming difference in the dilatations of the quickfilver in the
thermometers conſtructed in the Newtonian method, either by
Reaumur's rule or De l'Ifle's. Accordingly it has been found,.
that the quickfilver in De l'Ifle's thermometers has stood at
different degrees of the fcale when immerged in thawing ſnow :
having ſtood in fome at 154, while in others it has been at 156,
or even 158°.
Thermometers.
453
The thermometer at preſent uſed in France is called Reau-
mur's; but it is very different from the one originally invented
by Reaumur in 1730, and deſcribed in the Memoirs of the
Academy of Sciences. The one invented by Reaumur was
filled with ſpirit of wine; and though its fcale was divided by
the author into 80 parts, of which o was the freezing point, and
80 the boiling water-point, yet in fact 80 was only the boiling
point of the ſpirit of wine that he employed, which, as Dr.
Martine computes, correfponded with 180. of Fahrenheit. But
the thermometer now in ufe in France is filled with mercury;
and the boiling water point, which is at 80, correfponds with
the 212th degree of Fahrenheit. The ſcale indeed commences
at the freezing point, as the old one did. The new thermo-
meter ought more properly to be called De Luc's thermometer,
for it was firſt made by De Luc; and is in fac as different
from Reaumur's as it is from Sir Ifaac Newton's. When De
Luc had fixed the ſcale, and finiſhed an account of it, he fhewed
the manuſcript to M. De la Condamine. Condamine adviſed
him to change the number 80; remarking, that ſuch was the
inattention of philosophers, that they would probably confound it
with Reaumur's.., De Luc's modefty, as well as a predilection
for the number 80, founded, as he thought, on philofophical
reaſons, made him decline following this advice. But he found
by experience that the prediction of Condamine was too well
founded.
*
The thermometer of Celfius, which is uſed in Sweden, has a
ſcale of 100 degrees from the freezing to the boiling water
point.
Theſe are the principal thermometers now uſed in Europe;
and the temperatures indicated by any of them may be reduced
into the correſponding degrees on any of the others by means of
the following fimple theorems; in which R fignifies the degrees
on the ſcale of Reaumur, F thoſe of Fahrenheit, and S thoſe of
the Swediſh thermometer.
1. To convert the degrees of Reaumur into thofe of Fah-
renheit; +32= F.
RX 9
4
2. To convert the degrees of Fahrenheit into thoſe of
'Reaumur ;
(F-32) × 4
9
=R.
3. To convert the Swediſh degrees into thoſe of Fahrenheit;
SX9
5
+32=F.
4. To convert Fahrenheit's into Swediſh;
(F-32) X5
=S.
9
454
MACHINES.
5. To convert Swedish degrees into thofe of Reaumur
$ x 4
5
~R.
.6. To convert Reaumur's degrees into Swedish; =S.
RX5
4
To fuch readers as are unacquainted with the algebraic ex-
preffion of arithmetical formulæ, it will be fufficient to exprefs
one or two of theſe in words to explain their ufe.-1. Multiply
the degree of Reaumur by 9, divide the product by 4, and to
the quotient add 32, the fum expreffes the degree on the ſcale
of Fahrenheit.-2. From the degree of Fahrenheit fubtract 32,
multiply the remainder by 4, and divide the product by 9, the
quotient is the degree according to the ſcale of Reaumur, &c.
As in meteorological obfervations it is neceffary to attend to
the greateſt riſe and fall of the thermometer, attempts have been
made to conftruct a thermometer which might regiſter the
greateft degree of heat, or greateſt degree of cold, which took
place during the abfence of the obferver.
In 1782 Mr. Six propofed a felf-regiſtering thermometer.
It is properly a fpirit-of-wine thermometer, though mercury is
alfo employed for fupporting an index. ab (fig. 10. pl. XXXVII.)
is a thin tube of glafs 16 inches long, and 5-16ths of an inch
caliber: c d e and fg b are ſmaller tubes, about 1-20th of an inch
caliber. Theſe three tubes are filled with highly rectified ſpirit
of wine, except the ſpace between d and g, which is filled with
mercury. As the fpirit of wine contracts or expands in the
middle tube, the mercury falls or rifes in the outfide tubes.
An index, made of thin wire with a knob, is placed on the
furface, within each of theſe tubes, fo light as to float upon it.
k is a ſmall glaſs tube 3-4ths of an inch long, hermetically
fealed at each end, and inclofing a piece of fteel wire nearly of
its own length. At each end l, m, of this fmall tube, a ſhort
tube of black glafs is fixed, of fuch a diameter as to paſs freely
up and down within either of the outfide tubes of the thermo-
meter ce or fb, From the upper end of the index is drawn a
fpring of glaſs to the fineness of a hair, and about 5-7ths of an
inch long; which being placed a little oblique, preffes lightly
against the inner furface of the tube, and prevents the index
from defcending when the mercury defcends. Theſe indexes
being inferted one into each of the outfide tubes, it is eaſy to
underſtand how they point out the greateſt heat or cold that has
happened in the obferver's abfence. When the ſpirit of wine
in the middle tube expands, it preffes down the mercury in the
tube hf, and confequently raiſes it in the tube ec; confequently
the index on the left hand tube is left behind and marks the
•
•
Thermometers.
455
greateſt cold, and the index in the right hand tube riſes and
marks the greateſt heat.
In 1790 a paper was prefented to the Royal Society of Edin-
burgh, defcribing two thermometers, newly invented, by Dr.
John Rutherford of Middle Balilish; the one for regiſtering the
higheft and the other for regiſtering the loweſt degree of heat
to which the thermometer has rifen or fallen during the abſence
of the obferver. An account of them may be found in the
third volume of the Tranfactions of the Society.
A new felf-regiſtering_thermometer has more lately been
invented by Mr. Keith of Ravelftone, which we confider as the
moft ingenious, fimple, and perfect, of any which has hitherto
appeared. Its fimplicity is fo great, that it requires only a very
fhort deſcription to make it intelligible. It is conftituted, firſt,
of a thin glafs tube about fourteen inches long, and 3-4ths of an
inch caliber, cloſe or hermetically fealed at top. To the lower
end, which is open, there is joined a crooked glaſs tube feven
inches long, and 4-1oths of an inch caliber, and open at its
top, which, of courſe, is level with the middle of the firſt tube.
The former tube is filled with the ſtrongeſt ſpirit of wine, and
the latter tube with mercury. This is properly a ſpirit-of-wine
thermometer, and the mercury is uſed merely to fupport a piece
of ivory or glaſs, to which is affixed a wire for raiſing one index
or depreffing another, according as the mercury rifes or falls.
There is a fmall conical piece of ivory or glafs, of ſuch a weight
as to float on the ſurface of the mercury. To the float is joined
a wire called the float-wire, which reaches upwards, where it
terminates in a knee bent at right angles. The float-wire, by
means of an eye at its extremity, moves eafily along a fmall
vertical harpsichord wire. There are two indexes made of thin
black-oiled filk, which flide upwards or downwards with a force
not more than two grains. The one placed above the knee
points out the greateſt riſe, and the one placed below it points
out the greateft fall, of the thermometer.
When the inftrument is to be prepared for an obfervation,
both indexes are to be brought clofe to the knee. It is evident,
that when the mercury rifes, the float and float-wire, which
can be moved with the fmalleft force, will be pushed upwards
till the mercury becomes stationary. As the knee of the float-
wire moves upwards it will carry along with it the upper index.
When the mercury again fubfides, it leaves the index at the
higheſt point to which it was raifed, for it will not defcend by
its own weight: as the mercury falls, the float-wire does the
fame; it therefore brings along with it the lower index, and
continues to deprefs it till it again becomes ftationary or aſcends
in the tube; in which cafe it leaves the lower index behind it as

456
MACHINES.
་
it had formerly left the upper. The fcale to which the indexes
point is placed parallel to the flender harpfichord wire. That
the ſcale and indexes may not be injured by the wind and rain,
a cylindrical glafs cover, cloſe at top, and made fo as exactly to
fit, is placed over it.
1
The ingenious inventor has another improvement, which, if
upon trial it be found to anſwer, will make this thermometer, as
perfect as can be defired, provided there do not ariſe ſome errors
from the variable preffure of the atmoſphere. He própofes to
adapt clock-work to this thermometer, in fuch a way as to
regiſter with the utmoſt preciſion the degrees of heat and cold
for every month, day, and minute, in the year. An account of
this latter improvement may be feen in Nicholfon's Journal,
vol. iii. 4to feries, or Edin. Tranfac. vol. iv.
The common contrivance for a ſelf-regiſtering thermometer,
now fold in moſt of the London fhops, confifts fimply of two
thermometers, one mercurial and the other of alcohol (fig. 4.
pl. XXXI.) having their ftems horizontal: the former has for
its index a ſmall bit of magnetical ſteel wire, and the latter a
minute thread of glaſs, having its two ends formed into ſmall
knobs by fuſion in the flame of a candle.
The magnetical bit of wire lies in the vacant fpace of the
mercurial thermometer, and is pushed forward by the mercury
whenever the temperature rifes, and puſhes that fluid againſt it :
but when the temperature falls and the fluid retires, this index
is left behind, and confequently fhews the maximum. The
other index, or bit of glaſs, lies in the tube of the ſpirit thermo-
meter immerſed in the alcohol, and when the ſpirit retires by
depreffion of temperature, the index is carried along with it in
apparent contact with its interior furface: but on increaſe of
temperature the fpirit goes forward and leaves the index, which
therefore fhews the minimum of temperature fince it was fet.
As theſe indexes merely lie in the tubes, their reſiſtance to
motion is altogether inconfiderable. The ſteel index is brought
to the mercury by applying a magnet on the outſide of the
tube, and the other is duly placed at the end of the column of
alcohol by inclining the whole inſtrument.
Mr. Nicholſon explains the operation of this inftrument thus:
"When the furface of the column of ſpirit is viewed by a
magnifier, it is ſeen to have the form of a concave hemiſphere,
which thews that the liquid is attracted by the glafs., The
glafs in that place is confequently attracted in the oppofite
direction by a force equal to that which is ſo employed in main-
taining that concave figure; and if it were at liberty to move, it
would be drawn back till the flat ſurface was reftored. Let us
fuppofe a ſmall ſtick or piece of glafs to be loofe within the
Differential Thermometer.
457
tube, and to protrude into the vacant ſpace beyond the ſurface
of the alcohol. The fluid will be attracted alſo by this glaſs,
and form a concave between its furface and that of the bore of
the tube. But the ſmall interior piece being quite at liberty to
move, will be drawn towards the fpirit fo long as the attractive
force poffeffes any activity; that is, fo long as any additional
fluid hangs round the glaſs; or, in other words, until the end
of the ftick of glaſs is even with the furface. Whence it is
feen that the ſmall piece of glaſs will be refifted, in any action
that may tend to protrude it beyond the furface of the fluid;
and if this refiftance be greater than the force required to flide
it along in the tube (as in fact it is), the piece muſt be flided
along as the alcohol contracts; fo as always to keep the piect
within the fluid. And this fact is accordingly obſerved to take
place." Nich. Jour. N. S. N°. 47.

▼
Mr. Leflie, well known for his ingenious "Experimental
Enquiry into the Nature and Propagation of Heat," has invented
a Differential Thermometer for the meaſurement of minute varia-
tions of temperature. It confifts of two tubes, each terminating
in a ſmall bulb of the fame dimenſions, joined by the blow-
pipe, and bent in the form of a U, a ſmall portion of dark
coloured liquor having previouſly been introduced into one of
the balls. After many trials, the fluid beft adapted to the
purpoſe was found to be a ſolution of carmine in concentrated
fulphuric acid. By managing the included air with the heat of
the hand, this red liquor is made to ftand at the required point
of the oppofite tube. This is the zero of a ſcale faftened to
that tube, and divided into equal parts above and below that
point. The inftrument is then fixed on a ftand. It is manifeft
that when the liquor is at reft, or points at zero, the column is
preffed in oppofite directions by two portions of air equal in
elafticity, and containing equal quantities of caloric. Whatever
heat, then, may be applied to the whole inftrument, provided
both bulbs receive it in the fame degree, the liquor muſt remain
at reſt. But if the one ball receives the flighteſt exceſs of
temperature, the air which it contains will be proportionally
expanded, and will puſh the liquid againſt the air in the other
bulb with a force, varying as the difference between the tem-
peratures of thoſe two portions of air: thus the equilibrium
will be deftroyed, and the fluid will rife in the oppofite tube.
The degrees of the ſcale through which it paffes will mark the
fucceffive augmentations in the temperature of the, ball, which
is expoſed to the greatest heat. So that this inftrument is a
balance of extreme delicacy for comparing the temperatures of
its two ſcales.
It is a fmall variation from this thermometer that conſtitutes
458
MACHINES.
Mr. Lellie's Photometer. Thoſe who wish to learn more of the
nature of this latter-mentioned inſtrument, may confult Mr.
Leflie's Treatife on Heat, Nicholfon's Journal, vol. iii. 4to. or
fome acute remarks in the Edinburgh Review, No. 13.
When thermometers are deviſed to meaſure very great de-
grees of heat, they are uſually called by another name. See
PYROMETER.
The thermometer and barometer together are very uſeful in
determining the altitudes of mountains, &c. according to the
rules delivered in our firft volume, book v. For this purpoſe
they are fixed in fuch a frame as to be conveniently portable.
(See BAROMETER.) Other portable inftruments by Mr. M'Guire
and M. Humbolt, which we omitted mentioning in that article,
are deſcribed, the former in the Tranfactions of the Royal Irish
Academy for 1787, the latter in Journal de Phyfique, an 7.
or Tilloch's Philofophical Magazine, No. 15.
THRASHING MACHINES, in a country like ours, where
agriculture has been fo fuccefsfully cultivated, can hardly be
denied to be of great utility: for which reaſon, although theſe
machines are not yet brought to fuch a ſtate of perfection as is
to be wifhed, we conceive it will not be improper to give an
account of ſome of the moſt ingenious.
The first thrashing machine which has come to our know-
ledge is that manufactured in 1732 by Mr. Michael Menzies of
Edinburgh it confifted, as far as we have been able to aſcer-
tain, of numerous inftruments, refembling flails, which were
attached to a moveable beam, and inclined to the latter in an
angle of ten degrees. On each fide of fuch beam were placed
floors, or benches, on which the fheaves were fpread; the
flails being moved forward and backward on theſe benches by a
crank that was fixed to the end of an axle, revolving about
thirty times in a minute.
The fecond machine was inventedin 1753 by Mr. Michael
Sterling of Dumblaine, Perthfhire: his firft models were very
imperfect; but, after repeated alterations, he completed it in
its prefent form, in 1758; and it now confifts of an outer, or
water-wheel, having an inner wheel, furniſhed with forty-eight
cogs, and turning on the fame axle. With this cog-wheel is
connected a vertical trundle, or pinion, with feven notches;
and the axle of which paffes through a floor above the wheel;
its upper pivot being fecured in a beam fix inches above the
floor. At the height of three feet three inches from the latter,
two ftraight pieces of fquared wood (each being four feet in
length) are inferted through the axle of the pinion, at right
angles, ſo as to form four arms that are moved round horizon-
tally. To the end of thefe arms are affixed four iron plates,
Thrafbing Mashines.
439
each twenty inches in length, and eight inches in breadth at the
extremity neareſt to the arms, but tapering to a point at the op-
pofite ends.
The horizontal fly, here defcribed, conftitutes four thrashers,
and is incloſed in a cylindrical wooden box, that is three and a
half feet high, and eight feet in diameter: on the top of this
box is an opening eight inches in width, extending a foot and
a half from the circumference to its centre, and through which
the fheaves of corn defcend; the latter being previoufly opened,
and laid feparately on a board provided with two ledges, gra-
dually declining towards fuch port, or opening. Within the
cylindrical box there is an inclined plane, along which the
ſtraw and grain fall into a wire-riddle two feet ſquate, that is
placed immediately beneath a hole of a fimilar fize: the riddle
is jerked at each revolution of the fpindle, by means of a knob
fixed on its fide; and is thruſt backward by a fmall ſpring that
preſſes it in a contrary direction. Thus, the fhort straw, to-
gether with the grain and chaff, that pafs through the wide
riddle, fall inſtantly into an oblong ſtraight riddle, one end of
which is raifed, and the other depreffed, by a fimilar con-
trivance. And, as the riddle laft-mentioned is not provided
with a ledge at the lower end, the long chaff, which cannot
pafs through, drops thence to the ground, while the gram and
fmaller chaff defcend into a pair of common barn-fanners, and
are thus feparated with great exactneſs. Theſe fanners are
moved by means of a rope, that runs in a fhallow groove cut on
the circumference of the cog-wheel. In the mean tinre, the
ftraw collected in the lower part of the box over the wide
riddle, and through an opening two feet and a half ſquare, is
drawn down to the ground with a rake, by the perfons em
ployed to form it into truffes.
In 1772 another thrashing-machine was invented by Mr.
Alderton of Alnwick, and Mr. Smart of Wark, Northumber-
land. The operation was performed by rubbing: the theaves
being carried round between an indented drum fix feet in dia
meter, and numerous indented rollers, that were arranged
round; and attached to, this drum by means of ſprings; fo
that during the revolution of the machinery, the corn was fe-
parated from the ftraw by conftant friction against the flutings
of the drum. But this contrivance was foon difufed; as many
grains were thus cruſhed between the rollers.
The next invention is that of Mr. Andrew Meikle, in 1785,
who obtained a patent, which is now expired: we have there-
fore given a plate (XXXIV), reprefenting in fig. 1. the plan.
of elevation in fig. 2, the ground plan; and in fig. 3. the
1
460
MACHINES.
effential parts of the machinery, fo as to convey a tolerably ac-
curate idea of his principle.
A (fig. 1. and 2.) is a large horizontal fpur-wheel, which
has 276 cogs, and moves the pinion B, having fourteen teeth.
The latter imparts motion to a crown-wheel, C, that is pro-
vided with eighty-four cogs, and moves a fecond pinion, D,
which is furniſhed with fixteen teeth. This pinion D, turns
the drum H I K L (fig. 1. 2. and 3.), being a hollow cylin-
der, three feet and a half in diameter, and placed horizontally:
on its outfide are fixed, by means of fcrew-bolts, four fcutchers,
or pieces of wood, one fide of which is faced with a thin iron
plate; and which are difpofed at an equal diſtance from each
other, and at right angles to the axis of the drum.
P (fig. 2. and 3.) is an inclined board, on which the
fheaves are ſpread, and whence they are introduced between
two fluted cast-iron rollers, G, G (fig. 3.), that are three and
a half inches in diameter, and revolve about thirty-five times in
one minute. Thefe rollers being only three-fourths of an inch
from the fcutchers or leaves of the drum HIKL (fig. 1.
and 2.), ſerve to keep the fheaves ſteady, while the fcutchers
a, b, c, d (fig. 2. and 3.), move with confiderable velocity, and
thus feparate the grain from the ftraw, while both are thrown
on the concave rack M (fig. 2.), which lies horizontally with
flender parallel ribs; fo that the corn may paſs through them
into the fubjacent hopper N (fig. 1. and 3.).
O (fig. 3.) is a riddle or harp, through which the corn drops
into a pair of fanners, P (fig. 1. and 3.), and from theſe it is
generally obtained in a ftate fit for the market.
Q R´T S is a rake, conſiſting of four leaves, or thin
pieces of wood; at the extremity of each is placed a row of
teeth, e, f, g, h, that are five inches long. This rake moves
in the concave rack M, (fig. 2.), in a circular direction; while
the teeth catch the ſtraw that had been thrown by the fcutchers
a, b, c, d, into the rack, and remove it to the contiguous
place, V.
W (fig. 1.) reprefents the horſe's courſe, which is twenty-
feven feet in diameter.
X (fig. 1. and 2.) is the pillar for ſupporting the beams on
which the axle of the fpur-wheel is fixed.
Y, Y, Y (fig. 1.), and Y, Y (fig. 2.), fhew the ſpindles, the
defign of which is to move the two fluted rollers, the rake, and
the fanners.
To the deſcription now given we have only to add, that the
drum has a covering of wood at a ſmall diſtance above it, for the
purpoſe of keeping the fheaves cloſe to the fcutchers.
Thrashing Machines.
461
The number of perfons requifite for attending the mill when
working is fix: one perfon drives the horſes.; a fecond hands
the fheaves to a third who unites them, while a fourth fpreads
them on the inclined boards, and preffes them gently between
the rollers; a fifth perſon is neceſſary to riddle the corn as it
falls from the fanners, and a fixth to remove the ſtraw.
This machine can be moved equally well by water, wind, or
horfes. Mr. Meikle has made fuch improvements on the wind-
mill as to render it much more manageable and convenient than
formerly; and we are informed many wind-mills are now erect-
ing in different parts of the country. As to the comparative ex-
pence of theſe different machines, the erection of the horſe-ma-
chine is leaft; but then the expence of employing horfes muft
be taken into confideration. One of this kind may be erected
for 70l. A water-mill will coſt ic/ more, on account of the
expence of the water-wheel. A wind-mill will coſt from 2001.
to 300l. fterling.
In thrashing machines, however, cheapnefs fhould not be
the only confideration. It often happens in machinery, that
things apparently cheap are ultimately very dear. Thrashing of
corn requires a ſtrong power, which neither weak men nor
flight machines are competent to. On this account, ftrong and
durable machines are to be recommended as cheapeſt in the
end; performing more work, in a better manner, and not need-
ing frequent repairs.
Some other well-conftructed thrashing-machines are defcribed
in Gray's Experienced Mill-wright, and in the Repertory of
Arts and Manufactures.
+
With respect to the quantity of corn which a machine will
thraſh in a given time, it is not eaſy to give any preciſe in-
formation: the moſt important we have yet met with is given
by Mr. Fenwick, who found from numerous experiments that
a power capable of raiſing a weight of 1000 pounds with a
uniform velocity of fifteen feet per minute, will thrash two bolls-
(eight bushels) of wheat in an hour; and that a power fufficient.
to raiſe the fame weight with a velocity of twenty-two feet per
minute, will thrash three bolls of the fame grain in an hour.
From theſe facts, this gentleman has computed the following
table, which is applicable to machines that are driven either
by water or horſes.
462
MACHINES:
TABLE of the power of thrashing-machines.
Gallons of Gallons of [Gallons of
water per water per water per

minute, ale-minute, ale-minute, ale-
measure, micastre, measure,
discharged discharged discharged
fon an over-on an over-on an over-
shot wheel shot wheel
10. feet in
Number
of horses
working
shot wheel 9 hours.
20 feet in
diameter.
Bolts of Bolls thrash-
wheat ed in 94
thrashed
in an
hour.
hours actual
working, or
in a day
diameter.
15 feet in
diameter.
230
160
130
I
390
296
205
528
380
272
660
470
340
790
565
400
970
680
500
2357
1234 esto
19
28/12/
47-
9
85 32/25
to
95
I
2
3
4
5
6
The firft four columns of the preceding table contain different
quantities of impelling power, and the laft two exhibit the
number of bolts of wheat in Winehefter meaſure, which fuch
powers are capable of thrashing in an hour, or in a day. Six
horfes, for example, are capable of thrashing ten bolls of wheat
in an hour, or ninety-five in the ſpace of nine hours and a half,
or a working day; and 680 gallons of water diſcharged into
the buckets of an overfhot water-wheel during a minute, will
thrash the fame quantity of grain.
TIDE-MILLS, as their name imports, are fuch as employ
for their firſt mover the flowing and ebbing tide, either in the
fea or a river.
Mills of this kind have not often, we believe, been erected
in England, though feveral of our rivers, and particularly the
Thames, the Humber, and the Severn, in which the tide rifes
to a great height, furnish a very powerful mover to drive any
kind of machinery, and would allow of tide-mills being very
advantageouſly constructed upon their banks. The erection of
fuch mills is not to be recommended univerfally, as they are
attended with a confiderable original expence; befides that
fome of their parts will require frequent repairs: but in
fome places where coals are very dear they may, on the whole,
be found leſs expenſive than ſteam-engines to perform the fame
work, and may on that account be preferred even to them.
We have not been able to aſcertain who was the firft con-
triver of a tide-mill in this country, nor at what time one was
firft erected. The French have not been fo negligent refpecting
the origin of this important invention as to let it drop into ob-
Tide-mills.
463
fcurity; but have taken care to inform us that fuch mills were
uſed in France early in the last century. Belidor mentions the
name of the inventor, at the fame time that he ſtates ſomę pe-
culiar advantages of this fpecies of machine.
"L'on en at-
tribue," fays he, "la première invention à un nomme Perfe,
maître charpentier de Dunkerque, qui mérite affurément beau-
coup d'éloge, n'y ayant point de gloire plus digne d'un bon
citoyen, que celle de produire, quelqu' invention utile à la fo-
cieté. En effet, combien n'y a-t'il point de chofes effentielles
à la vie, dont on ne connoît le prix que quand on en eft privé:
les moulins en général font dans ce cas-là. On doit fçavoir bon
gré à ceux qui nous ont mis en état d'en conftruire par-tout:
par exemple à Calais, comme il n'y ferpente point de rivieres,
on n'y a point fait juſqu'ici de moulins à eau, & ceux qui vont
par le vent chômant un partie de l'année, il y a des tems où cette
ville fe trouve fans farine, & j'ai vu la garnifon en 1730, obligée
de faire venir du pain de Saint-Omer, au lieu qu'en ſe ſervant
du flux & reflux de la mer, on pourroit conftruire autant de
moulins à eau que l'on voudroit: il y a d'autres villes dans le
voifinage de la mer fujettes au même inconvénient, parce qu'
apparemment elles ignorent le moyen d'y remédier."
Mills to be worked by the rifing and falling of the tide admit
of great variety in the effential parts of their conftruction; but
this 'variety may perhaps be reduced to four general heads, ac-
cording to the manner of action of the water-wheel.
1. The
water-wheel may turn one way when the tide rifes, and the
contrary when it falls. 2. The water-wheel may be made to turn
always in one direction. 3. The water-wheel may fall and rife
as the tide ebbs and flows. 4. The axle of the water-wheel
may be fo fixed as that it fhall neither rife nor fall, though the
Fotatory motion ſhall be given to the wheel, while at one time
it is only partly, at another completely, immerſed in the fluid.
In the mills we have examined, the firſt and third of thefe di-
viſions have been ufually exemplified in one machine; and the
fecond and fourth may readily be united in another: we fhall,
therefore, fpeak of them under two divifions only.
I. When the water-wheel rifes and falls, and turns one way
with the rifing tide, and the contrary when it ebbs. In order to
explain the nature of this fpecies of tide-mill, we fhalf defcribe
one which has lately been erected on the right bank of the
Thames at Eaft-Greenwich, under the direction of Mr. John
Lloyd, an ingenious engineer of Brewer's-green, Weftminſter.
'This mill is intended to grind corn, and works 8 pairs of ftones.
The fide of the mill-houſe parallel to the courfe of the river
arcaſures 40 feet within; and as the whole of this may be
opened to the river by fluice-gates, which are carried down to
<
464.
MACHINES.
驾
​น
the low water-mark in the river, there is a forty-feet waterway
to the mill: through this waterway the water paffes during the
rifing tide into a large reſervoir, which occupies about 4 acres
of land and beyond this refervoir is a ſmaller one in which
water is kept, for the purpoſe of being let out occafionally at
low water to cleanſe the whole works from mud and ſediment,
which would otherwife in time clog the machinery. The
water-wheel has its axle in a pofition parallel to the fide of the
river, that is, parallel to the fluice-gates which admit water
from the river: the length of this wheel is 26 feet, its diameter
11. feet, and its number of float-boards 32. Theſe boards do
not each rum on in one plane from one end of the wheel to the
other, but the whole length of the wheel is divided into four
equal portions, and the parts of the float-boards belonging to
each of thefe portions fall: gradually one lower than another,
each by one fourth of the diſtance from one board to another,
meaſuring on the circumference of the wheel. This contriv
ance, which will be better understood by referring to fig. 6.
pl. XXXV. (fhewing a part of the wheel), is intended to equal-
ize the action of the water upon the wheel, and prevent its
moving by jerks. The wheel, with its incumbent apparatus,
weighs about 20 tons, the whole of which is raiſed by the im-
pulfe of the flowing tide when admitted through the fluice-
gates. It is placed in the middle of the water-way, leaving a
paffage on each ſide of about 6 feet for the water to flow into
the refervoir, befides that which in its motion turns the wheel
round. Soon after the tide has rifen to the higheſt (which at
this mill is often 20 feet above the low water-mark), the water
is permitted to run back again from the reſervoir into the river,
and by this means it gives a rotatory motion to the water-wheel,
in a contrary direction to that with which it moved when im- .
pelled by the rifing tide: the contrivance by which the wheel is
raiſed and depreffed, and that by which the whole interior mo-
tions of the mill are, preferved in the fame direction, although
that in which the water-wheel moves is changed, are fo truly
ingenious as to deferve a diftin&t defcription, illuftrated by dia-
grams: Let, then, AB (fig. 5. pl. XXXV.) be a fection of the
water wheel, 1, 2, 3, 4, 5, &c. its floats, CD the first cog-.
wheet upon the fame axis as the water-wheel: the vertical ſhaft
Picarries the two equal wallower-wheels E and F, which are
fo fituated on the fhaft that one or other of them may, as oc-
cafion requires; be brought to be driven by the firft wheel CD;
and thus (by what has been faid under the article REVERSING
of motions the firft. wheel acting upon Fand E at points dia-
metrically oppofite, will, although its own motion is reverſed,
communicate the rotatory motion to the vertical fhaft ways in
$
•
}
Tide-mills.
465
gear,
the fame direction. In the figure the wheel E is fhewn in
while F is clear of the cog-wheel CD; and at the turn of the
tide the wheel F is let into gear, and E is thrown out: this is
effected by the lever G, whofe fulcrum is at H, the other end
being fufpended by the rack K, which has hold of the pinion
L on the fame axle as the wheel M; into this wheel plays the
pinion N, the winch O on the other end of whoſe axle fur
niſhes ſufficient advantage to enable a man to elevate or de-
prefs the wallower-wheels, as required. The centre of the
lever may be shewn more clearly by fig. 6. pl. XXXV. where
ab is a fection of the lever, which is compofed of two ſtrong
bars of iron, as ab: there are two fteel ftuds or pins which
work in the grooves of the grooved wheel I, this wheel being
fixed on the four rods furrounding the ſhaft, of which three
only can be ſhewn in the figures, as c, d, e ; the ends of theſe
are ſcrewed fast by bolts to the fockets of the wallower-wheels,
and they are nicely fitted on the vertical ſhaft ſo as to flide with
little friction: thus the wallowers may be raiſed or lowered
upon the upright shaft, while the gudgeon on which it turns
retains the fame pofition. When the top wallower is in gear,
it reſts on a ſhoulder that prevents it from going too far down;
and when the bottom one is in gear there is a bolt that goes
through the top wheel ſocket and ſhaft, which takes the weight
from the lever G, at the fame time that it prevents much fric-
tion on the ftuds or pins of the lever which works in the
grooved wheel I.
When the tide is flowing after the mill has ftopped a fuffi-
cient time to gain a moderate head of water, the fluid is fuffered
to enter and fall upon the wheel at the fluice Q (fig. 5.), and
the tail water to run out at the fluice R. The hydrostatic
preffure of the head of water acting againſt the bottom of the
wheel-frame S, and at the fame time acting between the fold-
ing-gates TW, which are thus converted into very large hydro-
ſtatic bellows, buoys up the wheel and frame (though weigh-
ing, as before obferved, nearly 20 tons), and makes them gra-
dually to rife higher and higher, fo that the wheel is never, as
the workmen express it, drowned in the flowing water; nor
can the water efcape under the wheel-frame, being prevented
by the folding-gates, which pafs from one end to the other of
the wheel. In this way the wheel and frame are buoyed up by
a head of 4 feet; and the mill works with a head of 5 or 54
feet.
When the tide is ebbing, and the water from the reſervoir
running back again into the river, it might perhaps be expected
that in confequence of the gradual fubfiding of the water the
water-wheel thould as gradually lower: but left any of the


VOL. II.
HN
466:
MACHINES.
!
+
water confined between the wheel-frame at S and the folding-
gates TW fhould prevent this, there are ſtrong rackworks of
caft-iron, by which the wheel-frame can be either fufpended at
any altitude or gradually let down fo as to give the water re-
turning from the refervoir an advantageous head upon the
wheel: then the fluice R is fhut, and V opened as well as X,
the water entering at X to act upon the wheel, and flowing out
at R. The upper furface of the wheel-frame is quadrangular,
and at each angle is a ſtrong caft-irón bar, which flides up and
down in a proper groove, that admits of the vertical motion,
but prevents all fuch lateral deviation as might be occafioned by
the impulfion of the ftream.
At each end of the water-wheel there is a vertical fhaft, with
wallowers and a firft cog-wheel, as F, E, and CD; and each of
theſe vertical fhafts turns a large horizontal wheel at a ſuitable
diſtance above the wallowers, while each horizontal wheel
drives 4 equal pinions placed at equal or quadrantal diſtances
on its periphery, each pinion having a vertical fpindle, on the
upper part of which the upper millstone of its refpective pair is
fixed. Other wheels driven by one or other of thefe pinions.
giving motion to the bolting and dreffing machines, and differ-
ent fubordinate parts of the mill.
Although the vertical ſhaft at each end of the water-wheel
rifes and falls with that wheel, yet the large horizontal wheel
turning with fuch fhaft does not likewife rife and fall, but re-
mains always in the fame horizontal plane, and in contact
with the four pinions it drives. The contrivance for this pur-
pofe is very fimple, but very efficacious: each great horizontal
wheel has a nave, which runs upon friction-rollers, and has a
fquare aperture pafling through it vertically, juft large enough
to allow the fhaft P to flide freely up and down in it, but not
to turn round without communicating its rotatory motion to
the wheel: thus the weight of the wheel cauſes it to prefs
upon the friction-rollers, and retain the fame horizontal planes,
and the action of the angles of the vertical fhaft upon the cor-
refponding parts of the fquare orifice in the nave caufes it to
partake of the rotatory motion, fuch motion being always in
one direction in confequence of the contrivance by which one
or other of the wallowers EF is brought into contact with the
oppofite points of the first cog-wheel CD.
Several of the fubordinate parts of this mill are admirably
conftructed; but we can only notice here the means by which
The direction of the motion in the dreffing and bolting machines
may be varied at pleaſure. On a vertical thaft are fixed, at the
tiffance of about 15 or 18 inches, two equal cog-wheels, and an-
other toothed wheelattached to a horizontal axle is made fo as to
*
Tide-mills. -
467
be moveable up and down by a ſcrew, and thus brought into
contact with either the upper or lower of the two cog-wheels
on the vertical ſhaft; thus, it is manifeft the motion is reverfed
with great facility by changing the poſition of the horizontal
axle fo that the wheel upon it may be driven by the two cog
wheels alternately. A wheel and pinion working at the other
end of the horizontal axle will communicate the motion to the
dreffing-machines..
16
t
TO ROUTLoraind
MR 29ES TA
་་
Mr. W. Dryden, Mr. Lloyd's foreman, employed in the erec-
tion of this mill, fuggefts that a nearly fimilar mode may be
advantageouſly adopted in working the dreffing-machines ini
wind-mills: three wheels, all of different diameters, may be
employed, two of them, as A and C, turning upon a vertical
fhaft, and the third, B, upon an inclined one. In fig. 10.
pl. XXXV. the wheels A and B are fhewn in gear, while C is
out; and if A be ftruck out by fome fuch contrivance as is
adopted with regard to the firft cog-wheel and wallowers (fig.
5.6.), C would come in contact with B, while A would be
free, and fo communicate a motion to B the reverfe way. By
this contrivance it, would be eafy, when the winds are strong
and give a rapid motion to the vertical axle, to bring C to drive
B the wheel on the axle of the dreffing-machines, and on the
contrary, when the wind was flack, and the confequent motion
of the machinery flow, let C be thrown out of gear and the
wheel B driven by the larger wheel A, as fhewn in the figure.

{
We ſhould have been glad to fee adopted in this well-con-
ſtructed mill a contrivance recommended and purſued by the
American millwrights, for raifing the ground corn to the cool-
ing-boxes or beaches from which it is to be conveyed into the
bolting-machine. In this mill, as in all we have feen, the corn
is put into bags at the troughs below the mill-ftones, and thence
raifed to the top of the mill-houfe by a rope folding upon bar-
rels turned by fome of the interior machinery of the mill. In
the American method a large fcrew is placed horizontally in
the trough which receives the flour from the millstones. The
thread or fpiral line of the fcrew is compofed of pieces of wood
about two inches broad and three long, fixed into a wooden cy-
linder feven or eight feet in length, which forms the axis of the
fcrew, When the fcrew is turned round this axis, it forces
the meal from one end of the trough to the other, where it
falls into another trough, from which it is raifed to the top of
the mill-houfe by means of elevators, a piece of machinery
fimilar to the chain-pump. Theſe elevators confift of a chain
of buckets or concave veffels like large teacups, fixed at proper
diftances upon a leathern band, which goes round two wheels,
one of which is placed at the top of the mill-boule, and, the
MH 2
1.
0.1%
10.

SOGEIN
465
MACHINES.
}
other at the bottom, in the meal-trough. When the wheels
are put in motion, the band revolves, and the buckets, dipping
into the meal-trough, convey the flour to the upper story, where
they diſcharge their contents. The band of buckets is inclofed
in two fquare boxes, in order to keep them clean, and preferve
them from injury.
But it is time to direct our attention,
2. To tide-mills in which the axle of the water-wheel neither
rifes nor falls, and in which that wheel is made always to revolve
in the fame direction.
A water-wheel of this kind muft manifeftly at the time of
high-tide be almoft if not entirely immerfed in the fluid: and
to conſtruct a wheel to work under fuch circumftances is, ob-
viouſly, a matter which requires no fmall ſkill and ingenuity.
The firft perfons who deviſed a wheel which might be turn-
ed by the tide, when completely immerfed in it, were Meffrs,
Goffet and de la Deuille. Their wheel is defcribed by Belidor
in nearly the following terms: Suppofe GH (fig. 12. pl.
XXXV.) to denote the furface of the water at high-tide, the
line LM the furface at low water, and that the current follows
the direction of the arrow N; the problem is to construct the
wheel fuch that it may always turn upon its axis IK. The
figure juft referred to is a profile of an affemblage of carpentry
which must be repeated feveral times along the arbor, accord-
ing to the length which it is propoſed to give to the float-boards;
and the planks or plates which compofe thefe floats must be
hang to the other parts of the frame by as many joints as are
neceffary to enable them to fuftain the impulfe of the water
without bending. The fole peculiarity of this wheel confifts
in hanging upon the tranfverfe beams in the frame-work, by
hinges, the planks which are to compofe the float-boards; fo
that they may prefent themſelves in face, as D,D,D, when they
are at the bottom of the wheel, to receive the full ftroke of the
ftream; and, on the contrary, they prefent only their edges, as
at A, A, A, when they are brought towards the fummit of the
wheel: hence, the water having a far greater effect upon the
lower than the upper parts of the wheel, compels it to revolve
in the order of the letters; inftead of which, if the floatboards
were fixed, as in the ufual way, the impulfe of the fluid upon
the wheel would be nearly the fame in all its parts, and it
would remain immoveable.
We fee, at once, that the boards D, D, D, having moved to-
wards M, then begin to float, as at E, E, E, and more ftill at
EF, F, but that it is not till they arrive at A,A,A, that they
attain the horizontal poſition; after that, having arrived at
B, B, B, they begin to drop towards the beams to which they
Tide-mills.
469
are hooked, and as foon as they have paffed the level of the
axle IK, the ftream commences its full action upon them,
which it attains completely between C, C, C, and E, E, E, and
this whether the furface of the water be at GH or at EM!
for even in the latter cafe it is manifeft that the float-boards are
entirely immerſed when in the vertical pofition PQ. · Belidor
fays he was prefent at the firſt trial of fuch a wheel at Paris,
and that it was attended with all the fuccefs that could be
defired.
A water-wheel has been lately invented by Mr. Dryden,::
which will work when nearly immerfed in the water of a flow-
ing tide. Fig. 4. pl. XXXV. is an elevation of this wheel,
its upper parts being fuppofed to ftand a foot or two higher
than the tide ever rifes: the axis of this wheel remains always
in one place, and the wheel will work at high water when the
head is at B and the tail-water at the dotted line A; it will
alſo perform nearly the fame work when the head is at C, and
the tail-water level with the bottom of the wheel. The floats
are all fet at one and the fame angle with the reſpective radit
of the wheel, as may be ſeen in the figure, and are made fo as
to have an opening of at leaſt an inch between each float and
the drum-boarding of the wheel. This opening is intended
to prevent the wheel from being impeded by the tail-water
for as the bucket riſes out of the water there can be no vacuum”
formed in it, there being a full fupply of air, in confequence of
which the water leaves the wheel deliberately. The cafe is
different with regard to wheels made in the common way for
if fuch are open wheels, the floats are made in fuch a manner
as to throw the tail-water if they are immerſed any depth in
it; or, if they are close, the wheel wants proper vent for the
air to prevent the formation of a vacuum in the rifing bucket,
or what is called by the miller "fucking up the tail-water."
At D is planking made circular to fit the wheel pretty cloſe for
rather more than the ſpace of two floats, fo as to confine the
water nearly cloſe to the wheel. E, F, G, H, are fuites which
are all connected together by the iron bar I, and lifted with the
alliſtance of a wheel, two pinions, and a winch, the fifft pinion
working into the rack K: thefe fluices are merely for ftopping
the wheel when occafion requires, although one might be fuf
ficient to fupply the wheel. The rings of this wheel may be
made either of caft-iron or of wood; the floats may be on
plates riveted together. The flanches on the arms of the wheel
exhibited in the ketch are intended to facilitate the fixing of
the first cog-wheel: the ring of the wheel may be fixed to the
Hanches at the extremity of the arms, and the large flarel
made faft to the axle will receive the middle part of the wheel!
{

1
470
MACHINES.
Fig. 4. pl. XXXVII. is a plan of the houfe in which either
of the two latter wheels may be fixed, fhowing in what manner
the water may be conveyed always on one fide of the wheel
by the affiftance of the four gates A,B,C, and D. When the mill
is working from the river, A and B are open, the arrows point
out the way the water runs from the river to the bafin; and the
dotted lines on the contrary the courſe from the baſin to the
river, when A, B, are fhut, and C, D, opened. Thefe gates
are made to turn on an axle, which is about fix inches from the
middle of the gate; and on the top of the axle is a half-wheel :
by fome crane-work connected to it, the gate can be opened or
fhut at pleaſure: when a head of water preffes againſt the
gates, they will open great part of the way of themſelves, by
only letting the catches that keep them fhut be lifted out of
their place. X, Y, are two knees of caft-iron, to fupport the
poſts that the gates are fixed to. The walls of the building
are repreſented at a, b, c, and d.
The reader will now be able to form an eſtimate of the com-
parative value and ingenuity of the two kinds of tide-mills
here defcribed. The fimplicity of conſtruction of the wheels of
Goffet, de la Deuille, and Dryden, recommend them ſtrongly;
but we entertain fome doubts of their being completely fuccefs-
ful in practice: had the curious wheel with the folding gates, &c.
figs. 5. 6. pl. XXXV. been placed with its axle perpendicular
inſtead of parallel to the courſe of the river, the water might
then have always been admitted to act upon the ſame fide of it,
and the hydrostatic preffure would have operated as completely
in lowering it continually during the time of ebb, as in raifing it
continually during the rifing of the tide : thus, as appears to us,
would the labour of a man be faved, who according to the
prefent conftruction must attend the water-wheel; and all the
additional apparatus now requifite to fhift the fpur-wheels
would at the fame time be faved, and a confequent diminution
of original expence.
TURNING, the art of forming hard bodies, as wood, ivory,
iron, into a round or oval fhape by means of a machine called a
atbe. This art was well known to the ancients, and feems to
have been carried by them to a very great degree of perfection;
at leaſt, if we believe the teftimony of Pliny and ſeveral other
authors, who tell us, that thofe precious vafes enriched with
figures in half-relief, which ſtill adorn our cabinets, were turned
on the lathe.
The art of turning is of confiderable importance, as it contri-
butes effentially to the perfection of feveral other arts. The
architect uſes it for many ornaments both within and without
highly finiſhed houſes. The mathematician, the aſtronomer,
Maudflay's Turning Apparatus.
471
*
and the natural philofopher, have recourfe to it, not only to
embelliſh their inftruments, but alſo to give them the neceffary
dimenfion and precifion: and it is an art abfolutely neceflary to
the goldfmith, the watchmaker, the joiner, and the fmith.
Turning is performed by the lathe, of which there are
various kinds, and feveral inftruments, as gouges, chifels, drills,
formers, fcrew tales, uſed for cutting what is to be turned into
its proper form as the lathe turns round. The molt fimple
kind of lathe is a well-known inftrument, and need not be
defcribed here: the improved lathes manufactured by Mr.
Henry MaudЛlay, of Margaret-ftreet, Cavendish-ſquare, are the
moſt curious as well as the moft uſeful of any we have feen,
Mr. 7. Farey, jun. who took the drawings of thefe elegant
fpecimens of mechanical ingenuity, has accompanied them with
a defcription, nearly as below. A (pl. XXXVI. fig. 1.) is the
great wheel, with four grooves on the rim : it is worked by a
crank B and treadle C, in the common way; the catgut which
goes round this wheel paffes alfo round a fmaller wheel D,
called the mandrel, which has four grooves on its circumference
of different diameters for giving it different velocities, corre-
fponding with the four grooves on the great wheel A. In order
to make the fame band fuit, when applied to all the different
grooves on the mandrel D, the wheel A can be elevated or
depreffed by a fcrew a, and another at the other end of the
axle; and the connecting-rod C can be lengthened or fhortened
by fcrewing the hooks at each end of it further out of, or
into it. The end M, fig. 2., of the fpindle of the mandrel D, is
pointed, and works in a hole in the end of a ſcrew, put through
the ftandard E, fig. 1.; the other end of the bearing F, fig. 2. is
conical, and works in a conical focket in the ſtandard F, fig. г.
fo that by tightening up the fcrew in E, the conical end F may
at any time be made to fit its focket: the puppet G has a
cylindric hole through its top to receive the polished pointed
rod d, which is moved by the fcrew e, and fixed by the fcrew f
the whole puppet is fixed on the triangular prifmatic bar H,
by a clamp fig. 8., the two ends of which, a, b, are put through
holes, b, in the bottom of the puppet under the bar, and the
whole is fixed by the fcrew e preffing againſt it: by this means,
the puppet can be taken off the bar without firft taking off the
ftandard I, as in the common lathes: and the triangular bar 15
found to be far preferable to the double rectangular one in coms
mon ufe. The reft J is a fimilar contrivance; it is in three pieces;
fee figs. 3, 4, and 5. Fig. 4. is a piece, the opening (a, b, c)
which is laid upon the bar H, fig. 1.; the four legs dddd of
fig. 5. are then put up under the bar (into the receffes in fig. 4.
which are made to receive them) fo that the notches in dura
Weddled pidgi
"
N.
C
11
472.
MACHINES.
may be level with the top of fig. 4., the two beads eƒ in fig. 3.
are then flid into the notches in the top of dddd, fig. 4. to keep
the whole together; the groove is to receive a correſponding
piece on ef, fig. 3., to fteady it; the whole of fig. 3. has a
metallic cover, to keep the chips out of the grooves. It is plain,
that by tightening the fcrew h in the bottom of fig. 4. the
whole will be fixed and prevented from fliding along the bar H,
and fig. 3. from fliding in a direction perpendicular to the bar;.
the piece, fig. 3., on which the tool is laid, can be raiſed or
lowered at pleaſure, and fixed by the fcrew m. On the end n
of the fpindle P, figs. 1, and 2., is fcrewed occafionally an·
univerfal CHUCK for holding any kind of work which is to be
turned. (fee fig. 6.). A is the female fcrew to receive the fcrew 7,
fig. 1., near the bottom of the fcrew A is another fcrew BB,
which is prevented from moving endways by a collar in the
middle of it fixed to the fcrew Ã: one end of the fcrew BB is
cut right handed, and the other left handed; fo that by turning
the ſcrew one way, the two nuts EF will recede from each
other, or by turning it the contrary way, they will advance
towards each other: the two nuts EF país through an opening
in the plate C, and project beyond the fame, carrying jaws like
thofe of a vice, by which the ſubject to be turned is held.

C
"
For turning faces of wheels, hollow work, &c. where great
accuracy is wanted, Mr. Maudflay has contrived a curious
apparatus which he calls a ſlide-tool, reprefented by fig. 7., where
EEE is the opening to receive the bar H, fig. 1., and it is fixed
by the clamp, fig. 8. as before deſcribed: the tool for cutting, &c.
is fixed in the two holders bb by their ſcrews; theſe holders are
faſtened to a fliding plate 4, which can be moved backwards and
forwards by the fcrew c, caufing the tool to advance or recede;
fig. 9. reprefents the under fide (turned upward) of the part AA,
in which the ſcrew is feen fixed at each end, and the nut d,
which is attached to the underfide of the plate a, working upon
it. When it is neceffary, as in the turning of the infide of
cones, &c. that the tool ſhould not be parallel to the fpindle P,
the ſcrew e and another fimilar one behind muſt be loofened,
the tool ſet at the proper angle, and then be fcrewed tight
again. In order to make the piece AA move truly when it is
turned round, there is a hole f, fig. 9., to receive a knob g,
fig. 14., upon the plate B, which acts as a centre, and keeps it
in its place: there are three holes on each fide in the plate B,
fig. 12., to put the ſcrew e in at different times, thus giving to
the tool a greater range than the circular openings SS will
admit. The part EEEE, reprefented feparately, and inverted
in fig. 10, is of caft-iron, and has a fcrew b working in it fimilar
to fig. 9.; the nut of this fcrew is attached to the bottom of the

.
4
MaudЛlay's Turning Apparatus.
473
flide H, fig. II., at t, which flides in the groove i, figs. 7. and ro.;
at one end of it is a box containing a fcrew m, to be hereafter
defcribed, and at the other is a frame of brafs KK. Near the
fame end of the flide is a pin L, projecting above the plate,
which is put through an opening, Jin fig. 12., to ſteady it, while
the other end, C of fig. 12., is put through an opening M in the
box D, fig. 11. In the part C is an oblique flit // to receive a
ſtub which projects from the bottom of the nut n, worked by,
the fcrew m, fig. 11.: by this arrangement it is obvious that in
the ſcrew m` is worked, the ftub of the nut n, acting againſt the
flide of the ſlit // as an inclined plane, will move it either back-
wards or forwards through the opening M; a metal cover r,
fig. 14, is occafionally put over the opening for the nut z and
fcrew m, to prevent the chips from falling in. Near the four
corners of the frame, fig. 12., are four fmall projections 0000,
with inclined fides, which fit into the four openings pppp of
figs. 13. and 7.; theſe openings are cut out in two brafs plates,
which are ſcrewed on at right angles to the plate BB, figs. 7.
and 13.; the ends qqqq of thefe plates flide between the edges
of the frame KK and the box D, fo as to prevent any other
motion than a vertical one. When this fide-tool is uled, the
puppet G is to be removed or pushed back further from F, and
the tool is put upon the bar H, figs. 1., and fixed in the place of
the reft J by the clamp, fig. 8.; the diſtance from the centre z
is adjuſted by the fcrew b, which moves the flide, fig. 11. in the
grooves i, fig. 7. and 10. with the whole apparatus upon it: by
the fcrew m, figs. 7. and 11., as before deſcribed, the flide,
fig. 12., may be moved in a direction perpendicular to the
bar H, fig. 1.; and its projections oo acting againſt the flits pp,
figs. 7. and 13., as inclined planes, will raife or lower the plate B
as is required.


-
1
The tool, which has been before fixed in the holders bb, can
be fet at the proper angle, by loofening the ſcrew e, as previouſly
deſcribed : and, laſtly, the tool with the holders and flider a can
be advanced or withdrawn by working the fcrew e. The nuts
of the ſcrews cand b, fig. 7., are not fcrewed faſt to the fliding
plates, but are held by two pins t, fig. 11., which fit into
grooves u, fig. 10., in each fide of the nut: by thefe means, the
fliding plate can at any time be taken out by only unſcrewing
one of the braſs fides from the groove i, without taking out the
fcrew and nut. In order to make the grooves always fit their
flides, the two pieces of braſs yÿ, fig. 7., which compofe the
fides of the groove, have elliptic holes for their ſcrews v, ſo as
to admit, when the fcrews are flackened, of being pushed
inwards by the ſcrews w, which work in a lump of metal caft
with the part AA,d berior te
,
1
474
MACHINES.
1
The large lathes which Mr. Maudflay ufes in his manufac
tory, inſtead of being worked by the foot, as repreſented in
fig. 1., are worked by hand; the wheel and fly-wheel which the
men turn works by a ſtrap on another wheel, fixed to the
ceiling directly over it; on the axis of this wheel is a larger
one, which turns another ſmall wheel or pulley, fixed to the
ceiling, directly over the mandrel of the lathe; and this laft
has on its axis a larger one which works the mandrel D, by a
Band of catgut. Theſe latter wheels are fixed in a frame of caſt-
iron, moveable on a joint; and this frame has always a ſtrong
tendency to rife up, in confequence of the action of a heavy
weight; the rope from which, after paffling over a pulley, is
faftened to the frame: this weight not only operates to keep the
mandrill-band tight, when applied to any of the grooves therein,
but always makes the ftrap between the two wheels on the
ceiling fit. As it is neceffary that the workman ſhould be able
to ftop his lathe, without the men ſtopping who are turning the
great wheel, there are two pulleys or rollers (on the axis of the
wheel over the lathe), for the ftrap coming from the other wheel
on the ceiling; one of theſe pulleys, called the dead pulley, is fixed
to the axis and turns with it, and the other which flips round
it, is called the live pulley: theſe pulleys are put cloſe to each
other, ſo that by flipping the ftrap upon the live pulley, it will
not turn the axis; but if it is flipped on the other it will turn
with it: this is effected by an horizontal bar, with two upright
pins in it, between which the ſtrap paffes. This bar is moved in
fuch a direction as will throw the ftrap upon the live pulley, by
means of a ſtrong bell-fpring; and in a contrary direction it is
moved by a cord faftened to it, which paffes over a pulley, and
hangs down within reach of the workman's hand to this cord
is faftened a weight, heavy enough to counteract the bell-fpring,
and bring the ſtrap up to the dead pulley, to turn the lathe;
but when the weight is laid upon a little ſhelf, prepared for the
purpoſe, the ſpring will act and ſtop it.
+
→
Mr. Maudflay has likewife fome additional apparatus for cut-
ting the teeth of wheels, in which the face of the mandrel D,
fig. 1., has ſeventeen concentric circles upon it, each divided
into a different number of equal parts, by ſmall holes. There is
a thin ftop, x, fig. 1., which moves round on a ſcrew, fixed in
the ftandard F: this ftop is made of thin fteel, and is fo fixed,
that when it is turned up, and its point inferted into any of the
divifions of the mandrel, it will have a fufficient fpring to keep
it there the wheel to be cut is faftened, by means of a chuck,
to the fcrew n, and after it has been turned, and brought to the
proper fhape, the relt J is to be taken away, and the flide-tool
fubftituted: alquare bar is then put into the two holders, bb, fig.7. i
:
Smart's Turning Apparatus.
475
•
this bar has two branches for holding the ends of a ſpindle,
near one end of which is a pulley, and at the other are four
chifels; fixed perpendicularly into the fpindle for cutting out the
teeth (inftead of the circular faw commonly ufed): the pulley is
turned (with the intervention of feveral wheels to augment the
velocity) by the fame great wheel as the lathe, with 7300 re-
volutions per minute; the mandrel is then fixed by the ftopx,
fig. 1., and the cutter advanced towards the wheel, by the fcrew
c, fig. 7. When it has cut that tooth, the cutter is withdrawn
and the mandrel turned to another divifion, and a tooth is cut
again as before. At that part of the frame of the cutting-
ſpindle where the bar which is fixed in the holders of the flide-
tool connects with the two branches there is a joint, by which
the cutting-ſpindle can be ſet in an inclining pofition, for cut-
ting oblique teeth like thoſe which are to work with an endleſs
ferew. The great velocity with which this fpindle turns foon
generates, by friction and refiftance, a degree of heat fufficient
to expand it very fenfibly: but this ingenious mechanift, fore-
ſeeing fuch a circumftance, has judiciously compenfated for it
in his conftruction, by making the fpindle fo fhort as to play
looſely in its fockets at the commencement of the motion; but
after a few ſeconds the expanfion is fuch as to caufe the whole
to fit together as it ought to do, and the work of cutting to
proceed with accuracy and fafety.
*
}
Another ſkilful mechanic, Mr. Smart, of Ordnance Wharf,
Weſtminſter, whofe chimney-cleanfers, and faws, have been
noticed in earlier parts of this volume, has made fome very ufe-
ful improvements in the art of turning, and particularly has
ftruck out a fimple method of turning cylinders and cones, in
wood. The figures to illuftrate his turning machinery are
given in pl. XXVI. (figs. 3. 4.), where the legs or ftiles L, the
puppets A, B, the cheeks 0, 0, the pikes and ferews, M, N, R,
with the handle D, are but flightly varied from the ufual con-
ftruction. Round the mandrel E paffes a band F, F, which
alſo encompaffes a large wheel not fhewn in the figure; and
when this large wheel is turned round with moderate fwiftnefs,
it communicates a rapid velocity to the mandrel E, and the
long piece of wood G, which is propofed to be made cylindrical.
This piece is previouſly hewn into an octagonal form. The
cutting-frame H contains a fharp iron tool, which is to anfwer
the purpoſe of the common turning-gouge, and which is fitted
into the frame ſo as to project a little beyond its inner part, after
the manner of a carpenter's plane-iron for round or ogee work.
Then, while the piece G is turning ſwiftly round by a man
476
MACHINES.
working at the great wheel, another man pushes the frame H
gently on from L towards M, the lower part of that frame fitting
between the cheeks o, o, and fliding along between them. By
this procefs, the piece G is reduced to a cylinder, moderately
ſmooth ; ˇand, in order to render the ſmoothneſs as complete as
need be, a fecond cutter, and its frame I, adapted to a rather
fmaller cylinder than the former, is puſhed along in like man-
ner from I to M. This operation may be performed with
ſuch ſpeed, that a very accurate cylinder of 6 feet long, and 4
inches diameter, may be fixed to the lathe and turned in much
lefs than a minute.
Mr. Smart turns a conical end to one of theſe cylinders with
great facility, by means of a cutting-blade fixed in an iron hol-
low conical frame K, the ſmaller end of which admits the pike
from the ſcrew S (fig. 4.), to which one end of the cylinder G
is attached as the cylinder turns rapidly round, the cutter K is
conducted gently along it by means of the hollow frame, and
foon gives the conical fhape to the end of the cylinder, as re-
quired.
:

Some important directions for turning ſcrews, ovals, cubes,
rofe-work, fwaſh-work, &c. may be feen in Moxon's Mechanic
Exerciſes the infertion of them here would occupy more room
than is compatible with the plan of this work. See alfo, "Tour
pour faire fans Arbre toutés Sortes de Vis, par M. Grandjean,”
in.“- Recueil dés Machines et Inventions, approuvées par
l'Acad. Roy. des Sciences," tom. v.; and Mr. Healy's method
of cutting fcrews in the common turning-lathe, in Tilloch's
Phil. Mag. vol. xix.
--
WATCH,a fmall portable machine for meafuring time;
having its motion commonly regulated by a fpiral fpring. Per-
haps, ſtrictly speaking, watches are all fuch movements as fbew
the parts of time; as clocks are fuch as publiſh them, by ftriking
on a bell, &c. But commonly, the term watch is appropriated-
to fuch as are carried in the pocket; and clock to the large
movements, whether they ftrike the hour or not.
>
Spring or Pendulum WATCHES ftand pretty much on the fame
principle with pendulum clocks. For if a pendulum, defcrib
ing fmall circular arcs, make vibrations of unequal lengths, in
equal times it is becaufe it deferibes the greater arc with a
greater velocity; fo a fpring put in motion, and making greater
and lefs vibrations, as it 16 more or leſs ſtiff, and as it has a
greater et lefs degree of motion given it, performs them nearly
in equal times. Hence, as the vibrations of the pendulum had
been applied to large clocks, to rectify the inequality of their
motions; fo, to correct the unequal motions of the balance in
watches, a fpring is added, by the fochronifm of whofe vibra-

Watch.
477
tions the correction is to be affected. The fpring is ufually
wound into a ſpiral; that, in the little compaſs allotted it, it
may be as long as poffible; and may have ftrength enough not
to be maſtered, and dragged about, by the inequalities of the
balance it is to regulate. The vibrations of the two parts, viz.
the ſpring and the balance, fhould be of the fame length, but
fo adjuſted, as that the ſpring, being more regular in the length
of its vibrations than the balance, may occafionally communicate
its regularity to the latter.
+
▸
C
Striking WATCHES are fuch as, befides the proper watch-
part for meaſuring of time, have a clock-part for ſtriking the
hours, &c.
Repeating WATCHES are fuch as by pulling a firing.ì &c.
repeat the hour, quarter, or minute, at any time of the day or
night. This repetition was the invention of Mr. Barlow, and
firſt put in practice by him in larger movements or clocks about
the year 1676. The contrivance immediately fet the other
artiſts to work, who foon contrived divers ways of effecting the
fame but its application to pocket-watches was not known
before king James the Second's reign; when the ingenious in-
ventor above mentioned, having directed Mr. Thompfon to
make a repeating watch, was foliciting a patent for the fame.
The talk of a patent engaged Mr. Quare to reſume the thoughts
of a like contrivance, which he had had in view fome years be-
fore: he now effected it; and being preffed to endeavour to
prevent Mr. Barlow's patent, a watch of each kind was pro-
duced before the king and council; upon trial of which, the
preference was given to Mr. Quare's. The difference between ·
them was, that Barlow's was made to repeat by puſhing in two
pieces on each fide the watch-box; one of which repeated the
hour, and the other the quarter: whereas Quare's was made to
repeat by a pin that fuck out near the pendant, which being
thruft in (as now it is done by thruſting in the pendant itſelf),
repeated both the hour and quarter with the fame thruſt.

A
Of the Mechaniſm of a WATCH, properly ſo called. Watches,
as well as clocks, are compofed of wheels and pinions, and a
regulator to direct the quickneſs or flowneſs of the wheels, and
of a ſpring which communicates motion to the whole machine.
But the regulator and fpring of a watch are vaftly inferior to
the weight and pendulum of a clock, neither of which can be
employed in watches. Inftead of a pendulum, therefore, we
are obliged to ufe a balance (pl. XXXIII. fig. 1.) to regulate
the motion of a watch; and a fpring (fig. 2.) which ferves in-
ſtead of a weight, to give motion to the wheels and balance,
The wheels of a watch, like thofe of a clock, are placed in a
frame formed of two plates and four pillars. Fig.3., repreſents
478
MACHINES.
the infide of a watch, after the plate (fig. 4.) is taken off. A
is the barrel which contains the fpring (fig. 2.); the chain is
rolled about the barrel, with one end of it fixed to the barrel A,
(fig. 5.), and the other to the fufee B.
When a watch is wound up, the chain which was upon the
barrel winds about the fufee, and by this means the fpring is
ftretched; for the interior end of the ſpring is fixed by a hook
to the immoveable axis about which the barrel revolves; the
exterior end of the fpring is fixed to the infide of the barrel,
which turns upon an axis. It is therefore eaſy to perceive
how the ſpring extends itfelf, and how its elasticity forces the
barrel to turn round, and confequently obliges the chain which
is upon the fuſee to unfold and turn the fuſee: the motion of
the fufee is communicated to the wheel C (fig. 5.); then, by
means of the teeth, to the pinion c, which carries the wheel D;
then to the pinion d, which carries the wheel E; then to the
pinion e, which carries the wheel F; then to the pinion f, upon
which is the balance-wheel G, whofe pivot runs in the pieces A
called the potance, and B called a follower, which are fixed on
the plate fig. 4. This plate, of which only a part is repreſented,
is applied to that of fig. 3. in ſuch a manner that the pivots of
the wheels enter into holes made in the plate, fig. 3. Thus the
impreffed force of the ſpring is communicated to the wheels:
and the pinion ƒ being then connected to the wheel F, obliges it
to turn (fig. 5.) This wheel acts upon the palettes of the verge
1, 2 (fig. 1.), the axis of which carries the balance HH (fig. 1.).
The pivot I, in the end of the verge, enters into the hole in
the potance A (fig. 4.). In this figure the palettes are repre-
fented; but the balance is on the other fide of the plate, as
may be ſeen in fig. 6. The pivot 3 of the balance enters into
a hole of the cock BC (fig. 7.), a perfpective view of which is
repreſented in fig. 8. Thus the balance turns between the cock
and the potance (fig. 4.), as in a kind of cage. The action of
the balance-wheel upon the palettes 1, 2 (fig. 1.), is the fame
with what we have deſcribed with regard to the fame wheel in
the clock; i. e. in a watch, the balance-wheel obliges the ba-
lance to vibrate backwards and forwards like a pendulum. At
each vibration of the balance a palette allows a tooth of the ba-
lanée-wheel to eſcape; ſo that the quickneſs of the motion of
the wheels is entirely determined by the quickneſs of the vibra-
tions of the balance; and theſe vibrations of the balance and
motion of the wheels are produced by the action of the ſpring.
But the quickneſs or flowness of the vibrations of the balance
depend not folely upon the action of the great fpring, but
chiefly upon the action of the fpring a, b, c, called the Spiral
¿ fpring (fig, 9.), fituated under the balance H, and repreſented

1
Watch!
479
*
in perfpective (fig. 6.). The exterior end of the ſpiral is fixed
to the pin a (fig. 9.). This pin is applied near the plate in a
(fig. 6.); the interior end of the fpiral is fixed by a peg to the
centre of the balance. Hence if the balance is turned upon it-
felf, the plates remaining immoveable, the fpring will extend
itſelf, and make the balance perform one revolution. Now,
after the ſpiral is thus extended, if the balance be left to it-
felf, the elasticity of the fpiral will bring back the balance,
and in this manner the alternate vibrations of the balance are
produced.
In fig. 5. all the wheels above defcribed are reprefented in
fuch a manner, that it may be eaſily perceived at firſt fight how
the motion is communicated from the barrel to the balance.
In fig. 1o. are reprefented the wheels under the dial-plate by
which the hands are moved. The pinion a is adjuſted to the
force of the prolonged pivot of the whee! D (fig. 5.), and is
called a cannon pinion. This wheel revolves in an hour. The
end of the axis of the pinion a, upon which the minute-hand is
fixed, is fquare; the pinion (fig. 10.) is indented into the wheel
b, which is carried by the pinion a. Fig. 11. is a wheel fixed
upon a barrel, into the cavity of which the pinion a enters, and
upon which it turns freely. This wheel revolves in twelve
hours, and carries along with it the hour-hand.
!
t
Such in brief is the general mechaniſm of a watch: to
treat the fubject to the extent its importance demands would
require a volume: fome parts of the conftruction are further
explained under the words BALANCE and SCAPEMENT in this
volume; but for more ample information the reader muſt con-
fult fome of the treatifes mentioned in our general catalogue of
writings on CLOCK-WORK.
Mr. Elliot, of Clerkenwell, has lately invented a very fimple
repeating watch, in which the motion is performed with much
fewer parts than in the uſual conſtruction, by which means he
is enabled to reduce the price fo low as eight guineas for a good
repeater on this principle, or to add the repeating-work to an-
other watch for three.
The method by which this repeater is fo much fimpli-
fied is by the ufe of a finglé part, fo contrived as to perform
the operations of feveral: this is, a flat ring, or centreleſs
wheel, of nearly the' fame diameter as the watch, fupported'in
its place, to as to admit of circular motion, by four grooved
pulleys placed round its external circumference, in the fame
manner as the part in common clocks which denotes the moon's
age. "This part is put in motion by turning the pendants whófe
extremity is formed into a ſmall vertical wheel, which works in
teeth cut on the external part of the flat ring for almoſt a third

480
MACHINES. :
of its circumference. The lower part of the ring contains the
pins, at right angles to its face, which lift the hammers for
ftriking the hours and quarters; the internal part of the ring
contains indentations of regularly increaſing depths, which, re-
ceiving the tails of the levers, whofe other extremities are
preffed by their ſprings againſt the hour-fnail and the quarter-
Inail, is by them prevented from moving beyond a certain de-
gree proper for the time: after the pendant is turned, the ring
is brought back to its firft pofition, by a box-fpring, round
which a fine chain is coiled, whofe extremity is connected with
the inner part of the ring.
By turning the pendant to the left the hour is struck, and by
turning it to the right the quarters are repeated; and the re-
turning fpring juft mentioned is made to operate in both di-
rections, by its chain paffing between two little pulleys, which
on either fide convert the direction of the chain to the line of
traction of the fpring.

$
Hence it is evident this fingle flat ring performs all the fol-
lowing operations.
1. It receives the motion for ftriking the hour from the pen-
dant.
2. — The fame for ftriking the quarters.
3.
4.
5.:
6.
It carries the pins, or teeth, which lift the hour-hammer.
The fame for the quarter-hammer.
It contains the indentations by which the hour-fnail ope
rates on it by its lever.
The fame, by which the quarter-fnail operates on it.
7. It carries the part that recoils the movement which tells
the hour to its firſt pofition.
8. It carries the part, for the fame purpafe, for the quarter-
movement.
;
9. It contains a cavity, which moves over a fixed pin, that
prevents the pendant from turning it too far.
In this ring, the fame parts, in three inſtances, are made to
perform double operations, by which fimplicity of conſtruction *
is advanced, apparently to its greateft extent.´*
WATCHMAN'S NOCTUARY, the name given to an inſtru
ment lately contrived to remedy a great defect in an import-
ant branch of the police of great cities, that of night watching
Every twenty-four hours furnishes fome inftance of the inef
ficacy of the prefent fyftem, by the depredations which have
been committed in the night, or by the fatal accidents which
occur from a neglect of giving-families timely warning in eafes
of fudden fires. A refpectable magibig (8amuel Day, Efq.
of: Charter-houfe, Hinton, Somerfetare) has directed his latt
tention to the application of a mechanical check upon the di

•
\
Watchman's Noctuary.
481

gence and regularity of watchment, labourers, and all other
claffes of men whoſe duty requires that they ſhould attend at
certain places at appointed times: the inftrument he has in-
vented for this purpoſe he calls a Watchman's noctuary, or La-
bourer's regulator.
P
The invention confifts principally of a large horizontal
wheel, which is moved uniformly round every 12 hours by
clock-work. The upper side of this wheel is divided by two
circles, one within the other; the outer one, or periphery,
having the hours and quarters marked on it, which may be
called the lateral side; the inner circle having also a dial, which
may be called the vertical one. The ſpace between theſe circles
or dials is divided into cells, each cell correfponding with a
quarter or half-hour of the different hours marked on the dials;
and, if thought proper, the cells might be fo multiplied, as that
each would correſpond within a period of five minutes. Such
is the upper fide of the horizontal wheel, which may be made
of copper, or tin, or various other materials, and is about 9
inches in diameter. The under fide of the fame has a brafs
wheel with teeth, diameter 34 inches, fixed to its central part;
the teeth of which, letting in with thoſe of a ſmaller wheel or
pinion, give motion in conſequence to the large horizontal
wheel (of which it forms a part) by the motion it receives from
the pinion. This pinion being fet in motion by the common
clock-work and a weight or ſpring, the revolution of the hori-
zontal wheel is completed once in twelve hours, and thus, re-
gularly going round, will at all times fhew the time of day or
night. As it moves round it carries the cells above-mentioned
under a kind of chink, juft large enough to receive a token of
about the fize of a farthing. This chink finks down from an
external brafs box, which is fufficiently large to admit a man's
fingers to drop in the token by an external aperture or mouth
of the chink, the token being directed perpendicularly through
this chink into fuch cell as is immediately under it, and which
muſt correſpond with the time of night or day. The head of
the cafe of the machine has double doors in front; the outward.
door covers the whole face together, leaving a fufficient ſpace
above the horizontal wheel for examining the tokens and taking --.
them from the cells, or for removing the wheel when neceffary.
A faller door opens in this large one upon the brass box above-
mentioned, the opening of which belongs folely to the watch:
man, of ſuch other perſon as may be required to uſe the ſame,
for the purpoſe of feeing the time and dropping his tokens, a
minute-dial alfo being placed under the hour-index. If it be
found more convenient, a common dial-plate, to fhew the hours
COL. 4.



11
482
MACHINES.
and minutes, may be placed inftead of the minute-diak The
great outer door first mentioned is. to be opened only by the in-
ſpector or examiner of the tokens, and ought to be well feeured;
but, for greater fafety, both againſt thieves and weather, there
is an infide door, in which the fore-mentioned brass box is fixed;
and this inner door being opened, throws into view the hori
zontal wheel, for the purpoſe juſt ſpecified. Theſe are the eſ-
Lential parts of the invention: the different appendages may be
variouſly modified.
One fuch inftrument as this being placed at each end of a
watchman's round, it will be afcertained how the man continued
his movements through the night, to a nicety of 10 minutes (or
lefs if required) at any period of the watch; and the flighteft
irregularity or omiffion will be detected the next morning by
the perſon whofe office it fhall be to open the machine. No
trick or fraud on the watchman's part can counteract the move-
ment of the horizontal wheel comprising the cells into which
the tokens are to be dropped; each cell is, by this contrivance,
like time itſelf, irrevocable. when past: the watchman has no
command over it, and the whole will be a kind of ſpeaking wit-
neſs of his diligence and fidelity in going his rounds, anfwering
the next morning to the exact periods he either was or ought
to have been there. ´….

I
4
By this means the calls of the watchmen, which were only
inftituted for the purpoſe of his giving notice of being on his
duty, will be fuperfeded; and a confiderable expence of animal
exertion will be faved to the individual, which might better be
converted into that of going his rounds twice, where he now
only-goes once. Warnings to the nightly thief of timely attack
or retreat will likewife be taken away; and if inſtead of an open,
the watchman was to carry a dark, lanthorn, the robber would
have no fecurity whatever in calculating the moment of his
depredation, and might be detected in the very outlet of his at-
tack, as the flighteſt found would alarm the watchman walking
in filence, and not drowning diftant: noife by that of his own
voice.
Of the objections to this new mode of ameliorating the watch
ing of cities, the only one feems to be the expence of the times
pieces; and confidering the number which the larger parishes
will have occafion for, this expence will be ſuppoſed importante
but let it be confidered that it will never amount to more than
three-pence in the pound of a rate on houſes, and that the first
will be the fole expence probably to be faved by diminiſhing
the number of patroles to one half (or defs) of what they now
are. But trifling indeed will be the expence when compared
f
S
Water-mills&
483
•
with the loffes fuftained by the public in depredations, which,
according to a late work on the police of the metropolis, amounts
to two millions and upwards annually.
The beſt fituation for theſe machines will be at each end of
a watchman's round, perhaps certain rounds will require three.
They ought to ſtand in a convenient recefs in the ſtreet, fecured
by rivetings of iron, or let into a wall, or placed on a ſtrong
bracket within the iron railing of an area; and, if the dial-
plates were fuffered to appear, would be uſeful in the day as
well as in the night: as an eight-day clock it would require no
attention to its movement but once a week, and the morning
infpector might attend to the flight duty of winding it up.
The annual expence of keeping it in repair is too trifling to
be taken notice of.
The fame machine will anfwer in cuftom-houfes, ware-
houſes, banking-houſes, manufactories, bleaching-grounds, and
every place where watching or other attendance, to be uſeful
must be exact: even fentinels on military duty might be re-
quired to leave tokens as memorials of their vigilance.
Mr. Day has, we underſtand, obtained the uſual patent for
fecuring to himſelf the right of making and felling this inftru-
ment; yet furely not to the exclufion of others invented for the
ſame purpoſe: for the late Marquis of Exeter informed the
public more than two years ago, through the medium of Ni-
cholſon's Philofophical Journal, that a clock for a fimilar pur-
pofe had been invented by Meffrs. Boulton and Watt of Bir-
mingham, which costs no more than thirty fhillings. His lord-
fhip had then had two of them at Burleigh-Hall more than four
years; and he gives the following defcription of them: "They go
eight days, and have a face like a clock, but do not ſtrike. The
dial goes round, and the hour-finger is fixed: round the edge of
the dial are moveable iron pins, correfponding with the quarters
in each hour. A fmall hammer placed behind the hour-finger,
when moved downwards, puſhes into the dial one of the pins
which happens to be under it at the time, which pin remains fo
abafed until the dial nearly returns to the fame place, when by
an incloſed plane the pin is raiſed up into its firft pofition. This
gives time to have the machine examined in the morning, to fee
how many pins have been ftruck, and at what time they were
puſhed downwards. The hammer is moved by the pulling of
a chain with a handle, like houſe-door bells, which, by cranks'
and wires, is attached to it. I have one in my library, the
handle is out of doors. The other machine is placed in a build-
ing at the other end of my premiſes.

1
22
WATER-MILLS, the general term by which all kinds of
mills which have a ftream of water for their firſt mover, are
112
484
MACHINES.
defignated. The term is alfo fometimes applied to machines
driven by wind for the purpoſe of draining water out of fen
lands; but it is with more propriety confined to the preceding
acceptation.
?
It is not our intention in the prefent article to enter minutely
mto the defcription of the various kinds of machinery driven by
water as an active power, but to confine ourſelves to a few
general remarks upon the conſtruction of that part only which
is effential to water-mills, the water-wheel: for the axis of this
wheel may be employed to tranfmit the force impreffed upon it
to any fpecies of machinery. A concife view of the theory of
Water-wheels, together with a tolerably copious ſtatement of the
experiments and refults of Smeaton, have been laid before the
reader in book iv. of our firft volume: we propofe now to pre
fent fome obfervations on their fhape, magnitude, and velocity.
The moft general divifion of water-wheels is into two kinds,
refulting from the manner in which the fluid is made to act:
when water is made to act by its weight, it' is delivered from
the fpout as high on the wheel as poffible, that it may continue.
long to prefs it down; but when it is made to ftrike the wheel,
It is delivered as low as poffible, that it may have previouſly ac-
quired a great velocity: thus are the wheels faid to be overfbat.
or underfoot. The four kinds of wheels mentioned in art. 467.
vol. i. belong, in fact, to one or other of theſe general divifions.
1. An over hot-wheel is nothing but a frame of open buckets
to difpofed round the rim of a wheel as to receive the water
delivered from a ſpout in fuch a manner that one fide of the
wheel is loaded with water while the other is empty: of confe-
quence the loaded fide muft defcend; and by this motion the
fluid runs out of the lower buckets, while the empty buckets of
the rifing fide of the wheel, in their turn, come under the fpout,
and are filled with water. A flight infpection of the figure of
an overſhot water-wheel, in plate XVIII, of our first volume,
will convince the ftudent of the impoffibility of constructing.
the buckets fo as to remain completely filled with water tilk
they reach the bottom of the wheel; indeed, if the buckets are.
formed by partitions directed to the axis of the wheel, the
whole water muft be run out by the time that they have de->
fcended to the level of the axis; and, of confequence, there,
muft' be a great diminution in the mechanical effect of the
wheel. Millwrights have, therefore, turned their chief atten-
tion to the determination of a form for the buckets which shall
enable them to retain the water along a great portion of the
circumference of the wheel. It would require much more room
than we can align to this article, to defcribe half the contriv-
ances which have been propoſed: we fhall therefore only men- -




فير
"7
Water-mills.
483
tion one or two of the beft, as defcribéd by Dr. Robifon in the
Encyclopedia Britannica.

307
In fig. 11. pl. XXXII. AM is part of the throuding or ring
of buckets of an overſhot containing 40 buckets. GOFABCD
is the form of one of thefe buckets. The fhoulder AB of the
bucket ſhould be one half of AE, the depth of the throuding
AF fhould be more than AE. The arm BC of the bucket
muft be fo inclined to AB, that HC may be of AF and CD,
the wrift of the bucket, muft make fuch an angle with BC
I
the direction of the arm, that D n may be of En.
4
L
उ
از
i,
Iofe
From this conftruction it follows, that the area HABC is
very nearly equal to DABC: fo that the water which will fill
the ſpace HABC will all be contained in the buckes when it
hall come into fuch a poſition that AD is a horizontal fine
and the line AB will then make an angle of nearly 35 with the
vertical, or the bucket will be 35 from the perpendicular pafs
ing through the axis of motion. If the bucket defcend ſo much
lower that one-half of the water runs out, the line AB
make an angle of about 241° with the vertical. Therefore the
wheel, filled to the degree now mentioned, will begin to
water at about of the diameter from the bottom, and half of
the water will be discharged from the loweft bucket about 4th of
the diameter further down. Had a greater proportion of the,
buckets been filled with water when they were under the ſpout,
the diſcharge would have begun at a greater height from the
bottom, and a greater portion of the whole fall of water would
be loft. The lofs by the preceding conftruction is lefs than
th (fuppofing the water to be delivered into the wheel quite
at its top), and may be eftimated at about th; far the lols is
as the verfed fine of the angle which the radius of the bucket
makes with the vertical. The verfed fine of 35° is 18085
nearly 4th of the radius, orth of the diameter. Had only
of this water been fupplied to each bucket as it paffes the fpout,
it would have been retained for 10° more of a revolution, and
the loſs of fall would have only been about th

Τ
A very confiderable improvement in the conftruction of the
bucket has been made by Mr. Robert Burns of Cartfide, Ren-
frewshire. He divides the bucket by a partition m B, of fuch
a height, that the portions of the bucket on each fide of it may
be of equal capacity. Dr. Robifon juftly obferves, that this
principle is fufceptible of confiderable extenfion, and recom-
mends two or more partitions, particularly when the wheel is
made of iron. By this means the fluid is retained longer in the
lower buckets, and when there is a ſmall ſupply of water, it
may be delivered into the outer portion of the bucket, which,
being at a greater diftance from the centre of motion, increafes


་
į
486
MACHINES.

the power of the water to turn the wheel. The doctor adviſes
that the rim of the wheel, and confequently the breadth of the
buckets, fhould be pretty large, in order that the quantity of
water which they receive from the ſpout may not nearly fill the
bucket. The fpout which conveys the water fhould be con-
fiderably narrower than the breadth of the bucket; and the
houlder AB thould be perforated with a few holes, in order
to prevent the water from being lifted up by the afcending
buckets,, The diſtance of the fpout from the receiving bucket
fhould, în general, be two, three, or four inches, that the
water may be delivered with a velocity a little greater than that
of the rim of the wheel; otherwife the wheel will be retarded
by the impulfe of the buckets againſt the ftream, and much
power would be loft by the water dafhing over them.
With refpect to variations in the fall of water, fince the ac-
tive preffure is meaſured by the pillar of water reaching from
the horizontal plane where it is delivered on the wheel, to the
horizontal plane where it is fpilled by the wheel, it has been
concluded, that preffure must be proportional to the wheel;
and therefore the water muſt be delivered as high and retained
as long as poffible. This maxim, however, is fubject to limita-
tions, and is not perhaps ftrictly confiftent with found theory.
When the fall is exceedingly great, a wheel of an equal diameter
becomes enormoufly big and extremely expenfive. In cafes
like this where we are unwilling to lofe any part of the force of
a fall-ftream, the best form of a bucket-wheel is an inverted
chain-pump.
The velocity of an overfhot-wheel is a matter deferving of
great care and attention; and different authors have arrived at
very oppofite conclufions refpecting it. The most accurate
feems to be that an overfhot-wheel does the more work, as
it moves flower: the popular reafoning adduced to prove this
has been of the following kind. Suppoſe that a certain wheel
has 30 buckets, and that 6 cubic feet of water are delivered in a
fecond on the top of the wheel, and diſcharged, without any loſs
by the way, at a certain height from the bottom of the wheel.
Let this be the cafe whatever is the rate of the wheel's motion,
the buckets being of a fufficient capacity to hold all the water
which falls into them. Suppofe this wheel employed to raiſe
a weight of any kind, water, for inftance, in a chain of 30 buck-
ets, to the fame altitude and with the fame velocity. Suppoſe,
further, that when the load on the rifing fide of the machine is
one-half of that on the wheel, the wheel makes 4 revolutions
in a minute, or one turn in 15 feconds. During this time 90
cubic feet of water will have flowed into the go buckets, and
cach have received 3 cubic feet. In that cafe, each of the rifing


Water-mills.
487
buckets contains 14 feet; and 45 cubic feet are delivered into
the upper ciftern during one turn of the wheel, and 180 cubie
feet in one minute.
Now, fuppofe the machine fo loaded, by making the rifing
buckets more capacious, that it makes only 2 turns in a minute,
or I turn in 30 feconds; then each defcending bucket melt
contain 6 cubic feet of water. If each bucket of the rifing e
contained 3 cubic feet, the motion of the machine would be the
fame as before. This is a point none will controvert.
When
two pounds are fufpended to one end of a ſtring which paffes
over a pulley, and one pound to the other end, the velocity of
defcent of the two pounds will be the fame with that of a four-
pound weight, which is employed in the fame manner to draw
up two pounds. Our machine would therefore continue to
make four turns in a minute, and would deliver go cubic feet
during each turn, and 360 in a minute. But, by ſuppoſition,
it is making only two turns in a minute; which muſt proceed
from a greater load than 3 cubic feet of rifing water in each
rifing bucket. The machine muft, therefore, be raising more
than go fect of water during one turn of the wheel, and more
than 180 in a minute.



-
Thus it appears that if the machine is turning twice as flow
as before, there is more than twice the former quantity in the rifing
buckets; and more will be raiſed in a minute by the fame ex
penditure of power. In like manner, if the machine go three
times as flow, there muſt be more than three times the former
quantity in the rifing buckets, and more work will be done.
But further we may affert, that the more we retard the ma-
chine to a certain practical extent, by loading it with more
work of a fimilar kind, the greater will be its performance;
and the truth of the affertion may be thus demonftrated; Let
us call the firſt quantity of water in the rifing bucket, Q; the
water raifed by four turns in a minute will be 4 × 30 × Q
120 Q. The quantity in this bucket, when the machine goes
twice as flow, has been fhewn to be greater than 2 Q; call it
@ Q + x; the water raiſed by two turns in a minute will then
be 2 × 30 × (2 Q + x) = 120 Q + 60 x. Suppoſe, next,
the machine to go 4 times as flow, making but one turn in a
minute; the rifing bucket muft now contain more than twice
the quantity. 2 Qx, or more than 4 Q+2*, call it 4 Q +
2+y. The work done by one turn in a minute will now
be, 30 × (4 Q + 2 x + y) = 120 Q + 60 x + 30* By
fuch an induction of the work accompliſhed, with any rates of
motion we chooſe, it is evident that the performance of the ma-
chine increafes with every diminution of its velocity that is pro-
duced by the mere addition of a fimilar load of work, or that it



40$
MACHINES.

does the more work the flower it goes. This however is ab-
tracting from the effects of the friction upon the gudgeons of
the wheel, a caufe of refiftance which increaſes with the load,
though not in the fame ratio.
e have alfo fuppofed the machine to be in its ſtate of per
manent uniform motion. If we confider it only in the begin-
sing of its motion, the refult is ftill more in favour of flow mo-
tion: for, at the first action of the moving power, the inertia
of the machine itſelf confumes part of it, and it acquires its
per-
anent velocity by degrees, during which the refiftances arifing
from the work, friction, &c. increafe, till they exactly balance
the preffure of the water; and after this the machine no longer.
accelerates. Now, the greater the power and the refiftance
arising from the work are, in proportion to the inertia of the
machine, the fooner, it is obvious, will it arrive at its ftate of
permanent velocity.
1
The preceding difcuffion is fufficient to demonstrate, in gene-
the advantage of flow motion; but does not, it is confeffed,
point out in any degree the relation between the rate of motion
and the work performed; nor even the principles on which it
depends. This, however, is not neceflary for the improvement
of practical mechanics: but it is fufficiently manifeft that there
is not, in the nature of things, a maximum of performance at-
tached to any particular rate of motion, which' fhould, on that
account, be preferred. All, therefore, we have to do, is to load
the machine, and thus to diminiſh its ſpeed, unleſs other phyfi-
cal circumftances throw obftacles in the way: but there are
fuch obftacles; for in all machines there are fmall inequalities
of action which are unavoidable. In the action of a wheel and
pinion, though made with the utmoſt judgment and care, there
are fuch inequalities. Thefe increafe by the changes of form
occafioned by the wearing of the machine; and much greater
inequalities arife from the fubfultory motions of cranks, ftam-
pers, and other parts which move unequally or reciprocally.
Now, a machine may be fo loaded as juſt to be in equilibrio
with its work in the favourable pofition of its parts, and when
this changes into one lefs favourable, the machine may ſtop, or
at all events hobble, and work very irregularly; thus, the rub-
bing parts bear long on each other, with enormous preffures,
cut deep into one another, and greatly augment friction; to that
fuch flow motions as thefe must be avoided. A little more ve
locity enables the machine to overcome thofe increaſed refifte
ances by its inertia, or the great quantity of motion inherent in
it: great machines pollefs this advantage in a fuperior degree,
and will, confequently, work steadily with a fmaller velocity.v
atcieux, the inventor of the arcometer deſcribed in

↓
!
Water-mills.

arts. 401, &c. vol. i. was, we believe, the firft who deduced
both from theory and experiment, the important refult that the
work done by a water-wheel was increaſed by diminishing its
velocity. His differtations on this fübject were firit inferten in
Mem. Paris. Acad. Sciences, 1754: but lately the fubftance of
them has appeared in various places. This philofopher made
experiments upon a fmall wheel 20 inches in diameter, ONE
niſhed with 48 buckets, which received the water like a breaft-
wheel. On the axis of this wheel were placed cylinders of
different ſizes, the ſmalleſt being inch and the largeft 4 inches
in diameter, around which was wrapped a cord, with a weight
attached to it. When the one-inch cylinder was ufed, a weight
of 12 ounces was elevated to the height of 60 inches and
lines; and a weight of 24 ounces was elevated 40 inches. Whet
the four-inch cylinder was employed, a weight of 12 ounces
was raiſed to the altitude of 87 inches and 9 lines, and a weight?
of 24 ounces to the height of 45 inches and 3 lines. From
theſe reſults it is evident, that with the four-inch cylinder, when
the motion was floweft, the effect was greateft, and that when
a double weight was uſed, which diminished the wheel's Velo-
city, the weight was raiſed to more than half its former height.
The ftudent, by turning to page 455 of our firft volume, will
fee that Mr. Smeaton arrived at the fame conclufion; although
the greater extent and variety of his experiments enabled him to
afcertain that this general pofition was fubject to a limitation
varying with circumftances, which a judicious engineer will
always carefully diſcriminate.


î
1
2. Underfhot-wheels. To this clafs may be referred all wheels
in which the motion of the water is more rapid than that of the
float-boards of the wheel, ſo that the fluid impels them. “The
theory of this kind of water-wheels being fo exceedingly im-
perfect, we can do little elſe than recommend to the ſtudent
cautious examination of the experiments of Smeaton. We have
little to add to them here, except fome refults of De Parcieux
and Boffut, who have fhewn by very good experiments that there
is a fenfible advantage gained by inclining the float-boards to the
radius of the wheel about 20 degrees, fo that each float-board
when loweft fhall not be vertical, but have its edge turned up
the ftream about 20 degrees. Such inclination cauſes the water
to heap up along the float-board, and act by its weight: the floats
fhould therefore be made much broader than the vein of water
interrupted by them is deep.
Some engineers obferving the great fuperiority of overfhot
above undershot wheels, driven by the fame expence of power,
have propofed to bring the water home to the lower part of the
wheel on an even bottom, and to make the float-board no deeper

480
MACHINES.
than the aperture of the fluice, which would permit the water
to run out. The wheel they propofe to be fitted with a clofe
fole and fides, exactly fitted to the end of this trough, ſo that if
the wheel is at reft, the water may be dammed up by the fole
and float-board; it will, therefore, prefs forward the float-board
with the whole force of the head of water. But this, however
Ipecious, cannot anſwer; for if we fuppofe no float-boards, the
water will flow out at the bottom, propelled in the manner
thefe gentlemen fuppofe; and it will be fupplied from behind,
the water coming fowly from all parts of the trough to the hole
below the wheel. But now add the floats, and fuppofe the
wheel in motion with the yelocity that is expected. The other
floats, muft drag into motion all the water which lies between
them, giving to the greatest part of it a motion far greater than
it would have taken in confequence of the preffure of the water
behind it; and the water out of the reach of the floats will re-
main ftill, which it would not have done independent of the
float-boards above it, becauſe it would have contributed to the
expence of the hole, So that the motion which the wheel will
acquire by this conftruction must be widely different from what
us projectors fuppofe.

1


As far as we are able to judge, the best way of delivering the
water on an underfhot-wheel in a clofe mill courfe is, to let it
lide down a very ſmooth channel, without touching the wheel
till near its bottom, where the wheel thould be exactly fitted to
the courfe; or, to make the floats much broader than the depth
of the vein of water that glides down the courfe, and allow it
to be partly intercepted by the firft floats, and heap up along
them, acting by its weight, after its impulfe has been expended.
If the bottom of the courfe be an arch of a circle deſcribed with
a radius much greater than that of the wheel, the water which
flides down will be thus gradually intercepted by the floats.
Attempts have been made to conftruct water-wheels which
receive the impulfe obliquely, like the fails of a common wind-
mill. This would, in many fituations, be a great advantage.
A very flow but deep river could in this manner be made to
drive our mills; and although much power is loft by the obli-
quity of the impulfe, the remainder may be very great. Dr.
Robison (peaks of a wheel of this kind which was very power-
ful it was a long cylindrical frame, having a plate ſtanding
out from it about a foot broad, and furrounding it with a very
oblique fpiral, like a corkscrew. This was immerfed about th
of its diameter. (which was nearly 12 feet), having its axis in the
direction of the ftream. By the work which it was perform-
ing, it feemed more powerful than a common wheel which oc-
cupied the fame breadth of the river. Its length was not leſs



“Water-mills.
491
than 20 feet: had it been twice as much, it would have nearly
doubled its power without occupying more of the waterway.
Perhaps fuch a ſpiral, continued quite to the axis, and moving
in a hollow canal wholly filled by the ftream, might be a very
advantageous way of employing a deep and flow current.
In July, 1803, Mr. John Norton, of Rolls-buildings, took out
a patent for an improvement in the conftruction of water-mills,
which is exactly this of the Spiral wheel. How far an inven-
tion which had been publicly defcribed feven years before in
the Encyclopedia Britannica ought to be fecured to Mr. Nor-
ton by a patent, we need not decide.
•
An underſhot-wheel, with oblique float-boards, was invented
by the late Mr. Befant of Brompton; on whofe widow the
Society for the Encouragement of Arts, &c. in 1801, conferred
a reward of ten guineas: and, as it promiſes to be of great fer-
vice in many fituations, we have given a repreſentation of it in
pl. XXXV.
Fig. 7, A reprefents the body of the water-wheel, which is
hollow, in the form of a drum, and is fo conftructed as to refift
the admiffion of water. B is the axis on which the wheel
turns. C the float-boards, placed on the periphery of the
wheel, each of which is firmly fixed to its rim and to the body
of the drum, in an oblique direction. D is the reſervoir that
contains the water. E the penſtock, for regulating the quan-
tity of water which runs to the wheel. F reprefents the cur-
rent that has paffed fuch wheel.
Fig. 8. is a front view of the water-wheel, exhibiting the
oblique direction in which the float-boards, C, are placed on the
face of the wheel.
In the common water-wheels, more than half the quantity of
that fluid paffes from the gate through the wheel, without af-
fording it any affiftance: the action of the floats is refifted by
the incumbent atmoſphere, at the moment when thefe leave the
furface of the tail-water; and, as a fimilar proportion of water
with that which paffed between the floats at the head necef-
farily flows between them at the tail, the motion of the wheel
is greatly impeded. On the contrary, by Mr. Befant's contriv-
ance, no water can pafs, excepting that which acts with all its
force on the extremity of the wheel; and, as the floats emerge
from the water in an oblique direction, the weight of the atmo-
ſphere is thus prevented from taking any effect. Although his
new wheel is confiderably heavier than thofe conftructed on the
old plan, yet it revolves more eaſily on its axis; the water hay-
ing a tendency to float it. Laftly, repeated experiments have
proved Mr. Befant's wheel to be fo decidedly fuperior, that,
when working in deep tail-water, it will carry weights in the
善
​492
MACHINES.
proportion of three to one; on which account it will be parti
cularly ferviceable to tide-mills.
Mills with oblique floats are moſt uſeful for employing ſmalk
ftreams which can be delivered from a fpout with a great velo-
city. M. Boffut has confidered theſe with much attention, and
has afcertained the beſt modes of construction. There are two
which have nearly equal performances: 1. The vanes being
placed like thofe of a wind-mill round the rim of a horizontał
or vertical wheel, and being made much broader than the vein
of water which is to strike them perpendicularly. By theſe
means it will be ſpread about on the vane in a thin fheet, and
exert a preffure nearly equal to twice the weight of a column
whofe bafe is the orifice of the fpout, and whofe height is the
fall producing the velocity. Mills of this kind are much in uſe
in the fouth of Europe. The wheel is horizontal, and the ver-
tical axis carries the millftone; fo that the mill is of the ut-
moft fimplicity, and this is no fmall recommendation. Draw-
ings of fuch mills may be feen in Bockler, Leupold, and Bẹ-
lidor.
+
2. The vanes may be arranged round the rim of the wheel,
not like the fails of a windmill, but in planes inclined to the
radii, though parallel to the axis, or to the planes paffing through
the axis. They may either ftand on a fole, like the oblique.
floats recommended by De Parcieux, as before mentioned; or
they may ftand on the fide of the rim, not pointing to the axis,
but afide from it. This difpofition will admit of the ſpout
being more conveniently difpofed either for a horizontal or a
vertical wheel.
In the fouthern provinces of France, where horizontal wheels
are very generally employed, the float-boards are made of a
curvilineal form, fo as to be concave towards the ſtream. The
Chevalier de Borda obferves, that in theory a double effect is
produced when the float boards are concave, but that this effect
is diminiſhed in practice from the difficulty of making the fluid
enter and leave the curve in a proper direction. Notwithstand-
ing this difficuity, however, and other defects which might be
pointed out, horizontal wheels with concave float-boards are
always Tuperior to thoſe in which the float-boards are plane, and
fometimes to vertical wheels, when there is a ſufficient head of
water. If the fall of water be five or fix feet, a horizontal
wheel with concave float-boards may be erected, whoſe maxi
mum effect will be to that of ordinary vertical wheels as 3 to 2
Floating WATER MILLS. Although we are in this country
provided with many contrivances, in which the different powers
of water,iftazm,, wind, and animal force, have been fuccefsfully
applied to the purpoſe of grinding corn into flour, yet we have


Weighing-engines.
499
not, till very lately, met with floating water-mills to be worked
by tides or currents; and which are further defigned to put in
motion machinery adapted to any kind of manufacture.Meffrs.
Polfreeman, of Long-acre, in conjunction with Meffrs. Allen,
Foffenden, and Gray, have purchaſed the patent-right of Mr."
Hawkins, and have lately completed one of thofe mills, which;
by permiſſion of the Board of Navigation, is ftationed between
London and Blackfriars-bridge. Such grant was obtained with
the laudable view of reducing, if poffible, the price of flour in
the metropolis, and furniſhing a conftant fupply of that necef-
fary article of fubfiftence. The fimplicity of this invention
renders a long defcription fuperfluous; as it confifts in merely
applying the force of two or three water-wheels on each fide
of a barge, or any other veffel better calculated to contain the
interior part of the machinery. Were ſeveral mills of this kind
to be ſtationed on the Thames, or any other river where the
tide ebbs and flows, there would doubtleſs be numerous advan-
tagés refult; for they would be far lefs expenfive than fteam-
engines in the original erection, befides that they would lead to
a confiderable annual faving in the important article of coals."
Some other remarks connected with the fubject of water
mills, will be found under the words FLOUR-MILLS, PENSTOCK,
STREAM-MEASURERS, and TIDE-MILLS, in this volume and
chaps. 3. and 4. book iv. of our first volume. For further in
formation, confult Fabre fur les Machinës Hydrauliqués, "Langf-
dorf's Handbuch der Maschinenlehre, zweyter band, or fome other
of the treatiſes mentioned in the general catalogue under the
word MILL.
WEIGHING-ENGINES are often conftructed in order to
afcertain the weight of the loads on waggons and carts palling
along turnpike-roads. To prevent the roads from being toq
much worn, it has been found expedient to fix by an act of-
parliament a certain load for each breadth of wheel; and, that:
fuch loads may not be exceeded, there are weighing-machines
at ſeveral of the toll-gates, by which the loads of the feveral
waggons, &c. paffing through them can be determined.
+
In fome of theſe machines the contrivance is fuch, that the
carriage whofe load is to be weighed is lifted clear from the
ground by means of four ftrong chains and hooks attached to
large ſteel-yard, whofe fulcrum is raifed commonly by a com-
bination of tooth and pinion-work, moved by a winch-Handle
but it is far better to have the bufinefs performed by means of”
apparatus plaeed under a horizontal frame on which the carriage
aan ditu hobifon
may be drawn.:{
The most compendious and economical machine of this kind
that we have féén is one firſt uſed for weighing the riders of

1
+
494
MACHINES.
race-horſes, and afterwards applied to the more reputable fer-
vice of weighing loaded carriages.
Fig. 5. pl. XXXVII. is a plan of the machine; KLMN
is the plan of a rectangular box, which has a platform lid or
cover, of fize fufficient for placing the wheels of a cart or wag-
gon. The box is about a foot deep, and is funk into the ground
till the platform cover is even with the furface. In the middle
of the box is an iron lever fupported on the fulcrum pin i k
formed like the nail of a balance, which refts with its edges on
arches of hardened fteel, firmly faſtened to the bottom of the
box. This lever goes through one fide of the box, and is fur-
nifhed at its extremity with a hard ſteel pin / m, alſo formed to
an edge below. In the very middle of the box it is croffed by a
third nail of hardened fteel g b, alfo formed to an edge, but on
the upper fide. Theſe three edges are in one horizontal plane,
as in a well-made balance.

•
In the four corners A, A', E', E, of the box are firmly fixed
four blocks of tempered fteel, having their upper furfaces form-
ed into ſpherical cavities, well poliſhed, and hard tempered.
ABCDE repreſents the upper edge of an iron bar of con-
fiderable ſtrength, which refts on the cavities of the steel-blocks
in A and E, by means of two hard ſteel ſtuds projecting from
its under edge, and formed into obtufe-angled points or cones.
Thefe points are in a straight line parallel to the fide KN of
the box. The middle part C of this crooked bar is faced with
hard-tempered fteel below, and is there formed into an edge
parallel to AE and KN, by which it reſts on the upper edge of
the fteel pin g h which is in the lever. In a line parallel to
AE, and on the upper fide of the crooked bar ACE, are fixed
two ftuds or points of hardened fteel B and D projecting up-
wards above half an inch. The platform-cover has four short
feet like a ſtool, terminated by hard ſteel ſtuds, which are ſhaped
into fpherical cavities, and well poliſhed. With thefe it refts
on the four ſteel points B, B', D',D. The bar ACE is kneed
in fuch a manner vertically, that the points A, B, D, E, and
the edge are all in a horizontal plane. Theſe particulars will
be better underſtood by looking at the elevation in fig. 6. What
has been faid of the bar ACE muſt be underſtood as alſo ſaid of
the bar ACE'.
1
P
Draw through the centre of the box the line a be perpendi
cular to the line AE, BD. It is evident that the bar ACE is
equivalent to a lever abc, having the fulcrum or axis AE re-
ing with its extremity C on the pin bg, and loaded at b. It is
allo evident that a C is to a b as the load on this lever to the
preſſure which it exerts on the pin gh, and that the fame pro-
portion fubfifts between the whole load on the platform and

Weighing engines.
405
the preffure which it exerts on the ping b. It will alfo appear,
on an attentive confideration, that this proportion is nowife
deranged in whatever manner the load is placed on the plat
form. If very unequally, the two ends of the pin gb may be
unequally preffed, and the lever wrenched and ftrained a little gr
but the total preffure is not changed.
If there be now placed a balance or ſteel-yard at the fide EK,
in fuch a manner that one end of it may be directly above the
pin lim in the end of the lever EOF, they may be connected by
a wire or flender rod, and a weight on the other arm of the ba-
lance or ſteel-yard may be put in equilibrio with any load that
can be laid on the platform. A fmall counterpoife being firft
hung on to balance the apparatus when unloaded, any additional
weight will meaſure the load really laid on the platform. If
ab be to a cas 1 to 8, and EO to EF alſo as 1 to 8, and if a
Common balance be uſed above, 64 pounds on the platform will
be balanced by one pound in the ſcale, and every pound will be
balanced by one-fourth of an ounce. This would be a very con
venient partition for moſt purpoſes, as it would enable us to uſe
≈ common balance and common weights to complete the ma-
chine: or it may be made with a balance of unequal arms, or
with a ſteel-yard.
'
Some have thought to improve this inftrument by uſing
edges like thoſe of the nails of a balance inftead of points. But
unleſs made with uncommon accuracy, they will render the
balance very dull. The fmall deviation of the two edges A and
E, or of Band D, from perfect parallelifm to KN, is equiv
lent to a broad furface equal to the whole deviation. ¨'We ima-
gine that, with no extraordinary care, the machine may be made
to weigh within th of the truth, which is exact enough for
any purpoſe in commerce.
I
It is neceffary that the points be attached to the bars. Some
have put the points at A and E in the blocks of ſteel faftened to:
the bottom, becaufe the cavity there lodged water or dirt, which
foon destroyed the inftrument with ruft. But this occafions a
change of proportion in the firft lever by any fhifting of the
crooked bars; and this will frequently happen when the wheels
of a loaded cart are pushed on the platform. The cavity in the
ſteel ſtud ſhould have a little rim round it, and it fhould be kept
fall of oil. In a nice machine, a quarter of an inch of quick-
ſilver would effectually prevent all theſe inconveniences.
鲁
​The ſimpleft and moft economical form of this machine is
to have no balance or fecond ſteel-yard; but to make the hirit
fteel-yard EOF a lever of the first kind, viz. having the full-~
crum between O and F and allow it to project far beyond the
boys The long or outward arm of this lever is then divided"
into a ſcale of weights, commencing at the fide of the box.
496 -
MACHINES.
A counterpoife muft be chofen, fuch as will, when at the begin
ning of the ſcale, balance the fmalleſt load that will probably
be examined. It will be convenient to carry on this ſcale by
means of eke-weights hung on at the extremity of the lever, and
to uſe but one moveable weight. By this method the divifions
of the ſcale will have always one value. The beft arrangement
is as follows: place the mark o at the beginning of the fcale, and
let it extend only to 100, if for pounds; or to 112, if for cwts.;
or to 10, if for ftones; and let the eke-weights be numbered
1, 2, 3, &c. Let the lowest weight be marked on the beam.
This is always to be added to the weight fhewn by the opera-
tion. Let the eke-weights ftand at the end of the beam, and
let the general counterpoife always hang at o. When the cart
is put on the platform, the end of the beam tilts up. Hang on
the heavieſt eke-weight that is not fufficient to prefs it down.
Now complete the balance by fliding out the counterpoife.,
Suppoſe the conſtant load to be 312 lb. and that the counter-
poiſe ſtands at 86, and that the eke-weight is 9; we have the
Îoad = 986 + 312, 1298 lbs.
+312, =
WEIGHING-apparatus for goods. Account of a new patent
weighing-apparatus, invented by Mr. Hardie, of the Bengal
warehouſe.
Although the operation of weighing goods for ſale or pay-
ment of duty requires to be conducted in the way beft calcu-
lated to avoid miſtakes, yet we find that the ſeveral modes now
in uſe are fubject to frequent error through the complicated
proceſs of reckoning the totals of hundreds, quarters, and pounds
reſpectively, and retaining them in memory until called to the
book-keepers, generally amidst the buftle of porters, carmen,
cranemen, and others, at a time when the laborious exertions
of lifting the heavy weights on and off the board render the
weighers incapable of the cloſe attention which an accurate
performance of the operation demands.
Experience fhews, that in cafes of menfuration the uſe of a
fcale greatly contributes both to accuracy and diſpatch. Mr.
Hardie, therefore, by means of giving the weights a certain
form, has converted the operation of weighing into an opera-
tion of menfuration, for the purpoſe of obtaining the important
advantages of a ſcale in the following manner, viz.
Fig. 1. pl. XXXII. Plan of a board for the weights, about
38 inches by 32 inches, capable of weighing a ton, on which
are delineated two ſcales, one of larger divifions for the half-
hundred weights, and the other of fmaller divifions for the
pound weights.
Fig. 2. Plan of a half-hundred weight of caft-iron. A an
excavation forming the handle without projecting.
Fig. 3. Elevation of a half-hundred weight. A an ex-.
Hardie's Weighing Apparatus.
497
cavation forming the handle, with B a hole for lead to adjuſt
it.
Fig. 4 and 5. Plans of two half-hundred weights, fhewing
the manner they are placed to fill a fquare allotted for the
amount of one hundred weight.
Fig. 6. End elevation of the pound weights of brafs fitted
to the ſcale of one inch to a pound, the part: ſcooped out at
the fides being to receive the points of the fingers and thumb
to lift them without handles.
The larger weights are placed on their particular fcale be-
ginning at A on the left, and proceeding to the right, and ſo
on with each row. The firft hundred weight covers the blank
ſquare; the ſecond, the fquare marked 1; the third, that
marked 2; and ſo on, reſpectively.
The pound weights are placed on their particular ſcale, be-
ginning at B on the left, and proceeding to the right.
.
•
There is no fcale for the quarter weights, being at moſt
only two in number, namely, a half-hundred weight and a
quarter-hundred weight, of which the total is evident by mere
infpection, and which may be of any convenient ſhape, and
placed confpicuously above the two weights which complete
the hundreds. The totals of the hundreds and pounds are in-
dicated by the numbers next to the weights refpectively on the
right hand. Hence it follows that the amounts of the weights
on the board in hundreds, quarters, and pounds, are accurately
known to the weighers by mere inſpection; and that the book-
keeper has it in his power, with a glance, to diſcover whether
the weighers call the proper weight; which is impracticable by
the prefent modes of weighing. Boards for weighing ſmaller
quantities than a ton might be made on the fame principle, for
weights of the fame dimenfions, with fcales adapted to the
fize of the board. It is to be underſtood that the weighing is
performed without "ftriking the weights," which is the com-
mon phraſe for lifting all the weights off the board each opera-
tion: therefore an appropriate mode, according to fituation and
circumſtances, muſt be adopted to ſupport the board with the
weights, while the package weighed is removing from its board
to give place to another; when, in fome inftances, the large-
nefs of the package bulges out the ropes of the board, render-
ing it neceffary to raiſe the board with the weights a little
higher In fome cafes the prop, fig. 7., will anfwer the pur-
pofe, the pinion being moved by a winch. In other cafes the
lever, fig. 8., might be adopted, and, in particular inſtances, the
whole beam and fcales, with the goods and weights, might be
raiſed and lowered by the lever, fig. 9., affifted by the wheel
and pinion.

VOL. II.
K
498
MACHINES.
1
4
The greateſt individual weight, for the purpoſe of being
portable, is a half-hundred weight. The common balance is
uſed with this weighing apparatus, as it proves to be the beſt
kind of balance known; being more true for very ponderous
bodies than the ſteelyard, which is fometimes uſed where great
accuracy is not required. When a very light package is to be
weighed with a board adapted for a much greater weight, a
hook and eye are to be uſed at each of the two cords, fufpend-
ing the board for the weights at A and C, in order to fhorten
them and prevent the board from leaning to one fide. Where
a chain inſtead of a rope is uſed, one of its links will ferve as
an eye to the hook.
I WHEELS acting upon each other are the inftruments by
which the tranſmiſſion of mechanic force from one part of a
fyftem of machinery to another is commonly and conveniently
effected. The due connection of the moving parts is accom.
plished, either by the mutual action of proper formed teeth
(fee the article TEETH in this volume), by ftraps or endleſs
bands, or by the friction of one face of a wheel againſt another.
The latter method has, when adopted, been generally in ſmall
light works, where the preffure upon the different parts of the
machinery is never confiderable. Mr. Nicholfon faw a drawing
of a fpinning-wheel for children, at a charity ſchool, in which
a large horizontal wheel with a flip of buff-leather glued on its
upper furface, near the outer edge, drove 12 fpindles, at which
the fame number of children fat. The fpindles had each a
fmall roller likewife faced with leather, and were capable, by.
an eafy and inftantaneous motion, of being thrown into con-
tact with the large wheel at pleaſure. Each child, therefore,
could throw her own part of the apparatus into work, or cauſe
it to ftop, as often or as long as the pleafed. The winding
bobbins for yarn at the cotton-mills operate on the fame fimple
and elegant principle, which poffeffes the advantage of drawing
the thread with an equal velocity, whatever may be the quan-
tity on the bobbin, and cannot break it. We are not aware
that the fame mode of communication has been adopted in
large work, except in a faw-mill, by Mr. Taylor, of South-
ampton. In this the wheels act upon each other by the contact
of the end grain of wood inftead of cogs: the whole makes
very little noiſe, and wears very well,it has now been in ufe
nearly twenty years. There is, of confequence, a contrivance to
make the wheels bear firm againſt each other, either by wedges
at the fockets, or by levers. This principle and method o
tranfmitting mechanic power certainly deferves every attention
particularly as the cuſtomary mode by means of teeth requires
much fkill and care in the execution; and, after all, wants
fréquent repairs.

Wind-mills.
499
WIND-MILL, as its name imports, is a mill for any purpoſe,
which receives its motion from the impulſe of the wind.
The internal ſtructure of wind-mills is, of courſe, much
the fame as thoſe of water-mills: the difference between them
lying chiefly in the exterior apparatus, the one to receive the
force of the water, the other that of the wind. The external
apparatus in a wind-mill confifts chiefly of the fails or vanes,
which are commonly four, placed in nearly a vertical poſition,
and as they turn giving a rotatory motion to an axis inclining
but a little from the horizon. The uſual conſtruction and ap-
pearance of the fails are too well known to need any minute
deſcription.
As the direction of the wind is very uncertain, it becomes
neceſſary to have fome contrivance for turning the fails towards
it, in order to receive its force in whatever way it may turn ;
and for this purpoſe two general methods are in uſe. In the
one, the whole machine is ſuſtained upon a moveable arbor or
axis, perpendicular to the horizon, which is fupported by a
ftrong ftand or foot very firmly fixed in the earth; and thus,
by means of a lever, the whole machine may be turned round
as occafion requires. In the other method, only the roof, which
is circular, can be turned round by means of a lever and rollers,
upon which the circular roof moves. This laft kind of wind-
mill is moſtly built of ſtone, in the form of a round turret,
having a large wooden ring on the top of it, above which the
roof, which muſt likewiſe be of wood, moves upon rollers, as
has been already mentioned. To effect this motion the more
eafily, the wooden ring which lies on the top of the building
is furniſhed with a groove, at the bottom of which are placed
a number of brafs truckles at certain diftances, and within the
groove is placed another ring, by which the whole roof is
fupported. Beams are connected with the moveable ring, and
a rope is faftened to one of them, which at the lower ex-
tremity is fitted to a windlaſs or axis in peritrochio; and this
rope being drawn through an iron hook fixed at the ground,
and the windlafs turned round, the fails and roof will be turned
round alſo, in order to catch the wind in any direction. Both
theſe methods of conftruction have their advantages and dif-
advantages. The former is the leaſt expenſive, as the whole
may be made of wood, and of any form that is thought proper;
while the other requires a more coftly building and the roof
being round, the building muſt alfo be fo; while the former can
be made of any form, but has the inconvenience of being liable
to be carried off altogether by a very high wind.
In art. 50, of the introductory part of this volume, we have
ftated the principal refults of the experiments and reſearches of
K2
500
MACHINES.
Smeaton, relative to the ſhape, pofition, and magnitude of fails,
when four is the number adopted. To thefe it might be proper
to add here fome of the remarks which have been made by
Parent, Euler, and other philofophers: but as none of them,
except a few by Coulumb, which will be mentioned preſently,
appear any way comparable in point of practical utility with
thofe of Smeaton; and as they include, befides, fome very in-
tricate inveſtigations; we conceive they may be omitted without
any ſerious diſadvantage to the ſtudent. We fhall now, there-
fore, proceed to defcribe a wind-mill, varying in many reſpects
from the common conftruction, invented by Mr. James Verrier,
who received a premium from the Society of Arts, for this ufe-
ful ſpecimen of his ingenuity.
I
This mill, which has 8 quadrangular fails, is reprefented in
fig. 7. pl. XXXVII. where AAA are the three principal poſts,
27 feet 7 inches long, 22 inches broad at their lower ex-
tremities, 18 inches at their upper, and 17 inches thick. The
column B is 12 feet 24 inches long, 19 inches in diameter at
its lower extremity, and 16 inches at its upper: it is fixed in
the centre of the mill, paffes through the firſt floor E, having
its upper extremity fecured by the bars GG. EEE are the
girders of the firft floor, one of which only is feen, being 8
feet 3 inches long, 11 inches broad, and 9 thick: they are
mortifed into the pofts AAA and the column B, and are about
8 feet 3 inches diſtant from the ground floor. DDD are three
poſts, 6 feet 4 inches long, 9 inches broad, and 6 inches thick :
they are mortifed into the girders EF of the firſt and ſecond
floor, at the diſtance of 2 feet 4 inches from the pofts A, &c.
FFF are the girders of the fécond floor, 6 feet long, 11 inches
broad, and 9 thick: they are mortifed into the pofts A, &c.
and rest upon the upper extremities of the pofts D, &c. The
three bars GGG are 3 feet 1 inches long, 7 inches broad, and
3 thick: they are mortifed into the poſts D and the upper end
of the column B, 4 feet 3 inches above the floor, P is one of
the beams which fupport the extremities of the bray-trees or
brayers its length is 2 feet 4 inches, its breadth 8 inches, and
its thickneſs 6 inches. I is one of the bray-trees into which
the extremity of one of the bridge-trees K is mortifed.
mortifed. Each
bray-tree is 4 feet 9 inches long, 91 inches broad, and 7 thick;
and each bridge-tree is 4 feet 6 inches long, 9 inches broad,
and 7 thick, being furniſhed with a piece of brafs on its upper
furface to receive the under pivot of the mill-ſtones. LL are
two iron fcrew-bolts, which raiſe or deprefs the extremities of
the bray-trees. MMM are the three mill-ftones, and NNN the
iron ſpindles or arbors on which the turning mill-ftones are
fixed. O is one of three wheels or trundles which are fixed
Wind-mills.
501
on the upper ends of the fpindles NNN: they are 16 inches in
diameter, and each is furniſhed with 14 ftaves. fis one of the
carriage-rails on which the upper pivot of the fpindle turns,
and is 4 feet 2 inches long, 7 inches broad, and 4 thick. It
turns on an iron bolt at one end, and the other end flides in a
bracket fixed to one of the joifts, and forms a mortife in which
a wedge is driven to fet the rail and trundle in or out of work:
t is the horizontal ſpur-wheel that impels the trundles; it is 5
feet 6 inches diameter, is fixed to the perpendicular fhaft T,
and is furniſhed with 42 teeth. The perpendicular fhaft T is
9 feet 1 inch long, and 14 inches in diameter, having an iron
Ipindle at each of its extremities: the under fpindle turns in a
brafs block fixed into the higher end of the column B; and
the upper ſpindle moves in a brafs plate inferted into the lower
furface of the carriage-rail C. The fpur-wheel r is fixed on
the upper end of the fhaft T, and is turned by the crown
wheel v on the windshaft c; it is 3 feet 2 inches in diameter,
and is furniſhed with 15 cogs. The carriage-rail C, which is
fixed on the fliding kerb Z, is 17 feet 2 inches long, I foot
broad, and 9 inches thick. YYQ is the fixed kerb, 17 feet 3
inches diameter, 14 inches broad, and 10 thick, and is mortifed
into the pofts AAA, and faſtened with fcrew-bolts. The
fliding kerb Z is of the fame diameter and breadth as the fixed
kerb, but its thickneſs is only 7 inches. It revolves on 12
friction-rollers fixed on the upper furface of the kerb YYO,
and has 4 iron half-ftaples, Y, Y, &c. faftened on its outer
edge, whofe perpendicular arms are 10 inches long, 2 inches.
broad, and 1 inch thick, and embrace the outer edge of the
fixed kerb, to prevent the fliding one from being blown off.
The capfills X, V, are 13 feet 9 inches long, 14 inches broad,
and i foot thick: they are fixed at each end with strong iron
fcrew-bolts to the fliding kerb, and to the carriage-rail C. On
the right hand of w is feen the extremity of a cross-rail, which
is fixed into the capfills X and V by ftrong iron bolts: e is a
bracket 5 feet long, 16 inches broad, and to inches thick; it
is buſhed with a ſtrong braſs collar, in which the inferior ſpindle
of the windshaft turns, and is fixed to the cross-rail w: bis
another bracket 7 feet long, 4 feet broad, and 10 inches thick;
it is fixed into the fore ends of the capfills, and, in order to
embrace the collar of the windshaft, it is divided into two parts
which are fixed together with fcrew-bolts. The windfhaft'c is
15 feet long, 2 feet in diameter at the fore end, and 18 inches
at the other its pivot at the back end is 6 inches diameter;
and the fhaft is perforated, to admit an iron rod to paſs eafily
through it. The vertical crown-wheel is 6 feet in diameter,
and is furniſhed with 54 cogs which drive the fpur wheel r

602
MACHINES.
उ
The bolfter d, which is 6 feet 3 inches long, 13 inches broad,
and half a foot thick, is faſtened into the cross-rail w, directly
under the centre of the windſhaft, having a brafs pulley fixed
at its fore end. On the upper furface of this bolfter is a groove
In which the fliding bolt R moves, having a braſs ftud at its
føre end. This fliding bolt is not diſtinctly ſeen in the figure,
but the round top of the brafs ftud is viſible below the letter h:
the iron rod that paffes through the windshaft bears againſt this
brafs ftud. The fliding bolt is 4 feet 9 inches long, 9 inches
broad, and of a foot thick. At its fore end is fixed a line
which paffes over the brafs pulley in the bolfter, and appears at
a with a weight attached to its extremity, fufficient to make the
fails face the wind that is ftrong enough for the number of
ftones employed; and when the preffure of the wind is more
than fufficient, the fails turn on an edge, and prefs back the
fliding bolt, which prevents them from moving with too great
velocity; and as foon as the wind abates, the fails, by the
weight a, are preffed up to the wind till its force is fufficient to
give the mill a proper degree of velocity. By this apparatus
the wind is regulated and juftly proportioned to the reſiſtance
or work to be performed; an uniformity of motion is alſo ob-
tained, and the mill is lefs liable to be deftroyed by the rapidity
of its motion.
That the reader may underſtand how theſe effects are pro-
duced, we have repreſented, in fig. 8., the iron rod, and the
arms which bear againſt the vanes: ab is the iron rod which
paffes through the windfhaft e in fig. 7.; b is the extremity
which moves in the brafs ftud that is fixed upon the fliding
bolt; a i, a i, &c. are the croſs-arms at right angles to a h,
whofe extremities i, i, fimilarly marked in fig. 7., bear upon the
edges of the vanes. The arms a i are 6 feet long, reckoning
from the centre a, 1 foot broad at the centre, and 5. inches
thick; the arms n, n, &c. that carry the vanes or fails, are 18
feet long, their greateſt breadth is 1 foot, and their thickneſs
9 inches, gradually diminiſhing to their extremities, where they
are only 3 inches in diameter. The 4 cardinal fails, m, m,m,m,
are each 13 feet long, 8 feet broad at their outer ends, and 3
feet at their lower extremities; p, p, &c. are the four affiftant
fails which have the fame dimenfions as the cardinal ones, to
which they are joined by the line SSSS. The angle of the
fail's inclination when firft oppofed to the wind is 45 degrees,
and regularly the fame from end to end.
It is evident from the preceding deſcription of this machine,
that the windſhaft c moves along with the fails: the vertical
crown-wheel v impels the ſpur-wheel r, fixed upon the axis T,
which carries alfo the fpur-wheel t. This wheel drives the
Wind-mills.
503
three trundles H, one of which only is feen in the figure,
which being fixed upon the ſpindles N, &c. communicate mo-
tion to the turning mill-ftones.
That the wind may act with the greateſt efficacy upon the
fails, the windſhaft or principal axis muſt always have the fame
direction as the wind. But as this direction is perpetually
changing, fome apparatus is neceffary for bringing the windſhaft
and fails into their proper pofition. As both the common
methods of adjuſting the windshaft require human affiftance,
it would be very defirable that the fame effect ſhould be pro-
duced folely by the action of the wind. This may be done by
fixing a large wooden vane or weathercock at the extremity of
a long horizontal arm which lies in the fame vertical plane with
the windshaft. By this means, when the ſurface of the vane
and its diſtance from the centre of motion are fufficiently great,
a very gentle breeze will exert a fufficient force upon the vane
to turn the machinery, and will always bring the fails and
windſhaft to their proper pofition. This weathercock, it is
evident, may be applied either to machines which have a move-
able roof, or to those which revolve upon a vertical arbor.
Prior to the French revolution, wind-mills were more nu-
merous in Holland and the Netherlands than in any other part
of the world, and there they ſeem to have been brought to à
very high ftate of perfection. This is evident not only from
the experiments of Mr. Smeaton, from which it appears that
fails weathered in the Dutch manner produced nearly a maxi-
mum effect, but alſo from the obſervations of the celebrated
Coulomb. This philofopher examined above fifty wind-mills in
the neighbourhood of Lifle, and found that each of them per-
formed nearly the fame quantity of work when the wind moved
with the velocity of 18 or 20 feet per fecond, though there
"were fome trifling differences in the inclination of their wind-
fhafts, and in the difpofition of their fails. From this fact,
Coulomb juſtly concluded that the parts of the machine muſt
have been fo difpofed as to produce nearly a maximum effect.
t
In the wind-mills on which Coulomb's experiments were
made, the distance from the extremity of each fail to the
centre of the windſhaft or principal axis was 33 feet. The
fails were rectangular, and their width was a little more than
6 feet, 5 of which were formed with cloth ftretched upon a
frame, and the remaining foot confifted of a very light board.
The line which joined the board and the cloth formed, on the
fide which faced the wind, an angle fenfibly concave at the
commencement of the fail, which diminiſhed gradually till it
vaniſhed at its extremity. Though the furface of the cloth
was curved, it may be regarded as compofed of right lines
504
MACHINES.
perpendicular to the arm or whip which carries the frame, the
extremities of theſe lines correfponding with the concave angle
formed by the junction of the cloth and the board. Upon
this fuppofition theſe right lines at the commencement of the
fail, which was diſtant about 6 feet from the centre of the
windſhaft, formed an angle of 60 degrees with the axis or
windſhaft, and the lines at the extremity of the wing formed
an angle increaſing from 78 to 84 degrees, according as the
inclination of the axis of rotation to the horizon increaſed
from 8 to 15 degrees; or in the millwright's terms, the greateſt
angle of weather was 30 degrees, and the leaft varied from 12
to 6 degrees, as the inclination of the windſhaft varied from 8
to 15 degrees. A pretty diftinct idea of the furface of wind-
mill fails may be conveyed by conceiving a number of triangles
ſtanding perpendicular to the horizon, in which the angle con-
tained between the hypothenufe and the bafe is conſtantly
diminishing; the hypothenufe of each triangle will then be in
the fuperficies of the vane, and they would form that fuperficies
if their number were infinite.
Mr. Richard Hall Gower, a gentleman in the fea fervice of the
Eaft India Company, made fome judicious experiments with a
view of determining the proper angles of weather which ought
to be given to the vanes of a vertical wind-mill: his general con-
clufion is, that each vane fhould be a fpiral, generated by the
circular motion of a radius, and of a line moving at right angles
to the plane of a circular motion. The conftruction he de-
duces from his enquiries is fimple, being this:
The length, breadth, and angle of weather at the extremity
of a vane being given; to determine the angles of weather at
different diftances from the centre.
Let AB, fig. 9., pl. XXXV. be the length of the vane; BC its
breadth; and BCD the angle of weather at the extremity of the
vane, equal to 20 degrees. With the length of the vane AB,
and breadth BC, conftruct the ifofceles triangle ABC: from the
point B draw BD perpendicular to CB, then BD is the proper
depth of the vane.
Divide the line AB into any number of parts (five, for
inſtance); at thoſe divifions draw the lines 1E, 2F, 3G, and
4H, parallel to the line BC; alfo, from the points of divi-
fion 1, 2, 3, and 4, draw the lines II, 2K, 3L, and 4M,
perpendicular to 1E, 2F, 3G, &c. all of them equal in length
to BD. Join EI, FK, GL, and HM: then the angles EI,
2FK, 3GL, and 4HM, are the angles of weather at thofe divi-
fions of the vane; and if the triangles be conceived to ftand
perpendicularly to the plane of the paper, the angles I, K,
L, M, and D, becoming the vertical angles, the hypothenufe


Horizontal Wind-mills.
505
of theſe triangles will, as before ſuggeſted, give a perfect idea
of the weathering of the vane as it recedes from the centre.
Phil. Mag. No. 14.
Some theoretical remarks on this fubje& are inſerted in
vol. i. art. 547-
Mr. John Bywater, of Nottingham, took out a patent in
September, 1804, for a method of clothing and unclothing
the fails of windmills while in motion (provided they are made
after the Dutch manner), by which the mill may be clothed
either in whole or in part, in an eafy and expeditious manner,
by a few revolutions of the fails, whether they are going falt
or flow, leaving the ſurface ſmooth, even, and regular in breadth
from top to bottom; and in like manner the cloth, or any part,
of it, may be rolled or folded up to the whip at pleaſure, by
fimple and durable machinery. The invention confifts in either
folding or unfolding the cloths while the fails are in motion, by
means of cylinders or rollers of any ſhape, as long as the fails,
with a toothed wheel at one end of each, working either directly
or indirectly into two wheels without arms, which are hung fo
as to turn upon a ring of iron fixed to the fhaft-head clofe
behind the back-stocks, and which may be alternately stopped;
fo that the wheels at the ends of the cylinders muſt directly, or
by means of a connection of wheels called carriers or nuts,
work into them by revolving round them through the power of
the wind acting on the fails; fo that the cylinders muſt neceſ-
farily turn round, and roll up or fold, or unroll or unfold the
cloth which is fastened to them, according to the reſpective
wheel without arms, which is ſtopped for that purpoſe. Such
is the general contrivance: a detailed account, with figures,
may be ſeen in the Repertory of Arts, &c. vol. vi. N. S.

To
Horizontal WIND-MILLS. A variety of opinions have been
entertained reſpecting the relative advantages of horizontal and
vertical wind-mills. Mr. Smeaton, with great juftice, gives a
decided preference to the latter; but when he afferts that hori-
zontal wind-mills have only or of the power of vertical
ones, he certainly forms too low an estimate of their power.
Mr. Beatſon, on the contrary, who has received a patent for the
conſtruction of a new horizontal wind-mill*, feems to be
prejudiced in their favour, and greatly exaggerates their com-
parative value. From an impartial inveſtigation, it will probably
appear that the truth lies between theſe two oppofite opinions;
but before entering on this difcuffion, we muſt firſt conſider the
nature and form of horizontal wind-mills.
In fig. 9. of plate XXXVII. CK is the vertical axis or the
* See Repertory of Arts, &c. vol. ii. pa. 13. N. S.
506
MACHINES.
I
ነ
•
wind-fhaft, which moves upon pivots. Four croſs-bars, CA,
CD, IB, FG, are fixed to this arbor, which carry the frames
APIB, DEFG. The fails AI, EG, are ftretched upon theſe
frames, and are carried round the axis CK, by the perpendicular
impulſe of the wind. Upon the axis CK a toothed wheel is
fixed, which gives motion to the particular machinery that is
employed. In the figure, only two fails are reprefented; but
there are always other two placed at right angles to theſe.
Now, let the fails be expofed to the wind, and it will be evident.
that no motion will enfue; for the force of the wind
upon the
fail AI is counteracted by an equal and oppofite force upon
the fail EG. In order, then, that the wind may communicate
motion to the machine, the force upon the returning fail EG
muſt either be removed by fcreening it from the wind, or di
miniſhed by making it preſent a lefs furface when returning
against the wind. The first of thefe methods is adopted in
Tartary, and in fome provinces of Spain; but is objected to by
Mr. Beatſon, from the inconvenience and expence of the
machinery and attendance requifite for turning the ſcreens into
their proper pofitions. Notwithſtanding this objection, how-
ever, this is probably the beſt method of diminiſhing the action
of the wind upon the returning fails; for the moveable ſcreen
may eaſily be made to follow the direction of the wind, and
affume its proper pofition, by means of a large wooden weather-
cock, without the aid either of men or machinery. It is true,
indeed, that the refiftance of the air in the returning fails is
not completely removed; but it is at leaſt as much diminiſhed
as it can be by any method hitherto propoſed. Befides, when
this plan is reforted to, there is no occafion for any moveable
flaps and hinges, which muft add greatly to the expence of
every other method.
The mode of bringing the fails back againſt the wind, which
Mr. Beatfon invented, is, perhaps, the fimpleft and beſt for that
end. He inakes each fail AI to confift of 6 or 8 flaps or vanes,
AP b 1, b 1 c 2, &c. moving upon hinges repreſented by the
dark lines, AP, b 1, ¢ 2, &c. fo that the lower fide b 1 of the
firſt flap wraps over the hinge or higher fide of the ſecond flap,
and ſo on. When the wind, therefore, acts upon the fail AI,
each flap will prefs upon the hinge of the one immediately
below it, and the whole furface of the fail will be expoſed to its
action. But when the fail AI returns againſt the wind, the
flaps will revolve round upon their hinges, and preſent only
their edges to the wind, as is reprefented at EG, fo that the re-
fiftance occafioned by the return of the fail muſt be greatly
diminiſhed, and the motion will be continued by the great
fuperiority of force exerted upon the fails in the poſition AI,

Horizontal Wind-mills.
507
1
I
2
In computing the force of the wind upon the fail AI, and the
refiftance oppoſed to it by the edges of the flaps in EG, Mr.
Beatfon finds, that when the preffure upon the former is 1872
pounds, the refiſtance oppofed by the latter is only about 36
pounds, or part of the whole force; but he neglects the
action of the wind upon the arms, CA, &c. and the frames
which carry the fails, becauſe they expofe the fame furface in
the pofition AI, as in the poſition EG. This omiffion, how-
ever, has a tendency to miſlead us in the prefent cafe, as we
ſhall now fee; for we ought to compare the whole force exert-
ed upon the arms, as well as the fail, with the whole refiftance
which theſe arms and the edges of the flaps oppofe to the
motion of the wind-mill. By infpecting fig. 9., it will appear,
that if the force upon the edges of the flaps, which Mr. Beatſon
fuppofed to be 12 in number, amounts to 36 pounds, the force
fpent upon the bars CD, DG, GF, FE, &c. cannot be less than
60 pounds. Now, fince thefe bars are acted upon with an
equal force, when the fails have the pofition AI, 1872+66=1932
will be the force exerted upon the fail AI and its appendages,
while the oppofite force upon the bars and edges of the flaps
when returning againft the wind will be 36460= go pounds,
which is nearly of 1932, inftead of as computed by Mr.
Beatfon. Hence we may fee the advantages which will pro-
bably arife from uſing a fereen for the returning fail inftead of
moveable flaps, as it will preferve not only the fails, but the
arms and the frame which fupport it, from the action of the
wind *.

20
I
32
8
1
TO
Mr. Brewfter makes alfo the following remarks on the com-
parative power of horizontal and vertical wind-mills. It has
been already ſtated, that Mr. Smeaton rather under-rated the
former while he maintained that they have only or the
power of the latter. He obferves, that when the vanes of a hori
zontal and a vertical mill are of the fame dimenfions, the power
of the latter is 4 times that of the former, becaufe, in the first
cafe, only one fail is acted upon at once, while, in the ſecond cafe,
all the four receive the impulſe of the wind. This, however, is
not ſtrictly true, fince the vertical fails are all oblique to the
direction of the wind. Let us fuppofe that the area of each
fail is 100 ſquare feet; then the power of the horizontal fail
may be called foo × fin. 70° (which is the common angle of
*The fails of horizontal wind-mills are fometimes fixed like float-
boards on the circumference of a large drum ór cylinder. Theſe fails
move upon hinges fo as to ftand at right angles to the drum, when they
are to receive the impulſe of the wind; and when they return againſt
it, they fold down upon its circumference. See Repertory of Arts,
vól. 6.
1
508
MACHINES.
I
1
•
4.409
leſs
inclination) 88 nearly; but fince there are 4 vertical fails,
the power of them all will be 4 × 88 = 352: ſo that the power of
the horizontal fail is to that of the 4 vertical ones as I to 3.52,
and not as 1 to 4, according to Mr. Smeaton. But Mr. Smeaton
alſo obſerves, that if we confider the further difadvantage which
arifes from the difficulty of getting the fails back against the
wind, we need not wonder if horizontal wind-mills have
only about or of the common fort. We have already
feen that the refiftance occafioned by the return of the fails
amounts to of the whole force which they receive; by ſub-
tracting, therefore, from, we ſhall find that the power of
horizontal wind-mills is only 4%, or little more than
than that of vertical ones. This calculation proceeds upon a fup-
pofition that the whole force exerted upon vertical fails is
employed in turning them round the axis of motion; whereas
a confiderable part of this force is loft in preffing the pivot of
the axis or wind-fhaft against its gudgeon. Mr. Smeaton has
overlooked this circumftance, otherwife he could never have
maintained that the power of 4 vertical fails was quadruple the
power of one horizontal fail, the dimenſions of each being the
fame. Taking this circumftance into the account, we cannot
be far wrong in ſaying that, in theory at leaſt, if not in practice,
the power of a horizontal wind-mill is about or of the
power of a vertical one, when the quantity of furface and the
form of the fails are the ſame, and when all the parts of the hori-
zontal fails have the fame diſtance from the axis, of motion as
the correſponding parts of the vertical fails. But if the horizon-
tal fails have the pofition AI, EG, in fig. 9, inſtead of the
pofition CA dm, CD on, their effect will be greatly increaſed,
though the quantity of furface is the fame, becauſe the part
CP 3 m being transferred to BI 3 d, has much more power to
turn the fails. Having this method, therefore, of increafing
the effect of horizontal fails, which cannot be applied to vertical
ones, we would encourage every attempt to improve their con-
ſtruction, as not only laudable in itſelf, but calculated to be of
effential utility in a commercial country, Brewster's Ferguſon,
vol. ii. See also CONDENSER of Forces in this vol.
4

An ingenious horizontal mill by Meffrs. Claude François and
Jean Claude du Boft, is deſcribed in Recueil des Machines et
Inventions approuvées par l'Acad. Roy. des Sciences. tom. vii.
WIPERS, in fome kinds of machinery, as oil-mills, powder-
mills, fulling-mills, are pieces projecting generally from horizon-
tal axles, for the purpofe of raifing ftampers, pounders, or
heavy piſtons, in vertical directions, and then leaving them to
fall by their own weight.
When the wipers are only fmall cylinders projecting per-
Wipers.
509
pendicularly from the furface of the horizontal arbor on which
they are fixed, the force with which they elevate the reſpective
ftampers will not act uniformly during the whole time in which.
they are rifing: yet a uniformity of force and velocity is gene-
rally a defirable thing to be attained, and may always be effected
by affigning a proper form to the wipers and communicating
parts. A few directions for the determination of the due fhape
are here given for the uſe of the mechanic.
Suppofe that in fig. 15. pl. XXXII. the circle defcribed about
the centre a is a vertical ſection of the arbor on which the
wipers are placed; and that the line b a fhews the diftance of
an arm of one of the ſtampers from the centre a: deſcribe with
centre a and radius ab an arc bed...k, on which ſet off the
equal parts bc, cd, de, ef, &c. as ſmall as can conveniently be
done: draw the radii ac, ad, a e, &c. on the extremities of
which erect perpendiculars equal to the refpective arcs c b, d b,
eb, &c. and continue them until the laft of them Nk is equal
to the height to which the ſtamper is to be elevated: this being
done, draw the curve Nb through the extremities of the ſeveral
perpendiculars to the radii, it will form an involute of the
circular arc bk (which indeed may be either conſtructed thus, or
in the ufual way at once, with a thread), and will be the figure
that may be given to the upper ſurface of a wiper, when it is to
give a uniform motion to the riſing ſtamper. For as all the
radii of curvature of Nb are tangents to the circumference of
the generating circle bk, the arm Mb of the ſtamper can never
touch the wiper in more than one point (or horizontal line,
whofe fection is a point). When it is the point 8, for example,
the radius ad which answers to the tangent dd will be horizon-
tal; of confequence &d will be perpendicular to the horizon,
and its extremity & alone will touch Mb; dd at the fame time
will be the height to which the ftamper will be raiſed. As
the fame thing will obtain at all the points where the arm M
touches the wiper, the arm of the lever which communicates
the force will be conftantly the fame, that is, it will be, equal to
a b; and the arm of the lever at which the reſiſtance acts being
always equal to M b, it follows that the ſtampers will be raiſed
entirely with a uniform force, and in a direction perpendicular
to the horizon.
To determine the poſition of the point k, or the magnitude of
the arc kb, the diſtance ab muſt be known, and the circumfer-
ence e of the circle found correfponding to this radius: then
make the line L equal to the height to which the ſtamper is to
be raiſed; and fay as C to L, fo is 360° to the degrees and parts
in the arc bk or the angle bak: draw from a the line b k, mak¬
ing with ba the angle thus found, and k is then aſcertained.

510
MACHINES.
Divide the line L and the arc bk into an evenly even number of
parts, fet off from the points c, d, e, &c. of the arc the tangents
in arithmetical progreffion, and equal to the refpective parts on
the line L meafured from one of its extremities; and thus the
curve Nb will be traced with great facility. The ſhape of
the wipers, as they are fixed fingly in the arbor, will alſo
appear from the fame figure.
In the figure we have reprefented only one ftamper and one
wiper: but it often happens that 6, 8, 10, or more ftampers are
worked by wipers projecting from one horizontal arbor: in this
cafe the wipers fhould be fo diftributed that the refiftance
arifing from all the ftampers fhall be as nearly as poffible a con-
ftant quantity to effect this, let all the ftampers be placed at
equal diſtances in a line parallel to the axle or arbor; let alſo a
ſingle ſpiral run once completely round from one end of the
arbor to the other, and let the wipers be at equidiftant poſitions
on this ſpiral; then will all the ſtampers be raiſed and permitted
to fall at equidiftant intervals during every rotation of the arbor.
Sometimes a ſmall roller is fixed to the extremity of the arm
Mb, to diminish the friction; and in this cafe a curve muſt be
drawn within N b, parallel to it, and at a distance equal to the
radius of the roller; this new curve exhibiting the shape and
pofition of the upper face of the wiper.

:
In fome machines ftampers or piftons are raiſed by giving a
proper curvature to the arm M b, and fixing the roller upon
the extremity of a bent bar, whofe end is in the direction of a
radius produced: in this cafe the arm muſt be ſhaped into part
of a cycloid, the radius of whofe generating circle is equal to
the distance from the extremity of the wiper to the centre of
the arbor; and this curve muſt be placed at the outer part of
the rollers, to form the lower face of the arm.
The wiper may often be formed with great propriety like
the Archimedean fpiral, and thus raiſe a ftamper with a uni-
form motion. To this end let AH (fig. 12. pl. XXXII.) be a
wheel put into motion by any power which is fufficient to taife
the weight MN, by its extremity O, from O to e, in the fame.
time that the wheel moves round one fourth of its circumfer-
ence, it is required to fix upon its rim a wing OBCDEH which
fhall produce this effect with an uniform effort. Divide the
quadrant OH into any number of equal parts Om, mn; &c.
the more the better, and oe into the fame number ob, bc, c d,
&c. and through the points m, n, p, H draw the indefinite lines
AB, AC, AD, AE, and make AB equal to Ab, AC to A c, AD
to A d, and AE to Ae; then through the points O, B, C, D, E,
draw the curve OBCDE, which is a portion of the ſpiral of
Archimedes, and will be the proper form for the wiper or wing
Yarn-mill.
511
OHE. It is evident that when the point m has arrived at O,
the extremity of the frame will have arrived at b, becauſe AB
is equal to A b; and for the fame reaſon, when the points n, p,
H, have fucceffively arrived at O, the extremity of the frame
will have arrived at the correfponding points c, d, e.
The
motion therefore will be uniform, becauſe the ſpace deſcribed
by the weight is proportional to the fpace defcribed by the
moving power, Ob being to O cas Om to On. If it be re-
quired to raiſe the weight MN with an accelerated or retarded
motion, we have only to divide the line Oe, according to the
law of acceleration or retardation, and divide the curve ÖBCDE…
ás before. It is fcarcely neceffary to add, that the vertical bar
between N and M must be kept from lateral deviations, by.
Being made either to run between rollers, or to flide in a groove.
We have all along ſuppoſed that the wheel or the arbor which
carries the wipers turns upon a horizontal axis: we might
exhibit methods by which ſtampers, &c. could be raiſed uni-
formly by wheels moving at right angles to the plane in which
theſe ſtampers move; but fuch methods are intricate and not,
much to be recommended, as they may always be avoided by a
fmall addition to the machinery, or fome flight modifications.
in its general diſtribution.
YARN, in general, denotes the manufacture of wool,.
hemp, flax, cotton, &c. converted into filaments or threads,
which are ſubſervient to a variety of uſeful purpoſes.
+
Formerly all yarn was fpun or twifted by means of the,
diſtaff, or the wheel; but lately, the ingenuity of mechanics, and
the powers of machinery, have been called in aid to facilitate
that operation. In June, 1787, Meffrs. John Kendrew and
Thomas Porthouſe obtained a patent for their invention of a
machine, upon new principles, defigned to ſpin yarn from
hemp, tow, flax, or wool.-As this privilege is now expired,
and ſuch contrivance promifes to be very uſeful in the woollen:
as well as other manufactures, we ſhall fubjoin an account of
the conſtruction, as extracted from the ſpecification inſerted in
the Repertory of Arts and Manufactures.
This machine may be worked by water, or as a horſe-mill, or
in any other way, and is made and uſed in the following manner:
There is a cylinder, marked A in the drawing, fig. 1. plate
XXXVII., three feet diameter, and ten inches broad, made of
dry wood or métal, turned true, and covered on its circumfer-
ence with a fmooth leather, upon which are placed the rollers:
marked D, covered with leathers and ſupported in their fitua-
tions by the flits in the covered piece of wood marked K, in
which the iron axes of the rollers turn, but fuffers them to preſs
on the wheel marked A. There muſt be another piece fimilar
4
512
MACHINES.
to the above, to fupport the other end of the rollers. Thefe
rollers are of different weights. The upper roller marked DI
is two ſtone, the reft decreafing to the laft, which is only two
pounds weight and one half. There is an iron fluted roller,
marked F, furniſhed with a toothed wheel at each end, and a
wood one, marked G, covered with cloth, and over it a ſmooth
leather. There is an affifting roller, marked H, of fluted iron.
Theſe rollers are fupported by their axes, turning in the flit,
marked 2, of the piece of wood, marked M (fig. 3.), which is
here feparated from the end of the frame marked 8, to fhew the
rollers and wheelwork. The rollers marked G and F are
fqueezed together by means of the lever marked p, and its
weight marked w (fig. 3.). The roller marked H is preffed to
the mark G by its axis, acting upon the inclined plane marked x
(fig. 3.). There is a rubbing roller covered with woollen cloth,
and on its axis is a ſmall wheel, marked I, driven by the wheel
marked S. This roller refts upon the roller marked G, and by
its motion prevents any dirt or fibres from adhering to it.
There is a cloth, marked N, revolving over two rollers marked
O, O, which has motion given to it from the wheel marked C,
by means of another wheel marked P. This cloth moves at the
fame rate as the furface of the wheel marked A. There is a
fupporter, marked Y, of the axis of the wheels marked O, P,
but is removed, in order to fhew them; it is fixed by its tenons
in the mortifes marked Z, Z. The roller marked B is kept in
action by its endeavour to flip down the inclined plane at the
top of the piece marked Y, thereby preffing againſt the revolving
cylinder; and another piece, fimilar to this, must be underſtood.
to fupport the other end of the roller's axis. By the fide of this.
revolving cloth is a table placed, of the fame length and breadth
as the cloth is, to which belong two fmooth cloths or leathers, of
the fame fize as the table. The machine being thus prepared,
the attendant or workman muſt take a quantity of hemp, tow,
flax, or wool, more or lefs, according to the fineneſs of the
thread to be made, and lay or fpread it evenly upon one of the
fmooth cloths on the table; then place it on the revolving cloth
marked N, motion being communicated to the roller marked F
by wheel-work, as ufual, from a water, horſe, or other kind of
mill, which wheel-work is-communicated to the wheel marked
Q, on whofe axis is a nut, which turns the wheel marked C;
and thereby the cylinder marked A moves, and with it all the
rollers; by which motion the hemp, tow, flax, or wool, is drawn.
forward. The cloth turns down, but the hemp, tow, flax, or
wool, go upon the cylinder marked A, under the roller marked
B, and fo forward under all the rollers marked D, then falls in
between the rollers marked G, F, turns under the roller marked,
Yarn-mill.
ૐ13
Ĝ, and over the roller marked H, which, as it gives the rollers
hold of the hemp, tow, flax, or wool, in two places, enables them
to draw forward the long fibres thereof, though many of them
are to draw from under the marks 4 br 5 of the preffing-rollers,
marked D; it then falls into a cannifter, marked R, and as by
the wheel-work the rollers marked F, G, H, move three times
fafter than the cloth and cylinder, the fliver muft be three times
longer than when prefented. By the time this is drawing, the
other cloth is filled with hemp, tow, flax, or wool, as before,
and laid upon the revolving roller, laying the hemp, tow, flax,
or wool, over the end of the other, which goes forward as be-
fore, and thus a continued fliver is produced as long as the
machine continues its motion. But in order that this fliver
may come out of the cannifter marked R, without entangle-
ment, it muſt paſs through an inftrument marked 5 (fig. 3.),
placed over the rollers marked F, G, its open fide marked T,
to the cylinder at mark 4, fupported by its ends marked V,
V, in the flit marked W, of the before-deſcribed pieces marked
K. The aperture X is fo fmall as to prefs the fibres clofe to
each other in their paffage through it previous to their paffing
the rollers, by which means they remain preffed fide by fide in
the fliver, and will not entangle. Theſe thick flivers are drawn
fmaller by a fimilar procefs, and in the fame manner is uſed for
cotton, but the machines for drawing are all of the fame structure
as the above, except that they have no revolving cloth. The
fliver is applied to the cylinder under the roller marked B
which draws it forward under all the rollers, as before de-
ſcribed, drawing it out, or lengthening it, every freſh machine
through which it preffes, till it be ſmall enough for the ſpinning
machine. It must be remarked, that the cylinders are made lefs
in diameter, according to the different fmallneſs of the fliver
intended to be drawn upon them at the firft; whilft the fliver
is at its greatest thicknefs, the cylinder is required to be three
feet diameter, as above deſcribed, the next rather lefs, and ſo on
to the laft, which is only two feet. The aperture of the bottom
of the contractor belonging to each machine is alſo made one
third part ſmaller than another in fucceffion, from the greateſt
to the ſmalleſt cylinder; as alfo the drawing rollers marked
F, G, H, are furtheft from the preffing-roller marked D in the
longeft cylinder, and neareſt at the fmaller cylinder. At the
largeſt cylinder the diftance is about nine inches, and the
ſmalleſt about four inches; but their diſtance cannot in all
caſes be fixed, as it depends on the different length of the flivers
of the hemp, tow, flax, or wool; long ones requiring the di-
ſtances mentioned, and ſhort ones requiring the diftances much
ſhorter than is here ſpecified.
VOL. II.
L L
514
MACHINES.
The following feveral letters or marks are in the machine
figured 2. The fpinning machine, as to its drawing principle,
is the fame as the drawing machine. The flivers are prefented
to it in canniſters marked 4, and drawn over a cylinder marked
B, covered with rollers marked D. The fibres which are to
form the thread are drawn from the cylinder by the rollers
marked C, the under roller of which is made of fluted iron, the
other of wood, covered with leather; they move fix or eight
times faſter than the cylinder marked B; are enabled to draw the
hemp, tow, flax, or wool, forward from under the preffing-rollers
marked D, by being ſqueezed together with the weights and
crooks marked a, a, locked to the fmall part of the rollers
marked C. There is a belt of fmooth cloth, marked E, moving
on two rollers, which are turned by the wheel marked F, on
the axis of the fluted roller; at the oppofite end of which, as at
the mark G, is a nut, which turns the wheel marked H, on
whofe axis is another nut, turning the wheel marked I, and
thereby the cylinder marked B, with all its rollers. Thefe
rollers move in curved pieces of wooden metal, marked K,
which, to prevent confufion, are not reprefented in their
places: they have flits in them, in which the rollers' axes are
guided, but fo deep as at all times to fuffer the rollers to preſs
upon the cylinder. Thefe rollers are covered with cloth and
leather. The top roller is about ten pounds weight, decreafing to
the fixth roller, which is only about one pound weight: the yarn is
turned by the ſpindles marked L, and rubbed over the wet cloth
belt if ſpinning linen yarn, but if ſpinning worſted yarn the belt
muſt be removed, that it may not touch it as it paffes to the
fpool, which it coils round as faſt as the rollers let it out. The
fpindles marked L, are turned by a bolt from the wheel marked
M, which derives its motion from the mill, and by a wheel on
its axis communicates it to the roller under the mark C by the
wheel marked F, and fo to the reſt, as above deſcribed. The
hemp, tow, flax, or wool, is twined in the fame manner as cotton
is by mills.
1
>
FINIS.
INDEX.
A
The figures refer to the articles or paragraphs.)
A
ABUTMENTS,
Amplitude,..
Air, mechanical properties of, 484--490
-, density and elasticity of, 489
motion of,..
Air-pump, theory of,
Alembert, De. See D'Alembert.
Altitudes, measured by barometer
and thermometer,
of impression,
510-520
521-523
•
502-510
•
250.
•
330
Angle of position,
•
250
Angular accelerating force,
302
pendulum,
311
Animal force,
376-378
Arches and piers,.
199-208
Archivolt,
199
Areometer,
401-409
Art.
199
Banks, on comparative strength of
materials,
197
--, on velocity of air,
517
Barometer,..
483
Barometer, altitudes meas. by, 502,&c.
Bettancourt on steam, vol. II.
Billiards,...
Block of a pulley,
Body,..
hard, soft, and elastic,
Bossut's experiments on discharge
of fluids,
,
on resistance of water,.... 559
Brachystochronon,
Breast-wheels,
367
148
...
329
··458–46¤
2:77
• 467, &c
Ascent of bodies,,...
Attraction, centre of,
Art and nature, difference between,173
Atmosphere homogeneous,. . 495-498
Atmospherical logarithmic,
—-, capillary, ...... 426–435
C
240-245
Capillary tubes,
498
Catenarian curve,.
426-433
..198
279
Celerity,
.15
Central forces,.....
279-299
of spheres, &c.
•
293
Centre of attraction,.
279
universal,
Axioms,
294
21-27
gravity, • • • • * . . . 102-124
gyration,..
309-312
Axis in peritrochio,......
in motion,.... 267, 331, 367, 372
143--147
oscillation,
305-318
percussion, ...... 317-320
pressure,
391-393
spontaneous rotation,
B
322-326
velique,
note, 425
Palance. See Lever, and vol. II.
Ballistic pendulum,
Centrifugal force,....
.279
313
-pump, ·
537538
INDEX.
Art.
Centripetal force,
•
279
Equivalent,
Att.
201
Centrobaryc method,
125
Circular motion,
282-288
Extrados,
Clock, problem concerning the
Expansions of mercury and air, . . 503
Eytelwein, on hydraulics,
199
·463
junction of its hands,
223
Collision,
•
329-362
Composants,
•
29
F
Composition of forces,
28-101
of motions,
Conservatio virium vivarum,
Cords,
•
Condorcet on resistance of water, 559
on weight and gravity, 103
Coulumb on friction, vol. II.
217
Flanks of an arch,...
Floatation, plane of,..
Float-boards,..
....●
341
193-198
Fluid,......
, compressible and incom-
pressible,
Crown of an arch,
Curves, descents along,
Cycloid,...
199
Fly. See vol. II.
Cupola,
of swiftest descent,.. 277, 278
209
Force,
263,&c.
>
accelerating,
retarding,.
272
Forcing pump,
D
Friction. See vol. II.
Fulcrum,
-, pressure upon,.. 133, 140, 321
Funicular polygon,
193-197
199
411
480
3,380
381
17, 212
224
224
527
..
131
D'Alembert's principle of dy-
namics,
on varied motion,..
Deflecting force,
De Luc on altitudes by barom. .506
.267
•
234
G
279
··
Galileo, on falling bodies,.
246
Density,
of the planets,.
Depth of impression,..
Desaguliers's hydrometer,
Diminution of gravity,
Direction,
line of,
IO, 211
on the lever,
132
•
294
330
on the resist. of solids, 167,&c.
Girard, on the distinction between
403
Descents occasioned by gravity,
240-247
Gravity,
287
"
16
the operations of nature and art,173
Gravimeter. See vol. II.
102, 106, 237, 240
its proper measure,
242
centre of,
.102-124
106
diminution of,
287
Discharge of fluids through orifices,
438-457
specific,..
383,396-410
;
table of,
410
expr. relative to, 457-466
Divisibility,
Gunpowder, force of, vol. II.
4
Domes,
209
Gyration, centre of,
• •, ... 309,&c.
Dynamics,
210-389
E
Effects of machines,
..363—380
Efflux of water,....
Elasticity,
329
Elevation in projectiles,
Elliptical motion,..
250
290, 291
190
Emerson on relative strength of
materials,
English, on stability of canal boats, 425
Equator, centrifugal force at, 285
Equilibrium,
19, 28
of elastic fluids, 491–502
Horse, strength of,
Hunter, Mr. his screw,
161
Hutton, on altitudes by barom. ..508
>
on practical gunnery,255--2 57
,on resistance of fluids,555--558
Hydraulics,
2.0
H
Halley, on altitudes by barom..
499
Hammer, stroke of,
•
354
438, &c.
Hands of a clock, .
223
Height due to a velocity,
Homogeneous bodies,
•
244
106
atmosphere,
•
495
378
INDEX.
545
Hydrometer,..
Hydrodynamics,.
Hydrostatical paradox,
Hydrostatics,
Art.
Art.
401-409
Metacentre,
411
•
436-483
Mobility,
8
387
Moment, or momentuin,
31, 212
380--435
Momentum of impulse,
365
of inertia,
302
Motion, ..
II
A
I
Immateriality of the Supreme
→, absolute and relative,.. 12, 219
>
uniform, &c.
laws of,....*
Being,
18
Muffle,
215
21, 27
148
Impact oblique,
360-362-
Impelled point.
3.65
Impetus,
250
N
Impost of an arch,.
Inertia,..
centre of,
Inclined plane,
199
3, 18
108
152-157
motion along,.. 258, 260, 167,
Nature and art, difference between,173
Newton on the lever,
·
140
•
Intrados,...
315, 369, 371
199
on resistance of fluids,....541
Newtonian axioms,....
Nicholson's hydrometer,
21--27
404
J
Oblique impact,
360--362
Joints of fracture,..
199
Orbit,:
·279
Juan, Don, on percussion.... 330, &c.
Orifice, discharge of water through,
438--457
Oscillation, centre of,
305-308
K
of pendulums,.
268
of vessels,
423, 424
Keystone of an arch,
199
Overshot-wheels,
467, &c.
I
P
Laws of motion,
Lever,
, angular,
heavy,.
Lifting-pump,
Line of direction,
of support,
....21--27
131--142, 366
140, cor.7.
135,136
526
Logarithmic, atmospherical,
M
• À 106
4!1
•498
Papin, on motion of air into a
· vacuum,.,. 49, 4,0
Paradox, hydrostatic,
Parallelogram of forces,
Parcieux's areometer,
Pendulum, angular,
ballistic,
compound,
conical,
cycloidal,
51*
387
•
42
·405
311
313
simple,...
Percussion, centre of,
Machines,
...126
-, theory of,
maximum, effects of
363--380
Periodic time,
Man, strength of, ....
Mass,.
Materials, strength of,
Matter,
Measure of the force of gravity,
Mechanics,
Mechanical powers,
VOL. I.
Machinery, simplification of, vol. II,
9, 211
167--192
Perpetual screw,
Piers and arches,
its mean distance solely,
378
Pinion and tooth,
2
Piston,
..
242
Pivots, pressure upon,
145
I
Place, absolute and relative,.
•
7
126--166
Plane, inclined,.
.. 152-157
308
288
273-276
268--272
317--320
•
329-362
280
of planet depends on
...291
160
199--208
146
524
ee
546
INDEX.
Art.
Art.
Plane, motion along,
258, 260, 267,
Solid,
315, 369
Planets, double motion of,
327
Solids, equal in equal times,
Space, absolute,..
298
Pneumatics,
484--560
Polyspacton',.
148
relative,
•
Position, centre of,
109
Power,..
...
17
Pressure, centre of,
391-393
of non-elastic
fluids,
384-395
Pulley,
Projectile force,
Projectiles,
..
; motion of,
.279
, initial,.
Span of an arch,
Spandrils,
Specific gravity,
Spouting fluids,.
Spring of an arch,
Stability of vessels,
383, 396--410
454-456
199
6
•
192.
•
199
248--257
indifferent,
148--151
negative,
267,321,372
positive,
Pumps, theory of,..
• 524--538
Statics,
Steam, its effects, vol. II.
Steelyard,
411--425
412, 418-
21--209
•
137, 138
2
Quantity of matter. See Mass.
of motion,
Strain,
Strength and stress,
Sucking-pump,
212, 213
Symmetrical bodies,
168
167-192
524
107
Ꭱ
Radii of small cylinders, to esti-
mate,
Radius vector,
Random, or range,
Rarity, or rareness,
Reduction of forces,
Resistence of solids,
of fluids,
Resolution of forces,
of motions,
Resultant,
T
Tautochrones,
276
•
note, 408
279
Teeth of wheels, the best forms of, 147
Tension of a cord,...
193
250
Time, absolute and relative,
14
.. 211
55
Time in which the planets would
fall to the sun, .....
•
292
167
Tooth and pinion-work,
146
539-560
Trajectory,
279
28--101
Tubes, capillary,
426--435
•
217
to measure their diamet. note,426
29
540
254
Retardation,
Ricochet firing,
•
Robins's experiments on the re-
sistance of fluids, ..... 553--554
Robison, on altitudes by barom.
on domes,
on relative strength,.
...
505
•
209
U
Undershot-wheels,....
467, &c.
Uniformly varied motion,
..
224-230
Unit of time,
14
190
Rotation, spontaneous,.
322
---, centre of,
•
322-326
V
Rotatory motion,
300-328
Roy, on expansion of mercury, &c. 503
Variable motion,
Velique centre,.
Velocity,...
231--239
note, 475
15
S
Sailing of ships,....
Screw,
accelerated, or retarded, 15
virtual,. . . . . .………… note, 130
angular,
due to a height,
Vena contracta,
Venturi on motion of fluids,.
549
158--161
..
411
·425
.507
477--483
Vessels, stability of,
vol. II.
oscillations of,.
Vertical projectiles,
279
.244
440, 457
....
462
245
411
425
Ships, stability of,
, oscillations of,.
•
Shuckburgh, on alt. by barom.
Smeaton, on water-wheels
on windmills,...
ન
INDEX.
547
Vibrating cone,.
Vibration of pendulums,
i
Art:
Art.
2311
268
Weight,
Wheel and axle,.. 143-147, 367, 372
104
465
See vol. II.
-, pressure upon,...... 145, 321
Whirling motion of fluids,
444
note, 130
Windmill-sails,
547
199
Smeaton on. See vol.11.
1
Working point,
365
Vince, on motion of fluids,
--, on friction.
Virtual velocities,
Voussoirs,
W
Y
Water-wheels,
....467-476
Wedge,.
,Smeaton on, 477-483
162--166
Young, Dr. M. on the motion of
fluids,....
.464
1
!
:
↓
:
Fago. Line
ERRATA.
T
•
22,
,23,
35,
17,
17 from bottom, for o read O.
9, for magnitude read magnitudes.
17 and 19 from bottom, for Pr read Pr.
16, for into read in.
24,
9 from bottom, for Ç'= read C"-
"cos. a''
P ď
P d'
27,
14 from bottom, for sin, r=
cos. a
Y
read sin. r=
R
R
37,
66,
93,
119,
135,
136,
173,
181,
188,
.t
18 from bottom, for HG, IG, read HG"" IG””,
4 from bottom, for 112 read 119.
A from bottom, for he angle read of the angle.
15, for angle o read angle O,
9 from bottom, for zx read xx.
2 from bottom, √ X² +Ÿ³ read √ X² +Ÿ³,
24, for has read have.
2 from bottom for tread i.
12 from bottom, for 230 read 228.
14, for fig. 6 read fig. 5,
207,
226,
3, for P read O.
10.
254,
20, for fig. 4 read fig. 14.
294,
II, for a work read in a work,
3741
bottom line, for W sin. È read W sin. É.
:
7
Printed by T. Davison, Whitefriars.
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:
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*
The following Works have been lately published by the
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A TREATISE
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>>
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